From dd2a39e4f1a9cbf5dbafc608ea009467a829f28e Mon Sep 17 00:00:00 2001 From: array-api-bot Date: Thu, 31 Oct 2024 04:56:57 +0000 Subject: [PATCH] Deploy: 6d205d72dde3db8fc8668ad6aef5d003cc8ef80f --- .../API_specification/generated/array_api.array.__eq__.html | 4 ++++ .../API_specification/generated/array_api.array.__ge__.html | 4 ++++ .../API_specification/generated/array_api.array.__gt__.html | 4 ++++ .../API_specification/generated/array_api.array.__le__.html | 4 ++++ .../API_specification/generated/array_api.array.__lt__.html | 4 ++++ .../API_specification/generated/array_api.array.__ne__.html | 4 ++++ draft/API_specification/generated/array_api.equal.html | 4 ++++ draft/API_specification/generated/array_api.greater.html | 5 ++++- .../API_specification/generated/array_api.greater_equal.html | 5 ++++- draft/API_specification/generated/array_api.less.html | 5 ++++- draft/API_specification/generated/array_api.less_equal.html | 5 ++++- draft/API_specification/generated/array_api.not_equal.html | 4 ++++ draft/searchindex.js | 2 +- 13 files changed, 49 insertions(+), 5 deletions(-) diff --git a/draft/API_specification/generated/array_api.array.__eq__.html b/draft/API_specification/generated/array_api.array.__eq__.html index a4328d971..d45e1bb49 100644 --- a/draft/API_specification/generated/array_api.array.__eq__.html +++ b/draft/API_specification/generated/array_api.array.__eq__.html @@ -481,6 +481,10 @@

__eq__Note

Element-wise results, including special cases, must equal the results returned by the equivalent element-wise function equal().

+
+

Note

+

Comparison of arrays without a corresponding promotable data type (see Type Promotion Rules) is undefined and thus implementation-dependent.

+
diff --git a/draft/API_specification/generated/array_api.array.__ge__.html b/draft/API_specification/generated/array_api.array.__ge__.html index 509fa4fe3..aca7e07bb 100644 --- a/draft/API_specification/generated/array_api.array.__ge__.html +++ b/draft/API_specification/generated/array_api.array.__ge__.html @@ -485,6 +485,10 @@

__ge__Note

Element-wise results must equal the results returned by the equivalent element-wise function greater_equal().

+
+

Note

+

Comparison of arrays without a corresponding promotable data type (see Type Promotion Rules) is undefined and thus implementation-dependent.

+
diff --git a/draft/API_specification/generated/array_api.array.__gt__.html b/draft/API_specification/generated/array_api.array.__gt__.html index b318a3264..6b5e08542 100644 --- a/draft/API_specification/generated/array_api.array.__gt__.html +++ b/draft/API_specification/generated/array_api.array.__gt__.html @@ -485,6 +485,10 @@

__gt__Note

Element-wise results must equal the results returned by the equivalent element-wise function greater().

+
+

Note

+

Comparison of arrays without a corresponding promotable data type (see Type Promotion Rules) is undefined and thus implementation-dependent.

+
diff --git a/draft/API_specification/generated/array_api.array.__le__.html b/draft/API_specification/generated/array_api.array.__le__.html index ee2a9aac5..16fe2ae88 100644 --- a/draft/API_specification/generated/array_api.array.__le__.html +++ b/draft/API_specification/generated/array_api.array.__le__.html @@ -485,6 +485,10 @@

__le__Note

Element-wise results must equal the results returned by the equivalent element-wise function less_equal().

+
+

Note

+

Comparison of arrays without a corresponding promotable data type (see Type Promotion Rules) is undefined and thus implementation-dependent.

+
diff --git a/draft/API_specification/generated/array_api.array.__lt__.html b/draft/API_specification/generated/array_api.array.__lt__.html index 5217d7e33..8be489d21 100644 --- a/draft/API_specification/generated/array_api.array.__lt__.html +++ b/draft/API_specification/generated/array_api.array.__lt__.html @@ -485,6 +485,10 @@

__lt__Note

Element-wise results must equal the results returned by the equivalent element-wise function less().

+
+

Note

+

Comparison of arrays without a corresponding promotable data type (see Type Promotion Rules) is undefined and thus implementation-dependent.

+
diff --git a/draft/API_specification/generated/array_api.array.__ne__.html b/draft/API_specification/generated/array_api.array.__ne__.html index 223c58a9a..c93276f5e 100644 --- a/draft/API_specification/generated/array_api.array.__ne__.html +++ b/draft/API_specification/generated/array_api.array.__ne__.html @@ -482,6 +482,10 @@

__ne__Note

Element-wise results, including special cases, must equal the results returned by the equivalent element-wise function not_equal().

+
+

Note

+

Comparison of arrays without a corresponding promotable data type (see Type Promotion Rules) is undefined and thus implementation-dependent.

+

Changed in version 2022.12: Added complex data type support.

diff --git a/draft/API_specification/generated/array_api.equal.html b/draft/API_specification/generated/array_api.equal.html index 720ff94a6..66952e60e 100644 --- a/draft/API_specification/generated/array_api.equal.html +++ b/draft/API_specification/generated/array_api.equal.html @@ -498,6 +498,10 @@

equalNote

For discussion of complex number equality, see Complex Numbers.

+
+

Note

+

Comparison of arrays without a corresponding promotable data type (see Type Promotion Rules) is undefined and thus implementation-dependent.

+

Changed in version 2022.12: Added complex data type support.

diff --git a/draft/API_specification/generated/array_api.greater.html b/draft/API_specification/generated/array_api.greater.html index e71555424..6e40f5bb5 100644 --- a/draft/API_specification/generated/array_api.greater.html +++ b/draft/API_specification/generated/array_api.greater.html @@ -478,7 +478,10 @@

greater
Returns:
-

out (array) – an array containing the element-wise results. The returned array must have a data type of bool.

+
diff --git a/draft/API_specification/generated/array_api.greater_equal.html b/draft/API_specification/generated/array_api.greater_equal.html index c4c364759..3603620a0 100644 --- a/draft/API_specification/generated/array_api.greater_equal.html +++ b/draft/API_specification/generated/array_api.greater_equal.html @@ -478,7 +478,10 @@

greater_
Returns:
-

out (array) – an array containing the element-wise results. The returned array must have a data type of bool.

+
    +

  • out (array) – an array containing the element-wise results. The returned array must have a data type of bool.

    • +

  • .. note:: – Comparison of arrays without a corresponding promotable data type (see Type Promotion Rules) is undefined and thus implementation-dependent.

    • +
diff --git a/draft/API_specification/generated/array_api.less.html b/draft/API_specification/generated/array_api.less.html index 8fa31266f..9c318571f 100644 --- a/draft/API_specification/generated/array_api.less.html +++ b/draft/API_specification/generated/array_api.less.html @@ -478,7 +478,10 @@

lessReturns: -

out (array) – an array containing the element-wise results. The returned array must have a data type of bool.

+
diff --git a/draft/API_specification/generated/array_api.less_equal.html b/draft/API_specification/generated/array_api.less_equal.html index 1439133ad..d90579702 100644 --- a/draft/API_specification/generated/array_api.less_equal.html +++ b/draft/API_specification/generated/array_api.less_equal.html @@ -478,7 +478,10 @@

less_equal<
Returns:
-

out (array) – an array containing the element-wise results. The returned array must have a data type of bool.

+
    +

  • out (array) – an array containing the element-wise results. The returned array must have a data type of bool.

    • +

  • .. note:: – Comparison of arrays without a corresponding promotable data type (see Type Promotion Rules) is undefined and thus implementation-dependent.

    • +
diff --git a/draft/API_specification/generated/array_api.not_equal.html b/draft/API_specification/generated/array_api.not_equal.html index 8fb8a78ae..b6b7f83ce 100644 --- a/draft/API_specification/generated/array_api.not_equal.html +++ b/draft/API_specification/generated/array_api.not_equal.html @@ -496,6 +496,10 @@

not_equalNote

For discussion of complex number equality, see Complex Numbers.

+
+

Note

+

Comparison of arrays without a corresponding promotable data type (see Type Promotion Rules) is undefined and thus implementation-dependent.

+

Changed in version 2022.12: Added complex data type support.

