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321, 324], "argument": [2, 29, 149, 161, 162, 163, 174, 242, 317, 321, 322, 327, 328, 329], "singl": [2, 41, 51, 65, 87, 152, 177, 199, 320, 323, 327], "If": [2, 7, 9, 20, 21, 22, 25, 26, 29, 35, 45, 47, 51, 60, 61, 62, 64, 65, 73, 74, 77, 84, 87, 88, 90, 95, 98, 107, 123, 124, 125, 130, 134, 136, 137, 138, 141, 143, 144, 149, 150, 153, 155, 157, 161, 163, 178, 179, 180, 181, 189, 195, 197, 206, 208, 218, 224, 226, 229, 231, 233, 242, 262, 264, 275, 297, 320, 321, 322, 324, 327, 328, 329], "given": [2, 4, 11, 12, 13, 14, 15, 16, 20, 21, 22, 26, 27, 47, 60, 62, 64, 73, 77, 82, 90, 98, 100, 110, 118, 123, 125, 130, 134, 136, 142, 143, 144, 146, 147, 148, 150, 165, 176, 177, 182, 198, 199, 205, 221, 263, 265, 271], "node": [2, 153, 162, 163], "python": [2, 160, 161, 162, 163, 164, 293, 303, 304, 306, 319, 321, 322, 325], "list": [2, 12, 13, 15, 16, 18, 19, 21, 22, 26, 29, 41, 47, 60, 62, 64, 65, 77, 84, 87, 90, 94, 95, 96, 98, 99, 100, 103, 104, 113, 123, 125, 129, 130, 134, 141, 142, 145, 149, 150, 152, 155, 160, 163, 164, 174, 206, 208, 209, 210, 211, 216, 218, 219, 220, 293, 299, 300, 301, 302, 311, 319, 320, 321, 322, 324], "tupl": [2, 4, 41, 47, 48, 49, 87, 91, 108, 128, 149, 152, 160, 161, 162, 163, 164, 176, 177, 180, 181, 198, 199, 208, 210, 231, 242, 297, 299, 300, 301, 302, 319, 322], "dict": [2, 51, 67, 113, 114, 115, 159, 211, 216, 219, 220, 293, 303, 304, 306, 319, 322, 327], "leav": [2, 161, 162, 163], "ignor": [2, 297], "exponenti": [3, 5, 230, 251, 280, 310], "axi": [4, 7, 8, 11, 14, 17, 18, 19, 20, 21, 22, 23, 32, 47, 60, 62, 64, 77, 79, 87, 88, 90, 95, 107, 123, 124, 125, 128, 129, 130, 134, 135, 137, 138, 142, 143, 144, 145, 150, 151, 153, 176, 177, 187, 198, 199, 226, 255, 261, 263, 264, 268, 273, 275, 283, 284, 323], "int": [4, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 28, 29, 33, 40, 47, 50, 60, 62, 64, 67, 68, 69, 70, 73, 74, 77, 79, 84, 87, 88, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 107, 108, 110, 123, 124, 125, 128, 129, 130, 134, 135, 137, 138, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 153, 155, 157, 165, 174, 176, 177, 178, 179, 180, 181, 185, 187, 188, 189, 193, 194, 195, 197, 198, 199, 221, 223, 224, 225, 226, 229, 233, 241, 255, 263, 264, 268, 273, 275, 293, 309, 311, 312, 313], "sequenc": [4, 12, 13, 15, 16, 18, 19, 21, 22, 26, 60, 62, 64, 77, 84, 90, 94, 95, 96, 98, 99, 100, 103, 104, 108, 123, 125, 128, 130, 134, 141, 142, 145, 150, 155, 178, 179, 188, 194, 226, 241, 317, 328], "add": [4, 56, 87, 91, 179, 180, 181, 322, 328], "size": [4, 7, 8, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 26, 28, 32, 33, 40, 47, 69, 74, 91, 92, 95, 108, 125, 128, 151, 157, 174, 176, 177, 179, 180, 181, 185, 193, 198, 199, 223, 224, 242, 297, 321, 324, 325], "one": [4, 6, 7, 8, 47, 54, 61, 92, 95, 128, 133, 167, 218, 242, 264, 