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141, 210, 216, 218, 222, 231, 236, 243, 246, 251, 254, 258, 263, 264, 265, 266, 294, 300, 304, 305, 306, 307, 308, 309], "you": [1, 3, 4, 5, 6, 216, 258, 261, 294, 300, 303, 304, 306, 308, 309], "design": [1, 2, 5, 300, 309], "your": [1, 3, 6, 297, 303, 305], "own": [1, 6, 306], "link": [1, 6], "top": [1, 229], "core": [1, 2, 3, 4, 216, 218, 227, 238, 241, 244, 262, 263, 264, 265, 266, 267, 268, 269, 273, 275, 294, 297, 299, 306, 307], "we": [1, 2, 3, 4, 72, 141, 142, 201, 203, 216, 224, 256, 300, 302, 303, 305, 309], "inner": 1, "work": [1, 3, 6, 303, 304, 305], "go": [1, 3, 303], "over": [1, 3, 4, 12, 14, 22, 23, 24, 25, 65, 66, 86, 89, 92, 95, 104, 112, 114, 124, 126, 128, 129, 139, 140, 157, 169, 170, 178, 184, 190, 218, 219, 220, 226, 228, 252, 275, 303], "simpl": [1, 3, 4, 216, 224, 293, 303, 305], "learn": [1, 2, 4, 5, 197, 198, 199, 200, 201, 202, 203, 206, 207, 218, 226, 227, 228, 250, 252], "step": [1, 3, 4, 15, 198, 216], "involv": [1, 299], "ad": [1, 2, 6, 197, 198, 199, 200, 201, 202, 206, 227, 297, 305, 308], "let": [1, 2, 3, 303, 305, 306], "s": [1, 2, 3, 4, 35, 44, 72, 85, 86, 88, 89, 91, 92, 94, 95, 100, 112, 115, 128, 137, 141, 144, 156, 159, 160, 189, 190, 192, 196, 204, 216, 235, 236, 238, 242, 246, 299, 300, 303, 305, 306, 307, 308, 309], "sai": [1, 3, 294, 305], "would": [1, 3, 304, 305, 306, 309], "like": [1, 3, 5, 136, 195, 223, 281, 303, 305, 306, 307, 309], "an": [1, 3, 4, 6, 8, 12, 14, 26, 61, 65, 66, 80, 83, 96, 99, 103, 112, 115, 126, 129, 131, 135, 136, 138, 140, 141, 142, 154, 155, 156, 171, 174, 179, 180, 181, 184, 186, 192, 194, 195, 197, 204, 205, 208, 209, 216, 221, 226, 228, 229, 231, 249, 250, 251, 261, 262, 263, 264, 265, 266, 267, 268, 269, 271, 287, 294, 300, 302, 303, 304, 305, 306, 307, 308, 309, 310], "take": [1, 3, 4, 100, 109, 127, 130, 136, 142, 181, 189, 191, 192, 195, 249, 300, 303, 304, 308, 309, 310], "two": [1, 11, 13, 60, 74, 75, 77, 85, 88, 94, 101, 102, 110, 111, 113, 120, 125, 127, 130, 132, 137, 179, 251, 274, 303, 304, 309], "arrai": [1, 3, 4, 5, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 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, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 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, 194, 195, 216, 218, 231, 238, 241, 244, 250, 262, 263, 264, 265, 266, 267, 268, 269, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 292, 294, 297, 303, 305, 306, 307, 309], "x": [1, 2, 3, 4, 78, 103, 112, 142, 145, 156, 161, 165, 187, 188, 193, 203, 209, 216, 218, 225, 226, 227, 228, 229, 230, 231, 250, 252, 253, 255, 257, 258, 260, 270, 271, 272, 284, 286, 287, 288, 289, 290, 291, 292, 297, 299, 303, 304, 305, 306, 307, 309], "y": [1, 2, 3, 4, 193, 199, 216, 218, 222, 226, 227, 228, 229, 252, 277, 284, 299, 303, 305, 306], "scale": [1, 3, 72, 141, 142, 198, 222, 223, 249, 254, 255, 258, 289], "them": [1, 3, 216, 236, 246, 309], "both": [1, 11, 75, 76, 77, 101, 102, 110, 111, 112, 120, 127, 130, 132, 144, 177, 227, 299, 303, 307, 309], "some": [1, 2, 3, 4, 236, 246, 303, 305], "coeffici": [1, 