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258, 259, 260, 264, 266, 267], "defin": [0, 5, 12, 23, 30, 32, 41, 49, 60, 65, 79, 91, 102, 104, 105, 116, 123, 135, 136, 137, 139, 140, 141, 142, 155, 162, 167, 168, 171, 180, 181, 188, 189, 193, 196, 201, 208, 210, 211, 220, 224, 225, 228, 229, 232, 235, 236, 240, 241, 242, 249, 250, 252, 260, 265, 266, 267], "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, 91, 92, 94, 95, 97, 98, 99, 101, 102, 104, 106, 107, 108, 114, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 135, 136, 137, 139, 140, 142, 143, 144, 145, 146, 147, 148, 151, 152, 155, 160, 161, 162, 163, 164, 165, 166, 167, 171, 173, 176, 177, 182, 188, 189, 191, 193, 203, 208, 211, 223, 226, 230, 231, 232, 233, 234, 235, 236, 240, 241, 242, 244, 246, 249, 250, 251, 252, 253, 254, 256, 258, 261], "data": [0, 1, 2, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 28, 29, 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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, 110, 114, 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, 188, 189, 190, 191, 192, 193, 194, 196, 206, 209, 211, 212, 214, 216, 217, 218, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258, 260, 261, 264, 265], "__matmul__": [0, 193, 208], "matmul": [0, 40, 193, 203, 208, 260], "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, 91, 94, 95, 97, 100, 101, 102, 103, 106, 107, 108, 110, 111, 112, 114, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 139, 140, 141, 142, 143, 144, 145, 146, 149, 150, 151, 152, 153, 154, 155, 156, 160, 161, 162, 163, 164, 165, 166, 167, 168, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 188, 189, 190, 194, 203, 206, 208, 209, 210, 212, 213, 214, 215, 218, 219, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258, 259, 260, 261, 263, 264, 265, 266, 267], "__invert__": [0, 193], "inv": [0, 208, 260], "invert": [0, 68, 242, 245, 252], "__inv__": 0, "__and__": [0, 193], "__or__": [0, 193], "__xor__": [0, 193], "xor": [0, 72, 132], "__lshift__": [0, 193], "lshift": 0, "__rshift__": [0, 193], "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, 91, 101, 102, 104, 105, 109, 112, 116, 117, 123, 135, 137, 139, 143, 151, 152, 155, 156, 158, 160, 161, 171, 173, 174, 182, 188, 189, 193, 194, 208, 210, 211, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 237, 245, 246, 256, 258, 264], "boolean": [0, 5, 22, 24, 25, 26, 29, 35, 36, 43, 45, 52, 57, 60, 63, 67, 68, 70, 72, 88, 89, 103, 104, 105, 112, 116, 117, 123, 129, 130, 131, 132, 145, 193, 203, 208], "__lt__": [0, 193, 208], "lt": 0, "__le__": [0, 193, 208], "le": 0, "__gt__": [0, 193, 208], "gt": [0, 250, 253], "__ge__": [0, 193, 208], "ge": 0, "__eq__": [0, 193, 208, 215], "eq": 0, "__ne__": [0, 193, 208], "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, 91, 95, 98, 99, 100, 102, 103, 108, 115, 116, 123, 129, 130, 131, 132, 133, 142, 145, 151, 156, 159, 160, 164, 176, 177, 179, 183, 185, 189, 194, 203, 206, 208, 209, 210, 211, 212, 213, 214, 215, 216, 218, 219, 220, 222, 223, 224, 225, 227, 228, 229, 231, 232, 233, 234, 235, 237, 240, 241, 246, 249, 250, 253, 259, 260, 261, 264, 265, 266, 267], "onli": [0, 1, 5, 7, 16, 17, 23, 26, 40, 57, 58, 63, 100, 103, 108, 114, 116, 117, 123, 129, 130, 131, 132, 133, 137, 171, 188, 189, 193, 194, 203, 206, 208, 209, 211, 212, 214, 215, 216, 218, 220, 225, 237, 242, 249, 250, 252, 260, 261, 264, 265, 266, 267], "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, 91, 97, 102, 103, 126, 141, 142, 171, 188, 194, 196, 206, 208, 210, 211, 212, 213, 214, 215, 216, 220, 237, 249, 259, 260, 263, 264, 266], "ani": [0, 1, 9, 10, 11, 23, 24, 25, 26, 28, 29, 34, 35, 43, 59, 61, 62, 66, 89, 90, 94, 108, 118, 119, 146, 167, 193, 194, 203, 208, 211, 212, 214, 220, 253, 261, 263, 264, 267], "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, 91, 94, 95, 97, 101, 102, 106, 107, 108, 114, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 135, 136, 138, 139, 140, 142, 143, 144, 146, 151, 152, 154, 155, 156, 160, 161, 162, 163, 164, 165, 166, 167, 168, 170, 173, 176, 177, 182, 183, 184, 185, 186, 194, 201, 206, 210, 211, 213, 215, 218, 223, 232, 234, 251, 253, 254, 256, 264, 266, 267], "backward": [0, 13, 14, 16, 17, 18, 31, 33, 37, 39, 90, 106, 107, 121, 122, 123, 135, 136, 139, 140, 155, 166, 189, 194, 208, 211, 212, 216, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 237, 264], "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, 91, 94, 102, 106, 107, 108, 121, 122, 123, 128, 129, 131, 132, 133, 135, 136, 137, 139, 140, 142, 144, 146, 151, 152, 155, 156, 157, 166, 171, 172, 173, 175, 188, 189, 190, 203, 208, 211, 212, 216, 237, 244, 246, 249, 252, 258, 264, 266], "mai": [0, 5, 7, 15, 16, 17, 18, 23, 26, 28, 31, 33, 37, 39, 43, 51, 57, 58, 59, 60, 89, 90, 91, 94, 102, 103, 106, 107, 108, 111, 116, 117, 121, 122, 123, 129, 130, 131, 132, 135, 136, 137, 139, 140, 142, 145, 146, 156, 157, 161, 166, 171, 177, 183, 184, 185, 186, 188, 193, 194, 201, 203, 206, 209, 210, 211, 212, 213, 214, 215, 216, 218, 219, 220, 240, 250, 251, 253, 259, 260, 264, 265, 266], "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, 91, 94, 95, 97, 98, 99, 104, 105, 106, 107, 108, 110, 114, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 133, 135, 136, 138, 139, 140, 142, 143, 145, 146, 147, 148, 150, 151, 152, 153, 160, 162, 164, 165, 166, 167, 168, 172, 173, 176, 177, 178, 183, 184, 185, 186, 189, 203, 210, 214, 215, 217, 218, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258, 260, 264, 265], "howev": [0, 5, 16, 17, 18, 31, 33, 37, 39, 57, 88, 102, 106, 107, 108, 117, 121, 122, 123, 135, 136, 139, 140, 156, 161, 166, 174, 176, 177, 206, 209, 210, 211, 212, 213, 215, 260, 261, 264, 266], "inequ": [0, 16, 17, 18, 31, 33, 37, 39, 106, 107, 121, 122, 135, 136, 139, 140, 166], "unspecifi": [0, 5, 10, 11, 16, 17, 18, 30, 31, 32, 33, 37, 39, 41, 47, 51, 60, 62, 66, 77, 78, 87, 91, 95, 97, 102, 104, 105, 106, 107, 121, 122, 123, 135, 136, 139, 140, 151, 155, 161, 165, 166, 167, 170, 174, 175, 177, 194, 201, 203, 208, 224, 225, 228, 229, 232, 235, 240, 241, 264], "thu": [0, 5, 16, 17, 18, 30, 31, 32, 33, 37, 39, 41, 47, 57, 60, 71, 77, 102, 104, 105, 106, 107, 121, 122, 123, 135, 136, 139, 140, 151, 155, 161, 166, 176, 177, 194, 201, 210, 211, 224, 225, 228, 229, 232, 235, 240, 241, 253, 260], "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, 91, 95, 97, 106, 107, 112, 121, 122, 123, 124, 125, 126, 127, 142, 143, 151, 161, 164, 165, 166, 176, 177, 190, 201, 203, 210, 211, 214, 217, 218, 220, 240, 241, 250, 251, 252, 253, 260, 264, 266, 267], "see": [0, 5, 10, 11, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 32, 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, 91, 94, 97, 102, 103, 105, 106, 107, 108, 111, 112, 115, 121, 122, 124, 126, 128, 129, 131, 132, 133, 135, 136, 137, 139, 140, 142, 144, 145, 146, 151, 152, 154, 155, 156, 158, 162, 166, 167, 168, 171, 172, 173, 175, 183, 184, 185, 186, 188, 189, 190, 193, 194, 203, 205, 206, 209, 211, 213, 214, 215, 220, 237, 244, 246, 249, 252, 258, 259, 264, 265, 266, 267], "order": [0, 5, 7, 16, 17, 18, 19, 26, 31, 33, 37, 39, 55, 60, 63, 65, 89, 90, 100, 102, 103, 106, 107, 121, 122, 135, 136, 139, 140, 145, 156, 161, 166, 176, 177, 178, 183, 184, 185, 186, 194, 201, 203, 208, 210, 213, 214, 216, 231, 232, 240, 241, 244, 253, 254, 258, 260, 261, 264, 265], "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, 91, 94, 95, 97, 98, 99, 103, 104, 105, 118, 119, 120, 123, 124, 125, 126, 127, 133, 135, 138, 139, 142, 143, 145, 146, 147, 148, 150, 151, 152, 157, 160, 162, 164, 165, 167, 168, 172, 173, 174, 176, 177, 178, 183, 184, 185, 186, 189, 206, 222, 223, 224, 226, 227, 228, 231, 232, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258, 261, 264, 266, 267], "shape": [0, 1, 18, 40, 55, 63, 73, 74, 78, 88, 90, 92, 93, 96, 100, 104, 105, 112, 133, 134, 138, 147, 148, 157, 159, 161, 166, 170, 174, 175, 178, 179, 180, 181, 187, 189, 191, 192, 193, 208, 217, 218, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 238, 239, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 264, 266], "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, 91, 94, 95, 97, 101, 102, 106, 107, 108, 110, 118, 119, 120, 121, 122, 124, 125, 126, 127, 128, 129, 130, 131, 132, 135, 136, 137, 139, 140, 142, 143, 144, 146, 150, 151, 152, 153, 154, 155, 156, 158, 160, 161, 162, 163, 164, 165, 167, 168, 170, 171, 172, 173, 176, 177, 178, 182, 183, 188, 194, 201, 203, 208, 210, 211, 212, 218, 236, 237, 239, 244, 245, 251, 252, 258, 264, 265, 266, 267], "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, 91, 95, 97, 102, 105, 108, 123, 124, 125, 126, 127, 128, 133, 136, 137, 140, 142, 143, 151, 154, 155, 158, 164, 165, 167, 168, 170, 171, 172, 176, 177, 178, 188, 189, 190, 193, 208, 236, 237, 242, 244, 245, 246, 248, 249, 250, 251, 252, 258, 260], "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, 91, 95, 97, 102, 104, 105, 108, 123, 124, 125, 126, 127, 128, 133, 136, 140, 142, 143, 151, 154, 155, 158, 162, 164, 165, 167, 168, 170, 172, 176, 177, 178, 189, 190, 193, 194, 208, 211, 214, 236, 237, 242, 244, 245, 246, 248, 249, 250, 251, 252, 258, 260, 264, 266], "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, 91, 94, 102, 106, 107, 108, 121, 122, 128, 129, 131, 132, 133, 135, 136, 137, 139, 140, 142, 144, 146, 151, 152, 155, 156, 171, 172, 173, 175, 178, 188, 189, 190, 193, 208, 237, 244, 246, 249, 252, 258, 264], "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, 91, 93, 96, 99, 100, 101, 102, 103, 105, 110, 133, 134, 135, 137, 138, 139, 141, 142, 144, 148, 149, 150, 151, 152, 153, 155, 156, 157, 159, 160, 161, 162, 166, 169, 170, 171, 172, 173, 174, 175, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 192, 194, 203, 206, 208, 211, 212, 214, 215, 220, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 235, 236, 238, 239, 240, 242, 245, 249, 250, 251, 253, 254, 256, 259, 260, 264, 266], "behavior": [0, 5, 32, 47, 49, 59, 60, 63, 77, 91, 102, 104, 105, 108, 123, 142, 151, 155, 161, 174, 175, 183, 184, 185, 186, 193, 194, 196, 203, 206, 208, 210, 211, 218, 219, 224, 225, 228, 229, 232, 235, 260, 261, 264, 265, 266, 267], "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, 77, 85, 86, 87, 88, 91, 94, 95, 97, 101, 102, 108, 118, 119, 120, 124, 125, 126, 127, 128, 135, 136, 137, 139, 140, 142, 144, 146, 151, 152, 154, 155, 160, 162, 163, 164, 165, 167, 168, 171, 173, 176, 177, 182, 188, 208, 209, 211, 251, 256], "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, 77, 85, 86, 87, 88, 91, 94, 95, 97, 101, 102, 103, 108, 118, 119, 120, 124, 125, 126, 127, 128, 135, 136, 137, 138, 139, 140, 142, 144, 146, 151, 152, 154, 155, 160, 162, 163, 164, 165, 167, 168, 171, 173, 176, 177, 182, 188, 194, 206, 208, 209, 210, 211, 212, 215, 216, 218, 250, 251, 253, 256, 260, 262, 264, 267], "its": [0, 5, 26, 40, 73, 91, 99, 133, 142, 157, 159, 210, 211, 214, 215, 259, 264, 265, 266], "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, 91, 94, 102, 106, 107, 108, 114, 121, 122, 123, 128, 129, 131, 132, 136, 138, 140, 141, 142, 144, 146, 155, 165, 172, 176, 177, 178, 183, 184, 189, 208, 210, 213, 215, 240, 250, 253], "binari": [0, 5, 67, 70, 72, 176, 177, 209], "two": [0, 1, 5, 15, 19, 40, 55, 65, 71, 98, 103, 133, 134, 138, 160, 178, 180, 181, 183, 184, 185, 186, 189, 194, 203, 214, 215, 218, 219, 224, 225, 228, 229, 232, 235, 236, 238, 239, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 260, 264, 265, 266, 267], "operand": [0, 1, 9, 10, 11, 12, 24, 25, 29, 35, 61, 62, 64, 65, 66, 76, 85, 86, 87, 88, 91, 94, 95, 97, 101, 102, 108, 118, 119, 120, 124, 125, 126, 127, 128, 135, 136, 139, 140, 142, 144, 146, 151, 152, 154, 155, 160, 162, 163, 164, 165, 167, 168, 173, 176, 177, 182, 203, 208, 210, 251, 256], "assign": [0, 212], "exampl": [0, 5, 12, 23, 26, 116, 117, 170, 193, 194, 206, 211, 212, 213, 215, 218, 219, 220, 256, 260, 264, 266, 267], "after": [0, 1, 26, 40, 133, 167, 179], "addit": [0, 5, 7, 12, 26, 50, 59, 88, 116, 172, 193, 194, 203, 209, 211, 214, 260, 264, 265, 267], "modifi": [0, 26, 212, 263], "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, 95, 97, 98, 104, 105, 108, 117, 119, 124, 125, 126, 127, 137, 145, 146, 147, 148, 151, 152, 160, 165, 166, 167, 171, 173, 174, 175, 177, 178, 179, 183, 184, 185, 186, 188, 193, 194, 201, 208, 211, 215, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 237, 239, 245, 246, 249, 250, 251, 252, 256, 264], "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, 102, 108, 129, 130, 131, 132, 155, 160, 174, 194, 203, 211, 212, 246, 249, 252, 258, 264], "discuss": [0, 94, 146, 208, 214, 215, 219, 264, 265, 266], "copi": [0, 1, 26, 59, 60, 63, 103, 157, 166, 208, 209, 214, 215, 217, 263, 264], "view": [0, 103, 217], "behaviour": [0, 217, 264, 266], "mutabl": [0, 217], "via": [0, 26, 102, 103, 174, 194, 209, 214, 215, 219, 221, 249, 259, 260, 261, 264], "__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, 91, 142, 158, 160, 170, 178, 194, 203, 206, 211, 222, 224, 227, 228, 231, 232, 233, 235, 246, 249, 260, 264, 266], "match": [0, 1, 5, 9, 20, 26, 63, 102, 155, 178, 183, 184, 216, 226, 230, 231, 232, 233, 235, 240, 241, 244, 258, 266], "op": [0, 203], "__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, 112, 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, 192, 193, 195, 196, 197, 198, 199, 200, 201, 202, 204, 205, 206, 208, 209, 210, 211, 212, 213, 214, 215, 216, 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, 260, 261, 265, 267], "refer": [1, 13, 14, 90, 97, 98, 126, 171, 178, 179, 188, 189, 194, 211, 212, 220, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 237, 252], "automat": [1, 32, 264], "implicit": [1, 214, 215, 218, 264], "expans": [1, 264], "size": [1, 13, 14, 88, 90, 96, 123, 145, 159, 169, 174, 175, 178, 189, 193, 194, 213, 219, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 237, 239, 248, 250, 253, 264], "without": [1, 7, 26, 57, 103, 114, 116, 145, 156, 157, 183, 184, 185, 186, 206, 209, 210, 213, 263, 264, 266], "purpos": [1, 5, 97, 108, 126, 206, 251, 260, 262, 263, 266], "make": [1, 7, 206, 209, 210, 212, 214, 218, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 259, 261, 264], "differ": [1, 12, 26, 49, 50, 77, 78, 88, 90, 91, 99, 102, 103, 142, 152, 170, 172, 173, 194, 206, 212, 215, 216, 218, 229, 240, 250, 251, 253, 256, 260, 264, 265, 266], "element": [1, 9, 10, 11, 12, 13, 14, 15, 20, 21, 22, 24, 25, 28, 29, 30, 31, 32, 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, 91, 94, 95, 97, 98, 100, 101, 102, 104, 105, 106, 107, 108, 110, 118, 119, 120, 121, 122, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 135, 136, 137, 139, 140, 142, 143, 144, 145, 146, 150, 151, 152, 153, 154, 155, 156, 157, 159, 160, 161, 162, 163, 164, 165, 167, 168, 169, 171, 172, 173, 174, 175, 176, 177, 179, 180, 181, 182, 183, 184, 185, 186, 188, 190, 193, 194, 208, 210, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 237, 240, 249, 250, 251, 253, 256, 264], "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, 91, 94, 102, 106, 107, 108, 110, 121, 122, 128, 129, 130, 131, 132, 136, 140, 142, 144, 146, 151, 153, 154, 155, 172, 193, 208, 210, 264], "oper": [1, 12, 19, 24, 26, 34, 40, 57, 58, 59, 61, 64, 71, 86, 88, 91, 102, 125, 127, 133, 142, 151, 152, 154, 155, 158, 164, 168, 173, 176, 178, 193, 194, 200, 203, 208, 211, 212, 213, 214, 215, 256, 260, 261, 264, 265, 266], "facilit": [1, 201, 206], "user": [1, 7, 26, 111, 177, 206, 209, 210, 212, 215, 219, 260, 264, 265, 266], "ergonom": 1, "encourag": [1, 264, 265], "avoid": [1, 9, 63, 91, 97, 102, 108, 126, 142, 157, 209, 212, 215, 218, 260, 264, 266], "unnecessari": [1, 260], "can": [1, 7, 26, 32, 60, 75, 111, 115, 117, 194, 203, 206, 209, 211, 212, 214, 215, 220, 249, 250, 253, 259, 260, 264, 265, 266, 267], "potenti": [1, 26, 97, 112, 126, 156, 212, 264], "enabl": [1, 26, 103, 215, 219, 220, 264], "more": [1, 5, 7, 15, 19, 26, 32, 40, 58, 60, 63, 73, 88, 97, 100, 102, 126, 133, 145, 151, 156, 174, 183, 184, 185, 186, 194, 203, 206, 209, 210, 211, 212, 213, 214, 215, 216, 219, 220, 224, 225, 228, 229, 232, 235, 251, 260, 261, 264, 265, 267], "memori": [1, 26, 60, 103, 206, 212, 213, 215, 264, 266], "effici": [1, 206, 212], "through": [1, 60, 65, 259, 261, 265, 266], "vector": [1, 40, 133, 138, 189, 237, 248, 253, 254, 258, 260, 264], "reduc": [1, 13, 14, 16, 17, 135, 137, 139, 152, 171, 173, 188, 194, 250, 253, 260, 265, 266], "consumpt": [1, 26, 265], "cach": 1, "local": [1, 215], "given": [1, 23, 90, 100, 123, 159, 161, 187, 203, 208, 211, 212, 215, 216, 220, 241, 251, 260, 261, 264, 266], "involv": [1, 12, 91, 102, 142, 151, 158, 203, 210, 211, 215, 219], "singleton": [1, 13, 14, 16, 17, 96, 135, 137, 139, 152, 169, 171, 173, 179, 188, 244, 258, 264], "whose": [1, 5, 9, 11, 19, 20, 26, 47, 55, 62, 66, 85, 86, 87, 98, 100, 103, 134, 151, 159, 163, 164, 165, 174, 175, 176, 177, 178, 180, 181, 183, 184, 185, 194, 212, 226, 230, 231, 232, 233, 235, 236, 238, 239, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258, 264, 266], "one": [1, 15, 19, 26, 32, 40, 51, 58, 60, 63, 73, 75, 88, 91, 96, 98, 100, 102, 103, 116, 117, 123, 133, 138, 142, 145, 147, 148, 156, 161, 169, 174, 175, 183, 184, 185, 186, 189, 194, 206, 209, 211, 212, 214, 215, 218, 219, 220, 222, 224, 226, 227, 228, 229, 230, 231, 232, 233, 235, 248, 249, 250, 258, 260, 261, 264, 266], "virtual": 1, "repeat": [1, 193, 194, 208, 266], "across": [1, 5, 91, 102, 142, 177, 208, 210, 211, 215, 259, 264], "correspond": [1, 16, 17, 23, 47, 59, 65, 73, 77, 103, 112, 113, 114, 151, 157, 159, 161, 171, 175, 178, 183, 184, 185, 186, 188, 189, 194, 208, 210, 224, 228, 232, 235, 237, 240, 244, 263, 264], "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, 105, 108, 112, 114, 116, 117, 118, 119, 120, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 151, 152, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 169, 170, 171, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 191, 192, 194, 209, 211, 215, 221, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 235, 236, 237, 240, 241, 242, 244, 245, 246, 249, 250, 251, 252, 253, 256, 258, 259, 260, 264, 266], "unequ": 1, "lower": [1, 77, 98, 180, 236], "higher": [1, 5, 26, 90, 194, 209, 260, 265], "prepend": [1, 40, 90, 96, 133, 179], "until": [1, 26, 179], "store": [1, 26, 215, 256], "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, 91, 95, 97, 102, 108, 118, 119, 120, 124, 125, 126, 127, 128, 133, 136, 140, 142, 143, 151, 154, 155, 163, 164, 165, 167, 168, 172, 174, 175, 176, 177, 178, 183, 184, 185, 186, 189, 190, 203, 208, 211, 214, 215, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 236, 237, 238, 239, 242, 244, 245, 246, 248, 249, 250, 251, 252, 256, 258, 260, 264], "let": [1, 9, 10, 11, 12, 62, 66, 85, 87, 88, 90, 94, 95, 97, 103, 118, 119, 120, 123, 124, 126, 137, 146, 152, 156, 161, 162, 165, 167, 171, 173, 177, 179, 188, 189, 194, 219, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 236, 240, 241, 242, 250, 252, 253, 256], "b": [1, 9, 10, 11, 12, 57, 62, 66, 87, 91, 94, 95, 97, 102, 118, 119, 120, 123, 124, 126, 142, 146, 162, 165, 167, 170, 177, 189, 194, 208, 211, 212, 216, 249, 252, 266], "both": [1, 40, 44, 47, 51, 65, 77, 88, 91, 99, 102, 103, 108, 123, 133, 143, 151, 152, 173, 177, 178, 189, 194, 211, 212, 214, 218, 220, 237, 256, 260, 264, 265], "shape1": 1, "describ": [1, 5, 12, 88, 91, 94, 116, 117, 142, 146, 151, 152, 173, 196, 203, 211, 214, 218, 223, 234, 256, 264], "shape2": 1, "n1": [1, 90, 138], "len": [1, 138, 179], "n2": [1, 90, 138], "max": [1, 26, 77, 99, 109, 112, 179, 193, 194, 208, 244, 246, 249], "temporari": 1, "list": [1, 73, 78, 111, 115, 138, 170, 194, 206, 208, 215, 264, 266], "length": [1, 15, 108, 138, 157, 178, 194, 223, 225, 226, 229, 234, 253, 254], "while": [1, 102, 116, 123, 129, 130, 131, 132, 137, 141, 161, 171, 183, 184, 188, 193, 194, 201, 206, 208, 211, 212, 213, 215, 218, 249, 260, 265, 266, 