321, 328], "dimens": [4, 9, 18, 19, 21, 22, 23, 27, 28, 34, 45, 46, 47, 48, 49, 60, 61, 62, 64, 77, 90, 91, 95, 102, 130, 134, 138, 141, 145, 150, 178, 179, 180, 181, 183, 184, 187, 188, 189, 193, 194, 195, 221, 225, 226, 229, 241, 242, 255, 264, 320, 322], "ax": [4, 12, 13, 15, 16, 18, 19, 21, 22, 23, 34, 47, 60, 62, 64, 77, 87, 90, 123, 128, 130, 134, 135, 141, 145, 150, 322], "insert": [4, 328], "minu": 5, "1": [5, 10, 11, 12, 14, 15, 17, 18, 19, 20, 21, 22, 23, 32, 34, 40, 47, 48, 61, 65, 74, 86, 88, 91, 95, 98, 99, 104, 119, 124, 137, 143, 144, 149, 159, 162, 163, 167, 174, 176, 177, 178, 179, 180, 181, 182, 183, 184, 186, 187, 188, 189, 193, 194, 195, 197, 198, 199, 222, 225, 226, 229, 233, 239, 242, 244, 245, 246, 247, 248, 249, 250, 251, 253, 254, 255, 257, 260, 261, 262, 263, 264, 265, 266, 267, 268, 270, 271, 273, 274, 275, 280, 281, 283, 284, 285, 287, 290, 293, 295, 296, 297, 298, 299, 300, 301, 302, 304, 307, 308, 309, 310, 311, 312, 313, 320, 321, 322, 323, 325, 326, 327, 328], "exp": [5, 56, 60, 96, 123, 251, 268, 280, 281, 285, 320, 328], "x": [5, 7, 8, 28, 32, 33, 47, 92, 96, 110, 115, 119, 147, 148, 154, 161, 163, 174, 176, 177, 178, 186, 187, 189, 193, 195, 196, 197, 198, 199, 200, 201, 222, 225, 227, 233, 239, 242, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 274, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 293, 295, 302, 320, 321, 322, 323, 324, 325, 326, 328], "greater": [5, 31, 88, 159, 239, 287], "precis": [5, 10, 174, 186, 225, 303, 320], "small": [5, 7, 8, 178, 189, 195, 225, 265, 270, 275, 320, 321, 328], "n": [6, 11, 13, 14, 16, 17, 20, 22, 32, 33, 98, 130, 146, 150, 176, 177, 178, 179, 180, 181, 183, 184, 188, 194, 198, 199, 226, 242, 270, 275, 321], "m": [6, 27, 32, 47, 146, 176, 177, 198, 199, 296, 320], "k": [6, 10, 27, 32, 143, 146, 147, 148, 176, 197, 198, 206], "0": [6, 10, 23, 27, 29, 32, 46, 47, 48, 66, 73, 87, 94, 99, 104, 107, 110, 125, 129, 130, 144, 146, 147, 148, 149, 150, 153, 159, 160, 162, 163, 174, 176, 177, 178, 179, 180, 181, 182, 183, 184, 186, 189, 190, 193, 195, 196, 198, 199, 222, 227, 229, 233, 237, 239, 241, 243, 244, 245, 246, 247, 248, 249, 250, 251, 253, 254, 256, 257, 258, 259, 262, 264, 266, 267, 271, 274, 275, 277, 278, 279, 280, 286, 287, 290, 293, 296, 297, 299, 300, 301, 302, 304, 307, 308, 309, 310, 311, 312, 313, 317, 320, 321, 322, 323, 324, 325, 326, 327], "dtype": [6, 23, 26, 33, 40, 47, 48, 50, 84, 96, 98, 99, 100, 103, 104, 144, 146, 151, 155, 167, 213, 242, 243, 244, 245, 246, 247, 248, 249, 250, 262, 264, 271, 309, 310, 311, 312, 313, 320, 321, 322, 323, 325, 326, 327], "float32": [6, 10, 32, 33, 40, 47, 48, 50, 84, 96, 98, 99, 103, 104, 146, 155, 167, 242, 243, 244, 245, 246, 247, 248, 249, 250, 262, 264, 271, 309, 310, 311, 312, 313, 320, 321, 322, 323, 324, 325, 326, 327], "creat": [6, 33, 132, 174, 293, 295, 311, 320, 323, 325], "ident": [6, 