From 1da95dd2b928196bc673379cf57625d5cf6efd17 Mon Sep 17 00:00:00 2001
From: array-api-bot <noreply@data-apis.org>
Date: Thu, 15 Aug 2024 22:18:18 +0000
Subject: [PATCH] Deploy: b2e232b7b687ff201bab1565254c81ec2f428110

---
 ...ray_api.info.__array_namespace_info__.html |   1 +
 2023.12/API_specification/inspection.html     |   2 +-
 .../API_specification/inspection.rst.txt      |   2 ++
 2023.12/objects.inv                           | Bin 5969 -> 5983 bytes
 2023.12/searchindex.js                        |   2 +-
 ...ray_api.info.__array_namespace_info__.html |   1 +
 draft/API_specification/inspection.html       |   2 +-
 .../API_specification/inspection.rst.txt      |   2 ++
 draft/objects.inv                             | Bin 6011 -> 6023 bytes
 draft/searchindex.js                          |   2 +-
 ...ray_api.info.__array_namespace_info__.html |   1 +
 latest/API_specification/inspection.html      |   2 +-
 .../API_specification/inspection.rst.txt      |   2 ++
 latest/objects.inv                            | Bin 5969 -> 5983 bytes
 latest/searchindex.js                         |   2 +-
 15 files changed, 15 insertions(+), 6 deletions(-)

diff --git a/2023.12/API_specification/generated/array_api.info.__array_namespace_info__.html b/2023.12/API_specification/generated/array_api.info.__array_namespace_info__.html
index 46c650ea5..fb92ac4d4 100644
--- a/2023.12/API_specification/generated/array_api.info.__array_namespace_info__.html
+++ b/2023.12/API_specification/generated/array_api.info.__array_namespace_info__.html
@@ -466,6 +466,7 @@ <h1 id="api-specification-generated-array-api-info-array-namespace-info--page-ro
 <dt class="sig sig-object py" id="array_api.info.__array_namespace_info__">
 <span class="sig-name descname"><span class="pre">__array_namespace_info__</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">Info</span></span></span><a class="headerlink" href="#array_api.info.__array_namespace_info__" title="Link to this definition">¶</a></dt>
 <dd><p>Returns a namespace with Array API namespace inspection utilities.</p>
+<p>See <a class="reference internal" href="../inspection.html#inspection"><span class="std std-ref">Inspection</span></a> for a list of inspection APIs.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Returns<span class="colon">:</span></dt>
 <dd class="field-odd"><p><strong>out</strong> (<em>Info</em>) – An object containing Array API namespace inspection utilities.</p>
diff --git a/2023.12/API_specification/inspection.html b/2023.12/API_specification/inspection.html
index 4ddb888ee..38576a754 100644
--- a/2023.12/API_specification/inspection.html
+++ b/2023.12/API_specification/inspection.html
@@ -480,7 +480,7 @@
           <article class="md-content__inner md-typeset" role="main">
             
   <section id="inspection">
-<h1 id="api-specification-inspection--page-root">Inspection<a class="headerlink" href="#api-specification-inspection--page-root" title="Link to this heading">¶</a></h1>
+<span id="id1"></span><h1 id="api-specification-inspection--page-root">Inspection<a class="headerlink" href="#api-specification-inspection--page-root" title="Link to this heading">¶</a></h1>
 <blockquote>
 <div><p>Array API specification for namespace inspection utilities.</p>
 </div></blockquote>
diff --git a/2023.12/_sources/API_specification/inspection.rst.txt b/2023.12/_sources/API_specification/inspection.rst.txt
index 04691e712..89d9c602a 100644
--- a/2023.12/_sources/API_specification/inspection.rst.txt
+++ b/2023.12/_sources/API_specification/inspection.rst.txt
@@ -1,3 +1,5 @@
+.. _inspection:
+
 Inspection
 ==========
 
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diff --git a/2023.12/searchindex.js b/2023.12/searchindex.js
index e7860d181..db2799057 100644
--- a/2023.12/searchindex.js
+++ b/2023.12/searchindex.js
@@ -1 +1 @@
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181, 182, 190, 197, 199, 204, 205, 206, 207, 208, 209, 210, 211, 214, 222, 226, 227, 228, 229, 231, 236, 237, 240, 247, 249, 250, 252, 254, 255, 256, 257, 260, 261, 262], "numpi": [0, 19, 63, 190, 202, 207, 208, 210, 211, 256, 260, 261, 262, 263], "scalar": [0, 2, 49, 60, 189, 190, 204, 214, 254, 262], "valu": [0, 1, 2, 5, 7, 9, 10, 11, 12, 15, 16, 17, 18, 20, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 39, 41, 43, 49, 51, 57, 58, 60, 61, 62, 63, 64, 65, 66, 76, 77, 78, 85, 86, 87, 88, 89, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 104, 105, 106, 107, 111, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 143, 144, 145, 149, 150, 152, 153, 157, 158, 159, 160, 161, 162, 163, 164, 168, 170, 171, 172, 173, 178, 179, 180, 181, 182, 184, 185, 187, 189, 197, 199, 202, 204, 206, 208, 209, 210, 214, 216, 219, 222, 226, 227, 228, 229, 230, 231, 232, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 262], "rational": [0, 7, 88, 150, 170, 190, 210, 211, 252, 255, 257, 260], "alwai": [0, 12, 26, 42, 60, 63, 98, 102, 141, 154, 190, 202, 207, 208, 211, 236], "necessari": [0, 26, 60, 90, 102, 141, 154, 175, 190, 208, 260], "acceler": [0, 5, 107, 153, 202, 210], "where": [0, 1, 7, 13, 14, 15, 26, 47, 57, 65, 86, 87, 90, 94, 96, 97, 101, 103, 104, 124, 125, 126, 137, 141, 143, 147, 149, 153, 158, 159, 161, 162, 167, 168, 172, 173, 175, 183, 184, 185, 189, 190, 199, 205, 207, 210, 211, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 233, 236, 237, 238, 240, 242, 245, 246, 247, 248, 249, 250, 252, 256, 260, 261, 262], "non": [0, 1, 7, 13, 14, 16, 17, 63, 128, 129, 130, 131, 134, 136, 138, 143, 150, 168, 174, 184, 185, 190, 199, 204, 205, 211, 218, 220, 223, 224, 227, 228, 229, 231, 233, 234, 236, 240, 242, 249, 254, 262], "could": [0, 26, 179, 180, 181, 182, 202, 208, 215, 256, 260, 262], "forc": 0, "synchron": [0, 26, 59, 153, 260], "delai": [0, 24, 25, 29, 34, 35, 202, 214, 260], "execut": [0, 199, 202, 211, 213, 215, 260, 262], "model": [0, 57, 58, 90, 141, 207, 214, 262], "repres": [0, 8, 11, 12, 23, 24, 25, 26, 29, 34, 35, 62, 66, 87, 90, 101, 137, 141, 162, 172, 173, 204, 206, 210, 211, 247, 261, 262], "futur": [0, 26, 102, 203, 207, 208, 211, 215, 216, 236, 237, 258, 260, 262], "python": [0, 2, 5, 7, 24, 25, 26, 29, 34, 35, 49, 60, 101, 102, 152, 189, 190, 202, 204, 207, 210, 212, 214, 215, 216, 257, 259, 260, 261], "x": [0, 1, 5, 7, 9, 10, 11, 13, 14, 16, 17, 18, 20, 26, 61, 62, 63, 64, 65, 66, 68, 74, 76, 77, 79, 85, 86, 87, 88, 92, 94, 95, 96, 99, 100, 102, 104, 109, 117, 118, 119, 123, 124, 125, 126, 129, 133, 134, 136, 138, 140, 142, 143, 146, 147, 148, 150, 151, 153, 154, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 170, 171, 172, 173, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 188, 190, 207, 208, 216, 217, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 232, 234, 235, 236, 237, 238, 240, 241, 242, 243, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 262], "__pos__": [0, 189, 204], "po": 0, "__neg__": [0, 189, 204], "neg": [0, 13, 14, 15, 44, 47, 65, 78, 88, 90, 95, 97, 99, 101, 118, 123, 125, 141, 149, 152, 156, 160, 164, 171, 174, 185, 189, 190, 204, 207, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 254, 260], "x1": [0, 7, 12, 40, 65, 67, 69, 70, 71, 72, 77, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 144, 149, 152, 158, 169, 174, 185, 186, 204, 233, 239, 244, 248, 251, 253], "x2": [0, 7, 12, 40, 65, 67, 69, 70, 71, 72, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 144, 149, 152, 158, 169, 174, 185, 186, 204, 233, 239, 244, 248, 251, 253], "__add__": [0, 50, 189, 204], "add": [0, 7, 21, 88, 169, 170, 189, 190, 204, 205, 206, 211, 252], "__sub__": [0, 189, 204], "sub": [0, 190], "__mul__": [0, 189, 204], "mul": 0, "__truediv__": [0, 189, 204], "truediv": 0, "__floordiv__": [0, 189], "floordiv": 0, "__mod__": [0, 189], "mod": 0, "__pow__": [0, 189, 204], "pow": [0, 47, 189, 204, 206], "should": [0, 1, 5, 7, 9, 10, 11, 12, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 76, 77, 79, 85, 86, 87, 88, 90, 94, 95, 96, 98, 100, 101, 102, 105, 106, 107, 109, 113, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 137, 138, 139, 141, 142, 148, 149, 150, 151, 152, 154, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 168, 169, 170, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 184, 185, 190, 197, 204, 205, 206, 207, 210, 211, 212, 216, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 254, 255, 256, 260, 262, 263], "defin": [0, 5, 12, 23, 30, 41, 49, 60, 65, 79, 90, 101, 103, 104, 115, 122, 134, 135, 136, 138, 139, 140, 141, 152, 159, 164, 165, 168, 176, 177, 184, 185, 189, 192, 197, 204, 206, 207, 216, 220, 221, 224, 225, 228, 231, 232, 236, 237, 238, 245, 246, 248, 256, 261, 262, 263], "real": [0, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 24, 25, 29, 30, 31, 33, 35, 37, 39, 41, 44, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 85, 86, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 105, 106, 107, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 142, 143, 144, 145, 146, 149, 150, 152, 157, 158, 159, 160, 161, 162, 163, 164, 168, 170, 172, 173, 178, 184, 185, 187, 189, 199, 204, 207, 219, 222, 226, 227, 228, 229, 230, 231, 232, 236, 237, 238, 240, 242, 245, 246, 247, 248, 249, 250, 252, 254, 257], "data": [0, 1, 2, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 111, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 144, 145, 146, 147, 148, 149, 150, 151, 152, 154, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 184, 185, 186, 187, 188, 189, 192, 199, 202, 205, 207, 208, 211, 213, 214, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 256, 257, 258, 259, 260, 263], "type": [0, 2, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 192, 202, 205, 207, 208, 210, 212, 213, 214, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 256, 257, 260, 261], "__matmul__": [0, 189, 204], "matmul": [0, 40, 189, 199, 204, 256], "The": [0, 1, 5, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 58, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 90, 93, 94, 96, 99, 100, 101, 102, 105, 106, 107, 109, 110, 111, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 140, 141, 142, 143, 144, 147, 148, 149, 150, 151, 152, 153, 157, 158, 159, 160, 161, 162, 163, 164, 165, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 190, 199, 202, 204, 205, 206, 208, 209, 210, 211, 214, 215, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 255, 256, 257, 259, 260, 261, 262, 263], "__invert__": [0, 189], "inv": [0, 204, 256], "invert": [0, 68, 238, 241, 248], "__inv__": 0, "__and__": [0, 189], "__or__": [0, 189], "__xor__": [0, 189], "xor": [0, 72, 131], "__lshift__": [0, 189], "lshift": 0, "__rshift__": [0, 189], "rshift": 0, "integ": [0, 5, 9, 13, 14, 15, 20, 22, 26, 29, 30, 34, 35, 36, 38, 41, 44, 45, 47, 48, 51, 52, 60, 67, 68, 69, 70, 71, 72, 76, 77, 88, 90, 100, 101, 103, 104, 108, 115, 116, 122, 134, 136, 138, 142, 149, 150, 152, 153, 155, 157, 158, 168, 170, 171, 178, 184, 185, 189, 190, 204, 206, 207, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 241, 242, 252, 254, 260], "boolean": [0, 5, 22, 24, 25, 26, 29, 35, 36, 43, 45, 52, 57, 60, 63, 67, 68, 70, 72, 88, 89, 102, 103, 104, 111, 115, 116, 122, 128, 129, 130, 131, 143, 189, 199, 204], "__lt__": [0, 189, 204], "lt": 0, "__le__": [0, 189, 204], "le": 0, "__gt__": [0, 189, 204], "gt": [0, 246, 249], "__ge__": [0, 189, 204], "ge": 0, "__eq__": [0, 189, 204, 211], "eq": 0, "__ne__": [0, 189, 204], "ne": 0, "ar": [0, 1, 5, 7, 15, 16, 17, 19, 23, 24, 25, 26, 27, 29, 34, 35, 40, 49, 55, 58, 60, 77, 85, 86, 89, 90, 94, 97, 98, 99, 101, 102, 107, 114, 115, 122, 128, 129, 130, 131, 132, 141, 143, 149, 153, 156, 157, 161, 172, 173, 175, 179, 181, 185, 190, 199, 202, 204, 205, 206, 207, 208, 209, 210, 211, 212, 214, 215, 216, 218, 219, 220, 221, 223, 224, 225, 227, 228, 229, 230, 231, 233, 236, 237, 242, 245, 246, 249, 255, 256, 257, 260, 261, 262, 263], "onli": [0, 1, 5, 7, 16, 17, 23, 26, 40, 57, 58, 63, 99, 102, 107, 113, 115, 116, 122, 128, 129, 130, 131, 132, 136, 168, 184, 185, 189, 190, 199, 202, 204, 205, 207, 208, 210, 211, 212, 214, 216, 221, 233, 238, 245, 246, 248, 256, 257, 260, 261, 262, 263], "other": [0, 5, 21, 22, 23, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 50, 51, 52, 63, 89, 90, 96, 101, 102, 125, 140, 141, 168, 184, 190, 192, 202, 204, 206, 207, 208, 209, 210, 211, 212, 216, 233, 245, 255, 256, 259, 260, 262], "ani": [0, 1, 9, 10, 11, 23, 24, 25, 26, 28, 29, 34, 35, 43, 59, 61, 62, 66, 89, 93, 107, 117, 118, 144, 164, 189, 190, 199, 204, 207, 208, 210, 216, 249, 257, 259, 260, 263], "For": [0, 1, 5, 7, 9, 10, 11, 12, 16, 17, 18, 20, 24, 25, 26, 29, 30, 31, 33, 35, 37, 39, 41, 44, 57, 58, 61, 62, 64, 65, 66, 76, 79, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 105, 106, 107, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 134, 135, 137, 138, 139, 141, 142, 144, 149, 150, 152, 153, 157, 158, 159, 160, 161, 162, 163, 164, 165, 167, 170, 172, 173, 178, 179, 180, 181, 182, 190, 197, 202, 206, 207, 209, 211, 214, 219, 228, 230, 247, 249, 250, 252, 260, 262, 263], "backward": [0, 13, 14, 16, 17, 18, 31, 33, 37, 39, 105, 106, 120, 121, 122, 134, 135, 138, 139, 152, 163, 185, 190, 204, 207, 208, 212, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 260], "compat": [0, 1, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 74, 77, 85, 90, 93, 101, 105, 106, 107, 120, 121, 122, 127, 128, 130, 131, 132, 134, 135, 136, 138, 139, 141, 144, 149, 150, 152, 153, 154, 163, 168, 169, 170, 184, 185, 186, 199, 204, 207, 208, 212, 233, 240, 242, 245, 248, 254, 260, 262], "mai": [0, 5, 7, 15, 16, 17, 18, 23, 26, 28, 31, 33, 37, 39, 43, 51, 57, 58, 59, 60, 89, 90, 93, 101, 102, 105, 106, 107, 110, 115, 116, 120, 121, 122, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 143, 144, 153, 154, 158, 163, 168, 173, 179, 180, 181, 182, 184, 189, 190, 197, 199, 202, 205, 206, 207, 208, 209, 210, 211, 212, 214, 215, 216, 236, 246, 247, 249, 255, 256, 260, 261, 262], "complex": [0, 5, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 24, 25, 29, 31, 33, 35, 37, 39, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 88, 90, 93, 94, 96, 97, 98, 103, 104, 105, 106, 107, 109, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 132, 134, 135, 137, 138, 139, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 157, 159, 161, 162, 163, 164, 165, 169, 170, 172, 173, 174, 179, 180, 181, 182, 185, 199, 206, 210, 211, 213, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 261], "howev": [0, 5, 16, 17, 18, 31, 33, 37, 39, 57, 88, 101, 105, 106, 107, 116, 120, 121, 122, 134, 135, 138, 139, 153, 158, 163, 171, 172, 173, 202, 205, 206, 207, 208, 209, 211, 256, 257, 260, 262], "inequ": [0, 16, 17, 18, 31, 33, 37, 39, 105, 106, 120, 121, 134, 135, 138, 139, 163], "unspecifi": [0, 5, 10, 11, 16, 17, 18, 30, 31, 33, 37, 39, 41, 47, 51, 60, 62, 66, 77, 78, 87, 90, 94, 96, 101, 103, 104, 105, 106, 120, 121, 122, 134, 135, 138, 139, 149, 152, 158, 162, 163, 164, 167, 171, 173, 190, 197, 199, 204, 220, 221, 224, 225, 228, 231, 236, 237, 260], "thu": [0, 5, 16, 17, 18, 30, 31, 33, 37, 39, 41, 47, 57, 60, 71, 77, 101, 103, 104, 105, 106, 120, 121, 122, 134, 135, 138, 139, 149, 152, 158, 163, 172, 173, 190, 197, 206, 207, 220, 221, 224, 225, 228, 231, 236, 237, 249, 256], "depend": [0, 5, 9, 10, 11, 16, 17, 18, 20, 26, 29, 31, 33, 37, 39, 44, 47, 51, 57, 58, 59, 61, 62, 63, 64, 65, 66, 77, 86, 87, 90, 94, 96, 105, 106, 111, 120, 121, 122, 123, 124, 125, 126, 141, 142, 149, 158, 161, 162, 163, 172, 173, 186, 197, 199, 206, 207, 210, 213, 214, 216, 236, 237, 246, 247, 248, 249, 256, 260, 262, 263], "see": [0, 5, 10, 11, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 33, 34, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 53, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 74, 77, 85, 90, 93, 96, 101, 102, 104, 105, 106, 107, 111, 114, 120, 121, 123, 125, 127, 128, 130, 131, 132, 134, 135, 136, 138, 139, 141, 143, 144, 149, 150, 152, 153, 155, 159, 163, 164, 165, 168, 169, 170, 179, 180, 181, 182, 184, 185, 186, 189, 190, 199, 201, 202, 205, 207, 209, 210, 211, 216, 233, 240, 242, 245, 248, 254, 255, 260, 261, 262, 263], "order": [0, 5, 7, 16, 17, 18, 19, 26, 31, 33, 37, 39, 55, 60, 63, 65, 89, 99, 101, 102, 105, 106, 120, 121, 134, 135, 138, 139, 143, 153, 158, 163, 172, 173, 174, 179, 180, 181, 182, 190, 197, 199, 204, 206, 209, 210, 212, 227, 228, 236, 237, 240, 249, 250, 254, 256, 257, 260, 261], "chang": [0, 1, 9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 66, 86, 87, 90, 93, 94, 96, 97, 98, 102, 103, 104, 117, 118, 119, 122, 123, 124, 125, 126, 132, 134, 137, 138, 141, 142, 143, 144, 145, 146, 148, 149, 150, 154, 157, 159, 161, 162, 164, 165, 169, 170, 171, 172, 173, 174, 179, 180, 181, 182, 185, 202, 218, 219, 220, 222, 223, 224, 227, 228, 230, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 257, 260, 262, 263], "shape": [0, 1, 18, 40, 55, 63, 73, 74, 78, 88, 91, 92, 95, 99, 103, 104, 111, 132, 133, 137, 145, 146, 154, 156, 158, 163, 167, 171, 174, 175, 176, 177, 183, 185, 187, 188, 189, 204, 213, 214, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 260, 262], "result": [0, 1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 24, 25, 28, 29, 30, 31, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 79, 85, 86, 87, 90, 93, 94, 96, 100, 101, 105, 106, 107, 109, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 142, 144, 148, 149, 150, 151, 152, 153, 155, 157, 158, 159, 160, 161, 162, 164, 165, 167, 168, 169, 170, 172, 173, 174, 178, 179, 184, 190, 197, 199, 204, 206, 207, 208, 214, 232, 233, 235, 240, 241, 247, 248, 254, 260, 261, 262, 263], "promot": [0, 1, 5, 10, 11, 12, 21, 22, 30, 40, 41, 42, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 78, 85, 86, 87, 90, 94, 96, 101, 104, 107, 122, 123, 124, 125, 126, 127, 132, 135, 136, 139, 141, 142, 149, 152, 155, 161, 162, 164, 165, 167, 168, 169, 172, 173, 174, 184, 185, 186, 189, 204, 232, 233, 238, 240, 241, 242, 244, 245, 246, 247, 248, 254, 256], "rule": [0, 5, 7, 10, 11, 12, 21, 22, 30, 40, 41, 42, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 78, 85, 86, 87, 88, 90, 94, 96, 101, 103, 104, 107, 122, 123, 124, 125, 126, 127, 132, 135, 139, 141, 142, 149, 152, 155, 159, 161, 162, 164, 165, 167, 169, 172, 173, 174, 185, 186, 189, 190, 204, 207, 210, 232, 233, 238, 240, 241, 242, 244, 245, 246, 247, 248, 254, 256, 260, 262], "broadcast": [0, 12, 13, 14, 16, 17, 21, 22, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 73, 74, 77, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 134, 135, 136, 138, 139, 141, 144, 149, 150, 152, 153, 168, 169, 170, 174, 184, 185, 186, 189, 204, 233, 240, 242, 245, 248, 254, 260], "same": [0, 5, 7, 9, 12, 15, 18, 19, 20, 26, 32, 36, 38, 40, 41, 46, 48, 50, 55, 59, 63, 68, 73, 74, 76, 77, 78, 79, 88, 90, 92, 95, 98, 99, 100, 101, 102, 104, 109, 132, 133, 134, 136, 137, 138, 140, 141, 146, 147, 148, 149, 150, 151, 152, 153, 154, 156, 157, 158, 159, 163, 166, 167, 168, 169, 170, 171, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 188, 190, 199, 202, 204, 207, 208, 210, 211, 216, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 232, 234, 235, 236, 238, 241, 245, 246, 247, 249, 250, 252, 255, 256, 260, 262], "behavior": [0, 5, 47, 49, 59, 60, 63, 77, 90, 101, 103, 104, 107, 122, 141, 149, 152, 158, 171, 179, 180, 181, 182, 189, 190, 192, 199, 202, 204, 206, 207, 214, 215, 220, 221, 224, 225, 228, 231, 256, 257, 260, 261, 262, 263], "special": [0, 9, 10, 11, 12, 20, 21, 24, 25, 28, 29, 30, 35, 41, 42, 43, 47, 51, 61, 62, 64, 65, 66, 76, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 136, 138, 139, 141, 144, 149, 150, 152, 157, 159, 160, 161, 162, 164, 165, 168, 170, 172, 173, 178, 184, 204, 205, 207, 247, 252], "case": [0, 1, 5, 7, 9, 10, 11, 12, 15, 20, 21, 24, 25, 26, 28, 29, 30, 35, 41, 42, 43, 47, 51, 60, 61, 62, 64, 65, 66, 76, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 102, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 136, 137, 138, 139, 141, 144, 149, 150, 152, 157, 159, 160, 161, 162, 164, 165, 168, 170, 172, 173, 178, 184, 190, 202, 204, 205, 206, 207, 208, 211, 212, 214, 246, 247, 249, 252, 256, 258, 260, 263], "its": [0, 5, 26, 40, 73, 90, 98, 132, 141, 154, 156, 206, 207, 210, 211, 255, 260, 261, 262], "respect": [0, 9, 12, 20, 21, 22, 28, 30, 31, 33, 37, 38, 39, 41, 42, 43, 45, 48, 50, 51, 52, 65, 67, 69, 70, 71, 72, 77, 87, 90, 93, 101, 105, 106, 107, 113, 120, 121, 122, 127, 128, 130, 131, 135, 137, 139, 140, 141, 144, 152, 162, 169, 172, 173, 174, 179, 180, 185, 204, 206, 209, 211, 236, 246, 249], "binari": [0, 5, 67, 70, 72, 172, 173, 205], "two": [0, 1, 5, 15, 19, 40, 55, 65, 71, 97, 102, 132, 133, 137, 157, 174, 176, 177, 179, 180, 181, 182, 185, 190, 199, 210, 211, 214, 215, 220, 221, 224, 225, 228, 231, 232, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 256, 260, 261, 262, 263], "operand": [0, 1, 9, 10, 11, 12, 24, 25, 29, 35, 61, 62, 64, 65, 66, 76, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 138, 139, 141, 144, 149, 150, 152, 157, 159, 160, 161, 162, 164, 165, 170, 172, 173, 178, 199, 204, 206, 247, 252], "assign": [0, 208], "exampl": [0, 5, 12, 23, 26, 115, 116, 167, 189, 190, 202, 207, 208, 209, 211, 214, 215, 216, 252, 256, 260, 262, 263], "after": [0, 1, 26, 40, 132, 164, 175], "addit": [0, 5, 7, 12, 26, 50, 59, 88, 115, 169, 189, 190, 199, 205, 207, 210, 256, 260, 261, 263], "modifi": [0, 26, 208, 259], "equal": [0, 1, 9, 10, 11, 18, 20, 21, 22, 26, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 58, 61, 62, 63, 64, 65, 66, 69, 71, 77, 87, 89, 94, 96, 97, 103, 104, 107, 116, 118, 123, 124, 125, 126, 136, 143, 144, 145, 146, 149, 150, 157, 162, 163, 164, 168, 170, 171, 173, 174, 175, 179, 180, 181, 182, 184, 189, 190, 197, 204, 207, 211, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 235, 241, 242, 245, 246, 247, 248, 252, 260], "equival": [0, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 71, 101, 107, 128, 129, 130, 131, 152, 157, 171, 190, 199, 207, 208, 242, 245, 248, 254, 260], "discuss": [0, 93, 144, 204, 210, 211, 215, 260, 261, 262], "copi": [0, 1, 26, 59, 60, 63, 102, 154, 163, 204, 205, 210, 211, 213, 259, 260], "view": [0, 102, 213], "behaviour": [0, 213, 260, 262], "mutabl": [0, 213], "via": [0, 26, 101, 102, 171, 190, 205, 210, 211, 215, 217, 245, 255, 256, 257, 260], "__iadd__": 0, "__isub__": 0, "__imul__": 0, "__itruediv__": 0, "__ifloordiv__": 0, "__ipow__": 0, "__imod__": 0, "__imatmul__": 0, "__iand__": 0, "__ior__": 0, "__ixor__": 0, "__ilshift__": 0, "__irshift__": 0, "appli": [0, 12, 77, 78, 85, 90, 141, 155, 157, 167, 174, 190, 199, 202, 207, 218, 220, 223, 224, 227, 228, 229, 231, 242, 245, 256, 260, 262], "match": [0, 1, 5, 9, 20, 26, 63, 101, 152, 174, 179, 180, 212, 222, 226, 227, 228, 229, 231, 236, 237, 240, 254, 262], "op": 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181, 182, 183, 184, 185, 186, 187, 188, 189, 191, 192, 193, 194, 195, 196, 197, 198, 200, 201, 202, 204, 205, 206, 207, 208, 209, 210, 211, 212, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 261, 263], "refer": [1, 13, 14, 96, 97, 125, 168, 174, 175, 184, 185, 190, 207, 208, 216, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 248], "automat": [1, 260], "implicit": [1, 210, 211, 214, 260], "expans": [1, 260], "size": [1, 13, 14, 88, 95, 122, 143, 156, 166, 171, 174, 185, 189, 190, 209, 215, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 235, 244, 246, 249, 260], "without": [1, 7, 26, 57, 102, 113, 115, 143, 153, 154, 179, 180, 181, 182, 202, 205, 206, 209, 259, 260, 262], "purpos": [1, 5, 96, 107, 125, 202, 247, 256, 258, 259, 262], "make": [1, 7, 202, 205, 206, 208, 210, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 255, 257, 260], "differ": [1, 12, 26, 49, 50, 77, 78, 88, 90, 98, 101, 102, 141, 150, 167, 169, 170, 190, 202, 208, 211, 212, 214, 225, 236, 246, 247, 249, 252, 256, 260, 261, 262], "element": [1, 9, 10, 11, 12, 13, 14, 15, 20, 21, 22, 24, 25, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 54, 58, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 99, 100, 101, 103, 104, 105, 106, 107, 109, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 148, 149, 150, 151, 152, 153, 154, 156, 157, 158, 159, 160, 161, 162, 164, 165, 166, 168, 169, 170, 171, 172, 173, 175, 176, 177, 178, 179, 180, 181, 182, 184, 186, 189, 190, 204, 206, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 236, 245, 246, 247, 249, 252, 260], "wise": [1, 9, 10, 12, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 64, 65, 67, 68, 69, 70, 71, 72, 77, 79, 85, 90, 93, 101, 105, 106, 107, 109, 120, 121, 127, 128, 129, 130, 131, 135, 139, 141, 144, 149, 151, 152, 169, 189, 204, 206, 260], "oper": [1, 12, 19, 24, 26, 34, 40, 57, 58, 59, 61, 64, 71, 86, 88, 90, 101, 124, 126, 132, 141, 149, 150, 152, 155, 161, 165, 170, 172, 174, 189, 190, 196, 199, 204, 207, 208, 209, 210, 211, 252, 256, 257, 260, 261, 262], "facilit": [1, 197, 202], "user": [1, 7, 26, 110, 173, 202, 205, 206, 208, 211, 215, 256, 260, 261, 262], "ergonom": 1, "encourag": [1, 260, 261], "avoid": [1, 9, 63, 90, 96, 101, 107, 125, 141, 154, 205, 208, 211, 214, 256, 260, 262], "unnecessari": [1, 256], "can": [1, 7, 26, 60, 75, 110, 114, 116, 190, 199, 202, 205, 207, 208, 210, 211, 216, 245, 246, 249, 255, 256, 260, 261, 262, 263], "potenti": [1, 26, 96, 125, 153, 208, 260], "enabl": [1, 26, 102, 211, 215, 216, 260], "more": [1, 5, 7, 15, 19, 26, 40, 58, 60, 63, 73, 88, 96, 99, 101, 125, 132, 143, 149, 153, 171, 179, 180, 181, 182, 190, 199, 202, 205, 206, 207, 208, 209, 210, 211, 212, 215, 216, 220, 221, 224, 225, 228, 231, 247, 256, 257, 260, 261, 263], "memori": [1, 26, 60, 102, 202, 208, 209, 211, 260, 262], "effici": [1, 202, 208], "through": [1, 60, 65, 255, 257, 261, 262], "vector": [1, 40, 132, 137, 185, 233, 244, 249, 250, 254, 256, 260], "reduc": [1, 13, 14, 16, 17, 134, 136, 138, 150, 168, 170, 184, 190, 246, 249, 256, 261, 262], "consumpt": [1, 26, 261], "cach": 1, "local": [1, 211], "given": [1, 23, 99, 122, 156, 158, 183, 199, 204, 207, 208, 211, 212, 216, 237, 247, 256, 257, 260, 262], "involv": [1, 12, 90, 101, 141, 149, 155, 199, 206, 207, 211, 215], "singleton": [1, 13, 14, 16, 17, 95, 134, 136, 138, 150, 166, 168, 170, 175, 184, 240, 254, 260], "whose": [1, 5, 9, 11, 19, 20, 26, 47, 55, 62, 66, 85, 86, 87, 97, 99, 102, 133, 149, 156, 160, 161, 162, 171, 172, 173, 174, 176, 177, 179, 180, 181, 190, 208, 222, 226, 227, 228, 229, 231, 232, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 260, 262], "one": [1, 15, 19, 26, 40, 51, 58, 60, 63, 73, 75, 88, 90, 95, 97, 99, 101, 102, 115, 116, 122, 132, 137, 141, 143, 145, 146, 153, 158, 166, 171, 179, 180, 181, 182, 185, 190, 202, 205, 207, 208, 210, 211, 214, 215, 216, 218, 220, 222, 223, 224, 225, 226, 227, 228, 229, 231, 244, 245, 246, 254, 256, 257, 260, 262], "virtual": 1, "repeat": [1, 189, 190, 204, 262], "across": [1, 5, 90, 101, 141, 173, 204, 206, 207, 211, 255, 260], "correspond": [1, 16, 17, 23, 47, 59, 65, 73, 77, 102, 111, 112, 113, 149, 154, 156, 158, 168, 174, 179, 180, 181, 182, 184, 185, 190, 204, 206, 220, 224, 228, 231, 233, 236, 240, 259, 260], "If": [1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 29, 34, 35, 40, 44, 47, 51, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 74, 76, 77, 78, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 107, 111, 113, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 128, 129, 130, 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231, 232, 233, 234, 235, 238, 240, 241, 242, 244, 245, 246, 247, 248, 252, 254, 256, 260], "let": [1, 9, 10, 11, 12, 62, 66, 85, 87, 88, 93, 94, 96, 102, 117, 118, 119, 122, 123, 125, 136, 144, 150, 153, 158, 159, 162, 164, 168, 170, 173, 175, 184, 185, 190, 215, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 236, 237, 238, 246, 248, 249, 252], "b": [1, 9, 10, 11, 12, 57, 62, 66, 87, 90, 93, 94, 96, 101, 117, 118, 119, 122, 123, 125, 141, 144, 159, 162, 164, 167, 173, 185, 190, 204, 207, 208, 212, 245, 248, 262], "both": [1, 40, 44, 47, 51, 65, 77, 88, 90, 98, 101, 102, 107, 122, 132, 142, 149, 150, 170, 173, 174, 185, 190, 207, 208, 210, 214, 216, 233, 252, 256, 260, 261], "shape1": 1, "describ": [1, 5, 12, 88, 90, 93, 115, 116, 141, 144, 149, 150, 170, 192, 199, 207, 210, 214, 219, 230, 252, 260], "shape2": 1, "n1": [1, 137], "len": [1, 137, 175], "n2": [1, 137], "max": [1, 26, 77, 98, 108, 175, 189, 190, 204, 240, 242, 245], "temporari": 1, "list": [1, 73, 78, 114, 137, 167, 190, 202, 204, 211, 260, 262], "length": [1, 15, 107, 137, 154, 174, 190, 219, 221, 222, 225, 230, 249, 250], "while": [1, 101, 115, 122, 128, 129, 130, 131, 136, 140, 158, 168, 179, 180, 184, 189, 190, 197, 202, 204, 207, 208, 209, 211, 214, 245, 256, 261, 262, 263], "d1": 1, "els": [1, 26, 202, 261], "d2": 1, "set": [1, 18, 26, 49, 65, 102, 160, 163, 168, 176, 177, 179, 181, 182, 184, 189, 190, 204, 205, 206, 207, 208, 211, 212, 215, 216, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 236, 237, 238, 242, 245, 246, 248, 249, 255, 256, 260, 262, 263], "th": [1, 97, 175, 190, 220, 224, 228, 231], "throw": 1, "except": [1, 7, 13, 14, 26, 74, 78, 88, 97, 102, 122, 143, 153, 167, 171, 183, 190, 199, 202, 204, 206, 208, 211, 213, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 245, 257, 260, 261, 262], "demonstr": 1, "applic": [1, 26, 88, 150, 153, 170, 199, 252, 256, 260, 261], "4d": 1, "8": [1, 5, 7, 27, 175, 199, 202], "6": [1, 7, 175], "3d": 1, "7": [1, 7, 27, 216], "5": [1, 190, 260], "2d": 1, "1d": 1, "15": 1, "do": [1, 26, 90, 141, 152, 197, 202, 205, 207, 208, 210, 211, 212, 256, 257, 259, 260, 262, 263], "doe": [1, 15, 26, 102, 144, 171, 190, 199, 202, 205, 206, 207, 208, 209, 211, 212, 214, 216, 256, 260, 262, 263], "second": [1, 12, 65, 67, 69, 70, 71, 72, 93, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 144, 149, 167, 169, 174, 179, 180, 181, 185, 186, 233, 236, 244, 246, 247, 249, 250, 260], "append": [1, 40, 69, 95, 132, 235], "As": [1, 122, 149, 179, 180, 181, 182, 202, 210, 216, 262], "impli": [1, 179, 180, 181, 182, 259, 260], "__setitem__": [1, 171, 189, 204], "Such": [1, 206, 256], "right": [1, 69, 71, 107, 158, 164, 205, 249, 259], "hand": [1, 199], "left": [1, 5, 60, 69, 101, 103, 158, 171, 190, 199, 236, 237, 249, 260], "index": [1, 5, 16, 17, 18, 32, 34, 49, 57, 83, 97, 111, 113, 137, 140, 143, 158, 167, 171, 174, 179, 180, 181, 189, 204, 220, 224, 228, 231, 260, 262], "perform": [1, 5, 13, 14, 26, 40, 59, 60, 90, 107, 132, 141, 153, 174, 190, 205, 206, 207, 208, 209, 210, 218, 220, 223, 224, 225, 227, 228, 229, 231, 249, 250, 256, 260, 261, 262], "empti": [1, 13, 14, 15, 150, 170, 189, 190, 204, 252, 260], "ok": 1, "allow": [1, 24, 25, 26, 29, 34, 35, 113, 115, 149, 154, 174, 190, 204, 205, 206, 208, 211, 214, 215, 256, 262], "NOT": [1, 129, 259], "adher": [2, 7, 8, 189, 190, 202, 255, 260], "convent": [2, 7, 10, 11, 26, 40, 61, 62, 64, 65, 66, 88, 123, 125, 132, 149, 164, 189, 190, 197, 207, 211, 255, 256, 261], "each": [2, 9, 10, 11, 12, 20, 21, 22, 26, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 76, 77, 79, 85, 86, 87, 90, 93, 94, 96, 100, 101, 105, 106, 107, 109, 114, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 135, 137, 139, 140, 141, 142, 143, 144, 148, 149, 151, 152, 153, 156, 157, 158, 159, 160, 161, 162, 164, 165, 167, 169, 172, 173, 174, 175, 178, 179, 180, 190, 202, 204, 206, 210, 214, 216, 228, 232, 233, 234, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 255, 256, 260, 261, 262], "float": [2, 5, 9, 10, 11, 12, 13, 14, 15, 20, 21, 24, 25, 28, 29, 30, 31, 33, 34, 35, 37, 39, 40, 41, 42, 43, 44, 47, 49, 50, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 104, 107, 109, 113, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 145, 146, 149, 150, 151, 152, 155, 157, 158, 159, 160, 161, 162, 164, 165, 168, 169, 170, 172, 173, 174, 178, 179, 180, 181, 182, 184, 185, 187, 189, 197, 204, 206, 207, 214, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 234, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 261], "point": [2, 5, 9, 10, 11, 12, 13, 14, 15, 20, 24, 25, 26, 29, 34, 35, 40, 41, 42, 44, 47, 50, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 104, 107, 109, 113, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 145, 146, 149, 150, 151, 152, 155, 157, 158, 159, 160, 161, 162, 164, 165, 168, 169, 170, 172, 173, 174, 178, 179, 180, 181, 182, 184, 185, 187, 189, 197, 204, 206, 207, 211, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 234, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 262], "creat": [3, 15, 60, 91, 92, 97, 102, 103, 104, 122, 145, 146, 187, 188, 196, 202, 211, 219, 230, 256, 260], "main": [5, 97, 176, 177, 205, 210, 235, 252, 255, 262], "namespac": [5, 7, 23, 110, 192, 202, 204, 217, 255, 256, 257, 260, 263], "under": [5, 255, 259, 260], "specifi": [5, 13, 14, 15, 16, 17, 18, 26, 29, 59, 60, 63, 74, 78, 88, 91, 95, 98, 99, 103, 113, 115, 116, 122, 145, 150, 152, 153, 156, 166, 167, 170, 171, 175, 176, 177, 179, 180, 181, 182, 185, 187, 190, 199, 204, 206, 207, 208, 210, 211, 212, 216, 218, 220, 221, 222, 223, 224, 226, 227, 228, 229, 231, 235, 252, 254, 256, 257, 260, 262, 263], "name": [5, 7, 23, 26, 101, 115, 179, 180, 181, 190, 207, 236, 245, 246, 247, 249, 255, 260, 261], "descript": [5, 7, 204, 206, 240, 254], "bool": [5, 13, 14, 16, 17, 18, 22, 24, 26, 28, 31, 33, 37, 39, 43, 45, 49, 52, 60, 63, 75, 88, 89, 93, 102, 103, 104, 105, 106, 115, 116, 117, 118, 119, 120, 121, 122, 128, 129, 130, 131, 134, 136, 138, 144, 150, 154, 160, 163, 168, 170, 184, 199, 204, 214, 232, 240, 249, 254], "true": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 93, 98, 101, 102, 111, 117, 118, 119, 122, 128, 129, 130, 131, 134, 136, 138, 143, 144, 150, 154, 160, 163, 168, 170, 179, 180, 181, 182, 184, 186, 190, 204, 232, 240, 249, 254, 256], "fals": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 93, 102, 111, 117, 118, 119, 122, 128, 129, 130, 131, 134, 136, 138, 144, 150, 154, 160, 163, 168, 170, 179, 180, 181, 182, 184, 190, 232, 240, 249, 254], "int8": [5, 115, 116, 199], "bit": [5, 68, 69, 71, 85, 88, 98, 108, 150, 160, 170, 199, 204, 206, 252], "sign": [5, 9, 10, 11, 12, 15, 20, 41, 44, 62, 65, 66, 71, 85, 87, 88, 90, 94, 96, 101, 115, 116, 123, 125, 134, 135, 138, 139, 141, 142, 149, 150, 152, 158, 160, 162, 164, 170, 173, 179, 180, 181, 182, 189, 197, 204, 207, 246, 247, 252], "exist": [5, 7, 26, 60, 78, 102, 202, 204, 207, 210, 211, 212, 238, 257, 260, 261], "interv": [5, 10, 11, 13, 14, 15, 61, 62, 64, 66, 95, 122, 123, 125, 140, 167, 174, 176, 177, 183, 185, 190, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 257], "128": 5, "127": 5, "int16": [5, 88, 115, 116, 150, 170, 199, 252], "16": [5, 199], "32": [5, 199], "767": 5, "int32": [5, 88, 115, 116, 150, 170, 199, 252], "147": 5, "483": 5, "647": 5, "int64": [5, 88, 115, 116, 150, 170, 199, 252], "64": [5, 199], "9": [5, 27], "223": 5, "372": 5, "036": 5, "854": 5, "775": 5, "807": 5, "uint8": [5, 115, 116, 199], "unsign": [5, 88, 115, 116, 150, 170, 189, 252], "255": 5, "uint16": [5, 88, 115, 116, 150, 170, 199, 252], "65": 5, "535": [5, 204], "uint32": [5, 88, 115, 116, 150, 170, 199, 252], "294": 5, "967": 5, "295": 5, "uint64": [5, 115, 116, 199], "18": 5, "446": [5, 204], "744": [5, 204], "073": 5, "709": [5, 204], "551": [5, 204], "615": 5, "float32": [5, 109, 115, 116, 151, 199, 247, 249, 250], "ieee": [5, 12, 65, 80, 81, 82, 84, 90, 96, 98, 107, 125, 141, 152, 164, 172, 173, 189, 197, 206, 207, 260], "754": [5, 12, 65, 80, 81, 82, 84, 90, 96, 98, 107, 125, 141, 152, 164, 172, 173, 189, 197, 206, 207, 260], "singl": [5, 7, 24, 25, 29, 34, 35, 113, 115, 179, 180, 189, 199, 204, 205, 207, 210, 211, 216, 256, 260, 261, 262], "precis": [5, 9, 20, 42, 60, 98, 103, 104, 109, 141, 151, 164, 199, 204, 206, 222, 226, 227, 228, 229, 231, 236, 237, 240, 247, 249, 250, 254, 260], "2019": [5, 12, 90, 96, 107, 125, 141, 189, 206, 260, 262], "float64": [5, 9, 20, 115, 116, 199, 222, 226, 227, 228, 229, 231, 236, 237, 240, 254], "doubl": [5, 174, 199, 204], "complex64": [5, 109, 115, 116, 151, 199, 204, 247, 249, 250], "imaginari": [5, 10, 11, 12, 13, 14, 44, 61, 62, 63, 64, 66, 79, 87, 90, 93, 94, 96, 98, 109, 123, 125, 141, 142, 143, 144, 145, 146, 149, 157, 162, 164, 173, 204, 207], "compon": [5, 10, 11, 12, 13, 14, 44, 62, 63, 66, 79, 87, 90, 93, 94, 96, 98, 109, 123, 125, 141, 142, 143, 144, 145, 146, 149, 151, 157, 162, 164, 172, 173, 179, 180, 181, 182, 204, 207, 221, 230], "complex128": [5, 9, 20, 115, 116, 199, 204, 222, 226, 227, 228, 229, 231, 236, 237, 240, 254], "method": [5, 26, 34, 102, 189, 192, 202, 208, 210, 211, 214, 215, 216, 260, 261, 262], "attribut": [5, 23, 98, 108, 189, 201, 204, 257, 260, 261, 262], "requir": [5, 10, 11, 24, 25, 29, 34, 35, 59, 61, 62, 63, 64, 66, 88, 102, 107, 116, 150, 164, 167, 170, 171, 173, 179, 180, 182, 183, 189, 190, 197, 199, 202, 204, 205, 206, 207, 208, 209, 210, 211, 214, 216, 218, 219, 220, 222, 223, 224, 227, 228, 230, 233, 252, 255, 256, 260, 261, 262], "beyond": [5, 156, 199, 260], "It": [5, 23, 26, 102, 202, 208, 210, 260, 262, 263], "also": [5, 7, 26, 34, 102, 107, 159, 199, 202, 207, 208, 209, 210, 216, 220, 224, 228, 231, 249, 255, 262], "subnorm": [5, 107], "k": [5, 40, 97, 107, 132, 143, 176, 177, 190, 232, 236, 237, 238, 246, 248, 249, 250, 252, 260], "denorm": [5, 107], "gradual": [5, 107, 260], "underflow": [5, 9, 90, 101, 107, 247], "hardwar": [5, 53, 107, 153, 206, 210, 211, 236, 249, 256, 260], "univers": [5, 107, 205, 211, 256, 260], "mani": [5, 107, 175, 260, 262], "platform": [5, 26, 107], "compil": [5, 107, 173, 202, 205, 209, 260], "toggl": [5, 107], "daz": [5, 107], "flush": [5, 107], "ftz": [5, 107], "increas": [5, 107, 206, 261], "guard": [5, 107], "against": [5, 40, 73, 107, 132, 173, 190, 242, 245, 263], "time": [5, 7, 16, 17, 26, 107, 153, 179, 180, 202, 204, 209, 210, 215, 232, 236, 237, 238, 246, 248, 249, 256, 260, 262], "attack": [5, 107], "accordingli": [5, 10, 11, 13, 14, 16, 17, 59, 61, 62, 64, 66, 90, 96, 101, 107, 122, 123, 125, 134, 136, 137, 138, 141, 143, 150, 153, 158, 164, 168, 170, 179, 180, 181, 182, 184, 190, 199, 206, 207, 208, 209, 211, 240, 246, 254, 256], "vari": [5, 107, 158, 173, 179, 180, 181, 182, 199, 206], "function": [5, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 74, 78, 86, 87, 88, 94, 96, 99, 102, 107, 114, 115, 116, 122, 123, 125, 128, 129, 130, 131, 132, 136, 143, 149, 150, 152, 153, 154, 159, 161, 162, 163, 164, 167, 168, 170, 171, 172, 173, 174, 175, 179, 180, 181, 182, 183, 184, 185, 189, 192, 202, 204, 205, 207, 208, 209, 210, 211, 214, 215, 216, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 232, 233, 236, 237, 238, 242, 245, 246, 247, 248, 249, 250, 252, 255, 256, 257, 260, 261, 262], "access": [5, 26, 32, 102, 110, 190, 204, 210, 255, 257, 260], "variou": [5, 204], "cast": [5, 29, 49, 60, 63, 75, 88, 150, 170, 199, 207, 252, 260, 262], "introspect": 5, "isdtyp": [5, 189, 204], "integr": [5, 63, 113, 115, 116], "keyword": [5, 7, 26, 63, 88, 114, 137, 150, 170, 189, 204, 208, 211, 215, 216, 252, 256, 257, 260, 261, 262], "affect": [5, 15, 49, 208, 211], "intermedi": [5, 9, 107], "calcul": [5, 9, 10, 11, 12, 20, 21, 42, 47, 50, 61, 62, 64, 65, 66, 86, 87, 88, 90, 94, 96, 123, 124, 125, 126, 127, 134, 136, 138, 141, 149, 150, 161, 162, 164, 168, 169, 170, 172, 173, 184, 204, 247], "implementor": [5, 255], "free": [5, 211, 259], "when": [5, 7, 12, 16, 17, 26, 47, 49, 59, 63, 90, 96, 101, 102, 107, 113, 115, 122, 125, 134, 135, 138, 139, 141, 149, 150, 153, 154, 158, 168, 170, 173, 184, 186, 189, 190, 199, 204, 205, 207, 208, 209, 210, 212, 214, 215, 216, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 236, 238, 242, 245, 246, 247, 248, 249, 250, 252, 256, 260, 261, 262], "accumul": 5, "reduct": [5, 13, 14], "long": [5, 110, 216], "ha": [5, 9, 13, 14, 20, 23, 29, 34, 35, 40, 44, 47, 55, 86, 87, 88, 90, 94, 95, 96, 101, 104, 132, 136, 137, 140, 141, 142, 143, 149, 150, 161, 162, 166, 168, 170, 171, 172, 173, 174, 175, 179, 180, 181, 182, 184, 190, 199, 202, 207, 210, 211, 214, 215, 233, 240, 248, 249, 252, 254, 256, 257, 260, 262, 263], "wai": [5, 26, 63, 102, 202, 205, 211, 212, 257, 260, 261, 262, 263], "f4": [5, 199], "ensur": [5, 26, 158, 202, 206, 256, 260, 261, 262], "portabl": [5, 59, 122, 206, 208, 211, 212, 260], "consum": [5, 26, 63, 113, 115, 202, 207, 208, 216, 255, 260, 261], "recommend": [5, 7, 19, 23, 26, 122, 128, 129, 130, 131, 136, 152, 168, 184, 197, 204, 206, 210, 211, 260], "guidanc": [5, 7, 49, 204, 205, 212, 260], "govern": [5, 50, 169, 199, 256, 257], "interact": [5, 207], "either": [5, 9, 10, 11, 12, 24, 26, 35, 40, 65, 77, 87, 88, 90, 93, 94, 96, 98, 101, 102, 107, 110, 116, 117, 118, 122, 123, 124, 125, 126, 127, 132, 134, 135, 138, 139, 141, 150, 152, 159, 160, 161, 164, 170, 172, 173, 174, 190, 206, 207, 208, 212, 216, 247, 252, 260, 261, 263], "whether": [5, 13, 14, 26, 59, 60, 63, 88, 89, 102, 111, 116, 119, 122, 154, 160, 204, 211, 232, 236, 237, 246, 248, 255, 259, 260, 262], "otherwis": [5, 13, 14, 15, 16, 17, 26, 59, 60, 63, 75, 102, 111, 113, 115, 134, 136, 138, 150, 153, 154, 158, 159, 168, 170, 184, 185, 186, 189, 190, 202, 211, 232, 234, 240, 247, 248, 254, 259], "note": [5, 7, 9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 61, 62, 63, 64, 65, 66, 76, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 98, 100, 101, 103, 104, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 123, 124, 125, 126, 127, 132, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 152, 153, 157, 158, 159, 160, 161, 162, 164, 165, 168, 169, 170, 171, 172, 173, 174, 175, 178, 179, 180, 181, 182, 183, 184, 185, 189, 190, 204, 210, 214, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 260, 261, 262, 263], "possibl": [5, 26, 60, 101, 102, 134, 138, 154, 172, 173, 202, 205, 206, 207, 208, 210, 211, 212, 214, 216, 256, 260, 261, 262, 263], "multipl": [5, 7, 13, 14, 16, 17, 40, 42, 44, 132, 134, 136, 138, 141, 142, 150, 168, 170, 184, 190, 202, 205, 207, 210, 211, 215, 216, 237, 238, 256, 257, 260, 262], "In": [5, 12, 19, 26, 59, 88, 90, 93, 101, 116, 118, 119, 141, 144, 150, 152, 159, 170, 189, 190, 192, 199, 206, 207, 210, 212, 227, 228, 246, 247, 249, 252, 256, 257, 261, 262, 263], "clearli": [5, 59, 116, 197, 207, 256, 257], "warn": [5, 153, 212], "about": [5, 7, 26, 98, 108, 208, 256, 260, 262, 263], "": [5, 26, 29, 32, 49, 58, 59, 60, 80, 101, 102, 137, 152, 168, 175, 176, 177, 184, 190, 197, 202, 204, 205, 206, 207, 208, 210, 211, 214, 216, 220, 224, 228, 231, 245, 249, 250, 256, 257, 260, 262], "organ": [5, 204, 256, 261, 262], "within": [5, 15, 27, 190, 199, 202, 204, 207, 211, 218, 220, 223, 224, 227, 228, 229, 231, 260], "numer": [5, 9, 12, 20, 21, 40, 42, 44, 46, 47, 50, 51, 88, 90, 101, 115, 116, 117, 118, 119, 132, 137, 141, 142, 148, 149, 150, 157, 159, 165, 169, 170, 174, 199, 206, 218, 220, 223, 224, 227, 228, 229, 231, 233, 244, 245, 247, 252, 256, 260, 262], "accord": [5, 12, 60, 71, 75, 88, 90, 98, 101, 103, 122, 141, 149, 158, 159, 168, 184, 185, 190, 206, 207], "These": [5, 208, 236, 261], "intend": [5, 88, 150, 170, 202, 252], "posit": [7, 9, 10, 11, 13, 14, 20, 46, 62, 65, 66, 81, 90, 95, 97, 98, 101, 118, 123, 125, 140, 141, 143, 152, 156, 160, 162, 164, 173, 189, 190, 202, 204, 206, 216, 230, 232, 246, 261], "paramet": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 202, 204, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 256], "extern": [7, 262], "usabl": 7, "accept": [7, 26, 128, 129, 130, 131, 136, 152, 168, 184, 202, 257], "call": [7, 34, 210, 211, 214, 247, 260, 261, 262], "argument": [7, 10, 11, 26, 40, 61, 62, 63, 64, 65, 66, 86, 88, 107, 114, 123, 125, 132, 150, 155, 158, 161, 164, 170, 172, 173, 174, 189, 199, 204, 206, 208, 210, 211, 218, 220, 223, 224, 227, 228, 229, 231, 252, 256, 260, 261, 262], "map": [7, 207, 208], "base": [7, 47, 57, 58, 94, 95, 123, 124, 125, 126, 149, 179, 180, 181, 182, 190, 204, 208, 214, 216, 256, 257, 260, 261, 262], "sole": [7, 190, 197, 256], "incompat": [7, 26, 74, 102, 202, 257, 260], "us": [7, 19, 26, 27, 59, 60, 83, 98, 102, 107, 122, 124, 126, 156, 179, 181, 189, 190, 199, 204, 206, 207, 208, 209, 211, 212, 215, 216, 217, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 255, 256, 257, 258, 259, 260, 263], "normal": [7, 78, 167, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231], "practic": [7, 19, 190, 256, 261], "avail": [7, 102, 114, 202, 210, 255, 257, 261], "still": [7, 26, 216, 256, 261, 262, 263], "consid": [7, 26, 63, 102, 128, 129, 130, 131, 179, 180, 181, 182, 207, 211, 230, 245, 256, 260, 262, 263], "compliant": [7, 26, 51, 90, 96, 102, 122, 125, 128, 129, 130, 131, 134, 135, 136, 138, 139, 168, 184, 206, 209, 211, 257, 260], "altern": [7, 208, 210, 263], "thei": [7, 26, 199, 205, 210, 211, 215, 216, 255, 256, 257, 260, 262, 263], "were": [7, 101, 153, 158, 204, 260], "option": [7, 13, 14, 15, 16, 17, 23, 26, 57, 58, 59, 60, 63, 77, 78, 88, 91, 92, 97, 99, 102, 103, 104, 113, 115, 122, 134, 136, 138, 145, 146, 150, 153, 154, 156, 158, 168, 170, 171, 184, 187, 188, 189, 204, 215, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 240, 242, 245, 252, 254, 256, 261, 262], "lead": [7, 101, 207, 246, 249, 260], "readabl": [7, 199, 256, 261], "code": [7, 59, 199, 208, 209, 211, 214, 216, 256, 260, 261, 262], "easier": [7, 202, 208, 256], "evolv": [7, 202, 256], "over": [7, 13, 14, 26, 122, 134, 136, 138, 150, 168, 170, 171, 174, 184, 185, 206, 207, 208, 210, 211, 215, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 233, 252, 254, 256, 260], "ad": [7, 9, 10, 11, 12, 13, 14, 20, 21, 24, 26, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 86, 87, 90, 93, 94, 96, 97, 98, 102, 103, 104, 117, 118, 119, 122, 123, 124, 125, 126, 132, 137, 141, 142, 143, 144, 145, 146, 148, 149, 150, 157, 159, 161, 162, 164, 165, 169, 170, 172, 173, 174, 179, 180, 181, 182, 185, 190, 203, 204, 205, 211, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 257], "worri": 7, "xi": [7, 137], "annot": [7, 204, 216, 260], "individu": [7, 158, 211, 214, 215, 216, 219, 230, 260, 261], "aim": [7, 205, 216, 255, 256, 257, 260, 261, 262, 263], "strongli": [7, 208, 262], "look": [7, 262], "like": [7, 202, 205, 207, 208, 214, 216, 257, 260, 261, 262], "funcnam": 7, "key1": 7, "key2": 7, "none": [7, 13, 14, 15, 16, 17, 23, 26, 32, 49, 57, 58, 59, 60, 63, 77, 78, 83, 88, 91, 92, 97, 99, 102, 103, 104, 113, 115, 122, 134, 136, 138, 145, 146, 150, 153, 154, 156, 158, 168, 170, 171, 184, 187, 188, 190, 204, 211, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 240, 242, 245, 252, 253, 254, 260, 261, 263], "out": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 190, 204, 205, 208, 210, 214, 215, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 259, 262], "int": [7, 13, 14, 15, 16, 17, 18, 21, 22, 26, 27, 28, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 56, 57, 58, 59, 60, 74, 77, 78, 88, 91, 95, 97, 98, 99, 101, 103, 104, 108, 122, 134, 136, 138, 140, 145, 147, 150, 153, 154, 156, 163, 166, 167, 168, 170, 171, 174, 175, 176, 177, 183, 184, 185, 187, 190, 199, 214, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 235, 240, 241, 251, 252, 253, 254, 261], "str": [7, 8, 23, 115, 116, 137, 261], "modulo": 7, "self": [7, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 89, 204, 262], "few": [7, 206, 214, 260, 262], "enhanc": 7, "default": [7, 13, 14, 15, 16, 17, 18, 23, 26, 59, 60, 63, 77, 78, 88, 91, 92, 97, 99, 102, 103, 104, 112, 113, 115, 122, 134, 136, 137, 138, 143, 145, 146, 150, 153, 154, 156, 158, 163, 167, 168, 170, 174, 176, 177, 179, 180, 181, 183, 184, 185, 187, 188, 189, 190, 204, 206, 211, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 235, 240, 242, 245, 246, 249, 252, 254], "form": [7, 23, 26, 40, 79, 132, 133, 176, 177, 208, 232, 234, 235, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 257, 261], "question": [7, 205, 260], "commonli": [7, 168, 184, 205, 207, 209, 255, 256, 260, 261], "written": [7, 202, 260, 262], "yyyi": [8, 23, 257], "mm": [8, 23, 257], "string": [8, 23, 115, 116, 204, 257, 260], "version": [8, 9, 10, 11, 12, 13, 14, 20, 21, 23, 24, 25, 26, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 66, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 98, 102, 103, 104, 107, 108, 109, 116, 117, 118, 119, 122, 123, 124, 125, 126, 132, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 153, 157, 158, 159, 160, 161, 162, 164, 165, 169, 170, 171, 172, 173, 174, 175, 179, 180, 181, 182, 183, 185, 189, 202, 205, 211, 215, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 258, 260, 262], "absolut": [9, 20, 85, 159, 206, 208, 240, 241, 247, 256], "x_i": [9, 10, 11, 61, 62, 64, 66, 68, 76, 77, 79, 86, 87, 94, 96, 100, 109, 117, 118, 119, 123, 124, 125, 126, 129, 134, 136, 138, 142, 148, 151, 157, 159, 160, 161, 162, 164, 165, 168, 172, 173, 178, 184], "input": [9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 26, 30, 41, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 85, 86, 87, 88, 90, 92, 93, 94, 95, 96, 99, 100, 101, 102, 104, 105, 106, 107, 109, 116, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 188, 189, 197, 202, 204, 207, 209, 211, 212, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 249, 250, 252, 254, 256, 260, 262], "magnitud": [9, 12, 20, 85, 90, 101, 107, 141, 204, 249, 250], "represent": [9, 12, 20, 29, 44, 67, 70, 72, 80, 81, 82, 84, 90, 98, 101, 108, 141, 142, 172, 173, 206, 210, 261], "known": [9, 159, 206, 209, 210], "norm": [9, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 240, 254, 256], "modulu": [9, 152], "z": [9, 10, 11, 61, 62, 64, 66, 123, 207], "bj": [9, 12, 79, 90, 141], "comput": [9, 12, 28, 31, 33, 37, 39, 40, 43, 57, 58, 67, 70, 72, 79, 88, 89, 90, 93, 95, 101, 105, 106, 107, 120, 121, 128, 129, 130, 131, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 148, 150, 153, 168, 170, 174, 179, 180, 181, 182, 184, 185, 190, 204, 206, 209, 214, 218, 219, 220, 222, 223, 224, 226, 227, 228, 229, 230, 231, 232, 233, 236, 237, 238, 240, 242, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260], "operatornam": [9, 10, 11, 61, 62, 64, 66, 86, 87, 159, 161, 162, 172, 173, 207, 236, 237, 247, 249], "sqrt": [9, 10, 11, 61, 62, 189, 204, 207, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 254], "take": [9, 123, 125, 149, 164, 189, 204, 211, 216, 260], "care": [9, 208, 256], "undu": [9, 209], "overflow": [9, 12, 88, 90, 101, 107, 122, 150, 170, 199, 247, 252, 256], "dure": [9, 40, 59, 107, 132, 168, 184, 199, 202, 245, 260, 261], "stage": [9, 107, 257], "contain": [9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 26, 28, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 90, 91, 92, 93, 94, 96, 100, 101, 102, 105, 106, 107, 109, 110, 111, 113, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 157, 158, 159, 160, 161, 162, 164, 165, 168, 169, 170, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 184, 185, 187, 190, 204, 206, 207, 208, 210, 214, 215, 219, 220, 221, 224, 225, 228, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 260, 262], "nan": [9, 10, 11, 12, 13, 14, 24, 25, 35, 61, 62, 63, 64, 65, 66, 76, 85, 86, 87, 90, 93, 94, 96, 100, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 136, 138, 139, 141, 144, 149, 152, 157, 158, 159, 160, 161, 162, 164, 168, 172, 173, 178, 179, 180, 181, 182, 184, 189, 197, 207, 260], "infin": [9, 10, 11, 12, 13, 14, 24, 25, 35, 62, 63, 64, 65, 66, 76, 81, 86, 87, 90, 93, 94, 96, 100, 101, 107, 117, 118, 123, 124, 125, 126, 127, 134, 138, 141, 144, 149, 152, 157, 160, 161, 162, 164, 172, 173, 178, 207, 247, 254], "imag": [9, 10, 11, 12, 24, 62, 63, 66, 87, 93, 94, 96, 117, 118, 119, 122, 123, 125, 144, 157, 159, 162, 164, 173, 189, 204, 205, 260, 261, 262], "finit": [9, 10, 11, 12, 25, 35, 42, 62, 65, 66, 87, 90, 93, 94, 96, 101, 107, 117, 118, 123, 125, 141, 144, 149, 152, 160, 162, 164, 173, 206], "2022": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 90, 93, 94, 96, 97, 98, 103, 104, 108, 109, 116, 117, 118, 119, 122, 123, 124, 125, 126, 132, 137, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 157, 159, 161, 162, 164, 165, 169, 170, 171, 172, 173, 174, 179, 180, 181, 182, 185, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254], "12": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 66, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 98, 102, 103, 104, 107, 108, 109, 116, 117, 118, 119, 122, 123, 124, 125, 126, 132, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 153, 157, 158, 159, 160, 161, 162, 164, 165, 169, 170, 171, 172, 173, 174, 175, 179, 180, 181, 182, 183, 185, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 257], "approxim": [10, 11, 47, 61, 62, 64, 65, 66, 86, 87, 94, 96, 101, 123, 124, 125, 126, 149, 161, 162, 172, 173, 206, 242, 245], "princip": [10, 11, 61, 62, 64, 66, 123, 164, 207, 256], "invers": [10, 11, 61, 62, 64, 65, 66, 207, 218, 220, 223, 224, 225, 226, 227, 228, 229, 231, 238, 241, 245, 256], "cosin": [10, 11, 86, 87, 173], "express": [10, 61, 63, 64, 65, 86, 161, 172, 190, 199, 208, 256, 259], "radian": [10, 61, 64, 65, 86, 161, 172], "arc": [10, 61, 64], "frac": [10, 11, 61, 62, 64, 66, 86, 87, 90, 122, 124, 126, 159, 161, 162, 172, 173, 207, 247], "pi": [10, 11, 61, 62, 64, 66, 87, 123, 125, 162, 172, 173, 189], "j": [10, 11, 12, 25, 61, 62, 64, 66, 87, 90, 94, 96, 122, 123, 125, 141, 158, 159, 161, 162, 164, 172, 173, 190, 207, 236, 249, 252], "ln": [10, 11, 61, 62, 64, 66, 123], "zj": [10, 61, 62, 64, 66], "conj": [10, 11, 61, 62, 64, 66, 87, 94, 96, 123, 124, 125, 126, 162, 164, 173, 189, 204], "multi": [10, 11, 61, 62, 64, 66, 189, 207, 210, 211, 233, 262], "branch": [10, 11, 61, 62, 64, 65, 66, 86, 87, 90, 94, 96, 123, 125, 141, 149, 161, 162, 164, 172, 173, 260], "cut": [10, 11, 61, 62, 64, 66, 86, 87, 94, 96, 123, 125, 149, 161, 162, 164, 172, 173, 260], "plane": [10, 11, 61, 62, 64, 66, 86, 87, 90, 94, 96, 141, 161, 162, 164, 172, 173, 260], "By": [10, 11, 13, 14, 61, 62, 64, 65, 66, 88, 123, 125, 134, 136, 138, 149, 150, 164, 168, 170, 184, 185, 206, 207, 233, 256, 261], "place": [10, 11, 15, 60, 61, 62, 63, 64, 66, 91, 92, 97, 102, 103, 104, 122, 145, 146, 156, 187, 188, 189, 197, 199, 204, 208, 211, 219, 230, 245], "line": [10, 11, 61, 62, 64, 66, 172, 173, 199, 207, 260, 261, 262, 263], "segment": [10, 11, 61, 62, 64, 66, 207], "infti": [10, 11, 61, 62, 64, 66, 86, 123, 125, 149, 164, 207], "axi": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 95, 99, 123, 125, 134, 136, 138, 140, 149, 150, 153, 156, 163, 164, 166, 167, 168, 170, 171, 174, 175, 183, 184, 185, 189, 204, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 233, 240, 253, 254, 260], "rang": [10, 61, 62, 64, 66, 77, 88, 123, 125, 150, 164, 170, 190, 204, 210, 252, 260], "strip": [10, 61, 62, 64, 66, 123, 125], "unbound": [10, 61, 62, 64, 66, 123, 125], "along": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 97, 99, 123, 125, 134, 136, 138, 150, 153, 156, 163, 164, 167, 168, 170, 171, 172, 173, 175, 183, 184, 185, 190, 204, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 252, 254, 256], "c99": [10, 11, 61, 62, 64, 66, 90, 123, 125, 141, 149, 164, 207, 257], "provision": [10, 11, 61, 62, 64, 66, 123, 125, 149, 164, 207], "statu": [10, 11, 61, 62, 64, 66, 123, 125, 149, 164, 207], "greater": [10, 11, 33, 38, 48, 61, 62, 65, 66, 69, 71, 77, 85, 90, 100, 101, 123, 125, 149, 152, 159, 160, 162, 164, 166, 173, 189, 190, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 241], "than": [10, 11, 19, 26, 38, 40, 47, 48, 49, 55, 61, 62, 63, 65, 66, 69, 71, 76, 77, 85, 88, 90, 98, 99, 100, 101, 102, 123, 124, 125, 126, 132, 141, 149, 150, 152, 159, 160, 162, 164, 166, 168, 170, 171, 173, 178, 179, 180, 181, 182, 184, 190, 199, 202, 205, 208, 211, 212, 215, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 240, 241, 242, 245, 252, 254, 256, 257, 260, 262], "less": [10, 11, 39, 47, 61, 65, 66, 76, 85, 90, 101, 123, 124, 125, 126, 149, 152, 159, 160, 164, 168, 184, 189, 190, 208, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 240, 241, 242, 245, 254, 260], "\u03c0": [10, 64, 65, 84], "0j": [10, 11, 12, 25, 62, 63, 66, 87, 94, 96, 97, 123, 125, 145, 146, 159, 162, 164, 173, 207, 247], "nonzero": [10, 11, 12, 62, 66, 87, 90, 94, 96, 101, 141, 162, 173, 189, 190, 204, 245], "3\u03c0": [10, 65], "hyperbol": [11, 62, 66, 86, 87, 161, 162, 172, 173, 207], "aco": [11, 61, 189, 204, 206], "simpli": [11, 96, 125, 205, 216, 260, 262], "upper": [11, 77, 97, 177, 204, 232, 246], "half": [11, 15, 66, 122, 140, 164, 174, 190, 221], "area": [11, 62, 66], "sector": [11, 62, 66], "\u03c0j": [11, 62, 66, 123, 125], "3\u03c0j": [11, 123, 125], "sum": [12, 21, 88, 107, 127, 150, 189, 204, 240, 252, 254, 256], "x1_i": [12, 65, 67, 69, 70, 71, 72, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 135, 139, 141, 144, 149, 152, 169, 186, 204], "x2_i": [12, 65, 67, 69, 70, 71, 72, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 135, 139, 141, 144, 149, 152, 169, 186, 204], "first": [12, 16, 17, 19, 65, 67, 69, 70, 71, 72, 88, 93, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 144, 149, 156, 167, 169, 172, 173, 174, 179, 180, 181, 185, 186, 190, 207, 233, 236, 244, 246, 247, 249, 250, 256, 260, 261, 262, 263], "remain": [12, 90, 93, 101, 116, 118, 119, 141, 144, 152, 154, 159, 190, 208, 231], "neither": [12, 40, 90, 101, 132, 141, 174, 249, 261], "nor": [12, 90, 101, 141, 249, 261], "mathemat": [12, 19, 65, 84, 86, 87, 90, 96, 101, 123, 125, 141, 161, 162, 172, 173, 189, 207, 240, 254], "round": [12, 15, 76, 90, 100, 101, 141, 164, 178, 189, 204, 206], "nearest": [12, 90, 141, 157, 178, 206], "mode": [12, 90, 141, 206, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 246], "too": [12, 26, 90, 101, 141, 256, 260], "larg": [12, 90, 101, 141, 210, 216, 247, 260], "appropri": [12, 26, 90, 101, 141, 207, 212], "commut": 12, "associ": [12, 42, 141, 192, 199, 242, 245, 248, 256, 259, 261], "tabl": [12, 90, 141, 189], "c": [12, 90, 93, 122, 141, 143, 144, 153, 167, 168, 173, 184, 190, 204, 207, 210, 213, 232, 236, 237, 238, 246, 248, 249, 257, 259, 260, 262], "d": [12, 90, 93, 122, 141, 144, 199, 219, 230], "dj": [12, 90, 141], "independ": [12, 90, 141, 157, 190, 202, 210, 233, 246, 248, 256, 257, 260], "abov": [12, 88, 90, 93, 123, 125, 141, 144, 149, 150, 164, 170, 176, 177, 190, 199, 207, 208, 210, 211, 214, 235, 236, 252, 256, 259, 262], "similarli": [12, 57, 116, 137, 199, 232, 249], "henc": [12, 79, 95, 143, 153, 179, 180, 181, 182, 190, 205, 207, 208, 209, 210, 214, 215, 216, 260, 262], "z1": 12, "z2": 12, "keepdim": [13, 14, 16, 17, 134, 136, 138, 150, 168, 170, 184, 240, 254], "test": [13, 14, 89, 117, 118, 119, 204, 206, 258, 260, 261, 262], "evalu": [13, 14, 22, 30, 36, 38, 41, 44, 45, 46, 48, 51, 52, 94, 96, 123, 124, 125, 126, 142, 148, 159, 160, 165, 202, 260], "union": [13, 14, 15, 21, 22, 26, 28, 30, 31, 32, 33, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 59, 60, 75, 77, 78, 91, 98, 99, 103, 104, 108, 115, 116, 122, 134, 136, 138, 140, 145, 150, 153, 155, 156, 166, 167, 168, 170, 174, 184, 187, 221, 225, 240, 242, 245, 254, 261], "ax": [13, 14, 16, 17, 19, 55, 56, 99, 134, 136, 138, 140, 147, 150, 156, 166, 168, 170, 174, 175, 184, 185, 190, 204, 220, 221, 224, 225, 228, 231, 233, 240, 245, 248, 251, 254], "logic": [13, 14, 24, 26, 90, 93, 128, 129, 130, 131, 141, 144, 211, 214, 220, 224, 228, 231], "AND": [13, 67, 93, 128, 259], "entir": [13, 14, 86, 87, 94, 96, 134, 136, 138, 150, 161, 162, 168, 170, 184], "valid": [13, 14, 26, 27, 95, 114, 140, 167, 174, 183, 190, 206, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 236, 246, 249, 261], "count": [13, 14, 78, 88, 99, 171, 179, 180, 185, 190, 204, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 237], "last": [13, 14, 18, 19, 55, 78, 88, 99, 156, 163, 167, 171, 174, 185, 190, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 235, 240, 246, 249, 252], "invalid": [13, 14, 23, 95, 212, 260], "rais": [13, 14, 19, 23, 24, 25, 26, 29, 34, 35, 40, 47, 51, 55, 60, 74, 90, 94, 95, 102, 122, 132, 134, 138, 143, 149, 154, 166, 167, 183, 185, 190, 199, 202, 204, 210, 211, 212, 214, 233, 241, 260], "wa": [13, 14, 19, 26, 101, 134, 136, 138, 150, 168, 170, 184, 199, 211, 216, 260, 262], "OR": [14, 24, 70, 130, 144, 259], "start": [15, 122, 190, 204, 216, 260, 262], "stop": [15, 122, 190, 204, 261], "step": [15, 122, 190, 261], "evenli": [15, 122], "space": [15, 122, 219, 221, 230], "open": [15, 122, 140, 174, 190], "inclus": [15, 190, 260], "end": [15, 65, 86, 122, 159, 161, 172, 173, 197, 208, 247, 260, 261, 262], "exclus": [15, 190], "distanc": [15, 107], "between": [15, 26, 47, 51, 65, 78, 90, 93, 98, 122, 134, 135, 138, 139, 144, 149, 167, 179, 180, 181, 182, 199, 207, 208, 211, 219, 230, 256, 260, 262], "adjac": 15, "output": [15, 60, 63, 78, 88, 91, 92, 95, 97, 99, 102, 103, 104, 111, 122, 137, 145, 146, 154, 156, 158, 166, 167, 171, 175, 187, 188, 202, 204, 207, 208, 211, 213, 214, 216, 218, 219, 220, 222, 223, 224, 227, 228, 229, 230, 231, 252, 260], "infer": [15, 60, 63, 92, 103, 104, 146, 154, 188, 209, 256, 261], "cannot": [15, 26, 57, 102, 172, 173, 204, 207, 209, 260], "guarante": [15, 59, 179, 181, 202, 207, 211, 260, 262], "error": [15, 19, 23, 24, 25, 26, 29, 34, 35, 51, 55, 90, 102, 134, 138, 172, 173, 199, 206, 247, 260], "ceil": [15, 189], "indic": [16, 17, 18, 26, 60, 88, 89, 102, 111, 116, 122, 140, 143, 156, 158, 159, 171, 174, 176, 177, 179, 181, 190, 199, 204, 254, 260], "occur": [16, 17, 75, 107, 172, 173, 179, 180, 181, 182, 207, 261], "occurr": [16, 17, 179], "comparison": [16, 17, 18, 31, 33, 37, 39, 93, 105, 106, 120, 121, 134, 135, 138, 139, 144, 163, 189, 207, 257, 261], "search": [16, 17, 158, 189], "flatten": [16, 17, 78, 153, 156, 179, 180, 181, 182, 254, 256], "descend": [18, 163, 249, 250], "stabl": [18, 163, 210], "sort": [18, 158, 189, 204, 236, 237, 249, 250], "ascend": [18, 158, 163, 204], "stabil": [18, 163], "maintain": [18, 163, 205, 260, 262], "rel": [18, 19, 55, 99, 135, 139, 156, 163, 204, 235, 242, 245, 252], "compar": [18, 163, 179, 180, 181, 182, 206, 211, 261, 263], "properti": [19, 53, 54, 55, 56, 57, 58, 115, 204, 207, 211, 216, 260], "transpos": [19, 40, 55, 132, 133, 174, 232, 236, 245, 249, 256], "instanc": [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 55, 59, 89, 199, 202, 204, 211], "permut": [19, 55, 147], "revers": [19, 55, 65, 99], "origin": [19, 55, 65, 107, 140, 154, 156, 204, 208, 218, 220, 223, 224, 227, 228, 229, 231, 260, 261], "limit": [19, 98, 108, 116, 206, 256, 259], "matric": [19, 