197, 198, 200, 201, 202, 203], "alpha": [1, 141, 201, 206, 255, 285, 287, 289], "beta": [1, 72, 141, 200, 201, 202, 203, 218, 226, 227, 228, 284], "respect": [1, 2, 4, 100, 141, 189, 209, 216, 218, 225, 226, 227, 228, 297, 303, 307], "togeth": [1, 4, 141, 209], "get": [1, 2, 4, 6, 66, 146, 205, 216, 303, 305, 309], "z": [1, 305], "well": [1, 3, 216, 236, 246, 249, 305], "veri": [1, 3, 249, 305, 309], "easili": 1, "do": [1, 3, 6, 201, 216, 237, 246, 294, 297, 303, 305], "just": [1, 4, 304], "write": [1, 3, 216, 306], "out": [1, 6, 222, 223, 243, 303, 304], "follow": [1, 3, 4, 5, 6, 15, 67, 72, 112, 141, 197, 198, 199, 200, 201, 202, 203, 207, 216, 271, 272, 279, 300, 303, 309], "import": [1, 2, 3, 4, 6, 112, 161, 189, 208, 209, 210, 216, 218, 227, 238, 273, 275, 294, 297, 303, 304, 305, 306, 307], "mx": [1, 2, 3, 4, 96, 112, 113, 115, 161, 189, 216, 218, 227, 231, 238, 242, 253, 262, 263, 264, 265, 266, 267, 268, 269, 273, 274, 275, 279, 288, 294, 297, 299, 300, 303, 304, 305, 306, 307, 308, 309, 310], "def": [1, 2, 3, 4, 189, 216, 297, 303, 304, 305, 306, 309], "simple_axpbi": 1, "float": [1, 13, 15, 57, 98, 99, 112, 142, 143, 148, 151, 152, 197, 198, 199, 200, 201, 202, 203, 206, 207, 212, 218, 221, 222, 223, 226, 227, 228, 231, 252, 254, 258, 260, 261, 262, 263, 264, 265, 266, 268, 269, 274, 275, 276, 278, 284, 285, 291, 292], "return": [1, 2, 3, 4, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 33, 37, 50, 57, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 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, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 157, 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, 194, 195, 196, 208, 209, 210, 216, 233, 235, 237, 239, 240, 241, 244, 251, 262, 263, 264, 265, 266, 267, 268, 269, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 294, 297, 302, 303, 304, 305, 306, 308, 309], "thi": [1, 3, 4, 6, 12, 13, 14, 15, 22, 23, 24, 25, 109, 112, 113, 120, 124, 125, 126, 128, 129, 139, 140, 144, 169, 170, 171, 178, 180, 190, 216, 221, 222, 223, 232, 233, 235, 236, 239, 240, 241, 244, 246, 247, 248, 249, 251, 260, 263, 264, 265, 266, 271, 272, 281, 292, 297, 302, 303, 305, 306, 308], "perform": [1, 3, 5, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 125, 142, 156, 169, 180, 216, 226, 261, 265, 266, 304, 305, 309], "leav": [1, 209], "differenti": [1, 5], "howev": [1, 216, 225, 226, 300, 305, 306], "vector": [1, 2, 5, 104, 109, 112, 180, 191, 192, 224, 275, 307], "math": [1, 3, 285], "often": [1, 223], "realiz": 1, "axpbi": 1, "routin": 1, "defin": [1, 2, 3, 4, 6, 112, 142, 205, 208, 306], "same": [1, 3, 6, 13, 60, 61, 66, 67, 90, 93, 94, 95, 100, 109, 138, 144, 156, 191, 193, 216, 218, 221, 226, 227, 251, 262, 263, 264, 265, 266, 267, 268, 269, 275, 285, 297, 300, 304, 309], "realli": 1, "part": [1, 303, 304], "doe": [1, 3, 6, 216, 304, 305, 306], "fast": [1, 225, 272, 309], "so": [1, 3, 6, 100, 189, 221, 299, 305, 309], "decid": [1, 209, 235], "want": [1, 3, 303, 309], "reli": 1, "acceler": [1, 218], "framework": [1, 5], "continu": [1, 303], "impos": 1, "our": [1, 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122, 