131, 174, 215], "matrix": [6, 27, 28, 33, 45, 46, 47, 48, 49, 61, 65, 91, 92, 98, 223, 224, 248, 290], "gener": [6, 18, 19, 50, 65, 94, 98, 99, 100, 103, 104, 241, 317, 320, 323, 324, 329], "diagon": [6, 144, 146, 147, 148], "number": [6, 28, 29, 33, 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155, 157, 160, 161, 162, 163, 176, 177, 178, 179, 180, 181, 188, 194, 197, 198, 199, 201, 205, 206, 208, 213, 218, 221, 223, 224, 226, 229, 233, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 296, 297, 298, 299, 300, 301, 302, 304, 307, 308, 309, 317, 320, 327, 329], "column": [6, 33, 91], "default": [6, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 27, 28, 29, 33, 35, 45, 46, 47, 48, 49, 50, 51, 60, 62, 64, 65, 73, 74, 77, 84, 88, 90, 91, 92, 94, 95, 96, 98, 99, 100, 102, 103, 104, 107, 108, 110, 117, 118, 124, 125, 128, 129, 130, 132, 134, 136, 141, 143, 144, 145, 146, 147, 148, 149, 150, 153, 155, 157, 167, 176, 177, 178, 179, 180, 181, 187, 188, 190, 193, 194, 196, 197, 198, 199, 201, 206, 208, 213, 215, 218, 221, 222, 223, 224, 226, 229, 233, 237, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 255, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 293, 296, 297, 298, 299, 300, 301, 302, 307, 308, 309, 317, 319, 320, 322, 325, 327, 329], "where": [6, 35, 91, 149, 153, 176, 177, 178, 179, 180, 181, 182, 183, 184, 186, 188, 189, 193, 194, 195, 197, 198, 199, 205, 222, 225, 226, 239, 246, 247, 251, 252, 254, 265, 271, 277, 280, 282, 287, 304, 321, 322, 323], "all": [6, 13, 16, 19, 22, 27, 28, 49, 61, 87, 88, 128, 157, 174, 201, 202, 206, 209, 210, 211, 216, 218, 221, 233, 241, 242, 290, 293, 315, 317, 320, 323, 324, 326, 329], "equal": [6, 31, 35, 44, 83, 88, 100, 125, 193, 197], "zero": [6, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 65, 72, 146, 147, 148, 156, 174, 176, 177, 182, 183, 184, 208, 243, 244, 245, 246, 247, 248, 249, 250, 290, 297, 323], "th": [6, 311], "whose": [6, 157, 158], "valu": [6, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 35, 47, 49, 50, 67, 87, 94, 95, 96, 98, 99, 100, 103, 104, 113, 137, 138, 149, 153, 158, 160, 161, 162, 163, 167, 177, 182, 183, 184, 190, 193, 197, 199, 205, 221, 222, 237, 239, 241, 243, 262, 263, 264, 265, 266, 267, 269, 270, 271, 272, 273, 274, 287, 293, 297, 300, 309, 310, 312, 313, 322], "weight": [7, 8, 161, 174, 208, 212, 223, 224, 262, 264, 293, 297, 300, 302, 304, 308, 322, 324], "bia": [7, 28, 91, 92, 161, 174, 179, 180, 181, 188, 194, 195, 197, 206, 208, 218, 221, 224, 226, 299, 300, 301, 304, 322], "ep": [7, 8, 178, 189, 193, 195, 225, 263, 265, 275, 296, 297, 298, 299, 300, 301, 307], "float": [7, 8, 9, 10, 25, 26, 32, 35, 40, 47, 92, 94, 99, 159, 167, 178, 182, 183, 184, 189, 193, 195, 201, 213, 225, 229, 233, 239, 241, 242, 243, 244, 245, 246, 247, 249, 250, 263, 264, 265, 267, 271, 274, 275, 286, 287, 296, 297, 298, 299, 300, 301, 