40, 55, 132, 133, 137, 176, 177, 232, 234, 235, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 256], "deviat": [19, 168, 206, 212, 260, 262], "et": [19, 249, 250], "al": 19, "intent": [19, 65], "found": [19, 207, 210, 262, 263], "problemat": [19, 63, 205, 208], "conflict": 19, "definit": [19, 86, 87, 161, 162, 172, 173, 204, 232, 261], "batch": [19, 254, 256], "cetera": [19, 249, 250], "permute_dim": [19, 189], "interfac": [19, 210, 256, 260, 262], "ab": [20, 107, 149, 189, 204, 240, 254], "augend": 21, "addend": 21, "self_i": [22, 28, 30, 31, 33, 36, 37, 38, 39, 41, 43, 44, 45, 46, 48, 50, 51, 52], "other_i": [22, 28, 30, 31, 33, 37, 38, 39, 41, 43, 45, 47, 48, 50, 51, 52], "bitwise_and": [22, 189], "api_vers": [23, 260], "object": [23, 24, 25, 26, 29, 34, 35, 53, 57, 59, 60, 89, 98, 102, 108, 110, 112, 113, 114, 189, 190, 199, 202, 204, 208, 210, 211, 214, 216, 255, 257, 261, 262], "2020": [23, 216, 257, 259, 260], "10": [23, 27, 124, 190, 260], "latest": [23, 210], "modul": [23, 202, 257, 261, 262, 263], "everi": [23, 103, 104, 246, 260], "top": [23, 202, 260, 262], "level": [23, 199, 205, 210, 211, 255, 256, 260, 261], "public": [23, 255, 261, 262], "well": [23, 205, 207, 210, 211, 246, 262, 263], "part": [23, 35, 176, 177, 199, 204, 210, 215, 257, 260, 262], "convert": [24, 25, 29, 34, 35, 60, 102, 199, 204, 205, 207, 210, 260, 262], "handl": [24, 26, 61, 64, 86, 88, 102, 124, 126, 149, 150, 159, 161, 165, 170, 172, 204, 205, 207, 208, 211, 212, 252, 260], "lazi": [24, 25, 29, 34, 35, 202, 204, 213, 262], "languag": [24, 25, 29, 34, 35, 208, 212, 214, 256, 260, 262], "therefor": [24, 25, 29, 34, 35, 202, 210, 211, 212, 214, 216, 257, 260, 262], "abl": [24, 25, 29, 34, 35, 102, 208, 210, 211, 260, 262], "kind": [24, 25, 26, 29, 34, 35, 47, 51, 77, 90, 98, 102, 104, 108, 113, 115, 116, 149, 199, 204, 214, 256, 259], "here": [24, 25, 26, 29, 34, 35, 190, 199, 208, 210, 215, 216, 262], "valueerror": [24, 25, 26, 29, 34, 35, 60, 102, 154, 166, 262], "instead": [24, 25, 29, 34, 35, 63, 207, 210, 214, 261, 262], "2023": [24, 25, 26, 29, 34, 35, 59, 63, 77, 85, 88, 102, 107, 134, 135, 138, 139, 140, 150, 153, 158, 160, 170, 171, 174, 175, 179, 180, 181, 182, 183, 185, 218, 219, 220, 222, 223, 224, 227, 228, 230, 233, 252], "new": [25, 26, 77, 79, 85, 88, 95, 98, 102, 103, 104, 107, 108, 109, 116, 135, 139, 140, 145, 146, 151, 153, 154, 158, 160, 167, 171, 175, 183, 187, 188, 202, 204, 205, 208, 210, 211, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 257, 260, 261, 262], "stream": [26, 59, 211], "max_vers": [26, 204], "dl_devic": [26, 204], "enum": [26, 27], "pycapsul": 26, "export": [26, 102, 204, 210, 261], "from_dlpack": [26, 27, 189, 204, 210], "dlpack": [26, 27, 102, 204], "capsul": 26, "cuda": [26, 27, 205, 210, 262], "rocm": [26, 27, 205], "pointer": 26, "produc": [26, 236, 246, 249, 262], "instruct": 26, "safe": [26, 122], "insert": [26, 95, 158, 204], "wait": 26, "event": [26, 259], "larger": [26, 98, 156, 168, 184, 245], "below": [26, 101, 102, 176, 177, 192, 210, 211, 235, 252], "signal": [26, 222, 226, 262], "ownership": 26, "stai": 26, "On": 26, "cpu": [26, 27, 202, 205, 210, 211, 256, 260, 262], "queue": [26, 59, 211], "similar": [26, 152, 190, 205, 207, 209, 260, 261, 262], "mechan": [26, 102, 202, 204, 205, 213, 255, 260], "most": [26, 202, 211, 236, 256, 260, 262], "yet": [26, 216, 260], "sycl": 26, "want": [26, 90, 141, 205, 209, 210, 260, 262, 263], "cl": 26, "agre": 26, "assum": [26, 86, 102, 161, 172, 202, 207, 211, 255, 260], "legaci": 26, "per": [26, 153, 205, 210, 258], "thread": [26, 260, 262], "disallow": 26, "due": [26, 42, 57, 58, 122, 141, 153, 171, 206, 207, 256, 260], "ambigu": [26, 63, 101, 208], "construct": [26, 175, 202, 204, 205, 214, 260], "particular": [26, 190, 205, 207, 210, 211, 216, 256, 259, 260, 262, 263], "kdlcpu": 26, "safeti": [26, 59], "prefer": [26, 101, 202, 256, 262], "develop": [26, 206, 260, 261, 262, 263], "who": [26, 206, 260, 261], "think": 26, "cost": 26, "caller": 26, "major": [26, 143, 153, 190, 257], "minor": [26, 257], "verifi": [26, 260], "even": [26, 90, 141, 149, 157, 206, 207, 208, 219, 221, 225, 230, 246, 256, 260, 262], "pass": [26, 65, 202, 206, 211], "format": [26, 27, 257], "__dlpack_device__": [26, 102, 189, 210], "buffererror": [26, 102, 204, 210], "v2023": [26, 102], "mandat": [26, 102, 260], "offer": [26, 102, 205, 210, 211, 215, 260, 262], "referenc": [26, 260], "underli": [26, 67, 70, 72, 102, 206, 247, 256], "interpret": [26, 102, 107, 207, 208, 263], "enumer": 26, "made": [26, 102, 202, 207, 255, 257, 260, 262], "never": [26, 60, 102, 154, 210, 260], "deem": [26, 102], "cross": [26, 102, 204, 211, 256, 260], "movement": [26, 102], "request": [26, 102, 260], "reus": [26, 60, 102, 208, 260], "buffer": [26, 60, 102, 208, 210], "happen": [26, 102, 208, 211, 214, 256], "dlpack_flag_bitmask_is_copi": 26, "flag": 26, "understood": [26, 199], "interchang": [26, 102, 202, 205, 213, 260], "detail": [26, 102, 143, 153, 179, 180, 181, 182, 189, 190, 201, 202, 209, 211, 215, 256, 260, 262], "stride": [26, 102, 208, 210], "fail": [26, 102, 260], "reason": [26, 102, 152, 173, 208, 210, 212, 256, 260, 261], "incorrect": 26, "scheme": [26, 257], "semver": 26, "abi": [26, 205, 210], "break": [26, 212], "introduc": [26, 63, 101, 156, 216, 261], "goe": 26, "togeth": [26, 199, 210], "dlmanagedtensorvers": 26, "struct": 26, "later": 26, "introduct": 26, "becaus": [26, 199, 205, 208, 211, 212, 214, 216, 236, 249, 260, 262, 263], "keep": [26, 199, 205, 260], "march": 26, "2025": 26, "onward": 26, "ideal": [26, 256], "late": 26, "okai": 26, "we": [26, 207, 249, 260], "get": [26, 98, 108, 205, 208, 210, 211], "now": [26, 102, 214, 260, 262], "our_own_dlpack_vers": 26, "fill": [26, 103, 104, 145, 146, 187, 188, 204], "field": [26, 179, 180, 181, 207, 236, 246, 247, 249, 260], "understand": [26, 245, 260, 261], "u": [26, 232, 245, 249], "just": [26, 260, 262], "our": 26, "elif": 26, "fine": [26, 216, 260], "own": [26, 202, 208, 260], "re": [26, 156, 205, 208, 216, 262], "intern": [26, 262], "did": 26, "older": [26, 173, 210, 257, 260], "around": [26, 261], "y": [26, 65, 102, 207, 208, 262], "dlmanagedtensor": 26, "so": [26, 98, 102, 110, 190, 197, 210, 256, 259, 260, 263], "tell": 26, "old": 26, "exchang": [26, 102, 210], "And": [26, 190, 211], "try": [26, 216, 260], "succe": 26, "info": [26, 110], "dltensor_vers": 26, "need": [26, 190, 205, 206, 208, 210, 212, 216, 256, 257, 260, 261, 262, 263], "used_dltensor_vers": 26, "done": [26, 202], "typeerror": [26, 29, 34, 35, 260, 262], "read": [26, 204, 208], "dlpack_flag_bitmask_read_onli": 26, "ignor": [26, 137, 256], "respons": 26, "isn": [26, 205], "t": [26, 189, 205, 208, 211, 215, 216, 260, 262], "id": 27, "meant": 27, "device_typ": 27, "device_id": 27, "member": 27, "cpu_pin": 27, "opencl": 27, "vulkan": 27, "metal": 27, "vpi": 27, "cuda_manag": 27, "13": 27, "one_api": 27, "14": [27, 257], "truth": [28, 31, 33, 37, 39, 43, 89, 93, 105, 106, 120, 121, 144, 263], "outsid": [29, 167, 183, 190, 199, 204, 210], "bound": [29, 77, 171, 190, 199, 204, 216], "divis": [30, 41, 71, 90, 101, 152, 159, 207], "floor_divid": [30, 189], "greater_equ": [31, 189], "kei": [32, 49, 111, 113, 115, 260], "slice": [32, 49, 183, 189, 208], "ellipsi": [32, 49, 190], "pep": [34, 40, 101, 132, 210, 257], "357": 34, "overflowerror": 35, "bitwise_invert": [36, 189], "less_equ": [37, 189], "bitwise_left_shift": [38, 189], "matrix": [40, 55, 132, 133, 137, 174, 176, 177, 232, 234, 235, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 256, 260], "product": [40, 42, 58, 132, 141, 150, 174, 185, 204, 233, 244, 256], "semant": [40, 101, 132, 152, 171, 189, 190, 202, 208, 210, 212, 214, 215, 256, 260, 261, 262], "built": [40, 132, 190, 199, 260], "465": [40, 132], "least": [40, 90, 115, 116, 132, 141, 143, 179, 180, 181, 182, 205, 206, 245], "m": [40, 55, 132, 133, 137, 153, 158, 174, 175, 176, 177, 190, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252], "remov": [40, 132, 166, 190, 207, 235, 252], "innermost": [40, 132, 133, 176, 177, 232, 234, 235, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252], "conjug": [40, 79, 132, 174, 185, 204, 232, 236, 249, 256], "transposit": [40, 132, 174], "desir": [40, 63, 75, 132, 140, 174, 206, 207, 210, 216], "prior": [40, 132, 174], "inner": [40, 132, 204, 236, 256], "stack": [40, 55, 132, 133, 176, 177, 189, 215, 232, 234, 235, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 256], "l": [40, 132, 232, 252], "remaind": [41, 189, 190], "multipli": [42, 150, 165, 189, 204, 206, 236, 249], "not_equ": [43, 189, 204], "negat": [44, 79, 142], "bitwise_or": [45, 189], "exponenti": [47, 94, 96, 127, 149, 207], "power": [47, 71, 94, 149, 207, 241, 262], "expon": [47, 149, 241], "versu": [47, 51, 63, 77, 90, 141, 149, 204], "bitwise_right_shift": [48, 189], "mix": [49, 122, 136, 155, 168, 184, 189, 204, 208, 211, 256, 260], "how": [49, 90, 141, 202, 206, 211, 215, 261, 262, 263], "minuend": 50, "subtrahend": 50, "subtract": [50, 189, 204, 206], "choos": [51, 57, 59, 90, 101, 122, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 143, 153, 168, 179, 180, 181, 182, 184, 189, 190, 197, 207, 208, 209, 211, 214, 260, 262], "divid": [51, 101, 159, 189, 190, 204, 206], "bitwise_xor": [52, 189], "resid": [53, 59, 95, 140, 174, 190, 204, 210, 260], "fewer": 55, "unknown": [57, 58, 153], "graph": [57, 58, 143, 153, 179, 180, 181, 182, 190, 209, 214, 260], "static": [57, 209, 213], "resolv": [57, 60, 88, 95, 101, 103, 104, 150, 170, 220, 221, 224, 225, 228, 231, 252, 260], "know": [57, 143, 153, 179, 180, 181, 182, 202, 205, 206, 209, 260, 262], "content": [57, 209, 259], "warrant": 57, "custom": [57, 205, 212], "immut": 57, "retriev": [57, 190, 202, 217, 256, 262], "behav": [57, 207], "current": [59, 113, 115, 171, 197, 208, 211, 216, 260, 261, 262], "__dlpack__": [59, 102, 189, 204, 210], "caveat": 59, "would": [59, 60, 154, 158, 190, 204, 208, 214, 256, 260, 262], "locat": [59, 208], "explicit": [59, 60, 102, 171, 174, 211, 262], "enqueu": 59, "asynchron": 59, "explain": [59, 205], "clarifi": [59, 134, 138, 179, 180, 181, 204], "obj": 60, "nestedsequ": 60, "supportsbufferprotocol": 60, "possibli": [60, 215, 260], "nest": [60, 215], "sequenc": [60, 78, 122, 167, 174, 183, 190, 204, 220, 221, 224, 225, 228, 231, 251], "protocol": [60, 202, 210, 216, 260, 262], "turn": [60, 202, 255], "memoryview": 60, "preced": [60, 207, 210, 211], "mixtur": 60, "convers": [60, 122, 204, 205, 260], "obei": [60, 122], "permit": [60, 63, 122, 209, 259], "To": [60, 101, 190, 204, 206, 207, 216, 260, 261, 263], "array_api": [60, 260], "astyp": [60, 189, 204], "exce": [60, 103, 104, 122], "sine": [61, 62, 161, 162, 173], "1j": [61, 64, 86, 87, 94, 96, 107, 161, 162, 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"Backwards compatibility": [[202, "backwards-compatibility"], [257, "backwards-compatibility"]], "Production code & interactive use": [[202, "production-code-interactive-use"]], "Benchmark suite": [[203, "benchmark-suite"]], "Changelog per API standard version": [[204, "changelog-per-api-standard-version"]], "Changelog": [[204, "changelog"]], "v2023.12": [[204, "v2023-12"]], "Updates": [[204, "updates"], [204, "id3"]], "Normative": [[204, "normative"]], "APIs": [[204, "apis"], [204, "id1"], [204, "id4"], [204, "id8"]], "Extensions": [[204, "extensions"], [204, "id2"], [204, "id5"], [204, "id9"], [255, "extensions"]], "Additions": [[204, "additions"], [204, "id7"]], "Breaking Changes": [[204, "breaking-changes"]], "Errata": [[204, "errata"], [204, "id10"]], "v2022.12": [[204, "v2022-12"]], "Complex Number Support": [[204, "complex-number-support"], [204, "id6"]], "C API": [[205, "c-api"]], "Example situations for C/Cython usage": [[205, "example-situations-for-c-cython-usage"]], "Situation 1: a Python package that is mostly pure Python, with a limited number of Cython extensions": [[205, "situation-1-a-python-package-that-is-mostly-pure-python-with-a-limited-number-of-cython-extensions"]], "Situation 2: a Python package that contains a lot of Cython code": [[205, "situation-2-a-python-package-that-contains-a-lot-of-cython-code"]], "Situation 3: a Python package that uses the NumPy or Python C API directly": [[205, "situation-3-a-python-package-that-uses-the-numpy-or-python-c-api-directly"]], "Device support": [[205, "device-support"], [211, "device-support"]], "Other longer-term approaches": [[205, "other-longer-term-approaches"]], "Further Python API standardization": [[205, "further-python-api-standardization"]], "HPy": [[205, "hpy"]], "Accuracy": [[206, "accuracy"]], "Arithmetic Operations": [[206, "arithmetic-operations"]], "Mathematical Functions": [[206, "mathematical-functions"]], "Linear Algebra": [[206, "linear-algebra"]], "Complex Numbers": [[207, "complex-numbers"]], "The Complex Plane": [[207, "the-complex-plane"]], "Branch Cuts": [[207, "branch-cuts"]], "Complex Number Ordering": [[207, "complex-number-ordering"]], "Valued-based Promotion": [[207, "valued-based-promotion"]], "Copy-view behaviour and mutability": [[208, "copy-view-behaviour-and-mutability"]], "Mutating views": [[208, null]], "Data-dependent output shapes": [[209, "data-dependent-output-shapes"]], "Data interchange mechanisms": [[210, "data-interchange-mechanisms"]], "DLPack: An in-memory tensor structure": [[210, "dlpack-an-in-memory-tensor-structure"]], "Non-supported use cases": [[210, "non-supported-use-cases"]], "Intended usage": [[211, "intended-usage"]], "Syntax for device assignment": [[211, "syntax-for-device-assignment"]], "Semantics": [[211, "semantics"]], "Out of scope for device support": [[211, "out-of-scope-for-device-support"]], "Exceptions": [[212, "exceptions"]], "Design topics & constraints": [[213, "design-topics-constraints"], [213, null]], "Lazy vs. eager execution": [[214, "lazy-vs-eager-execution"]], "Parallelism": [[215, "parallelism"]], "Static typing": [[216, "static-typing"]], "Fourier transform Functions": [[217, "fourier-transform-functions"]], "Extension name and usage": [[217, "extension-name-and-usage"], [256, "extension-name-and-usage"]], "fft": [[218, "fft"]], "fftfreq": [[219, "fftfreq"]], "fftn": [[220, "fftn"]], "fftshift": [[221, "fftshift"]], "hfft": [[222, "hfft"]], "ifft": [[223, "ifft"]], "ifftn": [[224, "ifftn"]], "ifftshift": [[225, "ifftshift"]], "ihfft": [[226, "ihfft"]], "irfft": [[227, "irfft"]], "irfftn": [[228, "irfftn"]], "rfft": [[229, "rfft"]], "rfftfreq": [[230, "rfftfreq"]], "rfftn": [[231, "rfftn"]], "cholesky": [[232, "cholesky"]], "cross": [[233, "cross"]], "det": [[234, "det"]], "diagonal": [[235, "diagonal"]], "eigh": [[236, "eigh"]], "eigvalsh": [[237, "eigvalsh"]], "inv": [[238, "inv"]], "matrix_norm": [[240, "matrix-norm"]], "matrix_power": [[241, "matrix-power"]], "matrix_rank": [[242, "matrix-rank"]], "outer": [[244, "outer"]], "pinv": [[245, "pinv"]], "qr": [[246, "qr"]], "slogdet": [[247, "slogdet"]], "solve": [[248, "solve"]], "svd": [[249, "svd"]], "svdvals": [[250, "svdvals"]], "trace": [[252, "trace"]], "vector_norm": [[254, "vector-norm"]], "Extension modules:": [[255, null]], "Linear Algebra Extension": [[256, "linear-algebra-extension"]], "Design Principles": [[256, "design-principles"]], "Future API standard evolution": [[257, "future-api-standard-evolution"]], "Scope extensions": [[257, "scope-extensions"]], "Versioning": [[257, "versioning"]], "Python array API standard": [[258, "python-array-api-standard"]], "Contents": [[258, "contents"]], "Context": [[258, null]], "API": [[258, null]], "Methodology and Usage": [[258, null]], "Other": [[258, null]], "License": [[259, "license"]], "Purpose and scope": [[260, "purpose-and-scope"]], "Introduction": [[260, "introduction"], [261, "introduction"]], "This API standard": [[260, "this-api-standard"]], "History": [[260, "history"]], "Scope (includes out-of-scope / non-goals)": [[260, "scope-includes-out-of-scope-non-goals"]], "In scope": [[260, "in-scope"]], "Out of scope": [[260, "out-of-scope"]], "Implications of in/out of scope": [[260, "implications-of-in-out-of-scope"]], "Stakeholders": [[260, "stakeholders"]], "How to read this document": [[260, "how-to-read-this-document"]], "How to adopt this API": [[260, "how-to-adopt-this-api"]], "Checking an array object for Compliance": [[260, "checking-an-array-object-for-compliance"]], "Discoverability of conforming implementations": [[260, "discoverability-of-conforming-implementations"]], "Optional feature": [[260, null]], "Conformance": [[260, "conformance"]], "Terms and Definitions": [[260, "terms-and-definitions"]], "Normative References": [[260, "normative-references"]], "Usage Data": [[261, "usage-data"]], "Design": [[261, "design"]], "Usage": [[261, "usage"]], "Use in Decision-Making": [[261, "use-in-decision-making"]], "Use cases": [[262, "use-cases"]], "Types of use cases": [[262, "types-of-use-cases"]], "Concrete use cases": [[262, "concrete-use-cases"]], "Use case 1: add hardware accelerator and distributed support to SciPy": [[262, "use-case-1-add-hardware-accelerator-and-distributed-support-to-scipy"]], "Use case 2: simplify einops by removing the backend system": [[262, "use-case-2-simplify-einops-by-removing-the-backend-system"]], "Use case 3: adding a Python API to xtensor": [[262, "use-case-3-adding-a-python-api-to-xtensor"]], "Use case 4: make JIT compilation of array computations easier and more robust": [[262, "use-case-4-make-jit-compilation-of-array-computations-easier-and-more-robust"]], "Verification - test suite": [[263, "verification-test-suite"]], "Measuring conformance": [[263, "measuring-conformance"]], "Running the tests": [[263, "running-the-tests"]]}, "indexentries": {"__array_api_version__ (in module array_api)": [[8, "array_api.__array_api_version__"]], "abs() (in module array_api)": [[9, "array_api.abs"]], "acos() (in module array_api)": [[10, "array_api.acos"]], "acosh() (in module array_api)": [[11, "array_api.acosh"]], "add() (in module array_api)": [[12, "array_api.add"]], "all() (in module array_api)": [[13, "array_api.all"]], "any() (in module array_api)": [[14, "array_api.any"]], "arange() (in module array_api)": [[15, "array_api.arange"]], "argmax() (in module array_api)": [[16, "array_api.argmax"]], "argmin() (in module array_api)": [[17, "array_api.argmin"]], "argsort() (in module array_api)": [[18, "array_api.argsort"]], "t (array property)": [[19, "array_api.array.T"]], "__abs__() (array method)": [[20, "array_api.array.__abs__"]], "__add__() (array method)": [[21, "array_api.array.__add__"]], "__and__() (array method)": [[22, "array_api.array.__and__"]], "__array_namespace__() (array method)": [[23, "array_api.array.__array_namespace__"]], "__bool__() (array method)": [[24, "array_api.array.__bool__"]], "__complex__() (array method)": [[25, "array_api.array.__complex__"]], "__dlpack__() (array method)": [[26, "array_api.array.__dlpack__"]], "__dlpack_device__() (array method)": [[27, "array_api.array.__dlpack_device__"]], "__eq__() (array method)": [[28, "array_api.array.__eq__"]], "__float__() (array method)": [[29, "array_api.array.__float__"]], "__floordiv__() (array method)": [[30, "array_api.array.__floordiv__"]], "__ge__() (array method)": [[31, "array_api.array.__ge__"]], "__getitem__() (array method)": [[32, "array_api.array.__getitem__"]], "__gt__() (array method)": [[33, "array_api.array.__gt__"]], "__index__() (array method)": [[34, "array_api.array.__index__"]], "__int__() (array method)": [[35, "array_api.array.__int__"]], "__invert__() (array method)": [[36, "array_api.array.__invert__"]], "__le__() (array method)": [[37, "array_api.array.__le__"]], "__lshift__() (array method)": [[38, "array_api.array.__lshift__"]], "__lt__() (array method)": [[39, "array_api.array.__lt__"]], "__matmul__() (array method)": [[40, "array_api.array.__matmul__"]], "__mod__() (array method)": [[41, "array_api.array.__mod__"]], "__mul__() (array method)": [[42, "array_api.array.__mul__"]], "__ne__() (array method)": [[43, "array_api.array.__ne__"]], "__neg__() (array method)": [[44, "array_api.array.__neg__"]], "__or__() (array method)": [[45, "array_api.array.__or__"]], "__pos__() (array method)": [[46, "array_api.array.__pos__"]], "__pow__() (array method)": [[47, "array_api.array.__pow__"]], "__rshift__() (array method)": [[48, "array_api.array.__rshift__"]], "__setitem__() (array method)": [[49, "array_api.array.__setitem__"]], "__sub__() (array method)": [[50, "array_api.array.__sub__"]], "__truediv__() (array method)": [[51, "array_api.array.__truediv__"]], "__xor__() (array method)": [[52, "array_api.array.__xor__"]], "device (array property)": [[53, "array_api.array.device"]], "dtype (array property)": [[54, "array_api.array.dtype"]], "mt (array property)": [[55, "array_api.array.mT"]], "ndim (array property)": [[56, "array_api.array.ndim"]], "shape (array property)": [[57, "array_api.array.shape"]], "size (array property)": [[58, "array_api.array.size"]], "to_device() (array method)": [[59, "array_api.array.to_device"]], "asarray() (in module array_api)": [[60, "array_api.asarray"]], "asin() (in module array_api)": [[61, "array_api.asin"]], "asinh() (in module array_api)": [[62, "array_api.asinh"]], "astype() (in module array_api)": [[63, "array_api.astype"]], "atan() (in module array_api)": [[64, "array_api.atan"]], "atan2() (in module array_api)": [[65, "array_api.atan2"]], "atanh() (in module array_api)": [[66, "array_api.atanh"]], "bitwise_and() (in module array_api)": [[67, "array_api.bitwise_and"]], "bitwise_invert() (in module array_api)": [[68, "array_api.bitwise_invert"]], "bitwise_left_shift() (in module array_api)": [[69, "array_api.bitwise_left_shift"]], "bitwise_or() (in module array_api)": [[70, "array_api.bitwise_or"]], "bitwise_right_shift() (in module array_api)": [[71, "array_api.bitwise_right_shift"]], "bitwise_xor() (in module array_api)": [[72, "array_api.bitwise_xor"]], "broadcast_arrays() (in module array_api)": [[73, "array_api.broadcast_arrays"]], "broadcast_to() (in module array_api)": [[74, "array_api.broadcast_to"]], "can_cast() (in module array_api)": [[75, "array_api.can_cast"]], "ceil() (in module array_api)": [[76, "array_api.ceil"]], "clip() (in module array_api)": [[77, "array_api.clip"]], "concat() (in module array_api)": [[78, "array_api.concat"]], "conj() (in module array_api)": [[79, "array_api.conj"]], "e (in module array_api.constants)": [[80, "array_api.constants.e"]], "inf (in module array_api.constants)": [[81, "array_api.constants.inf"]], "nan (in module array_api.constants)": [[82, "array_api.constants.nan"]], "newaxis (in module array_api.constants)": [[83, "array_api.constants.newaxis"]], "pi (in module array_api.constants)": [[84, "array_api.constants.pi"]], "copysign() (in module array_api)": [[85, "array_api.copysign"]], "cos() (in module array_api)": [[86, "array_api.cos"]], "cosh() (in module array_api)": [[87, "array_api.cosh"]], "cumulative_sum() (in module array_api)": [[88, "array_api.cumulative_sum"]], "__eq__() (in module array_api.data_types)": [[89, "array_api.data_types.__eq__"]], "divide() (in module array_api)": [[90, "array_api.divide"]], "empty() (in module array_api)": [[91, "array_api.empty"]], "empty_like() (in module array_api)": [[92, "array_api.empty_like"]], "equal() (in module array_api)": [[93, "array_api.equal"]], "exp() (in module array_api)": [[94, "array_api.exp"]], "expand_dims() (in module array_api)": [[95, "array_api.expand_dims"]], "expm1() (in module array_api)": [[96, "array_api.expm1"]], "eye() (in module array_api)": [[97, "array_api.eye"]], "finfo() (in module array_api)": [[98, "array_api.finfo"]], "flip() (in module array_api)": [[99, "array_api.flip"]], "floor() (in module array_api)": [[100, "array_api.floor"]], "floor_divide() (in module array_api)": [[101, "array_api.floor_divide"]], "from_dlpack() (in module array_api)": [[102, "array_api.from_dlpack"]], "full() (in module array_api)": [[103, "array_api.full"]], "full_like() (in module array_api)": [[104, "array_api.full_like"]], "greater() (in module array_api)": [[105, "array_api.greater"]], "greater_equal() (in module array_api)": [[106, "array_api.greater_equal"]], "hypot() (in module array_api)": [[107, "array_api.hypot"]], "iinfo() (in module array_api)": [[108, "array_api.iinfo"]], "imag() (in module array_api)": [[109, "array_api.imag"]], "__array_namespace_info__() (in module array_api.info)": [[110, "array_api.info.__array_namespace_info__"]], "capabilities() (in module array_api.info)": [[111, "array_api.info.capabilities"]], "default_device() (in module array_api.info)": [[112, "array_api.info.default_device"]], "default_dtypes() (in module array_api.info)": [[113, "array_api.info.default_dtypes"]], "devices() (in module array_api.info)": [[114, "array_api.info.devices"]], "dtypes() (in module array_api.info)": [[115, "array_api.info.dtypes"]], "isdtype() (in module array_api)": [[116, "array_api.isdtype"]], "isfinite() (in module array_api)": [[117, "array_api.isfinite"]], "isinf() (in module array_api)": [[118, "array_api.isinf"]], "isnan() (in module array_api)": [[119, "array_api.isnan"]], "less() (in module array_api)": [[120, "array_api.less"]], "less_equal() (in module array_api)": [[121, "array_api.less_equal"]], "linspace() (in module array_api)": [[122, "array_api.linspace"]], "log() (in module array_api)": [[123, "array_api.log"]], "log10() (in module array_api)": [[124, "array_api.log10"]], "log1p() (in module array_api)": [[125, "array_api.log1p"]], "log2() (in module array_api)": [[126, "array_api.log2"]], "logaddexp() (in module array_api)": [[127, "array_api.logaddexp"]], "logical_and() (in module array_api)": [[128, "array_api.logical_and"]], "logical_not() (in module array_api)": [[129, "array_api.logical_not"]], "logical_or() (in module array_api)": [[130, "array_api.logical_or"]], "logical_xor() (in module array_api)": [[131, "array_api.logical_xor"]], "matmul() (in module array_api)": [[132, "array_api.matmul"]], "matrix_transpose() (in module array_api)": [[133, "array_api.matrix_transpose"]], "max() (in module array_api)": [[134, "array_api.max"]], "maximum() (in module array_api)": [[135, "array_api.maximum"]], "mean() (in module array_api)": [[136, "array_api.mean"]], "meshgrid() (in module array_api)": [[137, "array_api.meshgrid"]], "min() (in module array_api)": [[138, "array_api.min"]], "minimum() (in module array_api)": [[139, "array_api.minimum"]], "moveaxis() (in module array_api)": [[140, "array_api.moveaxis"]], "multiply() (in module array_api)": [[141, "array_api.multiply"]], "negative() (in module array_api)": [[142, "array_api.negative"]], "nonzero() (in module array_api)": [[143, "array_api.nonzero"]], "not_equal() (in module array_api)": [[144, "array_api.not_equal"]], "ones() (in module array_api)": [[145, "array_api.ones"]], "ones_like() (in module array_api)": [[146, "array_api.ones_like"]], "permute_dims() (in module array_api)": [[147, "array_api.permute_dims"]], "positive() (in module array_api)": [[148, "array_api.positive"]], "pow() (in module array_api)": [[149, "array_api.pow"]], "prod() (in module array_api)": [[150, "array_api.prod"]], "real() (in module array_api)": [[151, "array_api.real"]], "remainder() (in module array_api)": [[152, "array_api.remainder"]], "repeat() (in module array_api)": [[153, "array_api.repeat"]], "reshape() (in module array_api)": [[154, "array_api.reshape"]], "result_type() (in module array_api)": [[155, "array_api.result_type"]], "roll() (in module array_api)": [[156, "array_api.roll"]], "round() (in module array_api)": [[157, "array_api.round"]], "searchsorted() (in module array_api)": [[158, "array_api.searchsorted"]], "sign() (in module array_api)": [[159, "array_api.sign"]], "signbit() (in module array_api)": [[160, "array_api.signbit"]], "sin() (in module array_api)": [[161, "array_api.sin"]], "sinh() (in module array_api)": [[162, "array_api.sinh"]], "sort() (in module array_api)": [[163, "array_api.sort"]], "sqrt() (in module array_api)": [[164, "array_api.sqrt"]], "square() (in module array_api)": [[165, "array_api.square"]], "squeeze() (in module array_api)": [[166, "array_api.squeeze"]], "stack() (in module array_api)": [[167, "array_api.stack"]], "std() (in module array_api)": [[168, "array_api.std"]], "subtract() (in module array_api)": [[169, "array_api.subtract"]], "sum() (in module array_api)": [[170, "array_api.sum"]], "take() (in module array_api)": [[171, "array_api.take"]], "tan() (in module array_api)": [[172, "array_api.tan"]], "tanh() (in module array_api)": [[173, "array_api.tanh"]], "tensordot() (in module array_api)": [[174, "array_api.tensordot"]], "tile() (in module array_api)": [[175, "array_api.tile"]], "tril() (in module 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65, 66, 80, 86, 87, 90, 123, 125, 126, 132, 162, 165, 172, 173, 174, 175, 190, 207, 208, 216, 219, 222, 226, 227, 228, 229, 230, 231, 240, 242, 245, 246, 247, 248, 249, 250, 251, 252, 254], "3": [0, 1, 5, 7, 27, 84, 171, 175, 202, 207, 208, 211, 233], "4": [0, 1, 5, 10, 11, 27, 62, 65, 123, 125, 175, 190, 215, 261], "explicitli": [0, 26, 40, 63, 111, 132, 171, 174, 190, 202, 204, 232, 236, 237, 246, 248, 256, 260, 262], "document": [0, 5, 7, 59, 101, 116, 153, 192, 197, 205, 207, 210, 212, 255, 257, 259, 261, 262, 263], "maximum": [0, 1, 16, 26, 122, 134, 138, 189, 204, 206, 240], "n": [0, 1, 13, 14, 40, 55, 86, 88, 95, 122, 132, 133, 136, 137, 140, 143, 147, 150, 153, 158, 167, 168, 170, 172, 173, 174, 175, 176, 177, 183, 184, 185, 190, 204, 218, 219, 220, 222, 223, 224, 226, 227, 228, 229, 230, 231, 232, 233, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 249, 250, 252, 254, 260], "zero": [0, 5, 13, 14, 16, 17, 24, 25, 29, 30, 34, 35, 40, 41, 47, 63, 65, 69, 88, 90, 95, 96, 97, 101, 107, 125, 128, 129, 130, 131, 132, 134, 135, 136, 137, 138, 139, 141, 143, 145, 146, 149, 150, 152, 158, 160, 168, 170, 176, 177, 178, 179, 180, 181, 182, 184, 185, 188, 189, 190, 197, 199, 204, 205, 207, 210, 218, 220, 221, 222, 223, 224, 226, 227, 228, 229, 231, 234, 241, 242, 245, 246, 247, 254, 262], "dimension": [0, 13, 14, 15, 16, 17, 19, 24, 25, 29, 34, 35, 40, 88, 97, 122, 132, 134, 136, 137, 138, 143, 150, 153, 158, 168, 170, 171, 179, 180, 181, 182, 184, 185, 190, 199, 204, 216, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 234, 237, 238, 242, 244, 245, 254, 256, 260], "apart": 0, "from": [0, 5, 13, 14, 15, 19, 26, 44, 59, 60, 63, 75, 78, 88, 92, 99, 101, 102, 103, 104, 107, 122, 123, 125, 137, 142, 146, 149, 150, 154, 155, 164, 166, 168, 170, 171, 173, 179, 181, 184, 185, 186, 188, 190, 199, 202, 204, 205, 206, 207, 210, 211, 212, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 236, 247, 249, 252, 256, 257, 259, 260, 261, 262, 263], "ndim": [0, 185, 189, 233, 246, 249, 250], "devic": [0, 5, 15, 26, 27, 59, 60, 63, 91, 92, 97, 102, 103, 104, 110, 112, 113, 115, 122, 145, 146, 153, 176, 177, 187, 188, 189, 190, 192, 204, 210, 213, 219, 230, 246, 256, 260, 262], "dtype": [0, 5, 15, 26, 60, 63, 73, 75, 88, 89, 91, 92, 97, 98, 102, 103, 104, 108, 110, 116, 122, 145, 146, 150, 155, 170, 187, 188, 189, 199, 202, 204, 210, 216, 252, 260, 261, 262], "all": [0, 5, 15, 19, 23, 26, 60, 63, 87, 90, 97, 99, 102, 111, 115, 141, 156, 162, 173, 175, 176, 177, 183, 185, 189, 190, 202, 204, 205, 207, 208, 209, 210, 211, 212, 214, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 233, 245, 247, 248, 254, 255, 256, 259, 260, 262, 263], "thi": [0, 1, 5, 7, 15, 19, 26, 34, 58, 59, 63, 71, 78, 96, 101, 102, 107, 111, 115, 116, 122, 125, 128, 129, 130, 131, 136, 143, 149, 152, 153, 167, 168, 171, 179, 180, 181, 182, 184, 189, 190, 197, 199, 202, 204, 205, 206, 207, 208, 209, 210, 211, 212, 214, 215, 216, 217, 218, 220, 221, 223, 224, 227, 228, 229, 231, 246, 247, 248, 249, 255, 256, 257, 259, 261, 262, 263], "return": [0, 5, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 192, 197, 204, 205, 206, 208, 210, 211, 214, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 262], "tupl": [0, 1, 13, 14, 26, 27, 32, 49, 57, 74, 78, 91, 99, 103, 115, 116, 134, 136, 138, 140, 143, 145, 147, 150, 154, 156, 166, 167, 168, 170, 174, 175, 179, 180, 181, 183, 184, 187, 190, 202, 236, 246, 247, 249, 251, 254, 260], "includ": [0, 1, 7, 9, 13, 14, 15, 16, 17, 20, 21, 23, 28, 30, 40, 41, 42, 43, 47, 51, 88, 107, 111, 115, 116, 118, 122, 132, 134, 136, 138, 150, 153, 164, 168, 170, 184, 189, 190, 199, 204, 205, 206, 207, 208, 209, 210, 211, 215, 240, 254, 256, 257, 259, 261, 262], "those": [0, 5, 7, 15, 23, 88, 90, 113, 115, 141, 143, 150, 153, 170, 199, 204, 207, 208, 211, 212, 214, 246, 249, 250, 252, 255, 256, 257, 260, 261, 262], "mean": [0, 26, 189, 202, 208, 210, 211, 216, 257, 260], "var": [0, 189], "std": [0, 189], "which": [0, 1, 5, 7, 8, 13, 14, 15, 16, 17, 18, 19, 26, 30, 40, 41, 44, 59, 60, 63, 75, 77, 78, 83, 88, 91, 92, 95, 97, 98, 99, 101, 102, 103, 104, 107, 108, 111, 113, 114, 115, 122, 132, 134, 136, 138, 142, 143, 145, 146, 150, 152, 153, 156, 158, 163, 167, 168, 170, 171, 172, 176, 177, 179, 180, 181, 182, 183, 184, 185, 187, 188, 190, 204, 205, 206, 207, 208, 209, 210, 211, 212, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 240, 248, 249, 250, 252, 254, 255, 256, 257, 260, 261, 262], "some": [0, 96, 101, 113, 115, 125, 190, 205, 206, 207, 208, 211, 216, 260, 262, 263], "common": [0, 190, 199, 202, 211, 214, 215, 256, 260, 261, 262], "librari": [0, 5, 7, 26, 51, 57, 58, 59, 60, 63, 90, 96, 101, 102, 111, 113, 115, 116, 122, 125, 128, 129, 130, 131, 134, 135, 136, 138, 139, 143, 153, 158, 168, 173, 179, 180, 181, 182, 184, 189, 190, 202, 204, 205, 206, 207, 208, 209, 210, 211, 212, 214, 215, 216, 232, 236, 237, 246, 248, 255, 256, 257, 260, 261, 262, 263], "g": [0, 5, 9, 19, 20, 26, 47, 51, 57, 77, 88, 90, 102, 107, 109, 115, 116, 122, 134, 138, 141, 143, 150, 151, 153, 155, 157, 170, 175, 179, 180, 181, 182, 190, 197, 199, 204, 205, 206, 207, 208, 209, 210, 211, 214, 222, 226, 227, 228, 229, 231, 236, 237, 240, 247, 249, 250, 252, 254, 255, 256, 257, 260, 261, 262], "numpi": [0, 19, 63, 190, 202, 207, 208, 210, 211, 256, 260, 261, 262, 263], "scalar": [0, 2, 49, 60, 189, 190, 204, 214, 254, 262], "valu": [0, 1, 2, 5, 7, 9, 10, 11, 12, 15, 16, 17, 18, 20, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 39, 41, 43, 49, 51, 57, 58, 60, 61, 62, 63, 64, 65, 66, 76, 77, 78, 85, 86, 87, 88, 89, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 104, 105, 106, 107, 111, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 143, 144, 145, 149, 150, 152, 153, 157, 158, 159, 160, 161, 162, 163, 164, 168, 170, 171, 172, 173, 178, 179, 180, 181, 182, 184, 185, 187, 189, 197, 199, 202, 204, 206, 208, 209, 210, 214, 216, 219, 222, 226, 227, 228, 229, 230, 231, 232, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 262], "rational": [0, 7, 88, 150, 170, 190, 210, 211, 252, 255, 257, 260], "alwai": [0, 12, 26, 42, 60, 63, 98, 102, 141, 154, 190, 202, 207, 208, 211, 236], "necessari": [0, 26, 60, 90, 102, 141, 154, 175, 190, 208, 260], "acceler": [0, 5, 107, 153, 202, 210], "where": [0, 1, 7, 13, 14, 15, 26, 47, 57, 65, 86, 87, 90, 94, 96, 97, 101, 103, 104, 124, 125, 126, 137, 141, 143, 147, 149, 153, 158, 159, 161, 162, 167, 168, 172, 173, 175, 183, 184, 185, 189, 190, 199, 205, 207, 210, 211, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 233, 236, 237, 238, 240, 242, 245, 246, 247, 248, 249, 250, 252, 256, 260, 261, 262], "non": [0, 1, 7, 13, 14, 16, 17, 63, 128, 129, 130, 131, 134, 136, 138, 143, 150, 168, 174, 184, 185, 190, 199, 204, 205, 211, 218, 220, 223, 224, 227, 228, 229, 231, 233, 234, 236, 240, 242, 249, 254, 262], "could": [0, 26, 179, 180, 181, 182, 202, 208, 215, 256, 260, 262], "forc": 0, "synchron": [0, 26, 59, 153, 260], "delai": [0, 24, 25, 29, 34, 35, 202, 214, 260], "execut": [0, 199, 202, 211, 213, 215, 260, 262], "model": [0, 57, 58, 90, 141, 207, 214, 262], "repres": [0, 8, 11, 12, 23, 24, 25, 26, 29, 34, 35, 62, 66, 87, 90, 101, 137, 141, 162, 172, 173, 204, 206, 210, 211, 247, 261, 262], "futur": [0, 26, 102, 203, 207, 208, 211, 215, 216, 236, 237, 258, 260, 262], "python": [0, 2, 5, 7, 24, 25, 26, 29, 34, 35, 49, 60, 101, 102, 152, 189, 190, 202, 204, 207, 210, 212, 214, 215, 216, 257, 259, 260, 261], "x": [0, 1, 5, 7, 9, 10, 11, 13, 14, 16, 17, 18, 20, 26, 61, 62, 63, 64, 65, 66, 68, 74, 76, 77, 79, 85, 86, 87, 88, 92, 94, 95, 96, 99, 100, 102, 104, 109, 117, 118, 119, 123, 124, 125, 126, 129, 133, 134, 136, 138, 140, 142, 143, 146, 147, 148, 150, 151, 153, 154, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 170, 171, 172, 173, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 188, 190, 207, 208, 216, 217, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 232, 234, 235, 236, 237, 238, 240, 241, 242, 243, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 262], "__pos__": [0, 189, 204], "po": 0, "__neg__": [0, 189, 204], "neg": [0, 13, 14, 15, 44, 47, 65, 78, 88, 90, 95, 97, 99, 101, 118, 123, 125, 141, 149, 152, 156, 160, 164, 171, 174, 185, 189, 190, 204, 207, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 254, 260], "x1": [0, 7, 12, 40, 65, 67, 69, 70, 71, 72, 77, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 144, 149, 152, 158, 169, 174, 185, 186, 204, 233, 239, 244, 248, 251, 253], "x2": [0, 7, 12, 40, 65, 67, 69, 70, 71, 72, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 144, 149, 152, 158, 169, 174, 185, 186, 204, 233, 239, 244, 248, 251, 253], "__add__": [0, 50, 189, 204], "add": [0, 7, 21, 88, 169, 170, 189, 190, 204, 205, 206, 211, 252], "__sub__": [0, 189, 204], "sub": [0, 190], "__mul__": [0, 189, 204], "mul": 0, "__truediv__": [0, 189, 204], "truediv": 0, "__floordiv__": [0, 189], "floordiv": 0, "__mod__": [0, 189], "mod": 0, "__pow__": [0, 189, 204], "pow": [0, 47, 189, 204, 206], "should": [0, 1, 5, 7, 9, 10, 11, 12, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 76, 77, 79, 85, 86, 87, 88, 90, 94, 95, 96, 98, 100, 101, 102, 105, 106, 107, 109, 113, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 137, 138, 139, 141, 142, 148, 149, 150, 151, 152, 154, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 168, 169, 170, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 184, 185, 190, 197, 204, 205, 206, 207, 210, 211, 212, 216, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 254, 255, 256, 260, 262, 263], "defin": [0, 5, 12, 23, 30, 41, 49, 60, 65, 79, 90, 101, 103, 104, 115, 122, 134, 135, 136, 138, 139, 140, 141, 152, 159, 164, 165, 168, 176, 177, 184, 185, 189, 192, 197, 204, 206, 207, 216, 220, 221, 224, 225, 228, 231, 232, 236, 237, 238, 245, 246, 248, 256, 261, 262, 263], "real": [0, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 24, 25, 29, 30, 31, 33, 35, 37, 39, 41, 44, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 85, 86, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 105, 106, 107, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 142, 143, 144, 145, 146, 149, 150, 152, 157, 158, 159, 160, 161, 162, 163, 164, 168, 170, 172, 173, 178, 184, 185, 187, 189, 199, 204, 207, 219, 222, 226, 227, 228, 229, 230, 231, 232, 236, 237, 238, 240, 242, 245, 246, 247, 248, 249, 250, 252, 254, 257], "data": [0, 1, 2, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 111, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 144, 145, 146, 147, 148, 149, 150, 151, 152, 154, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 184, 185, 186, 187, 188, 189, 192, 199, 202, 205, 207, 208, 211, 213, 214, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 256, 257, 258, 259, 260, 263], "type": [0, 2, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 192, 202, 205, 207, 208, 210, 212, 213, 214, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 256, 257, 260, 261], "__matmul__": [0, 189, 204], "matmul": [0, 40, 189, 199, 204, 256], "The": [0, 1, 5, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 58, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 90, 93, 94, 96, 99, 100, 101, 102, 105, 106, 107, 109, 110, 111, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 140, 141, 142, 143, 144, 147, 148, 149, 150, 151, 152, 153, 157, 158, 159, 160, 161, 162, 163, 164, 165, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 190, 199, 202, 204, 205, 206, 208, 209, 210, 211, 214, 215, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 255, 256, 257, 259, 260, 261, 262, 263], "__invert__": [0, 189], "inv": [0, 204, 256], "invert": [0, 68, 238, 241, 248], "__inv__": 0, "__and__": [0, 189], "__or__": [0, 189], "__xor__": [0, 189], "xor": [0, 72, 131], "__lshift__": [0, 189], "lshift": 0, "__rshift__": [0, 189], "rshift": 0, "integ": [0, 5, 9, 13, 14, 15, 20, 22, 26, 29, 30, 34, 35, 36, 38, 41, 44, 45, 47, 48, 51, 52, 60, 67, 68, 69, 70, 71, 72, 76, 77, 88, 90, 100, 101, 103, 104, 108, 115, 116, 122, 134, 136, 138, 142, 149, 150, 152, 153, 155, 157, 158, 168, 170, 171, 178, 184, 185, 189, 190, 204, 206, 207, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 241, 242, 252, 254, 260], "boolean": [0, 5, 22, 24, 25, 26, 29, 35, 36, 43, 45, 52, 57, 60, 63, 67, 68, 70, 72, 88, 89, 102, 103, 104, 111, 115, 116, 122, 128, 129, 130, 131, 143, 189, 199, 204], "__lt__": [0, 189, 204], "lt": 0, "__le__": [0, 189, 204], "le": 0, "__gt__": [0, 189, 204], "gt": [0, 246, 249], "__ge__": [0, 189, 204], "ge": 0, "__eq__": [0, 189, 204, 211], "eq": 0, "__ne__": [0, 189, 204], "ne": 0, "ar": [0, 1, 5, 7, 15, 16, 17, 19, 23, 24, 25, 26, 27, 29, 34, 35, 40, 49, 55, 58, 60, 77, 85, 86, 89, 90, 94, 97, 98, 99, 101, 102, 107, 114, 115, 122, 128, 129, 130, 131, 132, 141, 143, 149, 153, 156, 157, 161, 172, 173, 175, 179, 181, 185, 190, 199, 202, 204, 205, 206, 207, 208, 209, 210, 211, 212, 214, 215, 216, 218, 219, 220, 221, 223, 224, 225, 227, 228, 229, 230, 231, 233, 236, 237, 242, 245, 246, 249, 255, 256, 257, 260, 261, 262, 263], "onli": [0, 1, 5, 7, 16, 17, 23, 26, 40, 57, 58, 63, 99, 102, 107, 113, 115, 116, 122, 128, 129, 130, 131, 132, 136, 168, 184, 185, 189, 190, 199, 202, 204, 205, 207, 208, 210, 211, 212, 214, 216, 221, 233, 238, 245, 246, 248, 256, 257, 260, 261, 262, 263], "other": [0, 5, 21, 22, 23, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 50, 51, 52, 63, 89, 90, 96, 101, 102, 125, 140, 141, 168, 184, 190, 192, 202, 204, 206, 207, 208, 209, 210, 211, 212, 216, 233, 245, 255, 256, 259, 260, 262], "ani": [0, 1, 9, 10, 11, 23, 24, 25, 26, 28, 29, 34, 35, 43, 59, 61, 62, 66, 89, 93, 107, 117, 118, 144, 164, 189, 190, 199, 204, 207, 208, 210, 216, 249, 257, 259, 260, 263], "For": [0, 1, 5, 7, 9, 10, 11, 12, 16, 17, 18, 20, 24, 25, 26, 29, 30, 31, 33, 35, 37, 39, 41, 44, 57, 58, 61, 62, 64, 65, 66, 76, 79, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 105, 106, 107, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 134, 135, 137, 138, 139, 141, 142, 144, 149, 150, 152, 153, 157, 158, 159, 160, 161, 162, 163, 164, 165, 167, 170, 172, 173, 178, 179, 180, 181, 182, 190, 197, 202, 206, 207, 209, 211, 214, 219, 228, 230, 247, 249, 250, 252, 260, 262, 263], "backward": [0, 13, 14, 16, 17, 18, 31, 33, 37, 39, 105, 106, 120, 121, 122, 134, 135, 138, 139, 152, 163, 185, 190, 204, 207, 208, 212, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 260], "compat": [0, 1, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 74, 77, 85, 90, 93, 101, 105, 106, 107, 120, 121, 122, 127, 128, 130, 131, 132, 134, 135, 136, 138, 139, 141, 144, 149, 150, 152, 153, 154, 163, 168, 169, 170, 184, 185, 186, 199, 204, 207, 208, 212, 233, 240, 242, 245, 248, 254, 260, 262], "mai": [0, 5, 7, 15, 16, 17, 18, 23, 26, 28, 31, 33, 37, 39, 43, 51, 57, 58, 59, 60, 89, 90, 93, 101, 102, 105, 106, 107, 110, 115, 116, 120, 121, 122, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 143, 144, 153, 154, 158, 163, 168, 173, 179, 180, 181, 182, 184, 189, 190, 197, 199, 202, 205, 206, 207, 208, 209, 210, 211, 212, 214, 215, 216, 236, 246, 247, 249, 255, 256, 260, 261, 262], "complex": [0, 5, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 24, 25, 29, 31, 33, 35, 37, 39, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 88, 90, 93, 94, 96, 97, 98, 103, 104, 105, 106, 107, 109, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 132, 134, 135, 137, 138, 139, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 157, 159, 161, 162, 163, 164, 165, 169, 170, 172, 173, 174, 179, 180, 181, 182, 185, 199, 206, 210, 211, 213, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 261], "howev": [0, 5, 16, 17, 18, 31, 33, 37, 39, 57, 88, 101, 105, 106, 107, 116, 120, 121, 122, 134, 135, 138, 139, 153, 158, 163, 171, 172, 173, 202, 205, 206, 207, 208, 209, 211, 256, 257, 260, 262], "inequ": [0, 16, 17, 18, 31, 33, 37, 39, 105, 106, 120, 121, 134, 135, 138, 139, 163], "unspecifi": [0, 5, 10, 11, 16, 17, 18, 30, 31, 33, 37, 39, 41, 47, 51, 60, 62, 66, 77, 78, 87, 90, 94, 96, 101, 103, 104, 105, 106, 120, 121, 122, 134, 135, 138, 139, 149, 152, 158, 162, 163, 164, 167, 171, 173, 190, 197, 199, 204, 220, 221, 224, 225, 228, 231, 236, 237, 260], "thu": [0, 5, 16, 17, 18, 30, 31, 33, 37, 39, 41, 47, 57, 60, 71, 77, 101, 103, 104, 105, 106, 120, 121, 122, 134, 135, 138, 139, 149, 152, 158, 163, 172, 173, 190, 197, 206, 207, 220, 221, 224, 225, 228, 231, 236, 237, 249, 256], "depend": [0, 5, 9, 10, 11, 16, 17, 18, 20, 26, 29, 31, 33, 37, 39, 44, 47, 51, 57, 58, 59, 61, 62, 63, 64, 65, 66, 77, 86, 87, 90, 94, 96, 105, 106, 111, 120, 121, 122, 123, 124, 125, 126, 141, 142, 149, 158, 161, 162, 163, 172, 173, 186, 197, 199, 206, 207, 210, 213, 214, 216, 236, 237, 246, 247, 248, 249, 256, 260, 262, 263], "see": [0, 5, 10, 11, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 33, 34, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 53, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 74, 77, 85, 90, 93, 96, 101, 102, 104, 105, 106, 107, 110, 111, 114, 120, 121, 123, 125, 127, 128, 130, 131, 132, 134, 135, 136, 138, 139, 141, 143, 144, 149, 150, 152, 153, 155, 159, 163, 164, 165, 168, 169, 170, 179, 180, 181, 182, 184, 185, 186, 189, 190, 199, 201, 202, 205, 207, 209, 210, 211, 216, 233, 240, 242, 245, 248, 254, 255, 260, 261, 262, 263], "order": [0, 5, 7, 16, 17, 18, 19, 26, 31, 33, 37, 39, 55, 60, 63, 65, 89, 99, 101, 102, 105, 106, 120, 121, 134, 135, 138, 139, 143, 153, 158, 163, 172, 173, 174, 179, 180, 181, 182, 190, 197, 199, 204, 206, 209, 210, 212, 227, 228, 236, 237, 240, 249, 250, 254, 256, 257, 260, 261], "chang": [0, 1, 9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 66, 86, 87, 90, 93, 94, 96, 97, 98, 102, 103, 104, 117, 118, 119, 122, 123, 124, 125, 126, 132, 134, 137, 138, 141, 142, 143, 144, 145, 146, 148, 149, 150, 154, 157, 159, 161, 162, 164, 165, 169, 170, 171, 172, 173, 174, 179, 180, 181, 182, 185, 202, 218, 219, 220, 222, 223, 224, 227, 228, 230, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 257, 260, 262, 263], "shape": [0, 1, 18, 40, 55, 63, 73, 74, 78, 88, 91, 92, 95, 99, 103, 104, 111, 132, 133, 137, 145, 146, 154, 156, 158, 163, 167, 171, 174, 175, 176, 177, 183, 185, 187, 188, 189, 204, 213, 214, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 260, 262], "result": [0, 1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 24, 25, 28, 29, 30, 31, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 79, 85, 86, 87, 90, 93, 94, 96, 100, 101, 105, 106, 107, 109, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 142, 144, 148, 149, 150, 151, 152, 153, 155, 157, 158, 159, 160, 161, 162, 164, 165, 167, 168, 169, 170, 172, 173, 174, 178, 179, 184, 190, 197, 199, 204, 206, 207, 208, 214, 232, 233, 235, 240, 241, 247, 248, 254, 260, 261, 262, 263], "promot": [0, 1, 5, 10, 11, 12, 21, 22, 30, 40, 41, 42, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 78, 85, 86, 87, 90, 94, 96, 101, 104, 107, 122, 123, 124, 125, 126, 127, 132, 135, 136, 139, 141, 142, 149, 152, 155, 161, 162, 164, 165, 167, 168, 169, 172, 173, 174, 184, 185, 186, 189, 204, 232, 233, 238, 240, 241, 242, 244, 245, 246, 247, 248, 254, 256], "rule": [0, 5, 7, 10, 11, 12, 21, 22, 30, 40, 41, 42, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 78, 85, 86, 87, 88, 90, 94, 96, 101, 103, 104, 107, 122, 123, 124, 125, 126, 127, 132, 135, 139, 141, 142, 149, 152, 155, 159, 161, 162, 164, 165, 167, 169, 172, 173, 174, 185, 186, 189, 190, 204, 207, 210, 232, 233, 238, 240, 241, 242, 244, 245, 246, 247, 248, 254, 256, 260, 262], "broadcast": [0, 12, 13, 14, 16, 17, 21, 22, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 73, 74, 77, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 134, 135, 136, 138, 139, 141, 144, 149, 150, 152, 153, 168, 169, 170, 174, 184, 185, 186, 189, 204, 233, 240, 242, 245, 248, 254, 260], "same": [0, 5, 7, 9, 12, 15, 18, 19, 20, 26, 32, 36, 38, 40, 41, 46, 48, 50, 55, 59, 63, 68, 73, 74, 76, 77, 78, 79, 88, 90, 92, 95, 98, 99, 100, 101, 102, 104, 109, 132, 133, 134, 136, 137, 138, 140, 141, 146, 147, 148, 149, 150, 151, 152, 153, 154, 156, 157, 158, 159, 163, 166, 167, 168, 169, 170, 171, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 188, 190, 199, 202, 204, 207, 208, 210, 211, 216, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 232, 234, 235, 236, 238, 241, 245, 246, 247, 249, 250, 252, 255, 256, 260, 262], "behavior": [0, 5, 47, 49, 59, 60, 63, 77, 90, 101, 103, 104, 107, 122, 141, 149, 152, 158, 171, 179, 180, 181, 182, 189, 190, 192, 199, 202, 204, 206, 207, 214, 215, 220, 221, 224, 225, 228, 231, 256, 257, 260, 261, 262, 263], "special": [0, 9, 10, 11, 12, 20, 21, 24, 25, 28, 29, 30, 35, 41, 42, 43, 47, 51, 61, 62, 64, 65, 66, 76, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 136, 138, 139, 141, 144, 149, 150, 152, 157, 159, 160, 161, 162, 164, 165, 168, 170, 172, 173, 178, 184, 204, 205, 207, 247, 252], "case": [0, 1, 5, 7, 9, 10, 11, 12, 15, 20, 21, 24, 25, 26, 28, 29, 30, 35, 41, 42, 43, 47, 51, 60, 61, 62, 64, 65, 66, 76, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 102, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 136, 137, 138, 139, 141, 144, 149, 150, 152, 157, 159, 160, 161, 162, 164, 165, 168, 170, 172, 173, 178, 184, 190, 202, 204, 205, 206, 207, 208, 211, 212, 214, 246, 247, 249, 252, 256, 258, 260, 263], "its": [0, 5, 26, 40, 73, 90, 98, 132, 141, 154, 156, 206, 207, 210, 211, 255, 260, 261, 262], "respect": [0, 9, 12, 20, 21, 22, 28, 30, 31, 33, 37, 38, 39, 41, 42, 43, 45, 48, 50, 51, 52, 65, 67, 69, 70, 71, 72, 77, 87, 90, 93, 101, 105, 106, 107, 113, 120, 121, 122, 127, 128, 130, 131, 135, 137, 139, 140, 141, 144, 152, 162, 169, 172, 173, 174, 179, 180, 185, 204, 206, 209, 211, 236, 246, 249], "binari": [0, 5, 67, 70, 72, 172, 173, 205], "two": [0, 1, 5, 15, 19, 40, 55, 65, 71, 97, 102, 132, 133, 137, 157, 174, 176, 177, 179, 180, 181, 182, 185, 190, 199, 210, 211, 214, 215, 220, 221, 224, 225, 228, 231, 232, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 256, 260, 261, 262, 263], "operand": [0, 1, 9, 10, 11, 12, 24, 25, 29, 35, 61, 62, 64, 65, 66, 76, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 138, 139, 141, 144, 149, 150, 152, 157, 159, 160, 161, 162, 164, 165, 170, 172, 173, 178, 199, 204, 206, 247, 252], "assign": [0, 208], "exampl": [0, 5, 12, 23, 26, 115, 116, 167, 189, 190, 202, 207, 208, 209, 211, 214, 215, 216, 252, 256, 260, 262, 263], "after": [0, 1, 26, 40, 132, 164, 175], "addit": [0, 5, 7, 12, 26, 50, 59, 88, 115, 169, 189, 190, 199, 205, 207, 210, 256, 260, 261, 263], "modifi": [0, 26, 208, 259], "equal": [0, 1, 9, 10, 11, 18, 20, 21, 22, 26, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 58, 61, 62, 63, 64, 65, 66, 69, 71, 77, 87, 89, 94, 96, 97, 103, 104, 107, 116, 118, 123, 124, 125, 126, 136, 143, 144, 145, 146, 149, 150, 157, 162, 163, 164, 168, 170, 171, 173, 174, 175, 179, 180, 181, 182, 184, 189, 190, 197, 204, 207, 211, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 235, 241, 242, 245, 246, 247, 248, 252, 260], "equival": [0, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 71, 101, 107, 128, 129, 130, 131, 152, 157, 171, 190, 199, 207, 208, 242, 245, 248, 254, 260], "discuss": [0, 93, 144, 204, 210, 211, 215, 260, 261, 262], "copi": [0, 1, 26, 59, 60, 63, 102, 154, 163, 204, 205, 210, 211, 213, 259, 260], "view": [0, 102, 213], "behaviour": [0, 213, 260, 262], "mutabl": [0, 213], "via": [0, 26, 101, 102, 171, 190, 205, 210, 211, 215, 217, 245, 255, 256, 257, 260], "__iadd__": 0, "__isub__": 0, "__imul__": 0, "__itruediv__": 0, "__ifloordiv__": 0, "__ipow__": 0, "__imod__": 0, "__imatmul__": 0, "__iand__": 0, "__ior__": 0, "__ixor__": 0, "__ilshift__": 0, "__irshift__": 0, "appli": [0, 12, 77, 78, 85, 90, 141, 155, 157, 167, 174, 190, 199, 202, 207, 218, 220, 223, 224, 227, 228, 229, 231, 242, 245, 256, 260, 262], "match": [0, 1, 5, 9, 20, 26, 63, 101, 152, 174, 179, 180, 212, 222, 226, 227, 228, 229, 231, 236, 237, 240, 254, 262], "op": [0, 199], "__radd__": 0, "__rsub__": 0, "__rmul__": 0, "__rtruediv__": 0, "__rfloordiv__": 0, "__rpow__": 0, "__rmod__": 0, "__rmatmul__": 0, "__rand__": 0, "__ror__": 0, "__rxor__": 0, "__rlshift__": 0, "__rrshift__": 0, "arrai": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 83, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 191, 192, 193, 194, 195, 196, 197, 198, 200, 201, 202, 204, 205, 206, 207, 208, 209, 210, 211, 212, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 261, 263], "refer": [1, 13, 14, 96, 97, 125, 168, 174, 175, 184, 185, 190, 207, 208, 216, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 248], "automat": [1, 260], "implicit": [1, 210, 211, 214, 260], "expans": [1, 260], "size": [1, 13, 14, 88, 95, 122, 143, 156, 166, 171, 174, 185, 189, 190, 209, 215, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 235, 244, 246, 249, 260], "without": [1, 7, 26, 57, 102, 113, 115, 143, 153, 154, 179, 180, 181, 182, 202, 205, 206, 209, 259, 260, 262], "purpos": [1, 5, 96, 107, 125, 202, 247, 256, 258, 259, 262], "make": [1, 7, 202, 205, 206, 208, 210, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 255, 257, 260], "differ": [1, 12, 26, 49, 50, 77, 78, 88, 90, 98, 101, 102, 141, 150, 167, 169, 170, 190, 202, 208, 211, 212, 214, 225, 236, 246, 247, 249, 252, 256, 260, 261, 262], "element": [1, 9, 10, 11, 12, 13, 14, 15, 20, 21, 22, 24, 25, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 54, 58, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 99, 100, 101, 103, 104, 105, 106, 107, 109, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 148, 149, 150, 151, 152, 153, 154, 156, 157, 158, 159, 160, 161, 162, 164, 165, 166, 168, 169, 170, 171, 172, 173, 175, 176, 177, 178, 179, 180, 181, 182, 184, 186, 189, 190, 204, 206, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 236, 245, 246, 247, 249, 252, 260], "wise": [1, 9, 10, 12, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 64, 65, 67, 68, 69, 70, 71, 72, 77, 79, 85, 90, 93, 101, 105, 106, 107, 109, 120, 121, 127, 128, 129, 130, 131, 135, 139, 141, 144, 149, 151, 152, 169, 189, 204, 206, 260], "oper": [1, 12, 19, 24, 26, 34, 40, 57, 58, 59, 61, 64, 71, 86, 88, 90, 101, 124, 126, 132, 141, 149, 150, 152, 155, 161, 165, 170, 172, 174, 189, 190, 196, 199, 204, 207, 208, 209, 210, 211, 252, 256, 257, 260, 261, 262], "facilit": [1, 197, 202], "user": [1, 7, 26, 110, 173, 202, 205, 206, 208, 211, 215, 256, 260, 261, 262], "ergonom": 1, "encourag": [1, 260, 261], "avoid": [1, 9, 63, 90, 96, 101, 107, 125, 141, 154, 205, 208, 211, 214, 256, 260, 262], "unnecessari": [1, 256], "can": [1, 7, 26, 60, 75, 110, 114, 116, 190, 199, 202, 205, 207, 208, 210, 211, 216, 245, 246, 249, 255, 256, 260, 261, 262, 263], "potenti": [1, 26, 96, 125, 153, 208, 260], "enabl": [1, 26, 102, 211, 215, 216, 260], "more": [1, 5, 7, 15, 19, 26, 40, 58, 60, 63, 73, 88, 96, 99, 101, 125, 132, 143, 149, 153, 171, 179, 180, 181, 182, 190, 199, 202, 205, 206, 207, 208, 209, 210, 211, 212, 215, 216, 220, 221, 224, 225, 228, 231, 247, 256, 257, 260, 261, 263], "memori": [1, 26, 60, 102, 202, 208, 209, 211, 260, 262], "effici": [1, 202, 208], "through": [1, 60, 65, 255, 257, 261, 262], "vector": [1, 40, 132, 137, 185, 233, 244, 249, 250, 254, 256, 260], "reduc": [1, 13, 14, 16, 17, 134, 136, 138, 150, 168, 170, 184, 190, 246, 249, 256, 261, 262], "consumpt": [1, 26, 261], "cach": 1, "local": [1, 211], "given": [1, 23, 99, 122, 156, 158, 183, 199, 204, 207, 208, 211, 212, 216, 237, 247, 256, 257, 260, 262], "involv": [1, 12, 90, 101, 141, 149, 155, 199, 206, 207, 211, 215], "singleton": [1, 13, 14, 16, 17, 95, 134, 136, 138, 150, 166, 168, 170, 175, 184, 240, 254, 260], "whose": [1, 5, 9, 11, 19, 20, 26, 47, 55, 62, 66, 85, 86, 87, 97, 99, 102, 133, 149, 156, 160, 161, 162, 171, 172, 173, 174, 176, 177, 179, 180, 181, 190, 208, 222, 226, 227, 228, 229, 231, 232, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 260, 262], "one": [1, 15, 19, 26, 40, 51, 58, 60, 63, 73, 75, 88, 90, 95, 97, 99, 101, 102, 115, 116, 122, 132, 137, 141, 143, 145, 146, 153, 158, 166, 171, 179, 180, 181, 182, 185, 190, 202, 205, 207, 208, 210, 211, 214, 215, 216, 218, 220, 222, 223, 224, 225, 226, 227, 228, 229, 231, 244, 245, 246, 254, 256, 257, 260, 262], "virtual": 1, "repeat": [1, 189, 190, 204, 262], "across": [1, 5, 90, 101, 141, 173, 204, 206, 207, 211, 255, 260], "correspond": [1, 16, 17, 23, 47, 59, 65, 73, 77, 102, 111, 112, 113, 149, 154, 156, 158, 168, 174, 179, 180, 181, 182, 184, 185, 190, 204, 206, 220, 224, 228, 231, 233, 236, 240, 259, 260], "If": [1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 29, 34, 35, 40, 44, 47, 51, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 74, 76, 77, 78, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 107, 111, 113, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 149, 150, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 166, 167, 168, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 187, 188, 190, 205, 207, 211, 217, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 232, 233, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 252, 254, 255, 256, 260, 262], "unequ": 1, "lower": [1, 77, 97, 176, 232], "higher": [1, 5, 26, 190, 205, 256, 261], "prepend": [1, 40, 95, 132, 175], "until": [1, 26, 175], "store": [1, 26, 211, 252], "determin": [1, 10, 11, 12, 13, 14, 21, 22, 26, 30, 40, 41, 42, 44, 45, 47, 50, 51, 52, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 75, 78, 85, 86, 87, 88, 90, 94, 96, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 132, 135, 139, 141, 142, 149, 152, 160, 161, 162, 164, 165, 169, 171, 172, 173, 174, 179, 180, 181, 182, 185, 186, 199, 204, 207, 210, 211, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 233, 234, 235, 238, 240, 241, 242, 244, 245, 246, 247, 248, 252, 254, 256, 260], "let": [1, 9, 10, 11, 12, 62, 66, 85, 87, 88, 93, 94, 96, 102, 117, 118, 119, 122, 123, 125, 136, 144, 150, 153, 158, 159, 162, 164, 168, 170, 173, 175, 184, 185, 190, 215, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 236, 237, 238, 246, 248, 249, 252], "b": [1, 9, 10, 11, 12, 57, 62, 66, 87, 90, 93, 94, 96, 101, 117, 118, 119, 122, 123, 125, 141, 144, 159, 162, 164, 167, 173, 185, 190, 204, 207, 208, 212, 245, 248, 262], "both": [1, 40, 44, 47, 51, 65, 77, 88, 90, 98, 101, 102, 107, 122, 132, 142, 149, 150, 170, 173, 174, 185, 190, 207, 208, 210, 214, 216, 233, 252, 256, 260, 261], "shape1": 1, "describ": [1, 5, 12, 88, 90, 93, 115, 116, 141, 144, 149, 150, 170, 192, 199, 207, 210, 214, 219, 230, 252, 260], "shape2": 1, "n1": [1, 137], "len": [1, 137, 175], "n2": [1, 137], "max": [1, 26, 77, 98, 108, 175, 189, 190, 204, 240, 242, 245], "temporari": 1, "list": [1, 73, 78, 110, 114, 137, 167, 190, 202, 204, 211, 260, 262], "length": [1, 15, 107, 137, 154, 174, 190, 219, 221, 222, 225, 230, 249, 250], "while": [1, 101, 115, 122, 128, 129, 130, 131, 136, 140, 158, 168, 179, 180, 184, 189, 190, 197, 202, 204, 207, 208, 209, 211, 214, 245, 256, 261, 262, 263], "d1": 1, "els": [1, 26, 202, 261], "d2": 1, "set": [1, 18, 26, 49, 65, 102, 160, 163, 168, 176, 177, 179, 181, 182, 184, 189, 190, 204, 205, 206, 207, 208, 211, 212, 215, 216, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 236, 237, 238, 242, 245, 246, 248, 249, 255, 256, 260, 262, 263], "th": [1, 97, 175, 190, 220, 224, 228, 231], "throw": 1, "except": [1, 7, 13, 14, 26, 74, 78, 88, 97, 102, 122, 143, 153, 167, 171, 183, 190, 199, 202, 204, 206, 208, 211, 213, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 245, 257, 260, 261, 262], "demonstr": 1, "applic": [1, 26, 88, 150, 153, 170, 199, 252, 256, 260, 261], "4d": 1, "8": [1, 5, 7, 27, 175, 199, 202], "6": [1, 7, 175], "3d": 1, "7": [1, 7, 27, 216], "5": [1, 190, 260], "2d": 1, "1d": 1, "15": 1, "do": [1, 26, 90, 141, 152, 197, 202, 205, 207, 208, 210, 211, 212, 256, 257, 259, 260, 262, 263], "doe": [1, 15, 26, 102, 144, 171, 190, 199, 202, 205, 206, 207, 208, 209, 211, 212, 214, 216, 256, 260, 262, 263], "second": [1, 12, 65, 67, 69, 70, 71, 72, 93, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 144, 149, 167, 169, 174, 179, 180, 181, 185, 186, 233, 236, 244, 246, 247, 249, 250, 260], "append": [1, 40, 69, 95, 132, 235], "As": [1, 122, 149, 179, 180, 181, 182, 202, 210, 216, 262], "impli": [1, 179, 180, 181, 182, 259, 260], "__setitem__": [1, 171, 189, 204], "Such": [1, 206, 256], "right": [1, 69, 71, 107, 158, 164, 205, 249, 259], "hand": [1, 199], "left": [1, 5, 60, 69, 101, 103, 158, 171, 190, 199, 236, 237, 249, 260], "index": [1, 5, 16, 17, 18, 32, 34, 49, 57, 83, 97, 111, 113, 137, 140, 143, 158, 167, 171, 174, 179, 180, 181, 189, 204, 220, 224, 228, 231, 260, 262], "perform": [1, 5, 13, 14, 26, 40, 59, 60, 90, 107, 132, 141, 153, 174, 190, 205, 206, 207, 208, 209, 210, 218, 220, 223, 224, 225, 227, 228, 229, 231, 249, 250, 256, 260, 261, 262], "empti": [1, 13, 14, 15, 150, 170, 189, 190, 204, 252, 260], "ok": 1, "allow": [1, 24, 25, 26, 29, 34, 35, 113, 115, 149, 154, 174, 190, 204, 205, 206, 208, 211, 214, 215, 256, 262], "NOT": [1, 129, 259], "adher": [2, 7, 8, 189, 190, 202, 255, 260], "convent": [2, 7, 10, 11, 26, 40, 61, 62, 64, 65, 66, 88, 123, 125, 132, 149, 164, 189, 190, 197, 207, 211, 255, 256, 261], "each": [2, 9, 10, 11, 12, 20, 21, 22, 26, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 76, 77, 79, 85, 86, 87, 90, 93, 94, 96, 100, 101, 105, 106, 107, 109, 114, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 135, 137, 139, 140, 141, 142, 143, 144, 148, 149, 151, 152, 153, 156, 157, 158, 159, 160, 161, 162, 164, 165, 167, 169, 172, 173, 174, 175, 178, 179, 180, 190, 202, 204, 206, 210, 214, 216, 228, 232, 233, 234, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 255, 256, 260, 261, 