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, 150, 151, 152, 153, 154, 155, 159, 160, 165, 166, 167, 168, 169, 170, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 212, 218, 219, 220, 221, 222, 223, 224, 226, 227, 228, 229, 232, 238, 242, 247, 248, 249, 251, 252, 254, 256, 258, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 292, 294, 297, 299, 303, 304, 305, 306, 307, 308, 309, 310], "structur": [1, 303], "from": [1, 3, 4, 5, 72, 74, 91, 92, 94, 95, 99, 112, 115, 125, 136, 141, 143, 144, 145, 146, 148, 151, 161, 174, 176, 177, 180, 181, 193, 195, 208, 209, 210, 216, 229, 236, 238, 249, 263, 264, 265, 266, 268, 269, 276, 284, 294, 302, 303, 305, 306, 307, 308, 309], "frontend": 1, "api": [1, 303], "redirect": 1, "when": [1, 3, 5, 6, 112, 115, 219, 220, 265, 266, 279, 284, 297, 300, 309], "appropri": 1, "fallback": 1, "metal": 1, "vjp": [1, 307], "jvp": [1, 307], "In": [1, 3, 4, 125, 141, 197, 199, 200, 202, 203, 209, 216, 222, 226, 297, 302, 303, 305, 308, 309], "one": [1, 3, 6, 57, 63, 66, 82, 83, 112, 118, 125, 142, 144, 174, 177, 246, 275, 309], "sentenc": 1, "comput": [1, 2, 3, 4, 5, 6, 72, 100, 109, 112, 120, 128, 137, 141, 169, 176, 184, 189, 190, 191, 196, 197, 198, 200, 201, 202, 203, 216, 218, 226, 227, 228, 236, 247, 251, 252, 254, 261, 263, 264, 265, 266, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 299, 303, 307, 309], "graph": [1, 3, 4, 5, 303], "rule": 1, "evalu": [1, 3, 4, 5, 80, 109, 191, 216, 234, 243, 297, 299, 307], "said": [1, 3], "start": [1, 2, 3, 5, 6, 15, 114, 171, 304, 309], "discuss": 1, "more": [1, 4, 8, 57, 74, 125, 159, 160, 216, 218, 222, 254, 258, 261, 263, 264, 265, 266, 300, 303, 304, 307, 309], "detail": [1, 8, 197, 199, 200, 202, 203, 216, 222, 254, 258, 263, 264, 265, 266, 304, 307], "thei": [1, 2, 3, 13, 67, 203, 256, 277, 297, 302, 305, 307, 308, 309], "c": [1, 3, 112, 212, 218, 219, 220, 222, 223, 227, 306, 307, 309], "scalar": [1, 11, 13, 26, 37, 57, 60, 61, 63, 75, 76, 77, 98, 99, 100, 101, 102, 110, 111, 112, 114, 120, 121, 122, 123, 125, 127, 130, 132, 138, 148, 151, 152, 159, 177, 189, 193, 196, 285, 303, 305, 307], "sum": [1, 2, 11, 104, 112, 124, 169, 184, 216, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 304, 306], "element": [1, 10, 11, 16, 17, 18, 19, 20, 21, 24, 52, 62, 68, 69, 72, 75, 76, 77, 78, 79, 81, 83, 97, 98, 101, 102, 105, 106, 107, 108, 110, 111, 116, 117, 118, 119, 120, 121, 122, 123, 127, 130, 132, 133, 139, 141, 142, 153, 154, 157, 165, 166, 167, 168, 172, 173, 177, 180, 182, 183, 189, 193, 221, 222, 223, 230, 250, 254, 257, 286, 287, 290, 303], "wise": [1, 10, 11, 16, 17, 18, 19, 20, 21, 62, 68, 69, 75, 76, 77, 78, 79, 81, 97, 98, 101, 102, 110, 111, 116, 117, 118, 119, 120, 121, 122, 123, 127, 130, 132, 133, 153, 157, 165, 166, 167, 168, 172, 173, 177, 182, 183, 222, 223, 230, 250, 257, 286, 287, 290], "numpi": [1, 3, 4, 5, 11, 13, 15, 61, 75, 76, 77, 101, 102, 110, 111, 120, 125, 127, 130, 132, 177, 305, 307, 308], "style": [1, 11, 13, 75, 76, 77, 101, 102, 110, 111, 120, 125, 127, 130, 132, 177], "broadcast": [1, 11, 13, 61, 63, 75, 76, 