267], "d1": 1, "els": [1, 26, 206, 265], "d2": 1, "set": [1, 18, 26, 49, 65, 103, 163, 166, 171, 180, 181, 183, 185, 186, 188, 193, 194, 208, 209, 210, 211, 212, 215, 216, 219, 220, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 236, 240, 241, 242, 246, 249, 250, 252, 253, 259, 260, 264, 266, 267], "th": [1, 90, 98, 179, 194, 224, 228, 232, 235], "throw": 1, "except": [1, 7, 13, 14, 26, 74, 78, 88, 90, 98, 103, 123, 145, 156, 170, 174, 175, 187, 194, 203, 206, 208, 210, 212, 215, 217, 218, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 249, 261, 264, 265, 266], "demonstr": 1, "applic": [1, 26, 88, 152, 156, 173, 203, 256, 260, 264, 265], "4d": 1, "8": [1, 5, 7, 27, 179, 203, 206], "6": [1, 7, 179], "3d": 1, "7": [1, 7, 27, 220], "5": [1, 194, 264], "2d": 1, "1d": 1, "15": 1, "do": [1, 26, 91, 142, 155, 201, 206, 209, 211, 212, 214, 215, 216, 260, 261, 263, 264, 266, 267], "doe": [1, 15, 26, 103, 146, 174, 175, 194, 203, 206, 209, 210, 211, 212, 213, 215, 216, 218, 220, 260, 264, 266, 267], "second": [1, 12, 65, 67, 69, 70, 71, 72, 94, 106, 107, 108, 121, 122, 128, 129, 131, 132, 133, 136, 140, 142, 144, 146, 151, 170, 172, 178, 183, 184, 185, 189, 190, 237, 240, 248, 250, 251, 253, 254, 264], "append": [1, 40, 69, 90, 96, 133, 239], "As": [1, 123, 151, 183, 184, 185, 186, 206, 214, 220, 266], "impli": [1, 183, 184, 185, 186, 263, 264], "__setitem__": [1, 174, 193, 208], "Such": [1, 210, 260], "right": [1, 69, 71, 108, 161, 167, 209, 253, 263], "hand": [1, 203], "left": [1, 5, 60, 69, 102, 104, 161, 174, 175, 194, 203, 240, 241, 253, 264], "index": [1, 5, 16, 17, 18, 32, 34, 49, 57, 83, 98, 112, 114, 138, 141, 145, 161, 170, 174, 178, 183, 184, 185, 193, 208, 224, 228, 232, 235, 264, 266], "perform": [1, 5, 13, 14, 26, 40, 59, 60, 91, 108, 133, 142, 156, 178, 194, 209, 210, 211, 212, 213, 214, 222, 224, 227, 228, 229, 231, 232, 233, 235, 253, 254, 260, 264, 265, 266], "empti": [1, 13, 14, 15, 152, 173, 193, 194, 208, 256, 264], "ok": 1, "allow": [1, 24, 25, 26, 29, 34, 35, 114, 116, 151, 157, 178, 194, 208, 209, 210, 212, 215, 218, 219, 260, 266], "NOT": [1, 130, 263], "adher": [2, 7, 8, 193, 194, 206, 259, 264], "convent": [2, 7, 10, 11, 26, 40, 61, 62, 64, 65, 66, 88, 124, 126, 133, 151, 167, 193, 194, 201, 211, 215, 259, 260, 265], "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, 91, 94, 95, 97, 101, 102, 106, 107, 108, 110, 115, 118, 119, 120, 121, 122, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 136, 138, 140, 141, 142, 143, 144, 145, 146, 150, 151, 153, 154, 155, 156, 159, 160, 161, 162, 163, 164, 165, 167, 168, 170, 172, 176, 177, 178, 179, 182, 183, 184, 194, 206, 208, 210, 214, 218, 220, 232, 236, 237, 238, 242, 244, 245, 246, 249, 250, 251, 252, 253, 254, 259, 260, 264, 265, 266], "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, 91, 92, 94, 95, 97, 98, 99, 101, 102, 104, 105, 108, 110, 114, 116, 117, 118, 119, 120, 123, 124, 125, 126, 127, 128, 133, 135, 136, 137, 139, 140, 142, 143, 144, 145, 146, 147, 148, 151, 152, 153, 154, 155, 158, 160, 161, 162, 163, 164, 165, 167, 168, 171, 172, 173, 176, 177, 178, 182, 183, 184, 185, 186, 188, 189, 191, 193, 201, 208, 210, 211, 218, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 238, 240, 241, 242, 244, 245, 246, 249, 250, 251, 252, 253, 254, 256, 258, 260, 264, 265], "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, 91, 92, 94, 95, 97, 98, 99, 101, 102, 104, 105, 108, 110, 114, 116, 117, 118, 119, 120, 123, 124, 125, 126, 127, 128, 133, 135, 136, 137, 139, 140, 142, 143, 144, 145, 146, 147, 148, 151, 152, 153, 154, 155, 158, 160, 161, 162, 163, 164, 165, 167, 168, 171, 172, 173, 176, 177, 178, 182, 183, 184, 185, 186, 188, 189, 191, 193, 201, 208, 210, 211, 215, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 238, 240, 241, 242, 244, 245, 246, 249, 250, 251, 252, 253, 254, 256, 258, 260, 264, 266], "creat": [3, 15, 60, 92, 93, 98, 103, 104, 105, 123, 147, 148, 191, 192, 200, 206, 215, 223, 234, 260, 264], "main": [5, 98, 180, 181, 209, 214, 239, 256, 259, 266], "namespac": [5, 7, 23, 111, 196, 206, 208, 221, 259, 260, 261, 264, 267], "under": [5, 259, 263, 264], "specifi": [5, 13, 14, 15, 16, 17, 18, 26, 29, 59, 60, 63, 74, 78, 88, 90, 92, 96, 99, 100, 104, 114, 116, 117, 123, 147, 152, 155, 156, 159, 169, 170, 173, 174, 175, 179, 180, 181, 183, 184, 185, 186, 189, 191, 194, 203, 208, 210, 211, 212, 214, 215, 216, 220, 222, 224, 225, 226, 227, 228, 230, 231, 232, 233, 235, 239, 256, 258, 260, 261, 264, 266, 267], "name": [5, 7, 23, 26, 102, 116, 183, 184, 185, 194, 211, 240, 249, 250, 251, 253, 259, 264, 265], "descript": [5, 7, 208, 210, 244, 258], "bool": [5, 13, 14, 16, 17, 18, 22, 24, 26, 28, 31, 33, 37, 39, 43, 45, 49, 52, 60, 63, 75, 88, 89, 94, 103, 104, 105, 106, 107, 116, 117, 118, 119, 120, 121, 122, 123, 129, 130, 131, 132, 135, 137, 139, 146, 152, 157, 163, 166, 171, 173, 188, 203, 208, 218, 236, 244, 253, 258], "true": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 94, 99, 102, 103, 112, 118, 119, 120, 123, 129, 130, 131, 132, 135, 137, 139, 145, 146, 152, 157, 163, 166, 171, 173, 183, 184, 185, 186, 188, 190, 194, 208, 236, 244, 253, 258, 260], "fals": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 94, 103, 112, 118, 119, 120, 123, 129, 130, 131, 132, 135, 137, 139, 146, 152, 157, 163, 166, 171, 173, 183, 184, 185, 186, 188, 194, 236, 244, 253, 258], "int8": [5, 116, 117, 203], "bit": [5, 68, 69, 71, 85, 88, 99, 109, 152, 163, 173, 203, 208, 210, 256], "sign": [5, 9, 10, 11, 12, 15, 20, 41, 44, 62, 65, 66, 71, 85, 87, 88, 91, 95, 97, 102, 116, 117, 124, 126, 135, 136, 139, 140, 142, 143, 151, 152, 155, 161, 163, 165, 167, 173, 177, 183, 184, 185, 186, 193, 201, 208, 211, 250, 251, 256], "exist": [5, 7, 26, 60, 78, 103, 206, 208, 211, 214, 215, 216, 242, 261, 264, 265], "interv": [5, 10, 11, 13, 14, 15, 61, 62, 64, 66, 90, 96, 123, 124, 126, 141, 170, 178, 180, 181, 187, 189, 194, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 237, 261], "128": 5, "127": 5, "int16": [5, 88, 116, 117, 152, 173, 203, 256], "16": [5, 203], "32": [5, 203], "767": 5, "int32": [5, 88, 116, 117, 152, 173, 203, 256], "147": 5, "483": 5, "647": 5, "int64": [5, 88, 116, 117, 152, 173, 203, 256], "64": [5, 203], "9": [5, 27], "223": 5, "372": 5, "036": 5, "854": 5, "775": 5, "807": 5, "uint8": [5, 116, 117, 203], "unsign": [5, 88, 116, 117, 152, 173, 193, 256], "255": 5, "uint16": [5, 88, 116, 117, 152, 173, 203, 256], "65": 5, "535": [5, 208], "uint32": [5, 88, 116, 117, 152, 173, 203, 256], "294": 5, "967": 5, "295": 5, "uint64": [5, 116, 117, 203], "18": 5, "446": [5, 208], "744": [5, 208], "073": 5, "709": [5, 208], "551": [5, 208], "615": 5, "float32": [5, 110, 116, 117, 153, 203, 251, 253, 254], "ieee": [5, 12, 65, 80, 81, 82, 84, 91, 97, 99, 108, 126, 142, 155, 167, 176, 177, 193, 201, 210, 211, 264], "754": [5, 12, 65, 80, 81, 82, 84, 91, 97, 99, 108, 126, 142, 155, 167, 176, 177, 193, 201, 210, 211, 264], "singl": [5, 7, 24, 25, 29, 34, 35, 114, 116, 183, 184, 193, 203, 208, 209, 211, 214, 215, 220, 260, 264, 265, 266], "precis": [5, 9, 20, 42, 60, 99, 104, 105, 110, 142, 153, 167, 203, 208, 210, 226, 230, 231, 232, 233, 235, 240, 241, 244, 251, 253, 254, 258, 264], "2019": [5, 12, 91, 97, 108, 126, 142, 193, 210, 264, 266], "float64": [5, 9, 20, 116, 117, 203, 226, 230, 231, 232, 233, 235, 240, 241, 244, 258], "doubl": [5, 178, 203, 208], "complex64": [5, 110, 116, 117, 153, 203, 208, 251, 253, 254], "imaginari": [5, 10, 11, 12, 13, 14, 44, 61, 62, 63, 64, 66, 79, 87, 91, 94, 95, 97, 99, 110, 124, 126, 142, 143, 145, 146, 147, 148, 151, 160, 165, 167, 177, 208, 211], "compon": [5, 10, 11, 12, 13, 14, 44, 62, 63, 66, 79, 87, 91, 94, 95, 97, 99, 110, 124, 126, 142, 143, 145, 146, 147, 148, 151, 153, 160, 165, 167, 176, 177, 183, 184, 185, 186, 208, 211, 225, 234], "complex128": [5, 9, 20, 116, 117, 203, 208, 226, 230, 231, 232, 233, 235, 240, 241, 244, 258], "method": [5, 26, 34, 103, 193, 196, 206, 212, 214, 215, 218, 219, 220, 264, 265, 266], "attribut": [5, 23, 99, 109, 193, 205, 208, 261, 264, 265, 266], "requir": [5, 10, 11, 24, 25, 29, 34, 35, 59, 61, 62, 63, 64, 66, 88, 103, 108, 117, 152, 167, 170, 173, 174, 175, 177, 183, 184, 186, 187, 193, 194, 201, 203, 206, 208, 209, 210, 211, 212, 213, 214, 215, 218, 220, 222, 223, 224, 226, 227, 228, 231, 232, 234, 237, 256, 259, 260, 264, 265, 266], "beyond": [5, 159, 203, 264], "It": [5, 23, 26, 103, 206, 212, 214, 264, 266, 267], "also": [5, 7, 26, 32, 34, 103, 108, 162, 203, 206, 211, 212, 213, 214, 220, 224, 228, 232, 235, 253, 259, 266], "subnorm": [5, 108], "k": [5, 40, 98, 108, 133, 145, 180, 181, 194, 236, 240, 241, 242, 250, 252, 253, 254, 256, 264], "denorm": [5, 108], "gradual": [5, 108, 264], "underflow": [5, 9, 91, 102, 108, 251], "hardwar": [5, 53, 108, 156, 210, 214, 215, 240, 253, 260, 264], "univers": [5, 108, 209, 215, 260, 264], "mani": [5, 108, 179, 264, 266], "platform": [5, 26, 108], "compil": [5, 108, 177, 206, 209, 213, 264], "toggl": [5, 108], "daz": [5, 108], "flush": [5, 108], "ftz": [5, 108], "increas": [5, 108, 210, 265], "guard": [5, 108], "against": [5, 40, 73, 108, 133, 177, 194, 246, 249, 267], "time": [5, 7, 16, 17, 26, 90, 108, 156, 183, 184, 206, 208, 213, 214, 219, 236, 240, 241, 242, 250, 252, 253, 260, 264, 266], "attack": [5, 108], "accordingli": [5, 10, 11, 13, 14, 16, 17, 59, 61, 62, 64, 66, 91, 97, 102, 108, 123, 124, 126, 135, 137, 138, 139, 142, 145, 152, 156, 161, 167, 171, 173, 183, 184, 185, 186, 188, 194, 203, 210, 211, 212, 213, 215, 244, 250, 258, 260], "vari": [5, 108, 161, 177, 183, 184, 185, 186, 203, 210], "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, 90, 95, 97, 100, 103, 108, 115, 116, 117, 123, 124, 126, 129, 130, 131, 132, 133, 137, 145, 151, 152, 155, 156, 157, 162, 164, 165, 166, 167, 170, 171, 173, 174, 175, 176, 177, 178, 179, 183, 184, 185, 186, 187, 188, 189, 193, 196, 206, 208, 209, 211, 212, 213, 214, 215, 218, 219, 220, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 235, 236, 237, 240, 241, 242, 246, 249, 250, 251, 252, 253, 254, 256, 259, 260, 261, 264, 265, 266], "access": [5, 26, 32, 103, 111, 194, 208, 214, 259, 261, 264], "variou": [5, 208], "cast": [5, 29, 49, 60, 63, 75, 88, 152, 173, 203, 211, 256, 264, 266], "introspect": 5, "isdtyp": [5, 193, 208], "integr": [5, 63, 114, 116, 117], "keyword": [5, 7, 26, 63, 88, 115, 138, 152, 173, 193, 208, 212, 215, 219, 220, 256, 260, 261, 264, 265, 266], "affect": [5, 15, 49, 212, 215], "intermedi": [5, 9, 108], "calcul": [5, 9, 10, 11, 12, 20, 21, 42, 47, 50, 61, 62, 64, 65, 66, 86, 87, 88, 90, 91, 95, 97, 124, 125, 126, 127, 128, 135, 137, 139, 142, 151, 152, 164, 165, 167, 171, 172, 173, 176, 177, 188, 208, 251], "implementor": [5, 259], "free": [5, 215, 263], "when": [5, 7, 12, 16, 17, 26, 32, 47, 49, 59, 63, 91, 97, 102, 103, 108, 114, 116, 123, 126, 135, 136, 139, 140, 142, 151, 152, 156, 157, 161, 171, 173, 177, 188, 190, 193, 194, 203, 208, 209, 211, 212, 213, 214, 216, 218, 219, 220, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 236, 240, 242, 246, 249, 250, 251, 252, 253, 254, 256, 260, 264, 265, 266], "accumul": 5, "reduct": [5, 13, 14], "long": [5, 111, 220], "ha": [5, 9, 13, 14, 20, 23, 29, 34, 35, 40, 44, 47, 55, 86, 87, 88, 91, 95, 96, 97, 102, 105, 133, 137, 138, 141, 142, 143, 145, 151, 152, 164, 165, 169, 171, 173, 174, 176, 177, 178, 179, 183, 184, 185, 186, 188, 194, 203, 206, 211, 214, 215, 218, 219, 237, 244, 252, 253, 256, 258, 260, 261, 264, 266, 267], "wai": [5, 26, 63, 103, 206, 209, 215, 216, 261, 264, 265, 266, 267], "f4": [5, 203], "ensur": [5, 26, 161, 206, 210, 260, 264, 265, 266], "portabl": [5, 59, 123, 210, 212, 215, 216, 264], "consum": [5, 26, 63, 114, 116, 206, 211, 212, 220, 259, 264, 265], "recommend": [5, 7, 19, 23, 26, 123, 129, 130, 131, 132, 137, 155, 171, 188, 201, 208, 210, 214, 215, 264], "guidanc": [5, 7, 49, 208, 209, 216, 264], "govern": [5, 50, 172, 203, 260, 261], "interact": [5, 211], "either": [5, 9, 10, 11, 12, 24, 26, 35, 40, 65, 77, 87, 88, 91, 94, 95, 97, 99, 102, 103, 108, 111, 117, 118, 119, 123, 124, 125, 126, 127, 128, 133, 135, 136, 139, 140, 142, 144, 152, 155, 162, 163, 164, 167, 173, 176, 177, 178, 194, 210, 211, 212, 216, 220, 251, 256, 264, 265, 267], "whether": [5, 13, 14, 26, 59, 60, 63, 88, 89, 103, 112, 117, 120, 123, 157, 163, 208, 215, 236, 240, 241, 250, 252, 259, 263, 264, 266], "otherwis": [5, 13, 14, 15, 16, 17, 26, 59, 60, 63, 75, 103, 112, 114, 116, 135, 137, 139, 152, 156, 157, 161, 162, 171, 173, 188, 189, 190, 193, 194, 206, 215, 236, 238, 244, 251, 252, 258, 263], "note": [5, 7, 9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 32, 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, 91, 94, 95, 97, 98, 99, 101, 102, 104, 105, 108, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 124, 125, 126, 127, 128, 133, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 160, 161, 162, 163, 164, 165, 167, 168, 171, 172, 173, 174, 176, 177, 178, 179, 182, 183, 184, 185, 186, 187, 188, 189, 193, 194, 208, 214, 218, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258, 264, 265, 266, 267], "possibl": [5, 26, 60, 102, 103, 135, 139, 157, 176, 177, 206, 209, 210, 211, 212, 214, 215, 216, 218, 220, 260, 264, 265, 266, 267], "multipl": [5, 7, 13, 14, 16, 17, 40, 42, 44, 133, 135, 137, 139, 142, 143, 152, 171, 173, 188, 194, 206, 209, 211, 214, 215, 219, 220, 241, 242, 260, 261, 264, 266], "In": [5, 12, 19, 26, 59, 88, 91, 94, 102, 117, 119, 120, 142, 146, 152, 155, 162, 173, 193, 194, 196, 203, 210, 211, 214, 216, 231, 232, 250, 251, 253, 256, 260, 261, 265, 266, 267], "clearli": [5, 59, 117, 201, 211, 260, 261], "warn": [5, 156, 216], "about": [5, 7, 26, 99, 109, 212, 260, 264, 266, 267], "": [5, 26, 29, 32, 49, 58, 59, 60, 80, 102, 103, 138, 155, 171, 179, 180, 181, 188, 194, 201, 206, 208, 209, 210, 211, 212, 214, 215, 218, 220, 224, 228, 232, 235, 249, 253, 254, 260, 261, 264, 266], "organ": [5, 208, 260, 265, 266], "within": [5, 15, 27, 194, 203, 206, 208, 211, 215, 222, 224, 227, 228, 231, 232, 233, 235, 264], "numer": [5, 9, 12, 20, 21, 40, 42, 44, 46, 47, 50, 51, 88, 90, 91, 102, 116, 117, 118, 119, 120, 133, 138, 142, 143, 150, 151, 152, 160, 162, 168, 172, 173, 178, 203, 210, 222, 224, 227, 228, 231, 232, 233, 235, 237, 248, 249, 251, 256, 260, 264, 266], "accord": [5, 12, 60, 71, 75, 88, 91, 99, 102, 104, 123, 142, 151, 161, 162, 171, 175, 188, 189, 194, 210, 211], "These": [5, 212, 240, 265], "intend": [5, 88, 152, 173, 206, 256], "posit": [7, 9, 10, 11, 13, 14, 20, 46, 62, 65, 66, 81, 91, 96, 98, 99, 102, 119, 124, 126, 141, 142, 145, 155, 159, 163, 165, 167, 177, 193, 194, 206, 208, 210, 220, 234, 236, 250, 265], "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, 110, 114, 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, 192, 193, 206, 208, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258, 260], "extern": [7, 266], "usabl": 7, "accept": [7, 26, 129, 130, 131, 132, 137, 155, 171, 188, 206, 261], "call": [7, 34, 90, 214, 215, 218, 251, 264, 265, 266], "argument": [7, 10, 11, 26, 40, 61, 62, 63, 64, 65, 66, 86, 88, 108, 115, 124, 126, 133, 152, 158, 161, 164, 167, 173, 176, 177, 178, 193, 203, 208, 210, 212, 214, 215, 222, 224, 227, 228, 231, 232, 233, 235, 256, 260, 264, 265, 266], "map": [7, 211, 212], "base": [7, 47, 57, 58, 95, 96, 124, 125, 126, 127, 151, 183, 184, 185, 186, 194, 208, 212, 218, 220, 260, 261, 264, 265, 266], "sole": [7, 194, 201, 260], "incompat": [7, 26, 74, 103, 206, 261, 264], "us": [7, 19, 26, 27, 59, 60, 83, 99, 103, 108, 123, 125, 127, 159, 183, 185, 193, 194, 203, 208, 210, 211, 212, 213, 215, 216, 219, 220, 221, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 259, 260, 261, 262, 263, 264, 267], "normal": [7, 78, 170, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235], "practic": [7, 19, 194, 260, 265], "avail": [7, 103, 115, 206, 214, 259, 261, 265], "still": [7, 26, 220, 260, 265, 266, 267], "consid": [7, 26, 63, 103, 129, 130, 131, 132, 183, 184, 185, 186, 211, 215, 234, 249, 260, 264, 266, 267], "compliant": [7, 26, 51, 91, 97, 103, 123, 126, 129, 130, 131, 132, 135, 136, 137, 139, 140, 171, 188, 210, 213, 215, 261, 264], "altern": [7, 212, 214, 267], "thei": [7, 26, 203, 209, 214, 215, 219, 220, 259, 260, 261, 264, 266, 267], "were": [7, 102, 156, 161, 208, 264], "option": [7, 13, 14, 15, 16, 17, 23, 26, 57, 58, 59, 60, 63, 77, 78, 88, 90, 92, 93, 98, 100, 103, 104, 105, 114, 116, 123, 135, 137, 139, 147, 148, 152, 156, 157, 159, 161, 171, 173, 174, 188, 191, 192, 193, 208, 219, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 244, 246, 249, 256, 258, 260, 265, 266], "lead": [7, 102, 211, 250, 253, 264], "readabl": [7, 203, 260, 265], "code": [7, 59, 203, 212, 213, 215, 218, 220, 260, 264, 265, 266], "easier": [7, 206, 212, 260], "evolv": [7, 206, 260], "over": [7, 13, 14, 26, 123, 135, 137, 139, 152, 171, 173, 174, 178, 188, 189, 210, 211, 212, 214, 215, 219, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 235, 237, 256, 258, 260, 264], "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, 91, 94, 95, 97, 98, 99, 103, 104, 105, 118, 119, 120, 123, 124, 125, 126, 127, 133, 138, 142, 143, 145, 146, 147, 148, 150, 151, 152, 160, 162, 164, 165, 167, 168, 172, 173, 176, 177, 178, 183, 184, 185, 186, 189, 194, 207, 208, 209, 215, 236, 237, 238, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258, 261], "worri": 7, "xi": [7, 138], "annot": [7, 208, 220, 264], "individu": [7, 161, 215, 218, 219, 220, 223, 234, 264, 265], "aim": [7, 209, 220, 259, 260, 261, 264, 265, 266, 267], "strongli": [7, 212, 266], "look": [7, 266], "like": [7, 206, 209, 211, 212, 218, 220, 261, 264, 265, 266], "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, 90, 92, 93, 98, 100, 103, 104, 105, 112, 114, 116, 123, 135, 137, 139, 147, 148, 152, 156, 157, 159, 161, 171, 173, 174, 188, 191, 192, 194, 208, 215, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 244, 246, 249, 256, 257, 258, 264, 265, 267], "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, 191, 192, 194, 208, 209, 212, 214, 218, 219, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258, 263, 266], "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, 90, 92, 96, 98, 99, 100, 102, 104, 105, 109, 123, 135, 137, 139, 141, 147, 149, 152, 156, 157, 159, 166, 169, 170, 171, 173, 174, 175, 178, 179, 180, 181, 187, 188, 189, 191, 194, 203, 218, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 239, 244, 245, 255, 256, 257, 258, 265], "str": [7, 8, 23, 116, 117, 138, 265], "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, 208, 266], "few": [7, 210, 218, 264, 266], "enhanc": 7, "default": [7, 13, 14, 15, 16, 17, 18, 23, 26, 59, 60, 63, 77, 78, 88, 90, 92, 93, 98, 100, 103, 104, 105, 113, 114, 116, 123, 135, 137, 138, 139, 145, 147, 148, 152, 156, 157, 159, 161, 166, 170, 171, 173, 175, 178, 180, 181, 183, 184, 185, 187, 188, 189, 191, 192, 193, 194, 208, 210, 215, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 239, 244, 246, 249, 250, 253, 256, 258], "form": [7, 23, 26, 40, 79, 133, 134, 180, 181, 212, 236, 238, 239, 240, 241, 242, 244, 245, 246, 249, 250, 251, 252, 253, 254, 256, 261, 265], "question": [7, 209, 264], "commonli": [7, 171, 188, 209, 211, 213, 259, 260, 264, 265], "written": [7, 206, 264, 266], "yyyi": [8, 23, 261], "mm": [8, 23, 261], "string": [8, 23, 116, 117, 208, 261, 264], "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, 91, 94, 95, 97, 98, 99, 103, 104, 105, 108, 109, 110, 117, 118, 119, 120, 123, 124, 125, 126, 127, 133, 135, 136, 138, 139, 140, 141, 142, 143, 145, 146, 147, 148, 150, 151, 152, 153, 156, 160, 161, 162, 163, 164, 165, 167, 168, 172, 173, 174, 176, 177, 178, 179, 183, 184, 185, 186, 187, 189, 193, 206, 209, 215, 219, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258, 262, 264, 266], "absolut": [9, 20, 85, 162, 210, 212, 244, 245, 251, 260], "x_i": [9, 10, 11, 61, 62, 64, 66, 68, 76, 77, 79, 86, 87, 95, 97, 101, 110, 118, 119, 120, 124, 125, 126, 