2024-07-12 06:32:08 +08:00
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< li class = "navelem" > < a class = "el" href = "dir_938ab0ecf10b8b860ff766c820f665fd.html" > mlx< / a > < / li > < li class = "navelem" > < a class = "el" href = "dir_1d446c9bd3c99228254c9484e0bc5c06.html" > backend< / a > < / li > < li class = "navelem" > < a class = "el" href = "dir_d0c977ea65824390717cdb7efc36c157.html" > metal< / a > < / li > < li class = "navelem" > < a class = "el" href = "dir_70a37effa88bcbd6b791977fa1e64356.html" > kernels< / a > < / li > < / ul >
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< div class = "headertitle" > < div class = "title" > hadamard.h< / div > < / div >
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< a href = "metal_2kernels_2hadamard_8h.html" > Go to the documentation of this file.< / a > < div class = "fragment" > < div class = "line" > < a id = "l00001" name = "l00001" > < / a > < span class = "lineno" > 1< / span > < span class = "comment" > // Copyright © 2024 Apple Inc.< / span > < / div >
< div class = "line" > < a id = "l00002" name = "l00002" > < / a > < span class = "lineno" > 2< / span > < span class = "preprocessor" > #include < metal_common> < / span > < / div >
< div class = "line" > < a id = "l00003" name = "l00003" > < / a > < span class = "lineno" > 3< / span > < span class = "preprocessor" > #include < metal_compute> < / span > < / div >
< div class = "line" > < a id = "l00004" name = "l00004" > < / a > < span class = "lineno" > 4< / span > < / div >
< div class = "line" > < a id = "l00005" name = "l00005" > < / a > < span class = "lineno" > 5< / span > < span class = "preprocessor" > #include " < a class = "code" href = "steel_2defines_8h.html" > mlx/backend/metal/kernels/steel/defines.h< / a > " < / span > < / div >
< div class = "line" > < a id = "l00006" name = "l00006" > < / a > < span class = "lineno" > 6< / span > < / div >
< div class = "line" > < a id = "l00007" name = "l00007" > < / a > < span class = "lineno" > 7< / span > < span class = "keyword" > using namespace < / span > < a class = "code hl_namespace" href = "namespacemetal.html" > metal< / a > ;< / div >
< div class = "line" > < a id = "l00008" name = "l00008" > < / a > < span class = "lineno" > 8< / span > < / div >
< div class = "line" > < a id = "l00009" name = "l00009" > < / a > < span class = "lineno" > 9< / span > < span class = "comment" > // Thread local Hadamard transform for 2^R< / span > < / div >
< div class = "line" > < a id = "l00010" name = "l00010" > < / a > < span class = "lineno" > 10< / span > < span class = "keyword" > template< / span > < < span class = "keywordtype" > short< / span > R> < / div >
< div class = "foldopen" id = "foldopen00011" data-start = "{" data-end = "}" >
< div class = "line" > < a id = "l00011" name = "l00011" > < / a > < span class = "lineno" > < a class = "line" href = "metal_2kernels_2hadamard_8h.html#a590e5366adc78bab4fe44e37885d413f" > 11< / a > < / span > METAL_FUNC < span class = "keywordtype" > void< / span > < a class = "code hl_function" href = "metal_2kernels_2hadamard_8h.html#a590e5366adc78bab4fe44e37885d413f" > radix_func< / a > (thread < span class = "keywordtype" > float< / span > * x) {< / div >
< div class = "line" > < a id = "l00012" name = "l00012" > < / a > < span class = "lineno" > 12< / span > < span class = "keyword" > constexpr< / span > < span class = "keywordtype" > short< / span > logR = __builtin_ctz(R);< / div >
< div class = "line" > < a id = "l00013" name = "l00013" > < / a > < span class = "lineno" > 13< / span > < span class = "keywordtype" > short< / span > h = 1;< / div >
< div class = "line" > < a id = "l00014" name = "l00014" > < / a > < span class = "lineno" > 14< / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6" > STEEL_PRAGMA_UNROLL< / a > < / div >
< div class = "line" > < a id = "l00015" name = "l00015" > < / a > < span class = "lineno" > 15< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > short< / span > s = 0; s < logR; s++) {< / div >