262], "float": [2, 5, 9, 10, 11, 12, 13, 14, 15, 20, 21, 24, 25, 28, 29, 30, 31, 33, 34, 35, 37, 39, 40, 41, 42, 43, 44, 47, 49, 50, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 104, 107, 109, 113, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 145, 146, 149, 150, 151, 152, 155, 157, 158, 159, 160, 161, 162, 164, 165, 168, 169, 170, 172, 173, 174, 178, 179, 180, 181, 182, 184, 185, 187, 189, 197, 204, 206, 207, 214, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 234, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 261], "point": [2, 5, 9, 10, 11, 12, 13, 14, 15, 20, 24, 25, 26, 29, 34, 35, 40, 41, 42, 44, 47, 50, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 104, 107, 109, 113, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 145, 146, 149, 150, 151, 152, 155, 157, 158, 159, 160, 161, 162, 164, 165, 168, 169, 170, 172, 173, 174, 178, 179, 180, 181, 182, 184, 185, 187, 189, 197, 204, 206, 207, 211, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 234, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 262], "creat": [3, 15, 60, 91, 92, 97, 102, 103, 104, 122, 145, 146, 187, 188, 196, 202, 211, 219, 230, 256, 260], "main": [5, 97, 176, 177, 205, 210, 235, 252, 255, 262], "namespac": [5, 7, 23, 110, 192, 202, 204, 217, 255, 256, 257, 260, 263], "under": [5, 255, 259, 260], "specifi": [5, 13, 14, 15, 16, 17, 18, 26, 29, 59, 60, 63, 74, 78, 88, 91, 95, 98, 99, 103, 113, 115, 116, 122, 145, 150, 152, 153, 156, 166, 167, 170, 171, 175, 176, 177, 179, 180, 181, 182, 185, 187, 190, 199, 204, 206, 207, 208, 210, 211, 212, 216, 218, 220, 221, 222, 223, 224, 226, 227, 228, 229, 231, 235, 252, 254, 256, 257, 260, 262, 263], "name": [5, 7, 23, 26, 101, 115, 179, 180, 181, 190, 207, 236, 245, 246, 247, 249, 255, 260, 261], "descript": [5, 7, 204, 206, 240, 254], "bool": [5, 13, 14, 16, 17, 18, 22, 24, 26, 28, 31, 33, 37, 39, 43, 45, 49, 52, 60, 63, 75, 88, 89, 93, 102, 103, 104, 105, 106, 115, 116, 117, 118, 119, 120, 121, 122, 128, 129, 130, 131, 134, 136, 138, 144, 150, 154, 160, 163, 168, 170, 184, 199, 204, 214, 232, 240, 249, 254], "true": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 93, 98, 101, 102, 111, 117, 118, 119, 122, 128, 129, 130, 131, 134, 136, 138, 143, 144, 150, 154, 160, 163, 168, 170, 179, 180, 181, 182, 184, 186, 190, 204, 232, 240, 249, 254, 256], "fals": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 93, 102, 111, 117, 118, 119, 122, 128, 129, 130, 131, 134, 136, 138, 144, 150, 154, 160, 163, 168, 170, 179, 180, 181, 182, 184, 190, 232, 240, 249, 254], "int8": [5, 115, 116, 199], "bit": [5, 68, 69, 71, 85, 88, 98, 108, 150, 160, 170, 199, 204, 206, 252], "sign": [5, 9, 10, 11, 12, 15, 20, 41, 44, 62, 65, 66, 71, 85, 87, 88, 90, 94, 96, 101, 115, 116, 123, 125, 134, 135, 138, 139, 141, 142, 149, 150, 152, 158, 160, 162, 164, 170, 173, 179, 180, 181, 182, 189, 197, 204, 207, 246, 247, 252], "exist": [5, 7, 26, 60, 78, 102, 202, 204, 207, 210, 211, 212, 238, 257, 260, 261], "interv": [5, 10, 11, 13, 14, 15, 61, 62, 64, 66, 95, 122, 123, 125, 140, 167, 174, 176, 177, 183, 185, 190, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 257], "128": 5, "127": 5, "int16": [5, 88, 115, 116, 150, 170, 199, 252], "16": [5, 199], "32": [5, 199], "767": 5, "int32": [5, 88, 115, 116, 150, 170, 199, 252], "147": 5, "483": 5, "647": 5, "int64": [5, 88, 115, 116, 150, 170, 199, 252], "64": [5, 199], "9": [5, 27], "223": 5, "372": 5, "036": 5, "854": 5, "775": 5, "807": 5, "uint8": [5, 115, 116, 199], "unsign": [5, 88, 115, 116, 150, 170, 189, 252], "255": 5, "uint16": [5, 88, 115, 116, 150, 170, 199, 252], "65": 5, "535": [5, 204], "uint32": [5, 88, 115, 116, 150, 170, 199, 252], "294": 5, "967": 5, "295": 5, "uint64": [5, 115, 116, 199], "18": 5, "446": [5, 204], "744": [5, 204], "073": 5, "709": [5, 204], "551": [5, 204], "615": 5, "float32": [5, 109, 115, 116, 151, 199, 247, 249, 250], "ieee": [5, 12, 65, 80, 81, 82, 84, 90, 96, 98, 107, 125, 141, 152, 164, 172, 173, 189, 197, 206, 207, 260], "754": [5, 12, 65, 80, 81, 82, 84, 90, 96, 98, 107, 125, 141, 152, 164, 172, 173, 189, 197, 206, 207, 260], "singl": [5, 7, 24, 25, 29, 34, 35, 113, 115, 179, 180, 189, 199, 204, 205, 207, 210, 211, 216, 256, 260, 261, 262], "precis": [5, 9, 20, 42, 60, 98, 103, 104, 109, 141, 151, 164, 199, 204, 206, 222, 226, 227, 228, 229, 231, 236, 237, 240, 247, 249, 250, 254, 260], "2019": [5, 12, 90, 96, 107, 125, 141, 189, 206, 260, 262], "float64": [5, 9, 20, 115, 116, 199, 222, 226, 227, 228, 229, 231, 236, 237, 240, 254], "doubl": [5, 174, 199, 204], "complex64": [5, 109, 115, 116, 151, 199, 204, 247, 249, 250], "imaginari": [5, 10, 11, 12, 13, 14, 44, 61, 62, 63, 64, 66, 79, 87, 90, 93, 94, 96, 98, 109, 123, 125, 141, 142, 143, 144, 145, 146, 149, 157, 162, 164, 173, 204, 207], "compon": [5, 10, 11, 12, 13, 14, 44, 62, 63, 66, 79, 87, 90, 93, 94, 96, 98, 109, 123, 125, 141, 142, 143, 144, 145, 146, 149, 151, 157, 162, 164, 172, 173, 179, 180, 181, 182, 204, 207, 221, 230], "complex128": [5, 9, 20, 115, 116, 199, 204, 222, 226, 227, 228, 229, 231, 236, 237, 240, 254], "method": [5, 26, 34, 102, 189, 192, 202, 208, 210, 211, 214, 215, 216, 260, 261, 262], "attribut": [5, 23, 98, 108, 189, 201, 204, 257, 260, 261, 262], "requir": [5, 10, 11, 24, 25, 29, 34, 35, 59, 61, 62, 63, 64, 66, 88, 102, 107, 116, 150, 164, 167, 170, 171, 173, 179, 180, 182, 183, 189, 190, 197, 199, 202, 204, 205, 206, 207, 208, 209, 210, 211, 214, 216, 218, 219, 220, 222, 223, 224, 227, 228, 230, 233, 252, 255, 256, 260, 261, 262], "beyond": [5, 156, 199, 260], "It": [5, 23, 26, 102, 202, 208, 210, 260, 262, 263], "also": [5, 7, 26, 34, 102, 107, 159, 199, 202, 207, 208, 209, 210, 216, 220, 224, 228, 231, 249, 255, 262], "subnorm": [5, 107], "k": [5, 40, 97, 107, 132, 143, 176, 177, 190, 232, 236, 237, 238, 246, 248, 249, 250, 252, 260], "denorm": [5, 107], "gradual": [5, 107, 260], "underflow": [5, 9, 90, 101, 107, 247], "hardwar": [5, 53, 107, 153, 206, 210, 211, 236, 249, 256, 260], "univers": [5, 107, 205, 211, 256, 260], "mani": [5, 107, 175, 260, 262], "platform": [5, 26, 107], "compil": [5, 107, 173, 202, 205, 209, 260], "toggl": [5, 107], "daz": [5, 107], "flush": [5, 107], "ftz": [5, 107], "increas": [5, 107, 206, 261], "guard": [5, 107], "against": [5, 40, 73, 107, 132, 173, 190, 242, 245, 263], "time": [5, 7, 16, 17, 26, 107, 153, 179, 180, 202, 204, 209, 210, 215, 232, 236, 237, 238, 246, 248, 249, 256, 260, 262], "attack": [5, 107], "accordingli": [5, 10, 11, 13, 14, 16, 17, 59, 61, 62, 64, 66, 90, 96, 101, 107, 122, 123, 125, 134, 136, 137, 138, 141, 143, 150, 153, 158, 164, 168, 170, 179, 180, 181, 182, 184, 190, 199, 206, 207, 208, 209, 211, 240, 246, 254, 256], "vari": [5, 107, 158, 173, 179, 180, 181, 182, 199, 206], "function": [5, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 74, 78, 86, 87, 88, 94, 96, 99, 102, 107, 114, 115, 116, 122, 123, 125, 128, 129, 130, 131, 132, 136, 143, 149, 150, 152, 153, 154, 159, 161, 162, 163, 164, 167, 168, 170, 171, 172, 173, 174, 175, 179, 180, 181, 182, 183, 184, 185, 189, 192, 202, 204, 205, 207, 208, 209, 210, 211, 214, 215, 216, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 232, 233, 236, 237, 238, 242, 245, 246, 247, 248, 249, 250, 252, 255, 256, 257, 260, 261, 262], "access": [5, 26, 32, 102, 110, 190, 204, 210, 255, 257, 260], "variou": [5, 204], "cast": [5, 29, 49, 60, 63, 75, 88, 150, 170, 199, 207, 252, 260, 262], "introspect": 5, "isdtyp": [5, 189, 204], "integr": [5, 63, 113, 115, 116], "keyword": [5, 7, 26, 63, 88, 114, 137, 150, 170, 189, 204, 208, 211, 215, 216, 252, 256, 257, 260, 261, 262], "affect": [5, 15, 49, 208, 211], "intermedi": [5, 9, 107], "calcul": [5, 9, 10, 11, 12, 20, 21, 42, 47, 50, 61, 62, 64, 65, 66, 86, 87, 88, 90, 94, 96, 123, 124, 125, 126, 127, 134, 136, 138, 141, 149, 150, 161, 162, 164, 168, 169, 170, 172, 173, 184, 204, 247], "implementor": [5, 255], "free": [5, 211, 259], "when": [5, 7, 12, 16, 17, 26, 47, 49, 59, 63, 90, 96, 101, 102, 107, 113, 115, 122, 125, 134, 135, 138, 139, 141, 149, 150, 153, 154, 158, 168, 170, 173, 184, 186, 189, 190, 199, 204, 205, 207, 208, 209, 210, 212, 214, 215, 216, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 236, 238, 242, 245, 246, 247, 248, 249, 250, 252, 256, 260, 261, 262], "accumul": 5, "reduct": [5, 13, 14], "long": [5, 110, 216], "ha": [5, 9, 13, 14, 20, 23, 29, 34, 35, 40, 44, 47, 55, 86, 87, 88, 90, 94, 95, 96, 101, 104, 132, 136, 137, 140, 141, 142, 143, 149, 150, 161, 162, 166, 168, 170, 171, 172, 173, 174, 175, 179, 180, 181, 182, 184, 190, 199, 202, 207, 210, 211, 214, 215, 233, 240, 248, 249, 252, 254, 256, 257, 260, 262, 263], "wai": [5, 26, 63, 102, 202, 205, 211, 212, 257, 260, 261, 262, 263], "f4": [5, 199], "ensur": [5, 26, 158, 202, 206, 256, 260, 261, 262], "portabl": [5, 59, 122, 206, 208, 211, 212, 260], "consum": [5, 26, 63, 113, 115, 202, 207, 208, 216, 255, 260, 261], "recommend": [5, 7, 19, 23, 26, 122, 128, 129, 130, 131, 136, 152, 168, 184, 197, 204, 206, 210, 211, 260], "guidanc": [5, 7, 49, 204, 205, 212, 260], "govern": [5, 50, 169, 199, 256, 257], "interact": [5, 207], "either": [5, 9, 10, 11, 12, 24, 26, 35, 40, 65, 77, 87, 88, 90, 93, 94, 96, 98, 101, 102, 107, 110, 116, 117, 118, 122, 123, 124, 125, 126, 127, 132, 134, 135, 138, 139, 141, 150, 152, 159, 160, 161, 164, 170, 172, 173, 174, 190, 206, 207, 208, 212, 216, 247, 252, 260, 261, 263], "whether": [5, 13, 14, 26, 59, 60, 63, 88, 89, 102, 111, 116, 119, 122, 154, 160, 204, 211, 232, 236, 237, 246, 248, 255, 259, 260, 262], "otherwis": [5, 13, 14, 15, 16, 17, 26, 59, 60, 63, 75, 102, 111, 113, 115, 134, 136, 138, 150, 153, 154, 158, 159, 168, 170, 184, 185, 186, 189, 190, 202, 211, 232, 234, 240, 247, 248, 254, 259], "note": [5, 7, 9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 61, 62, 63, 64, 65, 66, 76, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 98, 100, 101, 103, 104, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 123, 124, 125, 126, 127, 132, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 152, 153, 157, 158, 159, 160, 161, 162, 164, 165, 168, 169, 170, 171, 172, 173, 174, 175, 178, 179, 180, 181, 182, 183, 184, 185, 189, 190, 204, 210, 214, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 260, 261, 262, 263], "possibl": [5, 26, 60, 101, 102, 134, 138, 154, 172, 173, 202, 205, 206, 207, 208, 210, 211, 212, 214, 216, 256, 260, 261, 262, 263], "multipl": [5, 7, 13, 14, 16, 17, 40, 42, 44, 132, 134, 136, 138, 141, 142, 150, 168, 170, 184, 190, 202, 205, 207, 210, 211, 215, 216, 237, 238, 256, 257, 260, 262], "In": [5, 12, 19, 26, 59, 88, 90, 93, 101, 116, 118, 119, 141, 144, 150, 152, 159, 170, 189, 190, 192, 199, 206, 207, 210, 212, 227, 228, 246, 247, 249, 252, 256, 257, 261, 262, 263], "clearli": [5, 59, 116, 197, 207, 256, 257], "warn": [5, 153, 212], "about": [5, 7, 26, 98, 108, 208, 256, 260, 262, 263], "": [5, 26, 29, 32, 49, 58, 59, 60, 80, 101, 102, 137, 152, 168, 175, 176, 177, 184, 190, 197, 202, 204, 205, 206, 207, 208, 210, 211, 214, 216, 220, 224, 228, 231, 245, 249, 250, 256, 257, 260, 262], "organ": [5, 204, 256, 261, 262], "within": [5, 15, 27, 190, 199, 202, 204, 207, 211, 218, 220, 223, 224, 227, 228, 229, 231, 260], "numer": [5, 9, 12, 20, 21, 40, 42, 44, 46, 47, 50, 51, 88, 90, 101, 115, 116, 117, 118, 119, 132, 137, 141, 142, 148, 149, 150, 157, 159, 165, 169, 170, 174, 199, 206, 218, 220, 223, 224, 227, 228, 229, 231, 233, 244, 245, 247, 252, 256, 260, 262], "accord": [5, 12, 60, 71, 75, 88, 90, 98, 101, 103, 122, 141, 149, 158, 159, 168, 184, 185, 190, 206, 207], "These": [5, 208, 236, 261], "intend": [5, 88, 150, 170, 202, 252], "posit": [7, 9, 10, 11, 13, 14, 20, 46, 62, 65, 66, 81, 90, 95, 97, 98, 101, 118, 123, 125, 140, 141, 143, 152, 156, 160, 162, 164, 173, 189, 190, 202, 204, 206, 216, 230, 232, 246, 261], "paramet": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 202, 204, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 256], "extern": [7, 262], "usabl": 7, "accept": [7, 26, 128, 129, 130, 131, 136, 152, 168, 184, 202, 257], "call": [7, 34, 210, 211, 214, 247, 260, 261, 262], "argument": [7, 10, 11, 26, 40, 61, 62, 63, 64, 65, 66, 86, 88, 107, 114, 123, 125, 132, 150, 155, 158, 161, 164, 170, 172, 173, 174, 189, 199, 204, 206, 208, 210, 211, 218, 220, 223, 224, 227, 228, 229, 231, 252, 256, 260, 261, 262], "map": [7, 207, 208], "base": [7, 47, 57, 58, 94, 95, 123, 124, 125, 126, 149, 179, 180, 181, 182, 190, 204, 208, 214, 216, 256, 257, 260, 261, 262], "sole": [7, 190, 197, 256], "incompat": [7, 26, 74, 102, 202, 257, 260], "us": [7, 19, 26, 27, 59, 60, 83, 98, 102, 107, 122, 124, 126, 156, 179, 181, 189, 190, 199, 204, 206, 207, 208, 209, 211, 212, 215, 216, 217, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 255, 256, 257, 258, 259, 260, 263], "normal": [7, 78, 167, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231], "practic": [7, 19, 190, 256, 261], "avail": [7, 102, 114, 202, 210, 255, 257, 261], "still": [7, 26, 216, 256, 261, 262, 263], "consid": [7, 26, 63, 102, 128, 129, 130, 131, 179, 180, 181, 182, 207, 211, 230, 245, 256, 260, 262, 263], "compliant": [7, 26, 51, 90, 96, 102, 122, 125, 128, 129, 130, 131, 134, 135, 136, 138, 139, 168, 184, 206, 209, 211, 257, 260], "altern": [7, 208, 210, 263], "thei": [7, 26, 199, 205, 210, 211, 215, 216, 255, 256, 257, 260, 262, 263], "were": [7, 101, 153, 158, 204, 260], "option": [7, 13, 14, 15, 16, 17, 23, 26, 57, 58, 59, 60, 63, 77, 78, 88, 91, 92, 97, 99, 102, 103, 104, 113, 115, 122, 134, 136, 138, 145, 146, 150, 153, 154, 156, 158, 168, 170, 171, 184, 187, 188, 189, 204, 215, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 240, 242, 245, 252, 254, 256, 261, 262], "lead": [7, 101, 207, 246, 249, 260], "readabl": [7, 199, 256, 261], "code": [7, 59, 199, 208, 209, 211, 214, 216, 256, 260, 261, 262], "easier": [7, 202, 208, 256], "evolv": [7, 202, 256], "over": [7, 13, 14, 26, 122, 134, 136, 138, 150, 168, 170, 171, 174, 184, 185, 206, 207, 208, 210, 211, 215, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 233, 252, 254, 256, 260], "ad": [7, 9, 10, 11, 12, 13, 14, 20, 21, 24, 26, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 86, 87, 90, 93, 94, 96, 97, 98, 102, 103, 104, 117, 118, 119, 122, 123, 124, 125, 126, 132, 137, 141, 142, 143, 144, 145, 146, 148, 149, 150, 157, 159, 161, 162, 164, 165, 169, 170, 172, 173, 174, 179, 180, 181, 182, 185, 190, 203, 204, 205, 211, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 257], "worri": 7, "xi": [7, 137], "annot": [7, 204, 216, 260], "individu": [7, 158, 211, 214, 215, 216, 219, 230, 260, 261], "aim": [7, 205, 216, 255, 256, 257, 260, 261, 262, 263], "strongli": [7, 208, 262], "look": [7, 262], "like": [7, 202, 205, 207, 208, 214, 216, 257, 260, 261, 262], "funcnam": 7, "key1": 7, "key2": 7, "none": [7, 13, 14, 15, 16, 17, 23, 26, 32, 49, 57, 58, 59, 60, 63, 77, 78, 83, 88, 91, 92, 97, 99, 102, 103, 104, 113, 115, 122, 134, 136, 138, 145, 146, 150, 153, 154, 156, 158, 168, 170, 171, 184, 187, 188, 190, 204, 211, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 240, 242, 245, 252, 253, 254, 260, 261, 263], "out": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 190, 204, 205, 208, 210, 214, 215, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 259, 262], "int": [7, 13, 14, 15, 16, 17, 18, 21, 22, 26, 27, 28, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 56, 57, 58, 59, 60, 74, 77, 78, 88, 91, 95, 97, 98, 99, 101, 103, 104, 108, 122, 134, 136, 138, 140, 145, 147, 150, 153, 154, 156, 163, 166, 167, 168, 170, 171, 174, 175, 176, 177, 183, 184, 185, 187, 190, 199, 214, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 235, 240, 241, 251, 252, 253, 254, 261], "str": [7, 8, 23, 115, 116, 137, 261], "modulo": 7, "self": [7, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 89, 204, 262], "few": [7, 206, 214, 260, 262], "enhanc": 7, "default": [7, 13, 14, 15, 16, 17, 18, 23, 26, 59, 60, 63, 77, 78, 88, 91, 92, 97, 99, 102, 103, 104, 112, 113, 115, 122, 134, 136, 137, 138, 143, 145, 146, 150, 153, 154, 156, 158, 163, 167, 168, 170, 174, 176, 177, 179, 180, 181, 183, 184, 185, 187, 188, 189, 190, 204, 206, 211, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 235, 240, 242, 245, 246, 249, 252, 254], "form": [7, 23, 26, 40, 79, 132, 133, 176, 177, 208, 232, 234, 235, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 257, 261], "question": [7, 205, 260], "commonli": [7, 168, 184, 205, 207, 209, 255, 256, 260, 261], "written": [7, 202, 260, 262], "yyyi": [8, 23, 257], "mm": [8, 23, 257], "string": [8, 23, 115, 116, 204, 257, 260], "version": [8, 9, 10, 11, 12, 13, 14, 20, 21, 23, 24, 25, 26, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 66, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 98, 102, 103, 104, 107, 108, 109, 116, 117, 118, 119, 122, 123, 124, 125, 126, 132, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 153, 157, 158, 159, 160, 161, 162, 164, 165, 169, 170, 171, 172, 173, 174, 175, 179, 180, 181, 182, 183, 185, 189, 202, 205, 211, 215, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 258, 260, 262], "absolut": [9, 20, 85, 159, 206, 208, 240, 241, 247, 256], "x_i": [9, 10, 11, 61, 62, 64, 66, 68, 76, 77, 79, 86, 87, 94, 96, 100, 109, 117, 118, 119, 123, 124, 125, 126, 129, 134, 136, 138, 142, 148, 151, 157, 159, 160, 161, 162, 164, 165, 168, 172, 173, 178, 184], "input": [9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 26, 30, 41, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 85, 86, 87, 88, 90, 92, 93, 94, 95, 96, 99, 100, 101, 102, 104, 105, 106, 107, 109, 116, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 188, 189, 197, 202, 204, 207, 209, 211, 212, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 249, 250, 252, 254, 256, 260, 262], "magnitud": [9, 12, 20, 85, 90, 101, 107, 141, 204, 249, 250], "represent": [9, 12, 20, 29, 44, 67, 70, 72, 80, 81, 82, 84, 90, 98, 101, 108, 141, 142, 172, 173, 206, 210, 261], "known": [9, 159, 206, 209, 210], "norm": [9, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 240, 254, 256], "modulu": [9, 152], "z": [9, 10, 11, 61, 62, 64, 66, 123, 207], "bj": [9, 12, 79, 90, 141], "comput": [9, 12, 28, 31, 33, 37, 39, 40, 43, 57, 58, 67, 70, 72, 79, 88, 89, 90, 93, 95, 101, 105, 106, 107, 120, 121, 128, 129, 130, 131, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 148, 150, 153, 168, 170, 174, 179, 180, 181, 182, 184, 185, 190, 204, 206, 209, 214, 218, 219, 220, 222, 223, 224, 226, 227, 228, 229, 230, 231, 232, 233, 236, 237, 238, 240, 242, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260], "operatornam": [9, 10, 11, 61, 62, 64, 66, 86, 87, 159, 161, 162, 172, 173, 207, 236, 237, 247, 249], "sqrt": [9, 10, 11, 61, 62, 189, 204, 207, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 254], "take": [9, 123, 125, 149, 164, 189, 204, 211, 216, 260], "care": [9, 208, 256], "undu": [9, 209], "overflow": [9, 12, 88, 90, 101, 107, 122, 150, 170, 199, 247, 252, 256], "dure": [9, 40, 59, 107, 132, 168, 184, 199, 202, 245, 260, 261], "stage": [9, 107, 257], "contain": [9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 26, 28, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 90, 91, 92, 93, 94, 96, 100, 101, 102, 105, 106, 107, 109, 110, 111, 113, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 157, 158, 159, 160, 161, 162, 164, 165, 168, 169, 170, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 184, 185, 187, 190, 204, 206, 207, 208, 210, 214, 215, 219, 220, 221, 224, 225, 228, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 260, 262], "nan": [9, 10, 11, 12, 13, 14, 24, 25, 35, 61, 62, 63, 64, 65, 66, 76, 85, 86, 87, 90, 93, 94, 96, 100, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 136, 138, 139, 141, 144, 149, 152, 157, 158, 159, 160, 161, 162, 164, 168, 172, 173, 178, 179, 180, 181, 182, 184, 189, 197, 207, 260], "infin": [9, 10, 11, 12, 13, 14, 24, 25, 35, 62, 63, 64, 65, 66, 76, 81, 86, 87, 90, 93, 94, 96, 100, 101, 107, 117, 118, 123, 124, 125, 126, 127, 134, 138, 141, 144, 149, 152, 157, 160, 161, 162, 164, 172, 173, 178, 207, 247, 254], "imag": [9, 10, 11, 12, 24, 62, 63, 66, 87, 93, 94, 96, 117, 118, 119, 122, 123, 125, 144, 157, 159, 162, 164, 173, 189, 204, 205, 260, 261, 262], "finit": [9, 10, 11, 12, 25, 35, 42, 62, 65, 66, 87, 90, 93, 94, 96, 101, 107, 117, 118, 123, 125, 141, 144, 149, 152, 160, 162, 164, 173, 206], "2022": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 90, 93, 94, 96, 97, 98, 103, 104, 108, 109, 116, 117, 118, 119, 122, 123, 124, 125, 126, 132, 137, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 157, 159, 161, 162, 164, 165, 169, 170, 171, 172, 173, 174, 179, 180, 181, 182, 185, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254], "12": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 66, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 98, 102, 103, 104, 107, 108, 109, 116, 117, 118, 119, 122, 123, 124, 125, 126, 132, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 153, 157, 158, 159, 160, 161, 162, 164, 165, 169, 170, 171, 172, 173, 174, 175, 179, 180, 181, 182, 183, 185, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 257], "approxim": [10, 11, 47, 61, 62, 64, 65, 66, 86, 87, 94, 96, 101, 123, 124, 125, 126, 149, 161, 162, 172, 173, 206, 242, 245], "princip": [10, 11, 61, 62, 64, 66, 123, 164, 207, 256], "invers": [10, 11, 61, 62, 64, 65, 66, 207, 218, 220, 223, 224, 225, 226, 227, 228, 229, 231, 238, 241, 245, 256], "cosin": [10, 11, 86, 87, 173], "express": [10, 61, 63, 64, 65, 86, 161, 172, 190, 199, 208, 256, 259], "radian": [10, 61, 64, 65, 86, 161, 172], "arc": [10, 61, 64], "frac": [10, 11, 61, 62, 64, 66, 86, 87, 90, 122, 124, 126, 159, 161, 162, 172, 173, 207, 247], "pi": [10, 11, 61, 62, 64, 66, 87, 123, 125, 162, 172, 173, 189], "j": [10, 11, 12, 25, 61, 62, 64, 66, 87, 90, 94, 96, 122, 123, 125, 141, 158, 159, 161, 162, 164, 172, 173, 190, 207, 236, 249, 252], "ln": [10, 11, 61, 62, 64, 66, 123], "zj": [10, 61, 62, 64, 66], "conj": [10, 11, 61, 62, 64, 66, 87, 94, 96, 123, 124, 125, 126, 162, 164, 173, 189, 204], "multi": [10, 11, 61, 62, 64, 66, 189, 207, 210, 211, 233, 262], "branch": [10, 11, 61, 62, 64, 65, 66, 86, 87, 90, 94, 96, 123, 125, 141, 149, 161, 162, 164, 172, 173, 260], "cut": [10, 11, 61, 62, 64, 66, 86, 87, 94, 96, 123, 125, 149, 161, 162, 164, 172, 173, 260], "plane": [10, 11, 61, 62, 64, 66, 86, 87, 90, 94, 96, 141, 161, 162, 164, 172, 173, 260], "By": [10, 11, 13, 14, 61, 62, 64, 65, 66, 88, 123, 125, 134, 136, 138, 149, 150, 164, 168, 170, 184, 185, 206, 207, 233, 256, 261], "place": [10, 11, 15, 60, 61, 62, 63, 64, 66, 91, 92, 97, 102, 103, 104, 122, 145, 146, 156, 187, 188, 189, 197, 199, 204, 208, 211, 219, 230, 245], "line": [10, 11, 61, 62, 64, 66, 172, 173, 199, 207, 260, 261, 262, 263], "segment": [10, 11, 61, 62, 64, 66, 207], "infti": [10, 11, 61, 62, 64, 66, 86, 123, 125, 149, 164, 207], "axi": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 95, 99, 123, 125, 134, 136, 138, 140, 149, 150, 153, 156, 163, 164, 166, 167, 168, 170, 171, 174, 175, 183, 184, 185, 189, 204, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 233, 240, 253, 254, 260], "rang": [10, 61, 62, 64, 66, 77, 88, 123, 125, 150, 164, 170, 190, 204, 210, 252, 260], "strip": [10, 61, 62, 64, 66, 123, 125], "unbound": [10, 61, 62, 64, 66, 123, 125], "along": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 97, 99, 123, 125, 134, 136, 138, 150, 153, 156, 163, 164, 167, 168, 170, 171, 172, 173, 175, 183, 184, 185, 190, 204, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 252, 254, 256], "c99": [10, 11, 61, 62, 64, 66, 90, 123, 125, 141, 149, 164, 207, 257], "provision": [10, 11, 61, 62, 64, 66, 123, 125, 149, 164, 207], "statu": [10, 11, 61, 62, 64, 66, 123, 125, 149, 164, 207], "greater": [10, 11, 33, 38, 48, 61, 62, 65, 66, 69, 71, 77, 85, 90, 100, 101, 123, 125, 149, 152, 159, 160, 162, 164, 166, 173, 189, 190, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 241], "than": [10, 11, 19, 26, 38, 40, 47, 48, 49, 55, 61, 62, 63, 65, 66, 69, 71, 76, 77, 85, 88, 90, 98, 99, 100, 101, 102, 123, 124, 125, 126, 132, 141, 149, 150, 152, 159, 160, 162, 164, 166, 168, 170, 171, 173, 178, 179, 180, 181, 182, 184, 190, 199, 202, 205, 208, 211, 212, 215, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 240, 241, 242, 245, 252, 254, 256, 257, 260, 262], "less": [10, 11, 39, 47, 61, 65, 66, 76, 85, 90, 101, 123, 124, 125, 126, 149, 152, 159, 160, 164, 168, 184, 189, 190, 208, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 240, 241, 242, 245, 254, 260], "\u03c0": [10, 64, 65, 84], "0j": [10, 11, 12, 25, 62, 63, 66, 87, 94, 96, 97, 123, 125, 145, 146, 159, 162, 164, 173, 207, 247], "nonzero": [10, 11, 12, 62, 66, 87, 90, 94, 96, 101, 141, 162, 173, 189, 190, 204, 245], "3\u03c0": [10, 65], "hyperbol": [11, 62, 66, 86, 87, 161, 162, 172, 173, 207], "aco": [11, 61, 189, 204, 206], "simpli": [11, 96, 125, 205, 216, 260, 262], "upper": [11, 77, 97, 177, 204, 232, 246], "half": [11, 15, 66, 122, 140, 164, 174, 190, 221], "area": [11, 62, 66], "sector": [11, 62, 66], "\u03c0j": [11, 62, 66, 123, 125], "3\u03c0j": [11, 123, 125], "sum": [12, 21, 88, 107, 127, 150, 189, 204, 240, 252, 254, 256], "x1_i": [12, 65, 67, 69, 70, 71, 72, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 135, 139, 141, 144, 149, 152, 169, 186, 204], "x2_i": [12, 65, 67, 69, 70, 71, 72, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 135, 139, 141, 144, 149, 152, 169, 186, 204], "first": [12, 16, 17, 19, 65, 67, 69, 70, 71, 72, 88, 93, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 144, 149, 156, 167, 169, 172, 173, 174, 179, 180, 181, 185, 186, 190, 207, 233, 236, 244, 246, 247, 249, 250, 256, 260, 261, 262, 263], "remain": [12, 90, 93, 101, 116, 118, 119, 141, 144, 152, 154, 159, 190, 208, 231], "neither": [12, 40, 90, 101, 132, 141, 174, 249, 261], "nor": [12, 90, 101, 141, 249, 261], "mathemat": [12, 19, 65, 84, 86, 87, 90, 96, 101, 123, 125, 141, 161, 162, 172, 173, 189, 207, 240, 254], "round": [12, 15, 76, 90, 100, 101, 141, 164, 178, 189, 204, 206], "nearest": [12, 90, 141, 157, 178, 206], "mode": [12, 90, 141, 206, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 246], "too": [12, 26, 90, 101, 141, 256, 260], "larg": [12, 90, 101, 141, 210, 216, 247, 260], "appropri": [12, 26, 90, 101, 141, 207, 212], "commut": 12, "associ": [12, 42, 141, 192, 199, 242, 245, 248, 256, 259, 261], "tabl": [12, 90, 141, 189], "c": [12, 90, 93, 122, 141, 143, 144, 153, 167, 168, 173, 184, 190, 204, 207, 210, 213, 232, 236, 237, 238, 246, 248, 249, 257, 259, 260, 262], "d": [12, 90, 93, 122, 141, 144, 199, 219, 230], "dj": [12, 90, 141], "independ": [12, 90, 141, 157, 190, 202, 210, 233, 246, 248, 256, 257, 260], "abov": [12, 88, 90, 93, 123, 125, 141, 144, 149, 150, 164, 170, 176, 177, 190, 199, 207, 208, 210, 211, 214, 235, 236, 252, 256, 259, 262], "similarli": [12, 57, 116, 137, 199, 232, 249], "henc": [12, 79, 95, 143, 153, 179, 180, 181, 182, 190, 205, 207, 208, 209, 210, 214, 215, 216, 260, 262], "z1": 12, "z2": 12, "keepdim": [13, 14, 16, 17, 134, 136, 138, 150, 168, 170, 184, 240, 254], "test": [13, 14, 89, 117, 118, 119, 204, 206, 258, 260, 261, 262], "evalu": [13, 14, 22, 30, 36, 38, 41, 44, 45, 46, 48, 51, 52, 94, 96, 123, 124, 125, 126, 142, 148, 159, 160, 165, 202, 260], "union": [13, 14, 15, 21, 22, 26, 28, 30, 31, 32, 33, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 59, 60, 75, 77, 78, 91, 98, 99, 103, 104, 108, 115, 116, 122, 134, 136, 138, 140, 145, 150, 153, 155, 156, 166, 167, 168, 170, 174, 184, 187, 221, 225, 240, 242, 245, 254, 261], "ax": [13, 14, 16, 17, 19, 55, 56, 99, 134, 136, 138, 140, 147, 150, 156, 166, 168, 170, 174, 175, 184, 185, 190, 204, 220, 221, 224, 225, 228, 231, 233, 240, 245, 248, 251, 254], "logic": [13, 14, 24, 26, 90, 93, 128, 129, 130, 131, 141, 144, 211, 214, 220, 224, 228, 231], "AND": [13, 67, 93, 128, 259], "entir": [13, 14, 86, 87, 94, 96, 134, 136, 138, 150, 161, 162, 168, 170, 184], "valid": [13, 14, 26, 27, 95, 114, 140, 167, 174, 183, 190, 206, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 236, 246, 249, 261], "count": [13, 14, 78, 88, 99, 171, 179, 180, 185, 190, 204, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 237], "last": [13, 14, 18, 19, 55, 78, 88, 99, 156, 163, 167, 171, 174, 185, 190, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 235, 240, 246, 249, 252], "invalid": [13, 14, 23, 95, 212, 260], "rais": [13, 14, 19, 23, 24, 25, 26, 29, 34, 35, 40, 47, 51, 55, 60, 74, 90, 94, 95, 102, 122, 132, 134, 138, 143, 149, 154, 166, 167, 183, 185, 190, 199, 202, 204, 210, 211, 212, 214, 233, 241, 260], "wa": [13, 14, 19, 26, 101, 134, 136, 138, 150, 168, 170, 184, 199, 211, 216, 260, 262], "OR": [14, 24, 70, 130, 144, 259], "start": [15, 122, 190, 204, 216, 260, 262], "stop": [15, 122, 190, 204, 261], "step": [15, 122, 190, 261], "evenli": [15, 122], "space": [15, 122, 219, 221, 230], "open": [15, 122, 140, 174, 190], "inclus": [15, 190, 260], "end": [15, 65, 86, 122, 159, 161, 172, 173, 197, 208, 247, 260, 261, 262], "exclus": [15, 190], "distanc": [15, 107], "between": [15, 26, 47, 51, 65, 78, 90, 93, 98, 122, 134, 135, 138, 139, 144, 149, 167, 179, 180, 181, 182, 199, 207, 208, 211, 219, 230, 256, 260, 262], "adjac": 15, "output": [15, 60, 63, 78, 88, 91, 92, 95, 97, 99, 102, 103, 104, 111, 122, 137, 145, 146, 154, 156, 158, 166, 167, 171, 175, 187, 188, 202, 204, 207, 208, 211, 213, 214, 216, 218, 219, 220, 222, 223, 224, 227, 228, 229, 230, 231, 252, 260], "infer": [15, 60, 63, 92, 103, 104, 146, 154, 188, 209, 256, 261], "cannot": [15, 26, 57, 102, 172, 173, 204, 207, 209, 260], "guarante": [15, 59, 179, 181, 202, 207, 211, 260, 262], "error": [15, 19, 23, 24, 25, 26, 29, 34, 35, 51, 55, 90, 102, 134, 138, 172, 173, 199, 206, 247, 260], "ceil": [15, 189], "indic": [16, 17, 18, 26, 60, 88, 89, 102, 111, 116, 122, 140, 143, 156, 158, 159, 171, 174, 176, 177, 179, 181, 190, 199, 204, 254, 260], "occur": [16, 17, 75, 107, 172, 173, 179, 180, 181, 182, 207, 261], "occurr": [16, 17, 179], "comparison": [16, 17, 18, 31, 33, 37, 39, 93, 105, 106, 120, 121, 134, 135, 138, 139, 144, 163, 189, 207, 257, 261], "search": [16, 17, 158, 189], "flatten": [16, 17, 78, 153, 156, 179, 180, 181, 182, 254, 256], "descend": [18, 163, 249, 250], "stabl": [18, 163, 210], "sort": [18, 158, 189, 204, 236, 237, 249, 250], "ascend": [18, 158, 163, 204], "stabil": [18, 163], "maintain": [18, 163, 205, 260, 262], "rel": [18, 19, 55, 99, 135, 139, 156, 163, 204, 235, 242, 245, 252], "compar": [18, 163, 179, 180, 181, 182, 206, 211, 261, 263], "properti": [19, 53, 54, 55, 56, 57, 58, 115, 204, 207, 211, 216, 260], "transpos": [19, 40, 55, 132, 133, 174, 232, 236, 245, 249, 256], "instanc": [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 55, 59, 89, 199, 202, 204, 211], "permut": [19, 55, 147], "revers": [19, 55, 65, 99], "origin": [19, 55, 65, 107, 140, 154, 156, 204, 208, 218, 220, 223, 224, 227, 228, 229, 231, 260, 261], "limit": [19, 98, 108, 116, 206, 256, 259], "matric": [19, 40, 55, 132, 133, 137, 176, 177, 232, 234, 235, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 256], "deviat": [19, 168, 206, 212, 260, 262], "et": [19, 249, 250], "al": 19, "intent": [19, 65], "found": [19, 207, 210, 262, 263], "problemat": [19, 63, 205, 208], "conflict": 19, "definit": [19, 86, 87, 161, 162, 172, 173, 204, 232, 261], "batch": [19, 254, 256], "cetera": [19, 249, 250], "permute_dim": [19, 189], "interfac": [19, 210, 256, 260, 262], "ab": [20, 107, 149, 189, 204, 240, 254], "augend": 21, "addend": 21, "self_i": [22, 28, 30, 31, 33, 36, 37, 38, 39, 41, 43, 44, 45, 46, 48, 50, 51, 52], "other_i": [22, 28, 30, 31, 33, 37, 38, 39, 41, 43, 45, 47, 48, 50, 51, 52], "bitwise_and": [22, 189], "api_vers": [23, 260], "object": [23, 24, 25, 26, 29, 34, 35, 53, 57, 59, 60, 89, 98, 102, 108, 110, 112, 113, 114, 189, 190, 199, 202, 204, 208, 210, 211, 214, 216, 255, 257, 261, 262], "2020": [23, 216, 257, 259, 260], "10": [23, 27, 124, 190, 260], "latest": [23, 210], "modul": [23, 202, 257, 261, 262, 263], "everi": [23, 103, 104, 246, 260], "top": [23, 202, 260, 262], "level": [23, 199, 205, 210, 211, 255, 256, 260, 261], "public": [23, 255, 261, 262], "well": [23, 205, 207, 210, 211, 246, 262, 263], "part": [23, 35, 176, 177, 199, 204, 210, 215, 257, 260, 262], "convert": [24, 25, 29, 34, 35, 60, 102, 199, 204, 205, 207, 210, 260, 262], "handl": [24, 26, 61, 64, 86, 88, 102, 124, 126, 149, 150, 159, 161, 165, 170, 172, 204, 205, 207, 208, 211, 212, 252, 260], "lazi": [24, 25, 29, 34, 35, 202, 204, 213, 262], "languag": [24, 25, 29, 34, 35, 208, 212, 214, 256, 260, 262], "therefor": [24, 25, 29, 34, 35, 202, 210, 211, 212, 214, 216, 257, 260, 262], "abl": [24, 25, 29, 34, 35, 102, 208, 210, 211, 260, 262], "kind": [24, 25, 26, 29, 34, 35, 47, 51, 77, 90, 98, 102, 104, 108, 113, 115, 116, 149, 199, 204, 214, 256, 259], "here": [24, 25, 26, 29, 34, 35, 190, 199, 208, 210, 215, 216, 262], "valueerror": [24, 25, 26, 29, 34, 35, 60, 102, 154, 166, 262], "instead": [24, 25, 29, 34, 35, 63, 207, 210, 214, 261, 262], "2023": [24, 25, 26, 29, 34, 35, 59, 63, 77, 85, 88, 102, 107, 134, 135, 138, 139, 140, 150, 153, 158, 160, 170, 171, 174, 175, 179, 180, 181, 182, 183, 185, 218, 219, 220, 222, 223, 224, 227, 228, 230, 233, 252], "new": [25, 26, 77, 79, 85, 88, 95, 98, 102, 103, 104, 107, 108, 109, 116, 135, 139, 140, 145, 146, 151, 153, 154, 158, 160, 167, 171, 175, 183, 187, 188, 202, 204, 205, 208, 210, 211, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 257, 260, 261, 262], "stream": [26, 59, 211], "max_vers": [26, 204], "dl_devic": [26, 204], "enum": [26, 27], "pycapsul": 26, "export": [26, 102, 204, 210, 261], "from_dlpack": [26, 27, 189, 204, 210], "dlpack": [26, 27, 102, 204], "capsul": 26, "cuda": [26, 27, 205, 210, 262], "rocm": [26, 27, 205], "pointer": 26, "produc": [26, 236, 246, 249, 262], "instruct": 26, "safe": [26, 122], "insert": [26, 95, 158, 204], "wait": 26, "event": [26, 259], "larger": [26, 98, 156, 168, 184, 245], "below": [26, 101, 102, 176, 177, 192, 210, 211, 235, 252], "signal": [26, 222, 226, 262], "ownership": 26, "stai": 26, "On": 26, "cpu": [26, 27, 202, 205, 210, 211, 256, 260, 262], "queue": [26, 59, 211], "similar": [26, 152, 190, 205, 207, 209, 260, 261, 262], "mechan": [26, 102, 202, 204, 205, 213, 255, 260], "most": [26, 202, 211, 236, 256, 260, 262], "yet": [26, 216, 260], "sycl": 26, "want": [26, 90, 141, 205, 209, 210, 260, 262, 263], "cl": 26, "agre": 26, "assum": [26, 86, 102, 161, 172, 202, 207, 211, 255, 260], "legaci": 26, "per": [26, 153, 205, 210, 258], "thread": [26, 260, 262], "disallow": 26, "due": [26, 42, 57, 58, 122, 141, 153, 171, 206, 207, 256, 260], "ambigu": [26, 63, 101, 208], "construct": [26, 175, 202, 204, 205, 214, 260], "particular": [26, 190, 205, 207, 210, 211, 216, 256, 259, 260, 262, 263], "kdlcpu": 26, "safeti": [26, 59], "prefer": [26, 101, 202, 256, 262], "develop": [26, 206, 260, 261, 262, 263], "who": [26, 206, 260, 261], "think": 26, "cost": 26, "caller": 26, "major": [26, 143, 153, 190, 257], "minor": [26, 257], "verifi": [26, 260], "even": [26, 90, 141, 149, 157, 206, 207, 208, 219, 221, 225, 230, 246, 256, 260, 262], "pass": [26, 65, 202, 206, 211], "format": [26, 27, 257], "__dlpack_device__": [26, 102, 189, 210], "buffererror": [26, 102, 204, 210], "v2023": [26, 102], "mandat": [26, 102, 260], "offer": [26, 102, 205, 210, 211, 215, 260, 262], "referenc": [26, 260], "underli": [26, 67, 70, 72, 102, 206, 247, 256], "interpret": [26, 102, 107, 207, 208, 263], "enumer": 26, "made": [26, 102, 202, 207, 255, 257, 260, 262], "never": [26, 60, 102, 154, 210, 260], "deem": [26, 102], "cross": [26, 102, 204, 211, 256, 260], "movement": [26, 102], "request": [26, 102, 260], "reus": [26, 60, 102, 208, 260], "buffer": [26, 60, 102, 208, 210], "happen": [26, 102, 208, 211, 214, 256], "dlpack_flag_bitmask_is_copi": 26, "flag": 26, 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"__dlpack__": [[26, "dlpack"]], "Tip": [[26, null], [60, null]], "__dlpack_device__": [[27, "dlpack-device"]], "__eq__": [[28, "eq"], [89, "eq"]], "__float__": [[29, "float"]], "__floordiv__": [[30, "floordiv"]], "__ge__": [[31, "ge"]], "__getitem__": [[32, "getitem"]], "__gt__": [[33, "gt"]], "__index__": [[34, "index"]], "__int__": [[35, "int"]], "__invert__": [[36, "invert"]], "__le__": [[37, "le"]], "__lshift__": [[38, "lshift"]], "__lt__": [[39, "lt"]], "__matmul__": [[40, "matmul"]], "__mod__": [[41, "mod"]], "__mul__": [[42, "mul"]], "__ne__": [[43, "ne"]], "__neg__": [[44, "neg"]], "__or__": [[45, "or"]], "__pos__": [[46, "pos"]], "__pow__": [[47, "pow"]], "__rshift__": [[48, "rshift"]], "__setitem__": [[49, "setitem"]], "__sub__": [[50, "sub"]], "__truediv__": [[51, "truediv"]], "__xor__": [[52, "xor"]], "device": [[53, "device"]], "dtype": [[54, "dtype"]], "mT": [[55, "mt"]], "ndim": [[56, "ndim"]], "shape": [[57, "shape"]], "size": [[58, "size"]], "to_device": [[59, 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"set-functions"]], "Sorting Functions": [[197, "sorting-functions"]], "Statistical Functions": [[198, "statistical-functions"], [206, "statistical-functions"]], "Type Promotion Rules": [[199, "type-promotion-rules"]], "Rules": [[199, "rules"]], "Signed integer type promotion table": [[199, "signed-integer-type-promotion-table"]], "Unsigned integer type promotion table": [[199, "unsigned-integer-type-promotion-table"]], "Mixed unsigned and signed integer type promotion table": [[199, "mixed-unsigned-and-signed-integer-type-promotion-table"]], "Floating-point type promotion table": [[199, "floating-point-type-promotion-table"]], "Notes": [[199, "notes"]], "Mixing arrays with Python scalars": [[199, "mixing-arrays-with-python-scalars"]], "Utility Functions": [[200, "utility-functions"]], "Version": [[201, "version"]], "Assumptions": [[202, "assumptions"]], "Hardware and software environments": [[202, "hardware-and-software-environments"]], "Dependencies": [[202, "dependencies"]], "Backwards compatibility": [[202, "backwards-compatibility"], [257, "backwards-compatibility"]], "Production code & interactive use": [[202, "production-code-interactive-use"]], "Benchmark suite": [[203, "benchmark-suite"]], "Changelog per API standard version": [[204, "changelog-per-api-standard-version"]], "Changelog": [[204, "changelog"]], "v2023.12": [[204, "v2023-12"]], "Updates": [[204, "updates"], [204, "id3"]], "Normative": [[204, "normative"]], "APIs": [[204, "apis"], [204, "id1"], [204, "id4"], [204, "id8"]], "Extensions": [[204, "extensions"], [204, "id2"], [204, "id5"], [204, "id9"], [255, "extensions"]], "Additions": [[204, "additions"], [204, "id7"]], "Breaking Changes": [[204, "breaking-changes"]], "Errata": [[204, "errata"], [204, "id10"]], "v2022.12": [[204, "v2022-12"]], "Complex Number Support": [[204, "complex-number-support"], [204, "id6"]], "C API": [[205, "c-api"]], "Example situations for C/Cython usage": [[205, "example-situations-for-c-cython-usage"]], "Situation 1: a Python package that is mostly pure Python, with a limited number of Cython extensions": [[205, "situation-1-a-python-package-that-is-mostly-pure-python-with-a-limited-number-of-cython-extensions"]], "Situation 2: a Python package that contains a lot of Cython code": [[205, "situation-2-a-python-package-that-contains-a-lot-of-cython-code"]], "Situation 3: a Python package that uses the NumPy or Python C API directly": [[205, "situation-3-a-python-package-that-uses-the-numpy-or-python-c-api-directly"]], "Device support": [[205, "device-support"], [211, "device-support"]], "Other longer-term approaches": [[205, "other-longer-term-approaches"]], "Further Python API standardization": [[205, "further-python-api-standardization"]], "HPy": [[205, "hpy"]], "Accuracy": [[206, "accuracy"]], "Arithmetic Operations": [[206, "arithmetic-operations"]], "Mathematical Functions": [[206, "mathematical-functions"]], "Linear Algebra": [[206, "linear-algebra"]], "Complex Numbers": [[207, "complex-numbers"]], "The Complex Plane": [[207, "the-complex-plane"]], "Branch Cuts": [[207, "branch-cuts"]], "Complex Number Ordering": [[207, "complex-number-ordering"]], "Valued-based Promotion": [[207, "valued-based-promotion"]], "Copy-view behaviour and mutability": [[208, "copy-view-behaviour-and-mutability"]], "Mutating views": [[208, null]], "Data-dependent output shapes": [[209, "data-dependent-output-shapes"]], "Data interchange mechanisms": [[210, "data-interchange-mechanisms"]], "DLPack: An in-memory tensor structure": [[210, "dlpack-an-in-memory-tensor-structure"]], "Non-supported use cases": [[210, "non-supported-use-cases"]], "Intended usage": [[211, "intended-usage"]], "Syntax for device assignment": [[211, "syntax-for-device-assignment"]], "Semantics": [[211, "semantics"]], "Out of scope for device support": [[211, "out-of-scope-for-device-support"]], "Exceptions": [[212, "exceptions"]], "Design topics & constraints": [[213, "design-topics-constraints"], [213, null]], "Lazy vs. eager execution": [[214, "lazy-vs-eager-execution"]], "Parallelism": [[215, "parallelism"]], "Static typing": [[216, "static-typing"]], "Fourier transform Functions": [[217, "fourier-transform-functions"]], "Extension name and usage": [[217, "extension-name-and-usage"], [256, "extension-name-and-usage"]], "fft": [[218, "fft"]], "fftfreq": [[219, "fftfreq"]], "fftn": [[220, "fftn"]], "fftshift": [[221, "fftshift"]], "hfft": [[222, "hfft"]], "ifft": [[223, "ifft"]], "ifftn": [[224, "ifftn"]], "ifftshift": [[225, "ifftshift"]], "ihfft": [[226, "ihfft"]], "irfft": [[227, "irfft"]], "irfftn": [[228, "irfftn"]], "rfft": [[229, "rfft"]], "rfftfreq": [[230, "rfftfreq"]], "rfftn": [[231, "rfftn"]], "cholesky": [[232, "cholesky"]], "cross": [[233, "cross"]], "det": [[234, "det"]], "diagonal": [[235, "diagonal"]], "eigh": [[236, "eigh"]], "eigvalsh": [[237, "eigvalsh"]], "inv": [[238, "inv"]], "matrix_norm": [[240, "matrix-norm"]], "matrix_power": [[241, "matrix-power"]], "matrix_rank": [[242, "matrix-rank"]], "outer": [[244, "outer"]], "pinv": [[245, "pinv"]], "qr": [[246, "qr"]], "slogdet": [[247, "slogdet"]], "solve": [[248, "solve"]], "svd": [[249, "svd"]], "svdvals": [[250, "svdvals"]], "trace": [[252, "trace"]], "vector_norm": [[254, "vector-norm"]], "Extension modules:": [[255, null]], "Linear Algebra Extension": [[256, "linear-algebra-extension"]], "Design Principles": [[256, "design-principles"]], "Future API standard evolution": [[257, "future-api-standard-evolution"]], "Scope extensions": [[257, "scope-extensions"]], "Versioning": [[257, "versioning"]], "Python array API standard": [[258, "python-array-api-standard"]], "Contents": [[258, "contents"]], "Context": [[258, null]], "API": [[258, null]], "Methodology and Usage": [[258, null]], "Other": [[258, null]], "License": [[259, "license"]], "Purpose and scope": [[260, "purpose-and-scope"]], "Introduction": [[260, "introduction"], [261, "introduction"]], "This API standard": [[260, "this-api-standard"]], "History": [[260, "history"]], "Scope (includes out-of-scope / non-goals)": [[260, "scope-includes-out-of-scope-non-goals"]], "In scope": [[260, "in-scope"]], "Out of scope": [[260, "out-of-scope"]], "Implications of in/out of scope": [[260, "implications-of-in-out-of-scope"]], "Stakeholders": [[260, "stakeholders"]], "How to read this document": [[260, "how-to-read-this-document"]], "How to adopt this API": [[260, "how-to-adopt-this-api"]], "Checking an array object for Compliance": [[260, "checking-an-array-object-for-compliance"]], "Discoverability of conforming implementations": [[260, "discoverability-of-conforming-implementations"]], "Optional feature": [[260, null]], "Conformance": [[260, "conformance"]], "Terms and Definitions": [[260, "terms-and-definitions"]], "Normative References": [[260, "normative-references"]], "Usage Data": [[261, "usage-data"]], "Design": [[261, "design"]], "Usage": [[261, "usage"]], "Use in Decision-Making": [[261, "use-in-decision-making"]], "Use cases": [[262, "use-cases"]], "Types of use cases": [[262, "types-of-use-cases"]], "Concrete use cases": [[262, "concrete-use-cases"]], "Use case 1: add hardware accelerator and distributed support to SciPy": [[262, "use-case-1-add-hardware-accelerator-and-distributed-support-to-scipy"]], "Use case 2: simplify einops by removing the backend system": [[262, "use-case-2-simplify-einops-by-removing-the-backend-system"]], "Use case 3: adding a Python API to xtensor": [[262, "use-case-3-adding-a-python-api-to-xtensor"]], "Use case 4: make JIT compilation of array computations easier and more robust": [[262, "use-case-4-make-jit-compilation-of-array-computations-easier-and-more-robust"]], "Verification - test suite": [[263, "verification-test-suite"]], "Measuring conformance": [[263, "measuring-conformance"]], "Running the tests": [[263, "running-the-tests"]]}, "indexentries": {"__array_api_version__ (in module array_api)": [[8, "array_api.__array_api_version__"]], "abs() (in module array_api)": [[9, "array_api.abs"]], "acos() (in module array_api)": [[10, "array_api.acos"]], "acosh() (in module array_api)": [[11, "array_api.acosh"]], "add() (in module array_api)": [[12, "array_api.add"]], "all() (in module array_api)": [[13, "array_api.all"]], "any() (in module array_api)": [[14, "array_api.any"]], "arange() (in module array_api)": [[15, "array_api.arange"]], "argmax() (in module array_api)": [[16, "array_api.argmax"]], "argmin() (in module array_api)": [[17, "array_api.argmin"]], "argsort() (in module array_api)": [[18, "array_api.argsort"]], "t (array property)": [[19, "array_api.array.T"]], "__abs__() (array method)": [[20, "array_api.array.__abs__"]], "__add__() (array method)": [[21, "array_api.array.__add__"]], "__and__() (array method)": [[22, "array_api.array.__and__"]], "__array_namespace__() (array method)": [[23, "array_api.array.__array_namespace__"]], "__bool__() (array method)": [[24, "array_api.array.__bool__"]], "__complex__() (array method)": [[25, "array_api.array.__complex__"]], "__dlpack__() (array method)": [[26, "array_api.array.__dlpack__"]], "__dlpack_device__() (array method)": [[27, "array_api.array.__dlpack_device__"]], "__eq__() (array method)": [[28, "array_api.array.__eq__"]], "__float__() (array method)": [[29, "array_api.array.__float__"]], "__floordiv__() (array method)": [[30, "array_api.array.__floordiv__"]], "__ge__() (array method)": [[31, "array_api.array.__ge__"]], "__getitem__() (array method)": [[32, "array_api.array.__getitem__"]], "__gt__() (array method)": [[33, "array_api.array.__gt__"]], "__index__() (array method)": [[34, "array_api.array.__index__"]], "__int__() (array method)": [[35, "array_api.array.__int__"]], "__invert__() (array method)": [[36, "array_api.array.__invert__"]], "__le__() (array method)": [[37, "array_api.array.__le__"]], "__lshift__() (array method)": [[38, "array_api.array.__lshift__"]], "__lt__() (array method)": [[39, "array_api.array.__lt__"]], "__matmul__() (array method)": [[40, "array_api.array.__matmul__"]], "__mod__() (array method)": [[41, "array_api.array.__mod__"]], "__mul__() (array method)": [[42, "array_api.array.__mul__"]], "__ne__() (array method)": [[43, "array_api.array.__ne__"]], "__neg__() (array method)": [[44, "array_api.array.__neg__"]], "__or__() (array method)": [[45, "array_api.array.__or__"]], "__pos__() (array method)": [[46, "array_api.array.__pos__"]], "__pow__() (array method)": [[47, "array_api.array.__pow__"]], "__rshift__() (array method)": [[48, "array_api.array.__rshift__"]], "__setitem__() (array method)": [[49, "array_api.array.__setitem__"]], "__sub__() (array method)": [[50, "array_api.array.__sub__"]], "__truediv__() (array method)": [[51, "array_api.array.__truediv__"]], "__xor__() (array method)": [[52, "array_api.array.__xor__"]], "device (array property)": [[53, "array_api.array.device"]], "dtype (array property)": [[54, "array_api.array.dtype"]], "mt (array property)": [[55, "array_api.array.mT"]], "ndim (array property)": [[56, "array_api.array.ndim"]], "shape (array property)": [[57, "array_api.array.shape"]], "size (array property)": [[58, "array_api.array.size"]], "to_device() (array method)": [[59, "array_api.array.to_device"]], "asarray() (in module array_api)": [[60, "array_api.asarray"]], "asin() (in module array_api)": [[61, "array_api.asin"]], "asinh() (in module array_api)": [[62, "array_api.asinh"]], "astype() (in module array_api)": [[63, "array_api.astype"]], "atan() (in module array_api)": [[64, "array_api.atan"]], "atan2() (in module array_api)": [[65, "array_api.atan2"]], "atanh() (in module array_api)": [[66, "array_api.atanh"]], "bitwise_and() (in module array_api)": [[67, "array_api.bitwise_and"]], "bitwise_invert() (in module array_api)": [[68, "array_api.bitwise_invert"]], "bitwise_left_shift() (in module array_api)": [[69, "array_api.bitwise_left_shift"]], "bitwise_or() (in module array_api)": [[70, "array_api.bitwise_or"]], "bitwise_right_shift() (in module array_api)": [[71, "array_api.bitwise_right_shift"]], "bitwise_xor() (in module array_api)": [[72, "array_api.bitwise_xor"]], "broadcast_arrays() (in module array_api)": [[73, "array_api.broadcast_arrays"]], "broadcast_to() (in module array_api)": [[74, "array_api.broadcast_to"]], "can_cast() (in module array_api)": [[75, "array_api.can_cast"]], "ceil() (in module array_api)": [[76, "array_api.ceil"]], "clip() (in module array_api)": [[77, "array_api.clip"]], "concat() (in module array_api)": [[78, "array_api.concat"]], "conj() (in module array_api)": [[79, "array_api.conj"]], "e (in module array_api.constants)": [[80, "array_api.constants.e"]], "inf (in module array_api.constants)": [[81, "array_api.constants.inf"]], "nan (in module array_api.constants)": [[82, "array_api.constants.nan"]], "newaxis (in module array_api.constants)": [[83, "array_api.constants.newaxis"]], "pi (in module array_api.constants)": [[84, "array_api.constants.pi"]], "copysign() (in module array_api)": [[85, "array_api.copysign"]], "cos() (in module array_api)": [[86, "array_api.cos"]], "cosh() (in module array_api)": [[87, "array_api.cosh"]], "cumulative_sum() (in module array_api)": [[88, "array_api.cumulative_sum"]], "__eq__() (in module array_api.data_types)": [[89, "array_api.data_types.__eq__"]], "divide() (in module array_api)": [[90, "array_api.divide"]], "empty() (in module array_api)": [[91, "array_api.empty"]], "empty_like() (in module array_api)": [[92, "array_api.empty_like"]], "equal() (in module array_api)": [[93, "array_api.equal"]], "exp() (in module array_api)": [[94, "array_api.exp"]], "expand_dims() (in module array_api)": [[95, "array_api.expand_dims"]], "expm1() (in module array_api)": [[96, "array_api.expm1"]], "eye() (in module array_api)": [[97, "array_api.eye"]], "finfo() (in module array_api)": [[98, "array_api.finfo"]], "flip() (in module array_api)": [[99, "array_api.flip"]], "floor() (in module array_api)": [[100, "array_api.floor"]], "floor_divide() (in module array_api)": [[101, "array_api.floor_divide"]], "from_dlpack() (in module array_api)": [[102, "array_api.from_dlpack"]], "full() (in module array_api)": [[103, "array_api.full"]], "full_like() (in module array_api)": [[104, "array_api.full_like"]], "greater() (in module array_api)": [[105, "array_api.greater"]], "greater_equal() (in module array_api)": [[106, "array_api.greater_equal"]], "hypot() (in module array_api)": [[107, "array_api.hypot"]], "iinfo() (in module array_api)": [[108, "array_api.iinfo"]], "imag() (in module array_api)": [[109, "array_api.imag"]], "__array_namespace_info__() (in module array_api.info)": [[110, "array_api.info.__array_namespace_info__"]], "capabilities() (in module array_api.info)": [[111, "array_api.info.capabilities"]], "default_device() (in module array_api.info)": [[112, "array_api.info.default_device"]], "default_dtypes() (in module array_api.info)": [[113, "array_api.info.default_dtypes"]], "devices() (in module array_api.info)": [[114, "array_api.info.devices"]], "dtypes() (in module array_api.info)": [[115, "array_api.info.dtypes"]], "isdtype() (in module array_api)": [[116, "array_api.isdtype"]], "isfinite() (in module array_api)": [[117, "array_api.isfinite"]], "isinf() (in module array_api)": [[118, "array_api.isinf"]], "isnan() (in module array_api)": [[119, "array_api.isnan"]], "less() (in module array_api)": [[120, "array_api.less"]], "less_equal() (in module array_api)": [[121, "array_api.less_equal"]], "linspace() (in module array_api)": [[122, "array_api.linspace"]], "log() (in module array_api)": [[123, "array_api.log"]], "log10() (in module array_api)": [[124, "array_api.log10"]], "log1p() (in module array_api)": [[125, "array_api.log1p"]], "log2() (in module array_api)": [[126, "array_api.log2"]], "logaddexp() (in module array_api)": [[127, "array_api.logaddexp"]], "logical_and() (in module array_api)": [[128, "array_api.logical_and"]], "logical_not() (in module array_api)": [[129, "array_api.logical_not"]], "logical_or() (in module array_api)": [[130, "array_api.logical_or"]], "logical_xor() (in module array_api)": [[131, "array_api.logical_xor"]], "matmul() (in module array_api)": [[132, "array_api.matmul"]], "matrix_transpose() (in module array_api)": [[133, "array_api.matrix_transpose"]], "max() (in module array_api)": [[134, "array_api.max"]], "maximum() (in module array_api)": [[135, "array_api.maximum"]], "mean() (in module array_api)": [[136, "array_api.mean"]], "meshgrid() (in module array_api)": [[137, "array_api.meshgrid"]], "min() (in module array_api)": [[138, "array_api.min"]], "minimum() (in module array_api)": [[139, "array_api.minimum"]], "moveaxis() (in module array_api)": [[140, "array_api.moveaxis"]], "multiply() (in module array_api)": [[141, "array_api.multiply"]], "negative() (in module array_api)": [[142, "array_api.negative"]], "nonzero() (in module array_api)": [[143, "array_api.nonzero"]], "not_equal() (in module array_api)": [[144, "array_api.not_equal"]], "ones() (in module array_api)": [[145, "array_api.ones"]], "ones_like() (in module array_api)": [[146, "array_api.ones_like"]], "permute_dims() (in module array_api)": [[147, "array_api.permute_dims"]], "positive() (in module array_api)": [[148, "array_api.positive"]], "pow() (in module array_api)": [[149, "array_api.pow"]], "prod() (in module array_api)": [[150, "array_api.prod"]], "real() (in module array_api)": [[151, "array_api.real"]], "remainder() (in module array_api)": [[152, "array_api.remainder"]], "repeat() (in module array_api)": [[153, "array_api.repeat"]], "reshape() (in module array_api)": [[154, "array_api.reshape"]], "result_type() (in module array_api)": [[155, "array_api.result_type"]], "roll() (in module array_api)": [[156, "array_api.roll"]], "round() (in module array_api)": [[157, "array_api.round"]], "searchsorted() (in module array_api)": [[158, "array_api.searchsorted"]], "sign() (in module array_api)": [[159, "array_api.sign"]], "signbit() (in module array_api)": [[160, "array_api.signbit"]], "sin() (in module array_api)": [[161, "array_api.sin"]], "sinh() (in module array_api)": [[162, "array_api.sinh"]], "sort() (in module array_api)": [[163, "array_api.sort"]], "sqrt() (in module array_api)": [[164, "array_api.sqrt"]], "square() (in module array_api)": [[165, "array_api.square"]], "squeeze() (in module array_api)": [[166, "array_api.squeeze"]], "stack() (in module array_api)": [[167, "array_api.stack"]], "std() (in module array_api)": [[168, "array_api.std"]], "subtract() (in module array_api)": [[169, "array_api.subtract"]], "sum() (in module array_api)": [[170, "array_api.sum"]], "take() (in module array_api)": [[171, "array_api.take"]], "tan() (in module array_api)": [[172, "array_api.tan"]], "tanh() (in module array_api)": [[173, "array_api.tanh"]], "tensordot() (in module array_api)": [[174, "array_api.tensordot"]], "tile() (in module array_api)": [[175, "array_api.tile"]], "tril() (in module array_api)": [[176, "array_api.tril"]], "triu() (in module array_api)": [[177, "array_api.triu"]], "trunc() (in module array_api)": [[178, "array_api.trunc"]], "unique_all() (in module array_api)": [[179, "array_api.unique_all"]], "unique_counts() (in module array_api)": [[180, "array_api.unique_counts"]], "unique_inverse() (in module array_api)": [[181, "array_api.unique_inverse"]], "unique_values() (in module array_api)": [[182, "array_api.unique_values"]], "unstack() (in module array_api)": [[183, "array_api.unstack"]], "var() (in module array_api)": [[184, "array_api.var"]], "vecdot() (in module array_api)": [[185, "array_api.vecdot"]], "where() (in module array_api)": [[186, "array_api.where"]], "zeros() (in module array_api)": [[187, "array_api.zeros"]], "zeros_like() (in module array_api)": [[188, "array_api.zeros_like"]], "fft() (in module array_api.fft)": [[218, "array_api.fft.fft"]], "fftfreq() (in module array_api.fft)": [[219, "array_api.fft.fftfreq"]], "fftn() (in module array_api.fft)": [[220, "array_api.fft.fftn"]], "fftshift() (in module array_api.fft)": [[221, "array_api.fft.fftshift"]], "hfft() (in module array_api.fft)": [[222, "array_api.fft.hfft"]], "ifft() (in module array_api.fft)": [[223, "array_api.fft.ifft"]], "ifftn() (in module array_api.fft)": [[224, "array_api.fft.ifftn"]], "ifftshift() (in module array_api.fft)": [[225, "array_api.fft.ifftshift"]], "ihfft() (in module array_api.fft)": [[226, "array_api.fft.ihfft"]], "irfft() (in module array_api.fft)": [[227, "array_api.fft.irfft"]], "irfftn() (in module array_api.fft)": [[228, "array_api.fft.irfftn"]], "rfft() (in module array_api.fft)": [[229, "array_api.fft.rfft"]], "rfftfreq() (in module array_api.fft)": [[230, "array_api.fft.rfftfreq"]], "rfftn() (in module array_api.fft)": [[231, "array_api.fft.rfftn"]], "cholesky() (in module array_api.linalg)": [[232, "array_api.linalg.cholesky"]], "cross() (in module array_api.linalg)": [[233, "array_api.linalg.cross"]], "det() (in module array_api.linalg)": [[234, "array_api.linalg.det"]], "diagonal() (in module array_api.linalg)": [[235, "array_api.linalg.diagonal"]], "eigh() (in module array_api.linalg)": [[236, "array_api.linalg.eigh"]], "eigvalsh() (in module array_api.linalg)": [[237, "array_api.linalg.eigvalsh"]], "inv() (in module array_api.linalg)": [[238, "array_api.linalg.inv"]], "matmul() (in module array_api.linalg)": [[239, "array_api.linalg.matmul"]], "matrix_norm() (in module array_api.linalg)": [[240, "array_api.linalg.matrix_norm"]], "matrix_power() (in module array_api.linalg)": [[241, "array_api.linalg.matrix_power"]], "matrix_rank() (in module array_api.linalg)": [[242, "array_api.linalg.matrix_rank"]], "matrix_transpose() (in module array_api.linalg)": [[243, "array_api.linalg.matrix_transpose"]], "outer() (in module array_api.linalg)": [[244, "array_api.linalg.outer"]], "pinv() (in module array_api.linalg)": [[245, "array_api.linalg.pinv"]], "qr() (in module array_api.linalg)": [[246, "array_api.linalg.qr"]], "slogdet() (in module array_api.linalg)": [[247, "array_api.linalg.slogdet"]], "solve() (in module array_api.linalg)": [[248, "array_api.linalg.solve"]], "svd() (in module array_api.linalg)": [[249, "array_api.linalg.svd"]], "svdvals() (in module array_api.linalg)": [[250, "array_api.linalg.svdvals"]], "tensordot() (in module array_api.linalg)": [[251, "array_api.linalg.tensordot"]], "trace() (in module array_api.linalg)": [[252, "array_api.linalg.trace"]], "vecdot() (in module array_api.linalg)": [[253, "array_api.linalg.vecdot"]], "vector_norm() (in module array_api.linalg)": [[254, "array_api.linalg.vector_norm"]]}})
\ No newline at end of file
diff --git a/draft/API_specification/generated/array_api.info.__array_namespace_info__.html b/draft/API_specification/generated/array_api.info.__array_namespace_info__.html
index 123eb377f..a856a9ec8 100644
--- a/draft/API_specification/generated/array_api.info.__array_namespace_info__.html
+++ b/draft/API_specification/generated/array_api.info.__array_namespace_info__.html
@@ -466,6 +466,7 @@ <h1 id="api-specification-generated-array-api-info-array-namespace-info--page-ro
 <dt class="sig sig-object py" id="array_api.info.__array_namespace_info__">
 <span class="sig-name descname"><span class="pre">__array_namespace_info__</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">Info</span></span></span><a class="headerlink" href="#array_api.info.__array_namespace_info__" title="Link to this definition">¶</a></dt>
 <dd><p>Returns a namespace with Array API namespace inspection utilities.</p>
+<p>See <a class="reference internal" href="../inspection.html#inspection"><span class="std std-ref">Inspection</span></a> for a list of inspection APIs.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Returns<span class="colon">:</span></dt>
 <dd class="field-odd"><p><strong>out</strong> (<em>Info</em>) – An object containing Array API namespace inspection utilities.</p>
diff --git a/draft/API_specification/inspection.html b/draft/API_specification/inspection.html
index 9433b1ded..b6f44b7db 100644
--- a/draft/API_specification/inspection.html
+++ b/draft/API_specification/inspection.html
@@ -480,7 +480,7 @@
           <article class="md-content__inner md-typeset" role="main">
             
   <section id="inspection">
-<h1 id="api-specification-inspection--page-root">Inspection<a class="headerlink" href="#api-specification-inspection--page-root" title="Link to this heading">¶</a></h1>
+<span id="id1"></span><h1 id="api-specification-inspection--page-root">Inspection<a class="headerlink" href="#api-specification-inspection--page-root" title="Link to this heading">¶</a></h1>
 <blockquote>
 <div><p>Array API specification for namespace inspection utilities.</p>
 </div></blockquote>
diff --git a/draft/_sources/API_specification/inspection.rst.txt b/draft/_sources/API_specification/inspection.rst.txt
index 04691e712..89d9c602a 100644
--- a/draft/_sources/API_specification/inspection.rst.txt
+++ b/draft/_sources/API_specification/inspection.rst.txt
@@ -1,3 +1,5 @@
+.. _inspection:
+
 Inspection
 ==========
 
diff --git a/draft/objects.inv b/draft/objects.inv
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index efc4bea55..1b6100046 100644