77, 99, 101, 102, 110, 111, 120, 125, 127, 130, 132, 143, 144, 151, 152, 177, 181, 193, 249], "between": [1, 5, 63, 96, 261, 274, 277, 278, 281, 305, 309], "input": [1, 2, 3, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 73, 74, 75, 76, 77, 78, 79, 81, 82, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 100, 101, 102, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 136, 137, 138, 139, 140, 141, 142, 150, 153, 154, 155, 156, 157, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 187, 188, 189, 190, 192, 193, 195, 218, 219, 220, 222, 223, 224, 226, 227, 228, 229, 249, 251, 252, 254, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 273, 274, 276, 277, 278, 279, 281, 283, 285, 292, 294, 303, 304, 307, 308], "upcast": 1, "const": [1, 276], "factor": [1, 113, 275], "streamordevic": 1, "stream": [1, 5, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28, 29, 30, 31, 32, 33, 34, 36, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 51, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 106, 107, 108, 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, 147, 148, 150, 151, 152, 153, 154, 155, 156, 157, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 190, 193, 194, 195, 309], "schedul": [1, 309], "itself": 1, "call": [1, 3, 4, 27, 98, 216, 224, 236, 246, 256, 297, 299, 303, 305], "other": [1, 3, 5, 112, 203, 216, 237, 297, 304, 305, 307], "within": [1, 24], "simplest": [1, 216], "wai": [1, 3, 6, 216, 303, 304], "about": [1, 3, 4, 305, 309], "term": [1, 197, 198, 199, 200, 201, 202, 206, 276], "exist": [1, 3, 236, 246], "auto": [1, 6], "ax": [1, 12, 14, 22, 23, 58, 82, 85, 86, 88, 89, 91, 92, 94, 95, 96, 104, 112, 124, 126, 128, 129, 138, 140, 169, 174, 178, 179, 184, 185, 190, 303], "multipli": [1, 141, 142, 221, 258], "earlier": 1, "goal": 1, "themselv": 1, "contain": [1, 3, 24, 25, 50, 74, 90, 91, 92, 112, 121, 122, 123, 141, 171, 193, 216, 235, 237, 238, 261, 294, 297, 303], "act": [1, 281], "data": [1, 4, 5, 8, 15, 83, 93, 94, 99, 103, 114, 135, 151, 186, 194, 223, 262, 263, 264, 265, 266, 267, 268, 269, 304, 306], "nor": [1, 100, 189], "rather": [1, 303, 309], "easi": [1, 216], "interfac": 1, "block": [1, 3, 261], "A": [1, 3, 5, 6, 50, 60, 100, 109, 112, 113, 115, 124, 125, 141, 143, 144, 145, 147, 148, 151, 152, 171, 175, 189, 191, 192, 196, 200, 202, 208, 209, 210, 216, 218, 222, 226, 227, 228, 230, 235, 239, 240, 247, 248, 252, 256, 258, 261, 263, 264, 266, 272, 285, 286, 297, 299, 303, 305, 306], "It": [1, 3, 6, 100, 189, 204, 216, 248, 251, 306, 308], "creat": [1, 3, 6, 83, 103, 216, 297, 299, 304, 306], "output": [1, 3, 6, 12, 13, 14, 15, 24, 61, 83, 90, 93, 94, 95, 99, 100, 103, 112, 114, 124, 126, 128, 129, 135, 136, 139, 140, 143, 144, 145, 147, 148, 151, 152, 161, 162, 169, 174, 178, 181, 186, 189, 190, 191, 192, 193, 194, 195, 218, 219, 220, 227, 229, 249, 251, 260, 261, 263, 264, 265, 266, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 292, 294, 303, 304, 305, 306, 307, 308, 309], "given": [1, 12, 14, 24, 61, 63, 64, 72, 74, 80, 82, 84, 85, 86, 87, 88, 89, 93, 94, 95, 99, 112, 124, 126, 128, 129, 140, 148, 156, 