302, 307, 308, 309, 310, 312, 313], "normal": [7, 8, 98, 103, 174, 176, 177, 178, 189, 193, 195, 198, 199, 225, 241, 244, 246, 325, 328], "respect": [7, 8, 27, 28, 29, 91, 149, 161, 174, 178, 186, 189, 193, 195, 293, 322, 326], "last": [7, 8, 13, 16, 18, 19, 21, 22, 23, 27, 28, 34, 45, 46, 48, 49, 61, 70, 95, 124, 141, 151, 179, 180, 181, 183, 184, 189, 242, 325], "multipl": [7, 8, 27, 28, 61, 80, 91, 92, 221, 233, 310, 311, 313, 320, 324, 327], "scale": [7, 8, 9, 10, 28, 32, 91, 92, 99, 159, 183, 184, 195, 221, 229, 230, 233, 242, 280, 297], "result": [7, 8, 28, 47, 61, 92, 98, 107, 129, 161, 162, 163, 233, 320, 322, 325], "should": [7, 8, 10, 41, 66, 75, 91, 138, 144, 149, 152, 157, 160, 174, 179, 180, 181, 183, 184, 215, 221, 231, 264, 266, 271, 293, 319, 320, 321, 322, 324, 325, 329], "dimension": [7, 8, 11, 12, 13, 14, 15, 16, 20, 21, 22, 176, 177, 178, 179, 180, 181, 185, 197, 198, 199, 223, 224, 233, 323, 325], "same": [7, 8, 17, 20, 21, 22, 28, 29, 35, 41, 87, 95, 110, 151, 152, 154, 162, 174, 177, 178, 182, 189, 193, 199, 223, 243, 244, 245, 246, 247, 248, 249, 250, 264, 275, 293, 303, 317, 320, 321, 323, 328], "set": [7, 9, 67, 73, 74, 117, 118, 132, 186, 195, 197, 204, 206, 213, 214, 215, 218, 219, 224, 229, 239, 263, 275, 287, 293, 297, 304, 317, 322, 324], "happen": [7, 241, 295, 320, 324], "addit": 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177, 186, 198, 199, 229, 242, 253, 254, 265, 267, 275], "unchang": [9, 131, 229], "true": [9, 28, 35, 40, 45, 47, 51, 65, 74, 92, 123, 154, 157, 160, 161, 162, 163, 167, 174, 178, 179, 180, 181, 188, 189, 193, 194, 195, 197, 205, 206, 208, 215, 218, 224, 226, 229, 233, 241, 242, 262, 270, 297], "choos": [9, 229], "implement": [9, 10, 47, 185, 205, 221, 229, 231, 233, 239, 241, 242, 287, 296, 297, 298, 299, 301, 302, 303, 315, 320, 322], "consecut": [9, 91, 229], "angular": [9, 229], "frequenc": [9, 229, 233], "q": [10, 48], "v": [10, 174, 206, 325], "mask": [10, 215, 221, 323], "head": [10, 221, 241], "attent": [10, 206, 221, 233, 241], "o": [10, 194], "softmax": [10, 174, 261, 264], "t": [10, 28, 45, 92, 149, 174, 176, 188, 194, 198, 226, 296, 297, 298, 299, 300, 301, 302, 307, 308, 320, 322, 328], "group": [10, 28, 91, 92, 151, 157, 189, 223, 224, 321], "queri": [10, 221], "note": [10, 18, 19, 28, 35, 47, 68, 91, 95, 151, 157, 174, 225, 242, 325, 327], "regardless": 10, "For": [10, 27, 40, 47, 91, 164, 174, 178, 183, 201, 206, 215, 218, 224, 229, 233, 242, 244, 245, 246, 247, 290, 317, 320, 321, 322, 323, 324, 325, 326, 327, 328], "pre": 10, "tile": 10, "match": [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 68, 208, 242, 264, 321, 323, 325], "kei": [10, 67, 94, 95, 96, 98, 99, 100, 102, 103, 104, 160, 161, 205, 206, 218, 221, 304, 317, 319, 322], "typic": [10, 185, 295, 320, 324], "sqrt": [10, 178, 186, 189, 193, 195, 197, 225, 233, 244, 245, 246, 247, 253, 296, 