127, 130, 135, 137, 139, 143, 150, 153, 154, 160, 162, 163, 164, 165, 167, 168, 171, 176, 177, 182, 188], "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, 91, 93, 94, 95, 96, 97, 100, 101, 102, 103, 105, 106, 107, 108, 110, 117, 118, 119, 120, 121, 122, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 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, 193, 201, 206, 208, 211, 213, 215, 216, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 253, 254, 256, 258, 260, 264, 266], "magnitud": [9, 12, 20, 85, 91, 102, 108, 142, 208, 253, 254], "represent": [9, 12, 20, 29, 44, 67, 70, 72, 80, 81, 82, 84, 91, 99, 102, 109, 142, 143, 144, 176, 177, 210, 214, 265], "known": [9, 162, 210, 213, 214], "norm": [9, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 244, 258, 260], "modulu": [9, 155], "z": [9, 10, 11, 61, 62, 64, 66, 124, 211], "bj": [9, 12, 79, 91, 142], "comput": [9, 12, 28, 31, 33, 37, 39, 40, 43, 57, 58, 67, 70, 72, 79, 88, 89, 90, 91, 94, 96, 102, 106, 107, 108, 121, 122, 129, 130, 131, 132, 133, 135, 136, 137, 139, 140, 142, 143, 145, 146, 150, 152, 156, 171, 173, 178, 183, 184, 185, 186, 188, 189, 194, 208, 210, 213, 218, 222, 223, 224, 226, 227, 228, 230, 231, 232, 233, 234, 235, 236, 237, 240, 241, 242, 244, 246, 249, 250, 251, 252, 253, 254, 256, 258, 260, 264], "operatornam": [9, 10, 11, 61, 62, 64, 66, 86, 87, 162, 164, 165, 176, 177, 211, 240, 241, 251, 253], "sqrt": [9, 10, 11, 61, 62, 193, 208, 211, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 258], "take": [9, 124, 126, 151, 167, 193, 208, 215, 220, 264], "care": [9, 212, 260], "undu": [9, 213], "overflow": [9, 12, 88, 91, 102, 108, 123, 152, 173, 203, 251, 256, 260], "dure": [9, 40, 59, 108, 133, 171, 188, 203, 206, 249, 264, 265], "stage": [9, 108, 261], "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, 95, 97, 101, 102, 103, 106, 107, 108, 110, 111, 112, 114, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 160, 161, 162, 163, 164, 165, 167, 168, 171, 172, 173, 176, 177, 178, 180, 181, 182, 183, 184, 185, 186, 188, 189, 191, 194, 208, 210, 211, 212, 214, 218, 219, 223, 224, 225, 228, 229, 232, 234, 235, 236, 237, 238, 239, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258, 264, 266], "nan": [9, 10, 11, 12, 13, 14, 24, 25, 35, 61, 62, 63, 64, 65, 66, 76, 77, 85, 86, 87, 91, 94, 95, 97, 101, 102, 108, 118, 119, 120, 124, 125, 126, 127, 128, 135, 136, 137, 139, 140, 142, 144, 146, 151, 155, 160, 161, 162, 163, 164, 165, 167, 171, 176, 177, 182, 183, 184, 185, 186, 188, 193, 201, 211, 264], "infin": [9, 10, 11, 12, 13, 14, 24, 25, 35, 62, 63, 64, 65, 66, 76, 81, 86, 87, 91, 94, 95, 97, 101, 102, 108, 118, 119, 124, 125, 126, 127, 128, 135, 139, 142, 146, 151, 155, 160, 163, 164, 165, 167, 176, 177, 182, 211, 251, 258], "imag": [9, 10, 11, 12, 24, 62, 63, 66, 87, 94, 95, 97, 118, 119, 120, 123, 124, 126, 146, 160, 162, 165, 167, 177, 193, 208, 209, 264, 265, 266], "finit": [9, 10, 11, 12, 25, 35, 42, 62, 65, 66, 87, 91, 94, 95, 97, 102, 108, 112, 118, 119, 124, 126, 142, 146, 151, 155, 163, 165, 167, 177, 210], "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, 91, 94, 95, 97, 98, 99, 104, 105, 109, 110, 117, 118, 119, 120, 123, 124, 125, 126, 127, 133, 138, 142, 143, 145, 146, 147, 148, 150, 151, 152, 153, 160, 162, 164, 165, 167, 168, 172, 173, 174, 176, 177, 178, 183, 184, 185, 186, 189, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258], "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, 91, 94, 95, 97, 98, 99, 103, 104, 105, 108, 109, 110, 117, 118, 119, 120, 123, 124, 125, 126, 127, 133, 135, 136, 138, 139, 140, 141, 142, 143, 145, 146, 147, 148, 150, 151, 152, 153, 156, 160, 161, 162, 163, 164, 165, 167, 168, 172, 173, 174, 176, 177, 178, 179, 183, 184, 185, 186, 187, 189, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258, 261], "approxim": [10, 11, 47, 61, 62, 64, 65, 66, 86, 87, 95, 97, 102, 124, 125, 126, 127, 151, 164, 165, 176, 177, 210, 246, 249], "princip": [10, 11, 61, 62, 64, 66, 124, 167, 211, 260], "invers": [10, 11, 61, 62, 64, 65, 66, 211, 222, 224, 227, 228, 229, 230, 231, 232, 233, 235, 242, 245, 249, 260], "cosin": [10, 11, 86, 87, 177], "express": [10, 61, 63, 64, 65, 86, 164, 176, 194, 203, 212, 260, 263], "radian": [10, 61, 64, 65, 86, 164, 176], "arc": [10, 61, 64], "frac": [10, 11, 61, 62, 64, 66, 86, 87, 91, 123, 125, 127, 162, 164, 165, 176, 177, 211, 251], "pi": [10, 11, 61, 62, 64, 66, 87, 124, 126, 165, 176, 177, 193], "j": [10, 11, 12, 25, 61, 62, 64, 66, 87, 91, 95, 97, 123, 124, 126, 142, 161, 162, 164, 165, 167, 176, 177, 194, 211, 240, 253, 256], "ln": [10, 11, 61, 62, 64, 66, 124], "zj": [10, 61, 62, 64, 66], "conj": [10, 11, 61, 62, 64, 66, 87, 95, 97, 124, 125, 126, 127, 165, 167, 177, 193, 208], "multi": [10, 11, 61, 62, 64, 66, 193, 211, 214, 215, 237, 266], "branch": [10, 11, 61, 62, 64, 65, 66, 86, 87, 91, 95, 97, 124, 126, 142, 151, 164, 165, 167, 176, 177, 264], "cut": [10, 11, 61, 62, 64, 66, 86, 87, 95, 97, 124, 126, 151, 164, 165, 167, 176, 177, 264], "plane": [10, 11, 61, 62, 64, 66, 86, 87, 91, 95, 97, 142, 164, 165, 167, 176, 177, 264], "By": [10, 11, 13, 14, 61, 62, 64, 65, 66, 88, 124, 126, 135, 137, 139, 151, 152, 167, 171, 173, 188, 189, 210, 211, 237, 260, 265], "place": [10, 11, 15, 60, 61, 62, 63, 64, 66, 92, 93, 98, 103, 104, 105, 123, 147, 148, 159, 191, 192, 193, 201, 203, 208, 212, 215, 223, 234, 249], "line": [10, 11, 61, 62, 64, 66, 176, 177, 203, 211, 264, 265, 266, 267], "segment": [10, 11, 61, 62, 64, 66, 211], "infti": [10, 11, 61, 62, 64, 66, 86, 124, 126, 151, 167, 211], "axi": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 90, 96, 100, 124, 126, 135, 137, 139, 141, 151, 152, 156, 159, 166, 167, 169, 170, 171, 173, 174, 175, 178, 179, 187, 188, 189, 193, 208, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 235, 237, 244, 257, 258, 264], "rang": [10, 61, 62, 64, 66, 77, 88, 124, 126, 152, 167, 173, 194, 208, 214, 256, 264], "strip": [10, 61, 62, 64, 66, 124, 126], "unbound": [10, 61, 62, 64, 66, 124, 126], "along": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 90, 98, 100, 124, 126, 135, 137, 139, 152, 156, 159, 166, 167, 170, 171, 173, 174, 175, 176, 177, 179, 187, 188, 189, 194, 208, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 237, 256, 258, 260], "c99": [10, 11, 61, 62, 64, 66, 91, 124, 126, 142, 151, 167, 211, 261], "provision": [10, 11, 61, 62, 64, 66, 124, 126, 151, 167, 211], "statu": [10, 11, 61, 62, 64, 66, 124, 126, 151, 167, 211], "greater": [10, 11, 33, 38, 48, 61, 62, 65, 66, 69, 71, 77, 85, 91, 101, 102, 124, 126, 151, 155, 162, 163, 165, 167, 169, 177, 193, 194, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 237, 245], "than": [10, 11, 19, 26, 32, 38, 40, 47, 48, 49, 55, 61, 62, 63, 65, 66, 69, 71, 76, 77, 85, 88, 91, 99, 100, 101, 102, 103, 124, 125, 126, 127, 133, 142, 151, 152, 155, 162, 163, 165, 167, 169, 171, 173, 174, 177, 182, 183, 184, 185, 186, 188, 194, 203, 206, 209, 212, 215, 216, 219, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 237, 244, 245, 246, 249, 256, 258, 260, 261, 264, 266], "less": [10, 11, 39, 47, 61, 65, 66, 76, 85, 91, 102, 124, 125, 126, 127, 151, 155, 162, 163, 167, 171, 188, 193, 194, 212, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 244, 245, 246, 249, 258, 264], "\u03c0": [10, 64, 65, 84], "0j": [10, 11, 12, 25, 62, 63, 66, 87, 95, 97, 98, 124, 126, 147, 148, 162, 165, 167, 177, 211, 251], "nonzero": [10, 11, 12, 62, 66, 87, 91, 95, 97, 102, 142, 165, 177, 193, 194, 208, 249], "3\u03c0": [10, 65], "hyperbol": [11, 62, 66, 86, 87, 164, 165, 176, 177, 211], "aco": [11, 61, 193, 208, 210], "simpli": [11, 97, 126, 209, 220, 264, 266], "upper": [11, 77, 98, 181, 208, 236, 250], "half": [11, 15, 66, 123, 141, 167, 178, 194, 225], "area": [11, 62, 66], "sector": [11, 62, 66], "\u03c0j": [11, 62, 66, 124, 126], "3\u03c0j": [11, 124, 126], "sum": [12, 21, 88, 108, 128, 152, 193, 208, 244, 256, 258, 260], "x1_i": [12, 65, 67, 69, 70, 71, 72, 85, 91, 94, 102, 106, 107, 108, 121, 122, 128, 129, 131, 132, 136, 140, 142, 144, 146, 151, 155, 172, 190, 208], "x2_i": [12, 65, 67, 69, 70, 71, 72, 85, 91, 94, 102, 106, 107, 108, 121, 122, 128, 129, 131, 132, 136, 140, 142, 144, 146, 151, 155, 172, 190, 208], "first": [12, 16, 17, 19, 65, 67, 69, 70, 71, 72, 88, 90, 94, 106, 107, 108, 121, 122, 128, 129, 131, 132, 133, 136, 140, 142, 144, 146, 151, 159, 170, 172, 176, 177, 178, 183, 184, 185, 189, 190, 194, 211, 237, 240, 248, 250, 251, 253, 254, 260, 264, 265, 266, 267], "remain": [12, 91, 94, 102, 117, 119, 120, 142, 146, 155, 157, 162, 194, 212, 235], "neither": [12, 40, 91, 102, 133, 142, 178, 253, 265], "nor": [12, 91, 102, 142, 253, 265], "mathemat": [12, 19, 65, 84, 86, 87, 91, 97, 102, 124, 126, 142, 164, 165, 176, 177, 193, 211, 244, 258], "round": [12, 15, 76, 91, 101, 102, 142, 167, 182, 193, 208, 210], "nearest": [12, 91, 142, 160, 182, 210], "mode": [12, 91, 142, 210, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 250], "too": [12, 26, 91, 102, 142, 260, 264], "larg": [12, 91, 102, 142, 214, 220, 251, 264], "appropri": [12, 26, 91, 102, 142, 211, 216], "commut": 12, "associ": [12, 42, 142, 196, 203, 246, 249, 252, 260, 263, 265], "tabl": [12, 91, 142, 193], "c": [12, 91, 94, 123, 142, 145, 146, 156, 170, 171, 177, 188, 194, 208, 211, 214, 217, 236, 240, 241, 242, 250, 252, 253, 261, 263, 264, 266], "d": [12, 91, 94, 123, 142, 146, 203, 223, 234], "dj": [12, 91, 142], "independ": [12, 91, 142, 160, 194, 206, 214, 237, 250, 252, 260, 261, 264], "abov": [12, 88, 91, 94, 124, 126, 142, 146, 151, 152, 167, 173, 180, 181, 194, 203, 211, 212, 214, 215, 218, 239, 240, 256, 260, 263, 266], "similarli": [12, 57, 117, 138, 203, 236, 253], "henc": [12, 79, 96, 145, 156, 183, 184, 185, 186, 194, 209, 211, 212, 213, 214, 218, 219, 220, 264, 266], "z1": 12, "z2": 12, "keepdim": [13, 14, 16, 17, 135, 137, 139, 152, 171, 173, 188, 244, 258], "test": [13, 14, 89, 118, 119, 120, 208, 210, 262, 264, 265, 266], "evalu": [13, 14, 22, 30, 36, 38, 41, 44, 45, 46, 48, 51, 52, 95, 97, 124, 125, 126, 127, 143, 150, 162, 163, 168, 206, 264], "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, 92, 99, 100, 104, 105, 109, 116, 117, 123, 135, 137, 139, 141, 147, 152, 156, 158, 159, 169, 170, 171, 173, 178, 188, 191, 225, 229, 244, 246, 249, 258, 265], "ax": [13, 14, 16, 17, 19, 55, 56, 100, 135, 137, 139, 141, 149, 152, 159, 169, 171, 173, 178, 179, 188, 189, 194, 208, 224, 225, 228, 229, 232, 235, 237, 244, 249, 252, 255, 258], "logic": [13, 14, 24, 26, 91, 94, 129, 130, 131, 132, 142, 146, 215, 218, 224, 228, 232, 235], "AND": [13, 67, 94, 129, 263], "entir": [13, 14, 86, 87, 95, 97, 135, 137, 139, 152, 164, 165, 171, 173, 188], "valid": [13, 14, 26, 27, 90, 96, 115, 141, 170, 178, 187, 194, 210, 218, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 240, 250, 253, 265], "count": [13, 14, 78, 88, 90, 100, 174, 175, 183, 184, 189, 194, 208, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 237, 241], "last": [13, 14, 18, 19, 55, 78, 88, 90, 100, 159, 166, 170, 174, 175, 178, 189, 194, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 237, 239, 244, 250, 253, 256], "invalid": [13, 14, 23, 90, 96, 216, 264], "rais": [13, 14, 19, 23, 24, 25, 26, 29, 34, 35, 40, 47, 51, 55, 60, 74, 90, 91, 95, 96, 103, 123, 133, 135, 139, 145, 151, 157, 169, 170, 187, 189, 194, 203, 206, 208, 214, 215, 216, 218, 237, 245, 264], "wa": [13, 14, 19, 26, 102, 135, 137, 139, 152, 171, 173, 188, 203, 215, 220, 264, 266], "OR": [14, 24, 70, 131, 146, 263], "start": [15, 123, 194, 208, 220, 264, 266], "stop": [15, 123, 194, 208, 265], "step": [15, 123, 194, 265], "evenli": [15, 123], "space": [15, 123, 223, 225, 234], "open": [15, 123, 141, 178, 194], "inclus": [15, 194, 264], "end": [15, 65, 86, 123, 162, 164, 176, 177, 201, 212, 251, 264, 265, 266], "exclus": [15, 194], "distanc": [15, 108], "between": [15, 26, 47, 51, 65, 78, 91, 94, 99, 123, 135, 136, 139, 140, 146, 151, 170, 183, 184, 185, 186, 203, 211, 212, 215, 223, 234, 260, 264, 266], "adjac": 15, "output": [15, 60, 63, 78, 88, 92, 93, 96, 98, 100, 103, 104, 105, 112, 123, 138, 147, 148, 157, 159, 161, 169, 170, 174, 179, 191, 192, 206, 208, 211, 212, 215, 217, 218, 220, 222, 223, 224, 226, 227, 228, 231, 232, 233, 234, 235, 256, 264], "infer": [15, 60, 63, 93, 104, 105, 148, 157, 192, 213, 260, 265], "cannot": [15, 26, 57, 103, 176, 177, 208, 211, 213, 264], "guarante": [15, 59, 183, 185, 206, 211, 215, 264, 266], "error": [15, 19, 23, 24, 25, 26, 29, 34, 35, 51, 55, 91, 103, 135, 139, 176, 177, 203, 210, 251, 264], "ceil": [15, 193], "indic": [16, 17, 18, 26, 60, 88, 89, 103, 112, 117, 123, 141, 145, 159, 161, 162, 174, 175, 178, 180, 181, 183, 185, 194, 203, 208, 258, 264], "occur": [16, 17, 75, 108, 176, 177, 183, 184, 185, 186, 211, 265], "occurr": [16, 17, 183], "comparison": [16, 17, 18, 31, 33, 37, 39, 94, 106, 107, 121, 122, 135, 136, 139, 140, 146, 166, 193, 211, 261, 265], "search": [16, 17, 161, 193], "flatten": [16, 17, 78, 156, 159, 183, 184, 185, 186, 258, 260], "descend": [18, 166, 253, 254], "stabl": [18, 166, 214], "sort": [18, 161, 193, 208, 240, 241, 253, 254], "ascend": [18, 161, 166, 208], "stabil": [18, 166], "maintain": [18, 166, 209, 264, 266], "rel": [18, 19, 55, 100, 136, 140, 159, 166, 208, 239, 246, 249, 256], "compar": [18, 166, 183, 184, 185, 186, 210, 215, 265, 267], "properti": [19, 53, 54, 55, 56, 57, 58, 116, 208, 211, 215, 220, 264], "transpos": [19, 40, 55, 133, 134, 178, 236, 240, 249, 253, 260], "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, 203, 206, 208, 215], "permut": [19, 55, 149], "revers": [19, 55, 65, 100], "origin": [19, 55, 65, 108, 141, 157, 159, 208, 212, 222, 224, 227, 228, 231, 232, 233, 235, 264, 265], "limit": [19, 99, 109, 117, 210, 260, 263], "matric": [19, 40, 55, 133, 134, 138, 180, 181, 236, 238, 239, 240, 241, 242, 244, 245, 246, 249, 250, 251, 252, 253, 254, 256, 260], "deviat": [19, 171, 210, 216, 264, 266], "et": [19, 253, 254], "al": 19, "intent": [19, 65], "found": [19, 211, 214, 266, 267], "problemat": [19, 63, 209, 212], "conflict": 19, "definit": [19, 86, 87, 164, 165, 176, 177, 208, 236, 265], "batch": [19, 258, 260], "cetera": [19, 253, 254], "permute_dim": [19, 193], "interfac": [19, 214, 260, 264, 266], "ab": [20, 108, 151, 193, 208, 244, 258], "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, 193], "api_vers": [23, 264], "object": [23, 24, 25, 26, 29, 32, 34, 35, 53, 57, 59, 60, 89, 99, 103, 109, 111, 113, 114, 115, 193, 194, 203, 206, 208, 212, 214, 215, 218, 220, 259, 261, 265, 266], "2020": [23, 220, 261, 263, 264], "10": [23, 27, 125, 194, 264], "latest": [23, 214], "modul": [23, 206, 261, 265, 266, 267], "everi": [23, 104, 105, 250, 264], "top": [23, 206, 264, 266], "level": [23, 203, 209, 214, 215, 259, 260, 264, 265], "public": [23, 259, 265, 266], "well": [23, 209, 211, 214, 215, 250, 266, 267], "part": [23, 35, 180, 181, 203, 208, 214, 219, 261, 264, 266], "convert": [24, 25, 29, 34, 35, 60, 103, 203, 208, 209, 211, 214, 264, 266], "handl": [24, 26, 61, 64, 86, 88, 103, 125, 127, 151, 152, 154, 162, 164, 168, 173, 176, 208, 209, 211, 212, 215, 216, 256, 264], "lazi": [24, 25, 29, 34, 35, 206, 208, 217, 266], "languag": [24, 25, 29, 34, 35, 212, 216, 218, 260, 264, 266], "therefor": [24, 25, 29, 32, 34, 35, 206, 214, 215, 216, 218, 220, 261, 264, 266], "abl": [24, 25, 29, 34, 35, 103, 212, 214, 215, 264, 266], "kind": [24, 25, 26, 29, 34, 35, 47, 51, 77, 91, 99, 103, 105, 109, 114, 116, 117, 151, 203, 208, 218, 260, 263], "here": [24, 25, 26, 29, 34, 35, 194, 203, 212, 214, 219, 220, 266], "valueerror": [24, 25, 26, 29, 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7, 13, 14, 16, 17, 63, 129, 130, 131, 132, 135, 137, 139, 145, 152, 171, 178, 188, 189, 194, 203, 208, 209, 215, 222, 224, 227, 228, 231, 232, 233, 235, 237, 238, 240, 244, 246, 253, 258, 266], "could": [0, 26, 183, 184, 185, 186, 206, 212, 219, 260, 264, 266], "forc": 0, "synchron": [0, 26, 59, 156, 264], "delai": [0, 24, 25, 29, 34, 35, 206, 218, 264], "execut": [0, 203, 206, 215, 217, 219, 264, 266], "model": [0, 57, 58, 91, 142, 211, 218, 266], "repres": [0, 8, 11, 12, 23, 24, 25, 26, 29, 34, 35, 62, 66, 87, 91, 102, 138, 142, 165, 176, 177, 208, 210, 214, 215, 251, 265, 266], "futur": [0, 26, 103, 207, 211, 212, 215, 219, 220, 240, 241, 262, 264, 266], "python": [0, 2, 5, 7, 24, 25, 26, 29, 32, 34, 35, 49, 60, 102, 103, 155, 193, 194, 206, 208, 211, 214, 216, 218, 219, 220, 261, 263, 264, 265], "x": [0, 1, 5, 7, 9, 10, 11, 13, 14, 16, 17, 18, 20, 26, 32, 61, 62, 63, 64, 65, 66, 68, 74, 76, 77, 79, 85, 86, 87, 88, 90, 93, 95, 96, 97, 100, 101, 103, 105, 110, 118, 119, 120, 124, 125, 126, 127, 130, 134, 135, 137, 139, 141, 143, 145, 148, 149, 150, 152, 153, 154, 156, 157, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 173, 174, 175, 176, 177, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 192, 194, 211, 212, 220, 221, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 235, 236, 238, 239, 240, 241, 242, 244, 245, 246, 247, 249, 250, 251, 252, 253, 254, 256, 258, 260, 264, 266], "__pos__": [0, 193, 208], "po": 0, "__neg__": [0, 193, 208], "neg": [0, 13, 14, 15, 44, 47, 65, 78, 88, 90, 91, 96, 98, 100, 102, 119, 124, 126, 142, 151, 155, 159, 163, 167, 174, 175, 178, 189, 193, 194, 208, 211, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 237, 258, 264], "x1": [0, 7, 12, 40, 65, 67, 69, 70, 71, 72, 77, 85, 91, 94, 102, 106, 107, 108, 121, 122, 128, 129, 131, 132, 133, 136, 140, 142, 144, 146, 151, 155, 161, 172, 178, 189, 190, 208, 237, 243, 248, 252, 255, 257], "x2": [0, 7, 12, 40, 65, 67, 69, 70, 71, 72, 85, 91, 94, 102, 106, 107, 108, 121, 122, 128, 129, 131, 132, 133, 136, 140, 142, 144, 146, 151, 155, 161, 172, 178, 189, 190, 208, 237, 243, 248, 252, 255, 257], "__add__": [0, 50, 193, 208], "add": [0, 7, 21, 88, 172, 173, 193, 194, 208, 209, 210, 215, 256], "__sub__": [0, 193, 208], "sub": [0, 194], "__mul__": [0, 193, 208], "mul": 0, "__truediv__": [0, 193, 208], "truediv": 0, "__floordiv__": [0, 193], "floordiv": 0, "__mod__": [0, 193], "mod": 0, "__pow__": [0, 193, 208], "pow": [0, 47, 193, 208, 210], "should": [0, 1, 5, 7, 9, 10, 11, 12, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 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, 91, 95, 96, 97, 99, 101, 102, 103, 106, 107, 108, 110, 114, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 135, 136, 137, 138, 139, 140, 142, 143, 144, 150, 151, 152, 153, 154, 155, 157, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 171, 172, 173, 176, 177, 178, 180, 181, 182, 183, 184, 185, 186, 188, 189, 194, 201, 208, 209, 210, 211, 214, 215, 216, 220, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 249, 250, 251, 252, 253, 254, 256, 258, 259, 260, 264, 266, 267], "defin": [0, 5, 12, 23, 30, 32, 41, 49, 60, 65, 79, 91, 102, 104, 105, 116, 123, 135, 136, 137, 139, 140, 141, 142, 155, 162, 167, 168, 171, 180, 181, 188, 189, 193, 196, 201, 208, 210, 211, 220, 224, 225, 228, 229, 232, 235, 236, 240, 241, 242, 249, 250, 252, 260, 265, 266, 267], "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, 91, 92, 94, 95, 97, 98, 99, 101, 102, 104, 106, 107, 108, 114, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 135, 136, 137, 139, 140, 142, 143, 144, 145, 146, 147, 148, 151, 152, 155, 160, 161, 162, 163, 164, 165, 166, 167, 171, 173, 176, 177, 182, 188, 189, 191, 193, 203, 208, 211, 223, 226, 230, 231, 232, 233, 234, 235, 236, 240, 241, 242, 244, 246, 249, 250, 251, 252, 253, 254, 256, 258, 261], "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, 110, 112, 114, 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, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 157, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 188, 189, 190, 191, 192, 193, 196, 203, 206, 209, 211, 212, 215, 217, 218, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258, 260, 261, 262, 263, 264, 267], "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, 110, 114, 