169, 171, 178, 186, 187, 188, 190, 221, 235, 249, 274, 276], "set": [1, 3, 4, 6, 198, 205, 225, 229, 234, 236, 243, 246, 247, 251, 254, 260, 274, 285, 292, 297, 300, 303, 305], "further": [1, 6, 303], "class": [1, 3, 4, 7, 8, 9, 26, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 297], "under": [1, 112], "These": [1, 181, 275, 309], "word": 1, "bit": [1, 72, 141, 142, 212, 231, 251], "abstract": 1, "back": [1, 3, 306], "give": [1, 3, 4, 24], "ourselv": 1, "concret": [1, 229, 305, 309], "imag": [1, 220, 222, 223], "public": [1, 216], "explicit": [1, 300, 306], "alpha_": 1, "beta_": 1, "must": [1, 6, 63, 80, 99, 112, 143, 144, 148, 151, 152, 193, 306], "know": [1, 3], "popul": 1, "To": [1, 2, 3, 4, 6, 216, 294, 303, 307], "avoid": 1, "unnecessari": [1, 3], "alloc": [1, 297], "respons": 1, "space": [1, 114, 283], "void": 1, "eval_cpu": 1, "std": [1, 268], "overrid": 1, "eval_gpu": 1, "jacobian": [1, 109, 191, 307], "product": [1, 104, 109, 125, 137, 140, 184, 191, 249, 307], "primal": [1, 109, 191], "tangent": [1, 20, 21, 109, 182, 183], "int": [1, 3, 4, 7, 9, 12, 14, 15, 22, 23, 24, 25, 29, 30, 31, 32, 40, 41, 42, 43, 45, 48, 50, 53, 56, 57, 59, 61, 64, 65, 66, 72, 73, 74, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 99, 100, 103, 112, 114, 124, 126, 128, 129, 131, 135, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 154, 155, 156, 169, 170, 171, 174, 175, 178, 179, 180, 181, 184, 185, 186, 187, 188, 189, 190, 192, 194, 216, 218, 219, 220, 224, 226, 227, 228, 229, 249, 251, 252, 254, 258, 261, 274, 275, 279, 283, 285, 297], "argnum": [1, 100, 189, 303], "cotan": 1, "across": [1, 226], "pair": [1, 138, 238, 254], "repres": [1, 3, 285, 306], "axi": [1, 3, 4, 12, 14, 22, 23, 24, 25, 29, 30, 31, 32, 40, 41, 42, 43, 45, 53, 56, 59, 64, 74, 82, 84, 87, 90, 91, 92, 93, 94, 95, 96, 112, 124, 126, 128, 129, 131, 138, 139, 140, 144, 154, 169, 170, 171, 174, 175, 178, 179, 180, 181, 185, 190, 192, 274, 275, 279, 283, 285, 304], "correspond": [1, 12, 14, 57, 63, 72, 74, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 124, 126, 129, 140, 178, 184, 192, 209, 303], "dimens": [1, 3, 12, 14, 22, 23, 44, 50, 57, 66, 74, 82, 91, 92, 94, 95, 96, 104, 112, 113, 124, 125, 126, 128, 129, 140, 141, 144, 150, 178, 181, 184, 185, 190, 218, 219, 220, 222, 223, 226, 227, 228, 249, 252, 254, 261, 275, 303], "vmap": [1, 303, 305, 307], "print": [1, 2, 3, 4, 6, 208, 209, 210, 216, 300, 303, 304, 305, 306, 307], "ostream": 1, "os": [1, 6], "equival": [1, 27, 47, 58, 76, 98, 180, 225, 248, 250, 251, 259], "check": [1, 6, 60, 238, 303, 304], "bool": [1, 12, 13, 14, 22, 23, 29, 30, 31, 32, 40, 41, 42, 43, 45, 56, 57, 59, 60, 112, 115, 124, 126, 128, 129, 140, 142, 143, 148, 151, 152, 178, 190, 198, 207, 218, 219, 220, 226, 227, 228, 229, 231, 235, 236, 238, 243, 246, 249, 251, 254, 258, 261, 273, 276], "is_equival": 1, "privat": 1, "fall": 1, "eval": [1, 2, 3, 4, 216, 297, 299, 303, 305, 307], "deriv": [1, 303, 305], "base": [1, 112, 117, 119, 202, 204, 254, 261, 297, 299, 300, 304], "abov": [1, 3, 6, 141, 187, 201, 216, 303, 304, 305, 309], "demonstr": [1, 306], "treat": [1, 