298, 299, 300, 307, 320], "shape": [10, 11, 14, 17, 20, 21, 22, 26, 27, 41, 46, 61, 84, 85, 94, 95, 96, 98, 99, 100, 103, 104, 108, 138, 151, 152, 154, 155, 156, 174, 176, 177, 178, 179, 180, 181, 183, 184, 188, 193, 194, 197, 198, 199, 208, 226, 243, 244, 245, 246, 247, 248, 249, 250, 264, 275, 295, 320, 322, 323, 326, 328], "score": [10, 271], "union": [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 32, 38, 39, 67, 102, 103, 132, 144], "One": [11, 14, 20, 111, 320, 322], "discret": [11, 12, 13, 14, 15, 16, 20, 21, 22, 185, 223], "fourier": [11, 12, 13, 14, 15, 16, 20, 21, 22], "correspond": [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 60, 62, 77, 90, 134, 141, 153, 161, 322], "truncat": [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 103], "pad": [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 176, 177, 179, 180, 181, 198, 199], "along": [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 27, 28, 32, 47, 107, 123, 125, 129, 137, 138, 141, 142, 143, 144, 151, 174, 187, 226, 255], "dft": [11, 12, 13, 14, 15, 16, 20, 21, 22], "": [12, 13, 15, 16, 18, 19, 21, 22, 29, 47, 49, 51, 64, 86, 91, 95, 110, 113, 114, 130, 132, 149, 150, 151, 153, 158, 174, 177, 188, 194, 199, 205, 206, 208, 212, 213, 214, 218, 226, 295, 304, 305, 317, 320, 322, 324, 325, 326, 327, 328], "2": [12, 15, 17, 18, 19, 20, 21, 22, 23, 32, 40, 45, 46, 47, 48, 49, 55, 61, 91, 98, 102, 141, 144, 146, 147, 148, 159, 163, 167, 174, 176, 177, 180, 186, 196, 198, 199, 225, 233, 242, 243, 244, 245, 246, 247, 248, 249, 250, 253, 264, 265, 267, 274, 275, 290, 293, 296, 298, 299, 300, 304, 307, 320, 321, 322, 323, 324, 325, 326, 327, 328], "two": [12, 15, 21, 27, 28, 30, 31, 35, 43, 44, 45, 46, 48, 49, 56, 61, 63, 78, 80, 83, 86, 135, 163, 177, 187, 194, 199, 255, 263, 320, 321, 322, 323, 328], "case": [13, 16, 17, 19, 20, 21, 22, 23, 45, 46, 48, 49, 61, 108, 128, 177, 183, 199, 239, 256, 274, 280, 286, 287, 303, 304, 320, 322, 326, 327, 328, 329], "over": [13, 16, 19, 22, 34, 47, 49, 50, 60, 62, 64, 77, 88, 90, 111, 123, 124, 130, 134, 141, 143, 150, 178, 179, 180, 181, 189, 195, 225, 264, 309, 312, 321, 322], "len": [13, 16, 19, 22, 32, 311], "rfft": 17, "real": [17, 18, 19, 20, 21, 22, 45], "contain": [17, 18, 19, 27, 28, 47, 57, 58, 59, 91, 125, 154, 159, 174, 205, 207, 208, 214, 241, 271, 290, 293, 320, 321, 322], "rfft2": 18, "complex": [18, 19, 20, 21, 22, 160, 167, 174, 220, 320, 322], "specifi": [18, 19, 26, 29, 47, 50, 79, 84, 95, 107, 135, 137, 138, 141, 144, 145, 149, 153, 155, 178, 239, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 287, 321, 322, 328], "treat": [18, 19, 21, 22, 137, 242, 320], "have": [18, 19, 21, 22, 28, 35, 61, 75, 95, 151, 160, 194, 221, 231, 302, 304, 319, 320, 321, 323, 324, 328], "rfftn": 19, "silent": [20, 21, 22], "cast": [20, 21, 22, 51, 201, 213, 325], "start_axi": 23, "end_axi": 23, "inclus": 