< div class = "line" > < a id = "l00016" name = "l00016" > < / a > < span class = "lineno" > 16< / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6" > STEEL_PRAGMA_UNROLL< / a > < / div >
< div class = "line" > < a id = "l00017" name = "l00017" > < / a > < span class = "lineno" > 17< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > short< / span > i = 0; i < R / 2; i++) {< / div >
< div class = "line" > < a id = "l00018" name = "l00018" > < / a > < span class = "lineno" > 18< / span > < span class = "keywordtype" > short< / span > k = i & (h - 1);< / div >
< div class = "line" > < a id = "l00019" name = "l00019" > < / a > < span class = "lineno" > 19< / span > < span class = "keywordtype" > short< / span > j = ((i - k) < < 1) + k;< / div >
< div class = "line" > < a id = "l00020" name = "l00020" > < / a > < span class = "lineno" > 20< / span > < span class = "keywordtype" > float< / span > a = x[j];< / div >
< div class = "line" > < a id = "l00021" name = "l00021" > < / a > < span class = "lineno" > 21< / span > < span class = "keywordtype" > float< / span > b = x[j + h];< / div >
< div class = "line" > < a id = "l00022" name = "l00022" > < / a > < span class = "lineno" > 22< / span > x[j] = a + b;< / div >
< div class = "line" > < a id = "l00023" name = "l00023" > < / a > < span class = "lineno" > 23< / span > x[j + h] = a - b;< / div >
< div class = "line" > < a id = "l00024" name = "l00024" > < / a > < span class = "lineno" > 24< / span > }< / div >
< div class = "line" > < a id = "l00025" name = "l00025" > < / a > < span class = "lineno" > 25< / span > h < < = 1;< / div >
< div class = "line" > < a id = "l00026" name = "l00026" > < / a > < span class = "lineno" > 26< / span > }< / div >
< div class = "line" > < a id = "l00027" name = "l00027" > < / a > < span class = "lineno" > 27< / span > }< / div >
< / div >
< div class = "line" > < a id = "l00028" name = "l00028" > < / a > < span class = "lineno" > 28< / span > < / div >
< div class = "line" > < a id = "l00029" name = "l00029" > < / a > < span class = "lineno" > 29< / span > < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > T, < span class = "keywordtype" > int< / span > N, < span class = "keywordtype" > int< / span > max_radix, < span class = "keywordtype" > int< / span > read_w< span class = "keywordtype" > id< / span > th> < / div >
< div class = "foldopen" id = "foldopen00030" data-start = "{" data-end = "}" >
< div class = "line" > < a id = "l00030" name = "l00030" > < / a > < span class = "lineno" > < a class = "line" href = "metal_2kernels_2hadamard_8h.html#a63c0e8510e555cd065e1f0ddfb33ce18" > 30< / a > < / span > [[kernel]] < span class = "keywordtype" > void< / span > < a class = "code hl_function" href = "metal_2kernels_2hadamard_8h.html#a63c0e8510e555cd065e1f0ddfb33ce18" > hadamard_n< / a > (< / div >
< div class = "line" > < a id = "l00031" name = "l00031" > < / a > < span class = "lineno" > 31< / span > < span class = "keyword" > const< / span > device T* in [[buffer(0)]],< / div >
< div class = "line" > < a id = "l00032" name = "l00032" > < / a > < span class = "lineno" > 32< / span > device T* out [[buffer(1)]],< / div >
< div class = "line" > < a id = "l00033" name = "l00033" > < / a > < span class = "lineno" > 33< / span > constant < span class = "keyword" > const< / span > < span class = "keywordtype" > float< / span > & scale,< / div >
< div class = "line" > < a id = "l00034" name = "l00034" > < / a > < span class = "lineno" > 34< / span > uint3 elem [[thread_position_in_grid]],< / div >
< div class = "line" > < a id = "l00035" name = "l00035" > < / a > < span class = "lineno" > 35< / span > uint3 grid [[threads_per_grid]]) {< / div >
< div class = "line" > < a id = "l00036" name = "l00036" > < / a > < span class = "lineno" > 36< / span > < span class = "comment" > // Compute a Hadamard transform of size N = 2^k< / span > < / div >
< div class = "line" > < a id = "l00037" name = "l00037" > < / a > < span class = "lineno" > 37< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00038" name = "l00038" > < / a > < span class = "lineno" > 38< / span > < span class = "comment" > // Equivalent to:< / span > < / div >