91, 92, 94, 95, 180], "paramet": [1, 2, 3, 4, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 33, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 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, 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, 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, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 206, 207, 208, 209, 210, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 232, 235, 236, 238, 243, 246, 247, 248, 249, 250, 251, 252, 254, 256, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 292, 293, 294, 297, 299, 303, 305], "produc": [1, 249, 294], "through": [1, 176, 203, 261, 303, 306], "construct": [1, 4, 73, 99, 135, 194], "its": [1, 6, 125, 139, 150, 186, 196, 200, 201, 202, 210, 216, 251, 306, 309], "type": [1, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 33, 50, 57, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 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, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 157, 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, 194, 195, 204, 208, 216, 254, 261, 262, 263, 264, 265, 266, 267, 268, 269, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 304], "shape": [1, 3, 4, 47, 60, 61, 65, 66, 74, 84, 87, 90, 93, 94, 95, 99, 109, 125, 135, 136, 143, 144, 145, 147, 148, 151, 152, 155, 181, 191, 193, 194, 195, 216, 218, 219, 220, 222, 223, 227, 229, 238, 262, 263, 264, 265, 266, 267, 268, 269, 275, 285, 299, 303, 304, 307, 309], "pass": [1, 3, 4, 47, 58, 137, 138, 189, 196, 208, 209, 216, 236, 246, 247, 248, 251, 256, 305], "re": [1, 4, 6, 294], "now": [1, 3, 6, 251, 306], "promot": 1, "dtype": [1, 3, 15, 26, 33, 57, 83, 96, 99, 103, 112, 113, 114, 135, 145, 147, 148, 151, 152, 186, 194, 212, 262, 263, 264, 265, 266, 267, 268, 269, 273, 275, 303, 304, 306, 307, 308], "promoted_dtyp": 1, "promote_typ": 1, "float32": [1, 15, 83, 103, 112, 113, 114, 135, 145, 147, 151, 152, 186, 194, 212, 262, 263, 264, 265, 266, 267, 268, 269, 273, 275, 303, 304, 305, 306, 307, 308], "non": [1, 6, 230, 244, 286, 297], "point": [1, 2, 3, 6, 98, 142, 212], "out_dtyp": 1, "is_floating_point": 1, "cast": [1, 33, 93, 94, 95, 115, 231, 306], "up": [1, 3, 251], "determin": [1, 74, 242, 308], "x_cast": 1, "astyp": [1, 3, 231, 306], "y_cast": 1, "broadcasted_input": 1, "broadcast_arrai": 1, "out_shap": 1, "0": [1, 2, 3, 4, 6, 7, 15, 48, 53, 59, 64, 65, 66, 73, 74, 83, 96, 100, 112, 113, 138, 143, 152, 154, 156, 171, 175, 186, 187, 188, 189, 190, 192, 197, 198, 200, 201, 202, 203, 206, 207, 208, 216, 218, 219, 220, 221, 222, 223, 225, 226, 227, 228, 250, 253, 254, 255, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 271, 272, 273, 275, 277, 278, 284, 285, 287, 288, 289, 291, 292, 294, 297, 300, 303, 304, 305, 306, 307, 308], "unique_ptr": 1, "make_uniqu": 1, "to_stream": 1, "handl": [1, 216], "resolv": 1, "No": [1, 3], "happen": [1, 3, 261, 299, 305], "alon": [1, 306], "effect": [1, 222, 305], "onli": [1, 3, 5, 6, 60, 65, 66, 112, 141, 212, 216, 235, 236, 238, 243, 246, 247, 248, 297, 303, 308, 309], "execut": [1, 6, 306, 309], "depend": [1, 