23, "neg": [23, 38, 144, 196, 198, 199, 221, 265, 273, 275, 323], "after": [23, 25, 28, 66, 88, 91, 178, 189, 195, 201, 202, 206, 208, 215, 218, 219, 220, 221, 241, 274, 320, 328], "convert": [23, 93, 223, 224, 324, 325, 326], "outsid": 23, "valid": [23, 153, 160, 206, 218, 319], "rang": [23, 27, 50, 245, 247, 253, 254, 295, 309, 310, 311, 312, 313, 317, 320, 322, 324, 328], "clamp": 23, "ndim": [23, 47, 49, 242], "first": [23, 29, 42, 49, 57, 59, 61, 88, 102, 109, 135, 141, 144, 149, 160, 162, 163, 174, 177, 189, 199, 242, 263, 271, 297, 299, 300, 301, 304, 320, 322, 325, 328], "exampl": [23, 47, 48, 132, 137, 159, 162, 163, 174, 176, 177, 178, 193, 198, 199, 206, 208, 215, 218, 242, 243, 244, 245, 246, 247, 248, 249, 250, 262, 264, 271, 290, 295, 304, 309, 310, 311, 312, 313, 317, 322, 323, 324, 325, 326, 327], "mx": [23, 40, 47, 48, 51, 115, 149, 159, 174, 176, 177, 178, 193, 196, 198, 199, 201, 208, 212, 227, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 259, 262, 263, 264, 268, 271, 278, 288, 290, 293, 295, 317, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329], "3": [23, 40, 47, 48, 159, 163, 181, 186, 242, 245, 247, 253, 258, 297, 302, 317, 320, 323, 325, 326], "4": [23, 28, 47, 91, 92, 115, 157, 163, 167, 176, 177, 178, 193, 198, 199, 223, 224, 241, 242, 244, 245, 246, 262, 320, 321, 323, 326, 328], "int32": [23, 40, 47, 100, 167, 242, 323, 326], "scalar": [25, 26, 29, 30, 31, 32, 35, 42, 43, 44, 47, 50, 56, 57, 58, 59, 61, 63, 78, 80, 83, 87, 89, 94, 100, 103, 104, 106, 109, 113, 133, 149, 151, 154, 158, 275, 322, 324, 326], "b": [25, 27, 30, 31, 34, 35, 42, 43, 44, 47, 56, 57, 59, 61, 63, 78, 80, 83, 86, 89, 91, 106, 109, 133, 141, 149, 162, 163, 187, 197, 226, 242, 255, 322, 323, 324, 325, 326, 327, 328], "integ": [25, 27, 28, 40, 47, 67, 87, 91, 92, 94, 100, 125, 141, 153, 167, 185, 213, 311, 323], "divis": [25, 91, 106], "either": [25, 30, 31, 42, 43, 44, 47, 56, 61, 63, 78, 80, 83, 89, 106, 109, 133, 149, 177, 199, 231, 242, 246, 247, 325], "point": [25, 92, 167], "equival": [25, 28, 32, 137, 186, 190, 191, 192, 220, 222, 224, 227, 228, 230, 232, 234, 235, 236, 237, 238, 240], "call": [25, 66, 70, 174, 185, 206, 218, 223, 231, 293, 295, 304, 320, 321, 322, 324], "floor": 25, "divid": [25, 91, 106, 321], "quotient": 25, "val": 26, "construct": [26, 84, 142, 155], "fill": [26, 85, 146, 156, 243, 244, 245, 246, 247, 249, 250], "must": [26, 28, 47, 94, 95, 98, 100, 103, 104, 154, 242, 325], "broadcast": [26, 30, 31, 35, 42, 43, 44, 56, 61, 63, 78, 80, 83, 89, 94, 95, 98, 103, 104, 106, 109, 133, 138, 154, 221], "unspecifi": [26, 60, 62, 64, 77, 84, 88, 90, 107, 123, 124, 130, 134, 137, 143, 144, 150, 155, 329], "lhs_indic": [27, 28], "rhs_indic": [27, 28], "level": [27, 28, 246, 247], "gather": [27, 28], "operand": 27, "indic": [27, 28, 29, 35, 36, 37, 38, 39, 49, 125, 137, 138, 149, 215, 217, 264, 271, 311, 