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220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 236, 239, 240, 244, 246, 247, 256, 258, 262], "apart": 0, "from": [0, 5, 13, 14, 15, 19, 26, 44, 59, 60, 63, 75, 78, 88, 92, 99, 101, 102, 103, 104, 107, 122, 123, 125, 137, 142, 147, 150, 151, 156, 157, 166, 168, 170, 172, 173, 175, 181, 183, 186, 187, 188, 190, 192, 201, 204, 206, 207, 208, 209, 212, 213, 214, 216, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 238, 249, 251, 254, 258, 259, 261, 262, 263, 264, 265], "ndim": [0, 187, 191, 235, 248, 251, 252], "devic": [0, 5, 15, 26, 27, 59, 60, 63, 91, 92, 97, 102, 103, 104, 110, 112, 113, 115, 122, 146, 147, 155, 178, 179, 189, 190, 191, 192, 194, 206, 212, 215, 221, 232, 248, 258, 262, 264], "dtype": [0, 5, 15, 26, 60, 63, 73, 75, 88, 89, 91, 92, 97, 98, 102, 103, 104, 108, 110, 116, 122, 146, 147, 151, 157, 172, 189, 190, 191, 201, 204, 206, 212, 218, 254, 262, 263, 264], "all": [0, 5, 15, 19, 23, 26, 60, 63, 87, 90, 97, 99, 102, 111, 115, 141, 158, 164, 175, 177, 178, 179, 185, 187, 191, 192, 204, 206, 207, 209, 210, 211, 212, 213, 214, 216, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 235, 247, 249, 250, 256, 257, 258, 261, 262, 264, 265], "thi": [0, 1, 5, 7, 15, 19, 26, 34, 58, 59, 63, 71, 78, 96, 101, 102, 107, 111, 115, 116, 122, 125, 128, 129, 130, 131, 136, 144, 150, 154, 155, 169, 170, 173, 181, 182, 183, 184, 186, 191, 192, 199, 201, 204, 206, 207, 208, 209, 210, 211, 212, 213, 214, 216, 217, 218, 219, 220, 222, 223, 225, 226, 229, 230, 231, 233, 248, 249, 250, 251, 257, 258, 259, 261, 263, 264, 265], "return": [0, 5, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 194, 199, 206, 207, 208, 210, 212, 213, 216, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 258, 262, 264], "tupl": [0, 1, 13, 14, 26, 27, 32, 49, 57, 74, 78, 91, 99, 103, 115, 116, 134, 136, 138, 140, 144, 146, 148, 151, 156, 158, 168, 169, 170, 172, 176, 177, 181, 182, 183, 185, 186, 189, 192, 204, 238, 248, 249, 251, 253, 256, 262], "includ": [0, 1, 7, 9, 13, 14, 15, 16, 17, 20, 21, 23, 28, 30, 40, 41, 42, 43, 47, 51, 88, 107, 111, 115, 116, 118, 122, 132, 134, 136, 138, 151, 155, 166, 170, 172, 186, 191, 192, 201, 206, 207, 208, 209, 210, 211, 212, 213, 217, 242, 256, 258, 259, 261, 263, 264], "those": [0, 5, 7, 15, 23, 88, 90, 113, 115, 141, 144, 151, 155, 172, 201, 206, 209, 210, 213, 214, 216, 248, 251, 252, 254, 257, 258, 259, 262, 263, 264], "mean": [0, 26, 191, 204, 210, 212, 213, 218, 259, 262], "var": [0, 191], "std": [0, 191], "which": [0, 1, 5, 7, 8, 13, 14, 15, 16, 17, 18, 19, 26, 30, 40, 41, 44, 59, 60, 63, 75, 77, 78, 83, 88, 91, 92, 95, 97, 98, 99, 101, 102, 103, 104, 107, 108, 111, 113, 114, 115, 122, 132, 134, 136, 138, 142, 144, 146, 147, 151, 154, 155, 158, 160, 165, 169, 170, 172, 173, 174, 178, 179, 181, 182, 183, 184, 185, 186, 187, 189, 190, 192, 206, 207, 208, 209, 210, 211, 212, 213, 214, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 235, 242, 250, 251, 252, 254, 256, 257, 258, 259, 262, 263, 264], "some": [0, 96, 101, 113, 115, 125, 192, 207, 208, 209, 210, 213, 218, 262, 264, 265], "common": [0, 192, 201, 204, 213, 216, 217, 258, 262, 263, 264], "librari": [0, 5, 7, 26, 51, 57, 58, 59, 60, 63, 90, 96, 101, 102, 111, 113, 115, 116, 122, 125, 128, 129, 130, 131, 134, 135, 136, 138, 139, 144, 155, 160, 170, 175, 181, 182, 183, 184, 186, 191, 192, 204, 206, 207, 208, 209, 210, 211, 212, 213, 214, 216, 217, 218, 234, 238, 239, 248, 250, 257, 258, 259, 262, 263, 264, 265], "g": [0, 5, 9, 19, 20, 26, 47, 51, 57, 77, 88, 90, 102, 107, 109, 115, 116, 122, 134, 138, 141, 144, 151, 152, 155, 157, 159, 172, 177, 181, 182, 183, 184, 192, 199, 201, 206, 207, 208, 209, 210, 211, 212, 213, 216, 224, 228, 229, 230, 231, 233, 238, 239, 242, 249, 251, 252, 254, 256, 257, 258, 259, 262, 263, 264], "numpi": [0, 19, 63, 192, 204, 209, 210, 212, 213, 258, 262, 263, 264, 265], "scalar": [0, 2, 49, 60, 191, 192, 206, 216, 256, 264], "valu": [0, 1, 2, 5, 7, 9, 10, 11, 12, 15, 16, 17, 18, 20, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 39, 41, 43, 49, 51, 57, 58, 60, 61, 62, 63, 64, 65, 66, 76, 77, 78, 85, 86, 87, 88, 89, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 104, 105, 106, 107, 111, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 143, 144, 145, 146, 150, 151, 154, 155, 159, 160, 161, 162, 163, 164, 165, 166, 170, 172, 173, 174, 175, 180, 181, 182, 183, 184, 186, 187, 189, 191, 199, 201, 204, 206, 208, 210, 211, 212, 216, 218, 221, 224, 228, 229, 230, 231, 232, 233, 234, 238, 239, 240, 242, 243, 244, 247, 248, 249, 250, 251, 252, 254, 256, 258, 262, 264], "rational": [0, 7, 88, 151, 172, 192, 212, 213, 254, 257, 259, 262], "alwai": [0, 12, 26, 42, 60, 63, 98, 102, 141, 156, 192, 204, 209, 210, 213, 238], "necessari": [0, 26, 60, 90, 102, 141, 156, 177, 192, 210, 262], "acceler": [0, 5, 107, 155, 204, 212], "where": [0, 1, 7, 13, 14, 15, 26, 47, 57, 65, 86, 87, 90, 94, 96, 97, 101, 103, 104, 124, 125, 126, 137, 141, 144, 148, 150, 155, 160, 161, 163, 164, 169, 170, 174, 175, 177, 185, 186, 187, 191, 192, 201, 207, 209, 212, 213, 216, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 234, 235, 238, 239, 240, 242, 244, 247, 248, 249, 250, 251, 252, 254, 258, 262, 263, 264], "non": [0, 1, 7, 13, 14, 16, 17, 63, 128, 129, 130, 131, 134, 136, 138, 144, 151, 170, 176, 186, 187, 192, 201, 206, 207, 213, 220, 222, 225, 226, 229, 230, 231, 233, 235, 236, 238, 242, 244, 251, 256, 264], "could": [0, 26, 181, 182, 183, 184, 204, 210, 217, 258, 262, 264], "forc": 0, "synchron": [0, 26, 59, 155, 262], "delai": [0, 24, 25, 29, 34, 35, 204, 216, 262], "execut": [0, 201, 204, 213, 215, 217, 262, 264], "model": [0, 57, 58, 90, 141, 209, 216, 264], "repres": [0, 8, 11, 12, 23, 24, 25, 26, 29, 34, 35, 62, 66, 87, 90, 101, 137, 141, 164, 174, 175, 206, 208, 212, 213, 249, 263, 264], "futur": [0, 26, 102, 205, 209, 210, 213, 217, 218, 238, 239, 260, 262, 264], "python": [0, 2, 5, 7, 24, 25, 26, 29, 34, 35, 49, 60, 101, 102, 154, 191, 192, 204, 206, 209, 212, 214, 216, 217, 218, 259, 261, 262, 263], "x": [0, 1, 5, 7, 9, 10, 11, 13, 14, 16, 17, 18, 20, 26, 61, 62, 63, 64, 65, 66, 68, 74, 76, 77, 79, 85, 86, 87, 88, 92, 94, 95, 96, 99, 100, 102, 104, 109, 117, 118, 119, 123, 124, 125, 126, 129, 133, 134, 136, 138, 140, 142, 144, 147, 148, 149, 151, 152, 153, 155, 156, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 172, 173, 174, 175, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 190, 192, 209, 210, 218, 219, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 234, 236, 237, 238, 239, 240, 242, 243, 244, 245, 247, 248, 249, 250, 251, 252, 254, 256, 258, 262, 264], "__pos__": [0, 191, 206], "po": 0, "__neg__": [0, 191, 206], "neg": [0, 13, 14, 15, 44, 47, 65, 78, 88, 90, 95, 97, 99, 101, 118, 123, 125, 141, 150, 154, 158, 162, 166, 173, 176, 187, 191, 192, 206, 209, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 256, 262], "x1": [0, 7, 12, 40, 65, 67, 69, 70, 71, 72, 77, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 143, 145, 150, 154, 160, 171, 176, 187, 188, 206, 235, 241, 246, 250, 253, 255], "x2": [0, 7, 12, 40, 65, 67, 69, 70, 71, 72, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 143, 145, 150, 154, 160, 171, 176, 187, 188, 206, 235, 241, 246, 250, 253, 255], "__add__": [0, 50, 191, 206], "add": [0, 7, 21, 88, 171, 172, 191, 192, 206, 207, 208, 213, 254], "__sub__": [0, 191, 206], "sub": [0, 192], "__mul__": [0, 191, 206], "mul": 0, "__truediv__": [0, 191, 206], "truediv": 0, "__floordiv__": [0, 191], "floordiv": 0, "__mod__": [0, 191], "mod": 0, "__pow__": [0, 191, 206], "pow": [0, 47, 191, 206, 208], "should": [0, 1, 5, 7, 9, 10, 11, 12, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 76, 77, 79, 85, 86, 87, 88, 90, 94, 95, 96, 98, 100, 101, 102, 105, 106, 107, 109, 113, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 137, 138, 139, 141, 142, 143, 149, 150, 151, 152, 153, 154, 156, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 170, 171, 172, 174, 175, 176, 178, 179, 180, 181, 182, 183, 184, 186, 187, 192, 199, 206, 207, 208, 209, 212, 213, 214, 218, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 234, 235, 236, 238, 239, 240, 242, 243, 244, 247, 248, 249, 250, 251, 252, 254, 256, 257, 258, 262, 264, 265], "defin": [0, 5, 12, 23, 30, 41, 49, 60, 65, 79, 90, 101, 103, 104, 115, 122, 134, 135, 136, 138, 139, 140, 141, 154, 161, 166, 167, 170, 178, 179, 186, 187, 191, 194, 199, 206, 208, 209, 218, 222, 223, 226, 227, 230, 233, 234, 238, 239, 240, 247, 248, 250, 258, 263, 264, 265], "real": [0, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 24, 25, 29, 30, 31, 33, 35, 37, 39, 41, 44, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 85, 86, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 105, 106, 107, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 142, 143, 144, 145, 146, 147, 150, 151, 154, 159, 160, 161, 162, 163, 164, 165, 166, 170, 172, 174, 175, 180, 186, 187, 189, 191, 201, 206, 209, 221, 224, 228, 229, 230, 231, 232, 233, 234, 238, 239, 240, 242, 244, 247, 248, 249, 250, 251, 252, 254, 256, 259], "data": [0, 1, 2, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 111, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 156, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 186, 187, 188, 189, 190, 191, 194, 201, 204, 207, 209, 210, 213, 215, 216, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 258, 259, 260, 261, 262, 265], "type": [0, 2, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 186, 187, 188, 189, 190, 191, 192, 194, 204, 207, 209, 210, 212, 214, 215, 216, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 258, 259, 262, 263], "__matmul__": [0, 191, 206], "matmul": [0, 40, 191, 201, 206, 258], "The": [0, 1, 5, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 58, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 90, 93, 94, 96, 99, 100, 101, 102, 105, 106, 107, 109, 110, 111, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 140, 141, 142, 143, 144, 145, 148, 149, 150, 151, 152, 153, 154, 155, 159, 160, 161, 162, 163, 164, 165, 166, 167, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 186, 187, 188, 192, 201, 204, 206, 207, 208, 210, 211, 212, 213, 216, 217, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 257, 258, 259, 261, 262, 263, 264, 265], "__invert__": [0, 191], "inv": [0, 206, 258], "invert": [0, 68, 240, 243, 250], "__inv__": 0, "__and__": [0, 191], "__or__": [0, 191], "__xor__": [0, 191], "xor": [0, 72, 131], "__lshift__": [0, 191], "lshift": 0, "__rshift__": [0, 191], "rshift": 0, "integ": [0, 5, 9, 13, 14, 15, 20, 22, 26, 29, 30, 34, 35, 36, 38, 41, 44, 45, 47, 48, 51, 52, 60, 67, 68, 69, 70, 71, 72, 76, 77, 88, 90, 100, 101, 103, 104, 108, 111, 115, 116, 122, 134, 136, 138, 142, 150, 151, 154, 155, 157, 159, 160, 170, 172, 173, 180, 186, 187, 191, 192, 206, 208, 209, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 243, 244, 254, 256, 262], "boolean": [0, 5, 22, 24, 25, 26, 29, 35, 36, 43, 45, 52, 57, 60, 63, 67, 68, 70, 72, 88, 89, 102, 103, 104, 111, 115, 116, 122, 128, 129, 130, 131, 144, 191, 201, 206], "__lt__": [0, 191, 206], "lt": 0, "__le__": [0, 191, 206], "le": 0, "__gt__": [0, 191, 206], "gt": [0, 248, 251], "__ge__": [0, 191, 206], "ge": 0, "__eq__": [0, 191, 206, 213], "eq": 0, "__ne__": [0, 191, 206], "ne": 0, "ar": [0, 1, 5, 7, 15, 16, 17, 19, 23, 24, 25, 26, 27, 29, 34, 35, 40, 49, 55, 58, 60, 77, 85, 86, 89, 90, 94, 97, 98, 99, 101, 102, 107, 114, 115, 122, 128, 129, 130, 131, 132, 141, 144, 150, 155, 158, 159, 163, 174, 175, 177, 181, 183, 187, 192, 201, 204, 206, 207, 208, 209, 210, 211, 212, 213, 214, 216, 217, 218, 220, 221, 222, 223, 225, 226, 227, 229, 230, 231, 232, 233, 235, 238, 239, 244, 247, 248, 251, 257, 258, 259, 262, 263, 264, 265], "onli": [0, 1, 5, 7, 16, 17, 23, 26, 40, 57, 58, 63, 99, 102, 107, 113, 115, 116, 122, 128, 129, 130, 131, 132, 136, 170, 186, 187, 191, 192, 201, 204, 206, 207, 209, 210, 212, 213, 214, 216, 218, 223, 235, 240, 247, 248, 250, 258, 259, 262, 263, 264, 265], "other": [0, 5, 21, 22, 23, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 50, 51, 52, 63, 89, 90, 96, 101, 102, 125, 140, 141, 170, 186, 192, 194, 204, 206, 208, 209, 210, 211, 212, 213, 214, 218, 235, 247, 257, 258, 261, 262, 264], "ani": [0, 1, 9, 10, 11, 23, 24, 25, 26, 28, 29, 34, 35, 43, 59, 61, 62, 66, 89, 93, 107, 117, 118, 145, 166, 191, 192, 201, 206, 209, 210, 212, 218, 251, 259, 261, 262, 265], "For": [0, 1, 5, 7, 9, 10, 11, 12, 16, 17, 18, 20, 24, 25, 26, 29, 30, 31, 33, 35, 37, 39, 41, 44, 57, 58, 61, 62, 64, 65, 66, 76, 79, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 105, 106, 107, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 134, 135, 137, 138, 139, 141, 142, 143, 145, 150, 151, 153, 154, 155, 159, 160, 161, 162, 163, 164, 165, 166, 167, 169, 172, 174, 175, 180, 181, 182, 183, 184, 192, 199, 204, 208, 209, 211, 213, 216, 221, 230, 232, 249, 251, 252, 254, 262, 264, 265], "backward": [0, 13, 14, 16, 17, 18, 31, 33, 37, 39, 105, 106, 120, 121, 122, 134, 135, 138, 139, 154, 165, 187, 192, 206, 209, 210, 214, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 262], "compat": [0, 1, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 74, 77, 85, 90, 93, 101, 105, 106, 107, 120, 121, 122, 127, 128, 130, 131, 132, 134, 135, 136, 138, 139, 141, 143, 145, 150, 151, 154, 155, 156, 165, 170, 171, 172, 186, 187, 188, 201, 206, 209, 210, 214, 235, 242, 244, 247, 250, 256, 262, 264], "mai": [0, 5, 7, 15, 16, 17, 18, 23, 26, 28, 31, 33, 37, 39, 43, 51, 57, 58, 59, 60, 89, 90, 93, 101, 102, 105, 106, 107, 110, 115, 116, 120, 121, 122, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 144, 145, 155, 156, 160, 165, 170, 175, 181, 182, 183, 184, 186, 191, 192, 199, 201, 204, 207, 208, 209, 210, 211, 212, 213, 214, 216, 217, 218, 238, 248, 249, 251, 257, 258, 262, 263, 264], "complex": [0, 5, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 24, 25, 29, 31, 33, 35, 37, 39, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 88, 90, 93, 94, 96, 97, 98, 103, 104, 105, 106, 107, 109, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 132, 134, 135, 137, 138, 139, 141, 142, 144, 145, 146, 147, 149, 150, 151, 152, 159, 161, 163, 164, 165, 166, 167, 171, 172, 174, 175, 176, 181, 182, 183, 184, 187, 201, 208, 212, 213, 215, 216, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 234, 235, 236, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 258, 262, 263], "howev": [0, 5, 16, 17, 18, 31, 33, 37, 39, 57, 88, 101, 105, 106, 107, 116, 120, 121, 122, 134, 135, 138, 139, 155, 160, 165, 173, 174, 175, 204, 207, 208, 209, 210, 211, 213, 258, 259, 262, 264], "inequ": [0, 16, 17, 18, 31, 33, 37, 39, 105, 106, 120, 121, 134, 135, 138, 139, 165], "unspecifi": [0, 5, 10, 11, 16, 17, 18, 30, 31, 33, 37, 39, 41, 47, 51, 60, 62, 66, 77, 78, 87, 90, 94, 96, 101, 103, 104, 105, 106, 120, 121, 122, 134, 135, 138, 139, 150, 154, 160, 164, 165, 166, 169, 173, 175, 192, 199, 201, 206, 222, 223, 226, 227, 230, 233, 238, 239, 262], "thu": [0, 5, 16, 17, 18, 30, 31, 33, 37, 39, 41, 47, 57, 60, 71, 77, 101, 103, 104, 105, 106, 120, 121, 122, 134, 135, 138, 139, 150, 154, 160, 165, 174, 175, 192, 199, 208, 209, 222, 223, 226, 227, 230, 233, 238, 239, 251, 258], "depend": [0, 5, 9, 10, 11, 16, 17, 18, 20, 26, 29, 31, 33, 37, 39, 44, 47, 51, 57, 58, 59, 61, 62, 63, 64, 65, 66, 77, 86, 87, 90, 94, 96, 105, 106, 111, 120, 121, 122, 123, 124, 125, 126, 141, 142, 150, 160, 163, 164, 165, 174, 175, 188, 199, 201, 208, 209, 212, 215, 216, 218, 238, 239, 248, 249, 250, 251, 258, 262, 264, 265], "see": [0, 5, 10, 11, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 33, 34, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 53, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 74, 77, 85, 90, 93, 96, 101, 102, 104, 105, 106, 107, 111, 114, 120, 121, 123, 125, 127, 128, 130, 131, 132, 134, 135, 136, 138, 139, 141, 143, 144, 145, 150, 151, 153, 154, 155, 157, 161, 165, 166, 167, 170, 171, 172, 181, 182, 183, 184, 186, 187, 188, 191, 192, 201, 203, 204, 207, 209, 211, 212, 213, 218, 235, 242, 244, 247, 250, 256, 257, 262, 263, 264, 265], "order": [0, 5, 7, 16, 17, 18, 19, 26, 31, 33, 37, 39, 55, 60, 63, 65, 89, 99, 101, 102, 105, 106, 120, 121, 134, 135, 138, 139, 144, 155, 160, 165, 174, 175, 176, 181, 182, 183, 184, 192, 199, 201, 206, 208, 211, 212, 214, 229, 230, 238, 239, 242, 251, 252, 256, 258, 259, 262, 263], "chang": [0, 1, 9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 66, 86, 87, 90, 93, 94, 96, 97, 98, 102, 103, 104, 117, 118, 119, 122, 123, 124, 125, 126, 132, 134, 137, 138, 141, 142, 144, 145, 146, 147, 149, 150, 151, 156, 159, 161, 163, 164, 166, 167, 171, 172, 173, 174, 175, 176, 181, 182, 183, 184, 187, 204, 220, 221, 222, 224, 225, 226, 229, 230, 232, 234, 235, 236, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 259, 262, 264, 265], "shape": [0, 1, 18, 40, 55, 63, 73, 74, 78, 88, 91, 92, 95, 99, 103, 104, 111, 132, 133, 137, 146, 147, 156, 158, 160, 165, 169, 173, 176, 177, 178, 179, 185, 187, 189, 190, 191, 206, 215, 216, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 262, 264], "result": [0, 1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 24, 25, 28, 29, 30, 31, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 79, 85, 86, 87, 90, 93, 94, 96, 100, 101, 105, 106, 107, 109, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 142, 143, 145, 149, 150, 151, 152, 153, 154, 155, 157, 159, 160, 161, 162, 163, 164, 166, 167, 169, 170, 171, 172, 174, 175, 176, 180, 181, 186, 192, 199, 201, 206, 208, 209, 210, 216, 234, 235, 237, 242, 243, 249, 250, 256, 262, 263, 264, 265], "promot": [0, 1, 5, 10, 11, 12, 21, 22, 30, 40, 41, 42, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 78, 85, 86, 87, 90, 94, 96, 101, 104, 107, 122, 123, 124, 125, 126, 127, 132, 135, 136, 139, 141, 142, 150, 153, 154, 157, 163, 164, 166, 167, 169, 170, 171, 174, 175, 176, 186, 187, 188, 191, 206, 234, 235, 240, 242, 243, 244, 246, 247, 248, 249, 250, 256, 258], "rule": [0, 5, 7, 10, 11, 12, 21, 22, 30, 40, 41, 42, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 78, 85, 86, 87, 88, 90, 94, 96, 101, 103, 104, 107, 122, 123, 124, 125, 126, 127, 132, 135, 139, 141, 142, 150, 153, 154, 157, 161, 163, 164, 166, 167, 169, 171, 174, 175, 176, 187, 188, 191, 192, 206, 209, 212, 234, 235, 240, 242, 243, 244, 246, 247, 248, 249, 250, 256, 258, 262, 264], "broadcast": [0, 12, 13, 14, 16, 17, 21, 22, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 73, 74, 77, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 134, 135, 136, 138, 139, 141, 143, 145, 150, 151, 154, 155, 170, 171, 172, 176, 186, 187, 188, 191, 206, 235, 242, 244, 247, 250, 256, 262], "same": [0, 5, 7, 9, 12, 15, 18, 19, 20, 26, 32, 36, 38, 40, 41, 46, 48, 50, 55, 59, 63, 68, 73, 74, 76, 77, 78, 79, 88, 90, 92, 95, 98, 99, 100, 101, 102, 104, 109, 132, 133, 134, 136, 137, 138, 140, 141, 143, 147, 148, 149, 150, 151, 152, 154, 155, 156, 158, 159, 160, 161, 165, 168, 169, 170, 171, 172, 173, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 190, 192, 201, 204, 206, 209, 210, 212, 213, 218, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 234, 236, 237, 238, 240, 243, 247, 248, 249, 251, 252, 254, 257, 258, 262, 264], "behavior": [0, 5, 47, 49, 59, 60, 63, 77, 90, 101, 103, 104, 107, 122, 141, 150, 154, 160, 173, 181, 182, 183, 184, 191, 192, 194, 201, 204, 206, 208, 209, 216, 217, 222, 223, 226, 227, 230, 233, 258, 259, 262, 263, 264, 265], "special": [0, 9, 10, 11, 12, 20, 21, 24, 25, 28, 29, 30, 35, 41, 42, 43, 47, 51, 61, 62, 64, 65, 66, 76, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 136, 138, 139, 141, 143, 145, 150, 151, 153, 154, 159, 161, 162, 163, 164, 166, 167, 170, 172, 174, 175, 180, 186, 206, 207, 209, 249, 254], "case": [0, 1, 5, 7, 9, 10, 11, 12, 15, 20, 21, 24, 25, 26, 28, 29, 30, 35, 41, 42, 43, 47, 51, 60, 61, 62, 64, 65, 66, 76, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 102, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 136, 137, 138, 139, 141, 143, 145, 150, 151, 153, 154, 159, 161, 162, 163, 164, 166, 167, 170, 172, 174, 175, 180, 186, 192, 204, 206, 207, 208, 209, 210, 213, 214, 216, 248, 249, 251, 254, 258, 260, 262, 265], "its": [0, 5, 26, 40, 73, 90, 98, 132, 141, 156, 158, 208, 209, 212, 213, 257, 262, 263, 264], "respect": [0, 9, 12, 20, 21, 22, 28, 30, 31, 33, 37, 38, 39, 41, 42, 43, 45, 48, 50, 51, 52, 65, 67, 69, 70, 71, 72, 77, 87, 90, 93, 101, 105, 106, 107, 113, 120, 121, 122, 127, 128, 130, 131, 135, 137, 139, 140, 141, 143, 145, 154, 164, 171, 174, 175, 176, 181, 182, 187, 206, 208, 211, 213, 238, 248, 251], "binari": [0, 5, 67, 70, 72, 174, 175, 207], "two": [0, 1, 5, 15, 19, 40, 55, 65, 71, 97, 102, 132, 133, 137, 159, 176, 178, 179, 181, 182, 183, 184, 187, 192, 201, 212, 213, 216, 217, 222, 223, 226, 227, 230, 233, 234, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 258, 262, 263, 264, 265], "operand": [0, 1, 9, 10, 11, 12, 24, 25, 29, 35, 61, 62, 64, 65, 66, 76, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 138, 139, 141, 143, 145, 150, 151, 153, 154, 159, 161, 162, 163, 164, 166, 167, 172, 174, 175, 180, 201, 206, 208, 249, 254], "assign": [0, 210], "exampl": [0, 5, 12, 23, 26, 115, 116, 169, 191, 192, 204, 209, 210, 211, 213, 216, 217, 218, 254, 258, 262, 264, 265], "after": [0, 1, 26, 40, 132, 166, 177], "addit": [0, 5, 7, 12, 26, 50, 59, 88, 115, 171, 191, 192, 201, 207, 209, 212, 258, 262, 263, 265], "modifi": [0, 26, 210, 261], "equal": [0, 1, 9, 10, 11, 18, 20, 21, 22, 26, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 58, 61, 62, 63, 64, 65, 66, 69, 71, 77, 87, 89, 94, 96, 97, 103, 104, 107, 116, 118, 123, 124, 125, 126, 136, 144, 145, 146, 147, 150, 151, 159, 164, 165, 166, 170, 172, 173, 175, 176, 177, 181, 182, 183, 184, 186, 191, 192, 199, 206, 209, 213, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 237, 243, 244, 247, 248, 249, 250, 254, 262], "equival": [0, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 71, 101, 107, 128, 129, 130, 131, 154, 159, 173, 192, 201, 209, 210, 244, 247, 250, 256, 262], "discuss": [0, 93, 145, 206, 212, 213, 217, 262, 263, 264], "copi": [0, 1, 26, 59, 60, 63, 102, 156, 165, 206, 207, 212, 213, 215, 261, 262], "view": [0, 102, 215], "behaviour": [0, 215, 262, 264], "mutabl": [0, 215], "via": [0, 26, 101, 102, 173, 192, 207, 212, 213, 217, 219, 247, 257, 258, 259, 262], "__iadd__": 0, "__isub__": 0, "__imul__": 0, "__itruediv__": 0, "__ifloordiv__": 0, "__ipow__": 0, "__imod__": 0, "__imatmul__": 0, "__iand__": 0, "__ior__": 0, "__ixor__": 0, "__ilshift__": 0, "__irshift__": 0, "appli": [0, 12, 77, 78, 85, 90, 141, 157, 159, 169, 176, 192, 201, 204, 209, 220, 222, 225, 226, 229, 230, 231, 233, 244, 247, 258, 262, 264], "match": [0, 1, 5, 9, 20, 26, 63, 101, 154, 176, 181, 182, 214, 224, 228, 229, 230, 231, 233, 238, 239, 242, 256, 264], "op": [0, 201], "__radd__": 0, "__rsub__": 0, "__rmul__": 0, "__rtruediv__": 0, "__rfloordiv__": 0, "__rpow__": 0, "__rmod__": 0, "__rmatmul__": 0, "__rand__": 0, "__ror__": 0, "__rxor__": 0, "__rlshift__": 0, "__rrshift__": 0, "arrai": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 83, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 193, 194, 195, 196, 197, 198, 199, 200, 202, 203, 204, 206, 207, 208, 209, 210, 211, 212, 213, 214, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 263, 265], "refer": [1, 13, 14, 96, 97, 125, 170, 176, 177, 186, 187, 192, 209, 210, 218, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 250], "automat": [1, 262], "implicit": [1, 212, 213, 216, 262], "expans": [1, 262], "size": [1, 13, 14, 88, 95, 122, 144, 158, 168, 173, 176, 187, 191, 192, 211, 217, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 237, 246, 248, 251, 262], "without": [1, 7, 26, 57, 102, 113, 115, 144, 155, 156, 181, 182, 183, 184, 204, 207, 208, 211, 261, 262, 264], "purpos": [1, 5, 96, 107, 125, 204, 249, 258, 260, 261, 264], "make": [1, 7, 204, 207, 208, 210, 212, 216, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 257, 259, 262], "differ": [1, 12, 26, 49, 50, 77, 78, 88, 90, 98, 101, 102, 141, 151, 169, 171, 172, 192, 204, 210, 213, 214, 216, 227, 238, 248, 249, 251, 254, 258, 262, 263, 264], "element": [1, 9, 10, 11, 12, 13, 14, 15, 20, 21, 22, 24, 25, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 54, 58, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 99, 100, 101, 103, 104, 105, 106, 107, 109, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 145, 149, 150, 151, 152, 153, 154, 155, 156, 158, 159, 160, 161, 162, 163, 164, 166, 167, 168, 170, 171, 172, 173, 174, 175, 177, 178, 179, 180, 181, 182, 183, 184, 186, 188, 191, 192, 206, 208, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 238, 247, 248, 249, 251, 254, 262], "wise": [1, 9, 10, 12, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 64, 65, 67, 68, 69, 70, 71, 72, 77, 79, 85, 90, 93, 101, 105, 106, 107, 109, 120, 121, 127, 128, 129, 130, 131, 135, 139, 141, 143, 145, 150, 152, 153, 154, 171, 191, 206, 208, 262], "oper": [1, 12, 19, 24, 26, 34, 40, 57, 58, 59, 61, 64, 71, 86, 88, 90, 101, 124, 126, 132, 141, 150, 151, 153, 154, 157, 163, 167, 172, 174, 176, 191, 192, 198, 201, 206, 209, 210, 211, 212, 213, 254, 258, 259, 262, 263, 264], "facilit": [1, 199, 204], "user": [1, 7, 26, 110, 175, 204, 207, 208, 210, 213, 217, 258, 262, 263, 264], "ergonom": 1, "encourag": [1, 262, 263], "avoid": [1, 9, 63, 90, 96, 101, 107, 125, 141, 156, 207, 210, 213, 216, 258, 262, 264], "unnecessari": [1, 258], "can": [1, 7, 26, 60, 75, 110, 114, 116, 192, 201, 204, 207, 209, 210, 212, 213, 218, 247, 248, 251, 257, 258, 262, 263, 264, 265], "potenti": [1, 26, 96, 111, 125, 155, 210, 262], "enabl": [1, 26, 102, 213, 217, 218, 262], "more": [1, 5, 7, 15, 19, 26, 40, 58, 60, 63, 73, 88, 96, 99, 101, 125, 132, 144, 150, 155, 173, 181, 182, 183, 184, 192, 201, 204, 207, 208, 209, 210, 211, 212, 213, 214, 217, 218, 222, 223, 226, 227, 230, 233, 249, 258, 259, 262, 263, 265], "memori": [1, 26, 60, 102, 204, 210, 211, 213, 262, 264], "effici": [1, 204, 210], "through": [1, 60, 65, 257, 259, 263, 264], "vector": [1, 40, 132, 137, 187, 235, 246, 251, 252, 256, 258, 262], "reduc": [1, 13, 14, 16, 17, 134, 136, 138, 151, 170, 172, 186, 192, 248, 251, 258, 263, 264], "consumpt": [1, 26, 263], "cach": 1, "local": [1, 213], "given": [1, 23, 99, 122, 158, 160, 185, 201, 206, 209, 210, 213, 214, 218, 239, 249, 258, 259, 262, 264], "involv": [1, 12, 90, 101, 141, 150, 157, 201, 208, 209, 213, 217], "singleton": [1, 13, 14, 16, 17, 95, 134, 136, 138, 151, 168, 170, 172, 177, 186, 242, 256, 262], "whose": [1, 5, 9, 11, 19, 20, 26, 47, 55, 62, 66, 85, 86, 87, 97, 99, 102, 133, 150, 158, 162, 163, 164, 173, 174, 175, 176, 178, 179, 181, 182, 183, 192, 210, 224, 228, 229, 230, 231, 233, 234, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 262, 264], "one": [1, 15, 19, 26, 40, 51, 58, 60, 63, 73, 75, 88, 90, 95, 97, 99, 101, 102, 115, 116, 122, 132, 137, 141, 144, 146, 147, 155, 160, 168, 173, 181, 182, 183, 184, 187, 192, 204, 207, 209, 210, 212, 213, 216, 217, 218, 220, 222, 224, 225, 226, 227, 228, 229, 230, 231, 233, 246, 247, 248, 256, 258, 259, 262, 264], "virtual": 1, "repeat": [1, 191, 192, 206, 264], "across": [1, 5, 90, 101, 141, 175, 206, 208, 209, 213, 257, 262], "correspond": [1, 16, 17, 23, 47, 59, 65, 73, 77, 102, 111, 112, 113, 150, 156, 158, 160, 170, 176, 181, 182, 183, 184, 186, 187, 192, 206, 208, 222, 226, 230, 233, 235, 238, 242, 261, 262], "If": [1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 29, 34, 35, 40, 44, 47, 51, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 74, 76, 77, 78, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 107, 111, 113, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 150, 151, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 168, 169, 170, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 189, 190, 192, 207, 209, 213, 219, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 234, 235, 238, 239, 240, 242, 243, 244, 247, 248, 249, 250, 251, 254, 256, 257, 258, 262, 264], "unequ": 1, "lower": [1, 77, 97, 178, 234], "higher": [1, 5, 26, 192, 207, 258, 263], "prepend": [1, 40, 95, 132, 177], "until": [1, 26, 177], "store": [1, 26, 213, 254], "determin": [1, 10, 11, 12, 13, 14, 21, 22, 26, 30, 40, 41, 42, 44, 45, 47, 50, 51, 52, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 75, 78, 85, 86, 87, 88, 90, 94, 96, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 132, 135, 139, 141, 142, 150, 153, 154, 162, 163, 164, 166, 167, 171, 173, 174, 175, 176, 181, 182, 183, 184, 187, 188, 201, 206, 209, 212, 213, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 234, 235, 236, 237, 240, 242, 243, 244, 246, 247, 248, 249, 250, 254, 256, 258, 262], "let": [1, 9, 10, 11, 12, 62, 66, 85, 87, 88, 93, 94, 96, 102, 117, 118, 119, 122, 123, 125, 136, 145, 151, 155, 160, 161, 164, 166, 170, 172, 175, 177, 186, 187, 192, 217, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 234, 238, 239, 240, 248, 250, 251, 254], "b": [1, 9, 10, 11, 12, 57, 62, 66, 87, 90, 93, 94, 96, 101, 117, 118, 119, 122, 123, 125, 141, 145, 161, 164, 166, 169, 175, 187, 192, 206, 209, 210, 214, 247, 250, 264], "both": [1, 40, 44, 47, 51, 65, 77, 88, 90, 98, 101, 102, 107, 122, 132, 142, 150, 151, 172, 175, 176, 187, 192, 209, 210, 212, 216, 218, 235, 254, 258, 262, 263], "shape1": 1, "describ": [1, 5, 12, 88, 90, 93, 115, 116, 141, 145, 150, 151, 172, 194, 201, 209, 212, 216, 221, 232, 254, 262], "shape2": 1, "n1": [1, 137], "len": [1, 137, 177], "n2": [1, 137], "max": [1, 26, 77, 98, 108, 111, 177, 191, 192, 206, 242, 244, 247], "temporari": 1, "list": [1, 73, 78, 114, 137, 169, 192, 204, 206, 213, 262, 264], "length": [1, 15, 107, 137, 156, 176, 192, 221, 223, 224, 227, 232, 251, 252], "while": [1, 101, 115, 122, 128, 129, 130, 131, 136, 140, 160, 170, 181, 182, 186, 191, 192, 199, 204, 206, 209, 210, 211, 213, 216, 247, 258, 263, 264, 265], "d1": 1, "els": [1, 26, 204, 263], "d2": 1, "set": [1, 18, 26, 49, 65, 102, 162, 165, 170, 178, 179, 181, 183, 184, 186, 191, 192, 206, 207, 208, 209, 210, 213, 214, 217, 218, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 234, 238, 239, 240, 244, 247, 248, 250, 251, 257, 258, 262, 264, 265], "th": [1, 97, 177, 192, 222, 226, 230, 233], "throw": 1, "except": [1, 7, 13, 14, 26, 74, 78, 88, 97, 102, 122, 144, 155, 169, 173, 185, 192, 201, 204, 206, 208, 210, 213, 215, 216, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 247, 259, 262, 263, 264], "demonstr": 1, "applic": [1, 26, 88, 151, 155, 172, 201, 254, 258, 262, 263], "4d": 1, "8": [1, 5, 7, 27, 177, 201, 204], "6": [1, 7, 177], "3d": 1, "7": [1, 7, 27, 218], "5": [1, 192, 262], "2d": 1, "1d": 1, "15": 1, "do": [1, 26, 90, 141, 154, 199, 204, 207, 209, 210, 212, 213, 214, 258, 259, 261, 262, 264, 265], "doe": [1, 15, 26, 102, 145, 173, 192, 201, 204, 207, 208, 209, 210, 211, 213, 214, 216, 218, 258, 262, 264, 265], "second": [1, 12, 65, 67, 69, 70, 71, 72, 93, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 143, 145, 150, 169, 171, 176, 181, 182, 183, 187, 188, 235, 238, 246, 248, 249, 251, 252, 262], "append": [1, 40, 69, 95, 132, 237], "As": [1, 122, 150, 181, 182, 183, 184, 204, 212, 218, 264], "impli": [1, 181, 182, 183, 184, 261, 262], "__setitem__": [1, 173, 191, 206], "Such": [1, 208, 258], "right": [1, 69, 71, 107, 160, 166, 207, 251, 261], "hand": [1, 201], "left": [1, 5, 60, 69, 101, 103, 160, 173, 192, 201, 238, 239, 251, 262], "index": [1, 5, 16, 17, 18, 32, 34, 49, 57, 83, 97, 111, 113, 137, 140, 144, 160, 169, 173, 176, 181, 182, 183, 191, 206, 222, 226, 230, 233, 262, 264], "perform": [1, 5, 13, 14, 26, 40, 59, 60, 90, 107, 132, 141, 155, 176, 192, 207, 208, 209, 210, 211, 212, 220, 222, 225, 226, 227, 229, 230, 231, 233, 251, 252, 258, 262, 263, 264], "empti": [1, 13, 14, 15, 151, 172, 191, 192, 206, 254, 262], "ok": 1, "allow": [1, 24, 25, 26, 29, 34, 35, 113, 115, 150, 156, 176, 192, 206, 207, 208, 210, 213, 216, 217, 258, 264], "NOT": [1, 129, 261], "adher": [2, 7, 8, 191, 192, 204, 257, 262], "convent": [2, 7, 10, 11, 26, 40, 61, 62, 64, 65, 66, 88, 123, 125, 132, 150, 166, 191, 192, 199, 209, 213, 257, 258, 263], "each": [2, 9, 10, 11, 12, 20, 21, 22, 26, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 76, 77, 79, 85, 86, 87, 90, 93, 94, 96, 100, 101, 105, 106, 107, 109, 114, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 135, 137, 139, 140, 141, 142, 143, 144, 145, 149, 150, 152, 153, 154, 155, 158, 159, 160, 161, 162, 163, 164, 166, 167, 169, 171, 174, 175, 176, 177, 180, 181, 182, 192, 204, 206, 208, 212, 216, 218, 230, 234, 235, 236, 240, 242, 243, 244, 247, 248, 249, 250, 251, 252, 257, 258, 262, 263, 264], "float": [2, 5, 9, 10, 11, 12, 13, 14, 15, 20, 21, 24, 25, 28, 29, 30, 31, 33, 34, 35, 37, 39, 40, 41, 42, 43, 44, 47, 49, 50, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 104, 107, 109, 113, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 145, 146, 147, 150, 151, 152, 153, 154, 157, 159, 160, 161, 162, 163, 164, 166, 167, 170, 171, 172, 174, 175, 176, 180, 181, 182, 183, 184, 186, 187, 189, 191, 199, 206, 208, 209, 216, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 238, 239, 240, 242, 243, 244, 247, 248, 249, 250, 251, 252, 254, 256, 258, 262, 263], "point": [2, 5, 9, 10, 11, 12, 13, 14, 15, 20, 24, 25, 26, 29, 34, 35, 40, 41, 42, 44, 47, 50, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 104, 107, 109, 113, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 145, 146, 147, 150, 151, 152, 153, 154, 157, 159, 160, 161, 162, 163, 164, 166, 167, 170, 171, 172, 174, 175, 176, 180, 181, 182, 183, 184, 186, 187, 189, 191, 199, 206, 208, 209, 213, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 238, 239, 240, 242, 243, 244, 247, 248, 249, 250, 251, 252, 254, 256, 258, 262, 264], "creat": [3, 15, 60, 91, 92, 97, 102, 103, 104, 122, 146, 147, 189, 190, 198, 204, 213, 221, 232, 258, 262], "main": [5, 97, 178, 179, 207, 212, 237, 254, 257, 264], "namespac": [5, 7, 23, 110, 194, 204, 206, 219, 257, 258, 259, 262, 265], "under": [5, 257, 261, 262], "specifi": [5, 13, 14, 15, 16, 17, 18, 26, 29, 59, 60, 63, 74, 78, 88, 91, 95, 98, 99, 103, 113, 115, 116, 122, 146, 151, 154, 155, 158, 168, 169, 172, 173, 177, 178, 179, 181, 182, 183, 184, 187, 189, 192, 201, 206, 208, 209, 210, 212, 213, 214, 218, 220, 222, 223, 224, 225, 226, 228, 229, 230, 231, 233, 237, 254, 256, 258, 259, 262, 264, 265], "name": [5, 7, 23, 26, 101, 115, 181, 182, 183, 192, 209, 238, 247, 248, 249, 251, 257, 262, 263], "descript": [5, 7, 206, 208, 242, 256], "bool": [5, 13, 14, 16, 17, 18, 22, 24, 26, 28, 31, 33, 37, 39, 43, 45, 49, 52, 60, 63, 75, 88, 89, 93, 102, 103, 104, 105, 106, 115, 116, 117, 118, 119, 120, 121, 122, 128, 129, 130, 131, 134, 136, 138, 145, 151, 156, 162, 165, 170, 172, 186, 201, 206, 216, 234, 242, 251, 256], "true": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 93, 98, 101, 102, 111, 117, 118, 119, 122, 128, 129, 130, 131, 134, 136, 138, 144, 145, 151, 156, 162, 165, 170, 172, 181, 182, 183, 184, 186, 188, 192, 206, 234, 242, 251, 256, 258], "fals": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 93, 102, 111, 117, 118, 119, 122, 128, 129, 130, 131, 134, 136, 138, 145, 151, 156, 162, 165, 170, 172, 181, 182, 183, 184, 186, 192, 234, 242, 251, 256], "int8": [5, 115, 116, 201], "bit": [5, 68, 69, 71, 85, 88, 98, 108, 151, 162, 172, 201, 206, 208, 254], "sign": [5, 9, 10, 11, 12, 15, 20, 41, 44, 62, 65, 66, 71, 85, 87, 88, 90, 94, 96, 101, 115, 116, 123, 125, 134, 135, 138, 139, 141, 142, 150, 151, 154, 160, 162, 164, 166, 172, 175, 181, 182, 183, 184, 191, 199, 206, 209, 248, 249, 254], "exist": [5, 7, 26, 60, 78, 102, 204, 206, 209, 212, 213, 214, 240, 259, 262, 263], "interv": [5, 10, 11, 13, 14, 15, 61, 62, 64, 66, 95, 122, 123, 125, 140, 169, 176, 178, 179, 185, 187, 192, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 259], "128": 5, "127": 5, "int16": [5, 88, 115, 116, 151, 172, 201, 254], "16": [5, 201], "32": [5, 201], "767": 5, "int32": [5, 88, 115, 116, 151, 172, 201, 254], "147": 5, "483": 5, "647": 5, "int64": [5, 88, 115, 116, 151, 172, 201, 254], "64": [5, 201], "9": [5, 27], "223": 5, "372": 5, "036": 5, "854": 5, "775": 5, "807": 5, "uint8": [5, 115, 116, 201], "unsign": [5, 88, 115, 116, 151, 172, 191, 254], "255": 5, "uint16": [5, 88, 115, 116, 151, 172, 201, 254], "65": 5, "535": [5, 206], "uint32": [5, 88, 115, 116, 151, 172, 201, 254], "294": 5, "967": 5, "295": 5, "uint64": [5, 115, 116, 201], "18": 5, "446": [5, 206], "744": [5, 206], "073": 5, "709": [5, 206], "551": [5, 206], "615": 5, "float32": [5, 109, 115, 116, 152, 201, 249, 251, 252], "ieee": [5, 12, 65, 80, 81, 82, 84, 90, 96, 98, 107, 125, 141, 154, 166, 174, 175, 191, 199, 208, 209, 262], "754": [5, 12, 65, 80, 81, 82, 84, 90, 96, 98, 107, 125, 141, 154, 166, 174, 175, 191, 199, 208, 209, 262], "singl": [5, 7, 24, 25, 29, 34, 35, 113, 115, 181, 182, 191, 201, 206, 207, 209, 212, 213, 218, 258, 262, 263, 264], "precis": [5, 9, 20, 42, 60, 98, 103, 104, 109, 141, 152, 166, 201, 206, 208, 224, 228, 229, 230, 231, 233, 238, 239, 242, 249, 251, 252, 256, 262], "2019": [5, 12, 90, 96, 107, 125, 141, 191, 208, 262, 264], "float64": [5, 9, 20, 115, 116, 201, 224, 228, 229, 230, 231, 233, 238, 239, 242, 256], "doubl": [5, 176, 201, 206], "complex64": [5, 109, 115, 116, 152, 201, 206, 249, 251, 252], "imaginari": [5, 10, 11, 12, 13, 14, 44, 61, 62, 63, 64, 66, 79, 87, 90, 93, 94, 96, 98, 109, 123, 125, 141, 142, 144, 145, 146, 147, 150, 159, 164, 166, 175, 206, 209], "compon": [5, 10, 11, 12, 13, 14, 44, 62, 63, 66, 79, 87, 90, 93, 94, 96, 98, 109, 123, 125, 141, 142, 144, 145, 146, 147, 150, 152, 159, 164, 166, 174, 175, 181, 182, 183, 184, 206, 209, 223, 232], "complex128": [5, 9, 20, 115, 116, 201, 206, 224, 228, 229, 230, 231, 233, 238, 239, 242, 256], "method": [5, 26, 34, 102, 191, 194, 204, 210, 212, 213, 216, 217, 218, 262, 263, 264], "attribut": [5, 23, 98, 108, 191, 203, 206, 259, 262, 263, 264], "requir": [5, 10, 11, 24, 25, 29, 34, 35, 59, 61, 62, 63, 64, 66, 88, 102, 107, 116, 151, 166, 169, 172, 173, 175, 181, 182, 184, 185, 191, 192, 199, 201, 204, 206, 207, 208, 209, 210, 211, 212, 213, 216, 218, 220, 221, 222, 224, 225, 226, 229, 230, 232, 235, 254, 257, 258, 262, 263, 264], "beyond": [5, 158, 201, 262], "It": [5, 23, 26, 102, 204, 210, 212, 262, 264, 265], "also": [5, 7, 26, 34, 102, 107, 161, 201, 204, 209, 210, 211, 212, 218, 222, 226, 230, 233, 251, 257, 264], "subnorm": [5, 107], "k": [5, 40, 97, 107, 132, 144, 178, 179, 192, 234, 238, 239, 240, 248, 250, 251, 252, 254, 262], "denorm": [5, 107], "gradual": [5, 107, 262], "underflow": [5, 9, 90, 101, 107, 249], "hardwar": [5, 53, 107, 155, 208, 212, 213, 238, 251, 258, 262], "univers": [5, 107, 207, 213, 258, 262], "mani": [5, 107, 177, 262, 264], "platform": [5, 26, 107], "compil": [5, 107, 175, 204, 207, 211, 262], "toggl": [5, 107], "daz": [5, 107], "flush": [5, 107], "ftz": [5, 107], "increas": [5, 107, 208, 263], "guard": [5, 107], "against": [5, 40, 73, 107, 132, 175, 192, 244, 247, 265], "time": [5, 7, 16, 17, 26, 107, 155, 181, 182, 204, 206, 211, 212, 217, 234, 238, 239, 240, 248, 250, 251, 258, 262, 264], "attack": [5, 107], "accordingli": [5, 10, 11, 13, 14, 16, 17, 59, 61, 62, 64, 66, 90, 96, 101, 107, 122, 123, 125, 134, 136, 137, 138, 141, 144, 151, 155, 160, 166, 170, 172, 181, 182, 183, 184, 186, 192, 201, 208, 209, 210, 211, 213, 242, 248, 256, 258], "vari": [5, 107, 160, 175, 181, 182, 183, 184, 201, 208], "function": [5, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 74, 78, 86, 87, 88, 94, 96, 99, 102, 107, 114, 115, 116, 122, 123, 125, 128, 129, 130, 131, 132, 136, 144, 150, 151, 154, 155, 156, 161, 163, 164, 165, 166, 169, 170, 172, 173, 174, 175, 176, 177, 181, 182, 183, 184, 185, 186, 187, 191, 194, 204, 206, 207, 209, 210, 211, 212, 213, 216, 217, 218, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 234, 235, 238, 239, 240, 244, 247, 248, 249, 250, 251, 252, 254, 257, 258, 259, 262, 263, 264], "access": [5, 26, 32, 102, 110, 192, 206, 212, 257, 259, 262], "variou": [5, 206], "cast": [5, 29, 49, 60, 63, 75, 88, 151, 172, 201, 209, 254, 262, 264], "introspect": 5, "isdtyp": [5, 191, 206], "integr": [5, 63, 113, 115, 116], "keyword": [5, 7, 26, 63, 88, 114, 137, 151, 172, 191, 206, 210, 213, 217, 218, 254, 258, 259, 262, 263, 264], "affect": [5, 15, 49, 210, 213], "intermedi": [5, 9, 107], "calcul": [5, 9, 10, 11, 12, 20, 21, 42, 47, 50, 61, 62, 64, 65, 66, 86, 87, 88, 90, 94, 96, 123, 124, 125, 126, 127, 134, 136, 138, 141, 150, 151, 163, 164, 166, 170, 171, 172, 174, 175, 186, 206, 249], "implementor": [5, 257], "free": [5, 213, 261], "when": [5, 7, 12, 16, 17, 26, 47, 49, 59, 63, 90, 96, 101, 102, 107, 113, 115, 122, 125, 134, 135, 138, 139, 141, 150, 151, 155, 156, 160, 170, 172, 175, 186, 188, 191, 192, 201, 206, 207, 209, 210, 211, 212, 214, 216, 217, 218, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 234, 238, 240, 244, 247, 248, 249, 250, 251, 252, 254, 258, 262, 263, 264], "accumul": 5, "reduct": [5, 13, 14], "long": [5, 110, 218], "ha": [5, 9, 13, 14, 20, 23, 29, 34, 35, 40, 44, 47, 55, 86, 87, 88, 90, 94, 95, 96, 101, 104, 132, 136, 137, 140, 141, 142, 144, 150, 151, 163, 164, 168, 170, 172, 173, 174, 175, 176, 177, 181, 182, 183, 184, 186, 192, 201, 204, 209, 212, 213, 216, 217, 235, 242, 250, 251, 254, 256, 258, 259, 262, 264, 265], "wai": [5, 26, 63, 102, 204, 207, 213, 214, 259, 262, 263, 264, 265], "f4": [5, 201], "ensur": [5, 26, 160, 204, 208, 258, 262, 263, 264], "portabl": [5, 59, 122, 208, 210, 213, 214, 262], "consum": [5, 26, 63, 113, 115, 204, 209, 210, 218, 257, 262, 263], "recommend": [5, 7, 19, 23, 26, 122, 128, 129, 130, 131, 136, 154, 170, 186, 199, 206, 208, 212, 213, 262], "guidanc": [5, 7, 49, 206, 207, 214, 262], "govern": [5, 50, 171, 201, 258, 259], "interact": [5, 209], "either": [5, 9, 10, 11, 12, 24, 26, 35, 40, 65, 77, 87, 88, 90, 93, 94, 96, 98, 101, 102, 107, 110, 116, 117, 118, 122, 123, 124, 125, 126, 127, 132, 134, 135, 138, 139, 141, 143, 151, 154, 161, 162, 163, 166, 172, 174, 175, 176, 192, 208, 209, 210, 214, 218, 249, 254, 262, 263, 265], "whether": [5, 13, 14, 26, 59, 60, 63, 88, 89, 102, 111, 116, 119, 122, 156, 162, 206, 213, 234, 238, 239, 248, 250, 257, 261, 262, 264], "otherwis": [5, 13, 14, 15, 16, 17, 26, 59, 60, 63, 75, 102, 111, 113, 115, 134, 136, 138, 151, 155, 156, 160, 161, 170, 172, 186, 187, 188, 191, 192, 204, 213, 234, 236, 242, 249, 250, 256, 261], "note": [5, 7, 9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 61, 62, 63, 64, 65, 66, 76, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 98, 100, 101, 103, 104, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 123, 124, 125, 126, 127, 132, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 149, 150, 151, 152, 153, 154, 155, 159, 160, 161, 162, 163, 164, 166, 167, 170, 171, 172, 173, 174, 175, 176, 177, 180, 181, 182, 183, 184, 185, 186, 187, 191, 192, 206, 212, 216, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 262, 263, 264, 265], "possibl": [5, 26, 60, 101, 102, 134, 138, 156, 174, 175, 204, 207, 208, 209, 210, 212, 213, 214, 216, 218, 258, 262, 263, 264, 265], "multipl": [5, 7, 13, 14, 16, 17, 40, 42, 44, 132, 134, 136, 138, 141, 142, 151, 170, 172, 186, 192, 204, 207, 209, 212, 213, 217, 218, 239, 240, 258, 259, 262, 264], "In": [5, 12, 19, 26, 59, 88, 90, 93, 101, 116, 118, 119, 141, 145, 151, 154, 161, 172, 191, 192, 194, 201, 208, 209, 212, 214, 229, 230, 248, 249, 251, 254, 258, 259, 263, 264, 265], "clearli": [5, 59, 116, 199, 209, 258, 259], "warn": [5, 155, 214], "about": [5, 7, 26, 98, 108, 210, 258, 262, 264, 265], "": [5, 26, 29, 32, 49, 58, 59, 60, 80, 101, 102, 137, 154, 170, 177, 178, 179, 186, 192, 199, 204, 206, 207, 208, 209, 210, 212, 213, 216, 218, 222, 226, 230, 233, 247, 251, 252, 258, 259, 262, 264], "organ": [5, 206, 258, 263, 264], "within": [5, 15, 27, 192, 201, 204, 206, 209, 213, 220, 222, 225, 226, 229, 230, 231, 233, 262], "numer": [5, 9, 12, 20, 21, 40, 42, 44, 46, 47, 50, 51, 88, 90, 101, 115, 116, 117, 118, 119, 132, 137, 141, 142, 149, 150, 151, 159, 161, 167, 171, 172, 176, 201, 208, 220, 222, 225, 226, 229, 230, 231, 233, 235, 246, 247, 249, 254, 258, 262, 264], "accord": [5, 12, 60, 71, 75, 88, 90, 98, 101, 103, 122, 141, 150, 160, 161, 170, 186, 187, 192, 208, 209], "These": [5, 210, 238, 263], "intend": [5, 88, 151, 172, 204, 254], "posit": [7, 9, 10, 11, 13, 14, 20, 46, 62, 65, 66, 81, 90, 95, 97, 98, 101, 118, 123, 125, 140, 141, 144, 154, 158, 162, 164, 166, 175, 191, 192, 204, 206, 208, 218, 232, 234, 248, 263], "paramet": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 204, 206, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 258], "extern": [7, 264], "usabl": 7, "accept": [7, 26, 128, 129, 130, 131, 136, 154, 170, 186, 204, 259], "call": [7, 34, 212, 213, 216, 249, 262, 263, 264], "argument": [7, 10, 11, 26, 40, 61, 62, 63, 64, 65, 66, 86, 88, 107, 114, 123, 125, 132, 151, 157, 160, 163, 166, 172, 174, 175, 176, 191, 201, 206, 208, 210, 212, 213, 220, 222, 225, 226, 229, 230, 231, 233, 254, 258, 262, 263, 264], "map": [7, 209, 210], "base": [7, 47, 57, 58, 94, 95, 123, 124, 125, 126, 150, 181, 182, 183, 184, 192, 206, 210, 216, 218, 258, 259, 262, 263, 264], "sole": [7, 192, 199, 258], "incompat": [7, 26, 74, 102, 204, 259, 262], "us": [7, 19, 26, 27, 59, 60, 83, 98, 102, 107, 122, 124, 126, 158, 181, 183, 191, 192, 201, 206, 208, 209, 210, 211, 213, 214, 217, 218, 219, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 257, 258, 259, 260, 261, 262, 265], "normal": [7, 78, 169, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233], "practic": [7, 19, 192, 258, 263], "avail": [7, 102, 114, 204, 212, 257, 259, 263], "still": [7, 26, 218, 258, 263, 264, 265], "consid": [7, 26, 63, 102, 128, 129, 130, 131, 181, 182, 183, 184, 209, 213, 232, 247, 258, 262, 264, 265], "compliant": [7, 26, 51, 90, 96, 102, 122, 125, 128, 129, 130, 131, 134, 135, 136, 138, 139, 170, 186, 208, 211, 213, 259, 262], "altern": [7, 210, 212, 265], "thei": [7, 26, 201, 207, 212, 213, 217, 218, 257, 258, 259, 262, 264, 265], "were": [7, 101, 155, 160, 206, 262], "option": [7, 13, 14, 15, 16, 17, 23, 26, 57, 58, 59, 60, 63, 77, 78, 88, 91, 92, 97, 99, 102, 103, 104, 113, 115, 122, 134, 136, 138, 146, 147, 151, 155, 156, 158, 160, 170, 172, 173, 186, 189, 190, 191, 206, 217, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 242, 244, 247, 254, 256, 258, 263, 264], "lead": [7, 101, 209, 248, 251, 262], "readabl": [7, 201, 258, 263], "code": [7, 59, 201, 210, 211, 213, 216, 218, 258, 262, 263, 264], "easier": [7, 204, 210, 258], "evolv": [7, 204, 258], "over": [7, 13, 14, 26, 122, 134, 136, 138, 151, 170, 172, 173, 176, 186, 187, 208, 209, 210, 212, 213, 217, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 235, 254, 256, 258, 262], "ad": [7, 9, 10, 11, 12, 13, 14, 20, 21, 24, 26, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 86, 87, 90, 93, 94, 96, 97, 98, 102, 103, 104, 117, 118, 119, 122, 123, 124, 125, 126, 132, 137, 141, 142, 144, 145, 146, 147, 149, 150, 151, 159, 161, 163, 164, 166, 167, 171, 172, 174, 175, 176, 181, 182, 183, 184, 187, 192, 205, 206, 207, 213, 234, 235, 236, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 259], "worri": 7, "xi": [7, 137], "annot": [7, 206, 218, 262], "individu": [7, 160, 213, 216, 217, 218, 221, 232, 262, 263], "aim": [7, 207, 218, 257, 258, 259, 262, 263, 264, 265], "strongli": [7, 210, 264], "look": [7, 264], "like": [7, 204, 207, 209, 210, 216, 218, 259, 262, 263, 264], "funcnam": 7, "key1": 7, "key2": 7, "none": [7, 13, 14, 15, 16, 17, 23, 26, 32, 49, 57, 58, 59, 60, 63, 77, 78, 83, 88, 91, 92, 97, 99, 102, 103, 104, 111, 113, 115, 122, 134, 136, 138, 146, 147, 151, 155, 156, 158, 160, 170, 172, 173, 186, 189, 190, 192, 206, 213, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 242, 244, 247, 254, 255, 256, 262, 263, 265], "out": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 192, 206, 207, 210, 212, 216, 217, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 261, 264], "int": [7, 13, 14, 15, 16, 17, 18, 21, 22, 26, 27, 28, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 56, 57, 58, 59, 60, 74, 77, 78, 88, 91, 95, 97, 98, 99, 101, 103, 104, 108, 122, 134, 136, 138, 140, 146, 148, 151, 155, 156, 158, 165, 168, 169, 170, 172, 173, 176, 177, 178, 179, 185, 186, 187, 189, 192, 201, 216, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 235, 237, 242, 243, 253, 254, 255, 256, 263], "str": [7, 8, 23, 115, 116, 137, 263], "modulo": 7, "self": [7, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 89, 206, 264], "few": [7, 208, 216, 262, 264], "enhanc": 7, "default": [7, 13, 14, 15, 16, 17, 18, 23, 26, 59, 60, 63, 77, 78, 88, 91, 92, 97, 99, 102, 103, 104, 112, 113, 115, 122, 134, 136, 137, 138, 144, 146, 147, 151, 155, 156, 158, 160, 165, 169, 170, 172, 176, 178, 179, 181, 182, 183, 185, 186, 187, 189, 190, 191, 192, 206, 208, 213, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 242, 244, 247, 248, 251, 254, 256], "form": [7, 23, 26, 40, 79, 132, 133, 178, 179, 210, 234, 236, 237, 238, 239, 240, 242, 243, 244, 247, 248, 249, 250, 251, 252, 254, 259, 263], "question": [7, 207, 262], "commonli": [7, 170, 186, 207, 209, 211, 257, 258, 262, 263], "written": [7, 204, 262, 264], "yyyi": [8, 23, 259], "mm": [8, 23, 259], "string": [8, 23, 115, 116, 206, 259, 262], "version": [8, 9, 10, 11, 12, 13, 14, 20, 21, 23, 24, 25, 26, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 66, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 98, 102, 103, 104, 107, 108, 109, 116, 117, 118, 119, 122, 123, 124, 125, 126, 132, 134, 135, 137, 138, 139, 140, 141, 142, 144, 145, 146, 147, 149, 150, 151, 152, 155, 159, 160, 161, 162, 163, 164, 166, 167, 171, 172, 173, 174, 175, 176, 177, 181, 182, 183, 184, 185, 187, 191, 204, 207, 213, 217, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 260, 262, 264], "absolut": [9, 20, 85, 161, 208, 210, 242, 243, 249, 258], "x_i": [9, 10, 11, 61, 62, 64, 66, 68, 76, 77, 79, 86, 87, 94, 96, 100, 109, 117, 118, 119, 123, 124, 125, 126, 129, 134, 136, 138, 142, 149, 152, 153, 159, 161, 162, 163, 164, 166, 167, 170, 174, 175, 180, 186], "input": [9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 26, 30, 41, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 85, 86, 87, 88, 90, 92, 93, 94, 95, 96, 99, 100, 101, 102, 104, 105, 106, 107, 109, 116, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 190, 191, 199, 204, 206, 209, 211, 213, 214, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 251, 252, 254, 256, 258, 262, 264], "magnitud": [9, 12, 20, 85, 90, 101, 107, 141, 206, 251, 252], "represent": [9, 12, 20, 29, 44, 67, 70, 72, 80, 81, 82, 84, 90, 98, 101, 108, 141, 142, 143, 174, 175, 208, 212, 263], "known": [9, 161, 208, 211, 212], "norm": [9, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 242, 256, 258], "modulu": [9, 154], "z": [9, 10, 11, 61, 62, 64, 66, 123, 209], "bj": [9, 12, 79, 90, 141], "comput": [9, 12, 28, 31, 33, 37, 39, 40, 43, 57, 58, 67, 70, 72, 79, 88, 89, 90, 93, 95, 101, 105, 106, 107, 120, 121, 128, 129, 130, 131, 132, 134, 135, 136, 138, 139, 141, 142, 144, 145, 149, 151, 155, 170, 172, 176, 181, 182, 183, 184, 186, 187, 192, 206, 208, 211, 216, 220, 221, 222, 224, 225, 226, 228, 229, 230, 231, 232, 233, 234, 235, 238, 239, 240, 242, 244, 247, 248, 249, 250, 251, 252, 254, 256, 258, 262], "operatornam": [9, 10, 11, 61, 62, 64, 66, 86, 87, 161, 163, 164, 174, 175, 209, 238, 239, 249, 251], "sqrt": [9, 10, 11, 61, 62, 191, 206, 209, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 256], "take": [9, 123, 125, 150, 166, 191, 206, 213, 218, 262], "care": [9, 210, 258], "undu": [9, 211], "overflow": [9, 12, 88, 90, 101, 107, 122, 151, 172, 201, 249, 254, 258], "dure": [9, 40, 59, 107, 132, 170, 186, 201, 204, 247, 262, 263], "stage": [9, 107, 259], "contain": [9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 26, 28, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 90, 91, 92, 93, 94, 96, 100, 101, 102, 105, 106, 107, 109, 110, 111, 113, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 159, 160, 161, 162, 163, 164, 166, 167, 170, 171, 172, 174, 175, 176, 178, 179, 180, 181, 182, 183, 184, 186, 187, 189, 192, 206, 208, 209, 210, 212, 216, 217, 221, 222, 223, 226, 227, 230, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 262, 264], "nan": [9, 10, 11, 12, 13, 14, 24, 25, 35, 61, 62, 63, 64, 65, 66, 76, 85, 86, 87, 90, 93, 94, 96, 100, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 136, 138, 139, 141, 143, 145, 150, 154, 159, 160, 161, 162, 163, 164, 166, 170, 174, 175, 180, 181, 182, 183, 184, 186, 191, 199, 209, 262], "infin": [9, 10, 11, 12, 13, 14, 24, 25, 35, 62, 63, 64, 65, 66, 76, 81, 86, 87, 90, 93, 94, 96, 100, 101, 107, 117, 118, 123, 124, 125, 126, 127, 134, 138, 141, 145, 150, 154, 159, 162, 163, 164, 166, 174, 175, 180, 209, 249, 256], "imag": [9, 10, 11, 12, 24, 62, 63, 66, 87, 93, 94, 96, 117, 118, 119, 122, 123, 125, 145, 159, 161, 164, 166, 175, 191, 206, 207, 262, 263, 264], "finit": [9, 10, 11, 12, 25, 35, 42, 62, 65, 66, 87, 90, 93, 94, 96, 101, 107, 111, 117, 118, 123, 125, 141, 145, 150, 154, 162, 164, 166, 175, 208], "2022": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 90, 93, 94, 96, 97, 98, 103, 104, 108, 109, 116, 117, 118, 119, 122, 123, 124, 125, 126, 132, 137, 141, 142, 144, 145, 146, 147, 149, 150, 151, 152, 159, 161, 163, 164, 166, 167, 171, 172, 173, 174, 175, 176, 181, 182, 183, 184, 187, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256], "12": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 66, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 98, 102, 103, 104, 107, 108, 109, 116, 117, 118, 119, 122, 123, 124, 125, 126, 132, 134, 135, 137, 138, 139, 140, 141, 142, 144, 145, 146, 147, 149, 150, 151, 152, 155, 159, 160, 161, 162, 163, 164, 166, 167, 171, 172, 173, 174, 175, 176, 177, 181, 182, 183, 184, 185, 187, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 259], "approxim": [10, 11, 47, 61, 62, 64, 65, 66, 86, 87, 94, 96, 101, 123, 124, 125, 126, 150, 163, 164, 174, 175, 208, 244, 247], "princip": [10, 11, 61, 62, 64, 66, 123, 166, 209, 258], "invers": [10, 11, 61, 62, 64, 65, 66, 209, 220, 222, 225, 226, 227, 228, 229, 230, 231, 233, 240, 243, 247, 258], "cosin": [10, 11, 86, 87, 175], "express": [10, 61, 63, 64, 65, 86, 163, 174, 192, 201, 210, 258, 261], "radian": [10, 61, 64, 65, 86, 163, 174], "arc": [10, 61, 64], "frac": [10, 11, 61, 62, 64, 66, 86, 87, 90, 122, 124, 126, 161, 163, 164, 174, 175, 209, 249], "pi": [10, 11, 61, 62, 64, 66, 87, 123, 125, 164, 174, 175, 191], "j": [10, 11, 12, 25, 61, 62, 64, 66, 87, 90, 94, 96, 122, 123, 125, 141, 160, 161, 163, 164, 166, 174, 175, 192, 209, 238, 251, 254], "ln": [10, 11, 61, 62, 64, 66, 123], "zj": [10, 61, 62, 64, 66], "conj": [10, 11, 61, 62, 64, 66, 87, 94, 96, 123, 124, 125, 126, 164, 166, 175, 191, 206], "multi": [10, 11, 61, 62, 64, 66, 191, 209, 212, 213, 235, 264], "branch": [10, 11, 61, 62, 64, 65, 66, 86, 87, 90, 94, 96, 123, 125, 141, 150, 163, 164, 166, 174, 175, 262], "cut": [10, 11, 61, 62, 64, 66, 86, 87, 94, 96, 123, 125, 150, 163, 164, 166, 174, 175, 262], "plane": [10, 11, 61, 62, 64, 66, 86, 87, 90, 94, 96, 141, 163, 164, 166, 174, 175, 262], "By": [10, 11, 13, 14, 61, 62, 64, 65, 66, 88, 123, 125, 134, 136, 138, 150, 151, 166, 170, 172, 186, 187, 208, 209, 235, 258, 263], "place": [10, 11, 15, 60, 61, 62, 63, 64, 66, 91, 92, 97, 102, 103, 104, 122, 146, 147, 158, 189, 190, 191, 199, 201, 206, 210, 213, 221, 232, 247], "line": [10, 11, 61, 62, 64, 66, 174, 175, 201, 209, 262, 263, 264, 265], "segment": [10, 11, 61, 62, 64, 66, 209], "infti": [10, 11, 61, 62, 64, 66, 86, 123, 125, 150, 166, 209], "axi": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 95, 99, 123, 125, 134, 136, 138, 140, 150, 151, 155, 158, 165, 166, 168, 169, 170, 172, 173, 176, 177, 185, 186, 187, 191, 206, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 235, 242, 255, 256, 262], "rang": [10, 61, 62, 64, 66, 77, 88, 123, 125, 151, 166, 172, 192, 206, 212, 254, 262], "strip": [10, 61, 62, 64, 66, 123, 125], "unbound": [10, 61, 62, 64, 66, 123, 125], "along": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 97, 99, 123, 125, 134, 136, 138, 151, 155, 158, 165, 166, 169, 170, 172, 173, 174, 175, 177, 185, 186, 187, 192, 206, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 254, 256, 258], "c99": [10, 11, 61, 62, 64, 66, 90, 123, 125, 141, 150, 166, 209, 259], "provision": [10, 11, 61, 62, 64, 66, 123, 125, 150, 166, 209], "statu": [10, 11, 61, 62, 64, 66, 123, 125, 150, 166, 209], "greater": [10, 11, 33, 38, 48, 61, 62, 65, 66, 69, 71, 77, 85, 90, 100, 101, 123, 125, 150, 154, 161, 162, 164, 166, 168, 175, 191, 192, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 243], "than": [10, 11, 19, 26, 38, 40, 47, 48, 49, 55, 61, 62, 63, 65, 66, 69, 71, 76, 77, 85, 88, 90, 98, 99, 100, 101, 102, 123, 124, 125, 126, 132, 141, 150, 151, 154, 161, 162, 164, 166, 168, 170, 172, 173, 175, 180, 181, 182, 183, 184, 186, 192, 201, 204, 207, 210, 213, 214, 217, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 242, 243, 244, 247, 254, 256, 258, 259, 262, 264], "less": [10, 11, 39, 47, 61, 65, 66, 76, 85, 90, 101, 123, 124, 125, 126, 150, 154, 161, 162, 166, 170, 186, 191, 192, 210, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 242, 243, 244, 247, 256, 262], "\u03c0": [10, 64, 65, 84], "0j": [10, 11, 12, 25, 62, 63, 66, 87, 94, 96, 97, 123, 125, 146, 147, 161, 164, 166, 175, 209, 249], "nonzero": [10, 11, 12, 62, 66, 87, 90, 94, 96, 101, 141, 164, 175, 191, 192, 206, 247], "3\u03c0": [10, 65], "hyperbol": [11, 62, 66, 86, 87, 163, 164, 174, 175, 209], "aco": [11, 61, 191, 206, 208], "simpli": [11, 96, 125, 207, 218, 262, 264], "upper": [11, 77, 97, 179, 206, 234, 248], "half": [11, 15, 66, 122, 140, 166, 176, 192, 223], "area": [11, 62, 66], "sector": [11, 62, 66], "\u03c0j": [11, 62, 66, 123, 125], "3\u03c0j": [11, 123, 125], "sum": [12, 21, 88, 107, 127, 151, 191, 206, 242, 254, 256, 258], "x1_i": [12, 65, 67, 69, 70, 71, 72, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 135, 139, 141, 143, 145, 150, 154, 171, 188, 206], "x2_i": [12, 65, 67, 69, 70, 71, 72, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 135, 139, 141, 143, 145, 150, 154, 171, 188, 206], "first": [12, 16, 17, 19, 65, 67, 69, 70, 71, 72, 88, 93, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 143, 145, 150, 158, 169, 171, 174, 175, 176, 181, 182, 183, 187, 188, 192, 209, 235, 238, 246, 248, 249, 251, 252, 258, 262, 263, 264, 265], "remain": [12, 90, 93, 101, 116, 118, 119, 141, 145, 154, 156, 161, 192, 210, 233], "neither": [12, 40, 90, 101, 132, 141, 176, 251, 263], "nor": [12, 90, 101, 141, 251, 263], "mathemat": [12, 19, 65, 84, 86, 87, 90, 96, 101, 123, 125, 141, 163, 164, 174, 175, 191, 209, 242, 256], "round": [12, 15, 76, 90, 100, 101, 141, 166, 180, 191, 206, 208], "nearest": [12, 90, 141, 159, 180, 208], "mode": [12, 90, 141, 208, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 248], "too": [12, 26, 90, 101, 141, 258, 262], "larg": [12, 90, 101, 141, 212, 218, 249, 262], "appropri": [12, 26, 90, 101, 141, 209, 214], "commut": 12, "associ": [12, 42, 141, 194, 201, 244, 247, 250, 258, 261, 263], "tabl": [12, 90, 141, 191], "c": [12, 90, 93, 122, 141, 144, 145, 155, 169, 170, 175, 186, 192, 206, 209, 212, 215, 234, 238, 239, 240, 248, 250, 251, 259, 261, 262, 264], "d": [12, 90, 93, 122, 141, 145, 201, 221, 232], "dj": [12, 90, 141], "independ": [12, 90, 141, 159, 192, 204, 212, 235, 248, 250, 258, 259, 262], "abov": [12, 88, 90, 93, 123, 125, 141, 145, 150, 151, 166, 172, 178, 179, 192, 201, 209, 210, 212, 213, 216, 237, 238, 254, 258, 261, 264], "similarli": [12, 57, 116, 137, 201, 234, 251], "henc": [12, 79, 95, 144, 155, 181, 182, 183, 184, 192, 207, 209, 210, 211, 212, 216, 217, 218, 262, 264], "z1": 12, "z2": 12, "keepdim": [13, 14, 16, 17, 134, 136, 138, 151, 170, 172, 186, 242, 256], "test": [13, 14, 89, 117, 118, 119, 206, 208, 260, 262, 263, 264], "evalu": [13, 14, 22, 30, 36, 38, 41, 44, 45, 46, 48, 51, 52, 94, 96, 123, 124, 125, 126, 142, 149, 161, 162, 167, 204, 262], "union": [13, 14, 15, 21, 22, 26, 28, 30, 31, 32, 33, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 59, 60, 75, 77, 78, 91, 98, 99, 103, 104, 108, 115, 116, 122, 134, 136, 138, 140, 146, 151, 155, 157, 158, 168, 169, 170, 172, 176, 186, 189, 223, 227, 242, 244, 247, 256, 263], "ax": [13, 14, 16, 17, 19, 55, 56, 99, 134, 136, 138, 140, 148, 151, 158, 168, 170, 172, 176, 177, 186, 187, 192, 206, 222, 223, 226, 227, 230, 233, 235, 242, 247, 250, 253, 256], "logic": [13, 14, 24, 26, 90, 93, 128, 129, 130, 131, 141, 145, 213, 216, 222, 226, 230, 233], "AND": [13, 67, 93, 128, 261], "entir": [13, 14, 86, 87, 94, 96, 134, 136, 138, 151, 163, 164, 170, 172, 186], "valid": [13, 14, 26, 27, 95, 114, 140, 169, 176, 185, 192, 208, 216, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 238, 248, 251, 263], "count": [13, 14, 78, 88, 99, 173, 181, 182, 187, 192, 206, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 239], "last": [13, 14, 18, 19, 55, 78, 88, 99, 158, 165, 169, 173, 176, 187, 192, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 237, 242, 248, 251, 254], "invalid": [13, 14, 23, 95, 214, 262], "rais": [13, 14, 19, 23, 24, 25, 26, 29, 34, 35, 40, 47, 51, 55, 60, 74, 90, 94, 95, 102, 122, 132, 134, 138, 144, 150, 156, 168, 169, 185, 187, 192, 201, 204, 206, 212, 213, 214, 216, 235, 243, 262], "wa": [13, 14, 19, 26, 101, 134, 136, 138, 151, 170, 172, 186, 201, 213, 218, 262, 264], "OR": [14, 24, 70, 130, 145, 261], "start": [15, 122, 192, 206, 218, 262, 264], "stop": [15, 122, 192, 206, 263], "step": [15, 122, 192, 263], "evenli": [15, 122], "space": [15, 122, 221, 223, 232], "open": [15, 122, 140, 176, 192], "inclus": [15, 192, 262], "end": [15, 65, 86, 122, 161, 163, 174, 175, 199, 210, 249, 262, 263, 264], "exclus": [15, 192], "distanc": [15, 107], "between": [15, 26, 47, 51, 65, 78, 90, 93, 98, 122, 134, 135, 138, 139, 145, 150, 169, 181, 182, 183, 184, 201, 209, 210, 213, 221, 232, 258, 262, 264], "adjac": 15, "output": [15, 60, 63, 78, 88, 91, 92, 95, 97, 99, 102, 103, 104, 111, 122, 137, 146, 147, 156, 158, 160, 168, 169, 173, 177, 189, 190, 204, 206, 209, 210, 213, 215, 216, 218, 220, 221, 222, 224, 225, 226, 229, 230, 231, 232, 233, 254, 262], "infer": [15, 60, 63, 92, 103, 104, 147, 156, 190, 211, 258, 263], "cannot": [15, 26, 57, 102, 174, 175, 206, 209, 211, 262], "guarante": [15, 59, 181, 183, 204, 209, 213, 262, 264], "error": [15, 19, 23, 24, 25, 26, 29, 34, 35, 51, 55, 90, 102, 134, 138, 174, 175, 201, 208, 249, 262], "ceil": [15, 191], "indic": [16, 17, 18, 26, 60, 88, 89, 102, 111, 116, 122, 140, 144, 158, 160, 161, 173, 176, 