< div class = "line" > < a id = "l00039" name = "l00039" > < / a > < span class = "lineno" > 39< / span > < span class = "comment" > // from scipy.linalg import hadamard< / span > < / div >
< div class = "line" > < a id = "l00040" name = "l00040" > < / a > < span class = "lineno" > 40< / span > < span class = "comment" > // y = hadamard(len(x)) @ x< / span > < / div >
< div class = "line" > < a id = "l00041" name = "l00041" > < / a > < span class = "lineno" > 41< / span > < / div >
< div class = "line" > < a id = "l00042" name = "l00042" > < / a > < span class = "lineno" > 42< / span > < span class = "keyword" > constexpr< / span > < span class = "keywordtype" > short< / span > num_threads = N / max_radix;< / div >
< div class = "line" > < a id = "l00043" name = "l00043" > < / a > < span class = "lineno" > 43< / span > < span class = "keyword" > constexpr< / span > < span class = "keywordtype" > short< / span > logN = __builtin_ctz(N);< / div >
< div class = "line" > < a id = "l00044" name = "l00044" > < / a > < span class = "lineno" > 44< / span > < span class = "keyword" > constexpr< / span > < span class = "keywordtype" > short< / span > logR = __builtin_ctz(max_radix);< / div >
< div class = "line" > < a id = "l00045" name = "l00045" > < / a > < span class = "lineno" > 45< / span > < span class = "keyword" > constexpr< / span > < span class = "keywordtype" > short< / span > num_steps = logN / logR;< / div >
< div class = "line" > < a id = "l00046" name = "l00046" > < / a > < span class = "lineno" > 46< / span > < span class = "keyword" > constexpr< / span > < span class = "keywordtype" > short< / span > logFinal = logN % logR;< / div >
< div class = "line" > < a id = "l00047" name = "l00047" > < / a > < span class = "lineno" > 47< / span > < span class = "keyword" > constexpr< / span > < span class = "keywordtype" > short< / span > final_radix = 1 < < (logFinal);< / div >
< div class = "line" > < a id = "l00048" name = "l00048" > < / a > < span class = "lineno" > 48< / span > < / div >
< div class = "line" > < a id = "l00049" name = "l00049" > < / a > < span class = "lineno" > 49< / span > < span class = "keywordtype" > int< / span > batch_idx = elem.x * N;< / div >
< div class = "line" > < a id = "l00050" name = "l00050" > < / a > < span class = "lineno" > 50< / span > < span class = "keywordtype" > short< / span > i = elem.y;< / div >
< div class = "line" > < a id = "l00051" name = "l00051" > < / a > < span class = "lineno" > 51< / span > < / div >
< div class = "line" > < a id = "l00052" name = "l00052" > < / a > < span class = "lineno" > 52< / span > threadgroup T < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > [N];< / div >
< div class = "line" > < a id = "l00053" name = "l00053" > < / a > < span class = "lineno" > 53< / span > < / div >
< div class = "line" > < a id = "l00054" name = "l00054" > < / a > < span class = "lineno" > 54< / span > < span class = "comment" > // Read values from device< / span > < / div >
< div class = "line" > < a id = "l00055" name = "l00055" > < / a > < span class = "lineno" > 55< / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6" > STEEL_PRAGMA_UNROLL< / a > < / div >
< div class = "line" > < a id = "l00056" name = "l00056" > < / a > < span class = "lineno" > 56< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > short< / span > j = 0; j < max_radix / read_width; j++) {< / div >
< div class = "line" > < a id = "l00057" name = "l00057" > < / a > < span class = "lineno" > 57< / span > < span class = "keywordtype" > short< / span > index = j * read_width * num_threads + i * read_width;< / div >
< div class = "line" > < a id = "l00058" name = "l00058" > < / a > < span class = "lineno" > 58< / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6" > STEEL_PRAGMA_UNROLL< / a > < / div >
< div class = "line" > < a id = "l00059" name = "l00059" > < / a > < span class = "lineno" > 59< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > short< / span > r = 0; r < read_width; r++) {< / div >