323], "possibli": [27, 61, 159], "batch": [27, 28, 61, 98, 178, 179, 180, 181, 183, 184, 188, 194, 221, 226, 242, 324], "thi": [27, 28, 32, 35, 41, 45, 46, 47, 48, 49, 56, 60, 61, 62, 64, 66, 68, 77, 88, 90, 95, 118, 123, 124, 125, 130, 134, 137, 143, 150, 159, 162, 163, 174, 182, 183, 184, 187, 188, 194, 202, 203, 205, 206, 209, 210, 211, 216, 218, 219, 220, 221, 224, 226, 239, 244, 245, 246, 247, 253, 254, 255, 270, 287, 293, 304, 319, 320, 321, 322, 324, 325, 327], "more": [27, 45, 46, 49, 61, 73, 74, 113, 114, 167, 174, 178, 183, 229, 233, 241, 242, 244, 245, 246, 247, 317, 320, 321, 322, 323, 326, 328], "explicitli": [27, 174, 317], "take": [27, 29, 41, 63, 78, 85, 92, 138, 149, 152, 153, 156, 162, 163, 221, 317, 321, 322, 323, 327, 328, 329], "matmul": [27, 328], "flat": [27, 28, 160, 164], "e": [27, 28, 41, 119, 178, 179, 180, 181, 183, 184, 189, 193, 195, 206, 225, 260, 261, 283, 284, 289, 295, 298, 320, 324, 329], "a1": 27, "a2": 27, "AS": 27, "b1": 27, "b2": 27, "w": [28, 91, 92, 149, 162, 177, 178, 180, 181, 183, 184, 197, 199, 308, 322], "bias": [28, 91, 92, 188, 194, 206, 218, 221], "transpos": [28, 92], "group_siz": [28, 91, 92, 157, 223, 224], "64": [28, 91, 92, 157, 167, 223, 224], "bit": [28, 42, 91, 92, 109, 157, 167, 201, 223, 224, 225], "quantiz": [28, 51, 92, 223, 224], "gather_mm": 28, "similar": [28, 40, 161, 219, 220, 221, 263, 325, 327], "sinc": [28, 70, 293, 302, 311, 325, 328], "thei": [28, 35, 231, 266, 293, 302, 319, 320, 321, 324, 326, 327, 328], "repres": [28, 271, 275, 325], "pack": [28, 91, 92], "unsign": [28, 91, 92, 167], "per": [28, 91, 92, 157, 178, 189, 193, 195, 225, 315, 320, 321, 324], "defin": [28, 47, 92, 157, 160, 325], "whether": [28, 92, 188, 194, 205, 221, 226, 262, 265, 271], "multipli": [28, 91, 92, 182, 233, 242], "name": [28, 51, 91, 92, 113, 114, 115, 116, 174, 189, 205, 208, 210, 321, 323, 327], "we": [28, 91, 92, 174, 185, 223, 231, 300, 302, 317, 319, 320, 321, 322, 324, 328], "occupi": [28, 91, 92], "fun": [29, 41, 149, 152, 153, 320, 323, 324, 328], "callabl": [29, 41, 149, 152, 153, 157, 158, 160, 161, 162, 163, 201, 202, 205, 213, 226, 231, 241, 243, 244, 245, 246, 247, 248, 249, 250, 296, 297, 298, 299, 300, 301, 302, 307, 308, 309, 310, 311, 312, 313], "argnum": [29, 149, 322], "argnam": [29, 149], "str": [29, 47, 51, 65, 67, 75, 112, 113, 114, 115, 116, 149, 160, 164, 201, 202, 205, 206, 208, 210, 212, 218, 242, 246, 247, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275], "gradient": [29, 131, 149, 158, 159, 174, 206, 219, 224, 241, 270, 293, 295, 296, 297, 299, 300, 301, 302, 303, 306, 308, 320, 321, 322, 323, 324, 325, 326], "variabl": [29, 41, 149, 152, 153, 321], "neither": [29, 149], "nor": [29, 149], "provid": [29, 141, 149, 161, 163, 169, 174, 201, 206, 208, 218, 219, 220, 223, 224, 241, 242, 289, 293, 321, 327, 329], "keyword": [29, 115, 116, 149, 161, 174, 