178, 179, 181, 183, 192, 201, 206, 256, 262], "occur": [16, 17, 75, 107, 174, 175, 181, 182, 183, 184, 209, 263], "occurr": [16, 17, 181], "comparison": [16, 17, 18, 31, 33, 37, 39, 93, 105, 106, 120, 121, 134, 135, 138, 139, 145, 165, 191, 209, 259, 263], "search": [16, 17, 160, 191], "flatten": [16, 17, 78, 155, 158, 181, 182, 183, 184, 256, 258], "descend": [18, 165, 251, 252], "stabl": [18, 165, 212], "sort": [18, 160, 191, 206, 238, 239, 251, 252], "ascend": [18, 160, 165, 206], "stabil": [18, 165], "maintain": [18, 165, 207, 262, 264], "rel": [18, 19, 55, 99, 135, 139, 158, 165, 206, 237, 244, 247, 254], "compar": [18, 165, 181, 182, 183, 184, 208, 213, 263, 265], "properti": [19, 53, 54, 55, 56, 57, 58, 115, 206, 209, 213, 218, 262], "transpos": [19, 40, 55, 132, 133, 176, 234, 238, 247, 251, 258], "instanc": [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 55, 59, 89, 201, 204, 206, 213], "permut": [19, 55, 148], "revers": [19, 55, 65, 99], "origin": [19, 55, 65, 107, 140, 156, 158, 206, 210, 220, 222, 225, 226, 229, 230, 231, 233, 262, 263], "limit": [19, 98, 108, 116, 208, 258, 261], "matric": [19, 40, 55, 132, 133, 137, 178, 179, 234, 236, 237, 238, 239, 240, 242, 243, 244, 247, 248, 249, 250, 251, 252, 254, 258], "deviat": [19, 170, 208, 214, 262, 264], "et": [19, 251, 252], "al": 19, "intent": [19, 65], "found": [19, 209, 212, 264, 265], "problemat": [19, 63, 207, 210], "conflict": 19, "definit": [19, 86, 87, 163, 164, 174, 175, 206, 234, 263], "batch": [19, 256, 258], "cetera": [19, 251, 252], "permute_dim": [19, 191], "interfac": [19, 212, 258, 262, 264], "ab": [20, 107, 150, 191, 206, 242, 256], "augend": 21, "addend": 21, "self_i": [22, 28, 30, 31, 33, 36, 37, 38, 39, 41, 43, 44, 45, 46, 48, 50, 51, 52], "other_i": [22, 28, 30, 31, 33, 37, 38, 39, 41, 43, 45, 47, 48, 50, 51, 52], "bitwise_and": [22, 191], "api_vers": [23, 262], "object": [23, 24, 25, 26, 29, 34, 35, 53, 57, 59, 60, 89, 98, 102, 108, 110, 112, 113, 114, 191, 192, 201, 204, 206, 210, 212, 213, 216, 218, 257, 259, 263, 264], "2020": [23, 218, 259, 261, 262], "10": [23, 27, 124, 192, 262], "latest": [23, 212], "modul": [23, 204, 259, 263, 264, 265], "everi": [23, 103, 104, 248, 262], "top": [23, 204, 262, 264], "level": [23, 201, 207, 212, 213, 257, 258, 262, 263], "public": [23, 257, 263, 264], "well": [23, 207, 209, 212, 213, 248, 264, 265], "part": [23, 35, 178, 179, 201, 206, 212, 217, 259, 262, 264], "convert": [24, 25, 29, 34, 35, 60, 102, 201, 206, 207, 209, 212, 262, 264], "handl": [24, 26, 61, 64, 86, 88, 102, 124, 126, 150, 151, 153, 161, 163, 167, 172, 174, 206, 207, 209, 210, 213, 214, 254, 262], "lazi": [24, 25, 29, 34, 35, 204, 206, 215, 264], "languag": [24, 25, 29, 34, 35, 210, 214, 216, 258, 262, 264], "therefor": [24, 25, 29, 34, 35, 204, 212, 213, 214, 216, 218, 259, 262, 264], "abl": [24, 25, 29, 34, 35, 102, 210, 212, 213, 262, 264], "kind": [24, 25, 26, 29, 34, 35, 47, 51, 77, 90, 98, 102, 104, 108, 113, 115, 116, 150, 201, 206, 216, 258, 261], "here": [24, 25, 26, 29, 34, 35, 192, 201, 210, 212, 217, 218, 264], "valueerror": [24, 25, 26, 29, 34, 35, 60, 102, 156, 168, 264], "instead": [24, 25, 29, 34, 35, 63, 209, 212, 216, 263, 264], "2023": [24, 25, 26, 29, 34, 35, 59, 63, 77, 85, 88, 102, 107, 134, 135, 138, 139, 140, 151, 155, 160, 162, 172, 173, 176, 177, 181, 182, 183, 184, 185, 187, 220, 221, 222, 224, 225, 226, 229, 230, 232, 235, 254], "new": [25, 26, 77, 79, 85, 88, 95, 98, 102, 103, 104, 107, 108, 109, 116, 135, 139, 140, 146, 147, 152, 155, 156, 160, 162, 169, 173, 177, 185, 189, 190, 204, 206, 207, 210, 212, 213, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 259, 262, 263, 264], "stream": [26, 59, 213], "max_vers": [26, 206], "dl_devic": [26, 206], "enum": [26, 27], "pycapsul": 26, "export": [26, 102, 206, 212, 263], "from_dlpack": [26, 27, 191, 206, 212], "dlpack": [26, 27, 102, 206], "capsul": 26, "cuda": [26, 27, 207, 212, 264], "rocm": [26, 27, 207], "pointer": 26, "produc": [26, 238, 248, 251, 264], "instruct": 26, "safe": [26, 122], "insert": [26, 95, 160, 206], "wait": 26, "event": [26, 261], "larger": [26, 98, 158, 170, 186, 247], "below": [26, 101, 102, 178, 179, 194, 212, 213, 237, 254], "signal": [26, 224, 228, 264], "ownership": 26, "stai": 26, "On": 26, "cpu": [26, 27, 204, 207, 212, 213, 258, 262, 264], "queue": [26, 59, 213], "similar": [26, 154, 192, 207, 209, 211, 262, 263, 264], "mechan": [26, 102, 204, 206, 207, 215, 257, 262], "most": [26, 204, 213, 238, 258, 262, 264], "yet": [26, 218, 262], "sycl": 26, "want": [26, 90, 141, 207, 211, 212, 262, 264, 265], "cl": 26, "agre": 26, "assum": [26, 86, 102, 163, 174, 204, 209, 213, 257, 262], "legaci": 26, "per": [26, 155, 207, 212, 260], "thread": [26, 262, 264], "disallow": 26, "due": [26, 42, 57, 58, 122, 141, 155, 173, 208, 209, 258, 262], "ambigu": [26, 63, 101, 210], "construct": [26, 177, 204, 206, 207, 216, 262], "particular": [26, 192, 207, 209, 212, 213, 218, 258, 261, 262, 264, 265], "kdlcpu": 26, "safeti": [26, 59], "prefer": [26, 101, 204, 258, 264], "develop": [26, 208, 262, 263, 264, 265], "who": [26, 208, 262, 263], "think": 26, "cost": 26, "caller": 26, "major": [26, 144, 155, 192, 259], "minor": [26, 259], "verifi": [26, 262], "even": [26, 90, 141, 150, 159, 208, 209, 210, 221, 223, 227, 232, 248, 258, 262, 264], "pass": [26, 65, 204, 208, 213], "format": [26, 27, 259], "__dlpack_device__": [26, 102, 191, 212], "buffererror": [26, 102, 206, 212], "v2023": [26, 102], "mandat": [26, 102, 262], "offer": [26, 102, 207, 212, 213, 217, 262, 264], "referenc": [26, 262], "underli": [26, 67, 70, 72, 102, 208, 249, 258], "interpret": [26, 102, 107, 209, 210, 265], "enumer": 26, "made": [26, 102, 204, 209, 257, 259, 262, 264], "never": [26, 60, 102, 156, 212, 262], "deem": [26, 102], "cross": [26, 102, 206, 213, 258, 262], "movement": [26, 102], "request": [26, 102, 262], "reus": [26, 60, 102, 210, 262], "buffer": [26, 60, 102, 210, 212], "happen": [26, 102, 210, 213, 216, 258], "dlpack_flag_bitmask_is_copi": 26, "flag": 26, "understood": [26, 201], "interchang": [26, 102, 204, 207, 215, 262], "detail": [26, 102, 144, 155, 181, 182, 183, 184, 191, 192, 203, 204, 211, 213, 217, 258, 262, 264], "stride": [26, 102, 210, 212], "fail": [26, 102, 262], "reason": [26, 102, 154, 175, 210, 212, 214, 258, 262, 263], "incorrect": 26, "scheme": [26, 259], "semver": 26, "abi": [26, 207, 212], "break": [26, 214], "introduc": [26, 63, 101, 158, 218, 263], "goe": 26, "togeth": [26, 201, 212], "dlmanagedtensorvers": 26, "struct": 26, "later": 26, "introduct": 26, "becaus": [26, 201, 207, 210, 213, 214, 216, 218, 238, 251, 262, 264, 265], "keep": [26, 201, 207, 262], "march": 26, "2025": 26, "onward": 26, "ideal": [26, 258], "late": 26, "okai": 26, "we": [26, 209, 251, 262], "get": [26, 98, 108, 207, 210, 212, 213], "now": [26, 102, 216, 262, 264], "our_own_dlpack_vers": 26, "fill": [26, 103, 104, 146, 147, 189, 190, 206], "field": [26, 181, 182, 183, 209, 238, 248, 249, 251, 262], "understand": [26, 247, 262, 263], "u": [26, 234, 247, 251], "just": [26, 262, 264], "our": 26, "elif": 26, "fine": [26, 218, 262], "own": [26, 204, 210, 262], "re": [26, 158, 207, 210, 218, 264], 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[[60, "asarray"]], "Note": [[60, null], [102, null], [122, null]], "asin": [[61, "asin"]], "asinh": [[62, "asinh"]], "astype": [[63, "astype"]], "atan": [[64, "atan"]], "atan2": [[65, "atan2"]], "atanh": [[66, "atanh"]], "bitwise_and": [[67, "bitwise-and"]], "bitwise_invert": [[68, "bitwise-invert"]], "bitwise_left_shift": [[69, "bitwise-left-shift"]], "bitwise_or": [[70, "bitwise-or"]], "bitwise_right_shift": [[71, "bitwise-right-shift"]], "bitwise_xor": [[72, "bitwise-xor"]], "broadcast_arrays": [[73, "broadcast-arrays"]], "broadcast_to": [[74, "broadcast-to"]], "can_cast": [[75, "can-cast"]], "ceil": [[76, "ceil"]], "clip": [[77, "clip"]], "concat": [[78, "concat"]], "conj": [[79, "conj"]], "e": [[80, "e"]], "inf": [[81, "inf"]], "nan": [[82, "nan"]], "newaxis": [[83, "newaxis"]], "pi": [[84, "pi"]], "copysign": [[85, "copysign"]], "cos": [[86, "cos"]], "cosh": [[87, "cosh"]], "cumulative_sum": [[88, "cumulative-sum"]], "divide": [[90, "divide"]], "empty": [[91, "empty"]], "empty_like": [[92, "empty-like"]], "equal": [[93, "equal"]], "exp": [[94, "exp"]], "expand_dims": [[95, "expand-dims"]], "expm1": [[96, "expm1"]], "eye": [[97, "eye"]], "finfo": [[98, "finfo"]], "flip": [[99, "flip"]], "floor": [[100, "floor"]], "floor_divide": [[101, "floor-divide"]], "from_dlpack": [[102, "from-dlpack"]], "full": [[103, "full"]], "full_like": [[104, "full-like"]], "greater": [[105, "greater"]], "greater_equal": [[106, "greater-equal"]], "hypot": [[107, "hypot"]], "iinfo": [[108, "iinfo"]], "imag": [[109, "imag"]], "__array_namespace_info__": [[110, "array-namespace-info"]], "capabilities": [[111, "capabilities"]], "default_device": [[112, "default-device"]], "default_dtypes": [[113, "default-dtypes"]], "devices": [[114, "devices"]], "dtypes": [[115, "dtypes"]], "isdtype": [[116, "isdtype"]], "isfinite": [[117, "isfinite"]], "isinf": [[118, "isinf"]], "isnan": [[119, "isnan"]], "less": [[120, "less"]], "less_equal": [[121, "less-equal"]], "linspace": [[122, "linspace"]], "log": [[123, "log"]], "log10": [[124, "log10"]], "log1p": [[125, "log1p"]], "log2": [[126, "log2"]], "logaddexp": [[127, "logaddexp"]], "logical_and": [[128, "logical-and"]], "logical_not": [[129, "logical-not"]], "logical_or": [[130, "logical-or"]], "logical_xor": [[131, "logical-xor"]], "matmul": [[132, "matmul"], [241, "matmul"]], "matrix_transpose": [[133, "matrix-transpose"], [245, "matrix-transpose"]], "max": [[134, "max"]], "maximum": [[135, "maximum"]], "mean": [[136, "mean"]], "meshgrid": [[137, "meshgrid"]], "min": [[138, "min"]], "minimum": [[139, "minimum"]], "moveaxis": [[140, "moveaxis"]], "multiply": [[141, "multiply"]], "negative": [[142, "negative"]], "nextafter": [[143, "nextafter"]], "nonzero": [[144, "nonzero"]], "Data-dependent output shape": [[144, null], [155, null], [181, null], [182, null], [183, null], [184, null], [192, null], [211, null]], "not_equal": [[145, "not-equal"]], "ones": [[146, "ones"]], "ones_like": [[147, "ones-like"]], "permute_dims": [[148, "permute-dims"]], "positive": [[149, "positive"]], "pow": [[150, "pow"]], "prod": [[151, "prod"]], "real": [[152, "real"]], "reciprocal": [[153, "reciprocal"]], "remainder": [[154, "remainder"]], "repeat": [[155, "repeat"]], "reshape": [[156, "reshape"]], "result_type": [[157, "result-type"]], "roll": [[158, "roll"]], "round": [[159, "round"]], "searchsorted": [[160, "searchsorted"]], "sign": [[161, "sign"]], "signbit": [[162, "signbit"]], "sin": [[163, "sin"]], "sinh": [[164, "sinh"]], "sort": [[165, "sort"]], "sqrt": [[166, "sqrt"]], "square": [[167, "square"]], "squeeze": [[168, "squeeze"]], "stack": [[169, "stack"]], "std": [[170, "std"]], "subtract": [[171, "subtract"]], "sum": [[172, "sum"]], "take": [[173, "take"]], "tan": [[174, "tan"]], "tanh": [[175, "tanh"]], "tensordot": [[176, "tensordot"], [253, "tensordot"]], "tile": [[177, "tile"]], "tril": [[178, "tril"]], "triu": [[179, "triu"]], "trunc": [[180, "trunc"]], "unique_all": [[181, "unique-all"]], "unique_counts": [[182, "unique-counts"]], "unique_inverse": [[183, "unique-inverse"]], "unique_values": [[184, "unique-values"]], "unstack": [[185, "unstack"]], "var": [[186, "var"]], "vecdot": [[187, "vecdot"], [255, "vecdot"]], "where": [[188, "where"]], "zeros": [[189, "zeros"]], "zeros_like": [[190, "zeros-like"]], "API specification": [[191, "api-specification"], [191, null]], "Indexing": [[192, "indexing"]], "Single-axis Indexing": [[192, "single-axis-indexing"]], "Slice Syntax": [[192, "slice-syntax"]], "Multi-axis Indexing": [[192, "multi-axis-indexing"]], "Boolean Array Indexing": [[192, "boolean-array-indexing"]], "Return Values": [[192, "return-values"]], "Indexing Functions": [[193, "indexing-functions"]], "Inspection": [[194, "inspection"]], "Inspection APIs": [[194, "inspection-apis"], [206, "inspection-apis"]], "Linear Algebra Functions": [[195, "linear-algebra-functions"]], "Manipulation Functions": [[196, "manipulation-functions"]], "Searching Functions": [[197, "searching-functions"]], "Set Functions": [[198, "set-functions"]], "Sorting Functions": [[199, "sorting-functions"]], "Statistical Functions": [[200, "statistical-functions"], [208, "statistical-functions"]], "Type Promotion Rules": [[201, "type-promotion-rules"]], "Rules": [[201, "rules"]], "Signed integer type promotion table": [[201, "signed-integer-type-promotion-table"]], "Unsigned integer type promotion table": [[201, "unsigned-integer-type-promotion-table"]], "Mixed unsigned and signed integer type promotion table": [[201, "mixed-unsigned-and-signed-integer-type-promotion-table"]], "Floating-point type promotion table": [[201, "floating-point-type-promotion-table"]], "Notes": [[201, "notes"]], "Mixing arrays with Python scalars": [[201, "mixing-arrays-with-python-scalars"]], "Utility Functions": [[202, "utility-functions"]], "Version": [[203, "version"]], "Assumptions": [[204, "assumptions"]], "Hardware and software environments": [[204, "hardware-and-software-environments"]], "Dependencies": [[204, "dependencies"]], "Backwards compatibility": [[204, "backwards-compatibility"], [259, "backwards-compatibility"]], "Production code & interactive use": [[204, "production-code-interactive-use"]], "Benchmark suite": [[205, "benchmark-suite"]], "Changelog per API standard version": [[206, "changelog-per-api-standard-version"]], "Changelog": [[206, "changelog"]], "v2023.12": [[206, "v2023-12"]], "Updates": [[206, "updates"], [206, "id3"]], "Normative": [[206, "normative"]], "APIs": [[206, "apis"], [206, "id1"], [206, "id4"], [206, "id8"]], "Extensions": [[206, "extensions"], [206, "id2"], [206, "id5"], [206, "id9"], [257, "extensions"]], "Additions": [[206, "additions"], [206, "id7"]], "Breaking Changes": [[206, "breaking-changes"]], "Errata": [[206, "errata"], [206, "id10"]], "v2022.12": [[206, "v2022-12"]], "Complex Number Support": [[206, "complex-number-support"], [206, "id6"]], "C API": [[207, "c-api"]], "Example situations for C/Cython usage": [[207, "example-situations-for-c-cython-usage"]], "Situation 1: a Python package that is mostly pure Python, with a limited number of Cython extensions": [[207, "situation-1-a-python-package-that-is-mostly-pure-python-with-a-limited-number-of-cython-extensions"]], "Situation 2: a Python package that contains a lot of Cython code": [[207, "situation-2-a-python-package-that-contains-a-lot-of-cython-code"]], "Situation 3: a Python package that uses the NumPy or Python C API directly": [[207, "situation-3-a-python-package-that-uses-the-numpy-or-python-c-api-directly"]], "Device support": [[207, "device-support"], [213, "device-support"]], "Other longer-term approaches": [[207, "other-longer-term-approaches"]], "Further Python API standardization": [[207, "further-python-api-standardization"]], "HPy": [[207, "hpy"]], "Accuracy": [[208, "accuracy"]], "Arithmetic Operations": [[208, "arithmetic-operations"]], "Mathematical Functions": [[208, "mathematical-functions"]], "Linear Algebra": [[208, "linear-algebra"]], "Complex Numbers": [[209, "complex-numbers"]], "The Complex Plane": [[209, "the-complex-plane"]], "Branch Cuts": [[209, "branch-cuts"]], "Complex Number Ordering": [[209, "complex-number-ordering"]], "Valued-based Promotion": [[209, "valued-based-promotion"]], "Copy-view behaviour and mutability": [[210, "copy-view-behaviour-and-mutability"]], "Mutating views": [[210, null]], "Data-dependent output shapes": [[211, "data-dependent-output-shapes"]], "Data interchange mechanisms": [[212, "data-interchange-mechanisms"]], "DLPack: An in-memory tensor structure": [[212, "dlpack-an-in-memory-tensor-structure"]], "Non-supported use cases": [[212, "non-supported-use-cases"]], "Intended usage": [[213, "intended-usage"]], "Syntax for device assignment": [[213, "syntax-for-device-assignment"]], "Semantics": [[213, "semantics"]], "Out of scope for device support": [[213, "out-of-scope-for-device-support"]], "Exceptions": [[214, "exceptions"]], "Design topics & constraints": [[215, "design-topics-constraints"], [215, null]], "Lazy vs. eager execution": [[216, "lazy-vs-eager-execution"]], "Parallelism": [[217, "parallelism"]], "Static typing": [[218, "static-typing"]], "Fourier transform Functions": [[219, "fourier-transform-functions"]], "Extension name and usage": [[219, "extension-name-and-usage"], [258, "extension-name-and-usage"]], "fft": [[220, "fft"]], "fftfreq": [[221, "fftfreq"]], "fftn": [[222, "fftn"]], "fftshift": [[223, "fftshift"]], "hfft": [[224, "hfft"]], "ifft": [[225, "ifft"]], "ifftn": [[226, "ifftn"]], "ifftshift": [[227, "ifftshift"]], "ihfft": [[228, "ihfft"]], "irfft": [[229, "irfft"]], "irfftn": [[230, "irfftn"]], "rfft": [[231, "rfft"]], "rfftfreq": [[232, "rfftfreq"]], "rfftn": [[233, "rfftn"]], "cholesky": [[234, "cholesky"]], "cross": [[235, "cross"]], "det": [[236, "det"]], "diagonal": [[237, "diagonal"]], "eigh": [[238, "eigh"]], "eigvalsh": [[239, "eigvalsh"]], "inv": [[240, "inv"]], "matrix_norm": [[242, "matrix-norm"]], "matrix_power": [[243, "matrix-power"]], "matrix_rank": [[244, "matrix-rank"]], "outer": [[246, "outer"]], "pinv": [[247, "pinv"]], "qr": [[248, "qr"]], "slogdet": [[249, "slogdet"]], "solve": [[250, "solve"]], "svd": [[251, "svd"]], "svdvals": [[252, "svdvals"]], "trace": [[254, "trace"]], "vector_norm": [[256, "vector-norm"]], "Extension modules:": [[257, null]], "Linear Algebra Extension": [[258, "linear-algebra-extension"]], "Design Principles": [[258, "design-principles"]], "Future API standard evolution": [[259, "future-api-standard-evolution"]], "Scope extensions": [[259, "scope-extensions"]], "Versioning": [[259, "versioning"]], "Python array API standard": [[260, "python-array-api-standard"]], "Contents": [[260, "contents"]], "Context": [[260, null]], "API": [[260, null]], "Methodology and Usage": [[260, null]], "Other": [[260, null]], "License": [[261, "license"]], "Purpose and scope": [[262, "purpose-and-scope"]], "Introduction": [[262, "introduction"], [263, "introduction"]], "This API standard": [[262, "this-api-standard"]], "History": [[262, "history"]], "Scope (includes out-of-scope / non-goals)": [[262, "scope-includes-out-of-scope-non-goals"]], "In scope": [[262, "in-scope"]], "Out of scope": [[262, "out-of-scope"]], "Implications of in/out of scope": [[262, "implications-of-in-out-of-scope"]], "Stakeholders": [[262, "stakeholders"]], "How to read this document": [[262, "how-to-read-this-document"]], "How to adopt this API": [[262, "how-to-adopt-this-api"]], "Checking an array object for Compliance": [[262, "checking-an-array-object-for-compliance"]], "Discoverability of conforming implementations": [[262, "discoverability-of-conforming-implementations"]], "Optional feature": [[262, null]], "Conformance": [[262, "conformance"]], "Terms and Definitions": [[262, "terms-and-definitions"]], "Normative References": [[262, "normative-references"]], "Usage Data": [[263, "usage-data"]], "Design": [[263, "design"]], "Usage": [[263, "usage"]], "Use in Decision-Making": [[263, "use-in-decision-making"]], "Use cases": [[264, "use-cases"]], "Types of use cases": [[264, "types-of-use-cases"]], "Concrete use cases": [[264, "concrete-use-cases"]], "Use case 1: add hardware accelerator and distributed support to SciPy": [[264, "use-case-1-add-hardware-accelerator-and-distributed-support-to-scipy"]], "Use case 2: simplify einops by removing the backend system": [[264, "use-case-2-simplify-einops-by-removing-the-backend-system"]], "Use case 3: adding a Python API to xtensor": [[264, "use-case-3-adding-a-python-api-to-xtensor"]], "Use case 4: make JIT compilation of array computations easier and more robust": [[264, "use-case-4-make-jit-compilation-of-array-computations-easier-and-more-robust"]], "Verification - test suite": [[265, "verification-test-suite"]], "Measuring conformance": [[265, "measuring-conformance"]], "Running the tests": [[265, "running-the-tests"]]}, "indexentries": {"__array_api_version__ (in module array_api)": [[8, "array_api.__array_api_version__"]], "abs() (in module array_api)": [[9, "array_api.abs"]], "acos() (in module array_api)": [[10, "array_api.acos"]], "acosh() (in module array_api)": [[11, "array_api.acosh"]], "add() (in module array_api)": [[12, "array_api.add"]], "all() (in module array_api)": [[13, "array_api.all"]], "any() (in module array_api)": [[14, "array_api.any"]], "arange() (in module array_api)": [[15, "array_api.arange"]], "argmax() (in module array_api)": [[16, "array_api.argmax"]], "argmin() (in module array_api)": [[17, "array_api.argmin"]], "argsort() (in module array_api)": [[18, "array_api.argsort"]], "t (array property)": [[19, "array_api.array.T"]], "__abs__() (array method)": [[20, "array_api.array.__abs__"]], "__add__() (array method)": [[21, "array_api.array.__add__"]], "__and__() (array method)": [[22, "array_api.array.__and__"]], "__array_namespace__() (array method)": [[23, "array_api.array.__array_namespace__"]], "__bool__() (array method)": [[24, "array_api.array.__bool__"]], "__complex__() (array method)": [[25, "array_api.array.__complex__"]], "__dlpack__() (array method)": [[26, "array_api.array.__dlpack__"]], "__dlpack_device__() (array method)": [[27, "array_api.array.__dlpack_device__"]], "__eq__() (array method)": [[28, "array_api.array.__eq__"]], "__float__() (array method)": [[29, "array_api.array.__float__"]], "__floordiv__() (array method)": [[30, "array_api.array.__floordiv__"]], "__ge__() (array method)": [[31, "array_api.array.__ge__"]], "__getitem__() (array method)": [[32, "array_api.array.__getitem__"]], "__gt__() (array method)": [[33, "array_api.array.__gt__"]], "__index__() (array method)": [[34, "array_api.array.__index__"]], "__int__() (array method)": [[35, "array_api.array.__int__"]], "__invert__() (array method)": [[36, "array_api.array.__invert__"]], "__le__() (array method)": [[37, "array_api.array.__le__"]], "__lshift__() (array method)": [[38, "array_api.array.__lshift__"]], "__lt__() (array method)": [[39, "array_api.array.__lt__"]], "__matmul__() (array method)": [[40, "array_api.array.__matmul__"]], "__mod__() (array method)": [[41, "array_api.array.__mod__"]], "__mul__() (array method)": [[42, "array_api.array.__mul__"]], "__ne__() (array method)": [[43, "array_api.array.__ne__"]], "__neg__() (array method)": [[44, "array_api.array.__neg__"]], "__or__() (array method)": [[45, "array_api.array.__or__"]], "__pos__() (array method)": [[46, "array_api.array.__pos__"]], "__pow__() (array method)": [[47, "array_api.array.__pow__"]], "__rshift__() (array method)": [[48, "array_api.array.__rshift__"]], "__setitem__() (array method)": [[49, "array_api.array.__setitem__"]], "__sub__() (array method)": [[50, "array_api.array.__sub__"]], "__truediv__() (array method)": [[51, "array_api.array.__truediv__"]], "__xor__() (array method)": [[52, "array_api.array.__xor__"]], "device (array property)": [[53, "array_api.array.device"]], "dtype (array property)": [[54, "array_api.array.dtype"]], "mt (array property)": [[55, "array_api.array.mT"]], "ndim (array property)": [[56, "array_api.array.ndim"]], "shape (array property)": [[57, "array_api.array.shape"]], "size (array property)": [[58, "array_api.array.size"]], "to_device() (array method)": [[59, "array_api.array.to_device"]], "asarray() (in module array_api)": [[60, "array_api.asarray"]], "asin() (in module array_api)": [[61, "array_api.asin"]], "asinh() (in module array_api)": [[62, "array_api.asinh"]], "astype() (in module array_api)": [[63, "array_api.astype"]], "atan() (in module array_api)": [[64, "array_api.atan"]], "atan2() (in module array_api)": [[65, "array_api.atan2"]], "atanh() (in module array_api)": [[66, "array_api.atanh"]], "bitwise_and() (in module array_api)": [[67, "array_api.bitwise_and"]], "bitwise_invert() (in module array_api)": [[68, "array_api.bitwise_invert"]], "bitwise_left_shift() (in module array_api)": [[69, "array_api.bitwise_left_shift"]], "bitwise_or() (in module array_api)": [[70, "array_api.bitwise_or"]], "bitwise_right_shift() (in module array_api)": [[71, "array_api.bitwise_right_shift"]], "bitwise_xor() (in module array_api)": [[72, "array_api.bitwise_xor"]], "broadcast_arrays() (in module array_api)": [[73, "array_api.broadcast_arrays"]], "broadcast_to() (in module array_api)": [[74, "array_api.broadcast_to"]], "can_cast() (in module array_api)": [[75, "array_api.can_cast"]], "ceil() (in module array_api)": [[76, "array_api.ceil"]], "clip() (in module array_api)": [[77, "array_api.clip"]], "concat() (in module array_api)": [[78, "array_api.concat"]], "conj() (in module array_api)": [[79, "array_api.conj"]], "e (in module array_api.constants)": [[80, "array_api.constants.e"]], "inf (in module array_api.constants)": [[81, "array_api.constants.inf"]], "nan (in module array_api.constants)": [[82, "array_api.constants.nan"]], "newaxis (in module array_api.constants)": [[83, "array_api.constants.newaxis"]], "pi (in module 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265], "e": [0, 1, 2, 5, 7, 9, 10, 11, 18, 19, 20, 26, 40, 43, 47, 49, 51, 55, 57, 62, 63, 65, 66, 69, 71, 76, 77, 78, 86, 87, 88, 90, 93, 94, 95, 100, 101, 102, 107, 109, 115, 116, 122, 123, 124, 125, 126, 132, 134, 136, 137, 138, 140, 141, 142, 144, 145, 146, 147, 149, 150, 151, 152, 154, 155, 157, 159, 160, 162, 163, 164, 165, 166, 168, 169, 170, 172, 173, 174, 175, 176, 177, 181, 182, 183, 184, 186, 191, 192, 199, 201, 206, 207, 208, 209, 210, 211, 212, 213, 216, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 235, 238, 239, 242, 244, 247, 249, 250, 251, 252, 254, 256, 257, 258, 259, 262, 263, 264], "number": [0, 1, 5, 9, 10, 11, 12, 13, 14, 16, 17, 18, 25, 26, 31, 33, 35, 37, 39, 44, 56, 58, 60, 61, 62, 63, 64, 65, 66, 73, 76, 79, 82, 87, 88, 90, 93, 94, 95, 96, 97, 98, 100, 101, 103, 105, 106, 107, 108, 109, 111, 117, 118, 120, 121, 122, 123, 125, 134, 135, 136, 137, 138, 139, 140, 141, 142, 144, 145, 146, 147, 148, 150, 151, 152, 154, 155, 157, 158, 159, 160, 161, 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220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 236, 239, 240, 244, 246, 247, 256, 258, 262], "apart": 0, "from": [0, 5, 13, 14, 15, 19, 26, 44, 59, 60, 63, 75, 78, 88, 92, 99, 101, 102, 103, 104, 107, 122, 123, 125, 137, 142, 147, 150, 151, 156, 157, 166, 168, 170, 172, 173, 175, 181, 183, 186, 187, 188, 190, 192, 201, 204, 206, 207, 208, 209, 212, 213, 214, 216, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 238, 249, 251, 254, 258, 259, 261, 262, 263, 264, 265], "ndim": [0, 187, 191, 235, 248, 251, 252], "devic": [0, 5, 15, 26, 27, 59, 60, 63, 91, 92, 97, 102, 103, 104, 110, 112, 113, 115, 122, 146, 147, 155, 178, 179, 189, 190, 191, 192, 194, 206, 212, 215, 221, 232, 248, 258, 262, 264], "dtype": [0, 5, 15, 26, 60, 63, 73, 75, 88, 89, 91, 92, 97, 98, 102, 103, 104, 108, 110, 116, 122, 146, 147, 151, 157, 172, 189, 190, 191, 201, 204, 206, 212, 218, 254, 262, 263, 264], "all": [0, 5, 15, 19, 23, 26, 60, 63, 87, 90, 97, 99, 102, 111, 115, 141, 158, 164, 175, 177, 178, 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166, 170, 172, 186, 191, 192, 201, 206, 207, 208, 209, 210, 211, 212, 213, 217, 242, 256, 258, 259, 261, 263, 264], "those": [0, 5, 7, 15, 23, 88, 90, 113, 115, 141, 144, 151, 155, 172, 201, 206, 209, 210, 213, 214, 216, 248, 251, 252, 254, 257, 258, 259, 262, 263, 264], "mean": [0, 26, 191, 204, 210, 212, 213, 218, 259, 262], "var": [0, 191], "std": [0, 191], "which": [0, 1, 5, 7, 8, 13, 14, 15, 16, 17, 18, 19, 26, 30, 40, 41, 44, 59, 60, 63, 75, 77, 78, 83, 88, 91, 92, 95, 97, 98, 99, 101, 102, 103, 104, 107, 108, 111, 113, 114, 115, 122, 132, 134, 136, 138, 142, 144, 146, 147, 151, 154, 155, 158, 160, 165, 169, 170, 172, 173, 174, 178, 179, 181, 182, 183, 184, 185, 186, 187, 189, 190, 192, 206, 207, 208, 209, 210, 211, 212, 213, 214, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 235, 242, 250, 251, 252, 254, 256, 257, 258, 259, 262, 263, 264], "some": [0, 96, 101, 113, 115, 125, 192, 207, 208, 209, 210, 213, 218, 262, 264, 265], "common": [0, 192, 201, 204, 213, 216, 217, 258, 262, 263, 264], "librari": [0, 5, 7, 26, 51, 57, 58, 59, 60, 63, 90, 96, 101, 102, 111, 113, 115, 116, 122, 125, 128, 129, 130, 131, 134, 135, 136, 138, 139, 144, 155, 160, 170, 175, 181, 182, 183, 184, 186, 191, 192, 204, 206, 207, 208, 209, 210, 211, 212, 213, 214, 216, 217, 218, 234, 238, 239, 248, 250, 257, 258, 259, 262, 263, 264, 265], "g": [0, 5, 9, 19, 20, 26, 47, 51, 57, 77, 88, 90, 102, 107, 109, 115, 116, 122, 134, 138, 141, 144, 151, 152, 155, 157, 159, 172, 177, 181, 182, 183, 184, 192, 199, 201, 206, 207, 208, 209, 210, 211, 212, 213, 216, 224, 228, 229, 230, 231, 233, 238, 239, 242, 249, 251, 252, 254, 256, 257, 258, 259, 262, 263, 264], "numpi": [0, 19, 63, 192, 204, 209, 210, 212, 213, 258, 262, 263, 264, 265], "scalar": [0, 2, 49, 60, 191, 192, 206, 216, 256, 264], "valu": [0, 1, 2, 5, 7, 9, 10, 11, 12, 15, 16, 17, 18, 20, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 39, 41, 43, 49, 51, 57, 58, 60, 61, 62, 63, 64, 65, 66, 76, 77, 78, 85, 86, 87, 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154, 160, 171, 176, 187, 188, 206, 235, 241, 246, 250, 253, 255], "x2": [0, 7, 12, 40, 65, 67, 69, 70, 71, 72, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 143, 145, 150, 154, 160, 171, 176, 187, 188, 206, 235, 241, 246, 250, 253, 255], "__add__": [0, 50, 191, 206], "add": [0, 7, 21, 88, 171, 172, 191, 192, 206, 207, 208, 213, 254], "__sub__": [0, 191, 206], "sub": [0, 192], "__mul__": [0, 191, 206], "mul": 0, "__truediv__": [0, 191, 206], "truediv": 0, "__floordiv__": [0, 191], "floordiv": 0, "__mod__": [0, 191], "mod": 0, "__pow__": [0, 191, 206], "pow": [0, 47, 191, 206, 208], "should": [0, 1, 5, 7, 9, 10, 11, 12, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 76, 77, 79, 85, 86, 87, 88, 90, 94, 95, 96, 98, 100, 101, 102, 105, 106, 107, 109, 113, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 137, 138, 139, 141, 142, 143, 149, 150, 151, 152, 153, 154, 156, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 170, 171, 172, 174, 175, 176, 178, 179, 180, 181, 182, 183, 184, 186, 187, 192, 199, 206, 207, 208, 209, 212, 213, 214, 218, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 234, 235, 236, 238, 239, 240, 242, 243, 244, 247, 248, 249, 250, 251, 252, 254, 256, 257, 258, 262, 264, 265], "defin": [0, 5, 12, 23, 30, 41, 49, 60, 65, 79, 90, 101, 103, 104, 115, 122, 134, 135, 136, 138, 139, 140, 141, 154, 161, 166, 167, 170, 178, 179, 186, 187, 191, 194, 199, 206, 208, 209, 218, 222, 223, 226, 227, 230, 233, 234, 238, 239, 240, 247, 248, 250, 258, 263, 264, 265], "real": [0, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 24, 25, 29, 30, 31, 33, 35, 37, 39, 41, 44, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 85, 86, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 105, 106, 107, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 142, 143, 144, 145, 146, 147, 150, 151, 154, 159, 160, 161, 162, 163, 164, 165, 166, 170, 172, 174, 175, 180, 186, 187, 189, 191, 201, 206, 209, 221, 224, 228, 229, 230, 231, 232, 233, 234, 238, 239, 240, 242, 244, 247, 248, 249, 250, 251, 252, 254, 256, 259], "data": [0, 1, 2, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 111, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 156, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 186, 187, 188, 189, 190, 191, 194, 201, 204, 207, 209, 210, 213, 215, 216, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 258, 259, 260, 261, 262, 265], "type": [0, 2, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 186, 187, 188, 189, 190, 191, 192, 194, 204, 207, 209, 210, 212, 214, 215, 216, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 258, 259, 262, 263], "__matmul__": [0, 191, 206], "matmul": [0, 40, 191, 201, 206, 258], "The": [0, 1, 5, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 58, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 90, 93, 94, 96, 99, 100, 101, 102, 105, 106, 107, 109, 110, 111, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 140, 141, 142, 143, 144, 145, 148, 149, 150, 151, 152, 153, 154, 155, 159, 160, 161, 162, 163, 164, 165, 166, 167, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 186, 187, 188, 192, 201, 204, 206, 207, 208, 210, 211, 212, 213, 216, 217, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 257, 258, 259, 261, 262, 263, 264, 265], "__invert__": [0, 191], "inv": [0, 206, 258], "invert": [0, 68, 240, 243, 250], "__inv__": 0, "__and__": [0, 191], "__or__": [0, 191], "__xor__": [0, 191], "xor": [0, 72, 131], "__lshift__": [0, 191], "lshift": 0, "__rshift__": [0, 191], "rshift": 0, "integ": [0, 5, 9, 13, 14, 15, 20, 22, 26, 29, 30, 34, 35, 36, 38, 41, 44, 45, 47, 48, 51, 52, 60, 67, 68, 69, 70, 71, 72, 76, 77, 88, 90, 100, 101, 103, 104, 108, 111, 115, 116, 122, 134, 136, 138, 142, 150, 151, 154, 155, 157, 159, 160, 170, 172, 173, 180, 186, 187, 191, 192, 206, 208, 209, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 243, 244, 254, 256, 262], "boolean": [0, 5, 22, 24, 25, 26, 29, 35, 36, 43, 45, 52, 57, 60, 63, 67, 68, 70, 72, 88, 89, 102, 103, 104, 111, 115, 116, 122, 128, 129, 130, 131, 144, 191, 201, 206], "__lt__": [0, 191, 206], "lt": 0, "__le__": [0, 191, 206], "le": 0, "__gt__": [0, 191, 206], "gt": [0, 248, 251], "__ge__": [0, 191, 206], "ge": 0, "__eq__": [0, 191, 206, 213], "eq": 0, "__ne__": [0, 191, 206], "ne": 0, "ar": [0, 1, 5, 7, 15, 16, 17, 19, 23, 24, 25, 26, 27, 29, 34, 35, 40, 49, 55, 58, 60, 77, 85, 86, 89, 90, 94, 97, 98, 99, 101, 102, 107, 114, 115, 122, 128, 129, 130, 131, 132, 141, 144, 150, 155, 158, 159, 163, 174, 175, 177, 181, 183, 187, 192, 201, 204, 206, 207, 208, 209, 210, 211, 212, 213, 214, 216, 217, 218, 220, 221, 222, 223, 225, 226, 227, 229, 230, 231, 232, 233, 235, 238, 239, 244, 247, 248, 251, 257, 258, 259, 262, 263, 264, 265], "onli": [0, 1, 5, 7, 16, 17, 23, 26, 40, 57, 58, 63, 99, 102, 107, 113, 115, 116, 122, 128, 129, 130, 131, 132, 136, 170, 186, 187, 191, 192, 201, 204, 206, 207, 209, 210, 212, 213, 214, 216, 218, 223, 235, 240, 247, 248, 250, 258, 259, 262, 263, 264, 265], "other": [0, 5, 21, 22, 23, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 50, 51, 52, 63, 89, 90, 96, 101, 102, 125, 140, 141, 170, 186, 192, 194, 204, 206, 208, 209, 210, 211, 212, 213, 214, 218, 235, 247, 257, 258, 261, 262, 264], "ani": [0, 1, 9, 10, 11, 23, 24, 25, 26, 28, 29, 34, 35, 43, 59, 61, 62, 66, 89, 93, 107, 117, 118, 145, 166, 191, 192, 201, 206, 209, 210, 212, 218, 251, 259, 261, 262, 265], "For": [0, 1, 5, 7, 9, 10, 11, 12, 16, 17, 18, 20, 24, 25, 26, 29, 30, 31, 33, 35, 37, 39, 41, 44, 57, 58, 61, 62, 64, 65, 66, 76, 79, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 105, 106, 107, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 134, 135, 137, 138, 139, 141, 142, 143, 145, 150, 151, 153, 154, 155, 159, 160, 161, 162, 163, 164, 165, 166, 167, 169, 172, 174, 175, 180, 181, 182, 183, 184, 192, 199, 204, 208, 209, 211, 213, 216, 221, 230, 232, 249, 251, 252, 254, 262, 264, 265], "backward": [0, 13, 14, 16, 17, 18, 31, 33, 37, 39, 105, 106, 120, 121, 122, 134, 135, 138, 139, 154, 165, 187, 192, 206, 209, 210, 214, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 262], "compat": [0, 1, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 74, 77, 85, 90, 93, 101, 105, 106, 107, 120, 121, 122, 127, 128, 130, 131, 132, 134, 135, 136, 138, 139, 141, 143, 145, 150, 151, 154, 155, 156, 165, 170, 171, 172, 186, 187, 188, 201, 206, 209, 210, 214, 235, 242, 244, 247, 250, 256, 262, 264], "mai": [0, 5, 7, 15, 16, 17, 18, 23, 26, 28, 31, 33, 37, 39, 43, 51, 57, 58, 59, 60, 89, 90, 93, 101, 102, 105, 106, 107, 110, 115, 116, 120, 121, 122, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 144, 145, 155, 156, 160, 165, 170, 175, 181, 182, 183, 184, 186, 191, 192, 199, 201, 204, 207, 208, 209, 210, 211, 212, 213, 214, 216, 217, 218, 238, 248, 249, 251, 257, 258, 262, 263, 264], "complex": [0, 5, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 24, 25, 29, 31, 33, 35, 37, 39, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 88, 90, 93, 94, 96, 97, 98, 103, 104, 105, 106, 107, 109, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 132, 134, 135, 137, 138, 139, 141, 142, 144, 145, 146, 147, 149, 150, 151, 152, 159, 161, 163, 164, 165, 166, 167, 171, 172, 174, 175, 176, 181, 182, 183, 184, 187, 201, 208, 212, 213, 215, 216, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 234, 235, 236, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 258, 262, 263], "howev": [0, 5, 16, 17, 18, 31, 33, 37, 39, 57, 88, 101, 105, 106, 107, 116, 120, 121, 122, 134, 135, 138, 139, 155, 160, 165, 173, 174, 175, 204, 207, 208, 209, 210, 211, 213, 258, 259, 262, 264], "inequ": [0, 16, 17, 18, 31, 33, 37, 39, 105, 106, 120, 121, 134, 135, 138, 139, 165], "unspecifi": [0, 5, 10, 11, 16, 17, 18, 30, 31, 33, 37, 39, 41, 47, 51, 60, 62, 66, 77, 78, 87, 90, 94, 96, 101, 103, 104, 105, 106, 120, 121, 122, 134, 135, 138, 139, 150, 154, 160, 164, 165, 166, 169, 173, 175, 192, 199, 201, 206, 222, 223, 226, 227, 230, 233, 238, 239, 262], "thu": [0, 5, 16, 17, 18, 30, 31, 33, 37, 39, 41, 47, 57, 60, 71, 77, 101, 103, 104, 105, 106, 120, 121, 122, 134, 135, 138, 139, 150, 154, 160, 165, 174, 175, 192, 199, 208, 209, 222, 223, 226, 227, 230, 233, 238, 239, 251, 258], "depend": [0, 5, 9, 10, 11, 16, 17, 18, 20, 26, 29, 31, 33, 37, 39, 44, 47, 51, 57, 58, 59, 61, 62, 63, 64, 65, 66, 77, 86, 87, 90, 94, 96, 105, 106, 111, 120, 121, 122, 123, 124, 125, 126, 141, 142, 150, 160, 163, 164, 165, 174, 175, 188, 199, 201, 208, 209, 212, 215, 216, 218, 238, 239, 248, 249, 250, 251, 258, 262, 264, 265], "see": [0, 5, 10, 11, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 33, 34, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 53, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 74, 77, 85, 90, 93, 96, 101, 102, 104, 105, 106, 107, 110, 111, 114, 120, 121, 123, 125, 127, 128, 130, 131, 132, 134, 135, 136, 138, 139, 141, 143, 144, 145, 150, 151, 153, 154, 155, 157, 161, 165, 166, 167, 170, 171, 172, 181, 182, 183, 184, 186, 187, 188, 191, 192, 201, 203, 204, 207, 209, 211, 212, 213, 218, 235, 242, 244, 247, 250, 256, 257, 262, 263, 264, 265], "order": [0, 5, 7, 16, 17, 18, 19, 26, 31, 33, 37, 39, 55, 60, 63, 65, 89, 99, 101, 102, 105, 106, 120, 121, 134, 135, 138, 139, 144, 155, 160, 165, 174, 175, 176, 181, 182, 183, 184, 192, 199, 201, 206, 208, 211, 212, 214, 229, 230, 238, 239, 242, 251, 252, 256, 258, 259, 262, 263], "chang": [0, 1, 9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 66, 86, 87, 90, 93, 94, 96, 97, 98, 102, 103, 104, 117, 118, 119, 122, 123, 124, 125, 126, 132, 134, 137, 138, 141, 142, 144, 145, 146, 147, 149, 150, 151, 156, 159, 161, 163, 164, 166, 167, 171, 172, 173, 174, 175, 176, 181, 182, 183, 184, 187, 204, 220, 221, 222, 224, 225, 226, 229, 230, 232, 234, 235, 236, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 259, 262, 264, 265], "shape": [0, 1, 18, 40, 55, 63, 73, 74, 78, 88, 91, 92, 95, 99, 103, 104, 111, 132, 133, 137, 146, 147, 156, 158, 160, 165, 169, 173, 176, 177, 178, 179, 185, 187, 189, 190, 191, 206, 215, 216, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 262, 264], "result": [0, 1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 24, 25, 28, 29, 30, 31, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 79, 85, 86, 87, 90, 93, 94, 96, 100, 101, 105, 106, 107, 109, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 142, 143, 145, 149, 150, 151, 152, 153, 154, 155, 157, 159, 160, 161, 162, 163, 164, 166, 167, 169, 170, 171, 172, 174, 175, 176, 180, 181, 186, 192, 199, 201, 206, 208, 209, 210, 216, 234, 235, 237, 242, 243, 249, 250, 256, 262, 263, 264, 265], "promot": [0, 1, 5, 10, 11, 12, 21, 22, 30, 40, 41, 42, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 78, 85, 86, 87, 90, 94, 96, 101, 104, 107, 122, 123, 124, 125, 126, 127, 132, 135, 136, 139, 141, 142, 150, 153, 154, 157, 163, 164, 166, 167, 169, 170, 171, 174, 175, 176, 186, 187, 188, 191, 206, 234, 235, 240, 242, 243, 244, 246, 247, 248, 249, 250, 256, 258], "rule": [0, 5, 7, 10, 11, 12, 21, 22, 30, 40, 41, 42, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 78, 85, 86, 87, 88, 90, 94, 96, 101, 103, 104, 107, 122, 123, 124, 125, 126, 127, 132, 135, 139, 141, 142, 150, 153, 154, 157, 161, 163, 164, 166, 167, 169, 171, 174, 175, 176, 187, 188, 191, 192, 206, 209, 212, 234, 235, 240, 242, 243, 244, 246, 247, 248, 249, 250, 256, 258, 262, 264], "broadcast": [0, 12, 13, 14, 16, 17, 21, 22, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 73, 74, 77, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 134, 135, 136, 138, 139, 141, 143, 145, 150, 151, 154, 155, 170, 171, 172, 176, 186, 187, 188, 191, 206, 235, 242, 244, 247, 250, 256, 262], "same": [0, 5, 7, 9, 12, 15, 18, 19, 20, 26, 32, 36, 38, 40, 41, 46, 48, 50, 55, 59, 63, 68, 73, 74, 76, 77, 78, 79, 88, 90, 92, 95, 98, 99, 100, 101, 102, 104, 109, 132, 133, 134, 136, 137, 138, 140, 141, 143, 147, 148, 149, 150, 151, 152, 154, 155, 156, 158, 159, 160, 161, 165, 168, 169, 170, 171, 172, 173, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 190, 192, 201, 204, 206, 209, 210, 212, 213, 218, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 234, 236, 237, 238, 240, 243, 247, 248, 249, 251, 252, 254, 257, 258, 262, 264], "behavior": [0, 5, 47, 49, 59, 60, 63, 77, 90, 101, 103, 104, 107, 122, 141, 150, 154, 160, 173, 181, 182, 183, 184, 191, 192, 194, 201, 204, 206, 208, 209, 216, 217, 222, 223, 226, 227, 230, 233, 258, 259, 262, 263, 264, 265], "special": [0, 9, 10, 11, 12, 20, 21, 24, 25, 28, 29, 30, 35, 41, 42, 43, 47, 51, 61, 62, 64, 65, 66, 76, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 136, 138, 139, 141, 143, 145, 150, 151, 153, 154, 159, 161, 162, 163, 164, 166, 167, 170, 172, 174, 175, 180, 186, 206, 207, 209, 249, 254], "case": [0, 1, 5, 7, 9, 10, 11, 12, 15, 20, 21, 24, 25, 26, 28, 29, 30, 35, 41, 42, 43, 47, 51, 60, 61, 62, 64, 65, 66, 76, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 102, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 136, 137, 138, 139, 141, 143, 145, 150, 151, 153, 154, 159, 161, 162, 163, 164, 166, 167, 170, 172, 174, 175, 180, 186, 192, 204, 206, 207, 208, 209, 210, 213, 214, 216, 248, 249, 251, 254, 258, 260, 262, 265], "its": [0, 5, 26, 40, 73, 90, 98, 132, 141, 156, 158, 208, 209, 212, 213, 257, 262, 263, 264], "respect": [0, 9, 12, 20, 21, 22, 28, 30, 31, 33, 37, 38, 39, 41, 42, 43, 45, 48, 50, 51, 52, 65, 67, 69, 70, 71, 72, 77, 87, 90, 93, 101, 105, 106, 107, 113, 120, 121, 122, 127, 128, 130, 131, 135, 137, 139, 140, 141, 143, 145, 154, 164, 171, 174, 175, 176, 181, 182, 187, 206, 208, 211, 213, 238, 248, 251], "binari": [0, 5, 67, 70, 72, 174, 175, 207], "two": [0, 1, 5, 15, 19, 40, 55, 65, 71, 97, 102, 132, 133, 137, 159, 176, 178, 179, 181, 182, 183, 184, 187, 192, 201, 212, 213, 216, 217, 222, 223, 226, 227, 230, 233, 234, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 258, 262, 263, 264, 265], "operand": [0, 1, 9, 10, 11, 12, 24, 25, 29, 35, 61, 62, 64, 65, 66, 76, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 138, 139, 141, 143, 145, 150, 151, 153, 154, 159, 161, 162, 163, 164, 166, 167, 172, 174, 175, 180, 201, 206, 208, 249, 254], "assign": [0, 210], "exampl": [0, 5, 12, 23, 26, 115, 116, 169, 191, 192, 204, 209, 210, 211, 213, 216, 217, 218, 254, 258, 262, 264, 265], "after": [0, 1, 26, 40, 132, 166, 177], "addit": [0, 5, 7, 12, 26, 50, 59, 88, 115, 171, 191, 192, 201, 207, 209, 212, 258, 262, 263, 265], "modifi": [0, 26, 210, 261], "equal": [0, 1, 9, 10, 11, 18, 20, 21, 22, 26, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 58, 61, 62, 63, 64, 65, 66, 69, 71, 77, 87, 89, 94, 96, 97, 103, 104, 107, 116, 118, 123, 124, 125, 126, 136, 144, 145, 146, 147, 150, 151, 159, 164, 165, 166, 170, 172, 173, 175, 176, 177, 181, 182, 183, 184, 186, 191, 192, 199, 206, 209, 213, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 237, 243, 244, 247, 248, 249, 250, 254, 262], "equival": [0, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 71, 101, 107, 128, 129, 130, 131, 154, 159, 173, 192, 201, 209, 210, 244, 247, 250, 256, 262], "discuss": [0, 93, 145, 206, 212, 213, 217, 262, 263, 264], "copi": [0, 1, 26, 59, 60, 63, 102, 156, 165, 206, 207, 212, 213, 215, 261, 262], "view": [0, 102, 215], "behaviour": [0, 215, 262, 264], "mutabl": [0, 215], "via": [0, 26, 101, 102, 173, 192, 207, 212, 213, 217, 219, 247, 257, 258, 259, 262], "__iadd__": 0, "__isub__": 0, "__imul__": 0, "__itruediv__": 0, "__ifloordiv__": 0, "__ipow__": 0, "__imod__": 0, "__imatmul__": 0, "__iand__": 0, "__ior__": 0, "__ixor__": 0, "__ilshift__": 0, "__irshift__": 0, "appli": [0, 12, 77, 78, 85, 90, 141, 157, 159, 169, 176, 192, 201, 204, 209, 220, 222, 225, 226, 229, 230, 231, 233, 244, 247, 258, 262, 264], "match": [0, 1, 5, 9, 20, 26, 63, 101, 154, 176, 181, 182, 214, 224, 228, 229, 230, 231, 233, 238, 239, 242, 256, 264], "op": [0, 201], "__radd__": 0, "__rsub__": 0, "__rmul__": 0, "__rtruediv__": 0, "__rfloordiv__": 0, "__rpow__": 0, "__rmod__": 0, "__rmatmul__": 0, "__rand__": 0, "__ror__": 0, "__rxor__": 0, "__rlshift__": 0, "__rrshift__": 0, "arrai": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 83, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 193, 194, 195, 196, 197, 198, 199, 200, 202, 203, 204, 206, 207, 208, 209, 210, 211, 212, 213, 214, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 263, 265], "refer": [1, 13, 14, 96, 97, 125, 170, 176, 177, 186, 187, 192, 209, 210, 218, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 250], "automat": [1, 262], "implicit": [1, 212, 213, 216, 262], "expans": [1, 262], "size": [1, 13, 14, 88, 95, 122, 144, 158, 168, 173, 176, 187, 191, 192, 211, 217, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 237, 246, 248, 251, 262], "without": [1, 7, 26, 57, 102, 113, 115, 144, 155, 156, 181, 182, 183, 184, 204, 207, 208, 211, 261, 262, 264], "purpos": [1, 5, 96, 107, 125, 204, 249, 258, 260, 261, 264], "make": [1, 7, 204, 207, 208, 210, 212, 216, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 257, 259, 262], "differ": [1, 12, 26, 49, 50, 77, 78, 88, 90, 98, 101, 102, 141, 151, 169, 171, 172, 192, 204, 210, 213, 214, 216, 227, 238, 248, 249, 251, 254, 258, 262, 263, 264], "element": [1, 9, 10, 11, 12, 13, 14, 15, 20, 21, 22, 24, 25, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 54, 58, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 99, 100, 101, 103, 104, 105, 106, 107, 109, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 145, 149, 150, 151, 152, 153, 154, 155, 156, 158, 159, 160, 161, 162, 163, 164, 166, 167, 168, 170, 171, 172, 173, 174, 175, 177, 178, 179, 180, 181, 182, 183, 184, 186, 188, 191, 192, 206, 208, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 238, 247, 248, 249, 251, 254, 262], "wise": [1, 9, 10, 12, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 64, 65, 67, 68, 69, 70, 71, 72, 77, 79, 85, 90, 93, 101, 105, 106, 107, 109, 120, 121, 127, 128, 129, 130, 131, 135, 139, 141, 143, 145, 150, 152, 153, 154, 171, 191, 206, 208, 262], "oper": [1, 12, 19, 24, 26, 34, 40, 57, 58, 59, 61, 64, 71, 86, 88, 90, 101, 124, 126, 132, 141, 150, 151, 153, 154, 157, 163, 167, 172, 174, 176, 191, 192, 198, 201, 206, 209, 210, 211, 212, 213, 254, 258, 259, 262, 263, 264], "facilit": [1, 199, 204], "user": [1, 7, 26, 110, 175, 204, 207, 208, 210, 213, 217, 258, 262, 263, 264], "ergonom": 1, "encourag": [1, 262, 263], "avoid": [1, 9, 63, 90, 96, 101, 107, 125, 141, 156, 207, 210, 213, 216, 258, 262, 264], "unnecessari": [1, 258], "can": [1, 7, 26, 60, 75, 110, 114, 116, 192, 201, 204, 207, 209, 210, 212, 213, 218, 247, 248, 251, 257, 258, 262, 263, 264, 265], "potenti": [1, 26, 96, 111, 125, 155, 210, 262], "enabl": [1, 26, 102, 213, 217, 218, 262], "more": [1, 5, 7, 15, 19, 26, 40, 58, 60, 63, 73, 88, 96, 99, 101, 125, 132, 144, 150, 155, 173, 181, 182, 183, 184, 192, 201, 204, 207, 208, 209, 210, 211, 212, 213, 214, 217, 218, 222, 223, 226, 227, 230, 233, 249, 258, 259, 262, 263, 265], "memori": [1, 26, 60, 102, 204, 210, 211, 213, 262, 264], "effici": [1, 204, 210], "through": [1, 60, 65, 257, 259, 263, 264], "vector": [1, 40, 132, 137, 187, 235, 246, 251, 252, 256, 258, 262], "reduc": [1, 13, 14, 16, 17, 134, 136, 138, 151, 170, 172, 186, 192, 248, 251, 258, 263, 264], "consumpt": [1, 26, 263], "cach": 1, "local": [1, 213], "given": [1, 23, 99, 122, 158, 160, 185, 201, 206, 209, 210, 213, 214, 218, 239, 249, 258, 259, 262, 264], "involv": [1, 12, 90, 101, 141, 150, 157, 201, 208, 209, 213, 217], "singleton": [1, 13, 14, 16, 17, 95, 134, 136, 138, 151, 168, 170, 172, 177, 186, 242, 256, 262], "whose": [1, 5, 9, 11, 19, 20, 26, 47, 55, 62, 66, 85, 86, 87, 97, 99, 102, 133, 150, 158, 162, 163, 164, 173, 174, 175, 176, 178, 179, 181, 182, 183, 192, 210, 224, 228, 229, 230, 231, 233, 234, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 262, 264], "one": [1, 15, 19, 26, 40, 51, 58, 60, 63, 73, 75, 88, 90, 95, 97, 99, 101, 102, 115, 116, 122, 132, 137, 141, 144, 146, 147, 155, 160, 168, 173, 181, 182, 183, 184, 187, 192, 204, 207, 209, 210, 212, 213, 216, 217, 218, 220, 222, 224, 225, 226, 227, 228, 229, 230, 231, 233, 246, 247, 248, 256, 258, 259, 262, 264], "virtual": 1, "repeat": [1, 191, 192, 206, 264], "across": [1, 5, 90, 101, 141, 175, 206, 208, 209, 213, 257, 262], "correspond": [1, 16, 17, 23, 47, 59, 65, 73, 77, 102, 111, 112, 113, 150, 156, 158, 160, 170, 176, 181, 182, 183, 184, 186, 187, 192, 206, 208, 222, 226, 230, 233, 235, 238, 242, 261, 262], "If": [1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 29, 34, 35, 40, 44, 47, 51, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 74, 76, 77, 78, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 107, 111, 113, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 150, 151, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 168, 169, 170, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 189, 190, 192, 207, 209, 213, 219, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 234, 235, 238, 239, 240, 242, 243, 244, 247, 248, 249, 250, 251, 254, 256, 257, 258, 262, 264], "unequ": 1, "lower": [1, 77, 97, 178, 234], "higher": [1, 5, 26, 192, 207, 258, 263], "prepend": [1, 40, 95, 132, 177], "until": [1, 26, 177], "store": [1, 26, 213, 254], "determin": [1, 10, 11, 12, 13, 14, 21, 22, 26, 30, 40, 41, 42, 44, 45, 47, 50, 51, 52, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 75, 78, 85, 86, 87, 88, 90, 94, 96, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 132, 135, 139, 141, 142, 150, 153, 154, 162, 163, 164, 166, 167, 171, 173, 174, 175, 176, 181, 182, 183, 184, 187, 188, 201, 206, 209, 212, 213, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 234, 235, 236, 237, 240, 242, 243, 244, 246, 247, 248, 249, 250, 254, 256, 258, 262], "let": [1, 9, 10, 11, 12, 62, 66, 85, 87, 88, 93, 94, 96, 102, 117, 118, 119, 122, 123, 125, 136, 145, 151, 155, 160, 161, 164, 166, 170, 172, 175, 177, 186, 187, 192, 217, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 234, 238, 239, 240, 248, 250, 251, 254], "b": [1, 9, 10, 11, 12, 57, 62, 66, 87, 90, 93, 94, 96, 101, 117, 118, 119, 122, 123, 125, 141, 145, 161, 164, 166, 169, 175, 187, 192, 206, 209, 210, 214, 247, 250, 264], "both": [1, 40, 44, 47, 51, 65, 77, 88, 90, 98, 101, 102, 107, 122, 132, 142, 150, 151, 172, 175, 176, 187, 192, 209, 210, 212, 216, 218, 235, 254, 258, 262, 263], "shape1": 1, "describ": [1, 5, 12, 88, 90, 93, 115, 116, 141, 145, 150, 151, 172, 194, 201, 209, 212, 216, 221, 232, 254, 262], "shape2": 1, "n1": [1, 137], "len": [1, 137, 177], "n2": [1, 137], "max": [1, 26, 77, 98, 108, 111, 177, 191, 192, 206, 242, 244, 247], "temporari": 1, "list": [1, 73, 78, 110, 114, 137, 169, 192, 204, 206, 213, 262, 264], "length": [1, 15, 107, 137, 156, 176, 192, 221, 223, 224, 227, 232, 251, 252], "while": [1, 101, 115, 122, 128, 129, 130, 131, 136, 140, 160, 170, 181, 182, 186, 191, 192, 199, 204, 206, 209, 210, 211, 213, 216, 247, 258, 263, 264, 265], "d1": 1, "els": [1, 26, 204, 263], "d2": 1, "set": [1, 18, 26, 49, 65, 102, 162, 165, 170, 178, 179, 181, 183, 184, 186, 191, 192, 206, 207, 208, 209, 210, 213, 214, 217, 218, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 234, 238, 239, 240, 244, 247, 248, 250, 251, 257, 258, 262, 264, 265], "th": [1, 97, 177, 192, 222, 226, 230, 233], "throw": 1, "except": [1, 7, 13, 14, 26, 74, 78, 88, 97, 102, 122, 144, 155, 169, 173, 185, 192, 201, 204, 206, 208, 210, 213, 215, 216, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 247, 259, 262, 263, 264], "demonstr": 1, "applic": [1, 26, 88, 151, 155, 172, 201, 254, 258, 262, 263], "4d": 1, "8": [1, 5, 7, 27, 177, 201, 204], "6": [1, 7, 177], "3d": 1, "7": [1, 7, 27, 218], "5": [1, 192, 262], "2d": 1, "1d": 1, "15": 1, "do": [1, 26, 90, 141, 154, 199, 204, 207, 209, 210, 212, 213, 214, 258, 259, 261, 262, 264, 265], "doe": [1, 15, 26, 102, 145, 173, 192, 201, 204, 207, 208, 209, 210, 211, 213, 214, 216, 218, 258, 262, 264, 265], "second": [1, 12, 65, 67, 69, 70, 71, 72, 93, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 143, 145, 150, 169, 171, 176, 181, 182, 183, 187, 188, 235, 238, 246, 248, 249, 251, 252, 262], "append": [1, 40, 69, 95, 132, 237], "As": [1, 122, 150, 181, 182, 183, 184, 204, 212, 218, 264], "impli": [1, 181, 182, 183, 184, 261, 262], "__setitem__": [1, 173, 191, 206], "Such": [1, 208, 258], "right": [1, 69, 71, 107, 160, 166, 207, 251, 261], "hand": [1, 201], "left": [1, 5, 60, 69, 101, 103, 160, 173, 192, 201, 238, 239, 251, 262], "index": [1, 5, 16, 17, 18, 32, 34, 49, 57, 83, 97, 111, 113, 137, 140, 144, 160, 169, 173, 176, 181, 182, 183, 191, 206, 222, 226, 230, 233, 262, 264], "perform": [1, 5, 13, 14, 26, 40, 59, 60, 90, 107, 132, 141, 155, 176, 192, 207, 208, 209, 210, 211, 212, 220, 222, 225, 226, 227, 229, 230, 231, 233, 251, 252, 258, 262, 263, 264], "empti": [1, 13, 14, 15, 151, 172, 191, 192, 206, 254, 262], "ok": 1, "allow": [1, 24, 25, 26, 29, 34, 35, 113, 115, 150, 156, 176, 192, 206, 207, 208, 210, 213, 216, 217, 258, 264], "NOT": [1, 129, 261], "adher": [2, 7, 8, 191, 192, 204, 257, 262], "convent": [2, 7, 10, 11, 26, 40, 61, 62, 64, 65, 66, 88, 123, 125, 132, 150, 166, 191, 192, 199, 209, 213, 257, 258, 263], "each": [2, 9, 10, 11, 12, 20, 21, 22, 26, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 76, 77, 79, 85, 86, 87, 90, 93, 94, 96, 100, 101, 105, 106, 107, 109, 114, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 135, 137, 139, 140, 141, 142, 143, 144, 145, 149, 150, 152, 153, 154, 155, 158, 159, 160, 161, 162, 163, 164, 166, 167, 169, 171, 174, 175, 176, 177, 180, 181, 182, 192, 204, 206, 208, 212, 216, 218, 230, 234, 235, 236, 240, 242, 243, 244, 247, 248, 249, 250, 251, 252, 257, 258, 262, 263, 264], "float": [2, 5, 9, 10, 11, 12, 13, 14, 15, 20, 21, 24, 25, 28, 29, 30, 31, 33, 34, 35, 37, 39, 40, 41, 42, 43, 44, 47, 49, 50, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 104, 107, 109, 113, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 145, 146, 147, 150, 151, 152, 153, 154, 157, 159, 160, 161, 162, 163, 164, 166, 167, 170, 171, 172, 174, 175, 176, 180, 181, 182, 183, 184, 186, 187, 189, 191, 199, 206, 208, 209, 216, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 238, 239, 240, 242, 243, 244, 247, 248, 249, 250, 251, 252, 254, 256, 258, 262, 263], "point": [2, 5, 9, 10, 11, 12, 13, 14, 15, 20, 24, 25, 26, 29, 34, 35, 40, 41, 42, 44, 47, 50, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 104, 107, 109, 113, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 145, 146, 147, 150, 151, 152, 153, 154, 157, 159, 160, 161, 162, 163, 164, 166, 167, 170, 171, 172, 174, 175, 176, 180, 181, 182, 183, 184, 186, 187, 189, 191, 199, 206, 208, 209, 213, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 238, 239, 240, 242, 243, 244, 247, 248, 249, 250, 251, 252, 254, 256, 258, 262, 264], "creat": [3, 15, 60, 91, 92, 97, 102, 103, 104, 122, 146, 147, 189, 190, 198, 204, 213, 221, 232, 258, 262], "main": [5, 97, 178, 179, 207, 212, 237, 254, 257, 264], "namespac": [5, 7, 23, 110, 194, 204, 206, 219, 257, 258, 259, 262, 265], "under": [5, 257, 261, 262], "specifi": [5, 13, 14, 15, 16, 17, 18, 26, 29, 59, 60, 63, 74, 78, 88, 91, 95, 98, 99, 103, 113, 115, 116, 122, 146, 151, 154, 155, 158, 168, 169, 172, 173, 177, 178, 179, 181, 182, 183, 184, 187, 189, 192, 201, 206, 208, 209, 210, 212, 213, 214, 218, 220, 222, 223, 224, 225, 226, 228, 229, 230, 231, 233, 237, 254, 256, 258, 259, 262, 264, 265], "name": [5, 7, 23, 26, 101, 115, 181, 182, 183, 192, 209, 238, 247, 248, 249, 251, 257, 262, 263], "descript": [5, 7, 206, 208, 242, 256], "bool": [5, 13, 14, 16, 17, 18, 22, 24, 26, 28, 31, 33, 37, 39, 43, 45, 49, 52, 60, 63, 75, 88, 89, 93, 102, 103, 104, 105, 106, 115, 116, 117, 118, 119, 120, 121, 122, 128, 129, 130, 131, 134, 136, 138, 145, 151, 156, 162, 165, 170, 172, 186, 201, 206, 216, 234, 242, 251, 256], "true": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 93, 98, 101, 102, 111, 117, 118, 119, 122, 128, 129, 130, 131, 134, 136, 138, 144, 145, 151, 156, 162, 165, 170, 172, 181, 182, 183, 184, 186, 188, 192, 206, 234, 242, 251, 256, 258], "fals": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 93, 102, 111, 117, 118, 119, 122, 128, 129, 130, 131, 134, 136, 138, 145, 151, 156, 162, 165, 170, 172, 181, 182, 183, 184, 186, 192, 234, 242, 251, 256], "int8": [5, 115, 116, 201], "bit": [5, 68, 69, 71, 85, 88, 98, 108, 151, 162, 172, 201, 206, 208, 254], "sign": [5, 9, 10, 11, 12, 15, 20, 41, 44, 62, 65, 66, 71, 85, 87, 88, 90, 94, 96, 101, 115, 116, 123, 125, 134, 135, 138, 139, 141, 142, 150, 151, 154, 160, 162, 164, 166, 172, 175, 181, 182, 183, 184, 191, 199, 206, 209, 248, 249, 254], "exist": [5, 7, 26, 60, 78, 102, 204, 206, 209, 212, 213, 214, 240, 259, 262, 263], "interv": [5, 10, 11, 13, 14, 15, 61, 62, 64, 66, 95, 122, 123, 125, 140, 169, 176, 178, 179, 185, 187, 192, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 259], "128": 5, "127": 5, "int16": [5, 88, 115, 116, 151, 172, 201, 254], "16": [5, 201], "32": [5, 201], "767": 5, "int32": [5, 88, 115, 116, 151, 172, 201, 254], "147": 5, "483": 5, "647": 5, "int64": [5, 88, 115, 116, 151, 172, 201, 254], "64": [5, 201], "9": [5, 27], "223": 5, "372": 5, "036": 5, "854": 5, "775": 5, "807": 5, "uint8": [5, 115, 116, 201], "unsign": [5, 88, 115, 116, 151, 172, 191, 254], "255": 5, "uint16": [5, 88, 115, 116, 151, 172, 201, 254], "65": 5, "535": [5, 206], "uint32": [5, 88, 115, 116, 151, 172, 201, 254], "294": 5, "967": 5, "295": 5, "uint64": [5, 115, 116, 201], "18": 5, "446": [5, 206], "744": [5, 206], "073": 5, "709": [5, 206], "551": [5, 206], "615": 5, "float32": [5, 109, 115, 116, 152, 201, 249, 251, 252], "ieee": [5, 12, 65, 80, 81, 82, 84, 90, 96, 98, 107, 125, 141, 154, 166, 174, 175, 191, 199, 208, 209, 262], "754": [5, 12, 65, 80, 81, 82, 84, 90, 96, 98, 107, 125, 141, 154, 166, 174, 175, 191, 199, 208, 209, 262], "singl": [5, 7, 24, 25, 29, 34, 35, 113, 115, 181, 182, 191, 201, 206, 207, 209, 212, 213, 218, 258, 262, 263, 264], "precis": [5, 9, 20, 42, 60, 98, 103, 104, 109, 141, 152, 166, 201, 206, 208, 224, 228, 229, 230, 231, 233, 238, 239, 242, 249, 251, 252, 256, 262], "2019": [5, 12, 90, 96, 107, 125, 141, 191, 208, 262, 264], "float64": [5, 9, 20, 115, 116, 201, 224, 228, 229, 230, 231, 233, 238, 239, 242, 256], "doubl": [5, 176, 201, 206], "complex64": [5, 109, 115, 116, 152, 201, 206, 249, 251, 252], "imaginari": [5, 10, 11, 12, 13, 14, 44, 61, 62, 63, 64, 66, 79, 87, 90, 93, 94, 96, 98, 109, 123, 125, 141, 142, 144, 145, 146, 147, 150, 159, 164, 166, 175, 206, 209], "compon": [5, 10, 11, 12, 13, 14, 44, 62, 63, 66, 79, 87, 90, 93, 94, 96, 98, 109, 123, 125, 141, 142, 144, 145, 146, 147, 150, 152, 159, 164, 166, 174, 175, 181, 182, 183, 184, 206, 209, 223, 232], "complex128": [5, 9, 20, 115, 116, 201, 206, 224, 228, 229, 230, 231, 233, 238, 239, 242, 256], "method": [5, 26, 34, 102, 191, 194, 204, 210, 212, 213, 216, 217, 218, 262, 263, 264], "attribut": [5, 23, 98, 108, 191, 203, 206, 259, 262, 263, 264], "requir": [5, 10, 11, 24, 25, 29, 34, 35, 59, 61, 62, 63, 64, 66, 88, 102, 107, 116, 151, 166, 169, 172, 173, 175, 181, 182, 184, 185, 191, 192, 199, 201, 204, 206, 207, 208, 209, 210, 211, 212, 213, 216, 218, 220, 221, 222, 224, 225, 226, 229, 230, 232, 235, 254, 257, 258, 262, 263, 264], "beyond": [5, 158, 201, 262], "It": [5, 23, 26, 102, 204, 210, 212, 262, 264, 265], "also": [5, 7, 26, 34, 102, 107, 161, 201, 204, 209, 210, 211, 212, 218, 222, 226, 230, 233, 251, 257, 264], "subnorm": [5, 107], "k": [5, 40, 97, 107, 132, 144, 178, 179, 192, 234, 238, 239, 240, 248, 250, 251, 252, 254, 262], "denorm": [5, 107], "gradual": [5, 107, 262], "underflow": [5, 9, 90, 101, 107, 249], "hardwar": [5, 53, 107, 155, 208, 212, 213, 238, 251, 258, 262], "univers": [5, 107, 207, 213, 258, 262], "mani": [5, 107, 177, 262, 264], "platform": [5, 26, 107], "compil": [5, 107, 175, 204, 207, 211, 262], "toggl": [5, 107], "daz": [5, 107], "flush": [5, 107], "ftz": [5, 107], "increas": [5, 107, 208, 263], "guard": [5, 107], "against": [5, 40, 73, 107, 132, 175, 192, 244, 247, 265], "time": [5, 7, 16, 17, 26, 107, 155, 181, 182, 204, 206, 211, 212, 217, 234, 238, 239, 240, 248, 250, 251, 258, 262, 264], "attack": [5, 107], "accordingli": [5, 10, 11, 13, 14, 16, 17, 59, 61, 62, 64, 66, 90, 96, 101, 107, 122, 123, 125, 134, 136, 137, 138, 141, 144, 151, 155, 160, 166, 170, 172, 181, 182, 183, 184, 186, 192, 201, 208, 209, 210, 211, 213, 242, 248, 256, 258], "vari": [5, 107, 160, 175, 181, 182, 183, 184, 201, 208], "function": [5, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 74, 78, 86, 87, 88, 94, 96, 99, 102, 107, 114, 115, 116, 122, 123, 125, 128, 129, 130, 131, 132, 136, 144, 150, 151, 154, 155, 156, 161, 163, 164, 165, 166, 169, 170, 172, 173, 174, 175, 176, 177, 181, 182, 183, 184, 185, 186, 187, 191, 194, 204, 206, 207, 209, 210, 211, 212, 213, 216, 217, 218, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 234, 235, 238, 239, 240, 244, 247, 248, 249, 250, 251, 252, 254, 257, 258, 259, 262, 263, 264], "access": [5, 26, 32, 102, 110, 192, 206, 212, 257, 259, 262], "variou": [5, 206], "cast": [5, 29, 49, 60, 63, 75, 88, 151, 172, 201, 209, 254, 262, 264], "introspect": 5, "isdtyp": [5, 191, 206], "integr": [5, 