< div class = "line" > < a id = "l00060" name = "l00060" > < / a > < span class = "lineno" > 60< / span > < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > [index + r] = in[batch_idx + index + r];< / div >
< div class = "line" > < a id = "l00061" name = "l00061" > < / a > < span class = "lineno" > 61< / span > }< / div >
< div class = "line" > < a id = "l00062" name = "l00062" > < / a > < span class = "lineno" > 62< / span > }< / div >
< div class = "line" > < a id = "l00063" name = "l00063" > < / a > < span class = "lineno" > 63< / span > < / div >
< div class = "line" > < a id = "l00064" name = "l00064" > < / a > < span class = "lineno" > 64< / span > threadgroup_barrier(mem_flags::mem_threadgroup);< / div >
< div class = "line" > < a id = "l00065" name = "l00065" > < / a > < span class = "lineno" > 65< / span > < / div >
< div class = "line" > < a id = "l00066" name = "l00066" > < / a > < span class = "lineno" > 66< / span > < span class = "keywordtype" > float< / span > x[max_radix];< / div >
< div class = "line" > < a id = "l00067" name = "l00067" > < / a > < span class = "lineno" > 67< / span > < span class = "keywordtype" > short< / span > h = 1;< / div >
< div class = "line" > < a id = "l00068" name = "l00068" > < / a > < span class = "lineno" > 68< / span > < / div >
< div class = "line" > < a id = "l00069" name = "l00069" > < / a > < span class = "lineno" > 69< / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6" > STEEL_PRAGMA_UNROLL< / a > < / div >
< div class = "line" > < a id = "l00070" name = "l00070" > < / a > < span class = "lineno" > 70< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > short< / span > s = 0; s < num_steps; s++) {< / div >
< div class = "line" > < a id = "l00071" name = "l00071" > < / a > < span class = "lineno" > 71< / span > < span class = "keywordtype" > short< / span > k = i & (h - 1);< / div >
< div class = "line" > < a id = "l00072" name = "l00072" > < / a > < span class = "lineno" > 72< / span > < span class = "keywordtype" > short< / span > j = ((i - k) < < logR) + k;< / div >
< div class = "line" > < a id = "l00073" name = "l00073" > < / a > < span class = "lineno" > 73< / span > < / div >
< div class = "line" > < a id = "l00074" name = "l00074" > < / a > < span class = "lineno" > 74< / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6" > STEEL_PRAGMA_UNROLL< / a > < / div >
< div class = "line" > < a id = "l00075" name = "l00075" > < / a > < span class = "lineno" > 75< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > short< / span > r = 0; r < max_radix; r++) {< / div >
< div class = "line" > < a id = "l00076" name = "l00076" > < / a > < span class = "lineno" > 76< / span > x[r] = < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > [j + h * r];< / div >
< div class = "line" > < a id = "l00077" name = "l00077" > < / a > < span class = "lineno" > 77< / span > }< / div >
< div class = "line" > < a id = "l00078" name = "l00078" > < / a > < span class = "lineno" > 78< / span > < / div >
< div class = "line" > < a id = "l00079" name = "l00079" > < / a > < span class = "lineno" > 79< / span > radix_func< max_radix> (x);< / div >
< div class = "line" > < a id = "l00080" name = "l00080" > < / a > < span class = "lineno" > 80< / span > < / div >
< div class = "line" > < a id = "l00081" name = "l00081" > < / a > < span class = "lineno" > 81< / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6" > STEEL_PRAGMA_UNROLL< / a > < / div >
< div class = "line" > < a id = "l00082" name = "l00082" > < / a > < span class = "lineno" > 82< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > short< / span > r = 0; r < max_radix; r++) {< / div >
2024-07-26 02:59:11 +08:00
< div class = "line" > < a id = "l00083" name = "l00083" > < / a > < span class = "lineno" > 83< / span > < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > [j + h * r] = T(x[r]);< / div >
2024-07-12 06:32:08 +08:00
< div class = "line" > < a id = "l00084" name = "l00084" > < / a > < span class = "lineno" > 84< / span > }< / div >
< div class = "line" > < a id = "l00085" name = "l00085" > < / a > < span class = "lineno" > 85< / span > < / div >