317, 327, 329], "It": [29, 118, 149, 159, 163, 174, 220, 224, 303, 315, 325, 327], "so": [29, 149, 182, 242, 295, 320, 321, 324, 328], "strict": [30, 43, 206, 208, 218], "style": [30, 31, 35, 42, 43, 44, 56, 61, 63, 78, 80, 83, 89, 106, 109, 133], "semant": [30, 31, 42, 43, 44, 56, 61, 63, 78, 80, 83, 89, 106, 109, 133, 328], "both": [30, 31, 40, 42, 43, 44, 47, 56, 63, 78, 80, 83, 89, 95, 106, 109, 133, 157, 176, 177, 193, 194, 198, 199, 295, 320, 321, 322, 326, 328], "comparison": [30, 31, 43, 44, 83], "walsh": 32, "hadamard": 32, "final": [32, 309, 312], "scipi": 32, "linalg": 32, "import": [32, 47, 115, 149, 160, 161, 162, 163, 164, 174, 176, 177, 178, 193, 198, 199, 208, 242, 262, 264, 271, 290, 293, 320, 321, 322, 323, 324, 325, 326], "y": [32, 154, 174, 178, 183, 189, 193, 195, 197, 225, 266, 271, 274, 295, 298, 320, 321, 322, 324, 325], "12": [32, 311], "20": [32, 47], "28": 32, "8192": 32, "16384": 32, "float16": [32, 51, 167, 201, 324, 325], "bfloat16": [32, 167, 325], "factor": [32, 45, 48, 242, 264, 310, 313], "ordinari": 34, "product": [34, 41, 61, 86, 90, 141, 152, 221, 326], "d": [34, 47, 61, 65, 86, 137, 144, 146, 147, 148, 164, 181, 184, 188, 194, 226, 296, 299, 301, 328], "higher": [34, 271, 322], "sum": [34, 47, 60, 123, 141, 144, 174, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 321, 323, 325], "rtol": 35, "1e": [35, 178, 189, 193, 195, 196, 225, 263, 265, 275, 296, 297, 298, 299, 300, 301, 304, 307, 309, 310, 311, 312, 313], "05": [35, 178, 189, 193, 195, 225], "atol": 35, "08": [35, 263, 298, 299, 300, 301, 307], "equal_nan": 35, "fals": [35, 40, 45, 47, 51, 60, 62, 64, 65, 74, 77, 90, 130, 134, 150, 154, 157, 160, 161, 162, 163, 167, 189, 193, 195, 197, 206, 208, 218, 221, 224, 229, 233, 241, 242, 262, 265, 297, 308, 325], "boolean": [35, 36, 37, 38, 39, 57, 58, 59, 167, 217, 323], "within": 35, "toler": 35, "infinit": 35, "consid": [35, 160, 161, 162, 189, 319], "sign": [35, 167, 302], "nan": [35, 37], "unless": [35, 47, 293], "ab": [35, 47, 149, 189, 193, 195, 200, 225, 254, 276, 320], "unlik": [35, 183, 184, 214], "array_equ": 35, "rel": [35, 297, 320], "absolut": [35, 253, 254, 274], "inifn": 36, "infin": [36, 38, 39, 198, 199, 301], "dtypecategori": [40, 167], "check": [40, 71, 208, 322, 323], "subtyp": [40, 167], "anoth": [40, 61, 133, 154, 167, 174, 201, 320, 322, 323, 328], "subdtyp": 40, "float64": 40, "conveni": 40, "object": [40, 115, 153, 160, 161, 162, 163, 167, 183, 241, 319], "allow": [40, 159, 174, 220, 293, 315, 321, 323, 326], "too": [40, 320, 324], "inexact": 40, "signedinteg": 40, "primal": [41, 152], "tangent": [41, 139, 140, 240, 288], "jacobian": [41, 152, 326], "shift": [42, 109, 178], "second": [42, 57, 59, 61, 109, 135, 144, 149, 177, 199, 263, 271, 297, 299, 300, 301, 322, 328], "bitwis": [42, 109], "less": [44, 88, 229, 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