2, 57, 112, 304, 308, 309], "devic": [1, 5, 6, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 28, 29, 30, 31, 32, 33, 34, 36, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 51, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 106, 107, 108, 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, 147, 148, 150, 151, 152, 153, 154, 155, 156, 157, 163, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 190, 193, 194, 195, 309, 310], "specifi": [1, 15, 33, 66, 74, 91, 92, 99, 100, 112, 114, 131, 135, 144, 154, 179, 180, 181, 184, 185, 189, 192, 194, 218, 260, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 292, 303, 309], "memori": [1, 5, 198, 261, 297, 305, 306], "ha": [1, 3, 4, 5, 57, 74, 90, 91, 93, 94, 95, 100, 144, 218, 229, 297, 299, 304, 305, 307, 309], "been": [1, 3, 305], "try": [1, 6], "naiv": [1, 303], "gener": [1, 2, 15, 83, 91, 92, 114, 143, 147, 148, 151, 152, 261, 300, 304, 305, 310], "version": [1, 6, 72, 120, 124, 141, 169, 192, 300, 303, 304], "declar": 1, "member": [1, 216, 241, 244], "method": [1, 3, 7, 8, 9, 26, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 216, 242, 297], "each": [1, 50, 72, 80, 125, 138, 141, 142, 144, 154, 161, 162, 171, 185, 192, 193, 222, 223, 224, 226, 254, 261, 275, 300, 305], "find": [1, 2, 6], "pointwis": 1, "captur": [1, 216], "templat": 1, "axpby_impl": 1, "typenam": 1, "t": [1, 3, 78, 142, 189, 197, 198, 199, 200, 201, 202, 203, 206, 207, 216, 303, 309], "readi": 1, "fill": [1, 99, 136, 186, 195, 262, 263, 264, 265, 266, 268, 269], "malloc_or_wait": 1, "synchron": 1, "avail": [1, 2, 3, 4, 6, 8, 212, 309], "There": [1, 216], "wait": [1, 3], "here": [1, 3, 303, 305, 308, 309], "request": 1, "pressur": 1, "condit": [1, 193, 309], "set_data": 1, "nbyte": 1, "collect": [1, 205, 209, 302], "pointer": 1, "x_ptr": 1, "y_ptr": 1, "out_ptr": 1, "relev": 1, "static_cast": 1, "size_t": 1, "out_idx": 1, "size": [1, 3, 4, 50, 66, 72, 82, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 99, 103, 112, 141, 142, 144, 155, 171, 174, 198, 216, 219, 220, 224, 227, 251, 305, 306], "map": [1, 4, 115, 209, 224, 231], "linear": [1, 3, 4, 5, 209, 216, 225, 238, 251, 253, 255, 257, 270, 271, 272, 288, 289, 290, 294, 297], "indic": [1, 13, 22, 23, 24, 25, 100, 105, 106, 107, 108, 171, 180, 181, 189, 243, 245, 275, 304], "offset": [1, 3, 74], "x_offset": 1, "elem_to_loc": 1, "stride": [1, 65, 66, 219, 220, 254, 304], "y_offset": 1, "contigu": 1, "regularli": 1, "default": [1, 6, 12, 13, 14, 15, 22, 23, 24, 25, 60, 64, 65, 66, 72, 73, 74, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 100, 103, 112, 113, 114, 115, 124, 126, 128, 129, 135, 139, 140, 141, 142, 143, 144, 145, 147, 148, 150, 151, 152, 154, 155, 156, 170, 171, 174, 175, 178, 184, 185, 186, 187, 188, 189, 190, 192, 194, 197, 198, 199, 200, 201, 202, 203, 205, 206, 207, 212, 218, 219, 220, 227, 229, 231, 236, 238, 243, 246, 249, 250, 251, 254, 258, 259, 261, 262, 263, 264, 265, 266, 267, 268, 269, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 297, 300, 302, 303, 306, 308, 310], "row": [1, 83, 103, 141, 186], "major": 1, "henc": [1, 