< div class = "line" > < a id = "l00086" name = "l00086" > < / a > < span class = "lineno" > 86< / span > h < < = logR;< / div >
< div class = "line" > < a id = "l00087" name = "l00087" > < / a > < span class = "lineno" > 87< / span > threadgroup_barrier(mem_flags::mem_threadgroup);< / div >
< div class = "line" > < a id = "l00088" name = "l00088" > < / a > < span class = "lineno" > 88< / span > }< / div >
< div class = "line" > < a id = "l00089" name = "l00089" > < / a > < span class = "lineno" > 89< / span > < / div >
< div class = "line" > < a id = "l00090" name = "l00090" > < / a > < span class = "lineno" > 90< / span > < span class = "comment" > // Do the final radix< / span > < / div >
< div class = "line" > < a id = "l00091" name = "l00091" > < / a > < span class = "lineno" > 91< / span > < span class = "comment" > // e.g. max_radix = 16< / span > < / div >
< div class = "line" > < a id = "l00092" name = "l00092" > < / a > < span class = "lineno" > 92< / span > < span class = "comment" > // N = 1024 = 16 * 16 * 4< / span > < / div >
< div class = "line" > < a id = "l00093" name = "l00093" > < / a > < span class = "lineno" > 93< / span > < span class = "keywordflow" > if< / span > (final_radix > 1) {< / div >
< div class = "line" > < a id = "l00094" name = "l00094" > < / a > < span class = "lineno" > 94< / span > < span class = "comment" > // Each thread does multiple butterflies< / span > < / div >
< div class = "line" > < a id = "l00095" name = "l00095" > < / a > < span class = "lineno" > 95< / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6" > STEEL_PRAGMA_UNROLL< / a > < / div >
< div class = "line" > < a id = "l00096" name = "l00096" > < / a > < span class = "lineno" > 96< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > t = 0; t < max_radix / final_radix; t++) {< / div >
< div class = "line" > < a id = "l00097" name = "l00097" > < / a > < span class = "lineno" > 97< / span > < span class = "keywordtype" > short< / span > index = i + t * num_threads;< / div >
< div class = "line" > < a id = "l00098" name = "l00098" > < / a > < span class = "lineno" > 98< / span > < span class = "keywordtype" > short< / span > k = index & (h - 1);< / div >
< div class = "line" > < a id = "l00099" name = "l00099" > < / a > < span class = "lineno" > 99< / span > < span class = "keywordtype" > short< / span > j = ((index - k) < < logFinal) + k;< / div >
< div class = "line" > < a id = "l00100" name = "l00100" > < / a > < span class = "lineno" > 100< / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6" > STEEL_PRAGMA_UNROLL< / a > < / div >
< div class = "line" > < a id = "l00101" name = "l00101" > < / a > < span class = "lineno" > 101< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > short< / span > r = 0; r < final_radix; r++) {< / div >
< div class = "line" > < a id = "l00102" name = "l00102" > < / a > < span class = "lineno" > 102< / span > x[r] = < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > [j + h * r];< / div >
< div class = "line" > < a id = "l00103" name = "l00103" > < / a > < span class = "lineno" > 103< / span > }< / div >
< div class = "line" > < a id = "l00104" name = "l00104" > < / a > < span class = "lineno" > 104< / span > < / div >
< div class = "line" > < a id = "l00105" name = "l00105" > < / a > < span class = "lineno" > 105< / span > radix_func< final_radix> (x);< / div >
< div class = "line" > < a id = "l00106" name = "l00106" > < / a > < span class = "lineno" > 106< / span > < / div >
< div class = "line" > < a id = "l00107" name = "l00107" > < / a > < span class = "lineno" > 107< / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6" > STEEL_PRAGMA_UNROLL< / a > < / div >
< div class = "line" > < a id = "l00108" name = "l00108" > < / a > < span class = "lineno" > 108< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > short< / span > r = 0; r < final_radix; r++) {< / div >
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< div class = "line" > < a id = "l00109" name = "l00109" > < / a > < span class = "lineno" > 109< / span > < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > [j + h * r] = T(x[r]);< / div >