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, 188, 189, 190, 191, 192, 193, 194, 196, 206, 209, 211, 212, 214, 216, 217, 218, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258, 260, 261, 264, 265], "__matmul__": [0, 193, 208], "matmul": [0, 40, 193, 203, 208, 260], "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, 91, 94, 95, 97, 100, 101, 102, 103, 106, 107, 108, 110, 111, 112, 114, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 139, 140, 141, 142, 143, 144, 145, 146, 149, 150, 151, 152, 153, 154, 155, 156, 160, 161, 162, 163, 164, 165, 166, 167, 168, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 188, 189, 190, 194, 203, 206, 208, 209, 210, 212, 213, 214, 215, 218, 219, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258, 259, 260, 261, 263, 264, 265, 266, 267], "__invert__": [0, 193], "inv": [0, 208, 260], "invert": [0, 68, 242, 245, 252], "__inv__": 0, "__and__": [0, 193], "__or__": [0, 193], "__xor__": [0, 193], "xor": [0, 72, 132], "__lshift__": [0, 193], "lshift": 0, "__rshift__": [0, 193], "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, 91, 101, 102, 104, 105, 109, 112, 116, 117, 123, 135, 137, 139, 143, 151, 152, 155, 156, 158, 160, 161, 171, 173, 174, 182, 188, 189, 193, 194, 208, 210, 211, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 237, 245, 246, 256, 258, 264], "boolean": [0, 5, 22, 24, 25, 26, 29, 35, 36, 43, 45, 52, 57, 60, 63, 67, 68, 70, 72, 88, 89, 103, 104, 105, 112, 116, 117, 123, 129, 130, 131, 132, 145, 193, 203, 208], "__lt__": [0, 193, 208], "lt": 0, "__le__": [0, 193, 208], "le": 0, "__gt__": [0, 193, 208], "gt": [0, 250, 253], "__ge__": [0, 193, 208], "ge": 0, "__eq__": [0, 193, 208, 215], "eq": 0, "__ne__": [0, 193, 208], "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, 91, 95, 98, 99, 100, 102, 103, 108, 115, 116, 123, 129, 130, 131, 132, 133, 142, 145, 151, 156, 159, 160, 164, 176, 177, 179, 183, 185, 189, 194, 203, 206, 208, 209, 210, 211, 212, 213, 214, 215, 216, 218, 219, 220, 222, 223, 224, 225, 227, 228, 229, 231, 232, 233, 234, 235, 237, 240, 241, 246, 249, 250, 253, 259, 260, 261, 264, 265, 266, 267], "onli": [0, 1, 5, 7, 16, 17, 23, 26, 40, 57, 58, 63, 100, 103, 108, 114, 116, 117, 123, 129, 130, 131, 132, 133, 137, 171, 188, 189, 193, 194, 203, 206, 208, 209, 211, 212, 214, 215, 216, 218, 220, 225, 237, 242, 249, 250, 252, 260, 261, 264, 265, 266, 267], "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, 91, 97, 102, 103, 126, 141, 142, 171, 188, 194, 196, 206, 208, 210, 211, 212, 213, 214, 215, 216, 220, 237, 249, 259, 260, 263, 264, 266], "ani": [0, 1, 9, 10, 11, 23, 24, 25, 26, 28, 29, 34, 35, 43, 59, 61, 62, 66, 89, 90, 94, 108, 118, 119, 146, 167, 193, 194, 203, 208, 211, 212, 214, 220, 253, 261, 263, 264, 267], "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, 91, 94, 95, 97, 101, 102, 106, 107, 108, 114, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 135, 136, 138, 139, 140, 142, 143, 144, 146, 151, 152, 154, 155, 156, 160, 161, 162, 163, 164, 165, 166, 167, 168, 170, 173, 176, 177, 182, 183, 184, 185, 186, 194, 201, 206, 210, 211, 213, 215, 218, 223, 232, 234, 251, 253, 254, 256, 264, 266, 267], "backward": [0, 13, 14, 16, 17, 18, 31, 33, 37, 39, 90, 106, 107, 121, 122, 123, 135, 136, 139, 140, 155, 166, 189, 194, 208, 211, 212, 216, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 237, 264], "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, 91, 94, 102, 106, 107, 108, 121, 122, 123, 128, 129, 131, 132, 133, 135, 136, 137, 139, 140, 142, 144, 146, 151, 152, 155, 156, 157, 166, 171, 172, 173, 175, 188, 189, 190, 203, 208, 211, 212, 216, 237, 244, 246, 249, 252, 258, 264, 266], "mai": [0, 5, 7, 15, 16, 17, 18, 23, 26, 28, 31, 33, 37, 39, 43, 51, 57, 58, 59, 60, 89, 90, 91, 94, 102, 103, 106, 107, 108, 111, 116, 117, 121, 122, 123, 129, 130, 131, 132, 135, 136, 137, 139, 140, 142, 145, 146, 156, 157, 161, 166, 171, 177, 183, 184, 185, 186, 188, 193, 194, 201, 203, 206, 209, 210, 211, 212, 213, 214, 215, 216, 218, 219, 220, 240, 250, 251, 253, 259, 260, 264, 265, 266], "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, 91, 94, 95, 97, 98, 99, 104, 105, 106, 107, 108, 110, 114, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 133, 135, 136, 138, 139, 140, 142, 143, 145, 146, 147, 148, 150, 151, 152, 153, 160, 162, 164, 165, 166, 167, 168, 172, 173, 176, 177, 178, 183, 184, 185, 186, 189, 203, 210, 214, 215, 217, 218, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258, 260, 264, 265], "howev": [0, 5, 16, 17, 18, 31, 33, 37, 39, 57, 88, 102, 106, 107, 108, 117, 121, 122, 123, 135, 136, 139, 140, 156, 161, 166, 174, 176, 177, 206, 209, 210, 211, 212, 213, 215, 260, 261, 264, 266], "inequ": [0, 16, 17, 18, 31, 33, 37, 39, 106, 107, 121, 122, 135, 136, 139, 140, 166], "unspecifi": [0, 5, 10, 11, 16, 17, 18, 30, 31, 32, 33, 37, 39, 41, 47, 51, 60, 62, 66, 77, 78, 87, 91, 95, 97, 102, 104, 105, 106, 107, 121, 122, 123, 135, 136, 139, 140, 151, 155, 161, 165, 166, 167, 170, 174, 175, 177, 194, 201, 203, 208, 224, 225, 228, 229, 232, 235, 240, 241, 264], "thu": [0, 5, 16, 17, 18, 28, 30, 31, 32, 33, 37, 39, 41, 43, 47, 57, 60, 71, 77, 94, 102, 104, 105, 106, 107, 121, 122, 123, 135, 136, 139, 140, 146, 151, 155, 161, 166, 176, 177, 194, 201, 210, 211, 224, 225, 228, 229, 232, 235, 240, 241, 253, 260], "depend": [0, 5, 9, 10, 11, 16, 17, 18, 20, 26, 28, 29, 31, 33, 37, 39, 43, 44, 47, 51, 57, 58, 59, 61, 62, 63, 64, 65, 66, 77, 86, 87, 91, 94, 95, 97, 106, 107, 112, 121, 122, 123, 124, 125, 126, 127, 142, 143, 146, 151, 161, 164, 165, 166, 176, 177, 190, 201, 203, 210, 211, 214, 217, 218, 220, 240, 241, 250, 251, 252, 253, 260, 264, 266, 267], "see": [0, 5, 10, 11, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 32, 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, 91, 94, 97, 102, 103, 105, 106, 107, 108, 111, 112, 115, 121, 122, 124, 126, 128, 129, 131, 132, 133, 135, 136, 137, 139, 140, 142, 144, 145, 146, 151, 152, 154, 155, 156, 158, 162, 166, 167, 168, 171, 172, 173, 175, 183, 184, 185, 186, 188, 189, 190, 193, 194, 203, 205, 206, 209, 211, 213, 214, 215, 220, 237, 244, 246, 249, 252, 258, 259, 264, 265, 266, 267], "order": [0, 5, 7, 16, 17, 18, 19, 26, 31, 33, 37, 39, 55, 60, 63, 65, 89, 90, 100, 102, 103, 106, 107, 121, 122, 135, 136, 139, 140, 145, 156, 161, 166, 176, 177, 178, 183, 184, 185, 186, 194, 201, 203, 208, 210, 213, 214, 216, 231, 232, 240, 241, 244, 253, 254, 258, 260, 261, 264, 265], "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, 91, 94, 95, 97, 98, 99, 103, 104, 105, 118, 119, 120, 123, 124, 125, 126, 127, 133, 135, 138, 139, 142, 143, 145, 146, 147, 148, 150, 151, 152, 157, 160, 162, 164, 165, 167, 168, 172, 173, 174, 176, 177, 178, 183, 184, 185, 186, 189, 206, 222, 223, 224, 226, 227, 228, 231, 232, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258, 261, 264, 266, 267], "shape": [0, 1, 18, 40, 55, 63, 73, 74, 78, 88, 90, 92, 93, 96, 100, 104, 105, 112, 133, 134, 138, 147, 148, 157, 159, 161, 166, 170, 174, 175, 178, 179, 180, 181, 187, 189, 191, 192, 193, 208, 217, 218, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 238, 239, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 264, 266], "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, 91, 94, 95, 97, 101, 102, 106, 107, 108, 110, 118, 119, 120, 121, 122, 124, 125, 126, 127, 128, 129, 130, 131, 132, 135, 136, 137, 139, 140, 142, 143, 144, 146, 150, 151, 152, 153, 154, 155, 156, 158, 160, 161, 162, 163, 164, 165, 167, 168, 170, 171, 172, 173, 176, 177, 178, 182, 183, 188, 194, 201, 203, 208, 210, 211, 212, 218, 236, 237, 239, 244, 245, 251, 252, 258, 264, 265, 266, 267], "promot": [0, 1, 5, 10, 11, 12, 21, 22, 28, 30, 31, 33, 37, 39, 40, 41, 42, 43, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 78, 85, 86, 87, 91, 94, 95, 97, 102, 105, 106, 107, 108, 121, 122, 123, 124, 125, 126, 127, 128, 133, 136, 137, 140, 142, 143, 146, 151, 154, 155, 158, 164, 165, 167, 168, 170, 171, 172, 176, 177, 178, 188, 189, 190, 193, 208, 236, 237, 242, 244, 245, 246, 248, 249, 250, 251, 252, 258, 260], "rule": [0, 5, 7, 10, 11, 12, 21, 22, 28, 30, 31, 33, 37, 39, 40, 41, 42, 43, 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, 91, 94, 95, 97, 102, 104, 105, 106, 107, 108, 121, 122, 123, 124, 125, 126, 127, 128, 133, 136, 140, 142, 143, 146, 151, 154, 155, 158, 162, 164, 165, 167, 168, 170, 172, 176, 177, 178, 189, 190, 193, 194, 208, 211, 214, 236, 237, 242, 244, 245, 246, 248, 249, 250, 251, 252, 258, 260, 264, 266], "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, 91, 94, 102, 106, 107, 108, 121, 122, 128, 129, 131, 132, 133, 135, 136, 137, 139, 140, 142, 144, 146, 151, 152, 155, 156, 171, 172, 173, 175, 178, 188, 189, 190, 193, 208, 237, 244, 246, 249, 252, 258, 264], "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, 91, 93, 96, 99, 100, 101, 102, 103, 105, 110, 133, 134, 135, 137, 138, 139, 141, 142, 144, 148, 149, 150, 151, 152, 153, 155, 156, 157, 159, 160, 161, 162, 166, 169, 170, 171, 172, 173, 174, 175, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 192, 194, 203, 206, 208, 211, 212, 214, 215, 220, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 235, 236, 238, 239, 240, 242, 245, 249, 250, 251, 253, 254, 256, 259, 260, 264, 266], "behavior": [0, 5, 32, 47, 49, 59, 60, 63, 77, 91, 102, 104, 105, 108, 123, 142, 151, 155, 161, 174, 175, 183, 184, 185, 186, 193, 194, 196, 203, 206, 208, 210, 211, 218, 219, 224, 225, 228, 229, 232, 235, 260, 261, 264, 265, 266, 267], "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, 77, 85, 86, 87, 88, 91, 94, 95, 97, 101, 102, 108, 118, 119, 120, 124, 125, 126, 127, 128, 135, 136, 137, 139, 140, 142, 144, 146, 151, 152, 154, 155, 160, 162, 163, 164, 165, 167, 168, 171, 173, 176, 177, 182, 188, 208, 209, 211, 251, 256], "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, 77, 85, 86, 87, 88, 91, 94, 95, 97, 101, 102, 103, 108, 118, 119, 120, 124, 125, 126, 127, 128, 135, 136, 137, 138, 139, 140, 142, 144, 146, 151, 152, 154, 155, 160, 162, 163, 164, 165, 167, 168, 171, 173, 176, 177, 182, 188, 194, 206, 208, 209, 210, 211, 212, 215, 216, 218, 250, 251, 253, 256, 260, 262, 264, 267], "its": [0, 5, 26, 40, 73, 91, 99, 133, 142, 157, 159, 210, 211, 214, 215, 259, 264, 265, 266], "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, 91, 94, 102, 106, 107, 108, 114, 121, 122, 123, 128, 129, 131, 132, 136, 138, 140, 141, 142, 144, 146, 155, 165, 172, 176, 177, 178, 183, 184, 189, 208, 210, 213, 215, 240, 250, 253], "binari": [0, 5, 67, 70, 72, 176, 177, 209], "two": [0, 1, 5, 15, 19, 40, 55, 65, 71, 98, 103, 133, 134, 138, 160, 178, 180, 181, 183, 184, 185, 186, 189, 194, 203, 214, 215, 218, 219, 224, 225, 228, 229, 232, 235, 236, 238, 239, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 260, 264, 265, 266, 267], "operand": [0, 1, 9, 10, 11, 12, 24, 25, 29, 35, 61, 62, 64, 65, 66, 76, 85, 86, 87, 88, 91, 94, 95, 97, 101, 102, 108, 118, 119, 120, 124, 125, 126, 127, 128, 135, 136, 139, 140, 142, 144, 146, 151, 152, 154, 155, 160, 162, 163, 164, 165, 167, 168, 173, 176, 177, 182, 203, 208, 210, 251, 256], "assign": [0, 212], "exampl": [0, 5, 12, 23, 26, 116, 117, 170, 193, 194, 206, 211, 212, 213, 215, 218, 219, 220, 256, 260, 264, 266, 267], "after": [0, 1, 26, 40, 133, 167, 179], "addit": [0, 5, 7, 12, 26, 50, 59, 88, 116, 172, 193, 194, 203, 209, 211, 214, 260, 264, 265, 267], "modifi": [0, 26, 212, 263], "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, 95, 97, 98, 104, 105, 108, 117, 119, 124, 125, 126, 127, 137, 145, 146, 147, 148, 151, 152, 160, 165, 166, 167, 171, 173, 174, 175, 177, 178, 179, 183, 184, 185, 186, 188, 193, 194, 201, 208, 211, 215, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 237, 239, 245, 246, 249, 250, 251, 252, 256, 264], "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, 102, 108, 129, 130, 131, 132, 155, 160, 174, 194, 203, 211, 212, 246, 249, 252, 258, 264], "discuss": [0, 94, 146, 208, 214, 215, 219, 264, 265, 266], "copi": [0, 1, 26, 59, 60, 63, 103, 157, 166, 208, 209, 214, 215, 217, 263, 264], "view": [0, 103, 217], "behaviour": [0, 217, 264, 266], "mutabl": [0, 217], "via": [0, 26, 102, 103, 174, 194, 209, 214, 215, 219, 221, 249, 259, 260, 261, 264], "__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, 91, 142, 158, 160, 170, 178, 194, 203, 206, 211, 222, 224, 227, 228, 231, 232, 233, 235, 246, 249, 260, 264, 266], "match": [0, 1, 5, 9, 20, 26, 63, 102, 155, 178, 183, 184, 216, 226, 230, 231, 232, 233, 235, 240, 241, 244, 258, 266], "op": [0, 203], "__radd__": 0, "__rsub__": 0, "__rmul__": 0, "__rtruediv__": 0, "__rfloordiv__": 0, "__rpow__": 0, "__rmod__": 0, "__rmatmul__": 0, "__rand__": 0, "__ror__": 0, "__rxor__": 0, 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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, 260, 261, 265, 267], "refer": [1, 13, 14, 90, 97, 98, 126, 171, 178, 179, 188, 189, 194, 211, 212, 220, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 237, 252], "automat": [1, 32, 264], "implicit": [1, 214, 215, 218, 264], "expans": [1, 264], "size": [1, 13, 14, 88, 90, 96, 123, 145, 159, 169, 174, 175, 178, 189, 193, 194, 213, 219, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 237, 239, 248, 250, 253, 264], "without": [1, 7, 26, 28, 31, 33, 37, 39, 43, 57, 94, 103, 106, 107, 114, 116, 121, 122, 145, 146, 156, 157, 183, 184, 185, 186, 206, 209, 210, 213, 263, 264, 266], "purpos": [1, 5, 97, 108, 126, 206, 251, 260, 262, 263, 266], "make": [1, 7, 206, 209, 210, 212, 214, 218, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 259, 261, 264], "differ": [1, 12, 26, 49, 50, 77, 78, 88, 90, 91, 99, 102, 103, 142, 152, 170, 172, 173, 194, 206, 212, 215, 216, 218, 229, 240, 250, 251, 253, 256, 260, 264, 265, 266], "element": [1, 9, 10, 11, 12, 13, 14, 15, 20, 21, 22, 24, 25, 28, 29, 30, 31, 32, 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, 91, 94, 95, 97, 98, 100, 101, 102, 104, 105, 106, 107, 108, 110, 118, 119, 120, 121, 122, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 135, 136, 137, 139, 140, 142, 143, 144, 145, 146, 150, 151, 152, 153, 154, 155, 156, 157, 159, 160, 161, 162, 163, 164, 165, 167, 168, 169, 171, 172, 173, 174, 175, 176, 177, 179, 180, 181, 182, 183, 184, 185, 186, 188, 190, 193, 194, 208, 210, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 237, 240, 249, 250, 251, 253, 256, 264], "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, 91, 94, 102, 106, 107, 108, 110, 121, 122, 128, 129, 130, 131, 132, 136, 140, 142, 144, 146, 151, 153, 154, 155, 172, 193, 208, 210, 264], "oper": [1, 12, 19, 24, 26, 34, 40, 57, 58, 59, 61, 64, 71, 86, 88, 91, 102, 125, 127, 133, 142, 151, 152, 154, 155, 158, 164, 168, 173, 176, 178, 193, 194, 200, 203, 208, 211, 212, 213, 214, 215, 256, 260, 261, 264, 265, 266], "facilit": [1, 201, 206], "user": [1, 7, 26, 111, 177, 206, 209, 210, 212, 215, 219, 260, 264, 265, 266], "ergonom": 1, "encourag": [1, 264, 265], "avoid": [1, 9, 63, 91, 97, 102, 108, 126, 142, 157, 209, 212, 215, 218, 260, 264, 266], "unnecessari": [1, 260], "can": [1, 7, 26, 32, 60, 75, 111, 115, 117, 194, 203, 206, 209, 211, 212, 214, 215, 220, 249, 250, 253, 259, 260, 264, 265, 266, 267], "potenti": [1, 26, 97, 112, 126, 156, 212, 264], "enabl": [1, 26, 103, 215, 219, 220, 264], "more": [1, 5, 7, 15, 19, 26, 32, 40, 58, 60, 63, 73, 88, 97, 100, 102, 126, 133, 145, 151, 156, 174, 183, 184, 185, 186, 194, 203, 206, 209, 210, 211, 212, 213, 214, 215, 216, 219, 220, 224, 225, 228, 229, 232, 235, 251, 260, 261, 264, 265, 267], "memori": [1, 26, 60, 103, 206, 212, 213, 215, 264, 266], "effici": [1, 206, 212], "through": [1, 60, 65, 259, 261, 265, 266], "vector": [1, 40, 133, 138, 189, 237, 248, 253, 254, 258, 260, 264], "reduc": [1, 13, 14, 16, 17, 135, 137, 139, 152, 171, 173, 188, 194, 250, 253, 260, 265, 266], "consumpt": [1, 26, 265], "cach": 1, "local": [1, 215], "given": [1, 23, 90, 100, 123, 159, 161, 187, 203, 208, 211, 212, 215, 216, 220, 241, 251, 260, 261, 264, 266], "involv": [1, 12, 91, 102, 142, 151, 158, 203, 210, 211, 215, 219], "singleton": [1, 13, 14, 16, 17, 96, 135, 137, 139, 152, 169, 171, 173, 179, 188, 244, 258, 264], "whose": [1, 5, 9, 11, 19, 20, 26, 47, 55, 62, 66, 85, 86, 87, 98, 100, 103, 134, 151, 159, 163, 164, 165, 174, 175, 176, 177, 178, 180, 181, 183, 184, 185, 194, 212, 226, 230, 231, 232, 233, 235, 236, 238, 239, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258, 264, 266], "one": [1, 15, 19, 26, 32, 40, 51, 58, 60, 63, 73, 75, 88, 91, 96, 98, 100, 102, 103, 116, 117, 123, 133, 138, 142, 145, 147, 148, 156, 161, 169, 174, 175, 183, 184, 185, 186, 189, 194, 206, 209, 211, 212, 214, 215, 218, 219, 220, 222, 224, 226, 227, 228, 229, 230, 231, 232, 233, 235, 248, 249, 250, 258, 260, 261, 264, 266], "virtual": 1, "repeat": [1, 193, 194, 208, 266], "across": [1, 5, 91, 102, 142, 177, 208, 210, 211, 215, 259, 264], "correspond": [1, 16, 17, 23, 28, 31, 33, 37, 39, 43, 47, 59, 65, 73, 77, 94, 103, 106, 107, 112, 113, 114, 121, 122, 146, 151, 157, 159, 161, 171, 175, 178, 183, 184, 185, 186, 188, 189, 194, 208, 210, 224, 228, 232, 235, 237, 240, 244, 263, 264], "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, 105, 108, 112, 114, 116, 117, 118, 119, 120, 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189, 190, 203, 208, 211, 214, 215, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 236, 237, 238, 239, 242, 244, 245, 246, 248, 249, 250, 251, 252, 256, 258, 260, 264], "let": [1, 9, 10, 11, 12, 62, 66, 85, 87, 88, 90, 94, 95, 97, 103, 118, 119, 120, 123, 124, 126, 137, 146, 152, 156, 161, 162, 165, 167, 171, 173, 177, 179, 188, 189, 194, 219, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 236, 240, 241, 242, 250, 252, 253, 256], "b": [1, 9, 10, 11, 12, 57, 62, 66, 87, 91, 94, 95, 97, 102, 118, 119, 120, 123, 124, 126, 142, 146, 162, 165, 167, 170, 177, 189, 194, 208, 211, 212, 216, 249, 252, 266], "both": [1, 40, 44, 47, 51, 65, 77, 88, 91, 99, 102, 103, 108, 123, 133, 143, 151, 152, 173, 177, 178, 189, 194, 211, 212, 214, 218, 220, 237, 256, 260, 264, 265], "shape1": 1, "describ": [1, 5, 12, 88, 91, 94, 116, 117, 142, 146, 151, 152, 173, 196, 203, 211, 214, 218, 223, 234, 256, 264], "shape2": 1, "n1": [1, 90, 138], "len": [1, 138, 179], "n2": [1, 90, 138], "max": [1, 26, 77, 99, 109, 112, 179, 193, 194, 208, 244, 246, 249], "temporari": 1, "list": [1, 73, 78, 111, 115, 138, 170, 194, 206, 208, 215, 264, 266], "length": [1, 15, 108, 138, 157, 178, 194, 223, 225, 226, 229, 234, 253, 254], "while": [1, 102, 116, 123, 129, 130, 131, 132, 137, 141, 161, 171, 183, 184, 188, 193, 194, 201, 206, 208, 211, 212, 213, 215, 218, 249, 260, 265, 266, 267], "d1": 1, "els": [1, 26, 206, 265], "d2": 1, "set": [1, 18, 26, 49, 65, 103, 163, 166, 171, 180, 181, 183, 185, 186, 188, 193, 194, 208, 209, 210, 211, 212, 215, 216, 219, 220, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 236, 240, 241, 242, 246, 249, 250, 252, 253, 259, 260, 264, 266, 267], "th": [1, 90, 98, 179, 194, 224, 228, 232, 235], "throw": 1, "except": [1, 7, 13, 14, 26, 74, 78, 88, 90, 98, 103, 123, 145, 156, 170, 174, 175, 187, 194, 203, 206, 208, 210, 212, 215, 217, 218, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 249, 261, 264, 265, 266], "demonstr": 1, "applic": [1, 26, 88, 152, 156, 173, 203, 256, 260, 264, 265], "4d": 1, "8": [1, 5, 7, 27, 179, 203, 206], "6": [1, 7, 179], "3d": 1, "7": [1, 7, 27, 220], "5": [1, 194, 264], "2d": 1, "1d": 1, "15": 1, "do": [1, 26, 91, 142, 155, 201, 206, 209, 211, 212, 214, 215, 216, 260, 261, 263, 264, 266, 267], "doe": [1, 15, 26, 103, 146, 174, 175, 194, 203, 206, 209, 210, 211, 212, 213, 215, 216, 218, 220, 260, 264, 266, 267], "second": [1, 12, 65, 67, 69, 70, 71, 72, 94, 106, 107, 108, 121, 122, 128, 129, 131, 132, 133, 136, 140, 142, 144, 146, 151, 170, 172, 178, 183, 184, 185, 189, 190, 237, 240, 248, 250, 251, 253, 254, 264], "append": [1, 40, 69, 90, 96, 133, 239], "As": [1, 123, 151, 183, 184, 185, 186, 206, 214, 220, 