141], "doesn": [1, 216], "addit": [1, 3, 11, 115, 218, 226, 228, 249, 252, 297, 303], "abl": [1, 141], "all": [1, 4, 6, 13, 24, 66, 80, 83, 86, 89, 92, 95, 125, 138, 139, 174, 204, 216, 231, 232, 236, 239, 240, 241, 244, 246, 249, 251, 258, 261, 294, 297, 300, 304, 305, 307, 310], "incom": 1, "accordingli": 1, "dispatch": 1, "float16": [1, 115, 212, 231, 305, 306], "bfloat16": [1, 306], "complex64": 1, "throw": 1, "error": [1, 6, 78, 79, 171, 225, 251, 270, 271, 272, 281, 282, 303, 306], "encount": [1, 303], "unexpect": [1, 15], "regist": [1, 4], "op": [1, 137, 236, 305], "assert": 1, "2": [1, 2, 3, 4, 66, 73, 74, 78, 85, 88, 90, 91, 92, 93, 94, 95, 96, 112, 113, 119, 125, 141, 150, 184, 186, 187, 188, 197, 199, 200, 201, 206, 212, 216, 220, 225, 252, 258, 262, 263, 264, 265, 266, 267, 268, 269, 271, 275, 276, 278, 284, 285, 294, 297, 303, 304, 305, 306, 307, 308, 309], "1": [1, 3, 4, 15, 24, 25, 65, 66, 73, 74, 84, 85, 87, 88, 90, 91, 92, 93, 94, 95, 96, 104, 112, 113, 125, 137, 139, 141, 144, 152, 165, 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1, "transpos": [1, 3, 27, 142], "aren": 1, "guarante": 1, "fit": [1, 141, 309], "requir": [1, 3, 216, 305, 306], "column": [1, 83, 103, 141], "inplac": 1, "expect": [1, 3, 219, 220, 221, 222, 223, 258, 261, 276, 304], "answer": 1, "copi": [1, 3, 5, 139, 170, 306], "simpli": [1, 3, 6, 253, 288, 297, 303], "catlas_saxpbi": 1, "axpby_impl_acceler": 1, "first": [1, 2, 3, 4, 6, 74, 96, 100, 121, 123, 125, 139, 150, 179, 184, 189, 198, 200, 201, 202, 208, 216, 226, 274, 303, 306, 309], "mode": [1, 67, 234, 243, 245, 265, 266], "i": [1, 3, 109, 112, 201, 216, 219, 220, 222, 223, 236, 281, 303], "e": [1, 4, 6, 78, 109, 165, 199, 218, 219, 220, 222, 223, 226, 227, 228, 236, 252, 293, 299, 305, 310], "match": [1, 6, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 238, 275, 304, 306], "transposit": 1, "data_s": 1, "items": 1, "flag": [1, 306], "copy_inplac": 1, "copytyp": 1, "n": [1, 3, 26, 65, 66, 83, 84, 86, 87, 89, 90, 93, 95, 103, 186, 190, 218, 219, 220, 222, 223, 281, 285], "incx": 1, "inci": 1, "great": 1, "But": [1, 309], "criteria": 1, "luckili": [1, 305], "alwai": [1, 208, 303], "With": 1, "final": [1, 2, 3, 4], "singl": [1, 4, 80, 109, 115, 138, 191, 304, 308], "row_contigu": 1, "col_contigu": 1, "common": [1, 305], "hit": 1, "mileston": 1, "enough": [1, 305], "run": [1, 3, 4, 5, 6, 137, 197, 198, 200, 201, 202, 218, 231, 305, 309, 310], "If": [1, 3, 6, 12, 13, 14, 15, 22, 23, 24, 25, 57, 60, 63, 64, 67, 73, 74, 80, 93, 94, 95, 98, 99, 100, 112, 115, 124, 125, 126, 128, 129, 135, 138, 139, 140, 144, 154, 169, 170, 171, 178, 180, 181, 184, 189, 190, 192, 194, 198, 209, 218, 219, 220, 226, 228, 229, 236, 238, 246, 251, 254, 256, 258, 273, 275, 285, 303, 305, 308, 309, 310], "plan": 1, "stop": [1, 3, 15, 114, 176, 303, 304], "enjoi": 1, "speed": 1, "appl": [1, 3, 5, 6, 309], "silicon": [1, 3, 5, 6, 309], "address": 1, "shade": 1, "languag": [1, 212], "kernel": [1, 65, 66, 304], "written": 1, "help": [1, 3, 309], "resourc": 1, "walkthrough": 1, "pipelin": 1, 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