63, 113, 115, 116], "keyword": [5, 7, 26, 63, 88, 114, 137, 151, 172, 191, 206, 210, 213, 217, 218, 254, 258, 259, 262, 263, 264], "affect": [5, 15, 49, 210, 213], "intermedi": [5, 9, 107], "calcul": [5, 9, 10, 11, 12, 20, 21, 42, 47, 50, 61, 62, 64, 65, 66, 86, 87, 88, 90, 94, 96, 123, 124, 125, 126, 127, 134, 136, 138, 141, 150, 151, 163, 164, 166, 170, 171, 172, 174, 175, 186, 206, 249], "implementor": [5, 257], "free": [5, 213, 261], "when": [5, 7, 12, 16, 17, 26, 47, 49, 59, 63, 90, 96, 101, 102, 107, 113, 115, 122, 125, 134, 135, 138, 139, 141, 150, 151, 155, 156, 160, 170, 172, 175, 186, 188, 191, 192, 201, 206, 207, 209, 210, 211, 212, 214, 216, 217, 218, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 234, 238, 240, 244, 247, 248, 249, 250, 251, 252, 254, 258, 262, 263, 264], "accumul": 5, "reduct": [5, 13, 14], "long": [5, 110, 218], "ha": [5, 9, 13, 14, 20, 23, 29, 34, 35, 40, 44, 47, 55, 86, 87, 88, 90, 94, 95, 96, 101, 104, 132, 136, 137, 140, 141, 142, 144, 150, 151, 163, 164, 168, 170, 172, 173, 174, 175, 176, 177, 181, 182, 183, 184, 186, 192, 201, 204, 209, 212, 213, 216, 217, 235, 242, 250, 251, 254, 256, 258, 259, 262, 264, 265], "wai": [5, 26, 63, 102, 204, 207, 213, 214, 259, 262, 263, 264, 265], "f4": [5, 201], "ensur": [5, 26, 160, 204, 208, 258, 262, 263, 264], "portabl": [5, 59, 122, 208, 210, 213, 214, 262], "consum": [5, 26, 63, 113, 115, 204, 209, 210, 218, 257, 262, 263], "recommend": [5, 7, 19, 23, 26, 122, 128, 129, 130, 131, 136, 154, 170, 186, 199, 206, 208, 212, 213, 262], "guidanc": [5, 7, 49, 206, 207, 214, 262], "govern": [5, 50, 171, 201, 258, 259], "interact": [5, 209], "either": [5, 9, 10, 11, 12, 24, 26, 35, 40, 65, 77, 87, 88, 90, 93, 94, 96, 98, 101, 102, 107, 110, 116, 117, 118, 122, 123, 124, 125, 126, 127, 132, 134, 135, 138, 139, 141, 143, 151, 154, 161, 162, 163, 166, 172, 174, 175, 176, 192, 208, 209, 210, 214, 218, 249, 254, 262, 263, 265], "whether": [5, 13, 14, 26, 59, 60, 63, 88, 89, 102, 111, 116, 119, 122, 156, 162, 206, 213, 234, 238, 239, 248, 250, 257, 261, 262, 264], "otherwis": [5, 13, 14, 15, 16, 17, 26, 59, 60, 63, 75, 102, 111, 113, 115, 134, 136, 138, 151, 155, 156, 160, 161, 170, 172, 186, 187, 188, 191, 192, 204, 213, 234, 236, 242, 249, 250, 256, 261], "note": [5, 7, 9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 61, 62, 63, 64, 65, 66, 76, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 98, 100, 101, 103, 104, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 123, 124, 125, 126, 127, 132, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 149, 150, 151, 152, 153, 154, 155, 159, 160, 161, 162, 163, 164, 166, 167, 170, 171, 172, 173, 174, 175, 176, 177, 180, 181, 182, 183, 184, 185, 186, 187, 191, 192, 206, 212, 216, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 262, 263, 264, 265], "possibl": [5, 26, 60, 101, 102, 134, 138, 156, 174, 175, 204, 207, 208, 209, 210, 212, 213, 214, 216, 218, 258, 262, 263, 264, 265], "multipl": [5, 7, 13, 14, 16, 17, 40, 42, 44, 132, 134, 136, 138, 141, 142, 151, 170, 172, 186, 192, 204, 207, 209, 212, 213, 217, 218, 239, 240, 258, 259, 262, 264], "In": [5, 12, 19, 26, 59, 88, 90, 93, 101, 116, 118, 119, 141, 145, 151, 154, 161, 172, 191, 192, 194, 201, 208, 209, 212, 214, 229, 230, 248, 249, 251, 254, 258, 259, 263, 264, 265], "clearli": [5, 59, 116, 199, 209, 258, 259], "warn": [5, 155, 214], "about": [5, 7, 26, 98, 108, 210, 258, 262, 264, 265], "": [5, 26, 29, 32, 49, 58, 59, 60, 80, 101, 102, 137, 154, 170, 177, 178, 179, 186, 192, 199, 204, 206, 207, 208, 209, 210, 212, 213, 216, 218, 222, 226, 230, 233, 247, 251, 252, 258, 259, 262, 264], "organ": [5, 206, 258, 263, 264], "within": [5, 15, 27, 192, 201, 204, 206, 209, 213, 220, 222, 225, 226, 229, 230, 231, 233, 262], "numer": [5, 9, 12, 20, 21, 40, 42, 44, 46, 47, 50, 51, 88, 90, 101, 115, 116, 117, 118, 119, 132, 137, 141, 142, 149, 150, 151, 159, 161, 167, 171, 172, 176, 201, 208, 220, 222, 225, 226, 229, 230, 231, 233, 235, 246, 247, 249, 254, 258, 262, 264], "accord": [5, 12, 60, 71, 75, 88, 90, 98, 101, 103, 122, 141, 150, 160, 161, 170, 186, 187, 192, 208, 209], "These": [5, 210, 238, 263], "intend": [5, 88, 151, 172, 204, 254], "posit": [7, 9, 10, 11, 13, 14, 20, 46, 62, 65, 66, 81, 90, 95, 97, 98, 101, 118, 123, 125, 140, 141, 144, 154, 158, 162, 164, 166, 175, 191, 192, 204, 206, 208, 218, 232, 234, 248, 263], "paramet": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 204, 206, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 258], "extern": [7, 264], "usabl": 7, "accept": [7, 26, 128, 129, 130, 131, 136, 154, 170, 186, 204, 259], "call": [7, 34, 212, 213, 216, 249, 262, 263, 264], "argument": [7, 10, 11, 26, 40, 61, 62, 63, 64, 65, 66, 86, 88, 107, 114, 123, 125, 132, 151, 157, 160, 163, 166, 172, 174, 175, 176, 191, 201, 206, 208, 210, 212, 213, 220, 222, 225, 226, 229, 230, 231, 233, 254, 258, 262, 263, 264], "map": [7, 209, 210], "base": [7, 47, 57, 58, 94, 95, 123, 124, 125, 126, 150, 181, 182, 183, 184, 192, 206, 210, 216, 218, 258, 259, 262, 263, 264], "sole": [7, 192, 199, 258], "incompat": [7, 26, 74, 102, 204, 259, 262], "us": [7, 19, 26, 27, 59, 60, 83, 98, 102, 107, 122, 124, 126, 158, 181, 183, 191, 192, 201, 206, 208, 209, 210, 211, 213, 214, 217, 218, 219, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 257, 258, 259, 260, 261, 262, 265], "normal": [7, 78, 169, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233], "practic": [7, 19, 192, 258, 263], "avail": [7, 102, 114, 204, 212, 257, 259, 263], "still": [7, 26, 218, 258, 263, 264, 265], "consid": [7, 26, 63, 102, 128, 129, 130, 131, 181, 182, 183, 184, 209, 213, 232, 247, 258, 262, 264, 265], "compliant": [7, 26, 51, 90, 96, 102, 122, 125, 128, 129, 130, 131, 134, 135, 136, 138, 139, 170, 186, 208, 211, 213, 259, 262], "altern": [7, 210, 212, 265], "thei": [7, 26, 201, 207, 212, 213, 217, 218, 257, 258, 259, 262, 264, 265], "were": [7, 101, 155, 160, 206, 262], "option": [7, 13, 14, 15, 16, 17, 23, 26, 57, 58, 59, 60, 63, 77, 78, 88, 91, 92, 97, 99, 102, 103, 104, 113, 115, 122, 134, 136, 138, 146, 147, 151, 155, 156, 158, 160, 170, 172, 173, 186, 189, 190, 191, 206, 217, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 242, 244, 247, 254, 256, 258, 263, 264], "lead": [7, 101, 209, 248, 251, 262], "readabl": [7, 201, 258, 263], "code": [7, 59, 201, 210, 211, 213, 216, 218, 258, 262, 263, 264], "easier": [7, 204, 210, 258], "evolv": [7, 204, 258], "over": [7, 13, 14, 26, 122, 134, 136, 138, 151, 170, 172, 173, 176, 186, 187, 208, 209, 210, 212, 213, 217, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 235, 254, 256, 258, 262], "ad": [7, 9, 10, 11, 12, 13, 14, 20, 21, 24, 26, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 86, 87, 90, 93, 94, 96, 97, 98, 102, 103, 104, 117, 118, 119, 122, 123, 124, 125, 126, 132, 137, 141, 142, 144, 145, 146, 147, 149, 150, 151, 159, 161, 163, 164, 166, 167, 171, 172, 174, 175, 176, 181, 182, 183, 184, 187, 192, 205, 206, 207, 213, 234, 235, 236, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 259], "worri": 7, "xi": [7, 137], "annot": [7, 206, 218, 262], "individu": [7, 160, 213, 216, 217, 218, 221, 232, 262, 263], "aim": [7, 207, 218, 257, 258, 259, 262, 263, 264, 265], "strongli": [7, 210, 264], "look": [7, 264], "like": [7, 204, 207, 209, 210, 216, 218, 259, 262, 263, 264], "funcnam": 7, "key1": 7, "key2": 7, "none": [7, 13, 14, 15, 16, 17, 23, 26, 32, 49, 57, 58, 59, 60, 63, 77, 78, 83, 88, 91, 92, 97, 99, 102, 103, 104, 111, 113, 115, 122, 134, 136, 138, 146, 147, 151, 155, 156, 158, 160, 170, 172, 173, 186, 189, 190, 192, 206, 213, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 242, 244, 247, 254, 255, 256, 262, 263, 265], "out": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 192, 206, 207, 210, 212, 216, 217, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 261, 264], "int": [7, 13, 14, 15, 16, 17, 18, 21, 22, 26, 27, 28, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 56, 57, 58, 59, 60, 74, 77, 78, 88, 91, 95, 97, 98, 99, 101, 103, 104, 108, 122, 134, 136, 138, 140, 146, 148, 151, 155, 156, 158, 165, 168, 169, 170, 172, 173, 176, 177, 178, 179, 185, 186, 187, 189, 192, 201, 216, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 235, 237, 242, 243, 253, 254, 255, 256, 263], "str": [7, 8, 23, 115, 116, 137, 263], "modulo": 7, "self": [7, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 89, 206, 264], "few": [7, 208, 216, 262, 264], "enhanc": 7, "default": [7, 13, 14, 15, 16, 17, 18, 23, 26, 59, 60, 63, 77, 78, 88, 91, 92, 97, 99, 102, 103, 104, 112, 113, 115, 122, 134, 136, 137, 138, 144, 146, 147, 151, 155, 156, 158, 160, 165, 169, 170, 172, 176, 178, 179, 181, 182, 183, 185, 186, 187, 189, 190, 191, 192, 206, 208, 213, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 242, 244, 247, 248, 251, 254, 256], "form": [7, 23, 26, 40, 79, 132, 133, 178, 179, 210, 234, 236, 237, 238, 239, 240, 242, 243, 244, 247, 248, 249, 250, 251, 252, 254, 259, 263], "question": [7, 207, 262], "commonli": [7, 170, 186, 207, 209, 211, 257, 258, 262, 263], "written": [7, 204, 262, 264], "yyyi": [8, 23, 259], "mm": [8, 23, 259], "string": [8, 23, 115, 116, 206, 259, 262], "version": [8, 9, 10, 11, 12, 13, 14, 20, 21, 23, 24, 25, 26, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 66, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 98, 102, 103, 104, 107, 108, 109, 116, 117, 118, 119, 122, 123, 124, 125, 126, 132, 134, 135, 137, 138, 139, 140, 141, 142, 144, 145, 146, 147, 149, 150, 151, 152, 155, 159, 160, 161, 162, 163, 164, 166, 167, 171, 172, 173, 174, 175, 176, 177, 181, 182, 183, 184, 185, 187, 191, 204, 207, 213, 217, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 260, 262, 264], "absolut": [9, 20, 85, 161, 208, 210, 242, 243, 249, 258], "x_i": [9, 10, 11, 61, 62, 64, 66, 68, 76, 77, 79, 86, 87, 94, 96, 100, 109, 117, 118, 119, 123, 124, 125, 126, 129, 134, 136, 138, 142, 149, 152, 153, 159, 161, 162, 163, 164, 166, 167, 170, 174, 175, 180, 186], "input": [9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 26, 30, 41, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 85, 86, 87, 88, 90, 92, 93, 94, 95, 96, 99, 100, 101, 102, 104, 105, 106, 107, 109, 116, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 190, 191, 199, 204, 206, 209, 211, 213, 214, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 251, 252, 254, 256, 258, 262, 264], "magnitud": [9, 12, 20, 85, 90, 101, 107, 141, 206, 251, 252], "represent": [9, 12, 20, 29, 44, 67, 70, 72, 80, 81, 82, 84, 90, 98, 101, 108, 141, 142, 143, 174, 175, 208, 212, 263], "known": [9, 161, 208, 211, 212], "norm": [9, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 242, 256, 258], "modulu": [9, 154], "z": [9, 10, 11, 61, 62, 64, 66, 123, 209], "bj": [9, 12, 79, 90, 141], "comput": [9, 12, 28, 31, 33, 37, 39, 40, 43, 57, 58, 67, 70, 72, 79, 88, 89, 90, 93, 95, 101, 105, 106, 107, 120, 121, 128, 129, 130, 131, 132, 134, 135, 136, 138, 139, 141, 142, 144, 145, 149, 151, 155, 170, 172, 176, 181, 182, 183, 184, 186, 187, 192, 206, 208, 211, 216, 220, 221, 222, 224, 225, 226, 228, 229, 230, 231, 232, 233, 234, 235, 238, 239, 240, 242, 244, 247, 248, 249, 250, 251, 252, 254, 256, 258, 262], "operatornam": [9, 10, 11, 61, 62, 64, 66, 86, 87, 161, 163, 164, 174, 175, 209, 238, 239, 249, 251], "sqrt": [9, 10, 11, 61, 62, 191, 206, 209, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 256], "take": [9, 123, 125, 150, 166, 191, 206, 213, 218, 262], "care": [9, 210, 258], "undu": [9, 211], "overflow": [9, 12, 88, 90, 101, 107, 122, 151, 172, 201, 249, 254, 258], "dure": [9, 40, 59, 107, 132, 170, 186, 201, 204, 247, 262, 263], "stage": [9, 107, 259], "contain": [9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 26, 28, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 90, 91, 92, 93, 94, 96, 100, 101, 102, 105, 106, 107, 109, 110, 111, 113, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 159, 160, 161, 162, 163, 164, 166, 167, 170, 171, 172, 174, 175, 176, 178, 179, 180, 181, 182, 183, 184, 186, 187, 189, 192, 206, 208, 209, 210, 212, 216, 217, 221, 222, 223, 226, 227, 230, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 262, 264], "nan": [9, 10, 11, 12, 13, 14, 24, 25, 35, 61, 62, 63, 64, 65, 66, 76, 85, 86, 87, 90, 93, 94, 96, 100, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 136, 138, 139, 141, 143, 145, 150, 154, 159, 160, 161, 162, 163, 164, 166, 170, 174, 175, 180, 181, 182, 183, 184, 186, 191, 199, 209, 262], "infin": [9, 10, 11, 12, 13, 14, 24, 25, 35, 62, 63, 64, 65, 66, 76, 81, 86, 87, 90, 93, 94, 96, 100, 101, 107, 117, 118, 123, 124, 125, 126, 127, 134, 138, 141, 145, 150, 154, 159, 162, 163, 164, 166, 174, 175, 180, 209, 249, 256], "imag": [9, 10, 11, 12, 24, 62, 63, 66, 87, 93, 94, 96, 117, 118, 119, 122, 123, 125, 145, 159, 161, 164, 166, 175, 191, 206, 207, 262, 263, 264], "finit": [9, 10, 11, 12, 25, 35, 42, 62, 65, 66, 87, 90, 93, 94, 96, 101, 107, 111, 117, 118, 123, 125, 141, 145, 150, 154, 162, 164, 166, 175, 208], "2022": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 90, 93, 94, 96, 97, 98, 103, 104, 108, 109, 116, 117, 118, 119, 122, 123, 124, 125, 126, 132, 137, 141, 142, 144, 145, 146, 147, 149, 150, 151, 152, 159, 161, 163, 164, 166, 167, 171, 172, 173, 174, 175, 176, 181, 182, 183, 184, 187, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256], "12": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 66, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 98, 102, 103, 104, 107, 108, 109, 116, 117, 118, 119, 122, 123, 124, 125, 126, 132, 134, 135, 137, 138, 139, 140, 141, 142, 144, 145, 146, 147, 149, 150, 151, 152, 155, 159, 160, 161, 162, 163, 164, 166, 167, 171, 172, 173, 174, 175, 176, 177, 181, 182, 183, 184, 185, 187, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 238, 239, 240, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 254, 256, 259], "approxim": [10, 11, 47, 61, 62, 64, 65, 66, 86, 87, 94, 96, 101, 123, 124, 125, 126, 150, 163, 164, 174, 175, 208, 244, 247], "princip": [10, 11, 61, 62, 64, 66, 123, 166, 209, 258], "invers": [10, 11, 61, 62, 64, 65, 66, 209, 220, 222, 225, 226, 227, 228, 229, 230, 231, 233, 240, 243, 247, 258], "cosin": [10, 11, 86, 87, 175], "express": [10, 61, 63, 64, 65, 86, 163, 174, 192, 201, 210, 258, 261], "radian": [10, 61, 64, 65, 86, 163, 174], "arc": [10, 61, 64], "frac": [10, 11, 61, 62, 64, 66, 86, 87, 90, 122, 124, 126, 161, 163, 164, 174, 175, 209, 249], "pi": [10, 11, 61, 62, 64, 66, 87, 123, 125, 164, 174, 175, 191], "j": [10, 11, 12, 25, 61, 62, 64, 66, 87, 90, 94, 96, 122, 123, 125, 141, 160, 161, 163, 164, 166, 174, 175, 192, 209, 238, 251, 254], "ln": [10, 11, 61, 62, 64, 66, 123], "zj": [10, 61, 62, 64, 66], "conj": [10, 11, 61, 62, 64, 66, 87, 94, 96, 123, 124, 125, 126, 164, 166, 175, 191, 206], "multi": [10, 11, 61, 62, 64, 66, 191, 209, 212, 213, 235, 264], "branch": [10, 11, 61, 62, 64, 65, 66, 86, 87, 90, 94, 96, 123, 125, 141, 150, 163, 164, 166, 174, 175, 262], "cut": [10, 11, 61, 62, 64, 66, 86, 87, 94, 96, 123, 125, 150, 163, 164, 166, 174, 175, 262], "plane": [10, 11, 61, 62, 64, 66, 86, 87, 90, 94, 96, 141, 163, 164, 166, 174, 175, 262], "By": [10, 11, 13, 14, 61, 62, 64, 65, 66, 88, 123, 125, 134, 136, 138, 150, 151, 166, 170, 172, 186, 187, 208, 209, 235, 258, 263], "place": [10, 11, 15, 60, 61, 62, 63, 64, 66, 91, 92, 97, 102, 103, 104, 122, 146, 147, 158, 189, 190, 191, 199, 201, 206, 210, 213, 221, 232, 247], "line": [10, 11, 61, 62, 64, 66, 174, 175, 201, 209, 262, 263, 264, 265], "segment": [10, 11, 61, 62, 64, 66, 209], "infti": [10, 11, 61, 62, 64, 66, 86, 123, 125, 150, 166, 209], "axi": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 95, 99, 123, 125, 134, 136, 138, 140, 150, 151, 155, 158, 165, 166, 168, 169, 170, 172, 173, 176, 177, 185, 186, 187, 191, 206, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 235, 242, 255, 256, 262], "rang": [10, 61, 62, 64, 66, 77, 88, 123, 125, 151, 166, 172, 192, 206, 212, 254, 262], "strip": [10, 61, 62, 64, 66, 123, 125], "unbound": [10, 61, 62, 64, 66, 123, 125], "along": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 97, 99, 123, 125, 134, 136, 138, 151, 155, 158, 165, 166, 169, 170, 172, 173, 174, 175, 177, 185, 186, 187, 192, 206, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 254, 256, 258], "c99": [10, 11, 61, 62, 64, 66, 90, 123, 125, 141, 150, 166, 209, 259], "provision": [10, 11, 61, 62, 64, 66, 123, 125, 150, 166, 209], "statu": [10, 11, 61, 62, 64, 66, 123, 125, 150, 166, 209], "greater": [10, 11, 33, 38, 48, 61, 62, 65, 66, 69, 71, 77, 85, 90, 100, 101, 123, 125, 150, 154, 161, 162, 164, 166, 168, 175, 191, 192, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 243], "than": [10, 11, 19, 26, 38, 40, 47, 48, 49, 55, 61, 62, 63, 65, 66, 69, 71, 76, 77, 85, 88, 90, 98, 99, 100, 101, 102, 123, 124, 125, 126, 132, 141, 150, 151, 154, 161, 162, 164, 166, 168, 170, 172, 173, 175, 180, 181, 182, 183, 184, 186, 192, 201, 204, 207, 210, 213, 214, 217, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 242, 243, 244, 247, 254, 256, 258, 259, 262, 264], "less": [10, 11, 39, 47, 61, 65, 66, 76, 85, 90, 101, 123, 124, 125, 126, 150, 154, 161, 162, 166, 170, 186, 191, 192, 210, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 242, 243, 244, 247, 256, 262], "\u03c0": [10, 64, 65, 84], "0j": [10, 11, 12, 25, 62, 63, 66, 87, 94, 96, 97, 123, 125, 146, 147, 161, 164, 166, 175, 209, 249], "nonzero": [10, 11, 12, 62, 66, 87, 90, 94, 96, 101, 141, 164, 175, 191, 192, 206, 247], "3\u03c0": [10, 65], "hyperbol": [11, 62, 66, 86, 87, 163, 164, 174, 175, 209], "aco": [11, 61, 191, 206, 208], "simpli": [11, 96, 125, 207, 218, 262, 264], "upper": [11, 77, 97, 179, 206, 234, 248], "half": [11, 15, 66, 122, 140, 166, 176, 192, 223], "area": [11, 62, 66], "sector": [11, 62, 66], "\u03c0j": [11, 62, 66, 123, 125], "3\u03c0j": [11, 123, 125], "sum": [12, 21, 88, 107, 127, 151, 191, 206, 242, 254, 256, 258], "x1_i": [12, 65, 67, 69, 70, 71, 72, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 135, 139, 141, 143, 145, 150, 154, 171, 188, 206], "x2_i": [12, 65, 67, 69, 70, 71, 72, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 135, 139, 141, 143, 145, 150, 154, 171, 188, 206], "first": [12, 16, 17, 19, 65, 67, 69, 70, 71, 72, 88, 93, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 143, 145, 150, 158, 169, 171, 174, 175, 176, 181, 182, 183, 187, 188, 192, 209, 235, 238, 246, 248, 249, 251, 252, 258, 262, 263, 264, 265], "remain": [12, 90, 93, 101, 116, 118, 119, 141, 145, 154, 156, 161, 192, 210, 233], "neither": [12, 40, 90, 101, 132, 141, 176, 251, 263], "nor": [12, 90, 101, 141, 251, 263], "mathemat": [12, 19, 65, 84, 86, 87, 90, 96, 101, 123, 125, 141, 163, 164, 174, 175, 191, 209, 242, 256], "round": [12, 15, 76, 90, 100, 101, 141, 166, 180, 191, 206, 208], "nearest": [12, 90, 141, 159, 180, 208], "mode": [12, 90, 141, 208, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 248], "too": [12, 26, 90, 101, 141, 258, 262], "larg": [12, 90, 101, 141, 212, 218, 249, 262], "appropri": [12, 26, 90, 101, 141, 209, 214], "commut": 12, "associ": [12, 42, 141, 194, 201, 244, 247, 250, 258, 261, 263], "tabl": [12, 90, 141, 191], "c": [12, 90, 93, 122, 141, 144, 145, 155, 169, 170, 175, 186, 192, 206, 209, 212, 215, 234, 238, 239, 240, 248, 250, 251, 259, 261, 262, 264], "d": [12, 90, 93, 122, 141, 145, 201, 221, 232], "dj": [12, 90, 141], "independ": [12, 90, 141, 159, 192, 204, 212, 235, 248, 250, 258, 259, 262], "abov": [12, 88, 90, 93, 123, 125, 141, 145, 150, 151, 166, 172, 178, 179, 192, 201, 209, 210, 212, 213, 216, 237, 238, 254, 258, 261, 264], "similarli": [12, 57, 116, 137, 201, 234, 251], "henc": [12, 79, 95, 144, 155, 181, 182, 183, 184, 192, 207, 209, 210, 211, 212, 216, 217, 218, 262, 264], "z1": 12, "z2": 12, "keepdim": [13, 14, 16, 17, 134, 136, 138, 151, 170, 172, 186, 242, 256], "test": [13, 14, 89, 117, 118, 119, 206, 208, 260, 262, 263, 264], "evalu": [13, 14, 22, 30, 36, 38, 41, 44, 45, 46, 48, 51, 52, 94, 96, 123, 124, 125, 126, 142, 149, 161, 162, 167, 204, 262], "union": [13, 14, 15, 21, 22, 26, 28, 30, 31, 32, 33, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 59, 60, 75, 77, 78, 91, 98, 99, 103, 104, 108, 115, 116, 122, 134, 136, 138, 140, 146, 151, 155, 157, 158, 168, 169, 170, 172, 176, 186, 189, 223, 227, 242, 244, 247, 256, 263], "ax": [13, 14, 16, 17, 19, 55, 56, 99, 134, 136, 138, 140, 148, 151, 158, 168, 170, 172, 176, 177, 186, 187, 192, 206, 222, 223, 226, 227, 230, 233, 235, 242, 247, 250, 253, 256], "logic": [13, 14, 24, 26, 90, 93, 128, 129, 130, 131, 141, 145, 213, 216, 222, 226, 230, 233], "AND": [13, 67, 93, 128, 261], "entir": [13, 14, 86, 87, 94, 96, 134, 136, 138, 151, 163, 164, 170, 172, 186], "valid": [13, 14, 26, 27, 95, 114, 140, 169, 176, 185, 192, 208, 216, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 238, 248, 251, 263], "count": [13, 14, 78, 88, 99, 173, 181, 182, 187, 192, 206, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 239], "last": [13, 14, 18, 19, 55, 78, 88, 99, 158, 165, 169, 173, 176, 187, 192, 220, 222, 224, 225, 226, 228, 229, 230, 231, 233, 235, 237, 242, 248, 251, 254], "invalid": [13, 14, 23, 95, 214, 262], "rais": [13, 14, 19, 23, 24, 25, 26, 29, 34, 35, 40, 47, 51, 55, 60, 74, 90, 94, 95, 102, 122, 132, 134, 138, 144, 150, 156, 168, 169, 185, 187, 192, 201, 204, 206, 212, 213, 214, 216, 235, 243, 262], "wa": [13, 14, 19, 26, 101, 134, 136, 138, 151, 170, 172, 186, 201, 213, 218, 262, 264], "OR": [14, 24, 70, 130, 145, 261], "start": [15, 122, 192, 206, 218, 262, 264], "stop": [15, 122, 192, 206, 263], "step": [15, 122, 192, 263], "evenli": [15, 122], "space": [15, 122, 221, 223, 232], "open": [15, 122, 140, 176, 192], "inclus": [15, 192, 262], "end": [15, 65, 86, 122, 161, 163, 174, 175, 199, 210, 249, 262, 263, 264], "exclus": [15, 192], "distanc": [15, 107], "between": [15, 26, 47, 51, 65, 78, 90, 93, 98, 122, 134, 135, 138, 139, 145, 150, 169, 181, 182, 183, 184, 201, 209, 210, 213, 221, 232, 258, 262, 264], "adjac": 15, "output": [15, 60, 63, 78, 88, 91, 92, 95, 97, 99, 102, 103, 104, 111, 122, 137, 146, 147, 156, 158, 160, 168, 169, 173, 177, 189, 190, 204, 206, 209, 210, 213, 215, 216, 218, 220, 221, 222, 224, 225, 226, 229, 230, 231, 232, 233, 254, 262], "infer": [15, 60, 63, 92, 103, 104, 147, 156, 190, 211, 258, 263], "cannot": [15, 26, 57, 102, 174, 175, 206, 209, 211, 262], "guarante": [15, 59, 181, 183, 204, 209, 213, 262, 264], "error": [15, 19, 23, 24, 25, 26, 29, 34, 35, 51, 55, 90, 102, 134, 138, 174, 175, 201, 208, 249, 262], "ceil": [15, 191], "indic": [16, 17, 18, 26, 60, 88, 89, 102, 111, 116, 122, 140, 144, 158, 160, 161, 173, 176, 178, 179, 181, 183, 192, 201, 206, 256, 262], "occur": [16, 17, 75, 107, 174, 175, 181, 182, 183, 184, 209, 263], "occurr": [16, 17, 181], "comparison": [16, 17, 18, 31, 33, 37, 39, 93, 105, 106, 120, 121, 134, 135, 138, 139, 145, 165, 191, 209, 259, 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236, 237, 238, 239, 240, 242, 243, 244, 247, 248, 249, 250, 251, 252, 254, 258], "deviat": [19, 170, 208, 214, 262, 264], "et": [19, 251, 252], "al": 19, "intent": [19, 65], "found": [19, 209, 212, 264, 265], "problemat": [19, 63, 207, 210], "conflict": 19, "definit": [19, 86, 87, 163, 164, 174, 175, 206, 234, 263], "batch": [19, 256, 258], "cetera": [19, 251, 252], "permute_dim": [19, 191], "interfac": [19, 212, 258, 262, 264], "ab": [20, 107, 150, 191, 206, 242, 256], "augend": 21, "addend": 21, "self_i": [22, 28, 30, 31, 33, 36, 37, 38, 39, 41, 43, 44, 45, 46, 48, 50, 51, 52], "other_i": [22, 28, 30, 31, 33, 37, 38, 39, 41, 43, 45, 47, 48, 50, 51, 52], "bitwise_and": [22, 191], "api_vers": [23, 262], "object": [23, 24, 25, 26, 29, 34, 35, 53, 57, 59, 60, 89, 98, 102, 108, 110, 112, 113, 114, 191, 192, 201, 204, 206, 210, 212, 213, 216, 218, 257, 259, 263, 264], "2020": [23, 218, 259, 261, 262], "10": [23, 27, 124, 192, 262], "latest": [23, 212], "modul": [23, 204, 259, 263, 264, 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"Introduction": [[262, "introduction"], [263, "introduction"]], "This API standard": [[262, "this-api-standard"]], "History": [[262, "history"]], "Scope (includes out-of-scope / non-goals)": [[262, "scope-includes-out-of-scope-non-goals"]], "In scope": [[262, "in-scope"]], "Out of scope": [[262, "out-of-scope"]], "Implications of in/out of scope": [[262, "implications-of-in-out-of-scope"]], "Stakeholders": [[262, "stakeholders"]], "How to read this document": [[262, "how-to-read-this-document"]], "How to adopt this API": [[262, "how-to-adopt-this-api"]], "Checking an array object for Compliance": [[262, "checking-an-array-object-for-compliance"]], "Discoverability of conforming implementations": [[262, "discoverability-of-conforming-implementations"]], "Optional feature": [[262, null]], "Conformance": [[262, "conformance"]], "Terms and Definitions": [[262, "terms-and-definitions"]], "Normative References": [[262, "normative-references"]], "Usage Data": [[263, "usage-data"]], "Design": 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{"__array_api_version__ (in module array_api)": [[8, "array_api.__array_api_version__"]], "abs() (in module array_api)": [[9, "array_api.abs"]], "acos() (in module array_api)": [[10, "array_api.acos"]], "acosh() (in module array_api)": [[11, "array_api.acosh"]], "add() (in module array_api)": [[12, "array_api.add"]], "all() (in module array_api)": [[13, "array_api.all"]], "any() (in module array_api)": [[14, "array_api.any"]], "arange() (in module array_api)": [[15, "array_api.arange"]], "argmax() (in module array_api)": [[16, "array_api.argmax"]], "argmin() (in module array_api)": [[17, "array_api.argmin"]], "argsort() (in module array_api)": [[18, "array_api.argsort"]], "t (array property)": [[19, "array_api.array.T"]], "__abs__() (array method)": [[20, "array_api.array.__abs__"]], "__add__() (array method)": [[21, "array_api.array.__add__"]], "__and__() (array method)": [[22, "array_api.array.__and__"]], "__array_namespace__() (array method)": [[23, "array_api.array.__array_namespace__"]], "__bool__() (array method)": [[24, "array_api.array.__bool__"]], "__complex__() (array method)": [[25, "array_api.array.__complex__"]], "__dlpack__() (array method)": [[26, "array_api.array.__dlpack__"]], "__dlpack_device__() (array method)": [[27, "array_api.array.__dlpack_device__"]], "__eq__() (array method)": [[28, "array_api.array.__eq__"]], "__float__() (array method)": [[29, "array_api.array.__float__"]], "__floordiv__() (array method)": [[30, "array_api.array.__floordiv__"]], "__ge__() (array method)": [[31, "array_api.array.__ge__"]], "__getitem__() (array method)": [[32, "array_api.array.__getitem__"]], "__gt__() (array method)": [[33, "array_api.array.__gt__"]], "__index__() (array method)": [[34, "array_api.array.__index__"]], "__int__() (array method)": [[35, "array_api.array.__int__"]], "__invert__() (array method)": [[36, "array_api.array.__invert__"]], "__le__() (array method)": [[37, "array_api.array.__le__"]], "__lshift__() (array method)": [[38, "array_api.array.__lshift__"]], "__lt__() (array method)": [[39, "array_api.array.__lt__"]], "__matmul__() (array method)": [[40, "array_api.array.__matmul__"]], "__mod__() (array method)": [[41, "array_api.array.__mod__"]], "__mul__() (array method)": [[42, "array_api.array.__mul__"]], "__ne__() (array method)": [[43, "array_api.array.__ne__"]], "__neg__() (array method)": [[44, "array_api.array.__neg__"]], "__or__() (array method)": [[45, "array_api.array.__or__"]], "__pos__() (array method)": [[46, "array_api.array.__pos__"]], "__pow__() (array method)": [[47, "array_api.array.__pow__"]], "__rshift__() (array method)": [[48, "array_api.array.__rshift__"]], "__setitem__() (array method)": [[49, "array_api.array.__setitem__"]], "__sub__() (array method)": [[50, "array_api.array.__sub__"]], "__truediv__() (array method)": [[51, "array_api.array.__truediv__"]], "__xor__() (array method)": [[52, "array_api.array.__xor__"]], "device (array property)": [[53, "array_api.array.device"]], "dtype (array property)": [[54, "array_api.array.dtype"]], "mt (array property)": [[55, "array_api.array.mT"]], "ndim (array property)": [[56, "array_api.array.ndim"]], "shape (array property)": [[57, "array_api.array.shape"]], "size (array property)": [[58, "array_api.array.size"]], "to_device() (array method)": [[59, "array_api.array.to_device"]], "asarray() (in module array_api)": [[60, "array_api.asarray"]], "asin() (in module array_api)": [[61, "array_api.asin"]], "asinh() (in module array_api)": [[62, "array_api.asinh"]], "astype() (in module array_api)": [[63, "array_api.astype"]], "atan() (in module array_api)": [[64, "array_api.atan"]], "atan2() (in module array_api)": [[65, "array_api.atan2"]], "atanh() (in module array_api)": [[66, "array_api.atanh"]], "bitwise_and() (in module array_api)": [[67, "array_api.bitwise_and"]], "bitwise_invert() (in module array_api)": [[68, "array_api.bitwise_invert"]], "bitwise_left_shift() (in module array_api)": [[69, "array_api.bitwise_left_shift"]], "bitwise_or() (in module array_api)": [[70, "array_api.bitwise_or"]], "bitwise_right_shift() (in module array_api)": [[71, "array_api.bitwise_right_shift"]], "bitwise_xor() (in module array_api)": [[72, "array_api.bitwise_xor"]], "broadcast_arrays() (in module array_api)": [[73, "array_api.broadcast_arrays"]], "broadcast_to() (in module array_api)": [[74, "array_api.broadcast_to"]], "can_cast() (in module array_api)": [[75, "array_api.can_cast"]], "ceil() (in module array_api)": [[76, "array_api.ceil"]], "clip() (in module array_api)": [[77, "array_api.clip"]], "concat() (in module array_api)": [[78, "array_api.concat"]], "conj() (in module array_api)": [[79, "array_api.conj"]], "e (in module array_api.constants)": [[80, "array_api.constants.e"]], "inf (in module array_api.constants)": [[81, "array_api.constants.inf"]], "nan (in module array_api.constants)": [[82, "array_api.constants.nan"]], "newaxis (in module array_api.constants)": [[83, "array_api.constants.newaxis"]], "pi (in module array_api.constants)": [[84, "array_api.constants.pi"]], "copysign() (in module array_api)": [[85, "array_api.copysign"]], "cos() (in module array_api)": [[86, "array_api.cos"]], "cosh() (in module array_api)": [[87, "array_api.cosh"]], "cumulative_sum() (in module array_api)": [[88, "array_api.cumulative_sum"]], "__eq__() (in module array_api.data_types)": [[89, "array_api.data_types.__eq__"]], "divide() (in module array_api)": [[90, "array_api.divide"]], "empty() (in module array_api)": [[91, "array_api.empty"]], "empty_like() (in module array_api)": [[92, "array_api.empty_like"]], "equal() (in module array_api)": [[93, "array_api.equal"]], "exp() (in module array_api)": [[94, "array_api.exp"]], "expand_dims() (in module array_api)": [[95, "array_api.expand_dims"]], "expm1() (in module array_api)": [[96, "array_api.expm1"]], "eye() (in module array_api)": [[97, "array_api.eye"]], "finfo() (in module array_api)": [[98, "array_api.finfo"]], "flip() (in module array_api)": [[99, "array_api.flip"]], "floor() (in module array_api)": [[100, "array_api.floor"]], "floor_divide() (in module array_api)": [[101, "array_api.floor_divide"]], "from_dlpack() (in module array_api)": [[102, "array_api.from_dlpack"]], "full() (in module array_api)": [[103, "array_api.full"]], "full_like() (in module array_api)": [[104, "array_api.full_like"]], "greater() (in module array_api)": [[105, "array_api.greater"]], "greater_equal() (in module array_api)": [[106, "array_api.greater_equal"]], "hypot() (in module array_api)": [[107, "array_api.hypot"]], "iinfo() (in module array_api)": [[108, "array_api.iinfo"]], "imag() (in module array_api)": [[109, "array_api.imag"]], "__array_namespace_info__() (in module array_api.info)": [[110, "array_api.info.__array_namespace_info__"]], "capabilities() (in module array_api.info)": [[111, "array_api.info.capabilities"]], "default_device() (in module array_api.info)": [[112, "array_api.info.default_device"]], "default_dtypes() (in module array_api.info)": [[113, "array_api.info.default_dtypes"]], "devices() (in module array_api.info)": [[114, "array_api.info.devices"]], "dtypes() (in module array_api.info)": [[115, "array_api.info.dtypes"]], "isdtype() (in module array_api)": [[116, "array_api.isdtype"]], "isfinite() (in module array_api)": [[117, "array_api.isfinite"]], "isinf() (in module array_api)": [[118, "array_api.isinf"]], "isnan() (in module array_api)": [[119, "array_api.isnan"]], "less() (in module array_api)": [[120, "array_api.less"]], "less_equal() (in module array_api)": [[121, "array_api.less_equal"]], "linspace() (in module array_api)": [[122, "array_api.linspace"]], "log() (in module array_api)": [[123, "array_api.log"]], "log10() (in module array_api)": [[124, "array_api.log10"]], "log1p() (in module array_api)": [[125, "array_api.log1p"]], "log2() (in module array_api)": [[126, "array_api.log2"]], "logaddexp() (in module array_api)": [[127, "array_api.logaddexp"]], "logical_and() (in module array_api)": [[128, "array_api.logical_and"]], "logical_not() (in module array_api)": [[129, "array_api.logical_not"]], "logical_or() (in module array_api)": [[130, "array_api.logical_or"]], "logical_xor() (in module array_api)": [[131, "array_api.logical_xor"]], "matmul() (in module array_api)": [[132, "array_api.matmul"]], "matrix_transpose() (in module array_api)": [[133, "array_api.matrix_transpose"]], "max() (in module array_api)": [[134, "array_api.max"]], "maximum() (in module array_api)": [[135, "array_api.maximum"]], "mean() (in module array_api)": [[136, "array_api.mean"]], "meshgrid() (in module array_api)": [[137, "array_api.meshgrid"]], "min() (in module array_api)": [[138, "array_api.min"]], "minimum() (in module array_api)": [[139, "array_api.minimum"]], "moveaxis() (in module array_api)": [[140, "array_api.moveaxis"]], "multiply() (in module array_api)": [[141, "array_api.multiply"]], "negative() (in module array_api)": [[142, "array_api.negative"]], "nextafter() (in module array_api)": [[143, "array_api.nextafter"]], "nonzero() (in module array_api)": [[144, "array_api.nonzero"]], "not_equal() (in module array_api)": [[145, "array_api.not_equal"]], "ones() (in module array_api)": [[146, "array_api.ones"]], "ones_like() (in module array_api)": [[147, "array_api.ones_like"]], "permute_dims() (in module array_api)": [[148, "array_api.permute_dims"]], "positive() (in module array_api)": [[149, "array_api.positive"]], "pow() (in module array_api)": [[150, "array_api.pow"]], "prod() (in module array_api)": [[151, "array_api.prod"]], "real() (in module array_api)": [[152, "array_api.real"]], "reciprocal() (in module array_api)": [[153, "array_api.reciprocal"]], "remainder() (in module array_api)": [[154, "array_api.remainder"]], "repeat() (in module array_api)": [[155, "array_api.repeat"]], "reshape() (in module array_api)": [[156, "array_api.reshape"]], "result_type() (in module array_api)": [[157, "array_api.result_type"]], "roll() (in module array_api)": [[158, "array_api.roll"]], "round() (in module array_api)": [[159, "array_api.round"]], "searchsorted() (in module array_api)": [[160, "array_api.searchsorted"]], "sign() (in module array_api)": [[161, "array_api.sign"]], "signbit() (in module array_api)": [[162, "array_api.signbit"]], "sin() (in module array_api)": [[163, "array_api.sin"]], "sinh() (in module array_api)": [[164, "array_api.sinh"]], "sort() (in module array_api)": [[165, "array_api.sort"]], "sqrt() (in module array_api)": [[166, "array_api.sqrt"]], "square() (in module array_api)": [[167, "array_api.square"]], "squeeze() (in module array_api)": [[168, "array_api.squeeze"]], "stack() (in module array_api)": [[169, "array_api.stack"]], "std() (in module array_api)": [[170, "array_api.std"]], "subtract() (in module array_api)": [[171, "array_api.subtract"]], "sum() (in module array_api)": [[172, "array_api.sum"]], "take() (in module array_api)": [[173, "array_api.take"]], "tan() (in module array_api)": [[174, "array_api.tan"]], "tanh() (in module array_api)": [[175, "array_api.tanh"]], "tensordot() (in module array_api)": [[176, "array_api.tensordot"]], "tile() (in module array_api)": [[177, "array_api.tile"]], "tril() (in module array_api)": [[178, "array_api.tril"]], "triu() (in module array_api)": [[179, "array_api.triu"]], "trunc() (in module array_api)": [[180, "array_api.trunc"]], "unique_all() (in module array_api)": [[181, "array_api.unique_all"]], "unique_counts() (in module array_api)": [[182, "array_api.unique_counts"]], "unique_inverse() (in module array_api)": [[183, "array_api.unique_inverse"]], "unique_values() (in module array_api)": [[184, "array_api.unique_values"]], "unstack() (in module array_api)": [[185, "array_api.unstack"]], "var() (in module array_api)": [[186, "array_api.var"]], "vecdot() (in module array_api)": [[187, "array_api.vecdot"]], "where() (in module array_api)": [[188, "array_api.where"]], "zeros() (in module array_api)": [[189, "array_api.zeros"]], "zeros_like() (in module array_api)": [[190, "array_api.zeros_like"]], "fft() (in module array_api.fft)": [[220, "array_api.fft.fft"]], "fftfreq() (in module array_api.fft)": [[221, "array_api.fft.fftfreq"]], "fftn() (in module array_api.fft)": [[222, "array_api.fft.fftn"]], "fftshift() (in module array_api.fft)": [[223, "array_api.fft.fftshift"]], "hfft() (in module array_api.fft)": [[224, "array_api.fft.hfft"]], "ifft() (in module array_api.fft)": [[225, "array_api.fft.ifft"]], "ifftn() (in module array_api.fft)": [[226, "array_api.fft.ifftn"]], "ifftshift() (in module array_api.fft)": [[227, "array_api.fft.ifftshift"]], "ihfft() (in module array_api.fft)": [[228, "array_api.fft.ihfft"]], "irfft() (in module array_api.fft)": [[229, "array_api.fft.irfft"]], "irfftn() (in module array_api.fft)": [[230, "array_api.fft.irfftn"]], "rfft() (in module array_api.fft)": [[231, "array_api.fft.rfft"]], "rfftfreq() (in module array_api.fft)": [[232, "array_api.fft.rfftfreq"]], "rfftn() (in module array_api.fft)": [[233, "array_api.fft.rfftn"]], "cholesky() (in module array_api.linalg)": [[234, "array_api.linalg.cholesky"]], "cross() (in module array_api.linalg)": [[235, "array_api.linalg.cross"]], "det() (in module array_api.linalg)": [[236, "array_api.linalg.det"]], "diagonal() (in module array_api.linalg)": [[237, "array_api.linalg.diagonal"]], "eigh() (in module array_api.linalg)": [[238, "array_api.linalg.eigh"]], "eigvalsh() (in module array_api.linalg)": [[239, "array_api.linalg.eigvalsh"]], "inv() (in module array_api.linalg)": [[240, "array_api.linalg.inv"]], "matmul() (in module array_api.linalg)": [[241, "array_api.linalg.matmul"]], "matrix_norm() (in module array_api.linalg)": [[242, "array_api.linalg.matrix_norm"]], "matrix_power() (in module array_api.linalg)": [[243, "array_api.linalg.matrix_power"]], "matrix_rank() (in module array_api.linalg)": [[244, "array_api.linalg.matrix_rank"]], "matrix_transpose() (in module array_api.linalg)": [[245, "array_api.linalg.matrix_transpose"]], "outer() (in module array_api.linalg)": [[246, "array_api.linalg.outer"]], "pinv() (in module array_api.linalg)": [[247, "array_api.linalg.pinv"]], "qr() (in module array_api.linalg)": [[248, "array_api.linalg.qr"]], "slogdet() (in module array_api.linalg)": [[249, "array_api.linalg.slogdet"]], "solve() (in module array_api.linalg)": [[250, "array_api.linalg.solve"]], "svd() (in module array_api.linalg)": [[251, "array_api.linalg.svd"]], "svdvals() (in module array_api.linalg)": [[252, "array_api.linalg.svdvals"]], "tensordot() (in module array_api.linalg)": [[253, "array_api.linalg.tensordot"]], "trace() (in module array_api.linalg)": [[254, "array_api.linalg.trace"]], "vecdot() (in module array_api.linalg)": [[255, "array_api.linalg.vecdot"]], "vector_norm() (in module array_api.linalg)": [[256, "array_api.linalg.vector_norm"]]}})
\ No newline at end of file
diff --git a/latest/API_specification/generated/array_api.info.__array_namespace_info__.html b/latest/API_specification/generated/array_api.info.__array_namespace_info__.html
index 46c650ea5..fb92ac4d4 100644
--- a/latest/API_specification/generated/array_api.info.__array_namespace_info__.html
+++ b/latest/API_specification/generated/array_api.info.__array_namespace_info__.html
@@ -466,6 +466,7 @@ <h1 id="api-specification-generated-array-api-info-array-namespace-info--page-ro
 <dt class="sig sig-object py" id="array_api.info.__array_namespace_info__">
 <span class="sig-name descname"><span class="pre">__array_namespace_info__</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">Info</span></span></span><a class="headerlink" href="#array_api.info.__array_namespace_info__" title="Link to this definition">¶</a></dt>
 <dd><p>Returns a namespace with Array API namespace inspection utilities.</p>
+<p>See <a class="reference internal" href="../inspection.html#inspection"><span class="std std-ref">Inspection</span></a> for a list of inspection APIs.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Returns<span class="colon">:</span></dt>
 <dd class="field-odd"><p><strong>out</strong> (<em>Info</em>) – An object containing Array API namespace inspection utilities.</p>
diff --git a/latest/API_specification/inspection.html b/latest/API_specification/inspection.html
index 4ddb888ee..38576a754 100644
--- a/latest/API_specification/inspection.html
+++ b/latest/API_specification/inspection.html
@@ -480,7 +480,7 @@
           <article class="md-content__inner md-typeset" role="main">
             
   <section id="inspection">
-<h1 id="api-specification-inspection--page-root">Inspection<a class="headerlink" href="#api-specification-inspection--page-root" title="Link to this heading">¶</a></h1>
+<span id="id1"></span><h1 id="api-specification-inspection--page-root">Inspection<a class="headerlink" href="#api-specification-inspection--page-root" title="Link to this heading">¶</a></h1>
 <blockquote>
 <div><p>Array API specification for namespace inspection utilities.</p>
 </div></blockquote>
diff --git a/latest/_sources/API_specification/inspection.rst.txt b/latest/_sources/API_specification/inspection.rst.txt
index 04691e712..89d9c602a 100644
--- a/latest/_sources/API_specification/inspection.rst.txt
+++ b/latest/_sources/API_specification/inspection.rst.txt
@@ -1,3 +1,5 @@
+.. _inspection:
+
 Inspection
 ==========
 
diff --git a/latest/objects.inv b/latest/objects.inv
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diff --git a/latest/searchindex.js b/latest/searchindex.js
index e7860d181..db2799057 100644
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"floordiv": 0, "__mod__": [0, 189], "mod": 0, "__pow__": [0, 189, 204], "pow": [0, 47, 189, 204, 206], "should": [0, 1, 5, 7, 9, 10, 11, 12, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 76, 77, 79, 85, 86, 87, 88, 90, 94, 95, 96, 98, 100, 101, 102, 105, 106, 107, 109, 113, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 137, 138, 139, 141, 142, 148, 149, 150, 151, 152, 154, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 168, 169, 170, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 184, 185, 190, 197, 204, 205, 206, 207, 210, 211, 212, 216, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 254, 255, 256, 260, 262, 263], "defin": [0, 5, 12, 23, 30, 41, 49, 60, 65, 79, 90, 101, 103, 104, 115, 122, 134, 135, 136, 138, 139, 140, 141, 152, 159, 164, 165, 168, 176, 177, 184, 185, 189, 192, 197, 204, 206, 207, 216, 220, 221, 224, 225, 228, 231, 232, 236, 237, 238, 245, 246, 248, 256, 261, 262, 263], "real": [0, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 24, 25, 29, 30, 31, 33, 35, 37, 39, 41, 44, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 85, 86, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 105, 106, 107, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 142, 143, 144, 145, 146, 149, 150, 152, 157, 158, 159, 160, 161, 162, 163, 164, 168, 170, 172, 173, 178, 184, 185, 187, 189, 199, 204, 207, 219, 222, 226, 227, 228, 229, 230, 231, 232, 236, 237, 238, 240, 242, 245, 246, 247, 248, 249, 250, 252, 254, 257], "data": [0, 1, 2, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 111, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 144, 145, 146, 147, 148, 149, 150, 151, 152, 154, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 184, 185, 186, 187, 188, 189, 192, 199, 202, 205, 207, 208, 211, 213, 214, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 256, 257, 258, 259, 260, 263], "type": [0, 2, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 192, 202, 205, 207, 208, 210, 212, 213, 214, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 256, 257, 260, 261], "__matmul__": [0, 189, 204], "matmul": [0, 40, 189, 199, 204, 256], "The": [0, 1, 5, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 58, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 90, 93, 94, 96, 99, 100, 101, 102, 105, 106, 107, 109, 110, 111, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 140, 141, 142, 143, 144, 147, 148, 149, 150, 151, 152, 153, 157, 158, 159, 160, 161, 162, 163, 164, 165, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 190, 199, 202, 204, 205, 206, 208, 209, 210, 211, 214, 215, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 255, 256, 257, 259, 260, 261, 262, 263], "__invert__": [0, 189], "inv": [0, 204, 256], "invert": [0, 68, 238, 241, 248], "__inv__": 0, "__and__": [0, 189], "__or__": [0, 189], "__xor__": [0, 189], "xor": [0, 72, 131], "__lshift__": [0, 189], "lshift": 0, "__rshift__": [0, 189], "rshift": 0, "integ": [0, 5, 9, 13, 14, 15, 20, 22, 26, 29, 30, 34, 35, 36, 38, 41, 44, 45, 47, 48, 51, 52, 60, 67, 68, 69, 70, 71, 72, 76, 77, 88, 90, 100, 101, 103, 104, 108, 115, 116, 122, 134, 136, 138, 142, 149, 150, 152, 153, 155, 157, 158, 168, 170, 171, 178, 184, 185, 189, 190, 204, 206, 207, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 241, 242, 252, 254, 260], "boolean": [0, 5, 22, 24, 25, 26, 29, 35, 36, 43, 45, 52, 57, 60, 63, 67, 68, 70, 72, 88, 89, 102, 103, 104, 111, 115, 116, 122, 128, 129, 130, 131, 143, 189, 199, 204], "__lt__": [0, 189, 204], "lt": 0, "__le__": [0, 189, 204], "le": 0, "__gt__": [0, 189, 204], "gt": [0, 246, 249], "__ge__": [0, 189, 204], "ge": 0, "__eq__": [0, 189, 204, 211], "eq": 0, "__ne__": [0, 189, 204], "ne": 0, "ar": [0, 1, 5, 7, 15, 16, 17, 19, 23, 24, 25, 26, 27, 29, 34, 35, 40, 49, 55, 58, 60, 77, 85, 86, 89, 90, 94, 97, 98, 99, 101, 102, 107, 114, 115, 122, 128, 129, 130, 131, 132, 141, 143, 149, 153, 156, 157, 161, 172, 173, 175, 179, 181, 185, 190, 199, 202, 204, 205, 206, 207, 208, 209, 210, 211, 212, 214, 215, 216, 218, 219, 220, 221, 223, 224, 225, 227, 228, 229, 230, 231, 233, 236, 237, 242, 245, 246, 249, 255, 256, 257, 260, 261, 262, 263], "onli": [0, 1, 5, 7, 16, 17, 23, 26, 40, 57, 58, 63, 99, 102, 107, 113, 115, 116, 122, 128, 129, 130, 131, 132, 136, 168, 184, 185, 189, 190, 199, 202, 204, 205, 207, 208, 210, 211, 212, 214, 216, 221, 233, 238, 245, 246, 248, 256, 257, 260, 261, 262, 263], "other": [0, 5, 21, 22, 23, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 50, 51, 52, 63, 89, 90, 96, 101, 102, 125, 140, 141, 168, 184, 190, 192, 202, 204, 206, 207, 208, 209, 210, 211, 212, 216, 233, 245, 255, 256, 259, 260, 262], "ani": [0, 1, 9, 10, 11, 23, 24, 25, 26, 28, 29, 34, 35, 43, 59, 61, 62, 66, 89, 93, 107, 117, 118, 144, 164, 189, 190, 199, 204, 207, 208, 210, 216, 249, 257, 259, 260, 263], "For": [0, 1, 5, 7, 9, 10, 11, 12, 16, 17, 18, 20, 24, 25, 26, 29, 30, 31, 33, 35, 37, 39, 41, 44, 57, 58, 61, 62, 64, 65, 66, 76, 79, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 105, 106, 107, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 134, 135, 137, 138, 139, 141, 142, 144, 149, 150, 152, 153, 157, 158, 159, 160, 161, 162, 163, 164, 165, 167, 170, 172, 173, 178, 179, 180, 181, 182, 190, 197, 202, 206, 207, 209, 211, 214, 219, 228, 230, 247, 249, 250, 252, 260, 262, 263], "backward": [0, 13, 14, 16, 17, 18, 31, 33, 37, 39, 105, 106, 120, 121, 122, 134, 135, 138, 139, 152, 163, 185, 190, 204, 207, 208, 212, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 260], "compat": [0, 1, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 74, 77, 85, 90, 93, 101, 105, 106, 107, 120, 121, 122, 127, 128, 130, 131, 132, 134, 135, 136, 138, 139, 141, 144, 149, 150, 152, 153, 154, 163, 168, 169, 170, 184, 185, 186, 199, 204, 207, 208, 212, 233, 240, 242, 245, 248, 254, 260, 262], "mai": [0, 5, 7, 15, 16, 17, 18, 23, 26, 28, 31, 33, 37, 39, 43, 51, 57, 58, 59, 60, 89, 90, 93, 101, 102, 105, 106, 107, 110, 115, 116, 120, 121, 122, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 143, 144, 153, 154, 158, 163, 168, 173, 179, 180, 181, 182, 184, 189, 190, 197, 199, 202, 205, 206, 207, 208, 209, 210, 211, 212, 214, 215, 216, 236, 246, 247, 249, 255, 256, 260, 261, 262], "complex": [0, 5, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 24, 25, 29, 31, 33, 35, 37, 39, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 88, 90, 93, 94, 96, 97, 98, 103, 104, 105, 106, 107, 109, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 132, 134, 135, 137, 138, 139, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 157, 159, 161, 162, 163, 164, 165, 169, 170, 172, 173, 174, 179, 180, 181, 182, 185, 199, 206, 210, 211, 213, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 261], "howev": [0, 5, 16, 17, 18, 31, 33, 37, 39, 57, 88, 101, 105, 106, 107, 116, 120, 121, 122, 134, 135, 138, 139, 153, 158, 163, 171, 172, 173, 202, 205, 206, 207, 208, 209, 211, 256, 257, 260, 262], "inequ": [0, 16, 17, 18, 31, 33, 37, 39, 105, 106, 120, 121, 134, 135, 138, 139, 163], "unspecifi": [0, 5, 10, 11, 16, 17, 18, 30, 31, 33, 37, 39, 41, 47, 51, 60, 62, 66, 77, 78, 87, 90, 94, 96, 101, 103, 104, 105, 106, 120, 121, 122, 134, 135, 138, 139, 149, 152, 158, 162, 163, 164, 167, 171, 173, 190, 197, 199, 204, 220, 221, 224, 225, 228, 231, 236, 237, 260], "thu": [0, 5, 16, 17, 18, 30, 31, 33, 37, 39, 41, 47, 57, 60, 71, 77, 101, 103, 104, 105, 106, 120, 121, 122, 134, 135, 138, 139, 149, 152, 158, 163, 172, 173, 190, 197, 206, 207, 220, 221, 224, 225, 228, 231, 236, 237, 249, 256], "depend": [0, 5, 9, 10, 11, 16, 17, 18, 20, 26, 29, 31, 33, 37, 39, 44, 47, 51, 57, 58, 59, 61, 62, 63, 64, 65, 66, 77, 86, 87, 90, 94, 96, 105, 106, 111, 120, 121, 122, 123, 124, 125, 126, 141, 142, 149, 158, 161, 162, 163, 172, 173, 186, 197, 199, 206, 207, 210, 213, 214, 216, 236, 237, 246, 247, 248, 249, 256, 260, 262, 263], "see": [0, 5, 10, 11, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 33, 34, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 53, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 74, 77, 85, 90, 93, 96, 101, 102, 104, 105, 106, 107, 111, 114, 120, 121, 123, 125, 127, 128, 130, 131, 132, 134, 135, 136, 138, 139, 141, 143, 144, 149, 150, 152, 153, 155, 159, 163, 164, 165, 168, 169, 170, 179, 180, 181, 182, 184, 185, 186, 189, 190, 199, 201, 202, 205, 207, 209, 210, 211, 216, 233, 240, 242, 245, 248, 254, 255, 260, 261, 262, 263], "order": [0, 5, 7, 16, 17, 18, 19, 26, 31, 33, 37, 39, 55, 60, 63, 65, 89, 99, 101, 102, 105, 106, 120, 121, 134, 135, 138, 139, 143, 153, 158, 163, 172, 173, 174, 179, 180, 181, 182, 190, 197, 199, 204, 206, 209, 210, 212, 227, 228, 236, 237, 240, 249, 250, 254, 256, 257, 260, 261], "chang": [0, 1, 9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 66, 86, 87, 90, 93, 94, 96, 97, 98, 102, 103, 104, 117, 118, 119, 122, 123, 124, 125, 126, 132, 134, 137, 138, 141, 142, 143, 144, 145, 146, 148, 149, 150, 154, 157, 159, 161, 162, 164, 165, 169, 170, 171, 172, 173, 174, 179, 180, 181, 182, 185, 202, 218, 219, 220, 222, 223, 224, 227, 228, 230, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 257, 260, 262, 263], "shape": [0, 1, 18, 40, 55, 63, 73, 74, 78, 88, 91, 92, 95, 99, 103, 104, 111, 132, 133, 137, 145, 146, 154, 156, 158, 163, 167, 171, 174, 175, 176, 177, 183, 185, 187, 188, 189, 204, 213, 214, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 260, 262], "result": [0, 1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 24, 25, 28, 29, 30, 31, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 79, 85, 86, 87, 90, 93, 94, 96, 100, 101, 105, 106, 107, 109, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 142, 144, 148, 149, 150, 151, 152, 153, 155, 157, 158, 159, 160, 161, 162, 164, 165, 167, 168, 169, 170, 172, 173, 174, 178, 179, 184, 190, 197, 199, 204, 206, 207, 208, 214, 232, 233, 235, 240, 241, 247, 248, 254, 260, 261, 262, 263], "promot": [0, 1, 5, 10, 11, 12, 21, 22, 30, 40, 41, 42, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 78, 85, 86, 87, 90, 94, 96, 101, 104, 107, 122, 123, 124, 125, 126, 127, 132, 135, 136, 139, 141, 142, 149, 152, 155, 161, 162, 164, 165, 167, 168, 169, 172, 173, 174, 184, 185, 186, 189, 204, 232, 233, 238, 240, 241, 242, 244, 245, 246, 247, 248, 254, 256], "rule": [0, 5, 7, 10, 11, 12, 21, 22, 30, 40, 41, 42, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 78, 85, 86, 87, 88, 90, 94, 96, 101, 103, 104, 107, 122, 123, 124, 125, 126, 127, 132, 135, 139, 141, 142, 149, 152, 155, 159, 161, 162, 164, 165, 167, 169, 172, 173, 174, 185, 186, 189, 190, 204, 207, 210, 232, 233, 238, 240, 241, 242, 244, 245, 246, 247, 248, 254, 256, 260, 262], "broadcast": [0, 12, 13, 14, 16, 17, 21, 22, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 73, 74, 77, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 134, 135, 136, 138, 139, 141, 144, 149, 150, 152, 153, 168, 169, 170, 174, 184, 185, 186, 189, 204, 233, 240, 242, 245, 248, 254, 260], "same": [0, 5, 7, 9, 12, 15, 18, 19, 20, 26, 32, 36, 38, 40, 41, 46, 48, 50, 55, 59, 63, 68, 73, 74, 76, 77, 78, 79, 88, 90, 92, 95, 98, 99, 100, 101, 102, 104, 109, 132, 133, 134, 136, 137, 138, 140, 141, 146, 147, 148, 149, 150, 151, 152, 153, 154, 156, 157, 158, 159, 163, 166, 167, 168, 169, 170, 171, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 188, 190, 199, 202, 204, 207, 208, 210, 211, 216, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 232, 234, 235, 236, 238, 241, 245, 246, 247, 249, 250, 252, 255, 256, 260, 262], "behavior": [0, 5, 47, 49, 59, 60, 63, 77, 90, 101, 103, 104, 107, 122, 141, 149, 152, 158, 171, 179, 180, 181, 182, 189, 190, 192, 199, 202, 204, 206, 207, 214, 215, 220, 221, 224, 225, 228, 231, 256, 257, 260, 261, 262, 263], "special": [0, 9, 10, 11, 12, 20, 21, 24, 25, 28, 29, 30, 35, 41, 42, 43, 47, 51, 61, 62, 64, 65, 66, 76, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 136, 138, 139, 141, 144, 149, 150, 152, 157, 159, 160, 161, 162, 164, 165, 168, 170, 172, 173, 178, 184, 204, 205, 207, 247, 252], "case": [0, 1, 5, 7, 9, 10, 11, 12, 15, 20, 21, 24, 25, 26, 28, 29, 30, 35, 41, 42, 43, 47, 51, 60, 61, 62, 64, 65, 66, 76, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 102, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 136, 137, 138, 139, 141, 144, 149, 150, 152, 157, 159, 160, 161, 162, 164, 165, 168, 170, 172, 173, 178, 184, 190, 202, 204, 205, 206, 207, 208, 211, 212, 214, 246, 247, 249, 252, 256, 258, 260, 263], "its": [0, 5, 26, 40, 73, 90, 98, 132, 141, 154, 156, 206, 207, 210, 211, 255, 260, 261, 262], "respect": [0, 9, 12, 20, 21, 22, 28, 30, 31, 33, 37, 38, 39, 41, 42, 43, 45, 48, 50, 51, 52, 65, 67, 69, 70, 71, 72, 77, 87, 90, 93, 101, 105, 106, 107, 113, 120, 121, 122, 127, 128, 130, 131, 135, 137, 139, 140, 141, 144, 152, 162, 169, 172, 173, 174, 179, 180, 185, 204, 206, 209, 211, 236, 246, 249], "binari": [0, 5, 67, 70, 72, 172, 173, 205], "two": [0, 1, 5, 15, 19, 40, 55, 65, 71, 97, 102, 132, 133, 137, 157, 174, 176, 177, 179, 180, 181, 182, 185, 190, 199, 210, 211, 214, 215, 220, 221, 224, 225, 228, 231, 232, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 256, 260, 261, 262, 263], "operand": [0, 1, 9, 10, 11, 12, 24, 25, 29, 35, 61, 62, 64, 65, 66, 76, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 138, 139, 141, 144, 149, 150, 152, 157, 159, 160, 161, 162, 164, 165, 170, 172, 173, 178, 199, 204, 206, 247, 252], "assign": [0, 208], "exampl": [0, 5, 12, 23, 26, 115, 116, 167, 189, 190, 202, 207, 208, 209, 211, 214, 215, 216, 252, 256, 260, 262, 263], "after": [0, 1, 26, 40, 132, 164, 175], "addit": [0, 5, 7, 12, 26, 50, 59, 88, 115, 169, 189, 190, 199, 205, 207, 210, 256, 260, 261, 263], "modifi": [0, 26, 208, 259], "equal": [0, 1, 9, 10, 11, 18, 20, 21, 22, 26, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 58, 61, 62, 63, 64, 65, 66, 69, 71, 77, 87, 89, 94, 96, 97, 103, 104, 107, 116, 118, 123, 124, 125, 126, 136, 143, 144, 145, 146, 149, 150, 157, 162, 163, 164, 168, 170, 171, 173, 174, 175, 179, 180, 181, 182, 184, 189, 190, 197, 204, 207, 211, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 235, 241, 242, 245, 246, 247, 248, 252, 260], "equival": [0, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 71, 101, 107, 128, 129, 130, 131, 152, 157, 171, 190, 199, 207, 208, 242, 245, 248, 254, 260], "discuss": [0, 93, 144, 204, 210, 211, 215, 260, 261, 262], "copi": [0, 1, 26, 59, 60, 63, 102, 154, 163, 204, 205, 210, 211, 213, 259, 260], "view": [0, 102, 213], "behaviour": [0, 213, 260, 262], "mutabl": [0, 213], "via": [0, 26, 101, 102, 171, 190, 205, 210, 211, 215, 217, 245, 255, 256, 257, 260], "__iadd__": 0, "__isub__": 0, "__imul__": 0, "__itruediv__": 0, "__ifloordiv__": 0, "__ipow__": 0, "__imod__": 0, "__imatmul__": 0, "__iand__": 0, "__ior__": 0, "__ixor__": 0, "__ilshift__": 0, "__irshift__": 0, "appli": [0, 12, 77, 78, 85, 90, 141, 155, 157, 167, 174, 190, 199, 202, 207, 218, 220, 223, 224, 227, 228, 229, 231, 242, 245, 256, 260, 262], "match": [0, 1, 5, 9, 20, 26, 63, 101, 152, 174, 179, 180, 212, 222, 226, 227, 228, 229, 231, 236, 237, 240, 254, 262], "op": 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181, 182, 183, 184, 185, 186, 187, 188, 189, 191, 192, 193, 194, 195, 196, 197, 198, 200, 201, 202, 204, 205, 206, 207, 208, 209, 210, 211, 212, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 261, 263], "refer": [1, 13, 14, 96, 97, 125, 168, 174, 175, 184, 185, 190, 207, 208, 216, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 248], "automat": [1, 260], "implicit": [1, 210, 211, 214, 260], "expans": [1, 260], "size": [1, 13, 14, 88, 95, 122, 143, 156, 166, 171, 174, 185, 189, 190, 209, 215, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 235, 244, 246, 249, 260], "without": [1, 7, 26, 57, 102, 113, 115, 143, 153, 154, 179, 180, 181, 182, 202, 205, 206, 209, 259, 260, 262], "purpos": [1, 5, 96, 107, 125, 202, 247, 256, 258, 259, 262], "make": [1, 7, 202, 205, 206, 208, 210, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 255, 257, 260], "differ": [1, 12, 26, 49, 50, 77, 78, 88, 90, 98, 101, 102, 141, 150, 167, 169, 170, 190, 202, 208, 211, 212, 214, 225, 236, 246, 247, 249, 252, 256, 260, 261, 262], "element": [1, 9, 10, 11, 12, 13, 14, 15, 20, 21, 22, 24, 25, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 54, 58, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 99, 100, 101, 103, 104, 105, 106, 107, 109, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 148, 149, 150, 151, 152, 153, 154, 156, 157, 158, 159, 160, 161, 162, 164, 165, 166, 168, 169, 170, 171, 172, 173, 175, 176, 177, 178, 179, 180, 181, 182, 184, 186, 189, 190, 204, 206, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 236, 245, 246, 247, 249, 252, 260], "wise": [1, 9, 10, 12, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 64, 65, 67, 68, 69, 70, 71, 72, 77, 79, 85, 90, 93, 101, 105, 106, 107, 109, 120, 121, 127, 128, 129, 130, 131, 135, 139, 141, 144, 149, 151, 152, 169, 189, 204, 206, 260], "oper": [1, 12, 19, 24, 26, 34, 40, 57, 58, 59, 61, 64, 71, 86, 88, 90, 101, 124, 126, 132, 141, 149, 150, 152, 155, 161, 165, 170, 172, 174, 189, 190, 196, 199, 204, 207, 208, 209, 210, 211, 252, 256, 257, 260, 261, 262], "facilit": [1, 197, 202], "user": [1, 7, 26, 110, 173, 202, 205, 206, 208, 211, 215, 256, 260, 261, 262], "ergonom": 1, "encourag": [1, 260, 261], "avoid": [1, 9, 63, 90, 96, 101, 107, 125, 141, 154, 205, 208, 211, 214, 256, 260, 262], "unnecessari": [1, 256], "can": [1, 7, 26, 60, 75, 110, 114, 116, 190, 199, 202, 205, 207, 208, 210, 211, 216, 245, 246, 249, 255, 256, 260, 261, 262, 263], "potenti": [1, 26, 96, 125, 153, 208, 260], "enabl": [1, 26, 102, 211, 215, 216, 260], "more": [1, 5, 7, 15, 19, 26, 40, 58, 60, 63, 73, 88, 96, 99, 101, 125, 132, 143, 149, 153, 171, 179, 180, 181, 182, 190, 199, 202, 205, 206, 207, 208, 209, 210, 211, 212, 215, 216, 220, 221, 224, 225, 228, 231, 247, 256, 257, 260, 261, 263], "memori": [1, 26, 60, 102, 202, 208, 209, 211, 260, 262], "effici": [1, 202, 208], "through": [1, 60, 65, 255, 257, 261, 262], "vector": [1, 40, 132, 137, 185, 233, 244, 249, 250, 254, 256, 260], "reduc": [1, 13, 14, 16, 17, 134, 136, 138, 150, 168, 170, 184, 190, 246, 249, 256, 261, 262], "consumpt": [1, 26, 261], "cach": 1, "local": [1, 211], "given": [1, 23, 99, 122, 156, 158, 183, 199, 204, 207, 208, 211, 212, 216, 237, 247, 256, 257, 260, 262], "involv": [1, 12, 90, 101, 141, 149, 155, 199, 206, 207, 211, 215], "singleton": [1, 13, 14, 16, 17, 95, 134, 136, 138, 150, 166, 168, 170, 175, 184, 240, 254, 260], "whose": [1, 5, 9, 11, 19, 20, 26, 47, 55, 62, 66, 85, 86, 87, 97, 99, 102, 133, 149, 156, 160, 161, 162, 171, 172, 173, 174, 176, 177, 179, 180, 181, 190, 208, 222, 226, 227, 228, 229, 231, 232, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 260, 262], "one": [1, 15, 19, 26, 40, 51, 58, 60, 63, 73, 75, 88, 90, 95, 97, 99, 101, 102, 115, 116, 122, 132, 137, 141, 143, 145, 146, 153, 158, 166, 171, 179, 180, 181, 182, 185, 190, 202, 205, 207, 208, 210, 211, 214, 215, 216, 218, 220, 222, 223, 224, 225, 226, 227, 228, 229, 231, 244, 245, 246, 254, 256, 257, 260, 262], "virtual": 1, "repeat": [1, 189, 190, 204, 262], "across": [1, 5, 90, 101, 141, 173, 204, 206, 207, 211, 255, 260], "correspond": [1, 16, 17, 23, 47, 59, 65, 73, 77, 102, 111, 112, 113, 149, 154, 156, 158, 168, 174, 179, 180, 181, 182, 184, 185, 190, 204, 206, 220, 224, 228, 231, 233, 236, 240, 259, 260], "If": [1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 29, 34, 35, 40, 44, 47, 51, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 74, 76, 77, 78, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 107, 111, 113, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 149, 150, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 166, 167, 168, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 187, 188, 190, 205, 207, 211, 217, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 