266], "impli": [1, 183, 184, 185, 186, 263, 264], "__setitem__": [1, 174, 193, 208], "Such": [1, 210, 260], "right": [1, 69, 71, 108, 161, 167, 209, 253, 263], "hand": [1, 203], "left": [1, 5, 60, 69, 102, 104, 161, 174, 175, 194, 203, 240, 241, 253, 264], "index": [1, 5, 16, 17, 18, 32, 34, 49, 57, 83, 98, 112, 114, 138, 141, 145, 161, 170, 174, 178, 183, 184, 185, 193, 208, 224, 228, 232, 235, 264, 266], "perform": [1, 5, 13, 14, 26, 40, 59, 60, 91, 108, 133, 142, 156, 178, 194, 209, 210, 211, 212, 213, 214, 222, 224, 227, 228, 229, 231, 232, 233, 235, 253, 254, 260, 264, 265, 266], "empti": [1, 13, 14, 15, 152, 173, 193, 194, 208, 256, 264], "ok": 1, "allow": [1, 24, 25, 26, 29, 34, 35, 114, 116, 151, 157, 178, 194, 208, 209, 210, 212, 215, 218, 219, 260, 266], "NOT": [1, 130, 263], "adher": [2, 7, 8, 193, 194, 206, 259, 264], "convent": [2, 7, 10, 11, 26, 40, 61, 62, 64, 65, 66, 88, 124, 126, 133, 151, 167, 193, 194, 201, 211, 215, 259, 260, 265], "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, 91, 94, 95, 97, 101, 102, 106, 107, 108, 110, 115, 118, 119, 120, 121, 122, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 136, 138, 140, 141, 142, 143, 144, 145, 146, 150, 151, 153, 154, 155, 156, 159, 160, 161, 162, 163, 164, 165, 167, 168, 170, 172, 176, 177, 178, 179, 182, 183, 184, 194, 206, 208, 210, 214, 218, 220, 232, 236, 237, 238, 242, 244, 245, 246, 249, 250, 251, 252, 253, 254, 259, 260, 264, 265, 266], "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, 91, 92, 94, 95, 97, 98, 99, 101, 102, 104, 105, 108, 110, 114, 116, 117, 118, 119, 120, 123, 124, 125, 126, 127, 128, 133, 135, 136, 137, 139, 140, 142, 143, 144, 145, 146, 147, 148, 151, 152, 153, 154, 155, 158, 160, 161, 162, 163, 164, 165, 167, 168, 171, 172, 173, 176, 177, 178, 182, 183, 184, 185, 186, 188, 189, 191, 193, 201, 208, 210, 211, 218, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 238, 240, 241, 242, 244, 245, 246, 249, 250, 251, 252, 253, 254, 256, 258, 260, 264, 265], "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, 91, 92, 94, 95, 97, 98, 99, 101, 102, 104, 105, 108, 110, 114, 116, 117, 118, 119, 120, 123, 124, 125, 126, 127, 128, 133, 135, 136, 137, 139, 140, 142, 143, 144, 145, 146, 147, 148, 151, 152, 153, 154, 155, 158, 160, 161, 162, 163, 164, 165, 167, 168, 171, 172, 173, 176, 177, 178, 182, 183, 184, 185, 186, 188, 189, 191, 193, 201, 208, 210, 211, 215, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 238, 240, 241, 242, 244, 245, 246, 249, 250, 251, 252, 253, 254, 256, 258, 260, 264, 266], "creat": [3, 15, 60, 92, 93, 98, 103, 104, 105, 123, 147, 148, 191, 192, 200, 206, 215, 223, 234, 260, 264], "main": [5, 98, 180, 181, 209, 214, 239, 256, 259, 266], "namespac": [5, 7, 23, 111, 196, 206, 208, 221, 259, 260, 261, 264, 267], "under": [5, 259, 263, 264], "specifi": [5, 13, 14, 15, 16, 17, 18, 26, 29, 59, 60, 63, 74, 78, 88, 90, 92, 96, 99, 100, 104, 114, 116, 117, 123, 147, 152, 155, 156, 159, 169, 170, 173, 174, 175, 179, 180, 181, 183, 184, 185, 186, 189, 191, 194, 203, 208, 210, 211, 212, 214, 215, 216, 220, 222, 224, 225, 226, 227, 228, 230, 231, 232, 233, 235, 239, 256, 258, 260, 261, 264, 266, 267], "name": [5, 7, 23, 26, 102, 116, 183, 184, 185, 194, 211, 240, 249, 250, 251, 253, 259, 264, 265], "descript": [5, 7, 208, 210, 244, 258], "bool": [5, 13, 14, 16, 17, 18, 22, 24, 26, 28, 31, 33, 37, 39, 43, 45, 49, 52, 60, 63, 75, 88, 89, 94, 103, 104, 105, 106, 107, 116, 117, 118, 119, 120, 121, 122, 123, 129, 130, 131, 132, 135, 137, 139, 146, 152, 157, 163, 166, 171, 173, 188, 203, 208, 218, 236, 244, 253, 258], "true": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 94, 99, 102, 103, 112, 118, 119, 120, 123, 129, 130, 131, 132, 135, 137, 139, 145, 146, 152, 157, 163, 166, 171, 173, 183, 184, 185, 186, 188, 190, 194, 208, 236, 244, 253, 258, 260], "fals": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 94, 103, 112, 118, 119, 120, 123, 129, 130, 131, 132, 135, 137, 139, 146, 152, 157, 163, 166, 171, 173, 183, 184, 185, 186, 188, 194, 236, 244, 253, 258], "int8": [5, 116, 117, 203], "bit": [5, 68, 69, 71, 85, 88, 99, 109, 152, 163, 173, 203, 208, 210, 256], "sign": [5, 9, 10, 11, 12, 15, 20, 41, 44, 62, 65, 66, 71, 85, 87, 88, 91, 95, 97, 102, 116, 117, 124, 126, 135, 136, 139, 140, 142, 143, 151, 152, 155, 161, 163, 165, 167, 173, 177, 183, 184, 185, 186, 193, 201, 208, 211, 250, 251, 256], "exist": [5, 7, 26, 60, 78, 103, 206, 208, 211, 214, 215, 216, 242, 261, 264, 265], "interv": [5, 10, 11, 13, 14, 15, 61, 62, 64, 66, 90, 96, 123, 124, 126, 141, 170, 178, 180, 181, 187, 189, 194, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 237, 261], "128": 5, "127": 5, "int16": [5, 88, 116, 117, 152, 173, 203, 256], "16": [5, 203], "32": [5, 203], "767": 5, "int32": [5, 88, 116, 117, 152, 173, 203, 256], "147": 5, "483": 5, "647": 5, "int64": [5, 88, 116, 117, 152, 173, 203, 256], "64": [5, 203], "9": [5, 27], "223": 5, "372": 5, "036": 5, "854": 5, "775": 5, "807": 5, "uint8": [5, 116, 117, 203], "unsign": [5, 88, 116, 117, 152, 173, 193, 256], "255": 5, "uint16": [5, 88, 116, 117, 152, 173, 203, 256], "65": 5, "535": [5, 208], "uint32": [5, 88, 116, 117, 152, 173, 203, 256], "294": 5, "967": 5, "295": 5, "uint64": [5, 116, 117, 203], "18": 5, "446": [5, 208], "744": [5, 208], "073": 5, "709": [5, 208], "551": [5, 208], "615": 5, "float32": [5, 110, 116, 117, 153, 203, 251, 253, 254], "ieee": [5, 12, 65, 80, 81, 82, 84, 91, 97, 99, 108, 126, 142, 155, 167, 176, 177, 193, 201, 210, 211, 264], "754": [5, 12, 65, 80, 81, 82, 84, 91, 97, 99, 108, 126, 142, 155, 167, 176, 177, 193, 201, 210, 211, 264], "singl": [5, 7, 24, 25, 29, 34, 35, 114, 116, 183, 184, 193, 203, 208, 209, 211, 214, 215, 220, 260, 264, 265, 266], "precis": [5, 9, 20, 42, 60, 99, 104, 105, 110, 142, 153, 167, 203, 208, 210, 226, 230, 231, 232, 233, 235, 240, 241, 244, 251, 253, 254, 258, 264], "2019": [5, 12, 91, 97, 108, 126, 142, 193, 210, 264, 266], "float64": [5, 9, 20, 116, 117, 203, 226, 230, 231, 232, 233, 235, 240, 241, 244, 258], "doubl": [5, 178, 203, 208], "complex64": [5, 110, 116, 117, 153, 203, 208, 251, 253, 254], "imaginari": [5, 10, 11, 12, 13, 14, 44, 61, 62, 63, 64, 66, 79, 87, 91, 94, 95, 97, 99, 110, 124, 126, 142, 143, 145, 146, 147, 148, 151, 160, 165, 167, 177, 208, 211], "compon": [5, 10, 11, 12, 13, 14, 44, 62, 63, 66, 79, 87, 91, 94, 95, 97, 99, 110, 124, 126, 142, 143, 145, 146, 147, 148, 151, 153, 160, 165, 167, 176, 177, 183, 184, 185, 186, 208, 211, 225, 234], "complex128": [5, 9, 20, 116, 117, 203, 208, 226, 230, 231, 232, 233, 235, 240, 241, 244, 258], "method": [5, 26, 34, 103, 193, 196, 206, 212, 214, 215, 218, 219, 220, 264, 265, 266], "attribut": [5, 23, 99, 109, 193, 205, 208, 261, 264, 265, 266], "requir": [5, 10, 11, 24, 25, 29, 34, 35, 59, 61, 62, 63, 64, 66, 88, 103, 108, 117, 152, 167, 170, 173, 174, 175, 177, 183, 184, 186, 187, 193, 194, 201, 203, 206, 208, 209, 210, 211, 212, 213, 214, 215, 218, 220, 222, 223, 224, 226, 227, 228, 231, 232, 234, 237, 256, 259, 260, 264, 265, 266], "beyond": [5, 159, 203, 264], "It": [5, 23, 26, 103, 206, 212, 214, 264, 266, 267], "also": [5, 7, 26, 32, 34, 103, 108, 162, 203, 206, 211, 212, 213, 214, 220, 224, 228, 232, 235, 253, 259, 266], "subnorm": [5, 108], "k": [5, 40, 98, 108, 133, 145, 180, 181, 194, 236, 240, 241, 242, 250, 252, 253, 254, 256, 264], "denorm": [5, 108], "gradual": [5, 108, 264], "underflow": [5, 9, 91, 102, 108, 251], "hardwar": [5, 53, 108, 156, 210, 214, 215, 240, 253, 260, 264], "univers": [5, 108, 209, 215, 260, 264], "mani": [5, 108, 179, 264, 266], "platform": [5, 26, 108], "compil": [5, 108, 177, 206, 209, 213, 264], "toggl": [5, 108], "daz": [5, 108], "flush": [5, 108], "ftz": [5, 108], "increas": [5, 108, 210, 265], "guard": [5, 108], "against": [5, 40, 73, 108, 133, 177, 194, 246, 249, 267], "time": [5, 7, 16, 17, 26, 90, 108, 156, 183, 184, 206, 208, 213, 214, 219, 236, 240, 241, 242, 250, 252, 253, 260, 264, 266], "attack": [5, 108], "accordingli": [5, 10, 11, 13, 14, 16, 17, 59, 61, 62, 64, 66, 91, 97, 102, 108, 123, 124, 126, 135, 137, 138, 139, 142, 145, 152, 156, 161, 167, 171, 173, 183, 184, 185, 186, 188, 194, 203, 210, 211, 212, 213, 215, 244, 250, 258, 260], "vari": [5, 108, 161, 177, 183, 184, 185, 186, 203, 210], "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, 90, 95, 97, 100, 103, 108, 115, 116, 117, 123, 124, 126, 129, 130, 131, 132, 133, 137, 145, 151, 152, 155, 156, 157, 162, 164, 165, 166, 167, 170, 171, 173, 174, 175, 176, 177, 178, 179, 183, 184, 185, 186, 187, 188, 189, 193, 196, 206, 208, 209, 211, 212, 213, 214, 215, 218, 219, 220, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 235, 236, 237, 240, 241, 242, 246, 249, 250, 251, 252, 253, 254, 256, 259, 260, 261, 264, 265, 266], "access": [5, 26, 32, 103, 111, 194, 208, 214, 259, 261, 264], "variou": [5, 208], "cast": [5, 29, 49, 60, 63, 75, 88, 152, 173, 203, 211, 256, 264, 266], "introspect": 5, "isdtyp": [5, 193, 208], "integr": [5, 63, 114, 116, 117], "keyword": [5, 7, 26, 63, 88, 115, 138, 152, 173, 193, 208, 212, 215, 219, 220, 256, 260, 261, 264, 265, 266], "affect": [5, 15, 49, 212, 215], "intermedi": [5, 9, 108], "calcul": [5, 9, 10, 11, 12, 20, 21, 42, 47, 50, 61, 62, 64, 65, 66, 86, 87, 88, 90, 91, 95, 97, 124, 125, 126, 127, 128, 135, 137, 139, 142, 151, 152, 164, 165, 167, 171, 172, 173, 176, 177, 188, 208, 251], "implementor": [5, 259], "free": [5, 215, 263], "when": [5, 7, 12, 16, 17, 26, 32, 47, 49, 59, 63, 91, 97, 102, 103, 108, 114, 116, 123, 126, 135, 136, 139, 140, 142, 151, 152, 156, 157, 161, 171, 173, 177, 188, 190, 193, 194, 203, 208, 209, 211, 212, 213, 214, 216, 218, 219, 220, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 236, 240, 242, 246, 249, 250, 251, 252, 253, 254, 256, 260, 264, 265, 266], "accumul": 5, "reduct": [5, 13, 14], "long": [5, 111, 220], "ha": [5, 9, 13, 14, 20, 23, 29, 34, 35, 40, 44, 47, 55, 86, 87, 88, 91, 95, 96, 97, 102, 105, 133, 137, 138, 141, 142, 143, 145, 151, 152, 164, 165, 169, 171, 173, 174, 176, 177, 178, 179, 183, 184, 185, 186, 188, 194, 203, 206, 211, 214, 215, 218, 219, 237, 244, 252, 253, 256, 258, 260, 261, 264, 266, 267], "wai": [5, 26, 63, 103, 206, 209, 215, 216, 261, 264, 265, 266, 267], "f4": [5, 203], "ensur": [5, 26, 161, 206, 210, 260, 264, 265, 266], "portabl": [5, 59, 123, 210, 212, 215, 216, 264], "consum": [5, 26, 63, 114, 116, 206, 211, 212, 220, 259, 264, 265], "recommend": [5, 7, 19, 23, 26, 123, 129, 130, 131, 132, 137, 155, 171, 188, 201, 208, 210, 214, 215, 264], "guidanc": [5, 7, 49, 208, 209, 216, 264], "govern": [5, 50, 172, 203, 260, 261], "interact": [5, 211], "either": [5, 9, 10, 11, 12, 24, 26, 35, 40, 65, 77, 87, 88, 91, 94, 95, 97, 99, 102, 103, 108, 111, 117, 118, 119, 123, 124, 125, 126, 127, 128, 133, 135, 136, 139, 140, 142, 144, 152, 155, 162, 163, 164, 167, 173, 176, 177, 178, 194, 210, 211, 212, 216, 220, 251, 256, 264, 265, 267], "whether": [5, 13, 14, 26, 59, 60, 63, 88, 89, 103, 112, 117, 120, 123, 157, 163, 208, 215, 236, 240, 241, 250, 252, 259, 263, 264, 266], "otherwis": [5, 13, 14, 15, 16, 17, 26, 59, 60, 63, 75, 103, 112, 114, 116, 135, 137, 139, 152, 156, 157, 161, 162, 171, 173, 188, 189, 190, 193, 194, 206, 215, 236, 238, 244, 251, 252, 258, 263], "note": [5, 7, 9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 32, 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, 91, 94, 95, 97, 98, 99, 101, 102, 104, 105, 106, 107, 108, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 124, 125, 126, 127, 128, 133, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 160, 161, 162, 163, 164, 165, 167, 168, 171, 172, 173, 174, 176, 177, 178, 179, 182, 183, 184, 185, 186, 187, 188, 189, 193, 194, 208, 214, 218, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258, 264, 265, 266, 267], "possibl": [5, 26, 60, 102, 103, 135, 139, 157, 176, 177, 206, 209, 210, 211, 212, 214, 215, 216, 218, 220, 260, 264, 265, 266, 267], "multipl": [5, 7, 13, 14, 16, 17, 40, 42, 44, 133, 135, 137, 139, 142, 143, 152, 171, 173, 188, 194, 206, 209, 211, 214, 215, 219, 220, 241, 242, 260, 261, 264, 266], "In": [5, 12, 19, 26, 59, 88, 91, 94, 102, 117, 119, 120, 142, 146, 152, 155, 162, 173, 193, 194, 196, 203, 210, 211, 214, 216, 231, 232, 250, 251, 253, 256, 260, 261, 265, 266, 267], "clearli": [5, 59, 117, 201, 211, 260, 261], "warn": [5, 156, 216], "about": [5, 7, 26, 99, 109, 212, 260, 264, 266, 267], "": [5, 26, 29, 32, 49, 58, 59, 60, 80, 102, 103, 138, 155, 171, 179, 180, 181, 188, 194, 201, 206, 208, 209, 210, 211, 212, 214, 215, 218, 220, 224, 228, 232, 235, 249, 253, 254, 260, 261, 264, 266], "organ": [5, 208, 260, 265, 266], "within": [5, 15, 27, 194, 203, 206, 208, 211, 215, 222, 224, 227, 228, 231, 232, 233, 235, 264], "numer": [5, 9, 12, 20, 21, 40, 42, 44, 46, 47, 50, 51, 88, 90, 91, 102, 116, 117, 118, 119, 120, 133, 138, 142, 143, 150, 151, 152, 160, 162, 168, 172, 173, 178, 203, 210, 222, 224, 227, 228, 231, 232, 233, 235, 237, 248, 249, 251, 256, 260, 264, 266], "accord": [5, 12, 60, 71, 75, 88, 91, 99, 102, 104, 123, 142, 151, 161, 162, 171, 175, 188, 189, 194, 210, 211], "These": [5, 212, 240, 265], "intend": [5, 88, 152, 173, 206, 256], "posit": [7, 9, 10, 11, 13, 14, 20, 46, 62, 65, 66, 81, 91, 96, 98, 99, 102, 119, 124, 126, 141, 142, 145, 155, 159, 163, 165, 167, 177, 193, 194, 206, 208, 210, 220, 234, 236, 250, 265], "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, 110, 114, 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, 192, 193, 206, 208, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258, 260], "extern": [7, 266], "usabl": 7, "accept": [7, 26, 129, 130, 131, 132, 137, 155, 171, 188, 206, 261], "call": [7, 34, 90, 214, 215, 218, 251, 264, 265, 266], "argument": [7, 10, 11, 26, 40, 61, 62, 63, 64, 65, 66, 86, 88, 108, 115, 124, 126, 133, 152, 158, 161, 164, 167, 173, 176, 177, 178, 193, 203, 208, 210, 212, 214, 215, 222, 224, 227, 228, 231, 232, 233, 235, 256, 260, 264, 265, 266], "map": [7, 211, 212], "base": [7, 47, 57, 58, 95, 96, 124, 125, 126, 127, 151, 183, 184, 185, 186, 194, 208, 212, 218, 220, 260, 261, 264, 265, 266], "sole": [7, 194, 201, 260], "incompat": [7, 26, 74, 103, 206, 261, 264], "us": [7, 19, 26, 27, 59, 60, 83, 99, 103, 108, 123, 125, 127, 159, 183, 185, 193, 194, 203, 208, 210, 211, 212, 213, 215, 216, 219, 220, 221, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 259, 260, 261, 262, 263, 264, 267], "normal": [7, 78, 170, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235], "practic": [7, 19, 194, 260, 265], "avail": [7, 103, 115, 206, 214, 259, 261, 265], "still": [7, 26, 220, 260, 265, 266, 267], "consid": [7, 26, 63, 103, 129, 130, 131, 132, 183, 184, 185, 186, 211, 215, 234, 249, 260, 264, 266, 267], "compliant": [7, 26, 51, 91, 97, 103, 123, 126, 129, 130, 131, 132, 135, 136, 137, 139, 140, 171, 188, 210, 213, 215, 261, 264], "altern": [7, 212, 214, 267], "thei": [7, 26, 203, 209, 214, 215, 219, 220, 259, 260, 261, 264, 266, 267], "were": [7, 102, 156, 161, 208, 264], "option": [7, 13, 14, 15, 16, 17, 23, 26, 57, 58, 59, 60, 63, 77, 78, 88, 90, 92, 93, 98, 100, 103, 104, 105, 114, 116, 123, 135, 137, 139, 147, 148, 152, 156, 157, 159, 161, 171, 173, 174, 188, 191, 192, 193, 208, 219, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 244, 246, 249, 256, 258, 260, 265, 266], "lead": [7, 102, 211, 250, 253, 264], "readabl": [7, 203, 260, 265], "code": [7, 59, 203, 212, 213, 215, 218, 220, 260, 264, 265, 266], "easier": [7, 206, 212, 260], "evolv": [7, 206, 260], "over": [7, 13, 14, 26, 123, 135, 137, 139, 152, 171, 173, 174, 178, 188, 189, 210, 211, 212, 214, 215, 219, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 235, 237, 256, 258, 260, 264], "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, 91, 94, 95, 97, 98, 99, 103, 104, 105, 118, 119, 120, 123, 124, 125, 126, 127, 133, 138, 142, 143, 145, 146, 147, 148, 150, 151, 152, 160, 162, 164, 165, 167, 168, 172, 173, 176, 177, 178, 183, 184, 185, 186, 189, 194, 207, 208, 209, 215, 236, 237, 238, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258, 261], "worri": 7, "xi": [7, 138], "annot": [7, 208, 220, 264], "individu": [7, 161, 215, 218, 219, 220, 223, 234, 264, 265], "aim": [7, 209, 220, 259, 260, 261, 264, 265, 266, 267], "strongli": [7, 212, 266], "look": [7, 266], "like": [7, 206, 209, 211, 212, 218, 220, 261, 264, 265, 266], "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, 90, 92, 93, 98, 100, 103, 104, 105, 112, 114, 116, 123, 135, 137, 139, 147, 148, 152, 156, 157, 159, 161, 171, 173, 174, 188, 191, 192, 194, 208, 215, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 244, 246, 249, 256, 257, 258, 264, 265, 267], "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, 191, 192, 194, 208, 209, 212, 214, 218, 219, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258, 263, 266], "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, 90, 92, 96, 98, 99, 100, 102, 104, 105, 109, 123, 135, 137, 139, 141, 147, 149, 152, 156, 157, 159, 166, 169, 170, 171, 173, 174, 175, 178, 179, 180, 181, 187, 188, 189, 191, 194, 203, 218, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 239, 244, 245, 255, 256, 257, 258, 265], "str": [7, 8, 23, 116, 117, 138, 265], "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, 208, 266], "few": [7, 210, 218, 264, 266], "enhanc": 7, "default": [7, 13, 14, 15, 16, 17, 18, 23, 26, 59, 60, 63, 77, 78, 88, 90, 92, 93, 98, 100, 103, 104, 105, 113, 114, 116, 123, 135, 137, 138, 139, 145, 147, 148, 152, 156, 157, 159, 161, 166, 170, 171, 173, 175, 178, 180, 181, 183, 184, 185, 187, 188, 189, 191, 192, 193, 194, 208, 210, 215, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 239, 244, 246, 249, 250, 253, 256, 258], "form": [7, 23, 26, 40, 79, 133, 134, 180, 181, 212, 236, 238, 239, 240, 241, 242, 244, 245, 246, 249, 250, 251, 252, 253, 254, 256, 261, 265], "question": [7, 209, 264], "commonli": [7, 171, 188, 209, 211, 213, 259, 260, 264, 265], "written": [7, 206, 264, 266], "yyyi": [8, 23, 261], "mm": [8, 23, 261], "string": [8, 23, 116, 117, 208, 261, 264], "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, 91, 94, 95, 97, 98, 99, 103, 104, 105, 108, 109, 110, 117, 118, 119, 120, 123, 124, 125, 126, 127, 133, 135, 136, 138, 139, 140, 141, 142, 143, 145, 146, 147, 148, 150, 151, 152, 153, 156, 160, 161, 162, 163, 164, 165, 167, 168, 172, 173, 174, 176, 177, 178, 179, 183, 184, 185, 186, 187, 189, 193, 206, 209, 215, 219, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258, 262, 264, 266], "absolut": [9, 20, 85, 162, 210, 212, 244, 245, 251, 260], "x_i": [9, 10, 11, 61, 62, 64, 66, 68, 76, 77, 79, 86, 87, 95, 97, 101, 110, 118, 119, 120, 124, 125, 126, 127, 130, 135, 137, 139, 143, 150, 153, 154, 160, 162, 163, 164, 165, 167, 168, 171, 176, 177, 182, 188], "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, 91, 93, 94, 95, 96, 97, 100, 101, 102, 103, 105, 106, 107, 108, 110, 117, 118, 119, 120, 121, 122, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 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, 193, 201, 206, 208, 211, 213, 215, 216, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 253, 254, 256, 258, 260, 264, 266], "magnitud": [9, 12, 20, 85, 91, 102, 108, 142, 208, 253, 254], "represent": [9, 12, 20, 29, 44, 67, 70, 72, 80, 81, 82, 84, 91, 99, 102, 109, 142, 143, 144, 176, 177, 210, 214, 265], "known": [9, 162, 210, 213, 214], "norm": [9, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 244, 258, 260], "modulu": [9, 155], "z": [9, 10, 11, 61, 62, 64, 66, 124, 211], "bj": [9, 12, 79, 91, 142], "comput": [9, 12, 28, 31, 33, 37, 39, 40, 43, 57, 58, 67, 70, 72, 79, 88, 89, 90, 91, 94, 96, 102, 106, 107, 108, 121, 122, 129, 130, 131, 132, 133, 135, 136, 137, 139, 140, 142, 143, 145, 146, 150, 152, 156, 171, 173, 178, 183, 184, 185, 186, 188, 189, 194, 208, 210, 213, 218, 222, 223, 224, 226, 227, 228, 230, 231, 232, 233, 234, 235, 236, 237, 240, 241, 242, 244, 246, 249, 250, 251, 252, 253, 254, 256, 258, 260, 