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< div class = "line" > < a id = "l00110" name = "l00110" > < / a > < span class = "lineno" > 110< / span > }< / div >
< div class = "line" > < a id = "l00111" name = "l00111" > < / a > < span class = "lineno" > 111< / span > }< / div >
< div class = "line" > < a id = "l00112" name = "l00112" > < / a > < span class = "lineno" > 112< / span > threadgroup_barrier(mem_flags::mem_threadgroup);< / div >
< div class = "line" > < a id = "l00113" name = "l00113" > < / a > < span class = "lineno" > 113< / span > }< / div >
< div class = "line" > < a id = "l00114" name = "l00114" > < / a > < span class = "lineno" > 114< / span > < / div >
< div class = "line" > < a id = "l00115" name = "l00115" > < / a > < span class = "lineno" > 115< / span > < span class = "comment" > // Write values to device< / span > < / div >
< div class = "line" > < a id = "l00116" name = "l00116" > < / a > < span class = "lineno" > 116< / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6" > STEEL_PRAGMA_UNROLL< / a > < / div >
< div class = "line" > < a id = "l00117" name = "l00117" > < / a > < span class = "lineno" > 117< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > short< / span > j = 0; j < max_radix / read_width; j++) {< / div >
< div class = "line" > < a id = "l00118" name = "l00118" > < / a > < span class = "lineno" > 118< / span > < span class = "keywordtype" > short< / span > index = j * read_width * num_threads + i * read_width;< / div >
< div class = "line" > < a id = "l00119" name = "l00119" > < / a > < span class = "lineno" > 119< / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6" > STEEL_PRAGMA_UNROLL< / a > < / div >
< div class = "line" > < a id = "l00120" name = "l00120" > < / a > < span class = "lineno" > 120< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > short< / span > r = 0; r < read_width; r++) {< / div >
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< div class = "line" > < a id = "l00121" name = "l00121" > < / a > < span class = "lineno" > 121< / span > out[batch_idx + index + r] = T(< a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > [index + r] * scale);< / div >
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< div class = "line" > < a id = "l00122" name = "l00122" > < / a > < span class = "lineno" > 122< / span > }< / div >
< div class = "line" > < a id = "l00123" name = "l00123" > < / a > < span class = "lineno" > 123< / span > }< / div >
< div class = "line" > < a id = "l00124" name = "l00124" > < / a > < span class = "lineno" > 124< / span > }< / div >
< / div >
< div class = "line" > < a id = "l00125" name = "l00125" > < / a > < span class = "lineno" > 125< / span > < / div >
< div class = "line" > < a id = "l00126" name = "l00126" > < / a > < span class = "lineno" > 126< / span > < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > T, < span class = "keywordtype" > int< / span > N, < span class = "keywordtype" > int< / span > M, < span class = "keywordtype" > int< / span > read_w< span class = "keywordtype" > id< / span > th> < / div >
< div class = "foldopen" id = "foldopen00127" data-start = "{" data-end = "}" >
< div class = "line" > < a id = "l00127" name = "l00127" > < / a > < span class = "lineno" > < a class = "line" href = "metal_2kernels_2hadamard_8h.html#ab0bd478f2051af35aed1869005e3370a" > 127< / a > < / span > [[kernel]] < span class = "keywordtype" > void< / span > < a class = "code hl_function" href = "metal_2kernels_2hadamard_8h.html#ab0bd478f2051af35aed1869005e3370a" > hadamard_m< / a > (< / div >
< div class = "line" > < a id = "l00128" name = "l00128" > < / a > < span class = "lineno" > 128< / span > < span class = "keyword" > const< / span > device T* in [[buffer(0)]],< / div >
< div class = "line" > < a id = "l00129" name = "l00129" > < / a > < span class = "lineno" > 129< / span > device T* out [[buffer(1)]],< / div >
< div class = "line" > < a id = "l00130" name = "l00130" > < / a > < span class = "lineno" > 130< / span > constant < span class = "keyword" > const< / span > < span class = "keywordtype" > float< / span > & scale,< / div >