232, 233, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 252, 254, 255, 256, 260, 262], "unequ": 1, "lower": [1, 77, 97, 176, 232], "higher": [1, 5, 26, 190, 205, 256, 261], "prepend": [1, 40, 95, 132, 175], "until": [1, 26, 175], "store": [1, 26, 211, 252], "determin": [1, 10, 11, 12, 13, 14, 21, 22, 26, 30, 40, 41, 42, 44, 45, 47, 50, 51, 52, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 75, 78, 85, 86, 87, 88, 90, 94, 96, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 132, 135, 139, 141, 142, 149, 152, 160, 161, 162, 164, 165, 169, 171, 172, 173, 174, 179, 180, 181, 182, 185, 186, 199, 204, 207, 210, 211, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 233, 234, 235, 238, 240, 241, 242, 244, 245, 246, 247, 248, 252, 254, 256, 260], "let": [1, 9, 10, 11, 12, 62, 66, 85, 87, 88, 93, 94, 96, 102, 117, 118, 119, 122, 123, 125, 136, 144, 150, 153, 158, 159, 162, 164, 168, 170, 173, 175, 184, 185, 190, 215, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 236, 237, 238, 246, 248, 249, 252], "b": [1, 9, 10, 11, 12, 57, 62, 66, 87, 90, 93, 94, 96, 101, 117, 118, 119, 122, 123, 125, 141, 144, 159, 162, 164, 167, 173, 185, 190, 204, 207, 208, 212, 245, 248, 262], "both": [1, 40, 44, 47, 51, 65, 77, 88, 90, 98, 101, 102, 107, 122, 132, 142, 149, 150, 170, 173, 174, 185, 190, 207, 208, 210, 214, 216, 233, 252, 256, 260, 261], "shape1": 1, "describ": [1, 5, 12, 88, 90, 93, 115, 116, 141, 144, 149, 150, 170, 192, 199, 207, 210, 214, 219, 230, 252, 260], "shape2": 1, "n1": [1, 137], "len": [1, 137, 175], "n2": [1, 137], "max": [1, 26, 77, 98, 108, 175, 189, 190, 204, 240, 242, 245], "temporari": 1, "list": [1, 73, 78, 114, 137, 167, 190, 202, 204, 211, 260, 262], "length": [1, 15, 107, 137, 154, 174, 190, 219, 221, 222, 225, 230, 249, 250], "while": [1, 101, 115, 122, 128, 129, 130, 131, 136, 140, 158, 168, 179, 180, 184, 189, 190, 197, 202, 204, 207, 208, 209, 211, 214, 245, 256, 261, 262, 263], "d1": 1, "els": [1, 26, 202, 261], "d2": 1, "set": [1, 18, 26, 49, 65, 102, 160, 163, 168, 176, 177, 179, 181, 182, 184, 189, 190, 204, 205, 206, 207, 208, 211, 212, 215, 216, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 236, 237, 238, 242, 245, 246, 248, 249, 255, 256, 260, 262, 263], "th": [1, 97, 175, 190, 220, 224, 228, 231], "throw": 1, "except": [1, 7, 13, 14, 26, 74, 78, 88, 97, 102, 122, 143, 153, 167, 171, 183, 190, 199, 202, 204, 206, 208, 211, 213, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 245, 257, 260, 261, 262], "demonstr": 1, "applic": [1, 26, 88, 150, 153, 170, 199, 252, 256, 260, 261], "4d": 1, "8": [1, 5, 7, 27, 175, 199, 202], "6": [1, 7, 175], "3d": 1, "7": [1, 7, 27, 216], "5": [1, 190, 260], "2d": 1, "1d": 1, "15": 1, "do": [1, 26, 90, 141, 152, 197, 202, 205, 207, 208, 210, 211, 212, 256, 257, 259, 260, 262, 263], "doe": [1, 15, 26, 102, 144, 171, 190, 199, 202, 205, 206, 207, 208, 209, 211, 212, 214, 216, 256, 260, 262, 263], "second": [1, 12, 65, 67, 69, 70, 71, 72, 93, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 144, 149, 167, 169, 174, 179, 180, 181, 185, 186, 233, 236, 244, 246, 247, 249, 250, 260], "append": [1, 40, 69, 95, 132, 235], "As": [1, 122, 149, 179, 180, 181, 182, 202, 210, 216, 262], "impli": [1, 179, 180, 181, 182, 259, 260], "__setitem__": [1, 171, 189, 204], "Such": [1, 206, 256], "right": [1, 69, 71, 107, 158, 164, 205, 249, 259], "hand": [1, 199], "left": [1, 5, 60, 69, 101, 103, 158, 171, 190, 199, 236, 237, 249, 260], "index": [1, 5, 16, 17, 18, 32, 34, 49, 57, 83, 97, 111, 113, 137, 140, 143, 158, 167, 171, 174, 179, 180, 181, 189, 204, 220, 224, 228, 231, 260, 262], "perform": [1, 5, 13, 14, 26, 40, 59, 60, 90, 107, 132, 141, 153, 174, 190, 205, 206, 207, 208, 209, 210, 218, 220, 223, 224, 225, 227, 228, 229, 231, 249, 250, 256, 260, 261, 262], "empti": [1, 13, 14, 15, 150, 170, 189, 190, 204, 252, 260], "ok": 1, "allow": [1, 24, 25, 26, 29, 34, 35, 113, 115, 149, 154, 174, 190, 204, 205, 206, 208, 211, 214, 215, 256, 262], "NOT": [1, 129, 259], "adher": [2, 7, 8, 189, 190, 202, 255, 260], "convent": [2, 7, 10, 11, 26, 40, 61, 62, 64, 65, 66, 88, 123, 125, 132, 149, 164, 189, 190, 197, 207, 211, 255, 256, 261], "each": [2, 9, 10, 11, 12, 20, 21, 22, 26, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 76, 77, 79, 85, 86, 87, 90, 93, 94, 96, 100, 101, 105, 106, 107, 109, 114, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 135, 137, 139, 140, 141, 142, 143, 144, 148, 149, 151, 152, 153, 156, 157, 158, 159, 160, 161, 162, 164, 165, 167, 169, 172, 173, 174, 175, 178, 179, 180, 190, 202, 204, 206, 210, 214, 216, 228, 232, 233, 234, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 255, 256, 260, 261, 262], "float": [2, 5, 9, 10, 11, 12, 13, 14, 15, 20, 21, 24, 25, 28, 29, 30, 31, 33, 34, 35, 37, 39, 40, 41, 42, 43, 44, 47, 49, 50, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 104, 107, 109, 113, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 145, 146, 149, 150, 151, 152, 155, 157, 158, 159, 160, 161, 162, 164, 165, 168, 169, 170, 172, 173, 174, 178, 179, 180, 181, 182, 184, 185, 187, 189, 197, 204, 206, 207, 214, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 234, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 261], "point": [2, 5, 9, 10, 11, 12, 13, 14, 15, 20, 24, 25, 26, 29, 34, 35, 40, 41, 42, 44, 47, 50, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 104, 107, 109, 113, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 145, 146, 149, 150, 151, 152, 155, 157, 158, 159, 160, 161, 162, 164, 165, 168, 169, 170, 172, 173, 174, 178, 179, 180, 181, 182, 184, 185, 187, 189, 197, 204, 206, 207, 211, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 234, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 262], "creat": [3, 15, 60, 91, 92, 97, 102, 103, 104, 122, 145, 146, 187, 188, 196, 202, 211, 219, 230, 256, 260], "main": [5, 97, 176, 177, 205, 210, 235, 252, 255, 262], "namespac": [5, 7, 23, 110, 192, 202, 204, 217, 255, 256, 257, 260, 263], "under": [5, 255, 259, 260], "specifi": [5, 13, 14, 15, 16, 17, 18, 26, 29, 59, 60, 63, 74, 78, 88, 91, 95, 98, 99, 103, 113, 115, 116, 122, 145, 150, 152, 153, 156, 166, 167, 170, 171, 175, 176, 177, 179, 180, 181, 182, 185, 187, 190, 199, 204, 206, 207, 208, 210, 211, 212, 216, 218, 220, 221, 222, 223, 224, 226, 227, 228, 229, 231, 235, 252, 254, 256, 257, 260, 262, 263], "name": [5, 7, 23, 26, 101, 115, 179, 180, 181, 190, 207, 236, 245, 246, 247, 249, 255, 260, 261], "descript": [5, 7, 204, 206, 240, 254], "bool": [5, 13, 14, 16, 17, 18, 22, 24, 26, 28, 31, 33, 37, 39, 43, 45, 49, 52, 60, 63, 75, 88, 89, 93, 102, 103, 104, 105, 106, 115, 116, 117, 118, 119, 120, 121, 122, 128, 129, 130, 131, 134, 136, 138, 144, 150, 154, 160, 163, 168, 170, 184, 199, 204, 214, 232, 240, 249, 254], "true": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 93, 98, 101, 102, 111, 117, 118, 119, 122, 128, 129, 130, 131, 134, 136, 138, 143, 144, 150, 154, 160, 163, 168, 170, 179, 180, 181, 182, 184, 186, 190, 204, 232, 240, 249, 254, 256], "fals": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 93, 102, 111, 117, 118, 119, 122, 128, 129, 130, 131, 134, 136, 138, 144, 150, 154, 160, 163, 168, 170, 179, 180, 181, 182, 184, 190, 232, 240, 249, 254], "int8": [5, 115, 116, 199], "bit": [5, 68, 69, 71, 85, 88, 98, 108, 150, 160, 170, 199, 204, 206, 252], "sign": [5, 9, 10, 11, 12, 15, 20, 41, 44, 62, 65, 66, 71, 85, 87, 88, 90, 94, 96, 101, 115, 116, 123, 125, 134, 135, 138, 139, 141, 142, 149, 150, 152, 158, 160, 162, 164, 170, 173, 179, 180, 181, 182, 189, 197, 204, 207, 246, 247, 252], "exist": [5, 7, 26, 60, 78, 102, 202, 204, 207, 210, 211, 212, 238, 257, 260, 261], "interv": [5, 10, 11, 13, 14, 15, 61, 62, 64, 66, 95, 122, 123, 125, 140, 167, 174, 176, 177, 183, 185, 190, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 257], "128": 5, "127": 5, "int16": [5, 88, 115, 116, 150, 170, 199, 252], "16": [5, 199], "32": [5, 199], "767": 5, "int32": [5, 88, 115, 116, 150, 170, 199, 252], "147": 5, "483": 5, "647": 5, "int64": [5, 88, 115, 116, 150, 170, 199, 252], "64": [5, 199], "9": [5, 27], "223": 5, "372": 5, "036": 5, "854": 5, "775": 5, "807": 5, "uint8": [5, 115, 116, 199], "unsign": [5, 88, 115, 116, 150, 170, 189, 252], "255": 5, "uint16": [5, 88, 115, 116, 150, 170, 199, 252], "65": 5, "535": [5, 204], "uint32": [5, 88, 115, 116, 150, 170, 199, 252], "294": 5, "967": 5, "295": 5, "uint64": [5, 115, 116, 199], "18": 5, "446": [5, 204], "744": [5, 204], "073": 5, "709": [5, 204], "551": [5, 204], "615": 5, "float32": [5, 109, 115, 116, 151, 199, 247, 249, 250], "ieee": [5, 12, 65, 80, 81, 82, 84, 90, 96, 98, 107, 125, 141, 152, 164, 172, 173, 189, 197, 206, 207, 260], "754": [5, 12, 65, 80, 81, 82, 84, 90, 96, 98, 107, 125, 141, 152, 164, 172, 173, 189, 197, 206, 207, 260], "singl": [5, 7, 24, 25, 29, 34, 35, 113, 115, 179, 180, 189, 199, 204, 205, 207, 210, 211, 216, 256, 260, 261, 262], "precis": [5, 9, 20, 42, 60, 98, 103, 104, 109, 141, 151, 164, 199, 204, 206, 222, 226, 227, 228, 229, 231, 236, 237, 240, 247, 249, 250, 254, 260], "2019": [5, 12, 90, 96, 107, 125, 141, 189, 206, 260, 262], "float64": [5, 9, 20, 115, 116, 199, 222, 226, 227, 228, 229, 231, 236, 237, 240, 254], "doubl": [5, 174, 199, 204], "complex64": [5, 109, 115, 116, 151, 199, 204, 247, 249, 250], "imaginari": [5, 10, 11, 12, 13, 14, 44, 61, 62, 63, 64, 66, 79, 87, 90, 93, 94, 96, 98, 109, 123, 125, 141, 142, 143, 144, 145, 146, 149, 157, 162, 164, 173, 204, 207], "compon": [5, 10, 11, 12, 13, 14, 44, 62, 63, 66, 79, 87, 90, 93, 94, 96, 98, 109, 123, 125, 141, 142, 143, 144, 145, 146, 149, 151, 157, 162, 164, 172, 173, 179, 180, 181, 182, 204, 207, 221, 230], "complex128": [5, 9, 20, 115, 116, 199, 204, 222, 226, 227, 228, 229, 231, 236, 237, 240, 254], "method": [5, 26, 34, 102, 189, 192, 202, 208, 210, 211, 214, 215, 216, 260, 261, 262], "attribut": [5, 23, 98, 108, 189, 201, 204, 257, 260, 261, 262], "requir": [5, 10, 11, 24, 25, 29, 34, 35, 59, 61, 62, 63, 64, 66, 88, 102, 107, 116, 150, 164, 167, 170, 171, 173, 179, 180, 182, 183, 189, 190, 197, 199, 202, 204, 205, 206, 207, 208, 209, 210, 211, 214, 216, 218, 219, 220, 222, 223, 224, 227, 228, 230, 233, 252, 255, 256, 260, 261, 262], "beyond": [5, 156, 199, 260], "It": [5, 23, 26, 102, 202, 208, 210, 260, 262, 263], "also": [5, 7, 26, 34, 102, 107, 159, 199, 202, 207, 208, 209, 210, 216, 220, 224, 228, 231, 249, 255, 262], "subnorm": [5, 107], "k": [5, 40, 97, 107, 132, 143, 176, 177, 190, 232, 236, 237, 238, 246, 248, 249, 250, 252, 260], "denorm": [5, 107], "gradual": [5, 107, 260], "underflow": [5, 9, 90, 101, 107, 247], "hardwar": [5, 53, 107, 153, 206, 210, 211, 236, 249, 256, 260], "univers": [5, 107, 205, 211, 256, 260], "mani": [5, 107, 175, 260, 262], "platform": [5, 26, 107], "compil": [5, 107, 173, 202, 205, 209, 260], "toggl": [5, 107], "daz": [5, 107], "flush": [5, 107], "ftz": [5, 107], "increas": [5, 107, 206, 261], "guard": [5, 107], "against": [5, 40, 73, 107, 132, 173, 190, 242, 245, 263], "time": [5, 7, 16, 17, 26, 107, 153, 179, 180, 202, 204, 209, 210, 215, 232, 236, 237, 238, 246, 248, 249, 256, 260, 262], "attack": [5, 107], "accordingli": [5, 10, 11, 13, 14, 16, 17, 59, 61, 62, 64, 66, 90, 96, 101, 107, 122, 123, 125, 134, 136, 137, 138, 141, 143, 150, 153, 158, 164, 168, 170, 179, 180, 181, 182, 184, 190, 199, 206, 207, 208, 209, 211, 240, 246, 254, 256], "vari": [5, 107, 158, 173, 179, 180, 181, 182, 199, 206], "function": [5, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 74, 78, 86, 87, 88, 94, 96, 99, 102, 107, 114, 115, 116, 122, 123, 125, 128, 129, 130, 131, 132, 136, 143, 149, 150, 152, 153, 154, 159, 161, 162, 163, 164, 167, 168, 170, 171, 172, 173, 174, 175, 179, 180, 181, 182, 183, 184, 185, 189, 192, 202, 204, 205, 207, 208, 209, 210, 211, 214, 215, 216, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 232, 233, 236, 237, 238, 242, 245, 246, 247, 248, 249, 250, 252, 255, 256, 257, 260, 261, 262], "access": [5, 26, 32, 102, 110, 190, 204, 210, 255, 257, 260], "variou": [5, 204], "cast": [5, 29, 49, 60, 63, 75, 88, 150, 170, 199, 207, 252, 260, 262], "introspect": 5, "isdtyp": [5, 189, 204], "integr": [5, 63, 113, 115, 116], "keyword": [5, 7, 26, 63, 88, 114, 137, 150, 170, 189, 204, 208, 211, 215, 216, 252, 256, 257, 260, 261, 262], "affect": [5, 15, 49, 208, 211], "intermedi": [5, 9, 107], "calcul": [5, 9, 10, 11, 12, 20, 21, 42, 47, 50, 61, 62, 64, 65, 66, 86, 87, 88, 90, 94, 96, 123, 124, 125, 126, 127, 134, 136, 138, 141, 149, 150, 161, 162, 164, 168, 169, 170, 172, 173, 184, 204, 247], "implementor": [5, 255], "free": [5, 211, 259], "when": [5, 7, 12, 16, 17, 26, 47, 49, 59, 63, 90, 96, 101, 102, 107, 113, 115, 122, 125, 134, 135, 138, 139, 141, 149, 150, 153, 154, 158, 168, 170, 173, 184, 186, 189, 190, 199, 204, 205, 207, 208, 209, 210, 212, 214, 215, 216, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 236, 238, 242, 245, 246, 247, 248, 249, 250, 252, 256, 260, 261, 262], "accumul": 5, "reduct": [5, 13, 14], "long": [5, 110, 216], "ha": [5, 9, 13, 14, 20, 23, 29, 34, 35, 40, 44, 47, 55, 86, 87, 88, 90, 94, 95, 96, 101, 104, 132, 136, 137, 140, 141, 142, 143, 149, 150, 161, 162, 166, 168, 170, 171, 172, 173, 174, 175, 179, 180, 181, 182, 184, 190, 199, 202, 207, 210, 211, 214, 215, 233, 240, 248, 249, 252, 254, 256, 257, 260, 262, 263], "wai": [5, 26, 63, 102, 202, 205, 211, 212, 257, 260, 261, 262, 263], "f4": [5, 199], "ensur": [5, 26, 158, 202, 206, 256, 260, 261, 262], "portabl": [5, 59, 122, 206, 208, 211, 212, 260], "consum": [5, 26, 63, 113, 115, 202, 207, 208, 216, 255, 260, 261], "recommend": [5, 7, 19, 23, 26, 122, 128, 129, 130, 131, 136, 152, 168, 184, 197, 204, 206, 210, 211, 260], "guidanc": [5, 7, 49, 204, 205, 212, 260], "govern": [5, 50, 169, 199, 256, 257], "interact": [5, 207], "either": [5, 9, 10, 11, 12, 24, 26, 35, 40, 65, 77, 87, 88, 90, 93, 94, 96, 98, 101, 102, 107, 110, 116, 117, 118, 122, 123, 124, 125, 126, 127, 132, 134, 135, 138, 139, 141, 150, 152, 159, 160, 161, 164, 170, 172, 173, 174, 190, 206, 207, 208, 212, 216, 247, 252, 260, 261, 263], "whether": [5, 13, 14, 26, 59, 60, 63, 88, 89, 102, 111, 116, 119, 122, 154, 160, 204, 211, 232, 236, 237, 246, 248, 255, 259, 260, 262], "otherwis": [5, 13, 14, 15, 16, 17, 26, 59, 60, 63, 75, 102, 111, 113, 115, 134, 136, 138, 150, 153, 154, 158, 159, 168, 170, 184, 185, 186, 189, 190, 202, 211, 232, 234, 240, 247, 248, 254, 259], "note": [5, 7, 9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 61, 62, 63, 64, 65, 66, 76, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 98, 100, 101, 103, 104, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 123, 124, 125, 126, 127, 132, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 152, 153, 157, 158, 159, 160, 161, 162, 164, 165, 168, 169, 170, 171, 172, 173, 174, 175, 178, 179, 180, 181, 182, 183, 184, 185, 189, 190, 204, 210, 214, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 260, 261, 262, 263], "possibl": [5, 26, 60, 101, 102, 134, 138, 154, 172, 173, 202, 205, 206, 207, 208, 210, 211, 212, 214, 216, 256, 260, 261, 262, 263], "multipl": [5, 7, 13, 14, 16, 17, 40, 42, 44, 132, 134, 136, 138, 141, 142, 150, 168, 170, 184, 190, 202, 205, 207, 210, 211, 215, 216, 237, 238, 256, 257, 260, 262], "In": [5, 12, 19, 26, 59, 88, 90, 93, 101, 116, 118, 119, 141, 144, 150, 152, 159, 170, 189, 190, 192, 199, 206, 207, 210, 212, 227, 228, 246, 247, 249, 252, 256, 257, 261, 262, 263], "clearli": [5, 59, 116, 197, 207, 256, 257], "warn": [5, 153, 212], "about": [5, 7, 26, 98, 108, 208, 256, 260, 262, 263], "": [5, 26, 29, 32, 49, 58, 59, 60, 80, 101, 102, 137, 152, 168, 175, 176, 177, 184, 190, 197, 202, 204, 205, 206, 207, 208, 210, 211, 214, 216, 220, 224, 228, 231, 245, 249, 250, 256, 257, 260, 262], "organ": [5, 204, 256, 261, 262], "within": [5, 15, 27, 190, 199, 202, 204, 207, 211, 218, 220, 223, 224, 227, 228, 229, 231, 260], "numer": [5, 9, 12, 20, 21, 40, 42, 44, 46, 47, 50, 51, 88, 90, 101, 115, 116, 117, 118, 119, 132, 137, 141, 142, 148, 149, 150, 157, 159, 165, 169, 170, 174, 199, 206, 218, 220, 223, 224, 227, 228, 229, 231, 233, 244, 245, 247, 252, 256, 260, 262], "accord": [5, 12, 60, 71, 75, 88, 90, 98, 101, 103, 122, 141, 149, 158, 159, 168, 184, 185, 190, 206, 207], "These": [5, 208, 236, 261], "intend": [5, 88, 150, 170, 202, 252], "posit": [7, 9, 10, 11, 13, 14, 20, 46, 62, 65, 66, 81, 90, 95, 97, 98, 101, 118, 123, 125, 140, 141, 143, 152, 156, 160, 162, 164, 173, 189, 190, 202, 204, 206, 216, 230, 232, 246, 261], "paramet": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 202, 204, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 256], "extern": [7, 262], "usabl": 7, "accept": [7, 26, 128, 129, 130, 131, 136, 152, 168, 184, 202, 257], "call": [7, 34, 210, 211, 214, 247, 260, 261, 262], "argument": [7, 10, 11, 26, 40, 61, 62, 63, 64, 65, 66, 86, 88, 107, 114, 123, 125, 132, 150, 155, 158, 161, 164, 170, 172, 173, 174, 189, 199, 204, 206, 208, 210, 211, 218, 220, 223, 224, 227, 228, 229, 231, 252, 256, 260, 261, 262], "map": [7, 207, 208], "base": [7, 47, 57, 58, 94, 95, 123, 124, 125, 126, 149, 179, 180, 181, 182, 190, 204, 208, 214, 216, 256, 257, 260, 261, 262], "sole": [7, 190, 197, 256], "incompat": [7, 26, 74, 102, 202, 257, 260], "us": [7, 19, 26, 27, 59, 60, 83, 98, 102, 107, 122, 124, 126, 156, 179, 181, 189, 190, 199, 204, 206, 207, 208, 209, 211, 212, 215, 216, 217, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 255, 256, 257, 258, 259, 260, 263], "normal": [7, 78, 167, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231], "practic": [7, 19, 190, 256, 261], "avail": [7, 102, 114, 202, 210, 255, 257, 261], "still": [7, 26, 216, 256, 261, 262, 263], "consid": [7, 26, 63, 102, 128, 129, 130, 131, 179, 180, 181, 182, 207, 211, 230, 245, 256, 260, 262, 263], "compliant": [7, 26, 51, 90, 96, 102, 122, 125, 128, 129, 130, 131, 134, 135, 136, 138, 139, 168, 184, 206, 209, 211, 257, 260], "altern": [7, 208, 210, 263], "thei": [7, 26, 199, 205, 210, 211, 215, 216, 255, 256, 257, 260, 262, 263], "were": [7, 101, 153, 158, 204, 260], "option": [7, 13, 14, 15, 16, 17, 23, 26, 57, 58, 59, 60, 63, 77, 78, 88, 91, 92, 97, 99, 102, 103, 104, 113, 115, 122, 134, 136, 138, 145, 146, 150, 153, 154, 156, 158, 168, 170, 171, 184, 187, 188, 189, 204, 215, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 240, 242, 245, 252, 254, 256, 261, 262], "lead": [7, 101, 207, 246, 249, 260], "readabl": [7, 199, 256, 261], "code": [7, 59, 199, 208, 209, 211, 214, 216, 256, 260, 261, 262], "easier": [7, 202, 208, 256], "evolv": [7, 202, 256], "over": [7, 13, 14, 26, 122, 134, 136, 138, 150, 168, 170, 171, 174, 184, 185, 206, 207, 208, 210, 211, 215, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 233, 252, 254, 256, 260], "ad": [7, 9, 10, 11, 12, 13, 14, 20, 21, 24, 26, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 86, 87, 90, 93, 94, 96, 97, 98, 102, 103, 104, 117, 118, 119, 122, 123, 124, 125, 126, 132, 137, 141, 142, 143, 144, 145, 146, 148, 149, 150, 157, 159, 161, 162, 164, 165, 169, 170, 172, 173, 174, 179, 180, 181, 182, 185, 190, 203, 204, 205, 211, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 257], "worri": 7, "xi": [7, 137], "annot": [7, 204, 216, 260], "individu": [7, 158, 211, 214, 215, 216, 219, 230, 260, 261], "aim": [7, 205, 216, 255, 256, 257, 260, 261, 262, 263], "strongli": [7, 208, 262], "look": [7, 262], "like": [7, 202, 205, 207, 208, 214, 216, 257, 260, 261, 262], "funcnam": 7, "key1": 7, "key2": 7, "none": [7, 13, 14, 15, 16, 17, 23, 26, 32, 49, 57, 58, 59, 60, 63, 77, 78, 83, 88, 91, 92, 97, 99, 102, 103, 104, 113, 115, 122, 134, 136, 138, 145, 146, 150, 153, 154, 156, 158, 168, 170, 171, 184, 187, 188, 190, 204, 211, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 240, 242, 245, 252, 253, 254, 260, 261, 263], "out": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 190, 204, 205, 208, 210, 214, 215, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 259, 262], "int": [7, 13, 14, 15, 16, 17, 18, 21, 22, 26, 27, 28, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 56, 57, 58, 59, 60, 74, 77, 78, 88, 91, 95, 97, 98, 99, 101, 103, 104, 108, 122, 134, 136, 138, 140, 145, 147, 150, 153, 154, 156, 163, 166, 167, 168, 170, 171, 174, 175, 176, 177, 183, 184, 185, 187, 190, 199, 214, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 235, 240, 241, 251, 252, 253, 254, 261], "str": [7, 8, 23, 115, 116, 137, 261], "modulo": 7, "self": [7, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 89, 204, 262], "few": [7, 206, 214, 260, 262], "enhanc": 7, "default": [7, 13, 14, 15, 16, 17, 18, 23, 26, 59, 60, 63, 77, 78, 88, 91, 92, 97, 99, 102, 103, 104, 112, 113, 115, 122, 134, 136, 137, 138, 143, 145, 146, 150, 153, 154, 156, 158, 163, 167, 168, 170, 174, 176, 177, 179, 180, 181, 183, 184, 185, 187, 188, 189, 190, 204, 206, 211, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 235, 240, 242, 245, 246, 249, 252, 254], "form": [7, 23, 26, 40, 79, 132, 133, 176, 177, 208, 232, 234, 235, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 257, 261], "question": [7, 205, 260], "commonli": [7, 168, 184, 205, 207, 209, 255, 256, 260, 261], "written": [7, 202, 260, 262], "yyyi": [8, 23, 257], "mm": [8, 23, 257], "string": [8, 23, 115, 116, 204, 257, 260], "version": [8, 9, 10, 11, 12, 13, 14, 20, 21, 23, 24, 25, 26, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 66, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 98, 102, 103, 104, 107, 108, 109, 116, 117, 118, 119, 122, 123, 124, 125, 126, 132, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 153, 157, 158, 159, 160, 161, 162, 164, 165, 169, 170, 171, 172, 173, 174, 175, 179, 180, 181, 182, 183, 185, 189, 202, 205, 211, 215, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 258, 260, 262], "absolut": [9, 20, 85, 159, 206, 208, 240, 241, 247, 256], "x_i": [9, 10, 11, 61, 62, 64, 66, 68, 76, 77, 79, 86, 87, 94, 96, 100, 109, 117, 118, 119, 123, 124, 125, 126, 129, 134, 136, 138, 142, 148, 151, 157, 159, 160, 161, 162, 164, 165, 168, 172, 173, 178, 184], "input": [9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 26, 30, 41, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 85, 86, 87, 88, 90, 92, 93, 94, 95, 96, 99, 100, 101, 102, 104, 105, 106, 107, 109, 116, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 188, 189, 197, 202, 204, 207, 209, 211, 212, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 249, 250, 252, 254, 256, 260, 262], "magnitud": [9, 12, 20, 85, 90, 101, 107, 141, 204, 249, 250], "represent": [9, 12, 20, 29, 44, 67, 70, 72, 80, 81, 82, 84, 90, 98, 101, 108, 141, 142, 172, 173, 206, 210, 261], "known": [9, 159, 206, 209, 210], "norm": [9, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 240, 254, 256], "modulu": [9, 152], "z": [9, 10, 11, 61, 62, 64, 66, 123, 207], "bj": [9, 12, 79, 90, 141], "comput": [9, 12, 28, 31, 33, 37, 39, 40, 43, 57, 58, 67, 70, 72, 79, 88, 89, 90, 93, 95, 101, 105, 106, 107, 120, 121, 128, 129, 130, 131, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 148, 150, 153, 168, 170, 174, 179, 180, 181, 182, 184, 185, 190, 204, 206, 209, 214, 218, 219, 220, 222, 223, 224, 226, 227, 228, 229, 230, 231, 232, 233, 236, 237, 238, 240, 242, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260], "operatornam": [9, 10, 11, 61, 62, 64, 66, 86, 87, 159, 161, 162, 172, 173, 207, 236, 237, 247, 249], "sqrt": [9, 10, 11, 61, 62, 189, 204, 207, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 254], "take": [9, 123, 125, 149, 164, 189, 204, 211, 216, 260], "care": [9, 208, 256], "undu": [9, 209], "overflow": [9, 12, 88, 90, 101, 107, 122, 150, 170, 199, 247, 252, 256], "dure": [9, 40, 59, 107, 132, 168, 184, 199, 202, 245, 260, 261], "stage": [9, 107, 257], "contain": [9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 26, 28, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 90, 91, 92, 93, 94, 96, 100, 101, 102, 105, 106, 107, 109, 110, 111, 113, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 157, 158, 159, 160, 161, 162, 164, 165, 168, 169, 170, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 184, 185, 187, 190, 204, 206, 207, 208, 210, 214, 215, 219, 220, 221, 224, 225, 228, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 260, 262], "nan": [9, 10, 11, 12, 13, 14, 24, 25, 35, 61, 62, 63, 64, 65, 66, 76, 85, 86, 87, 90, 93, 94, 96, 100, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 136, 138, 139, 141, 144, 149, 152, 157, 158, 159, 160, 161, 162, 164, 168, 172, 173, 178, 179, 180, 181, 182, 184, 189, 197, 207, 260], "infin": [9, 10, 11, 12, 13, 14, 24, 25, 35, 62, 63, 64, 65, 66, 76, 81, 86, 87, 90, 93, 94, 96, 100, 101, 107, 117, 118, 123, 124, 125, 126, 127, 134, 138, 141, 144, 149, 152, 157, 160, 161, 162, 164, 172, 173, 178, 207, 247, 254], "imag": [9, 10, 11, 12, 24, 62, 63, 66, 87, 93, 94, 96, 117, 118, 119, 122, 123, 125, 144, 157, 159, 162, 164, 173, 189, 204, 205, 260, 261, 262], "finit": [9, 10, 11, 12, 25, 35, 42, 62, 65, 66, 87, 90, 93, 94, 96, 101, 107, 117, 118, 123, 125, 141, 144, 149, 152, 160, 162, 164, 173, 206], "2022": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 90, 93, 94, 96, 97, 98, 103, 104, 108, 109, 116, 117, 118, 119, 122, 123, 124, 125, 126, 132, 137, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 157, 159, 161, 162, 164, 165, 169, 170, 171, 172, 173, 174, 179, 180, 181, 182, 185, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254], "12": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 66, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 98, 102, 103, 104, 107, 108, 109, 116, 117, 118, 119, 122, 123, 124, 125, 126, 132, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 153, 157, 158, 159, 160, 161, 162, 164, 165, 169, 170, 171, 172, 173, 174, 175, 179, 180, 181, 182, 183, 185, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 257], "approxim": [10, 11, 47, 61, 62, 64, 65, 66, 86, 87, 94, 96, 101, 123, 124, 125, 126, 149, 161, 162, 172, 173, 206, 242, 245], "princip": [10, 11, 61, 62, 64, 66, 123, 164, 207, 256], "invers": [10, 11, 61, 62, 64, 65, 66, 207, 218, 220, 223, 224, 225, 226, 227, 228, 229, 231, 238, 241, 245, 256], "cosin": [10, 11, 86, 87, 173], "express": [10, 61, 63, 64, 65, 86, 161, 172, 190, 199, 208, 256, 259], "radian": [10, 61, 64, 65, 86, 161, 172], "arc": [10, 61, 64], "frac": [10, 11, 61, 62, 64, 66, 86, 87, 90, 122, 124, 126, 159, 161, 162, 172, 173, 207, 247], "pi": [10, 11, 61, 62, 64, 66, 87, 123, 125, 162, 172, 173, 189], "j": [10, 11, 12, 25, 61, 62, 64, 66, 87, 90, 94, 96, 122, 123, 125, 141, 158, 159, 161, 162, 164, 172, 173, 190, 207, 236, 249, 252], "ln": [10, 11, 61, 62, 64, 66, 123], "zj": [10, 61, 62, 64, 66], "conj": [10, 11, 61, 62, 64, 66, 87, 94, 96, 123, 124, 125, 126, 162, 164, 173, 189, 204], "multi": [10, 11, 61, 62, 64, 66, 189, 207, 210, 211, 233, 262], "branch": [10, 11, 61, 62, 64, 65, 66, 86, 87, 90, 94, 96, 123, 125, 141, 149, 161, 162, 164, 172, 173, 260], "cut": [10, 11, 61, 62, 64, 66, 86, 87, 94, 96, 123, 125, 149, 161, 162, 164, 172, 173, 260], "plane": [10, 11, 61, 62, 64, 66, 86, 87, 90, 94, 96, 141, 161, 162, 164, 172, 173, 260], "By": [10, 11, 13, 14, 61, 62, 64, 65, 66, 88, 123, 125, 134, 136, 138, 149, 150, 164, 168, 170, 184, 185, 206, 207, 233, 256, 261], "place": [10, 11, 15, 60, 61, 62, 63, 64, 66, 91, 92, 97, 102, 103, 104, 122, 145, 146, 156, 187, 188, 189, 197, 199, 204, 208, 211, 219, 230, 245], "line": [10, 11, 61, 62, 64, 66, 172, 173, 199, 207, 260, 261, 262, 263], "segment": [10, 11, 61, 62, 64, 66, 207], "infti": [10, 11, 61, 62, 64, 66, 86, 123, 125, 149, 164, 207], "axi": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 95, 99, 123, 125, 134, 136, 138, 140, 149, 150, 153, 156, 163, 164, 166, 167, 168, 170, 171, 174, 175, 183, 184, 185, 189, 204, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 233, 240, 253, 254, 260], "rang": [10, 61, 62, 64, 66, 77, 88, 123, 125, 150, 164, 170, 190, 204, 210, 252, 260], "strip": [10, 61, 62, 64, 66, 123, 125], "unbound": [10, 61, 62, 64, 66, 123, 125], "along": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 97, 99, 123, 125, 134, 136, 138, 150, 153, 156, 163, 164, 167, 168, 170, 171, 172, 173, 175, 183, 184, 185, 190, 204, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 252, 254, 256], "c99": [10, 11, 61, 62, 64, 66, 90, 123, 125, 141, 149, 164, 207, 257], "provision": [10, 11, 61, 62, 64, 66, 123, 125, 149, 164, 207], "statu": [10, 11, 61, 62, 64, 66, 123, 125, 149, 164, 207], "greater": [10, 11, 33, 38, 48, 61, 62, 65, 66, 69, 71, 77, 85, 90, 100, 101, 123, 125, 149, 152, 159, 160, 162, 164, 166, 173, 189, 190, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 241], "than": [10, 11, 19, 26, 38, 40, 47, 48, 49, 55, 61, 62, 63, 65, 66, 69, 71, 76, 77, 85, 88, 90, 98, 99, 100, 101, 102, 123, 124, 125, 126, 132, 141, 149, 150, 152, 159, 160, 162, 164, 166, 168, 170, 171, 173, 178, 179, 180, 181, 182, 184, 190, 199, 202, 205, 208, 211, 212, 215, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 240, 241, 242, 245, 252, 254, 256, 257, 260, 262], "less": [10, 11, 39, 47, 61, 65, 66, 76, 85, 90, 101, 123, 124, 125, 126, 149, 152, 159, 160, 164, 168, 184, 189, 190, 208, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 240, 241, 242, 245, 254, 260], "\u03c0": [10, 64, 65, 84], "0j": [10, 11, 12, 25, 62, 63, 66, 87, 94, 96, 97, 123, 125, 145, 146, 159, 162, 164, 173, 207, 247], "nonzero": [10, 11, 12, 62, 66, 87, 90, 94, 96, 101, 141, 162, 173, 189, 190, 204, 245], "3\u03c0": [10, 65], "hyperbol": [11, 62, 66, 86, 87, 161, 162, 172, 173, 207], "aco": [11, 61, 189, 204, 206], "simpli": [11, 96, 125, 205, 216, 260, 262], "upper": [11, 77, 97, 177, 204, 232, 246], "half": [11, 15, 66, 122, 140, 164, 174, 190, 221], "area": [11, 62, 66], "sector": [11, 62, 66], "\u03c0j": [11, 62, 66, 123, 125], "3\u03c0j": [11, 123, 125], "sum": [12, 21, 88, 107, 127, 150, 189, 204, 240, 252, 254, 256], "x1_i": [12, 65, 67, 69, 70, 71, 72, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 135, 139, 141, 144, 149, 152, 169, 186, 204], "x2_i": [12, 65, 67, 69, 70, 71, 72, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 135, 139, 141, 144, 149, 152, 169, 186, 204], "first": [12, 16, 17, 19, 65, 67, 69, 70, 71, 72, 88, 93, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 144, 149, 156, 167, 169, 172, 173, 174, 179, 180, 181, 185, 186, 190, 207, 233, 236, 244, 246, 247, 249, 250, 256, 260, 261, 262, 263], "remain": [12, 90, 93, 101, 116, 118, 119, 141, 144, 152, 154, 159, 190, 208, 231], "neither": [12, 40, 90, 101, 132, 141, 174, 249, 261], "nor": [12, 90, 101, 141, 249, 261], "mathemat": [12, 19, 65, 84, 86, 87, 90, 96, 101, 123, 125, 141, 161, 162, 172, 173, 189, 207, 240, 254], "round": [12, 15, 76, 90, 100, 101, 141, 164, 178, 189, 204, 206], "nearest": [12, 90, 141, 157, 178, 206], "mode": [12, 90, 141, 206, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 246], "too": [12, 26, 90, 101, 141, 256, 260], "larg": [12, 90, 101, 141, 210, 216, 247, 260], "appropri": [12, 26, 90, 101, 141, 207, 212], "commut": 12, "associ": [12, 42, 141, 192, 199, 242, 245, 248, 256, 259, 261], "tabl": [12, 90, 141, 189], "c": [12, 90, 93, 122, 141, 143, 144, 153, 167, 168, 173, 184, 190, 204, 207, 210, 213, 232, 236, 237, 238, 246, 248, 249, 257, 259, 260, 262], "d": [12, 90, 93, 122, 141, 144, 199, 219, 230], "dj": [12, 90, 141], "independ": [12, 90, 141, 157, 190, 202, 210, 233, 246, 248, 256, 257, 260], "abov": [12, 88, 90, 93, 123, 125, 141, 144, 149, 150, 164, 170, 176, 177, 190, 199, 207, 208, 210, 211, 214, 235, 236, 252, 256, 259, 262], "similarli": [12, 57, 116, 137, 199, 232, 249], "henc": [12, 79, 95, 143, 153, 179, 180, 181, 182, 190, 205, 207, 208, 209, 210, 214, 215, 216, 260, 262], "z1": 12, "z2": 12, "keepdim": [13, 14, 16, 17, 134, 136, 138, 150, 168, 170, 184, 240, 254], "test": [13, 14, 89, 117, 118, 119, 204, 206, 258, 260, 261, 262], "evalu": [13, 14, 22, 30, 36, 38, 41, 44, 45, 46, 48, 51, 52, 94, 96, 123, 124, 125, 126, 142, 148, 159, 160, 165, 202, 260], "union": [13, 14, 15, 21, 22, 26, 28, 30, 31, 32, 33, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 59, 60, 75, 77, 78, 91, 98, 99, 103, 104, 108, 115, 116, 122, 134, 136, 138, 140, 145, 150, 153, 155, 156, 166, 167, 168, 170, 174, 184, 187, 221, 225, 240, 242, 245, 254, 261], "ax": [13, 14, 16, 17, 19, 55, 56, 99, 134, 136, 138, 140, 147, 150, 156, 166, 168, 170, 174, 175, 184, 185, 190, 204, 220, 221, 224, 225, 228, 231, 233, 240, 245, 248, 251, 254], "logic": [13, 14, 24, 26, 90, 93, 128, 129, 130, 131, 141, 144, 211, 214, 220, 224, 228, 231], "AND": [13, 67, 93, 128, 259], "entir": [13, 14, 86, 87, 94, 96, 134, 136, 138, 150, 161, 162, 168, 170, 184], "valid": [13, 14, 26, 27, 95, 114, 140, 167, 174, 183, 190, 206, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 236, 246, 249, 261], "count": [13, 14, 78, 88, 99, 171, 179, 180, 185, 190, 204, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 237], "last": [13, 14, 18, 19, 55, 78, 88, 99, 156, 163, 167, 171, 174, 185, 190, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 235, 240, 246, 249, 252], "invalid": [13, 14, 23, 95, 212, 260], "rais": [13, 14, 19, 23, 24, 25, 26, 29, 34, 35, 40, 47, 51, 55, 60, 74, 90, 94, 95, 102, 122, 132, 134, 138, 143, 149, 154, 166, 167, 183, 185, 190, 199, 202, 204, 210, 211, 212, 214, 233, 241, 260], "wa": [13, 14, 19, 26, 101, 134, 136, 138, 150, 168, 170, 184, 199, 211, 216, 260, 262], "OR": [14, 24, 70, 130, 144, 259], "start": [15, 122, 190, 204, 216, 260, 262], "stop": [15, 122, 190, 204, 261], "step": [15, 122, 190, 261], "evenli": [15, 122], "space": [15, 122, 219, 221, 230], "open": [15, 122, 140, 174, 190], "inclus": [15, 190, 260], "end": [15, 65, 86, 122, 159, 161, 172, 173, 197, 208, 247, 260, 261, 262], "exclus": [15, 190], "distanc": [15, 107], "between": [15, 26, 47, 51, 65, 78, 90, 93, 98, 122, 134, 135, 138, 139, 144, 149, 167, 179, 180, 181, 182, 199, 207, 208, 211, 219, 230, 256, 260, 262], "adjac": 15, "output": [15, 60, 63, 78, 88, 91, 92, 95, 97, 99, 102, 103, 104, 111, 122, 137, 145, 146, 154, 156, 158, 166, 167, 171, 175, 187, 188, 202, 204, 207, 208, 211, 213, 214, 216, 218, 219, 220, 222, 223, 224, 227, 228, 229, 230, 231, 252, 260], "infer": [15, 60, 63, 92, 103, 104, 146, 154, 188, 209, 256, 261], "cannot": [15, 26, 57, 102, 172, 173, 204, 207, 209, 260], "guarante": [15, 59, 179, 181, 202, 207, 211, 260, 262], "error": [15, 19, 23, 24, 25, 26, 29, 34, 35, 51, 55, 90, 102, 134, 138, 172, 173, 199, 206, 247, 260], "ceil": [15, 189], "indic": [16, 17, 18, 26, 60, 88, 89, 102, 111, 116, 122, 140, 143, 156, 158, 159, 171, 174, 176, 177, 179, 181, 190, 199, 204, 254, 260], "occur": [16, 17, 75, 107, 172, 173, 179, 180, 181, 182, 207, 261], "occurr": [16, 17, 179], 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181, 182, 190, 197, 199, 204, 205, 206, 207, 208, 209, 210, 211, 214, 222, 226, 227, 228, 229, 231, 236, 237, 240, 247, 249, 250, 252, 254, 255, 256, 257, 260, 261, 262], "numpi": [0, 19, 63, 190, 202, 207, 208, 210, 211, 256, 260, 261, 262, 263], "scalar": [0, 2, 49, 60, 189, 190, 204, 214, 254, 262], "valu": [0, 1, 2, 5, 7, 9, 10, 11, 12, 15, 16, 17, 18, 20, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 39, 41, 43, 49, 51, 57, 58, 60, 61, 62, 63, 64, 65, 66, 76, 77, 78, 85, 86, 87, 88, 89, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 104, 105, 106, 107, 111, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 143, 144, 145, 149, 150, 152, 153, 157, 158, 159, 160, 161, 162, 163, 164, 168, 170, 171, 172, 173, 178, 179, 180, 181, 182, 184, 185, 187, 189, 197, 199, 202, 204, 206, 208, 209, 210, 214, 216, 219, 222, 226, 227, 228, 229, 230, 231, 232, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 262], "rational": [0, 7, 88, 150, 170, 190, 210, 211, 252, 255, 257, 260], "alwai": [0, 12, 26, 42, 60, 63, 98, 102, 141, 154, 190, 202, 207, 208, 211, 236], "necessari": [0, 26, 60, 90, 102, 141, 154, 175, 190, 208, 260], "acceler": [0, 5, 107, 153, 202, 210], "where": [0, 1, 7, 13, 14, 15, 26, 47, 57, 65, 86, 87, 90, 94, 96, 97, 101, 103, 104, 124, 125, 126, 137, 141, 143, 147, 149, 153, 158, 159, 161, 162, 167, 168, 172, 173, 175, 183, 184, 185, 189, 190, 199, 205, 207, 210, 211, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 233, 236, 237, 238, 240, 242, 245, 246, 247, 248, 249, 250, 252, 256, 260, 261, 262], "non": [0, 1, 7, 13, 14, 16, 17, 63, 128, 129, 130, 131, 134, 136, 138, 143, 150, 168, 174, 184, 185, 190, 199, 204, 205, 211, 218, 220, 223, 224, 227, 228, 229, 231, 233, 234, 236, 240, 242, 249, 254, 262], "could": [0, 26, 179, 180, 181, 182, 202, 208, 215, 256, 260, 262], "forc": 0, "synchron": [0, 26, 59, 153, 260], "delai": [0, 24, 25, 29, 34, 35, 202, 214, 260], "execut": [0, 199, 202, 211, 213, 215, 260, 262], "model": [0, 57, 58, 90, 141, 207, 214, 262], "repres": [0, 8, 11, 12, 23, 24, 25, 26, 29, 34, 35, 62, 66, 87, 90, 101, 137, 141, 162, 172, 173, 204, 206, 210, 211, 247, 261, 262], "futur": [0, 26, 102, 203, 207, 208, 211, 215, 216, 236, 237, 258, 260, 262], "python": [0, 2, 5, 7, 24, 25, 26, 29, 34, 35, 49, 60, 101, 102, 152, 189, 190, 202, 204, 207, 210, 212, 214, 215, 216, 257, 259, 260, 261], "x": [0, 1, 5, 7, 9, 10, 11, 13, 14, 16, 17, 18, 20, 26, 61, 62, 63, 64, 65, 66, 68, 74, 76, 77, 79, 85, 86, 87, 88, 92, 94, 95, 96, 99, 100, 102, 104, 109, 117, 118, 119, 123, 124, 125, 126, 129, 133, 134, 136, 138, 140, 142, 143, 146, 147, 148, 150, 151, 153, 154, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 170, 171, 172, 173, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 188, 190, 207, 208, 216, 217, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 232, 234, 235, 236, 237, 238, 240, 241, 242, 243, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 262], "__pos__": [0, 189, 204], "po": 0, "__neg__": [0, 189, 204], "neg": [0, 13, 14, 15, 44, 47, 65, 78, 88, 90, 95, 97, 99, 101, 118, 123, 125, 141, 149, 152, 156, 160, 164, 171, 174, 185, 189, 190, 204, 207, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 254, 260], "x1": [0, 7, 12, 40, 65, 67, 69, 70, 71, 72, 77, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 144, 149, 152, 158, 169, 174, 185, 186, 204, 233, 239, 244, 248, 251, 253], "x2": [0, 7, 12, 40, 65, 67, 69, 70, 71, 72, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 144, 149, 152, 158, 169, 174, 185, 186, 204, 233, 239, 244, 248, 251, 253], "__add__": [0, 50, 189, 204], "add": [0, 7, 21, 88, 169, 170, 189, 190, 204, 205, 206, 211, 252], "__sub__": [0, 189, 204], "sub": [0, 190], "__mul__": [0, 189, 204], "mul": 0, "__truediv__": [0, 189, 204], "truediv": 0, "__floordiv__": [0, 189], "floordiv": 0, "__mod__": [0, 189], "mod": 0, "__pow__": [0, 189, 204], "pow": [0, 47, 189, 204, 206], "should": [0, 1, 5, 7, 9, 10, 11, 12, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 76, 77, 79, 85, 86, 87, 88, 90, 94, 95, 96, 98, 100, 101, 102, 105, 106, 107, 109, 113, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 137, 138, 139, 141, 142, 148, 149, 150, 151, 152, 154, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 168, 169, 170, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 184, 185, 190, 197, 204, 205, 206, 207, 210, 211, 212, 216, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 254, 255, 256, 260, 262, 263], "defin": [0, 5, 12, 23, 30, 41, 49, 60, 65, 79, 90, 101, 103, 104, 115, 122, 134, 135, 136, 138, 139, 140, 141, 152, 159, 164, 165, 168, 176, 177, 184, 185, 189, 192, 197, 204, 206, 207, 216, 220, 221, 224, 225, 228, 231, 232, 236, 237, 238, 245, 246, 248, 256, 261, 262, 263], "real": [0, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 24, 25, 29, 30, 31, 33, 35, 37, 39, 41, 44, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 85, 86, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 105, 106, 107, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 142, 143, 144, 145, 146, 149, 150, 152, 157, 158, 159, 160, 161, 162, 163, 164, 168, 170, 172, 173, 178, 184, 185, 187, 189, 199, 204, 207, 219, 222, 226, 227, 228, 229, 230, 231, 232, 236, 237, 238, 240, 242, 245, 246, 247, 248, 249, 250, 252, 254, 257], "data": [0, 1, 2, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 111, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 144, 145, 146, 147, 148, 149, 150, 151, 152, 154, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 184, 185, 186, 187, 188, 189, 192, 199, 202, 205, 207, 208, 211, 213, 214, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 256, 257, 258, 259, 260, 263], "type": [0, 2, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 192, 202, 205, 207, 208, 210, 212, 213, 214, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 256, 257, 260, 261], "__matmul__": [0, 189, 204], "matmul": [0, 40, 189, 199, 204, 256], "The": [0, 1, 5, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 58, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 90, 93, 94, 96, 99, 100, 101, 102, 105, 106, 107, 109, 110, 111, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 140, 141, 142, 143, 144, 147, 148, 149, 150, 151, 152, 153, 157, 158, 159, 160, 161, 162, 163, 164, 165, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 190, 199, 202, 204, 205, 206, 208, 209, 210, 211, 214, 215, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 255, 256, 257, 259, 260, 261, 262, 263], "__invert__": [0, 189], "inv": [0, 204, 256], "invert": [0, 68, 238, 241, 248], "__inv__": 0, "__and__": [0, 189], "__or__": [0, 189], "__xor__": [0, 189], "xor": [0, 72, 131], "__lshift__": [0, 189], "lshift": 0, "__rshift__": [0, 189], "rshift": 0, "integ": [0, 5, 9, 13, 14, 15, 20, 22, 26, 29, 30, 34, 35, 36, 38, 41, 44, 45, 47, 48, 51, 52, 60, 67, 68, 69, 70, 71, 72, 76, 77, 88, 90, 100, 101, 103, 104, 108, 115, 116, 122, 134, 136, 138, 142, 149, 150, 152, 153, 155, 157, 158, 168, 170, 171, 178, 184, 185, 189, 190, 204, 206, 207, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 241, 242, 252, 254, 260], "boolean": [0, 5, 22, 24, 25, 26, 29, 35, 36, 43, 45, 52, 57, 60, 63, 67, 68, 70, 72, 88, 89, 102, 103, 104, 111, 115, 116, 122, 128, 129, 130, 131, 143, 189, 199, 204], "__lt__": [0, 189, 204], "lt": 0, "__le__": [0, 189, 204], "le": 0, "__gt__": [0, 189, 204], "gt": [0, 246, 249], "__ge__": [0, 189, 204], "ge": 0, "__eq__": [0, 189, 204, 211], "eq": 0, "__ne__": [0, 189, 204], "ne": 0, "ar": [0, 1, 5, 7, 15, 16, 17, 19, 23, 24, 25, 26, 27, 29, 34, 35, 40, 49, 55, 58, 60, 77, 85, 86, 89, 90, 94, 97, 98, 99, 101, 102, 107, 114, 115, 122, 128, 129, 130, 131, 132, 141, 143, 149, 153, 156, 157, 161, 172, 173, 175, 179, 181, 185, 190, 199, 202, 204, 205, 206, 207, 208, 209, 210, 211, 212, 214, 215, 216, 218, 219, 220, 221, 223, 224, 225, 227, 228, 229, 230, 231, 233, 236, 237, 242, 245, 246, 249, 255, 256, 257, 260, 261, 262, 263], "onli": [0, 1, 5, 7, 16, 17, 23, 26, 40, 57, 58, 63, 99, 102, 107, 113, 115, 116, 122, 128, 129, 130, 131, 132, 136, 168, 184, 185, 189, 190, 199, 202, 204, 205, 207, 208, 210, 211, 212, 214, 216, 221, 233, 238, 245, 246, 248, 256, 257, 260, 261, 262, 263], "other": [0, 5, 21, 22, 23, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 50, 51, 52, 63, 89, 90, 96, 101, 102, 125, 140, 141, 168, 184, 190, 192, 202, 204, 206, 207, 208, 209, 210, 211, 212, 216, 233, 245, 255, 256, 259, 260, 262], "ani": [0, 1, 9, 10, 11, 23, 24, 25, 26, 28, 29, 34, 35, 43, 59, 61, 62, 66, 89, 93, 107, 117, 118, 144, 164, 189, 190, 199, 204, 207, 208, 210, 216, 249, 257, 259, 260, 263], "For": [0, 1, 5, 7, 9, 10, 11, 12, 16, 17, 18, 20, 24, 25, 26, 29, 30, 31, 33, 35, 37, 39, 41, 44, 57, 58, 61, 62, 64, 65, 66, 76, 79, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 105, 106, 107, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 134, 135, 137, 138, 139, 141, 142, 144, 149, 150, 152, 153, 157, 158, 159, 160, 161, 162, 163, 164, 165, 167, 170, 172, 173, 178, 179, 180, 181, 182, 190, 197, 202, 206, 207, 209, 211, 214, 219, 228, 230, 247, 249, 250, 252, 260, 262, 263], "backward": [0, 13, 14, 16, 17, 18, 31, 33, 37, 39, 105, 106, 120, 121, 122, 134, 135, 138, 139, 152, 163, 185, 190, 204, 207, 208, 212, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 260], "compat": [0, 1, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 74, 77, 85, 90, 93, 101, 105, 106, 107, 120, 121, 122, 127, 128, 130, 131, 132, 134, 135, 136, 138, 139, 141, 144, 149, 150, 152, 153, 154, 163, 168, 169, 170, 184, 185, 186, 199, 204, 207, 208, 212, 233, 240, 242, 245, 248, 254, 260, 262], "mai": [0, 5, 7, 15, 16, 17, 18, 23, 26, 28, 31, 33, 37, 39, 43, 51, 57, 58, 59, 60, 89, 90, 93, 101, 102, 105, 106, 107, 110, 115, 116, 120, 121, 122, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 143, 144, 153, 154, 158, 163, 168, 173, 179, 180, 181, 182, 184, 189, 190, 197, 199, 202, 205, 206, 207, 208, 209, 210, 211, 212, 214, 215, 216, 236, 246, 247, 249, 255, 256, 260, 261, 262], "complex": [0, 5, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 24, 25, 29, 31, 33, 35, 37, 39, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 88, 90, 93, 94, 96, 97, 98, 103, 104, 105, 106, 107, 109, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 132, 134, 135, 137, 138, 139, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 157, 159, 161, 162, 163, 164, 165, 169, 170, 172, 173, 174, 179, 180, 181, 182, 185, 199, 206, 210, 211, 213, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 261], "howev": [0, 5, 16, 17, 18, 31, 33, 37, 39, 57, 88, 101, 105, 106, 107, 116, 120, 121, 122, 134, 135, 138, 139, 153, 158, 163, 171, 172, 173, 202, 205, 206, 207, 208, 209, 211, 256, 257, 260, 262], "inequ": [0, 16, 17, 18, 31, 33, 37, 39, 105, 106, 120, 121, 134, 135, 138, 139, 163], "unspecifi": [0, 5, 10, 11, 16, 17, 18, 30, 31, 33, 37, 39, 41, 47, 51, 60, 62, 66, 77, 78, 87, 90, 94, 96, 101, 103, 104, 105, 106, 120, 121, 122, 134, 135, 138, 139, 149, 152, 158, 162, 163, 164, 167, 171, 173, 190, 197, 199, 204, 220, 221, 224, 225, 228, 231, 236, 237, 260], "thu": [0, 5, 16, 17, 18, 30, 31, 33, 37, 39, 41, 47, 57, 60, 71, 77, 101, 103, 104, 105, 106, 120, 121, 122, 134, 135, 138, 139, 149, 152, 158, 163, 172, 173, 190, 197, 206, 207, 220, 221, 224, 225, 228, 231, 236, 237, 249, 256], "depend": [0, 5, 9, 10, 11, 16, 17, 18, 20, 26, 29, 31, 33, 37, 39, 44, 47, 51, 57, 58, 59, 61, 62, 63, 64, 65, 66, 77, 86, 87, 90, 94, 96, 105, 106, 111, 120, 121, 122, 123, 124, 125, 126, 141, 142, 149, 158, 161, 162, 163, 172, 173, 186, 197, 199, 206, 207, 210, 213, 214, 216, 236, 237, 246, 247, 248, 249, 256, 260, 262, 263], "see": [0, 5, 10, 11, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 33, 34, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 53, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 74, 77, 85, 90, 93, 96, 101, 102, 104, 105, 106, 107, 110, 111, 114, 120, 121, 123, 125, 127, 128, 130, 131, 132, 134, 135, 136, 138, 139, 141, 143, 144, 149, 150, 152, 153, 155, 159, 163, 164, 165, 168, 169, 170, 179, 180, 181, 182, 184, 185, 186, 189, 190, 199, 201, 202, 205, 207, 209, 210, 211, 216, 233, 240, 242, 245, 248, 254, 255, 260, 261, 262, 263], "order": [0, 5, 7, 16, 17, 18, 19, 26, 31, 33, 37, 39, 55, 60, 63, 65, 89, 99, 101, 102, 105, 106, 120, 121, 134, 135, 138, 139, 143, 153, 158, 163, 172, 173, 174, 179, 180, 181, 182, 190, 197, 199, 204, 206, 209, 210, 212, 227, 228, 236, 237, 240, 249, 250, 254, 256, 257, 260, 261], "chang": [0, 1, 9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 66, 86, 87, 90, 93, 94, 96, 97, 98, 102, 103, 104, 117, 118, 119, 122, 123, 124, 125, 126, 132, 134, 137, 138, 141, 142, 143, 144, 145, 146, 148, 149, 150, 154, 157, 159, 161, 162, 164, 165, 169, 170, 171, 172, 173, 174, 179, 180, 181, 182, 185, 202, 218, 219, 220, 222, 223, 224, 227, 228, 230, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 257, 260, 262, 263], "shape": [0, 1, 18, 40, 55, 63, 73, 74, 78, 88, 91, 92, 95, 99, 103, 104, 111, 132, 133, 137, 145, 146, 154, 156, 158, 163, 167, 171, 174, 175, 176, 177, 183, 185, 187, 188, 189, 204, 213, 214, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 260, 262], "result": [0, 1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 24, 25, 28, 29, 30, 31, 33, 35, 36, 37, 38, 39, 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66, 67, 69, 70, 71, 72, 75, 78, 85, 86, 87, 88, 90, 94, 96, 101, 103, 104, 107, 122, 123, 124, 125, 126, 127, 132, 135, 139, 141, 142, 149, 152, 155, 159, 161, 162, 164, 165, 167, 169, 172, 173, 174, 185, 186, 189, 190, 204, 207, 210, 232, 233, 238, 240, 241, 242, 244, 245, 246, 247, 248, 254, 256, 260, 262], "broadcast": [0, 12, 13, 14, 16, 17, 21, 22, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 73, 74, 77, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 134, 135, 136, 138, 139, 141, 144, 149, 150, 152, 153, 168, 169, 170, 174, 184, 185, 186, 189, 204, 233, 240, 242, 245, 248, 254, 260], "same": [0, 5, 7, 9, 12, 15, 18, 19, 20, 26, 32, 36, 38, 40, 41, 46, 48, 50, 55, 59, 63, 68, 73, 74, 76, 77, 78, 79, 88, 90, 92, 95, 98, 99, 100, 101, 102, 104, 109, 132, 133, 134, 136, 137, 138, 140, 141, 146, 147, 148, 149, 150, 151, 152, 153, 154, 156, 157, 158, 159, 163, 166, 167, 168, 169, 170, 171, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 188, 190, 199, 202, 204, 207, 208, 210, 211, 216, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 232, 234, 235, 236, 238, 241, 245, 246, 247, 249, 250, 252, 255, 256, 260, 262], "behavior": [0, 5, 47, 49, 59, 60, 63, 77, 90, 101, 103, 104, 107, 122, 141, 149, 152, 158, 171, 179, 180, 181, 182, 189, 190, 192, 199, 202, 204, 206, 207, 214, 215, 220, 221, 224, 225, 228, 231, 256, 257, 260, 261, 262, 263], "special": [0, 9, 10, 11, 12, 20, 21, 24, 25, 28, 29, 30, 35, 41, 42, 43, 47, 51, 61, 62, 64, 65, 66, 76, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 136, 138, 139, 141, 144, 149, 150, 152, 157, 159, 160, 161, 162, 164, 165, 168, 170, 172, 173, 178, 184, 204, 205, 207, 247, 252], "case": [0, 1, 5, 7, 9, 10, 11, 12, 15, 20, 21, 24, 25, 26, 28, 29, 30, 35, 41, 42, 43, 47, 51, 60, 61, 62, 64, 65, 66, 76, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 102, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 136, 137, 138, 139, 141, 144, 149, 150, 152, 157, 159, 160, 161, 162, 164, 165, 168, 170, 172, 173, 178, 184, 190, 202, 204, 205, 206, 207, 208, 211, 212, 214, 246, 247, 249, 252, 256, 258, 260, 263], "its": [0, 5, 26, 40, 73, 90, 98, 132, 141, 154, 156, 206, 207, 210, 211, 255, 260, 261, 262], "respect": [0, 9, 12, 20, 21, 22, 28, 30, 31, 33, 37, 38, 39, 41, 42, 43, 45, 48, 50, 51, 52, 65, 67, 69, 70, 71, 72, 77, 87, 90, 93, 101, 105, 106, 107, 113, 120, 121, 122, 127, 128, 130, 131, 135, 137, 139, 140, 141, 144, 152, 162, 169, 172, 173, 174, 179, 180, 185, 204, 206, 209, 211, 236, 246, 249], "binari": [0, 5, 67, 70, 72, 172, 173, 205], "two": [0, 1, 5, 15, 19, 40, 55, 65, 71, 97, 102, 132, 133, 137, 157, 174, 176, 177, 179, 180, 181, 182, 185, 190, 199, 210, 211, 214, 215, 220, 221, 224, 225, 228, 231, 232, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 256, 260, 261, 262, 263], "operand": [0, 1, 9, 10, 11, 12, 24, 25, 29, 35, 61, 62, 64, 65, 66, 76, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 138, 139, 141, 144, 149, 150, 152, 157, 159, 160, 161, 162, 164, 165, 170, 172, 173, 178, 199, 204, 206, 247, 252], "assign": [0, 208], "exampl": [0, 5, 12, 23, 26, 115, 116, 167, 189, 190, 202, 207, 208, 209, 211, 214, 215, 216, 252, 256, 260, 262, 263], "after": [0, 1, 26, 40, 132, 164, 175], "addit": [0, 5, 7, 12, 26, 50, 59, 88, 115, 169, 189, 190, 199, 205, 207, 210, 256, 260, 261, 263], "modifi": [0, 26, 208, 259], "equal": [0, 1, 9, 10, 11, 18, 20, 21, 22, 26, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 58, 61, 62, 63, 64, 65, 66, 69, 71, 77, 87, 89, 94, 96, 97, 103, 104, 107, 116, 118, 123, 124, 125, 126, 136, 143, 144, 145, 146, 149, 150, 157, 162, 163, 164, 168, 170, 171, 173, 174, 175, 179, 180, 181, 182, 184, 189, 190, 197, 204, 207, 211, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 235, 241, 242, 245, 246, 247, 248, 252, 260], "equival": [0, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 71, 101, 107, 128, 129, 130, 131, 152, 157, 171, 190, 199, 207, 208, 242, 245, 248, 254, 260], "discuss": [0, 93, 144, 204, 210, 211, 215, 260, 261, 262], "copi": [0, 1, 26, 59, 60, 63, 102, 154, 163, 204, 205, 210, 211, 213, 259, 260], "view": [0, 102, 213], "behaviour": [0, 213, 260, 262], "mutabl": [0, 213], "via": [0, 26, 101, 102, 171, 190, 205, 210, 211, 215, 217, 245, 255, 256, 257, 260], "__iadd__": 0, "__isub__": 0, "__imul__": 0, "__itruediv__": 0, "__ifloordiv__": 0, "__ipow__": 0, "__imod__": 0, "__imatmul__": 0, "__iand__": 0, "__ior__": 0, "__ixor__": 0, "__ilshift__": 0, "__irshift__": 0, "appli": [0, 12, 77, 78, 85, 90, 141, 155, 157, 167, 174, 190, 199, 202, 207, 218, 220, 223, 224, 227, 228, 229, 231, 242, 245, 256, 260, 262], "match": [0, 1, 5, 9, 20, 26, 63, 101, 152, 174, 179, 180, 212, 222, 226, 227, 228, 229, 231, 236, 237, 240, 254, 262], "op": 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181, 182, 183, 184, 185, 186, 187, 188, 189, 191, 192, 193, 194, 195, 196, 197, 198, 200, 201, 202, 204, 205, 206, 207, 208, 209, 210, 211, 212, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 261, 263], "refer": [1, 13, 14, 96, 97, 125, 168, 174, 175, 184, 185, 190, 207, 208, 216, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 248], "automat": [1, 260], "implicit": [1, 210, 211, 214, 260], "expans": [1, 260], "size": [1, 13, 14, 88, 95, 122, 143, 156, 166, 171, 174, 185, 189, 190, 209, 215, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 235, 244, 246, 249, 260], "without": [1, 7, 26, 57, 102, 113, 115, 143, 153, 154, 179, 180, 181, 182, 202, 205, 206, 209, 259, 260, 262], "purpos": [1, 5, 96, 107, 125, 202, 247, 256, 258, 259, 262], "make": [1, 7, 202, 205, 206, 208, 210, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 255, 257, 260], "differ": [1, 12, 26, 49, 50, 77, 78, 88, 90, 98, 101, 102, 141, 150, 167, 169, 170, 190, 202, 208, 211, 212, 214, 225, 236, 246, 247, 249, 252, 256, 260, 261, 262], "element": [1, 9, 10, 11, 12, 13, 14, 15, 20, 21, 22, 24, 25, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 54, 58, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 99, 100, 101, 103, 104, 105, 106, 107, 109, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 148, 149, 150, 151, 152, 153, 154, 156, 157, 158, 159, 160, 161, 162, 164, 165, 166, 168, 169, 170, 171, 172, 173, 175, 176, 177, 178, 179, 180, 181, 182, 184, 186, 189, 190, 204, 206, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 236, 245, 246, 247, 249, 252, 260], "wise": [1, 9, 10, 12, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 64, 65, 67, 68, 69, 70, 71, 72, 77, 79, 85, 90, 93, 101, 105, 106, 107, 109, 120, 121, 127, 128, 129, 130, 131, 135, 139, 141, 144, 149, 151, 152, 169, 189, 204, 206, 260], "oper": [1, 12, 19, 24, 26, 34, 40, 57, 58, 59, 61, 64, 71, 86, 88, 90, 101, 124, 126, 132, 141, 149, 150, 152, 155, 161, 165, 170, 172, 174, 189, 190, 196, 199, 204, 207, 208, 209, 210, 211, 252, 256, 257, 260, 261, 262], "facilit": [1, 197, 202], "user": [1, 7, 26, 110, 173, 202, 205, 206, 208, 211, 215, 256, 260, 261, 262], "ergonom": 1, "encourag": [1, 260, 261], "avoid": [1, 9, 63, 90, 96, 101, 107, 125, 141, 154, 205, 208, 211, 214, 256, 260, 262], "unnecessari": [1, 256], "can": [1, 7, 26, 60, 75, 110, 114, 116, 190, 199, 202, 205, 207, 208, 210, 211, 216, 245, 246, 249, 255, 256, 260, 261, 262, 263], "potenti": [1, 26, 96, 125, 153, 208, 260], "enabl": [1, 26, 102, 211, 215, 216, 260], "more": [1, 5, 7, 15, 19, 26, 40, 58, 60, 63, 73, 88, 96, 99, 101, 125, 132, 143, 149, 153, 171, 179, 180, 181, 182, 190, 199, 202, 205, 206, 207, 208, 209, 210, 211, 212, 215, 216, 220, 221, 224, 225, 228, 231, 247, 256, 257, 260, 261, 263], "memori": [1, 26, 60, 102, 202, 208, 209, 211, 260, 262], "effici": [1, 202, 208], "through": [1, 60, 65, 255, 257, 261, 262], "vector": [1, 40, 132, 137, 185, 233, 244, 249, 250, 254, 256, 260], "reduc": [1, 13, 14, 16, 17, 134, 136, 138, 150, 168, 170, 184, 190, 246, 249, 256, 261, 262], "consumpt": [1, 26, 261], "cach": 1, "local": [1, 211], "given": [1, 23, 99, 122, 156, 158, 183, 199, 204, 207, 208, 211, 212, 216, 237, 247, 256, 257, 260, 262], "involv": [1, 12, 90, 101, 141, 149, 155, 199, 206, 207, 211, 215], "singleton": [1, 13, 14, 16, 17, 95, 134, 136, 138, 150, 166, 168, 170, 175, 184, 240, 254, 260], "whose": [1, 5, 9, 11, 19, 20, 26, 47, 55, 62, 66, 85, 86, 87, 97, 99, 102, 133, 149, 156, 160, 161, 162, 171, 172, 173, 174, 176, 177, 179, 180, 181, 190, 208, 222, 226, 227, 228, 229, 231, 232, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 260, 262], "one": [1, 15, 19, 26, 40, 51, 58, 60, 63, 73, 75, 88, 90, 95, 97, 99, 101, 102, 115, 116, 122, 132, 137, 141, 143, 145, 146, 153, 158, 166, 171, 179, 180, 181, 182, 185, 190, 202, 205, 207, 208, 210, 211, 214, 215, 216, 218, 220, 222, 223, 224, 225, 226, 227, 228, 229, 231, 244, 245, 246, 254, 256, 257, 260, 262], "virtual": 1, "repeat": [1, 189, 190, 204, 262], "across": [1, 5, 90, 101, 141, 173, 204, 206, 207, 211, 255, 260], "correspond": [1, 16, 17, 23, 47, 59, 65, 73, 77, 102, 111, 112, 113, 149, 154, 156, 158, 168, 174, 179, 180, 181, 182, 184, 185, 190, 204, 206, 220, 224, 228, 231, 233, 236, 240, 259, 260], "If": [1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 29, 34, 35, 40, 44, 47, 51, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 74, 76, 77, 78, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 107, 111, 113, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 128, 129, 130, 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231, 232, 233, 234, 235, 238, 240, 241, 242, 244, 245, 246, 247, 248, 252, 254, 256, 260], "let": [1, 9, 10, 11, 12, 62, 66, 85, 87, 88, 93, 94, 96, 102, 117, 118, 119, 122, 123, 125, 136, 144, 150, 153, 158, 159, 162, 164, 168, 170, 173, 175, 184, 185, 190, 215, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 236, 237, 238, 246, 248, 249, 252], "b": [1, 9, 10, 11, 12, 57, 62, 66, 87, 90, 93, 94, 96, 101, 117, 118, 119, 122, 123, 125, 141, 144, 159, 162, 164, 167, 173, 185, 190, 204, 207, 208, 212, 245, 248, 262], "both": [1, 40, 44, 47, 51, 65, 77, 88, 90, 98, 101, 102, 107, 122, 132, 142, 149, 150, 170, 173, 174, 185, 190, 207, 208, 210, 214, 216, 233, 252, 256, 260, 261], "shape1": 1, "describ": [1, 5, 12, 88, 90, 93, 115, 116, 141, 144, 149, 150, 170, 192, 199, 207, 210, 214, 219, 230, 252, 260], "shape2": 1, "n1": [1, 137], "len": [1, 137, 175], "n2": [1, 137], "max": [1, 26, 77, 98, 108, 175, 189, 190, 204, 240, 242, 245], "temporari": 1, "list": [1, 73, 78, 110, 114, 137, 167, 190, 202, 204, 211, 260, 262], "length": [1, 15, 107, 137, 154, 174, 190, 219, 221, 222, 225, 230, 249, 250], "while": [1, 101, 115, 122, 128, 129, 130, 131, 136, 140, 158, 168, 179, 180, 184, 189, 190, 197, 202, 204, 207, 208, 209, 211, 214, 245, 256, 261, 262, 263], "d1": 1, "els": [1, 26, 202, 261], "d2": 1, "set": [1, 18, 26, 49, 65, 102, 160, 163, 168, 176, 177, 179, 181, 182, 184, 189, 190, 204, 205, 206, 207, 208, 211, 212, 215, 216, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 236, 237, 238, 242, 245, 246, 248, 249, 255, 256, 260, 262, 263], "th": [1, 97, 175, 190, 220, 224, 228, 231], "throw": 1, "except": [1, 7, 13, 14, 26, 74, 78, 88, 97, 102, 122, 143, 153, 167, 171, 183, 190, 199, 202, 204, 206, 208, 211, 213, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 245, 257, 260, 261, 262], "demonstr": 1, "applic": [1, 26, 88, 150, 153, 170, 199, 252, 256, 260, 261], "4d": 1, "8": [1, 5, 7, 27, 175, 199, 202], "6": [1, 7, 175], "3d": 1, "7": [1, 7, 27, 216], "5": [1, 190, 260], "2d": 1, "1d": 1, "15": 1, "do": [1, 26, 90, 141, 152, 197, 202, 205, 207, 208, 210, 211, 212, 256, 257, 259, 260, 262, 263], "doe": [1, 15, 26, 102, 144, 171, 190, 199, 202, 205, 206, 207, 208, 209, 211, 212, 214, 216, 256, 260, 262, 263], "second": [1, 12, 65, 67, 69, 70, 71, 72, 93, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 144, 149, 167, 169, 174, 179, 180, 181, 185, 186, 233, 236, 244, 246, 247, 249, 250, 260], "append": [1, 40, 69, 95, 132, 235], "As": [1, 122, 149, 179, 180, 181, 182, 202, 210, 216, 262], "impli": [1, 179, 180, 181, 182, 259, 260], "__setitem__": [1, 171, 189, 204], "Such": [1, 206, 256], "right": [1, 69, 71, 107, 158, 164, 205, 249, 259], "hand": [1, 199], "left": [1, 5, 60, 69, 101, 103, 158, 171, 190, 199, 236, 237, 249, 260], "index": [1, 5, 16, 17, 18, 32, 34, 49, 57, 83, 97, 111, 113, 137, 140, 143, 158, 167, 171, 174, 179, 180, 181, 189, 204, 220, 224, 228, 231, 260, 262], "perform": [1, 5, 13, 14, 26, 40, 59, 60, 90, 107, 132, 141, 153, 174, 190, 205, 206, 207, 208, 209, 210, 218, 220, 223, 224, 225, 227, 228, 229, 231, 249, 250, 256, 260, 261, 262], "empti": [1, 13, 14, 15, 150, 170, 189, 190, 204, 252, 260], "ok": 1, "allow": [1, 24, 25, 26, 29, 34, 35, 113, 115, 149, 154, 174, 190, 204, 205, 206, 208, 211, 214, 215, 256, 262], "NOT": [1, 129, 259], "adher": [2, 7, 8, 189, 190, 202, 255, 260], "convent": [2, 7, 10, 11, 26, 40, 61, 62, 64, 65, 66, 88, 123, 125, 132, 149, 164, 189, 190, 197, 207, 211, 255, 256, 261], "each": [2, 9, 10, 11, 12, 20, 21, 22, 26, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 76, 77, 79, 85, 86, 87, 90, 93, 94, 96, 100, 101, 105, 106, 107, 109, 114, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 135, 137, 139, 140, 141, 142, 143, 144, 148, 149, 151, 152, 153, 156, 157, 158, 159, 160, 161, 162, 164, 165, 167, 169, 172, 173, 174, 175, 178, 179, 180, 190, 202, 204, 206, 210, 214, 216, 228, 232, 233, 234, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 255, 256, 260, 261, 262], "float": [2, 5, 9, 10, 11, 12, 13, 14, 15, 20, 21, 24, 25, 28, 29, 30, 31, 33, 34, 35, 37, 39, 40, 41, 42, 43, 44, 47, 49, 50, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 104, 107, 109, 113, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 145, 146, 149, 150, 151, 152, 155, 157, 158, 159, 160, 161, 162, 164, 165, 168, 169, 170, 172, 173, 174, 178, 179, 180, 181, 182, 184, 185, 187, 189, 197, 204, 206, 207, 214, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 234, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 261], "point": [2, 5, 9, 10, 11, 12, 13, 14, 15, 20, 24, 25, 26, 29, 34, 35, 40, 41, 42, 44, 47, 50, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 104, 107, 109, 113, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 145, 146, 149, 150, 151, 152, 155, 157, 158, 159, 160, 161, 162, 164, 165, 168, 169, 170, 172, 173, 174, 178, 179, 180, 181, 182, 184, 185, 187, 