264], "operatornam": [9, 10, 11, 61, 62, 64, 66, 86, 87, 162, 164, 165, 176, 177, 211, 240, 241, 251, 253], "sqrt": [9, 10, 11, 61, 62, 193, 208, 211, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 258], "take": [9, 124, 126, 151, 167, 193, 208, 215, 220, 264], "care": [9, 212, 260], "undu": [9, 213], "overflow": [9, 12, 88, 91, 102, 108, 123, 152, 173, 203, 251, 256, 260], "dure": [9, 40, 59, 108, 133, 171, 188, 203, 206, 249, 264, 265], "stage": [9, 108, 261], "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, 95, 97, 101, 102, 103, 106, 107, 108, 110, 111, 112, 114, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 160, 161, 162, 163, 164, 165, 167, 168, 171, 172, 173, 176, 177, 178, 180, 181, 182, 183, 184, 185, 186, 188, 189, 191, 194, 208, 210, 211, 212, 214, 218, 219, 223, 224, 225, 228, 229, 232, 234, 235, 236, 237, 238, 239, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258, 264, 266], "nan": [9, 10, 11, 12, 13, 14, 24, 25, 35, 61, 62, 63, 64, 65, 66, 76, 77, 85, 86, 87, 91, 94, 95, 97, 101, 102, 108, 118, 119, 120, 124, 125, 126, 127, 128, 135, 136, 137, 139, 140, 142, 144, 146, 151, 155, 160, 161, 162, 163, 164, 165, 167, 171, 176, 177, 182, 183, 184, 185, 186, 188, 193, 201, 211, 264], "infin": [9, 10, 11, 12, 13, 14, 24, 25, 35, 62, 63, 64, 65, 66, 76, 81, 86, 87, 91, 94, 95, 97, 101, 102, 108, 118, 119, 124, 125, 126, 127, 128, 135, 139, 142, 146, 151, 155, 160, 163, 164, 165, 167, 176, 177, 182, 211, 251, 258], "imag": [9, 10, 11, 12, 24, 62, 63, 66, 87, 94, 95, 97, 118, 119, 120, 123, 124, 126, 146, 160, 162, 165, 167, 177, 193, 208, 209, 264, 265, 266], "finit": [9, 10, 11, 12, 25, 35, 42, 62, 65, 66, 87, 91, 94, 95, 97, 102, 108, 112, 118, 119, 124, 126, 142, 146, 151, 155, 163, 165, 167, 177, 210], "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, 91, 94, 95, 97, 98, 99, 104, 105, 109, 110, 117, 118, 119, 120, 123, 124, 125, 126, 127, 133, 138, 142, 143, 145, 146, 147, 148, 150, 151, 152, 153, 160, 162, 164, 165, 167, 168, 172, 173, 174, 176, 177, 178, 183, 184, 185, 186, 189, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258], "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, 91, 94, 95, 97, 98, 99, 103, 104, 105, 108, 109, 110, 117, 118, 119, 120, 123, 124, 125, 126, 127, 133, 135, 136, 138, 139, 140, 141, 142, 143, 145, 146, 147, 148, 150, 151, 152, 153, 156, 160, 161, 162, 163, 164, 165, 167, 168, 172, 173, 174, 176, 177, 178, 179, 183, 184, 185, 186, 187, 189, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256, 258, 261], "approxim": [10, 11, 47, 61, 62, 64, 65, 66, 86, 87, 95, 97, 102, 124, 125, 126, 127, 151, 164, 165, 176, 177, 210, 246, 249], "princip": [10, 11, 61, 62, 64, 66, 124, 167, 211, 260], "invers": [10, 11, 61, 62, 64, 65, 66, 211, 222, 224, 227, 228, 229, 230, 231, 232, 233, 235, 242, 245, 249, 260], "cosin": [10, 11, 86, 87, 177], "express": [10, 61, 63, 64, 65, 86, 164, 176, 194, 203, 212, 260, 263], "radian": [10, 61, 64, 65, 86, 164, 176], "arc": [10, 61, 64], "frac": [10, 11, 61, 62, 64, 66, 86, 87, 91, 123, 125, 127, 162, 164, 165, 176, 177, 211, 251], "pi": [10, 11, 61, 62, 64, 66, 87, 124, 126, 165, 176, 177, 193], "j": [10, 11, 12, 25, 61, 62, 64, 66, 87, 91, 95, 97, 123, 124, 126, 142, 161, 162, 164, 165, 167, 176, 177, 194, 211, 240, 253, 256], "ln": [10, 11, 61, 62, 64, 66, 124], "zj": [10, 61, 62, 64, 66], "conj": [10, 11, 61, 62, 64, 66, 87, 95, 97, 124, 125, 126, 127, 165, 167, 177, 193, 208], "multi": [10, 11, 61, 62, 64, 66, 193, 211, 214, 215, 237, 266], "branch": [10, 11, 61, 62, 64, 65, 66, 86, 87, 91, 95, 97, 124, 126, 142, 151, 164, 165, 167, 176, 177, 264], "cut": [10, 11, 61, 62, 64, 66, 86, 87, 95, 97, 124, 126, 151, 164, 165, 167, 176, 177, 264], "plane": [10, 11, 61, 62, 64, 66, 86, 87, 91, 95, 97, 142, 164, 165, 167, 176, 177, 264], "By": [10, 11, 13, 14, 61, 62, 64, 65, 66, 88, 124, 126, 135, 137, 139, 151, 152, 167, 171, 173, 188, 189, 210, 211, 237, 260, 265], "place": [10, 11, 15, 60, 61, 62, 63, 64, 66, 92, 93, 98, 103, 104, 105, 123, 147, 148, 159, 191, 192, 193, 201, 203, 208, 212, 215, 223, 234, 249], "line": [10, 11, 61, 62, 64, 66, 176, 177, 203, 211, 264, 265, 266, 267], "segment": [10, 11, 61, 62, 64, 66, 211], "infti": [10, 11, 61, 62, 64, 66, 86, 124, 126, 151, 167, 211], "axi": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 90, 96, 100, 124, 126, 135, 137, 139, 141, 151, 152, 156, 159, 166, 167, 169, 170, 171, 173, 174, 175, 178, 179, 187, 188, 189, 193, 208, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 235, 237, 244, 257, 258, 264], "rang": [10, 61, 62, 64, 66, 77, 88, 124, 126, 152, 167, 173, 194, 208, 214, 256, 264], "strip": [10, 61, 62, 64, 66, 124, 126], "unbound": [10, 61, 62, 64, 66, 124, 126], "along": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 90, 98, 100, 124, 126, 135, 137, 139, 152, 156, 159, 166, 167, 170, 171, 173, 174, 175, 176, 177, 179, 187, 188, 189, 194, 208, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 237, 256, 258, 260], "c99": [10, 11, 61, 62, 64, 66, 91, 124, 126, 142, 151, 167, 211, 261], "provision": [10, 11, 61, 62, 64, 66, 124, 126, 151, 167, 211], "statu": [10, 11, 61, 62, 64, 66, 124, 126, 151, 167, 211], "greater": [10, 11, 33, 38, 48, 61, 62, 65, 66, 69, 71, 77, 85, 91, 101, 102, 124, 126, 151, 155, 162, 163, 165, 167, 169, 177, 193, 194, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 237, 245], "than": [10, 11, 19, 26, 32, 38, 40, 47, 48, 49, 55, 61, 62, 63, 65, 66, 69, 71, 76, 77, 85, 88, 91, 99, 100, 101, 102, 103, 124, 125, 126, 127, 133, 142, 151, 152, 155, 162, 163, 165, 167, 169, 171, 173, 174, 177, 182, 183, 184, 185, 186, 188, 194, 203, 206, 209, 212, 215, 216, 219, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 237, 244, 245, 246, 249, 256, 258, 260, 261, 264, 266], "less": [10, 11, 39, 47, 61, 65, 66, 76, 85, 91, 102, 124, 125, 126, 127, 151, 155, 162, 163, 167, 171, 188, 193, 194, 212, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 244, 245, 246, 249, 258, 264], "\u03c0": [10, 64, 65, 84], "0j": [10, 11, 12, 25, 62, 63, 66, 87, 95, 97, 98, 124, 126, 147, 148, 162, 165, 167, 177, 211, 251], "nonzero": [10, 11, 12, 62, 66, 87, 91, 95, 97, 102, 142, 165, 177, 193, 194, 208, 249], "3\u03c0": [10, 65], "hyperbol": [11, 62, 66, 86, 87, 164, 165, 176, 177, 211], "aco": [11, 61, 193, 208, 210], "simpli": [11, 97, 126, 209, 220, 264, 266], "upper": [11, 77, 98, 181, 208, 236, 250], "half": [11, 15, 66, 123, 141, 167, 178, 194, 225], "area": [11, 62, 66], "sector": [11, 62, 66], "\u03c0j": [11, 62, 66, 124, 126], "3\u03c0j": [11, 124, 126], "sum": [12, 21, 88, 108, 128, 152, 193, 208, 244, 256, 258, 260], "x1_i": [12, 65, 67, 69, 70, 71, 72, 85, 91, 94, 102, 106, 107, 108, 121, 122, 128, 129, 131, 132, 136, 140, 142, 144, 146, 151, 155, 172, 190, 208], "x2_i": [12, 65, 67, 69, 70, 71, 72, 85, 91, 94, 102, 106, 107, 108, 121, 122, 128, 129, 131, 132, 136, 140, 142, 144, 146, 151, 155, 172, 190, 208], "first": [12, 16, 17, 19, 65, 67, 69, 70, 71, 72, 88, 90, 94, 106, 107, 108, 121, 122, 128, 129, 131, 132, 133, 136, 140, 142, 144, 146, 151, 159, 170, 172, 176, 177, 178, 183, 184, 185, 189, 190, 194, 211, 237, 240, 248, 250, 251, 253, 254, 260, 264, 265, 266, 267], "remain": [12, 91, 94, 102, 117, 119, 120, 142, 146, 155, 157, 162, 194, 212, 235], "neither": [12, 40, 91, 102, 133, 142, 178, 253, 265], "nor": [12, 91, 102, 142, 253, 265], "mathemat": [12, 19, 65, 84, 86, 87, 91, 97, 102, 124, 126, 142, 164, 165, 176, 177, 193, 211, 244, 258], "round": [12, 15, 76, 91, 101, 102, 142, 167, 182, 193, 208, 210], "nearest": [12, 91, 142, 160, 182, 210], "mode": [12, 91, 142, 210, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 250], "too": [12, 26, 91, 102, 142, 260, 264], "larg": [12, 91, 102, 142, 214, 220, 251, 264], "appropri": [12, 26, 91, 102, 142, 211, 216], "commut": 12, "associ": [12, 42, 142, 196, 203, 246, 249, 252, 260, 263, 265], "tabl": [12, 91, 142, 193], "c": [12, 91, 94, 123, 142, 145, 146, 156, 170, 171, 177, 188, 194, 208, 211, 214, 217, 236, 240, 241, 242, 250, 252, 253, 261, 263, 264, 266], "d": [12, 91, 94, 123, 142, 146, 203, 223, 234], "dj": [12, 91, 142], "independ": [12, 91, 142, 160, 194, 206, 214, 237, 250, 252, 260, 261, 264], "abov": [12, 88, 91, 94, 124, 126, 142, 146, 151, 152, 167, 173, 180, 181, 194, 203, 211, 212, 214, 215, 218, 239, 240, 256, 260, 263, 266], "similarli": [12, 57, 117, 138, 203, 236, 253], "henc": [12, 79, 96, 145, 156, 183, 184, 185, 186, 194, 209, 211, 212, 213, 214, 218, 219, 220, 264, 266], "z1": 12, "z2": 12, "keepdim": [13, 14, 16, 17, 135, 137, 139, 152, 171, 173, 188, 244, 258], "test": [13, 14, 89, 118, 119, 120, 208, 210, 262, 264, 265, 266], "evalu": [13, 14, 22, 30, 36, 38, 41, 44, 45, 46, 48, 51, 52, 95, 97, 124, 125, 126, 127, 143, 150, 162, 163, 168, 206, 264], "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, 92, 99, 100, 104, 105, 109, 116, 117, 123, 135, 137, 139, 141, 147, 152, 156, 158, 159, 169, 170, 171, 173, 178, 188, 191, 225, 229, 244, 246, 249, 258, 265], "ax": [13, 14, 16, 17, 19, 55, 56, 100, 135, 137, 139, 141, 149, 152, 159, 169, 171, 173, 178, 179, 188, 189, 194, 208, 224, 225, 228, 229, 232, 235, 237, 244, 249, 252, 255, 258], "logic": [13, 14, 24, 26, 91, 94, 129, 130, 131, 132, 142, 146, 215, 218, 224, 228, 232, 235], "AND": [13, 67, 94, 129, 263], "entir": [13, 14, 86, 87, 95, 97, 135, 137, 139, 152, 164, 165, 171, 173, 188], "valid": [13, 14, 26, 27, 90, 96, 115, 141, 170, 178, 187, 194, 210, 218, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 240, 250, 253, 265], "count": [13, 14, 78, 88, 90, 100, 174, 175, 183, 184, 189, 194, 208, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 237, 241], "last": [13, 14, 18, 19, 55, 78, 88, 90, 100, 159, 166, 170, 174, 175, 178, 189, 194, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 237, 239, 244, 250, 253, 256], "invalid": [13, 14, 23, 90, 96, 216, 264], "rais": [13, 14, 19, 23, 24, 25, 26, 29, 34, 35, 40, 47, 51, 55, 60, 74, 90, 91, 95, 96, 103, 123, 133, 135, 139, 145, 151, 157, 169, 170, 187, 189, 194, 203, 206, 208, 214, 215, 216, 218, 237, 245, 264], "wa": [13, 14, 19, 26, 102, 135, 137, 139, 152, 171, 173, 188, 203, 215, 220, 264, 266], "OR": [14, 24, 70, 131, 146, 263], "start": [15, 123, 194, 208, 220, 264, 266], "stop": [15, 123, 194, 208, 265], "step": [15, 123, 194, 265], "evenli": [15, 123], "space": [15, 123, 223, 225, 234], "open": [15, 123, 141, 178, 194], "inclus": [15, 194, 264], "end": [15, 65, 86, 123, 162, 164, 176, 177, 201, 212, 251, 264, 265, 266], "exclus": [15, 194], "distanc": [15, 108], "between": [15, 26, 47, 51, 65, 78, 91, 94, 99, 123, 135, 136, 139, 140, 146, 151, 170, 183, 184, 185, 186, 203, 211, 212, 215, 223, 234, 260, 264, 266], "adjac": 15, "output": [15, 60, 63, 78, 88, 92, 93, 96, 98, 100, 103, 104, 105, 112, 123, 138, 147, 148, 157, 159, 161, 169, 170, 174, 179, 191, 192, 206, 208, 211, 212, 215, 217, 218, 220, 222, 223, 224, 226, 227, 228, 231, 232, 233, 234, 235, 256, 264], "infer": [15, 60, 63, 93, 104, 105, 148, 157, 192, 213, 260, 265], "cannot": [15, 26, 57, 103, 176, 177, 208, 211, 213, 264], "guarante": [15, 59, 183, 185, 206, 211, 215, 264, 266], "error": [15, 19, 23, 24, 25, 26, 29, 34, 35, 51, 55, 91, 103, 135, 139, 176, 177, 203, 210, 251, 264], "ceil": [15, 193], "indic": [16, 17, 18, 26, 60, 88, 89, 103, 112, 117, 123, 141, 145, 159, 161, 162, 174, 175, 178, 180, 181, 183, 185, 194, 203, 208, 258, 264], "occur": [16, 17, 75, 108, 176, 177, 183, 184, 185, 186, 211, 265], "occurr": [16, 17, 183], "comparison": [16, 17, 18, 28, 31, 33, 37, 39, 43, 94, 106, 107, 121, 122, 135, 136, 139, 140, 146, 166, 193, 211, 261, 265], "search": [16, 17, 161, 193], "flatten": [16, 17, 78, 156, 159, 183, 184, 185, 186, 258, 260], "descend": [18, 166, 253, 254], "stabl": [18, 166, 214], "sort": [18, 161, 193, 208, 240, 241, 253, 254], "ascend": [18, 161, 166, 208], "stabil": [18, 166], "maintain": [18, 166, 209, 264, 266], "rel": [18, 19, 55, 100, 136, 140, 159, 166, 208, 239, 246, 249, 256], "compar": [18, 166, 183, 184, 185, 186, 210, 215, 265, 267], "properti": [19, 53, 54, 55, 56, 57, 58, 116, 208, 211, 215, 220, 264], "transpos": [19, 40, 55, 133, 134, 178, 236, 240, 249, 253, 260], "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, 203, 206, 208, 215], "permut": [19, 55, 149], "revers": [19, 55, 65, 100], "origin": [19, 55, 65, 108, 141, 157, 159, 208, 212, 222, 224, 227, 228, 231, 232, 233, 235, 264, 265], "limit": [19, 99, 109, 117, 210, 260, 263], "matric": [19, 40, 55, 133, 134, 138, 180, 181, 236, 238, 239, 240, 241, 242, 244, 245, 246, 249, 250, 251, 252, 253, 254, 256, 260], "deviat": [19, 171, 210, 216, 264, 266], "et": [19, 253, 254], "al": 19, "intent": [19, 65], "found": [19, 211, 214, 266, 267], "problemat": [19, 63, 209, 212], "conflict": 19, "definit": [19, 86, 87, 164, 165, 176, 177, 208, 236, 265], "batch": [19, 258, 260], "cetera": [19, 253, 254], "permute_dim": [19, 193], "interfac": [19, 214, 260, 264, 266], "ab": [20, 108, 151, 193, 208, 244, 258], "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, 193], "api_vers": [23, 264], "object": [23, 24, 25, 26, 29, 32, 34, 35, 53, 57, 59, 60, 89, 99, 103, 109, 111, 113, 114, 115, 193, 194, 203, 206, 208, 212, 214, 215, 218, 220, 259, 261, 265, 266], "2020": [23, 220, 261, 263, 264], "10": [23, 27, 125, 194, 264], "latest": [23, 214], "modul": [23, 206, 261, 265, 266, 267], "everi": [23, 104, 105, 250, 264], "top": [23, 206, 264, 266], "level": [23, 203, 209, 214, 215, 259, 260, 264, 265], "public": [23, 259, 265, 266], "well": [23, 209, 211, 214, 215, 250, 266, 267], "part": [23, 35, 180, 181, 203, 208, 214, 219, 261, 264, 266], "convert": [24, 25, 29, 34, 35, 60, 103, 203, 208, 209, 211, 214, 264, 266], "handl": [24, 26, 61, 64, 86, 88, 103, 125, 127, 151, 152, 154, 162, 164, 168, 173, 176, 208, 209, 211, 212, 215, 216, 256, 264], "lazi": [24, 25, 29, 34, 35, 206, 208, 217, 266], "languag": [24, 25, 29, 34, 35, 212, 216, 218, 260, 264, 266], "therefor": [24, 25, 29, 32, 34, 35, 206, 214, 215, 216, 218, 220, 261, 264, 266], "abl": [24, 25, 29, 34, 35, 103, 212, 214, 215, 264, 266], "kind": [24, 25, 26, 29, 34, 35, 47, 51, 77, 91, 99, 103, 105, 109, 114, 116, 117, 151, 203, 208, 218, 260, 263], "here": [24, 25, 26, 29, 34, 35, 194, 203, 212, 214, 219, 220, 266], "valueerror": [24, 25, 26, 29, 34, 35, 60, 103, 157, 169, 266], "instead": [24, 25, 29, 34, 35, 63, 211, 214, 218, 265, 266], "2023": [24, 25, 26, 29, 34, 35, 59, 63, 77, 85, 88, 103, 108, 135, 136, 139, 140, 141, 152, 156, 161, 163, 173, 174, 178, 179, 183, 184, 185, 186, 187, 189, 222, 223, 224, 226, 227, 228, 231, 232, 234, 237, 256], "new": [25, 26, 77, 79, 85, 88, 96, 99, 103, 104, 105, 108, 109, 110, 117, 136, 140, 141, 147, 148, 153, 156, 157, 161, 163, 170, 174, 179, 187, 191, 192, 206, 208, 209, 212, 214, 215, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 261, 264, 265, 266], "stream": [26, 59, 215], "max_vers": [26, 208], "dl_devic": [26, 208], "enum": [26, 27], "pycapsul": 26, "export": [26, 103, 208, 214, 265], "from_dlpack": [26, 27, 193, 208, 214], "dlpack": [26, 27, 103, 208], "capsul": 26, "cuda": [26, 27, 209, 214, 266], "rocm": [26, 27, 209], "pointer": 26, "produc": [26, 32, 240, 250, 253, 266], "instruct": 26, "safe": [26, 123], "insert": [26, 96, 161, 208], "wait": 26, "event": [26, 263], "larger": [26, 99, 159, 171, 188, 249], "below": [26, 102, 103, 180, 181, 196, 214, 215, 239, 256], "signal": [26, 226, 230, 266], "ownership": 26, "stai": 26, "On": 26, "cpu": [26, 27, 206, 209, 214, 215, 260, 264, 266], "queue": [26, 59, 215], "similar": [26, 155, 194, 209, 211, 213, 264, 265, 266], "mechan": [26, 103, 206, 208, 209, 217, 259, 264], "most": [26, 206, 215, 240, 260, 264, 266], "yet": [26, 220, 264], "sycl": 26, "want": [26, 91, 142, 209, 213, 214, 264, 266, 267], "cl": 26, "agre": 26, "assum": [26, 86, 103, 164, 176, 206, 211, 215, 259, 264], "legaci": 26, "per": [26, 156, 209, 214, 262], "thread": [26, 264, 266], "disallow": 26, "due": [26, 42, 57, 58, 123, 142, 156, 174, 210, 211, 260, 264], "ambigu": [26, 63, 102, 212], "construct": [26, 179, 206, 208, 209, 218, 264], "particular": [26, 194, 209, 211, 214, 215, 220, 260, 263, 264, 266, 267], "kdlcpu": 26, "safeti": [26, 59], "prefer": [26, 102, 206, 260, 266], "develop": [26, 210, 264, 265, 266, 267], "who": [26, 210, 264, 265], "think": 26, "cost": 26, "caller": 26, "major": [26, 145, 156, 194, 261], "minor": [26, 261], "verifi": [26, 264], "even": [26, 91, 142, 151, 160, 210, 211, 212, 223, 225, 229, 234, 250, 260, 264, 266], "pass": [26, 65, 206, 210, 215], "format": [26, 27, 261], "__dlpack_device__": [26, 103, 193, 214], "buffererror": [26, 103, 208, 214], "v2023": [26, 103], "mandat": [26, 103, 264], "offer": [26, 103, 209, 214, 215, 219, 264, 266], "referenc": [26, 264], "underli": [26, 67, 70, 72, 103, 210, 251, 260], "interpret": [26, 103, 108, 211, 212, 267], "enumer": 26, "made": [26, 103, 206, 211, 259, 261, 264, 266], "never": [26, 60, 103, 157, 214, 264], "deem": [26, 103], "cross": [26, 103, 208, 215, 260, 264], "movement": [26, 103], "request": [26, 103, 264], "reus": [26, 60, 103, 212, 264], "buffer": [26, 60, 103, 212, 214], "happen": [26, 103, 212, 215, 218, 260], "dlpack_flag_bitmask_is_copi": 26, "flag": 26, "understood": [26, 203], "interchang": [26, 103, 206, 209, 217, 264], "detail": [26, 32, 49, 103, 145, 156, 183, 184, 185, 186, 193, 194, 205, 206, 213, 215, 219, 260, 264, 266], "stride": [26, 103, 212, 214], "fail": [26, 103, 264], "reason": [26, 103, 155, 177, 212, 214, 216, 260, 264, 265], "incorrect": 26, "scheme": [26, 261], "semver": 26, "abi": [26, 209, 214], "break": [26, 216], "introduc": [26, 63, 102, 159, 220, 265], "goe": 26, "togeth": [26, 203, 214], "dlmanagedtensorvers": 26, "struct": 26, "later": 26, "introduct": 26, "becaus": [26, 203, 209, 212, 215, 216, 218, 220, 240, 253, 264, 266, 267], "keep": [26, 203, 209, 264], "march": 26, "2025": 26, "onward": 26, "ideal": [26, 260], "late": 26, "okai": 26, "we": [26, 211, 253, 264], "get": [26, 99, 109, 209, 212, 214, 215], "now": [26, 103, 218, 264, 266], "our_own_dlpack_vers": 26, "fill": [26, 104, 105, 147, 148, 191, 192, 208], "field": [26, 183, 184, 185, 211, 240, 250, 251, 253, 264], "understand": [26, 249, 264, 265], "u": [26, 236, 249, 253], "just": [26, 264, 266], "our": 26, "elif": 26, "fine": [26, 220, 264], "own": [26, 206, 212, 264], "re": [26, 159, 209, 212, 220, 266], "intern": [26, 266], "did": 26, "older": [26, 177, 214, 261, 264], "around": [26, 265], "y": [26, 65, 103, 211, 212, 266], "dlmanagedtensor": 26, "so": [26, 99, 103, 111, 194, 201, 214, 260, 263, 264, 267], "tell": 26, "old": 26, "exchang": [26, 103, 214], "And": [26, 194, 215], "try": [26, 220, 264], "succe": 26, "info": [26, 111], "dltensor_vers": 26, "need": [26, 194, 209, 210, 212, 214, 216, 220, 260, 261, 264, 265, 266, 267], "used_dltensor_vers": 26, "done": [26, 206], "typeerror": [26, 29, 34, 35, 264, 266], "read": [26, 208, 212], "dlpack_flag_bitmask_read_onli": 26, "ignor": [26, 138, 260], "respons": 26, "isn": [26, 209], "t": [26, 193, 209, 212, 215, 219, 220, 264, 266], "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, 261], "truth": [28, 31, 33, 37, 39, 43, 89, 94, 106, 107, 121, 122, 146, 267], "undefin": [28, 31, 33, 37, 39, 43, 94, 106, 107, 121, 122, 146, 203, 260], "outsid": [29, 170, 187, 194, 203, 208, 214], "bound": [29, 77, 174, 175, 194, 203, 208, 220], "divis": [30, 41, 71, 91, 102, 155, 162, 211], "floor_divid": [30, 193], "greater_equ": [31, 193], "kei": [32, 49, 112, 114, 116, 264], "slice": [32, 49, 187, 193, 212], "ellipsi": [32, 49, 194], "semant": [32, 40, 49, 102, 133, 155, 174, 193, 194, 206, 212, 214, 216, 218, 219, 260, 264, 265, 266], "iter": [32, 194], "directli": [32, 264, 266], "__iter__": 32, "sequenc": [32, 60, 78, 123, 170, 178, 187, 194, 208, 224, 225, 228, 229, 232, 235, 255], "pep": [34, 40, 102, 133, 214, 261], "357": 34, "overflowerror": 35, "bitwise_invert": [36, 193], "less_equ": [37, 