< div class = "line" > < a id = "l00131" name = "l00131" > < / a > < span class = "lineno" > 131< / span > uint3 elem [[thread_position_in_grid]],< / div >
< div class = "line" > < a id = "l00132" name = "l00132" > < / a > < span class = "lineno" > 132< / span > uint3 grid [[threads_per_grid]]) {< / div >
< div class = "line" > < a id = "l00133" name = "l00133" > < / a > < span class = "lineno" > 133< / span > < span class = "comment" > // Compute a Hadamard transform of size M< / span > < / div >
< div class = "line" > < a id = "l00134" name = "l00134" > < / a > < span class = "lineno" > 134< / span > < span class = "comment" > // using a naive O(M^2) codelet.< / span > < / div >
< div class = "line" > < a id = "l00135" name = "l00135" > < / a > < span class = "lineno" > 135< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00136" name = "l00136" > < / a > < span class = "lineno" > 136< / span > < span class = "comment" > // This kernel is the second stage in the computation< / span > < / div >
< div class = "line" > < a id = "l00137" name = "l00137" > < / a > < span class = "lineno" > 137< / span > < span class = "comment" > // of a Hadamard transform of size M*N where N = 2^k.< / span > < / div >
< div class = "line" > < a id = "l00138" name = "l00138" > < / a > < span class = "lineno" > 138< / span > < / div >
< div class = "line" > < a id = "l00139" name = "l00139" > < / a > < span class = "lineno" > 139< / span > < span class = "keywordtype" > int< / span > index = elem.x * grid.y + elem.y;< / div >
< div class = "line" > < a id = "l00140" name = "l00140" > < / a > < span class = "lineno" > 140< / span > < span class = "keywordtype" > short< / span > i = index % (N / read_width);< / div >
< div class = "line" > < a id = "l00141" name = "l00141" > < / a > < span class = "lineno" > 141< / span > < span class = "keywordtype" > int< / span > batch_idx = index / (N / read_width) * M * N;< / div >
< div class = "line" > < a id = "l00142" name = "l00142" > < / a > < span class = "lineno" > 142< / span > < / div >
< div class = "line" > < a id = "l00143" name = "l00143" > < / a > < span class = "lineno" > 143< / span > < span class = "keywordtype" > float< / span > x[read_width][M];< / div >
< div class = "line" > < a id = "l00144" name = "l00144" > < / a > < span class = "lineno" > 144< / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6" > STEEL_PRAGMA_UNROLL< / a > < / div >
< div class = "line" > < a id = "l00145" name = "l00145" > < / a > < span class = "lineno" > 145< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > short< / span > c = 0; c < M; c++) {< / div >
< div class = "line" > < a id = "l00146" name = "l00146" > < / a > < span class = "lineno" > 146< / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6" > STEEL_PRAGMA_UNROLL< / a > < / div >
< div class = "line" > < a id = "l00147" name = "l00147" > < / a > < span class = "lineno" > 147< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > short< / span > r = 0; r < read_width; r++) {< / div >
< div class = "line" > < a id = "l00148" name = "l00148" > < / a > < span class = "lineno" > 148< / span > x[r][c] = in[batch_idx + c * N + i * read_width + r];< / div >
< div class = "line" > < a id = "l00149" name = "l00149" > < / a > < span class = "lineno" > 149< / span > }< / div >
< div class = "line" > < a id = "l00150" name = "l00150" > < / a > < span class = "lineno" > 150< / span > }< / div >
< div class = "line" > < a id = "l00151" name = "l00151" > < / a > < span class = "lineno" > 151< / span > < / div >
< div class = "line" > < a id = "l00152" name = "l00152" > < / a > < span class = "lineno" > 152< / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6" > STEEL_PRAGMA_UNROLL< / a > < / div >
< div class = "line" > < a id = "l00153" name = "l00153" > < / a > < span class = "lineno" > 153< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > short< / span > r = 0; r < read_width; r++) {< / div >