189, 197, 204, 206, 207, 211, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 234, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 262], "creat": [3, 15, 60, 91, 92, 97, 102, 103, 104, 122, 145, 146, 187, 188, 196, 202, 211, 219, 230, 256, 260], "main": [5, 97, 176, 177, 205, 210, 235, 252, 255, 262], "namespac": [5, 7, 23, 110, 192, 202, 204, 217, 255, 256, 257, 260, 263], "under": [5, 255, 259, 260], "specifi": [5, 13, 14, 15, 16, 17, 18, 26, 29, 59, 60, 63, 74, 78, 88, 91, 95, 98, 99, 103, 113, 115, 116, 122, 145, 150, 152, 153, 156, 166, 167, 170, 171, 175, 176, 177, 179, 180, 181, 182, 185, 187, 190, 199, 204, 206, 207, 208, 210, 211, 212, 216, 218, 220, 221, 222, 223, 224, 226, 227, 228, 229, 231, 235, 252, 254, 256, 257, 260, 262, 263], "name": [5, 7, 23, 26, 101, 115, 179, 180, 181, 190, 207, 236, 245, 246, 247, 249, 255, 260, 261], "descript": [5, 7, 204, 206, 240, 254], "bool": [5, 13, 14, 16, 17, 18, 22, 24, 26, 28, 31, 33, 37, 39, 43, 45, 49, 52, 60, 63, 75, 88, 89, 93, 102, 103, 104, 105, 106, 115, 116, 117, 118, 119, 120, 121, 122, 128, 129, 130, 131, 134, 136, 138, 144, 150, 154, 160, 163, 168, 170, 184, 199, 204, 214, 232, 240, 249, 254], "true": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 93, 98, 101, 102, 111, 117, 118, 119, 122, 128, 129, 130, 131, 134, 136, 138, 143, 144, 150, 154, 160, 163, 168, 170, 179, 180, 181, 182, 184, 186, 190, 204, 232, 240, 249, 254, 256], "fals": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 93, 102, 111, 117, 118, 119, 122, 128, 129, 130, 131, 134, 136, 138, 144, 150, 154, 160, 163, 168, 170, 179, 180, 181, 182, 184, 190, 232, 240, 249, 254], "int8": [5, 115, 116, 199], "bit": [5, 68, 69, 71, 85, 88, 98, 108, 150, 160, 170, 199, 204, 206, 252], "sign": [5, 9, 10, 11, 12, 15, 20, 41, 44, 62, 65, 66, 71, 85, 87, 88, 90, 94, 96, 101, 115, 116, 123, 125, 134, 135, 138, 139, 141, 142, 149, 150, 152, 158, 160, 162, 164, 170, 173, 179, 180, 181, 182, 189, 197, 204, 207, 246, 247, 252], "exist": [5, 7, 26, 60, 78, 102, 202, 204, 207, 210, 211, 212, 238, 257, 260, 261], "interv": [5, 10, 11, 13, 14, 15, 61, 62, 64, 66, 95, 122, 123, 125, 140, 167, 174, 176, 177, 183, 185, 190, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 257], "128": 5, "127": 5, "int16": [5, 88, 115, 116, 150, 170, 199, 252], "16": [5, 199], "32": [5, 199], "767": 5, "int32": [5, 88, 115, 116, 150, 170, 199, 252], "147": 5, "483": 5, "647": 5, "int64": [5, 88, 115, 116, 150, 170, 199, 252], "64": [5, 199], "9": [5, 27], "223": 5, "372": 5, "036": 5, "854": 5, "775": 5, "807": 5, "uint8": [5, 115, 116, 199], "unsign": [5, 88, 115, 116, 150, 170, 189, 252], "255": 5, "uint16": [5, 88, 115, 116, 150, 170, 199, 252], "65": 5, "535": [5, 204], "uint32": [5, 88, 115, 116, 150, 170, 199, 252], "294": 5, "967": 5, "295": 5, "uint64": [5, 115, 116, 199], "18": 5, "446": [5, 204], "744": [5, 204], "073": 5, "709": [5, 204], "551": [5, 204], "615": 5, "float32": [5, 109, 115, 116, 151, 199, 247, 249, 250], "ieee": [5, 12, 65, 80, 81, 82, 84, 90, 96, 98, 107, 125, 141, 152, 164, 172, 173, 189, 197, 206, 207, 260], "754": [5, 12, 65, 80, 81, 82, 84, 90, 96, 98, 107, 125, 141, 152, 164, 172, 173, 189, 197, 206, 207, 260], "singl": [5, 7, 24, 25, 29, 34, 35, 113, 115, 179, 180, 189, 199, 204, 205, 207, 210, 211, 216, 256, 260, 261, 262], "precis": [5, 9, 20, 42, 60, 98, 103, 104, 109, 141, 151, 164, 199, 204, 206, 222, 226, 227, 228, 229, 231, 236, 237, 240, 247, 249, 250, 254, 260], "2019": [5, 12, 90, 96, 107, 125, 141, 189, 206, 260, 262], "float64": [5, 9, 20, 115, 116, 199, 222, 226, 227, 228, 229, 231, 236, 237, 240, 254], "doubl": [5, 174, 199, 204], "complex64": [5, 109, 115, 116, 151, 199, 204, 247, 249, 250], "imaginari": [5, 10, 11, 12, 13, 14, 44, 61, 62, 63, 64, 66, 79, 87, 90, 93, 94, 96, 98, 109, 123, 125, 141, 142, 143, 144, 145, 146, 149, 157, 162, 164, 173, 204, 207], "compon": [5, 10, 11, 12, 13, 14, 44, 62, 63, 66, 79, 87, 90, 93, 94, 96, 98, 109, 123, 125, 141, 142, 143, 144, 145, 146, 149, 151, 157, 162, 164, 172, 173, 179, 180, 181, 182, 204, 207, 221, 230], "complex128": [5, 9, 20, 115, 116, 199, 204, 222, 226, 227, 228, 229, 231, 236, 237, 240, 254], "method": [5, 26, 34, 102, 189, 192, 202, 208, 210, 211, 214, 215, 216, 260, 261, 262], "attribut": [5, 23, 98, 108, 189, 201, 204, 257, 260, 261, 262], "requir": [5, 10, 11, 24, 25, 29, 34, 35, 59, 61, 62, 63, 64, 66, 88, 102, 107, 116, 150, 164, 167, 170, 171, 173, 179, 180, 182, 183, 189, 190, 197, 199, 202, 204, 205, 206, 207, 208, 209, 210, 211, 214, 216, 218, 219, 220, 222, 223, 224, 227, 228, 230, 233, 252, 255, 256, 260, 261, 262], "beyond": [5, 156, 199, 260], "It": [5, 23, 26, 102, 202, 208, 210, 260, 262, 263], "also": [5, 7, 26, 34, 102, 107, 159, 199, 202, 207, 208, 209, 210, 216, 220, 224, 228, 231, 249, 255, 262], "subnorm": [5, 107], "k": [5, 40, 97, 107, 132, 143, 176, 177, 190, 232, 236, 237, 238, 246, 248, 249, 250, 252, 260], "denorm": [5, 107], "gradual": [5, 107, 260], "underflow": [5, 9, 90, 101, 107, 247], "hardwar": [5, 53, 107, 153, 206, 210, 211, 236, 249, 256, 260], "univers": [5, 107, 205, 211, 256, 260], "mani": [5, 107, 175, 260, 262], "platform": [5, 26, 107], "compil": [5, 107, 173, 202, 205, 209, 260], "toggl": [5, 107], "daz": [5, 107], "flush": [5, 107], "ftz": [5, 107], "increas": [5, 107, 206, 261], "guard": [5, 107], "against": [5, 40, 73, 107, 132, 173, 190, 242, 245, 263], "time": [5, 7, 16, 17, 26, 107, 153, 179, 180, 202, 204, 209, 210, 215, 232, 236, 237, 238, 246, 248, 249, 256, 260, 262], "attack": [5, 107], "accordingli": [5, 10, 11, 13, 14, 16, 17, 59, 61, 62, 64, 66, 90, 96, 101, 107, 122, 123, 125, 134, 136, 137, 138, 141, 143, 150, 153, 158, 164, 168, 170, 179, 180, 181, 182, 184, 190, 199, 206, 207, 208, 209, 211, 240, 246, 254, 256], "vari": [5, 107, 158, 173, 179, 180, 181, 182, 199, 206], "function": [5, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 74, 78, 86, 87, 88, 94, 96, 99, 102, 107, 114, 115, 116, 122, 123, 125, 128, 129, 130, 131, 132, 136, 143, 149, 150, 152, 153, 154, 159, 161, 162, 163, 164, 167, 168, 170, 171, 172, 173, 174, 175, 179, 180, 181, 182, 183, 184, 185, 189, 192, 202, 204, 205, 207, 208, 209, 210, 211, 214, 215, 216, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 232, 233, 236, 237, 238, 242, 245, 246, 247, 248, 249, 250, 252, 255, 256, 257, 260, 261, 262], "access": [5, 26, 32, 102, 110, 190, 204, 210, 255, 257, 260], "variou": [5, 204], "cast": [5, 29, 49, 60, 63, 75, 88, 150, 170, 199, 207, 252, 260, 262], "introspect": 5, "isdtyp": [5, 189, 204], "integr": [5, 63, 113, 115, 116], "keyword": [5, 7, 26, 63, 88, 114, 137, 150, 170, 189, 204, 208, 211, 215, 216, 252, 256, 257, 260, 261, 262], "affect": [5, 15, 49, 208, 211], "intermedi": [5, 9, 107], "calcul": [5, 9, 10, 11, 12, 20, 21, 42, 47, 50, 61, 62, 64, 65, 66, 86, 87, 88, 90, 94, 96, 123, 124, 125, 126, 127, 134, 136, 138, 141, 149, 150, 161, 162, 164, 168, 169, 170, 172, 173, 184, 204, 247], "implementor": [5, 255], "free": [5, 211, 259], "when": [5, 7, 12, 16, 17, 26, 47, 49, 59, 63, 90, 96, 101, 102, 107, 113, 115, 122, 125, 134, 135, 138, 139, 141, 149, 150, 153, 154, 158, 168, 170, 173, 184, 186, 189, 190, 199, 204, 205, 207, 208, 209, 210, 212, 214, 215, 216, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 236, 238, 242, 245, 246, 247, 248, 249, 250, 252, 256, 260, 261, 262], "accumul": 5, "reduct": [5, 13, 14], "long": [5, 110, 216], "ha": [5, 9, 13, 14, 20, 23, 29, 34, 35, 40, 44, 47, 55, 86, 87, 88, 90, 94, 95, 96, 101, 104, 132, 136, 137, 140, 141, 142, 143, 149, 150, 161, 162, 166, 168, 170, 171, 172, 173, 174, 175, 179, 180, 181, 182, 184, 190, 199, 202, 207, 210, 211, 214, 215, 233, 240, 248, 249, 252, 254, 256, 257, 260, 262, 263], "wai": [5, 26, 63, 102, 202, 205, 211, 212, 257, 260, 261, 262, 263], "f4": [5, 199], "ensur": [5, 26, 158, 202, 206, 256, 260, 261, 262], "portabl": [5, 59, 122, 206, 208, 211, 212, 260], "consum": [5, 26, 63, 113, 115, 202, 207, 208, 216, 255, 260, 261], "recommend": [5, 7, 19, 23, 26, 122, 128, 129, 130, 131, 136, 152, 168, 184, 197, 204, 206, 210, 211, 260], "guidanc": [5, 7, 49, 204, 205, 212, 260], "govern": [5, 50, 169, 199, 256, 257], "interact": [5, 207], "either": [5, 9, 10, 11, 12, 24, 26, 35, 40, 65, 77, 87, 88, 90, 93, 94, 96, 98, 101, 102, 107, 110, 116, 117, 118, 122, 123, 124, 125, 126, 127, 132, 134, 135, 138, 139, 141, 150, 152, 159, 160, 161, 164, 170, 172, 173, 174, 190, 206, 207, 208, 212, 216, 247, 252, 260, 261, 263], "whether": [5, 13, 14, 26, 59, 60, 63, 88, 89, 102, 111, 116, 119, 122, 154, 160, 204, 211, 232, 236, 237, 246, 248, 255, 259, 260, 262], "otherwis": [5, 13, 14, 15, 16, 17, 26, 59, 60, 63, 75, 102, 111, 113, 115, 134, 136, 138, 150, 153, 154, 158, 159, 168, 170, 184, 185, 186, 189, 190, 202, 211, 232, 234, 240, 247, 248, 254, 259], "note": [5, 7, 9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 61, 62, 63, 64, 65, 66, 76, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 98, 100, 101, 103, 104, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 123, 124, 125, 126, 127, 132, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 152, 153, 157, 158, 159, 160, 161, 162, 164, 165, 168, 169, 170, 171, 172, 173, 174, 175, 178, 179, 180, 181, 182, 183, 184, 185, 189, 190, 204, 210, 214, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 260, 261, 262, 263], "possibl": [5, 26, 60, 101, 102, 134, 138, 154, 172, 173, 202, 205, 206, 207, 208, 210, 211, 212, 214, 216, 256, 260, 261, 262, 263], "multipl": [5, 7, 13, 14, 16, 17, 40, 42, 44, 132, 134, 136, 138, 141, 142, 150, 168, 170, 184, 190, 202, 205, 207, 210, 211, 215, 216, 237, 238, 256, 257, 260, 262], "In": [5, 12, 19, 26, 59, 88, 90, 93, 101, 116, 118, 119, 141, 144, 150, 152, 159, 170, 189, 190, 192, 199, 206, 207, 210, 212, 227, 228, 246, 247, 249, 252, 256, 257, 261, 262, 263], "clearli": [5, 59, 116, 197, 207, 256, 257], "warn": [5, 153, 212], "about": [5, 7, 26, 98, 108, 208, 256, 260, 262, 263], "": [5, 26, 29, 32, 49, 58, 59, 60, 80, 101, 102, 137, 152, 168, 175, 176, 177, 184, 190, 197, 202, 204, 205, 206, 207, 208, 210, 211, 214, 216, 220, 224, 228, 231, 245, 249, 250, 256, 257, 260, 262], "organ": [5, 204, 256, 261, 262], "within": [5, 15, 27, 190, 199, 202, 204, 207, 211, 218, 220, 223, 224, 227, 228, 229, 231, 260], "numer": [5, 9, 12, 20, 21, 40, 42, 44, 46, 47, 50, 51, 88, 90, 101, 115, 116, 117, 118, 119, 132, 137, 141, 142, 148, 149, 150, 157, 159, 165, 169, 170, 174, 199, 206, 218, 220, 223, 224, 227, 228, 229, 231, 233, 244, 245, 247, 252, 256, 260, 262], "accord": [5, 12, 60, 71, 75, 88, 90, 98, 101, 103, 122, 141, 149, 158, 159, 168, 184, 185, 190, 206, 207], "These": [5, 208, 236, 261], "intend": [5, 88, 150, 170, 202, 252], "posit": [7, 9, 10, 11, 13, 14, 20, 46, 62, 65, 66, 81, 90, 95, 97, 98, 101, 118, 123, 125, 140, 141, 143, 152, 156, 160, 162, 164, 173, 189, 190, 202, 204, 206, 216, 230, 232, 246, 261], "paramet": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 202, 204, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 256], "extern": [7, 262], "usabl": 7, "accept": [7, 26, 128, 129, 130, 131, 136, 152, 168, 184, 202, 257], "call": [7, 34, 210, 211, 214, 247, 260, 261, 262], "argument": [7, 10, 11, 26, 40, 61, 62, 63, 64, 65, 66, 86, 88, 107, 114, 123, 125, 132, 150, 155, 158, 161, 164, 170, 172, 173, 174, 189, 199, 204, 206, 208, 210, 211, 218, 220, 223, 224, 227, 228, 229, 231, 252, 256, 260, 261, 262], "map": [7, 207, 208], "base": [7, 47, 57, 58, 94, 95, 123, 124, 125, 126, 149, 179, 180, 181, 182, 190, 204, 208, 214, 216, 256, 257, 260, 261, 262], "sole": [7, 190, 197, 256], "incompat": [7, 26, 74, 102, 202, 257, 260], "us": [7, 19, 26, 27, 59, 60, 83, 98, 102, 107, 122, 124, 126, 156, 179, 181, 189, 190, 199, 204, 206, 207, 208, 209, 211, 212, 215, 216, 217, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 255, 256, 257, 258, 259, 260, 263], "normal": [7, 78, 167, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231], "practic": [7, 19, 190, 256, 261], "avail": [7, 102, 114, 202, 210, 255, 257, 261], "still": [7, 26, 216, 256, 261, 262, 263], "consid": [7, 26, 63, 102, 128, 129, 130, 131, 179, 180, 181, 182, 207, 211, 230, 245, 256, 260, 262, 263], "compliant": [7, 26, 51, 90, 96, 102, 122, 125, 128, 129, 130, 131, 134, 135, 136, 138, 139, 168, 184, 206, 209, 211, 257, 260], "altern": [7, 208, 210, 263], "thei": [7, 26, 199, 205, 210, 211, 215, 216, 255, 256, 257, 260, 262, 263], "were": [7, 101, 153, 158, 204, 260], "option": [7, 13, 14, 15, 16, 17, 23, 26, 57, 58, 59, 60, 63, 77, 78, 88, 91, 92, 97, 99, 102, 103, 104, 113, 115, 122, 134, 136, 138, 145, 146, 150, 153, 154, 156, 158, 168, 170, 171, 184, 187, 188, 189, 204, 215, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 240, 242, 245, 252, 254, 256, 261, 262], "lead": [7, 101, 207, 246, 249, 260], "readabl": [7, 199, 256, 261], "code": [7, 59, 199, 208, 209, 211, 214, 216, 256, 260, 261, 262], "easier": [7, 202, 208, 256], "evolv": [7, 202, 256], "over": [7, 13, 14, 26, 122, 134, 136, 138, 150, 168, 170, 171, 174, 184, 185, 206, 207, 208, 210, 211, 215, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 233, 252, 254, 256, 260], "ad": [7, 9, 10, 11, 12, 13, 14, 20, 21, 24, 26, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 86, 87, 90, 93, 94, 96, 97, 98, 102, 103, 104, 117, 118, 119, 122, 123, 124, 125, 126, 132, 137, 141, 142, 143, 144, 145, 146, 148, 149, 150, 157, 159, 161, 162, 164, 165, 169, 170, 172, 173, 174, 179, 180, 181, 182, 185, 190, 203, 204, 205, 211, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 257], "worri": 7, "xi": [7, 137], "annot": [7, 204, 216, 260], "individu": [7, 158, 211, 214, 215, 216, 219, 230, 260, 261], "aim": [7, 205, 216, 255, 256, 257, 260, 261, 262, 263], "strongli": [7, 208, 262], "look": [7, 262], "like": [7, 202, 205, 207, 208, 214, 216, 257, 260, 261, 262], "funcnam": 7, "key1": 7, "key2": 7, "none": [7, 13, 14, 15, 16, 17, 23, 26, 32, 49, 57, 58, 59, 60, 63, 77, 78, 83, 88, 91, 92, 97, 99, 102, 103, 104, 113, 115, 122, 134, 136, 138, 145, 146, 150, 153, 154, 156, 158, 168, 170, 171, 184, 187, 188, 190, 204, 211, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 240, 242, 245, 252, 253, 254, 260, 261, 263], "out": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 190, 204, 205, 208, 210, 214, 215, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 259, 262], "int": [7, 13, 14, 15, 16, 17, 18, 21, 22, 26, 27, 28, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 56, 57, 58, 59, 60, 74, 77, 78, 88, 91, 95, 97, 98, 99, 101, 103, 104, 108, 122, 134, 136, 138, 140, 145, 147, 150, 153, 154, 156, 163, 166, 167, 168, 170, 171, 174, 175, 176, 177, 183, 184, 185, 187, 190, 199, 214, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 235, 240, 241, 251, 252, 253, 254, 261], "str": [7, 8, 23, 115, 116, 137, 261], "modulo": 7, "self": [7, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 89, 204, 262], "few": [7, 206, 214, 260, 262], "enhanc": 7, "default": [7, 13, 14, 15, 16, 17, 18, 23, 26, 59, 60, 63, 77, 78, 88, 91, 92, 97, 99, 102, 103, 104, 112, 113, 115, 122, 134, 136, 137, 138, 143, 145, 146, 150, 153, 154, 156, 158, 163, 167, 168, 170, 174, 176, 177, 179, 180, 181, 183, 184, 185, 187, 188, 189, 190, 204, 206, 211, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 235, 240, 242, 245, 246, 249, 252, 254], "form": [7, 23, 26, 40, 79, 132, 133, 176, 177, 208, 232, 234, 235, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 257, 261], "question": [7, 205, 260], "commonli": [7, 168, 184, 205, 207, 209, 255, 256, 260, 261], "written": [7, 202, 260, 262], "yyyi": [8, 23, 257], "mm": [8, 23, 257], "string": [8, 23, 115, 116, 204, 257, 260], "version": [8, 9, 10, 11, 12, 13, 14, 20, 21, 23, 24, 25, 26, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 66, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 98, 102, 103, 104, 107, 108, 109, 116, 117, 118, 119, 122, 123, 124, 125, 126, 132, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 153, 157, 158, 159, 160, 161, 162, 164, 165, 169, 170, 171, 172, 173, 174, 175, 179, 180, 181, 182, 183, 185, 189, 202, 205, 211, 215, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 258, 260, 262], "absolut": [9, 20, 85, 159, 206, 208, 240, 241, 247, 256], "x_i": [9, 10, 11, 61, 62, 64, 66, 68, 76, 77, 79, 86, 87, 94, 96, 100, 109, 117, 118, 119, 123, 124, 125, 126, 129, 134, 136, 138, 142, 148, 151, 157, 159, 160, 161, 162, 164, 165, 168, 172, 173, 178, 184], "input": [9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 26, 30, 41, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 85, 86, 87, 88, 90, 92, 93, 94, 95, 96, 99, 100, 101, 102, 104, 105, 106, 107, 109, 116, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 188, 189, 197, 202, 204, 207, 209, 211, 212, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 249, 250, 252, 254, 256, 260, 262], "magnitud": [9, 12, 20, 85, 90, 101, 107, 141, 204, 249, 250], "represent": [9, 12, 20, 29, 44, 67, 70, 72, 80, 81, 82, 84, 90, 98, 101, 108, 141, 142, 172, 173, 206, 210, 261], "known": [9, 159, 206, 209, 210], "norm": [9, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 240, 254, 256], "modulu": [9, 152], "z": [9, 10, 11, 61, 62, 64, 66, 123, 207], "bj": [9, 12, 79, 90, 141], "comput": [9, 12, 28, 31, 33, 37, 39, 40, 43, 57, 58, 67, 70, 72, 79, 88, 89, 90, 93, 95, 101, 105, 106, 107, 120, 121, 128, 129, 130, 131, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 148, 150, 153, 168, 170, 174, 179, 180, 181, 182, 184, 185, 190, 204, 206, 209, 214, 218, 219, 220, 222, 223, 224, 226, 227, 228, 229, 230, 231, 232, 233, 236, 237, 238, 240, 242, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260], "operatornam": [9, 10, 11, 61, 62, 64, 66, 86, 87, 159, 161, 162, 172, 173, 207, 236, 237, 247, 249], "sqrt": [9, 10, 11, 61, 62, 189, 204, 207, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 254], "take": [9, 123, 125, 149, 164, 189, 204, 211, 216, 260], "care": [9, 208, 256], "undu": [9, 209], "overflow": [9, 12, 88, 90, 101, 107, 122, 150, 170, 199, 247, 252, 256], "dure": [9, 40, 59, 107, 132, 168, 184, 199, 202, 245, 260, 261], "stage": [9, 107, 257], "contain": [9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 26, 28, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 90, 91, 92, 93, 94, 96, 100, 101, 102, 105, 106, 107, 109, 110, 111, 113, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 157, 158, 159, 160, 161, 162, 164, 165, 168, 169, 170, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 184, 185, 187, 190, 204, 206, 207, 208, 210, 214, 215, 219, 220, 221, 224, 225, 228, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 260, 262], "nan": [9, 10, 11, 12, 13, 14, 24, 25, 35, 61, 62, 63, 64, 65, 66, 76, 85, 86, 87, 90, 93, 94, 96, 100, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 136, 138, 139, 141, 144, 149, 152, 157, 158, 159, 160, 161, 162, 164, 168, 172, 173, 178, 179, 180, 181, 182, 184, 189, 197, 207, 260], "infin": [9, 10, 11, 12, 13, 14, 24, 25, 35, 62, 63, 64, 65, 66, 76, 81, 86, 87, 90, 93, 94, 96, 100, 101, 107, 117, 118, 123, 124, 125, 126, 127, 134, 138, 141, 144, 149, 152, 157, 160, 161, 162, 164, 172, 173, 178, 207, 247, 254], "imag": [9, 10, 11, 12, 24, 62, 63, 66, 87, 93, 94, 96, 117, 118, 119, 122, 123, 125, 144, 157, 159, 162, 164, 173, 189, 204, 205, 260, 261, 262], "finit": [9, 10, 11, 12, 25, 35, 42, 62, 65, 66, 87, 90, 93, 94, 96, 101, 107, 117, 118, 123, 125, 141, 144, 149, 152, 160, 162, 164, 173, 206], "2022": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 90, 93, 94, 96, 97, 98, 103, 104, 108, 109, 116, 117, 118, 119, 122, 123, 124, 125, 126, 132, 137, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 157, 159, 161, 162, 164, 165, 169, 170, 171, 172, 173, 174, 179, 180, 181, 182, 185, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254], "12": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 66, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 98, 102, 103, 104, 107, 108, 109, 116, 117, 118, 119, 122, 123, 124, 125, 126, 132, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 153, 157, 158, 159, 160, 161, 162, 164, 165, 169, 170, 171, 172, 173, 174, 175, 179, 180, 181, 182, 183, 185, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 257], "approxim": [10, 11, 47, 61, 62, 64, 65, 66, 86, 87, 94, 96, 101, 123, 124, 125, 126, 149, 161, 162, 172, 173, 206, 242, 245], "princip": [10, 11, 61, 62, 64, 66, 123, 164, 207, 256], "invers": [10, 11, 61, 62, 64, 65, 66, 207, 218, 220, 223, 224, 225, 226, 227, 228, 229, 231, 238, 241, 245, 256], "cosin": [10, 11, 86, 87, 173], "express": [10, 61, 63, 64, 65, 86, 161, 172, 190, 199, 208, 256, 259], "radian": [10, 61, 64, 65, 86, 161, 172], "arc": [10, 61, 64], "frac": [10, 11, 61, 62, 64, 66, 86, 87, 90, 122, 124, 126, 159, 161, 162, 172, 173, 207, 247], "pi": [10, 11, 61, 62, 64, 66, 87, 123, 125, 162, 172, 173, 189], "j": [10, 11, 12, 25, 61, 62, 64, 66, 87, 90, 94, 96, 122, 123, 125, 141, 158, 159, 161, 162, 164, 172, 173, 190, 207, 236, 249, 252], "ln": [10, 11, 61, 62, 64, 66, 123], "zj": [10, 61, 62, 64, 66], "conj": [10, 11, 61, 62, 64, 66, 87, 94, 96, 123, 124, 125, 126, 162, 164, 173, 189, 204], "multi": [10, 11, 61, 62, 64, 66, 189, 207, 210, 211, 233, 262], "branch": [10, 11, 61, 62, 64, 65, 66, 86, 87, 90, 94, 96, 123, 125, 141, 149, 161, 162, 164, 172, 173, 260], "cut": [10, 11, 61, 62, 64, 66, 86, 87, 94, 96, 123, 125, 149, 161, 162, 164, 172, 173, 260], "plane": [10, 11, 61, 62, 64, 66, 86, 87, 90, 94, 96, 141, 161, 162, 164, 172, 173, 260], "By": [10, 11, 13, 14, 61, 62, 64, 65, 66, 88, 123, 125, 134, 136, 138, 149, 150, 164, 168, 170, 184, 185, 206, 207, 233, 256, 261], "place": [10, 11, 15, 60, 61, 62, 63, 64, 66, 91, 92, 97, 102, 103, 104, 122, 145, 146, 156, 187, 188, 189, 197, 199, 204, 208, 211, 219, 230, 245], "line": [10, 11, 61, 62, 64, 66, 172, 173, 199, 207, 260, 261, 262, 263], "segment": [10, 11, 61, 62, 64, 66, 207], "infti": [10, 11, 61, 62, 64, 66, 86, 123, 125, 149, 164, 207], "axi": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 95, 99, 123, 125, 134, 136, 138, 140, 149, 150, 153, 156, 163, 164, 166, 167, 168, 170, 171, 174, 175, 183, 184, 185, 189, 204, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 233, 240, 253, 254, 260], "rang": [10, 61, 62, 64, 66, 77, 88, 123, 125, 150, 164, 170, 190, 204, 210, 252, 260], "strip": [10, 61, 62, 64, 66, 123, 125], "unbound": [10, 61, 62, 64, 66, 123, 125], "along": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 97, 99, 123, 125, 134, 136, 138, 150, 153, 156, 163, 164, 167, 168, 170, 171, 172, 173, 175, 183, 184, 185, 190, 204, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 252, 254, 256], "c99": [10, 11, 61, 62, 64, 66, 90, 123, 125, 141, 149, 164, 207, 257], "provision": [10, 11, 61, 62, 64, 66, 123, 125, 149, 164, 207], "statu": [10, 11, 61, 62, 64, 66, 123, 125, 149, 164, 207], "greater": [10, 11, 33, 38, 48, 61, 62, 65, 66, 69, 71, 77, 85, 90, 100, 101, 123, 125, 149, 152, 159, 160, 162, 164, 166, 173, 189, 190, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 241], "than": [10, 11, 19, 26, 38, 40, 47, 48, 49, 55, 61, 62, 63, 65, 66, 69, 71, 76, 77, 85, 88, 90, 98, 99, 100, 101, 102, 123, 124, 125, 126, 132, 141, 149, 150, 152, 159, 160, 162, 164, 166, 168, 170, 171, 173, 178, 179, 180, 181, 182, 184, 190, 199, 202, 205, 208, 211, 212, 215, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 240, 241, 242, 245, 252, 254, 256, 257, 260, 262], "less": [10, 11, 39, 47, 61, 65, 66, 76, 85, 90, 101, 123, 124, 125, 126, 149, 152, 159, 160, 164, 168, 184, 189, 190, 208, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 240, 241, 242, 245, 254, 260], "\u03c0": [10, 64, 65, 84], "0j": [10, 11, 12, 25, 62, 63, 66, 87, 94, 96, 97, 123, 125, 145, 146, 159, 162, 164, 173, 207, 247], "nonzero": [10, 11, 12, 62, 66, 87, 90, 94, 96, 101, 141, 162, 173, 189, 190, 204, 245], "3\u03c0": [10, 65], "hyperbol": [11, 62, 66, 86, 87, 161, 162, 172, 173, 207], "aco": [11, 61, 189, 204, 206], "simpli": [11, 96, 125, 205, 216, 260, 262], "upper": [11, 77, 97, 177, 204, 232, 246], "half": [11, 15, 66, 122, 140, 164, 174, 190, 221], "area": [11, 62, 66], "sector": [11, 62, 66], "\u03c0j": [11, 62, 66, 123, 125], "3\u03c0j": [11, 123, 125], "sum": [12, 21, 88, 107, 127, 150, 189, 204, 240, 252, 254, 256], "x1_i": [12, 65, 67, 69, 70, 71, 72, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 135, 139, 141, 144, 149, 152, 169, 186, 204], "x2_i": [12, 65, 67, 69, 70, 71, 72, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 135, 139, 141, 144, 149, 152, 169, 186, 204], "first": [12, 16, 17, 19, 65, 67, 69, 70, 71, 72, 88, 93, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 144, 149, 156, 167, 169, 172, 173, 174, 179, 180, 181, 185, 186, 190, 207, 233, 236, 244, 246, 247, 249, 250, 256, 260, 261, 262, 263], "remain": [12, 90, 93, 101, 116, 118, 119, 141, 144, 152, 154, 159, 190, 208, 231], "neither": [12, 40, 90, 101, 132, 141, 174, 249, 261], "nor": [12, 90, 101, 141, 249, 261], "mathemat": [12, 19, 65, 84, 86, 87, 90, 96, 101, 123, 125, 141, 161, 162, 172, 173, 189, 207, 240, 254], "round": [12, 15, 76, 90, 100, 101, 141, 164, 178, 189, 204, 206], "nearest": [12, 90, 141, 157, 178, 206], "mode": [12, 90, 141, 206, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 246], "too": [12, 26, 90, 101, 141, 256, 260], "larg": [12, 90, 101, 141, 210, 216, 247, 260], "appropri": [12, 26, 90, 101, 141, 207, 212], "commut": 12, "associ": [12, 42, 141, 192, 199, 242, 245, 248, 256, 259, 261], "tabl": [12, 90, 141, 189], "c": [12, 90, 93, 122, 141, 143, 144, 153, 167, 168, 173, 184, 190, 204, 207, 210, 213, 232, 236, 237, 238, 246, 248, 249, 257, 259, 260, 262], "d": [12, 90, 93, 122, 141, 144, 199, 219, 230], "dj": [12, 90, 141], "independ": [12, 90, 141, 157, 190, 202, 210, 233, 246, 248, 256, 257, 260], "abov": [12, 88, 90, 93, 123, 125, 141, 144, 149, 150, 164, 170, 176, 177, 190, 199, 207, 208, 210, 211, 214, 235, 236, 252, 256, 259, 262], "similarli": [12, 57, 116, 137, 199, 232, 249], "henc": [12, 79, 95, 143, 153, 179, 180, 181, 182, 190, 205, 207, 208, 209, 210, 214, 215, 216, 260, 262], "z1": 12, "z2": 12, "keepdim": [13, 14, 16, 17, 134, 136, 138, 150, 168, 170, 184, 240, 254], "test": [13, 14, 89, 117, 118, 119, 204, 206, 258, 260, 261, 262], "evalu": [13, 14, 22, 30, 36, 38, 41, 44, 45, 46, 48, 51, 52, 94, 96, 123, 124, 125, 126, 142, 148, 159, 160, 165, 202, 260], "union": [13, 14, 15, 21, 22, 26, 28, 30, 31, 32, 33, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 59, 60, 75, 77, 78, 91, 98, 99, 103, 104, 108, 115, 116, 122, 134, 136, 138, 140, 145, 150, 153, 155, 156, 166, 167, 168, 170, 174, 184, 187, 221, 225, 240, 242, 245, 254, 261], "ax": [13, 14, 16, 17, 19, 55, 56, 99, 134, 136, 138, 140, 147, 150, 156, 166, 168, 170, 174, 175, 184, 185, 190, 204, 220, 221, 224, 225, 228, 231, 233, 240, 245, 248, 251, 254], "logic": [13, 14, 24, 26, 90, 93, 128, 129, 130, 131, 141, 144, 211, 214, 220, 224, 228, 231], "AND": [13, 67, 93, 128, 259], "entir": [13, 14, 86, 87, 94, 96, 134, 136, 138, 150, 161, 162, 168, 170, 184], "valid": [13, 14, 26, 27, 95, 114, 140, 167, 174, 183, 190, 206, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 236, 246, 249, 261], "count": [13, 14, 78, 88, 99, 171, 179, 180, 185, 190, 204, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 237], "last": [13, 14, 18, 19, 55, 78, 88, 99, 156, 163, 167, 171, 174, 185, 190, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 235, 240, 246, 249, 252], "invalid": [13, 14, 23, 95, 212, 260], "rais": [13, 14, 19, 23, 24, 25, 26, 29, 34, 35, 40, 47, 51, 55, 60, 74, 90, 94, 95, 102, 122, 132, 134, 138, 143, 149, 154, 166, 167, 183, 185, 190, 199, 202, 204, 210, 211, 212, 214, 233, 241, 260], "wa": [13, 14, 19, 26, 101, 134, 136, 138, 150, 168, 170, 184, 199, 211, 216, 260, 262], "OR": [14, 24, 70, 130, 144, 259], "start": [15, 122, 190, 204, 216, 260, 262], "stop": [15, 122, 190, 204, 261], "step": [15, 122, 190, 261], "evenli": [15, 122], "space": [15, 122, 219, 221, 230], "open": [15, 122, 140, 174, 190], "inclus": [15, 190, 260], "end": [15, 65, 86, 122, 159, 161, 172, 173, 197, 208, 247, 260, 261, 262], "exclus": [15, 190], "distanc": [15, 107], "between": [15, 26, 47, 51, 65, 78, 90, 93, 98, 122, 134, 135, 138, 139, 144, 149, 167, 179, 180, 181, 182, 199, 207, 208, 211, 219, 230, 256, 260, 262], "adjac": 15, "output": [15, 60, 63, 78, 88, 91, 92, 95, 97, 99, 102, 103, 104, 111, 122, 137, 145, 146, 154, 156, 158, 166, 167, 171, 175, 187, 188, 202, 204, 207, 208, 211, 213, 214, 216, 218, 219, 220, 222, 223, 224, 227, 228, 229, 230, 231, 252, 260], "infer": [15, 60, 63, 92, 103, 104, 146, 154, 188, 209, 256, 261], "cannot": [15, 26, 57, 102, 172, 173, 204, 207, 209, 260], "guarante": [15, 59, 179, 181, 202, 207, 211, 260, 262], "error": [15, 19, 23, 24, 25, 26, 29, 34, 35, 51, 55, 90, 102, 134, 138, 172, 173, 199, 206, 247, 260], "ceil": [15, 189], "indic": [16, 17, 18, 26, 60, 88, 89, 102, 111, 116, 122, 140, 143, 156, 158, 159, 171, 174, 176, 177, 179, 181, 190, 199, 204, 254, 260], "occur": [16, 17, 75, 107, 172, 173, 179, 180, 181, 182, 207, 261], "occurr": [16, 17, 179], "comparison": [16, 17, 18, 31, 33, 37, 39, 93, 105, 106, 120, 121, 134, 135, 138, 139, 144, 163, 189, 207, 257, 261], "search": [16, 17, 158, 189], "flatten": [16, 17, 78, 153, 156, 179, 180, 181, 182, 254, 256], "descend": [18, 163, 249, 250], "stabl": [18, 163, 210], "sort": [18, 158, 189, 204, 236, 237, 249, 250], "ascend": [18, 158, 163, 204], "stabil": [18, 163], "maintain": [18, 163, 205, 260, 262], "rel": [18, 19, 55, 99, 135, 139, 156, 163, 204, 235, 242, 245, 252], "compar": [18, 163, 179, 180, 181, 182, 206, 211, 261, 263], "properti": [19, 53, 54, 55, 56, 57, 58, 115, 204, 207, 211, 216, 260], "transpos": [19, 40, 55, 132, 133, 174, 232, 236, 245, 249, 256], "instanc": [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 55, 59, 89, 199, 202, 204, 211], "permut": [19, 55, 147], "revers": [19, 55, 65, 99], "origin": [19, 55, 65, 107, 140, 154, 156, 204, 208, 218, 220, 223, 224, 227, 228, 229, 231, 260, 261], "limit": [19, 98, 108, 116, 206, 256, 259], "matric": [19, 40, 55, 132, 133, 137, 176, 177, 232, 234, 235, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 256], "deviat": [19, 168, 206, 212, 260, 262], "et": [19, 249, 250], "al": 19, "intent": [19, 65], "found": [19, 207, 210, 262, 263], "problemat": [19, 63, 205, 208], "conflict": 19, "definit": [19, 86, 87, 161, 162, 172, 173, 204, 232, 261], "batch": [19, 254, 256], "cetera": [19, 249, 250], "permute_dim": [19, 189], "interfac": [19, 210, 256, 260, 262], "ab": [20, 107, 149, 189, 204, 240, 254], "augend": 21, "addend": 21, "self_i": [22, 28, 30, 31, 33, 36, 37, 38, 39, 41, 43, 44, 45, 46, 48, 50, 51, 52], "other_i": [22, 28, 30, 31, 33, 37, 38, 39, 41, 43, 45, 47, 48, 50, 51, 52], "bitwise_and": [22, 189], "api_vers": [23, 260], "object": [23, 24, 25, 26, 29, 34, 35, 53, 57, 59, 60, 89, 98, 102, 108, 110, 112, 113, 114, 189, 190, 199, 202, 204, 208, 210, 211, 214, 216, 255, 257, 261, 262], "2020": [23, 216, 257, 259, 260], "10": [23, 27, 124, 190, 260], "latest": [23, 210], "modul": [23, 202, 257, 261, 262, 263], "everi": [23, 103, 104, 246, 260], "top": [23, 202, 260, 262], "level": [23, 199, 205, 210, 211, 255, 256, 260, 261], "public": [23, 255, 261, 262], "well": [23, 205, 207, 210, 211, 246, 262, 263], "part": [23, 35, 176, 177, 199, 204, 210, 215, 257, 260, 262], "convert": [24, 25, 29, 34, 35, 60, 102, 199, 204, 205, 207, 210, 260, 262], "handl": [24, 26, 61, 64, 86, 88, 102, 124, 126, 149, 150, 159, 161, 165, 170, 172, 204, 205, 207, 208, 211, 212, 252, 260], "lazi": [24, 25, 29, 34, 35, 202, 204, 213, 262], "languag": [24, 25, 29, 34, 35, 208, 212, 214, 256, 260, 262], "therefor": [24, 25, 29, 34, 35, 202, 210, 211, 212, 214, 216, 257, 260, 262], "abl": [24, 25, 29, 34, 35, 102, 208, 210, 211, 260, 262], "kind": [24, 25, 26, 29, 34, 35, 47, 51, 77, 90, 98, 102, 104, 108, 113, 115, 116, 149, 199, 204, 214, 256, 259], "here": [24, 25, 26, 29, 34, 35, 190, 199, 208, 210, 215, 216, 262], "valueerror": [24, 25, 26, 29, 34, 35, 60, 102, 154, 166, 262], "instead": [24, 25, 29, 34, 35, 63, 207, 210, 214, 261, 262], "2023": [24, 25, 26, 29, 34, 35, 59, 63, 77, 85, 88, 102, 107, 134, 135, 138, 139, 140, 150, 153, 158, 160, 170, 171, 174, 175, 179, 180, 181, 182, 183, 185, 218, 219, 220, 222, 223, 224, 227, 228, 230, 233, 252], "new": [25, 26, 77, 79, 85, 88, 95, 98, 102, 103, 104, 107, 108, 109, 116, 135, 139, 140, 145, 146, 151, 153, 154, 158, 160, 167, 171, 175, 183, 187, 188, 202, 204, 205, 208, 210, 211, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 257, 260, 261, 262], "stream": [26, 59, 211], "max_vers": [26, 204], "dl_devic": [26, 204], "enum": [26, 27], "pycapsul": 26, "export": [26, 102, 204, 210, 261], "from_dlpack": [26, 27, 189, 204, 210], "dlpack": [26, 27, 102, 204], "capsul": 26, "cuda": [26, 27, 205, 210, 262], "rocm": [26, 27, 205], "pointer": 26, "produc": [26, 236, 246, 249, 262], "instruct": 26, "safe": [26, 122], "insert": [26, 95, 158, 204], "wait": 26, "event": [26, 259], "larger": [26, 98, 156, 168, 184, 245], "below": [26, 101, 102, 176, 177, 192, 210, 211, 235, 252], "signal": [26, 222, 226, 262], "ownership": 26, "stai": 26, "On": 26, "cpu": [26, 27, 202, 205, 210, 211, 256, 260, 262], "queue": [26, 59, 211], "similar": [26, 152, 190, 205, 207, 209, 260, 261, 262], "mechan": [26, 102, 202, 204, 205, 213, 255, 260], "most": [26, 202, 211, 236, 256, 260, 262], "yet": [26, 216, 260], "sycl": 26, "want": [26, 90, 141, 205, 209, 210, 260, 262, 263], "cl": 26, "agre": 26, "assum": [26, 86, 102, 161, 172, 202, 207, 211, 255, 260], "legaci": 26, "per": [26, 153, 205, 210, 258], "thread": [26, 260, 262], "disallow": 26, "due": [26, 42, 57, 58, 122, 141, 153, 171, 206, 207, 256, 260], "ambigu": [26, 63, 101, 208], "construct": [26, 175, 202, 204, 205, 214, 260], "particular": [26, 190, 205, 207, 210, 211, 216, 256, 259, 260, 262, 263], "kdlcpu": 26, "safeti": [26, 59], "prefer": [26, 101, 202, 256, 262], "develop": [26, 206, 260, 261, 262, 263], "who": [26, 206, 260, 261], "think": 26, "cost": 26, "caller": 26, "major": [26, 143, 153, 190, 257], "minor": [26, 257], "verifi": [26, 260], "even": [26, 90, 141, 149, 157, 206, 207, 208, 219, 221, 225, 230, 246, 256, 260, 262], "pass": [26, 65, 202, 206, 211], "format": [26, 27, 257], "__dlpack_device__": [26, 102, 189, 210], "buffererror": [26, 102, 204, 210], "v2023": [26, 102], "mandat": [26, 102, 260], "offer": [26, 102, 205, 210, 211, 215, 260, 262], "referenc": [26, 260], "underli": [26, 67, 70, 72, 102, 206, 247, 256], "interpret": [26, 102, 107, 207, 208, 263], "enumer": 26, "made": [26, 102, 202, 207, 255, 257, 260, 262], "never": [26, 60, 102, 154, 210, 260], "deem": [26, 102], "cross": [26, 102, 204, 211, 256, 260], "movement": [26, 102], "request": [26, 102, 260], "reus": [26, 60, 102, 208, 260], "buffer": [26, 60, 102, 208, 210], "happen": [26, 102, 208, 211, 214, 256], "dlpack_flag_bitmask_is_copi": 26, "flag": 26, "understood": [26, 199], "interchang": [26, 102, 202, 205, 213, 260], "detail": [26, 102, 143, 153, 179, 180, 181, 182, 189, 190, 201, 202, 209, 211, 215, 256, 260, 262], "stride": [26, 102, 208, 210], "fail": [26, 102, 260], "reason": [26, 102, 152, 173, 208, 210, 212, 256, 260, 261], "incorrect": 26, "scheme": [26, 257], "semver": 26, "abi": [26, 205, 210], "break": [26, 212], "introduc": [26, 63, 101, 156, 216, 261], "goe": 26, "togeth": [26, 199, 210], "dlmanagedtensorvers": 26, "struct": 26, "later": 26, "introduct": 26, "becaus": [26, 199, 205, 208, 211, 212, 214, 216, 236, 249, 260, 262, 263], "keep": [26, 199, 205, 260], "march": 26, "2025": 26, "onward": 26, "ideal": [26, 256], "late": 26, "okai": 26, "we": [26, 207, 249, 260], "get": [26, 98, 108, 205, 208, 210, 211], "now": [26, 102, 214, 260, 262], "our_own_dlpack_vers": 26, "fill": [26, 103, 104, 145, 146, 187, 188, 204], "field": [26, 179, 180, 181, 207, 236, 246, 247, 249, 260], "understand": [26, 245, 260, 261], "u": [26, 232, 245, 249], "just": [26, 260, 262], "our": 26, "elif": 26, "fine": [26, 216, 260], "own": [26, 202, 208, 260], "re": [26, 156, 205, 208, 216, 262], "intern": [26, 262], "did": 26, "older": [26, 173, 210, 257, 260], "around": [26, 261], "y": [26, 65, 102, 207, 208, 262], "dlmanagedtensor": 26, "so": [26, 98, 102, 110, 190, 197, 210, 256, 259, 260, 263], "tell": 26, "old": 26, "exchang": [26, 102, 210], "And": [26, 190, 211], "try": [26, 216, 260], "succe": 26, "info": [26, 110], "dltensor_vers": 26, "need": [26, 190, 205, 206, 208, 210, 212, 216, 256, 257, 260, 261, 262, 263], "used_dltensor_vers": 26, "done": [26, 202], "typeerror": [26, 29, 34, 35, 260, 262], "read": [26, 204, 208], "dlpack_flag_bitmask_read_onli": 26, "ignor": [26, 137, 256], "respons": 26, "isn": [26, 205], "t": [26, 189, 205, 208, 211, 215, 216, 260, 262], "id": 27, "meant": 27, "device_typ": 27, "device_id": 27, "member": 27, "cpu_pin": 27, "opencl": 27, "vulkan": 27, "metal": 27, "vpi": 27, "cuda_manag": 27, "13": 27, "one_api": 27, "14": [27, 257], "truth": [28, 31, 33, 37, 39, 43, 89, 93, 105, 106, 120, 121, 144, 263], "outsid": [29, 167, 183, 190, 199, 204, 210], "bound": [29, 77, 171, 190, 199, 204, 216], "divis": [30, 41, 71, 90, 101, 152, 159, 207], "floor_divid": [30, 189], "greater_equ": [31, 189], "kei": [32, 49, 111, 113, 115, 260], "slice": [32, 49, 183, 189, 208], "ellipsi": [32, 49, 190], "pep": [34, 40, 101, 132, 210, 257], "357": 34, "overflowerror": 35, "bitwise_invert": [36, 189], "less_equ": [37, 189], "bitwise_left_shift": [38, 189], "matrix": [40, 55, 132, 133, 137, 174, 176, 177, 232, 234, 235, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 256, 260], "product": [40, 42, 58, 132, 141, 150, 174, 185, 204, 233, 244, 256], "semant": [40, 101, 132, 152, 171, 189, 190, 202, 208, 210, 212, 214, 215, 256, 260, 261, 262], "built": [40, 132, 190, 199, 260], "465": [40, 132], "least": [40, 90, 115, 116, 132, 141, 143, 179, 180, 181, 182, 205, 206, 245], "m": [40, 55, 132, 133, 137, 153, 158, 174, 175, 176, 177, 190, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252], "remov": [40, 132, 166, 190, 207, 235, 252], "innermost": [40, 132, 133, 176, 177, 232, 234, 235, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252], "conjug": [40, 79, 132, 174, 185, 204, 232, 236, 249, 256], "transposit": [40, 132, 174], "desir": [40, 63, 75, 132, 140, 174, 206, 207, 210, 216], "prior": [40, 132, 174], "inner": [40, 132, 204, 236, 256], "stack": [40, 55, 132, 133, 176, 177, 189, 215, 232, 234, 235, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 256], "l": [40, 132, 232, 252], "remaind": [41, 189, 190], "multipli": [42, 150, 165, 189, 204, 206, 236, 249], "not_equ": [43, 189, 204], "negat": [44, 79, 142], "bitwise_or": [45, 189], "exponenti": [47, 94, 96, 127, 149, 207], "power": [47, 71, 94, 149, 207, 241, 262], "expon": [47, 149, 241], "versu": [47, 51, 63, 77, 90, 141, 149, 204], "bitwise_right_shift": [48, 189], "mix": [49, 122, 136, 155, 168, 184, 189, 204, 208, 211, 256, 260], "how": [49, 90, 141, 202, 206, 211, 215, 261, 262, 263], "minuend": 50, "subtrahend": 50, "subtract": [50, 189, 204, 206], "choos": [51, 57, 59, 90, 101, 122, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 143, 153, 168, 179, 180, 181, 182, 184, 189, 190, 197, 207, 208, 209, 211, 214, 260, 262], "divid": [51, 101, 159, 189, 190, 204, 206], "bitwise_xor": [52, 189], "resid": [53, 59, 95, 140, 174, 190, 204, 210, 260], "fewer": 55, "unknown": [57, 58, 153], "graph": [57, 58, 143, 153, 179, 180, 181, 182, 190, 209, 214, 260], "static": [57, 209, 213], "resolv": [57, 60, 88, 95, 101, 103, 104, 150, 170, 220, 221, 224, 225, 228, 231, 252, 260], "know": [57, 143, 153, 179, 180, 181, 182, 202, 205, 206, 209, 260, 262], "content": [57, 209, 259], "warrant": 57, "custom": [57, 205, 212], "immut": 57, "retriev": [57, 190, 202, 217, 256, 262], "behav": [57, 207], "current": [59, 113, 115, 171, 197, 208, 211, 216, 260, 261, 262], "__dlpack__": [59, 102, 189, 204, 210], "caveat": 59, "would": [59, 60, 154, 158, 190, 204, 208, 214, 256, 260, 262], "locat": [59, 208], "explicit": [59, 60, 102, 171, 174, 211, 262], "enqueu": 59, "asynchron": 59, "explain": [59, 205], "clarifi": [59, 134, 138, 179, 180, 181, 204], "obj": 60, "nestedsequ": 60, "supportsbufferprotocol": 60, "possibli": [60, 215, 260], "nest": [60, 215], "sequenc": [60, 78, 122, 167, 174, 183, 190, 204, 220, 221, 224, 225, 228, 231, 251], "protocol": [60, 202, 210, 216, 260, 262], "turn": [60, 202, 255], "memoryview": 60, "preced": [60, 207, 210, 211], "mixtur": 60, "convers": [60, 122, 204, 205, 260], "obei": [60, 122], "permit": [60, 63, 122, 209, 259], "To": [60, 101, 190, 204, 206, 207, 216, 260, 261, 263], "array_api": [60, 260], "astyp": [60, 189, 204], "exce": [60, 103, 104, 122], "sine": [61, 62, 161, 162, 173], "1j": [61, 64, 86, 87, 94, 96, 107, 161, 162, 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"Backwards compatibility": [[202, "backwards-compatibility"], [257, "backwards-compatibility"]], "Production code & interactive use": [[202, "production-code-interactive-use"]], "Benchmark suite": [[203, "benchmark-suite"]], "Changelog per API standard version": [[204, "changelog-per-api-standard-version"]], "Changelog": [[204, "changelog"]], "v2023.12": [[204, "v2023-12"]], "Updates": [[204, "updates"], [204, "id3"]], "Normative": [[204, "normative"]], "APIs": [[204, "apis"], [204, "id1"], [204, "id4"], [204, "id8"]], "Extensions": [[204, "extensions"], [204, "id2"], [204, "id5"], [204, "id9"], [255, "extensions"]], "Additions": [[204, "additions"], [204, "id7"]], "Breaking Changes": [[204, "breaking-changes"]], "Errata": [[204, "errata"], [204, "id10"]], "v2022.12": [[204, "v2022-12"]], "Complex Number Support": [[204, "complex-number-support"], [204, "id6"]], "C API": [[205, "c-api"]], "Example situations for C/Cython usage": [[205, "example-situations-for-c-cython-usage"]], "Situation 1: a Python package that is mostly pure Python, with a limited number of Cython extensions": [[205, "situation-1-a-python-package-that-is-mostly-pure-python-with-a-limited-number-of-cython-extensions"]], "Situation 2: a Python package that contains a lot of Cython code": [[205, "situation-2-a-python-package-that-contains-a-lot-of-cython-code"]], "Situation 3: a Python package that uses the NumPy or Python C API directly": [[205, "situation-3-a-python-package-that-uses-the-numpy-or-python-c-api-directly"]], "Device support": [[205, "device-support"], [211, "device-support"]], "Other longer-term approaches": [[205, "other-longer-term-approaches"]], "Further Python API standardization": [[205, "further-python-api-standardization"]], "HPy": [[205, "hpy"]], "Accuracy": [[206, "accuracy"]], "Arithmetic Operations": [[206, "arithmetic-operations"]], "Mathematical Functions": [[206, "mathematical-functions"]], "Linear Algebra": [[206, "linear-algebra"]], "Complex Numbers": [[207, "complex-numbers"]], "The Complex Plane": [[207, "the-complex-plane"]], "Branch Cuts": [[207, "branch-cuts"]], "Complex Number Ordering": [[207, "complex-number-ordering"]], "Valued-based Promotion": [[207, "valued-based-promotion"]], "Copy-view behaviour and mutability": [[208, "copy-view-behaviour-and-mutability"]], "Mutating views": [[208, null]], "Data-dependent output shapes": [[209, "data-dependent-output-shapes"]], "Data interchange mechanisms": [[210, "data-interchange-mechanisms"]], "DLPack: An in-memory tensor structure": [[210, "dlpack-an-in-memory-tensor-structure"]], "Non-supported use cases": [[210, "non-supported-use-cases"]], "Intended usage": [[211, "intended-usage"]], "Syntax for device assignment": [[211, "syntax-for-device-assignment"]], "Semantics": [[211, "semantics"]], "Out of scope for device support": [[211, "out-of-scope-for-device-support"]], "Exceptions": [[212, "exceptions"]], "Design topics & constraints": [[213, "design-topics-constraints"], [213, null]], "Lazy vs. eager execution": [[214, "lazy-vs-eager-execution"]], "Parallelism": [[215, "parallelism"]], "Static typing": [[216, "static-typing"]], "Fourier transform Functions": [[217, "fourier-transform-functions"]], "Extension name and usage": [[217, "extension-name-and-usage"], [256, "extension-name-and-usage"]], "fft": [[218, "fft"]], "fftfreq": [[219, "fftfreq"]], "fftn": [[220, "fftn"]], "fftshift": [[221, "fftshift"]], "hfft": [[222, "hfft"]], "ifft": [[223, "ifft"]], "ifftn": [[224, "ifftn"]], "ifftshift": [[225, "ifftshift"]], "ihfft": [[226, "ihfft"]], "irfft": [[227, "irfft"]], "irfftn": [[228, "irfftn"]], "rfft": [[229, "rfft"]], "rfftfreq": [[230, "rfftfreq"]], "rfftn": [[231, "rfftn"]], "cholesky": [[232, "cholesky"]], "cross": [[233, "cross"]], "det": [[234, "det"]], "diagonal": [[235, "diagonal"]], "eigh": [[236, "eigh"]], "eigvalsh": [[237, "eigvalsh"]], "inv": [[238, "inv"]], "matrix_norm": [[240, "matrix-norm"]], "matrix_power": [[241, "matrix-power"]], "matrix_rank": [[242, "matrix-rank"]], "outer": [[244, "outer"]], "pinv": [[245, "pinv"]], "qr": [[246, "qr"]], "slogdet": [[247, "slogdet"]], "solve": [[248, "solve"]], "svd": [[249, "svd"]], "svdvals": [[250, "svdvals"]], "trace": [[252, "trace"]], "vector_norm": [[254, "vector-norm"]], "Extension modules:": [[255, null]], "Linear Algebra Extension": [[256, "linear-algebra-extension"]], "Design Principles": [[256, "design-principles"]], "Future API standard evolution": [[257, "future-api-standard-evolution"]], "Scope extensions": [[257, "scope-extensions"]], "Versioning": [[257, "versioning"]], "Python array API standard": [[258, "python-array-api-standard"]], "Contents": [[258, "contents"]], "Context": [[258, null]], "API": [[258, null]], "Methodology and Usage": [[258, null]], "Other": [[258, null]], "License": [[259, "license"]], "Purpose and scope": [[260, "purpose-and-scope"]], "Introduction": [[260, "introduction"], [261, "introduction"]], "This API standard": [[260, "this-api-standard"]], "History": [[260, "history"]], "Scope (includes out-of-scope / non-goals)": [[260, "scope-includes-out-of-scope-non-goals"]], "In scope": [[260, "in-scope"]], "Out of scope": [[260, "out-of-scope"]], "Implications of in/out of scope": [[260, "implications-of-in-out-of-scope"]], "Stakeholders": [[260, "stakeholders"]], "How to read this document": [[260, "how-to-read-this-document"]], "How to adopt this API": [[260, "how-to-adopt-this-api"]], "Checking an array object for Compliance": [[260, "checking-an-array-object-for-compliance"]], "Discoverability of conforming implementations": [[260, "discoverability-of-conforming-implementations"]], "Optional feature": [[260, null]], "Conformance": [[260, "conformance"]], "Terms and Definitions": [[260, "terms-and-definitions"]], "Normative References": [[260, "normative-references"]], "Usage Data": [[261, "usage-data"]], "Design": [[261, "design"]], "Usage": [[261, "usage"]], "Use in Decision-Making": [[261, "use-in-decision-making"]], "Use cases": [[262, "use-cases"]], "Types of use cases": [[262, "types-of-use-cases"]], "Concrete use cases": [[262, "concrete-use-cases"]], "Use case 1: add hardware accelerator and distributed support to SciPy": [[262, "use-case-1-add-hardware-accelerator-and-distributed-support-to-scipy"]], "Use case 2: simplify einops by removing the backend system": [[262, "use-case-2-simplify-einops-by-removing-the-backend-system"]], "Use case 3: adding a Python API to xtensor": [[262, "use-case-3-adding-a-python-api-to-xtensor"]], "Use case 4: make JIT compilation of array computations easier and more robust": [[262, "use-case-4-make-jit-compilation-of-array-computations-easier-and-more-robust"]], "Verification - test suite": [[263, "verification-test-suite"]], "Measuring conformance": [[263, "measuring-conformance"]], "Running the tests": [[263, "running-the-tests"]]}, "indexentries": {"__array_api_version__ (in module array_api)": [[8, "array_api.__array_api_version__"]], "abs() (in module array_api)": [[9, "array_api.abs"]], "acos() (in module array_api)": [[10, "array_api.acos"]], "acosh() (in module array_api)": [[11, "array_api.acosh"]], "add() (in module array_api)": [[12, "array_api.add"]], "all() (in module array_api)": [[13, "array_api.all"]], "any() (in module array_api)": [[14, "array_api.any"]], "arange() (in module array_api)": [[15, "array_api.arange"]], "argmax() (in module array_api)": [[16, "array_api.argmax"]], "argmin() (in module array_api)": [[17, "array_api.argmin"]], "argsort() (in module array_api)": [[18, "array_api.argsort"]], "t (array property)": [[19, "array_api.array.T"]], "__abs__() (array method)": [[20, "array_api.array.__abs__"]], "__add__() (array method)": [[21, "array_api.array.__add__"]], "__and__() (array method)": [[22, "array_api.array.__and__"]], "__array_namespace__() (array method)": [[23, "array_api.array.__array_namespace__"]], "__bool__() (array method)": [[24, "array_api.array.__bool__"]], "__complex__() (array method)": [[25, "array_api.array.__complex__"]], "__dlpack__() (array method)": [[26, "array_api.array.__dlpack__"]], "__dlpack_device__() (array method)": [[27, "array_api.array.__dlpack_device__"]], "__eq__() (array method)": [[28, "array_api.array.__eq__"]], "__float__() (array method)": [[29, "array_api.array.__float__"]], "__floordiv__() (array method)": [[30, "array_api.array.__floordiv__"]], "__ge__() (array method)": [[31, "array_api.array.__ge__"]], "__getitem__() (array method)": [[32, "array_api.array.__getitem__"]], "__gt__() (array method)": [[33, "array_api.array.__gt__"]], "__index__() (array method)": [[34, "array_api.array.__index__"]], "__int__() (array method)": [[35, "array_api.array.__int__"]], "__invert__() (array method)": [[36, "array_api.array.__invert__"]], "__le__() (array method)": [[37, "array_api.array.__le__"]], "__lshift__() (array method)": [[38, "array_api.array.__lshift__"]], "__lt__() (array method)": [[39, "array_api.array.__lt__"]], "__matmul__() (array method)": [[40, "array_api.array.__matmul__"]], "__mod__() (array method)": [[41, "array_api.array.__mod__"]], "__mul__() (array method)": [[42, "array_api.array.__mul__"]], "__ne__() (array method)": [[43, "array_api.array.__ne__"]], "__neg__() (array method)": [[44, "array_api.array.__neg__"]], "__or__() (array method)": [[45, "array_api.array.__or__"]], "__pos__() (array method)": [[46, "array_api.array.__pos__"]], "__pow__() (array method)": [[47, "array_api.array.__pow__"]], "__rshift__() (array method)": [[48, "array_api.array.__rshift__"]], "__setitem__() (array method)": [[49, "array_api.array.__setitem__"]], "__sub__() (array method)": [[50, "array_api.array.__sub__"]], "__truediv__() (array method)": [[51, "array_api.array.__truediv__"]], "__xor__() (array method)": [[52, "array_api.array.__xor__"]], "device (array property)": [[53, "array_api.array.device"]], "dtype (array property)": [[54, "array_api.array.dtype"]], "mt (array property)": [[55, "array_api.array.mT"]], "ndim (array property)": [[56, "array_api.array.ndim"]], "shape (array property)": [[57, "array_api.array.shape"]], "size (array property)": [[58, "array_api.array.size"]], "to_device() (array method)": [[59, "array_api.array.to_device"]], "asarray() (in module array_api)": [[60, "array_api.asarray"]], "asin() (in module array_api)": [[61, "array_api.asin"]], "asinh() (in module array_api)": [[62, "array_api.asinh"]], "astype() (in module array_api)": [[63, "array_api.astype"]], "atan() (in module array_api)": [[64, "array_api.atan"]], "atan2() (in module array_api)": [[65, "array_api.atan2"]], "atanh() (in module array_api)": [[66, "array_api.atanh"]], "bitwise_and() (in module array_api)": [[67, "array_api.bitwise_and"]], "bitwise_invert() (in module array_api)": [[68, "array_api.bitwise_invert"]], "bitwise_left_shift() (in module array_api)": [[69, "array_api.bitwise_left_shift"]], "bitwise_or() (in module array_api)": [[70, "array_api.bitwise_or"]], "bitwise_right_shift() (in module array_api)": [[71, "array_api.bitwise_right_shift"]], "bitwise_xor() (in module array_api)": [[72, "array_api.bitwise_xor"]], "broadcast_arrays() (in module array_api)": [[73, "array_api.broadcast_arrays"]], "broadcast_to() (in module array_api)": [[74, "array_api.broadcast_to"]], "can_cast() (in module array_api)": [[75, "array_api.can_cast"]], "ceil() (in module array_api)": [[76, "array_api.ceil"]], "clip() (in module array_api)": [[77, "array_api.clip"]], "concat() (in module array_api)": [[78, "array_api.concat"]], "conj() (in module array_api)": [[79, "array_api.conj"]], "e (in module array_api.constants)": [[80, "array_api.constants.e"]], "inf (in module array_api.constants)": [[81, "array_api.constants.inf"]], "nan (in module array_api.constants)": [[82, "array_api.constants.nan"]], "newaxis (in module array_api.constants)": [[83, "array_api.constants.newaxis"]], "pi (in module array_api.constants)": [[84, "array_api.constants.pi"]], "copysign() (in module array_api)": [[85, "array_api.copysign"]], "cos() (in module array_api)": [[86, "array_api.cos"]], "cosh() (in module array_api)": [[87, "array_api.cosh"]], "cumulative_sum() (in module array_api)": [[88, "array_api.cumulative_sum"]], "__eq__() (in module array_api.data_types)": [[89, "array_api.data_types.__eq__"]], "divide() (in module array_api)": [[90, "array_api.divide"]], "empty() (in module array_api)": [[91, "array_api.empty"]], "empty_like() (in module array_api)": [[92, "array_api.empty_like"]], "equal() (in module array_api)": [[93, "array_api.equal"]], "exp() (in module array_api)": [[94, "array_api.exp"]], "expand_dims() (in module array_api)": [[95, "array_api.expand_dims"]], "expm1() (in module array_api)": [[96, "array_api.expm1"]], "eye() (in module array_api)": [[97, "array_api.eye"]], "finfo() (in module array_api)": [[98, "array_api.finfo"]], "flip() (in module array_api)": [[99, "array_api.flip"]], "floor() (in module array_api)": [[100, "array_api.floor"]], "floor_divide() (in module array_api)": [[101, "array_api.floor_divide"]], "from_dlpack() (in module array_api)": [[102, "array_api.from_dlpack"]], "full() (in module array_api)": [[103, "array_api.full"]], "full_like() (in module array_api)": [[104, "array_api.full_like"]], "greater() (in module array_api)": [[105, "array_api.greater"]], "greater_equal() (in module array_api)": [[106, "array_api.greater_equal"]], "hypot() (in module array_api)": [[107, "array_api.hypot"]], "iinfo() (in module array_api)": [[108, "array_api.iinfo"]], "imag() (in module array_api)": [[109, "array_api.imag"]], "__array_namespace_info__() (in module array_api.info)": [[110, "array_api.info.__array_namespace_info__"]], "capabilities() (in module array_api.info)": [[111, "array_api.info.capabilities"]], "default_device() (in module array_api.info)": [[112, "array_api.info.default_device"]], "default_dtypes() (in module array_api.info)": [[113, "array_api.info.default_dtypes"]], "devices() (in module array_api.info)": [[114, "array_api.info.devices"]], "dtypes() (in module array_api.info)": [[115, "array_api.info.dtypes"]], "isdtype() (in module array_api)": [[116, "array_api.isdtype"]], "isfinite() (in module array_api)": [[117, "array_api.isfinite"]], "isinf() (in module array_api)": [[118, "array_api.isinf"]], "isnan() (in module array_api)": [[119, "array_api.isnan"]], "less() (in module array_api)": [[120, "array_api.less"]], "less_equal() (in module array_api)": [[121, "array_api.less_equal"]], "linspace() (in module array_api)": [[122, "array_api.linspace"]], "log() (in module array_api)": [[123, "array_api.log"]], "log10() (in module array_api)": [[124, "array_api.log10"]], "log1p() (in module array_api)": [[125, "array_api.log1p"]], "log2() (in module array_api)": [[126, "array_api.log2"]], "logaddexp() (in module array_api)": [[127, "array_api.logaddexp"]], "logical_and() (in module array_api)": [[128, "array_api.logical_and"]], "logical_not() (in module array_api)": [[129, "array_api.logical_not"]], "logical_or() (in module array_api)": [[130, "array_api.logical_or"]], "logical_xor() (in module array_api)": [[131, "array_api.logical_xor"]], "matmul() (in module array_api)": [[132, "array_api.matmul"]], "matrix_transpose() (in module array_api)": [[133, "array_api.matrix_transpose"]], "max() (in module array_api)": [[134, "array_api.max"]], "maximum() (in module array_api)": [[135, "array_api.maximum"]], "mean() (in module array_api)": [[136, "array_api.mean"]], "meshgrid() (in module array_api)": [[137, "array_api.meshgrid"]], "min() (in module array_api)": [[138, "array_api.min"]], "minimum() (in module array_api)": [[139, "array_api.minimum"]], "moveaxis() (in module array_api)": [[140, "array_api.moveaxis"]], "multiply() (in module array_api)": [[141, "array_api.multiply"]], "negative() (in module array_api)": [[142, "array_api.negative"]], "nonzero() (in module array_api)": [[143, "array_api.nonzero"]], "not_equal() (in module array_api)": [[144, "array_api.not_equal"]], "ones() (in module array_api)": [[145, "array_api.ones"]], "ones_like() (in module array_api)": [[146, "array_api.ones_like"]], "permute_dims() (in module array_api)": [[147, "array_api.permute_dims"]], "positive() (in module array_api)": [[148, "array_api.positive"]], "pow() (in module array_api)": [[149, "array_api.pow"]], "prod() (in module array_api)": [[150, "array_api.prod"]], "real() (in module array_api)": [[151, "array_api.real"]], "remainder() (in module array_api)": [[152, "array_api.remainder"]], "repeat() (in module array_api)": [[153, "array_api.repeat"]], "reshape() (in module array_api)": [[154, "array_api.reshape"]], "result_type() (in module array_api)": [[155, "array_api.result_type"]], "roll() (in module array_api)": [[156, "array_api.roll"]], "round() (in module array_api)": [[157, "array_api.round"]], "searchsorted() (in module array_api)": [[158, "array_api.searchsorted"]], "sign() (in module array_api)": [[159, "array_api.sign"]], "signbit() (in module array_api)": [[160, "array_api.signbit"]], "sin() (in module array_api)": [[161, "array_api.sin"]], "sinh() (in module array_api)": [[162, "array_api.sinh"]], "sort() (in module array_api)": [[163, "array_api.sort"]], "sqrt() (in module array_api)": [[164, "array_api.sqrt"]], "square() (in module array_api)": [[165, "array_api.square"]], "squeeze() (in module array_api)": [[166, "array_api.squeeze"]], "stack() (in module array_api)": [[167, "array_api.stack"]], "std() (in module array_api)": [[168, "array_api.std"]], "subtract() (in module array_api)": [[169, "array_api.subtract"]], "sum() (in module array_api)": [[170, "array_api.sum"]], "take() (in module array_api)": [[171, "array_api.take"]], "tan() (in module array_api)": [[172, "array_api.tan"]], "tanh() (in module array_api)": [[173, "array_api.tanh"]], "tensordot() (in module array_api)": [[174, "array_api.tensordot"]], "tile() (in module array_api)": [[175, "array_api.tile"]], "tril() (in module array_api)": [[176, "array_api.tril"]], "triu() (in module array_api)": [[177, "array_api.triu"]], "trunc() (in module array_api)": [[178, "array_api.trunc"]], "unique_all() (in module array_api)": [[179, "array_api.unique_all"]], "unique_counts() (in module array_api)": [[180, "array_api.unique_counts"]], "unique_inverse() (in module array_api)": [[181, "array_api.unique_inverse"]], "unique_values() (in module array_api)": [[182, "array_api.unique_values"]], "unstack() (in module array_api)": [[183, "array_api.unstack"]], "var() (in module array_api)": [[184, "array_api.var"]], "vecdot() (in module array_api)": [[185, "array_api.vecdot"]], "where() (in module array_api)": [[186, "array_api.where"]], "zeros() (in module array_api)": [[187, "array_api.zeros"]], "zeros_like() (in module array_api)": [[188, "array_api.zeros_like"]], "fft() (in module array_api.fft)": [[218, "array_api.fft.fft"]], "fftfreq() (in module array_api.fft)": [[219, "array_api.fft.fftfreq"]], "fftn() (in module array_api.fft)": [[220, "array_api.fft.fftn"]], "fftshift() (in module array_api.fft)": [[221, "array_api.fft.fftshift"]], "hfft() (in module array_api.fft)": [[222, "array_api.fft.hfft"]], "ifft() (in module array_api.fft)": [[223, "array_api.fft.ifft"]], "ifftn() (in module array_api.fft)": [[224, "array_api.fft.ifftn"]], "ifftshift() (in module array_api.fft)": [[225, "array_api.fft.ifftshift"]], "ihfft() (in module array_api.fft)": [[226, "array_api.fft.ihfft"]], "irfft() (in module array_api.fft)": [[227, "array_api.fft.irfft"]], "irfftn() (in module array_api.fft)": [[228, "array_api.fft.irfftn"]], "rfft() (in module array_api.fft)": [[229, "array_api.fft.rfft"]], "rfftfreq() (in module array_api.fft)": [[230, "array_api.fft.rfftfreq"]], "rfftn() (in module array_api.fft)": [[231, "array_api.fft.rfftn"]], "cholesky() (in module array_api.linalg)": [[232, "array_api.linalg.cholesky"]], "cross() (in module array_api.linalg)": [[233, "array_api.linalg.cross"]], "det() (in module array_api.linalg)": [[234, "array_api.linalg.det"]], "diagonal() (in module array_api.linalg)": [[235, "array_api.linalg.diagonal"]], "eigh() (in module array_api.linalg)": [[236, "array_api.linalg.eigh"]], "eigvalsh() (in module array_api.linalg)": [[237, "array_api.linalg.eigvalsh"]], "inv() (in module array_api.linalg)": [[238, "array_api.linalg.inv"]], "matmul() (in module array_api.linalg)": [[239, "array_api.linalg.matmul"]], "matrix_norm() (in module array_api.linalg)": [[240, "array_api.linalg.matrix_norm"]], "matrix_power() (in module array_api.linalg)": [[241, "array_api.linalg.matrix_power"]], "matrix_rank() (in module array_api.linalg)": [[242, "array_api.linalg.matrix_rank"]], "matrix_transpose() (in module array_api.linalg)": [[243, "array_api.linalg.matrix_transpose"]], "outer() (in module array_api.linalg)": [[244, "array_api.linalg.outer"]], "pinv() (in module array_api.linalg)": [[245, "array_api.linalg.pinv"]], "qr() (in module array_api.linalg)": [[246, "array_api.linalg.qr"]], "slogdet() (in module array_api.linalg)": [[247, "array_api.linalg.slogdet"]], "solve() (in module array_api.linalg)": [[248, "array_api.linalg.solve"]], "svd() (in module array_api.linalg)": [[249, "array_api.linalg.svd"]], "svdvals() (in module array_api.linalg)": [[250, "array_api.linalg.svdvals"]], "tensordot() (in module array_api.linalg)": [[251, "array_api.linalg.tensordot"]], "trace() (in module array_api.linalg)": [[252, "array_api.linalg.trace"]], "vecdot() (in module array_api.linalg)": [[253, "array_api.linalg.vecdot"]], "vector_norm() (in module array_api.linalg)": [[254, "array_api.linalg.vector_norm"]]}})
\ No newline at end of file