193], "bitwise_left_shift": [38, 193], "matrix": [40, 55, 133, 134, 138, 178, 180, 181, 236, 238, 239, 240, 241, 242, 244, 245, 246, 249, 250, 251, 252, 253, 254, 256, 260, 264], "product": [40, 42, 58, 133, 142, 152, 178, 189, 208, 237, 248, 260], "built": [40, 133, 194, 203, 264], "465": [40, 133], "least": [40, 91, 116, 117, 133, 142, 145, 183, 184, 185, 186, 209, 210, 249], "m": [40, 55, 90, 133, 134, 138, 156, 161, 178, 179, 180, 181, 194, 222, 224, 226, 227, 228, 230, 231, 232, 233, 235, 236, 238, 239, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 256], "remov": [40, 133, 169, 194, 211, 239, 256], "innermost": [40, 133, 134, 180, 181, 236, 238, 239, 240, 241, 242, 244, 245, 246, 249, 250, 251, 252, 253, 254, 256], "conjug": [40, 79, 133, 178, 189, 208, 236, 240, 253, 260], "transposit": [40, 133, 178], "desir": [40, 63, 75, 133, 141, 178, 210, 211, 214, 220], "prior": [40, 90, 133, 178], "inner": [40, 133, 208, 240, 260], "stack": [40, 55, 133, 134, 180, 181, 193, 219, 236, 238, 239, 240, 241, 242, 244, 245, 246, 249, 250, 251, 252, 253, 254, 256, 260], "l": [40, 133, 236, 256], "remaind": [41, 193, 194], "multipli": [42, 152, 168, 193, 208, 210, 240, 253], "not_equ": [43, 193, 208], "negat": [44, 79, 143], "bitwise_or": [45, 193], "exponenti": [47, 95, 97, 128, 151, 211], "power": [47, 71, 95, 151, 211, 245, 266], "expon": [47, 151, 245], "versu": [47, 51, 63, 77, 91, 142, 151, 208], "bitwise_right_shift": [48, 193], "mix": [49, 123, 137, 158, 171, 188, 193, 208, 212, 215, 260, 264], "how": [49, 91, 142, 206, 210, 215, 219, 265, 266, 267], "minuend": 50, "subtrahend": 50, "subtract": [50, 193, 208, 210], "choos": [51, 57, 59, 91, 102, 123, 129, 130, 131, 132, 135, 136, 137, 139, 140, 142, 145, 156, 171, 183, 184, 185, 186, 188, 193, 194, 201, 211, 212, 213, 215, 218, 264, 266], "divid": [51, 102, 154, 162, 193, 194, 208, 210], "bitwise_xor": [52, 193], "resid": [53, 59, 96, 141, 178, 194, 208, 214, 264], "fewer": 55, "unknown": [57, 58, 156], "graph": [57, 58, 145, 156, 183, 184, 185, 186, 194, 213, 218, 264], "static": [57, 213, 217], "resolv": [57, 60, 88, 96, 102, 104, 105, 152, 173, 224, 225, 228, 229, 232, 235, 256, 264], "know": [57, 145, 156, 183, 184, 185, 186, 206, 209, 210, 213, 264, 266], "content": [57, 213, 263], "warrant": 57, "custom": [57, 209, 216], "immut": 57, "retriev": [57, 194, 206, 221, 260, 266], "behav": [57, 211], "current": [59, 114, 116, 174, 201, 212, 215, 220, 264, 265, 266], "__dlpack__": [59, 103, 193, 208, 214], "caveat": 59, "would": [59, 60, 157, 161, 194, 208, 212, 218, 260, 264, 266], "locat": [59, 212], "explicit": [59, 60, 103, 174, 178, 215, 266], "enqueu": 59, "asynchron": 59, "explain": [59, 209], "clarifi": [59, 135, 139, 183, 184, 185, 208], "obj": 60, "nestedsequ": 60, "supportsbufferprotocol": 60, "possibli": [60, 219, 264], "nest": [60, 219], "protocol": [60, 206, 214, 220, 264, 266], "turn": [60, 206, 259], "memoryview": 60, "preced": [60, 211, 214, 215], "mixtur": 60, "convers": [60, 123, 208, 209, 264], "obei": [60, 123], "permit": [60, 63, 123, 213, 263], "To": [60, 102, 194, 208, 210, 211, 220, 264, 265, 267], "array_api": [60, 264], "astyp": [60, 193, 208], "exce": [60, 104, 105, 123], "sine": [61, 62, 164, 165, 177], "1j": [61, 64, 86, 87, 95, 97, 108, 164, 165, 176], "asinh": [61, 193, 208, 210], "asin": [62, 193, 208, 210], "irrespect": [63, 211], "histor": [63, 177, 260], "discard": 63, "choic": [63, 171, 188, 206, 210, 211, 215, 216, 218, 219, 260, 261, 264, 266], "arbitrari": [63, 73, 112, 138, 158, 210], "achiev": [63, 194, 210], 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environments": [[206, "hardware-and-software-environments"]], "Dependencies": [[206, "dependencies"]], "Backwards compatibility": [[206, "backwards-compatibility"], [261, "backwards-compatibility"]], "Production code & interactive use": [[206, "production-code-interactive-use"]], "Benchmark suite": [[207, "benchmark-suite"]], "Changelog per API standard version": [[208, "changelog-per-api-standard-version"]], "Changelog": [[208, "changelog"]], "v2023.12": [[208, "v2023-12"]], "Updates": [[208, "updates"], [208, "id3"]], "Normative": [[208, "normative"]], "APIs": [[208, "apis"], [208, "id1"], [208, "id4"], [208, "id8"]], "Extensions": [[208, "extensions"], [208, "id2"], [208, "id5"], [208, "id9"], [259, "extensions"]], "Additions": [[208, "additions"], [208, "id7"]], "Breaking Changes": [[208, "breaking-changes"]], "Errata": [[208, "errata"], [208, "id10"]], "v2022.12": [[208, "v2022-12"]], "Complex Number Support": [[208, "complex-number-support"], [208, "id6"]], "C API": [[209, "c-api"]], "Example situations for C/Cython usage": [[209, "example-situations-for-c-cython-usage"]], "Situation 1: a Python package that is mostly pure Python, with a limited number of Cython extensions": [[209, "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": [[209, "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": [[209, "situation-3-a-python-package-that-uses-the-numpy-or-python-c-api-directly"]], "Device support": [[209, "device-support"], [215, "device-support"]], "Other longer-term approaches": [[209, "other-longer-term-approaches"]], "Further Python API standardization": [[209, "further-python-api-standardization"]], "HPy": [[209, "hpy"]], "Accuracy": [[210, "accuracy"]], "Arithmetic Operations": [[210, "arithmetic-operations"]], "Mathematical Functions": [[210, "mathematical-functions"]], "Linear Algebra": [[210, "linear-algebra"]], "Complex Numbers": [[211, "complex-numbers"]], "The Complex Plane": [[211, "the-complex-plane"]], "Branch Cuts": [[211, "branch-cuts"]], "Complex Number Ordering": [[211, "complex-number-ordering"]], "Valued-based Promotion": [[211, "valued-based-promotion"]], "Copy-view behaviour and mutability": [[212, "copy-view-behaviour-and-mutability"]], "Mutating views": [[212, null]], "Data-dependent output shapes": [[213, "data-dependent-output-shapes"]], "Data interchange mechanisms": [[214, "data-interchange-mechanisms"]], "DLPack: An in-memory tensor structure": [[214, "dlpack-an-in-memory-tensor-structure"]], "Non-supported use cases": [[214, "non-supported-use-cases"]], "Intended usage": [[215, "intended-usage"]], "Syntax for device assignment": [[215, "syntax-for-device-assignment"]], "Semantics": [[215, "semantics"]], "Out of scope for device support": [[215, "out-of-scope-for-device-support"]], "Exceptions": [[216, "exceptions"]], "Design topics & constraints": [[217, "design-topics-constraints"], [217, null]], "Lazy vs. eager execution": [[218, "lazy-vs-eager-execution"]], "Parallelism": [[219, "parallelism"]], "Static typing": [[220, "static-typing"]], "Fourier transform Functions": [[221, "fourier-transform-functions"]], "Extension name and usage": [[221, "extension-name-and-usage"], [260, "extension-name-and-usage"]], "fft": [[222, "fft"]], "fftfreq": [[223, "fftfreq"]], "fftn": [[224, "fftn"]], "fftshift": [[225, "fftshift"]], "hfft": [[226, "hfft"]], "ifft": [[227, "ifft"]], "ifftn": [[228, "ifftn"]], "ifftshift": [[229, "ifftshift"]], "ihfft": [[230, "ihfft"]], "irfft": [[231, "irfft"]], "irfftn": [[232, "irfftn"]], "rfft": [[233, "rfft"]], "rfftfreq": [[234, "rfftfreq"]], "rfftn": [[235, "rfftn"]], "cholesky": [[236, "cholesky"]], "cross": [[237, "cross"]], "det": [[238, "det"]], "diagonal": [[239, "diagonal"]], "eigh": [[240, "eigh"]], "eigvalsh": [[241, "eigvalsh"]], "inv": [[242, "inv"]], "matrix_norm": [[244, "matrix-norm"]], "matrix_power": [[245, "matrix-power"]], "matrix_rank": [[246, "matrix-rank"]], "outer": [[248, "outer"]], "pinv": [[249, "pinv"]], "qr": [[250, "qr"]], "slogdet": [[251, "slogdet"]], "solve": [[252, "solve"]], "svd": [[253, "svd"]], "svdvals": [[254, "svdvals"]], "trace": [[256, "trace"]], "vector_norm": [[258, "vector-norm"]], "Extension modules:": [[259, null]], "Linear Algebra Extension": [[260, "linear-algebra-extension"]], "Design Principles": [[260, "design-principles"]], "Future API standard evolution": [[261, "future-api-standard-evolution"]], "Scope extensions": [[261, "scope-extensions"]], "Versioning": [[261, "versioning"]], "Python array API standard": [[262, "python-array-api-standard"]], "Contents": [[262, "contents"]], "Context": [[262, null]], "API": [[262, null]], "Methodology and Usage": [[262, null]], "Other": [[262, null]], "License": [[263, "license"]], "Purpose and scope": [[264, "purpose-and-scope"]], "Introduction": [[264, "introduction"], [265, "introduction"]], "This API standard": [[264, "this-api-standard"]], "History": [[264, "history"]], "Scope (includes out-of-scope / non-goals)": [[264, "scope-includes-out-of-scope-non-goals"]], "In scope": [[264, "in-scope"]], "Out of scope": [[264, "out-of-scope"]], "Implications of in/out of scope": [[264, "implications-of-in-out-of-scope"]], "Stakeholders": [[264, "stakeholders"]], "How to read this document": [[264, "how-to-read-this-document"]], "How to adopt this API": [[264, "how-to-adopt-this-api"]], "Checking an array object for Compliance": [[264, "checking-an-array-object-for-compliance"]], "Discoverability of conforming implementations": [[264, "discoverability-of-conforming-implementations"]], "Optional feature": [[264, null]], "Conformance": [[264, "conformance"]], "Terms and Definitions": [[264, "terms-and-definitions"]], "Normative References": [[264, "normative-references"]], "Usage Data": [[265, "usage-data"]], "Design": [[265, "design"]], "Usage": [[265, "usage"]], "Use in Decision-Making": [[265, "use-in-decision-making"]], "Use cases": [[266, "use-cases"]], "Types of use cases": [[266, "types-of-use-cases"]], "Concrete use cases": [[266, "concrete-use-cases"]], "Use case 1: add hardware accelerator and distributed support to SciPy": [[266, "use-case-1-add-hardware-accelerator-and-distributed-support-to-scipy"]], "Use case 2: simplify einops by removing the backend system": [[266, "use-case-2-simplify-einops-by-removing-the-backend-system"]], "Use case 3: adding a Python API to xtensor": [[266, "use-case-3-adding-a-python-api-to-xtensor"]], "Use case 4: make JIT compilation of array computations easier and more robust": [[266, "use-case-4-make-jit-compilation-of-array-computations-easier-and-more-robust"]], "Verification - test suite": [[267, "verification-test-suite"]], "Measuring conformance": [[267, "measuring-conformance"]], "Running the tests": [[267, "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__"]], "diff() (in module array_api)": [[90, "array_api.diff"]], "divide() (in module array_api)": [[91, "array_api.divide"]], "empty() (in module array_api)": [[92, "array_api.empty"]], "empty_like() (in module array_api)": [[93, "array_api.empty_like"]], "equal() (in module array_api)": [[94, "array_api.equal"]], "exp() (in module array_api)": [[95, "array_api.exp"]], "expand_dims() (in module array_api)": [[96, "array_api.expand_dims"]], "expm1() (in module array_api)": [[97, "array_api.expm1"]], "eye() (in module array_api)": [[98, "array_api.eye"]], "finfo() (in module array_api)": [[99, "array_api.finfo"]], "flip() (in module array_api)": [[100, "array_api.flip"]], "floor() (in module array_api)": [[101, "array_api.floor"]], "floor_divide() (in module array_api)": [[102, "array_api.floor_divide"]], "from_dlpack() (in module array_api)": [[103, "array_api.from_dlpack"]], "full() (in module array_api)": [[104, "array_api.full"]], "full_like() (in module array_api)": [[105, "array_api.full_like"]], "greater() (in module array_api)": [[106, "array_api.greater"]], "greater_equal() (in module array_api)": [[107, "array_api.greater_equal"]], "hypot() (in module array_api)": [[108, "array_api.hypot"]], "iinfo() (in module array_api)": [[109, "array_api.iinfo"]], "imag() (in module array_api)": [[110, "array_api.imag"]], "__array_namespace_info__() (in module array_api.info)": [[111, "array_api.info.__array_namespace_info__"]], "capabilities() (in module array_api.info)": [[112, "array_api.info.capabilities"]], "default_device() (in module array_api.info)": [[113, "array_api.info.default_device"]], "default_dtypes() (in module array_api.info)": [[114, "array_api.info.default_dtypes"]], "devices() (in module array_api.info)": [[115, "array_api.info.devices"]], "dtypes() (in module array_api.info)": [[116, "array_api.info.dtypes"]], "isdtype() (in module array_api)": [[117, "array_api.isdtype"]], "isfinite() (in module array_api)": [[118, "array_api.isfinite"]], "isinf() (in module array_api)": [[119, "array_api.isinf"]], "isnan() (in module array_api)": [[120, "array_api.isnan"]], "less() (in module array_api)": [[121, "array_api.less"]], "less_equal() (in module array_api)": [[122, "array_api.less_equal"]], "linspace() (in module array_api)": [[123, "array_api.linspace"]], "log() (in module array_api)": [[124, "array_api.log"]], "log10() (in module array_api)": [[125, "array_api.log10"]], "log1p() (in module array_api)": [[126, "array_api.log1p"]], "log2() (in module array_api)": [[127, "array_api.log2"]], "logaddexp() (in module array_api)": [[128, "array_api.logaddexp"]], "logical_and() (in module array_api)": [[129, "array_api.logical_and"]], "logical_not() (in module array_api)": [[130, "array_api.logical_not"]], "logical_or() (in module array_api)": [[131, "array_api.logical_or"]], "logical_xor() (in module array_api)": [[132, "array_api.logical_xor"]], "matmul() (in module array_api)": [[133, "array_api.matmul"]], "matrix_transpose() (in module array_api)": [[134, "array_api.matrix_transpose"]], "max() (in module array_api)": [[135, "array_api.max"]], "maximum() (in module array_api)": [[136, "array_api.maximum"]], "mean() (in module array_api)": [[137, "array_api.mean"]], "meshgrid() (in module array_api)": [[138, "array_api.meshgrid"]], "min() (in module array_api)": [[139, "array_api.min"]], "minimum() (in module array_api)": [[140, "array_api.minimum"]], "moveaxis() (in module array_api)": [[141, "array_api.moveaxis"]], "multiply() (in module array_api)": [[142, "array_api.multiply"]], "negative() (in module array_api)": [[143, "array_api.negative"]], "nextafter() (in module array_api)": [[144, "array_api.nextafter"]], "nonzero() (in module array_api)": [[145, "array_api.nonzero"]], "not_equal() (in module array_api)": [[146, "array_api.not_equal"]], "ones() (in module array_api)": [[147, "array_api.ones"]], "ones_like() (in module array_api)": [[148, "array_api.ones_like"]], "permute_dims() (in module array_api)": [[149, "array_api.permute_dims"]], "positive() (in module array_api)": [[150, "array_api.positive"]], "pow() (in module array_api)": [[151, "array_api.pow"]], "prod() (in module array_api)": [[152, "array_api.prod"]], "real() (in module array_api)": [[153, "array_api.real"]], "reciprocal() (in module array_api)": [[154, "array_api.reciprocal"]], "remainder() (in module array_api)": [[155, "array_api.remainder"]], "repeat() (in module array_api)": [[156, "array_api.repeat"]], "reshape() (in module array_api)": [[157, "array_api.reshape"]], "result_type() (in module array_api)": [[158, "array_api.result_type"]], "roll() (in module array_api)": [[159, "array_api.roll"]], "round() (in module array_api)": [[160, "array_api.round"]], "searchsorted() (in module array_api)": [[161, "array_api.searchsorted"]], "sign() (in module array_api)": [[162, "array_api.sign"]], "signbit() (in module array_api)": [[163, "array_api.signbit"]], "sin() (in module array_api)": [[164, "array_api.sin"]], "sinh() (in module array_api)": [[165, "array_api.sinh"]], "sort() (in module array_api)": [[166, "array_api.sort"]], "sqrt() (in module array_api)": [[167, "array_api.sqrt"]], "square() (in module array_api)": [[168, "array_api.square"]], "squeeze() (in module array_api)": [[169, "array_api.squeeze"]], "stack() (in module array_api)": [[170, "array_api.stack"]], "std() (in module array_api)": [[171, "array_api.std"]], "subtract() (in module array_api)": [[172, "array_api.subtract"]], "sum() (in module array_api)": [[173, "array_api.sum"]], "take() (in module array_api)": [[174, "array_api.take"]], "take_along_axis() (in module array_api)": [[175, "array_api.take_along_axis"]], "tan() (in module array_api)": [[176, "array_api.tan"]], "tanh() (in module array_api)": [[177, "array_api.tanh"]], "tensordot() (in module array_api)": [[178, "array_api.tensordot"]], "tile() (in module array_api)": [[179, "array_api.tile"]], "tril() (in module array_api)": [[180, "array_api.tril"]], "triu() (in module array_api)": [[181, "array_api.triu"]], "trunc() (in module array_api)": [[182, "array_api.trunc"]], "unique_all() (in module array_api)": [[183, "array_api.unique_all"]], "unique_counts() (in module array_api)": [[184, "array_api.unique_counts"]], "unique_inverse() (in module array_api)": [[185, "array_api.unique_inverse"]], "unique_values() (in module array_api)": [[186, "array_api.unique_values"]], "unstack() (in module array_api)": [[187, "array_api.unstack"]], "var() (in module array_api)": [[188, "array_api.var"]], "vecdot() (in module array_api)": [[189, "array_api.vecdot"]], "where() (in module array_api)": [[190, "array_api.where"]], "zeros() (in module array_api)": [[191, "array_api.zeros"]], "zeros_like() (in module array_api)": [[192, "array_api.zeros_like"]], "fft() (in module array_api.fft)": [[222, "array_api.fft.fft"]], "fftfreq() (in module array_api.fft)": [[223, "array_api.fft.fftfreq"]], "fftn() (in module array_api.fft)": [[224, "array_api.fft.fftn"]], "fftshift() (in module array_api.fft)": [[225, "array_api.fft.fftshift"]], "hfft() (in module array_api.fft)": [[226, "array_api.fft.hfft"]], "ifft() (in module array_api.fft)": [[227, "array_api.fft.ifft"]], "ifftn() (in module array_api.fft)": [[228, "array_api.fft.ifftn"]], "ifftshift() (in module array_api.fft)": [[229, "array_api.fft.ifftshift"]], "ihfft() (in module array_api.fft)": [[230, "array_api.fft.ihfft"]], "irfft() (in module array_api.fft)": [[231, "array_api.fft.irfft"]], "irfftn() (in module array_api.fft)": [[232, "array_api.fft.irfftn"]], "rfft() (in module array_api.fft)": [[233, "array_api.fft.rfft"]], "rfftfreq() (in module array_api.fft)": [[234, "array_api.fft.rfftfreq"]], "rfftn() (in module array_api.fft)": [[235, "array_api.fft.rfftn"]], "cholesky() (in module array_api.linalg)": [[236, "array_api.linalg.cholesky"]], "cross() (in module array_api.linalg)": [[237, "array_api.linalg.cross"]], "det() (in module array_api.linalg)": [[238, "array_api.linalg.det"]], "diagonal() (in module array_api.linalg)": [[239, "array_api.linalg.diagonal"]], "eigh() (in module array_api.linalg)": [[240, "array_api.linalg.eigh"]], "eigvalsh() (in module array_api.linalg)": [[241, "array_api.linalg.eigvalsh"]], "inv() (in module array_api.linalg)": [[242, "array_api.linalg.inv"]], "matmul() (in module array_api.linalg)": [[243, "array_api.linalg.matmul"]], "matrix_norm() (in module array_api.linalg)": [[244, "array_api.linalg.matrix_norm"]], "matrix_power() (in module array_api.linalg)": [[245, "array_api.linalg.matrix_power"]], "matrix_rank() (in module array_api.linalg)": [[246, "array_api.linalg.matrix_rank"]], "matrix_transpose() (in module array_api.linalg)": [[247, "array_api.linalg.matrix_transpose"]], "outer() (in module array_api.linalg)": [[248, "array_api.linalg.outer"]], "pinv() (in module array_api.linalg)": [[249, "array_api.linalg.pinv"]], "qr() (in module array_api.linalg)": [[250, "array_api.linalg.qr"]], "slogdet() (in module array_api.linalg)": [[251, "array_api.linalg.slogdet"]], "solve() (in module array_api.linalg)": [[252, "array_api.linalg.solve"]], "svd() (in module array_api.linalg)": [[253, "array_api.linalg.svd"]], "svdvals() (in module array_api.linalg)": [[254, "array_api.linalg.svdvals"]], "tensordot() (in module array_api.linalg)": [[255, "array_api.linalg.tensordot"]], "trace() (in module array_api.linalg)": [[256, "array_api.linalg.trace"]], "vecdot() (in module array_api.linalg)": [[257, "array_api.linalg.vecdot"]], "vector_norm() (in module array_api.linalg)": [[258, "array_api.linalg.vector_norm"]]}}) \ No newline at end of file