< div class = "line" > < a id = "l00154" name = "l00154" > < / a > < span class = "lineno" > 154< / span > < span class = "comment" > // This function is JIT compiled for M< / span > < / div >
< div class = "line" > < a id = "l00155" name = "l00155" > < / a > < span class = "lineno" > 155< / span > < span class = "comment" > // using the Hadamard matrix strings in `metal/hadamard.cpp`< / span > < / div >
< div class = "line" > < a id = "l00156" name = "l00156" > < / a > < span class = "lineno" > 156< / span > hadamard_radix_m(x[r]);< / div >
< div class = "line" > < a id = "l00157" name = "l00157" > < / a > < span class = "lineno" > 157< / span > }< / div >
< div class = "line" > < a id = "l00158" name = "l00158" > < / a > < span class = "lineno" > 158< / span > < / div >
< div class = "line" > < a id = "l00159" name = "l00159" > < / a > < span class = "lineno" > 159< / span > < span class = "comment" > // Write back to device< / span > < / div >
< div class = "line" > < a id = "l00160" name = "l00160" > < / a > < span class = "lineno" > 160< / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6" > STEEL_PRAGMA_UNROLL< / a > < / div >
< div class = "line" > < a id = "l00161" name = "l00161" > < / a > < span class = "lineno" > 161< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > short< / span > c = 0; c < M; c++) {< / div >
< div class = "line" > < a id = "l00162" name = "l00162" > < / a > < span class = "lineno" > 162< / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6" > STEEL_PRAGMA_UNROLL< / a > < / div >
< div class = "line" > < a id = "l00163" name = "l00163" > < / a > < span class = "lineno" > 163< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > short< / span > r = 0; r < read_width; r++) {< / div >
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< div class = "line" > < a id = "l00164" name = "l00164" > < / a > < span class = "lineno" > 164< / span > out[batch_idx + c * N + i * read_width + r] = T(x[r][c] * scale);< / div >
2024-07-12 06:32:08 +08:00
< div class = "line" > < a id = "l00165" name = "l00165" > < / a > < span class = "lineno" > 165< / span > }< / div >
< div class = "line" > < a id = "l00166" name = "l00166" > < / a > < span class = "lineno" > 166< / span > }< / div >
< div class = "line" > < a id = "l00167" name = "l00167" > < / a > < span class = "lineno" > 167< / span > }< / div >
< / div >
< div class = "ttc" id = "abackend_2metal_2allocator_8h_html_a15aa5cc1baf29be08d55cca88509e697" > < div class = "ttname" > < a href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > < / div > < div class = "ttdeci" > MTL::Buffer * buf< / div > < div class = "ttdef" > < b > Definition< / b > allocator.h:38< / div > < / div >
< div class = "ttc" id = "ametal_2kernels_2hadamard_8h_html_a590e5366adc78bab4fe44e37885d413f" > < div class = "ttname" > < a href = "metal_2kernels_2hadamard_8h.html#a590e5366adc78bab4fe44e37885d413f" > radix_func< / a > < / div > < div class = "ttdeci" > METAL_FUNC void radix_func(thread float *x)< / div > < div class = "ttdef" > < b > Definition< / b > hadamard.h:11< / div > < / div >
< div class = "ttc" id = "ametal_2kernels_2hadamard_8h_html_a63c0e8510e555cd065e1f0ddfb33ce18" > < div class = "ttname" > < a href = "metal_2kernels_2hadamard_8h.html#a63c0e8510e555cd065e1f0ddfb33ce18" > hadamard_n< / a > < / div > < div class = "ttdeci" > void hadamard_n(const device T *in, device T *out, constant const float & scale, uint3 elem, uint3 grid)< / div > < div class = "ttdef" > < b > Definition< / b > hadamard.h:30< / div > < / div >
< div class = "ttc" id = "ametal_2kernels_2hadamard_8h_html_ab0bd478f2051af35aed1869005e3370a" > < div class = "ttname" > < a href = "metal_2kernels_2hadamard_8h.html#ab0bd478f2051af35aed1869005e3370a" > hadamard_m< / a > < / div > < div class = "ttdeci" > void hadamard_m(const device T *in, device T *out, constant const float & scale, uint3 elem, uint3 grid)< / div > < div class = "ttdef" > < b > Definition< / b > hadamard.h:127< / div > < / div >
< div class = "ttc" id = "anamespacemetal_html" > < div class = "ttname" > < a href = "namespacemetal.html" > metal< / a > < / div > < div class = "ttdef" > < b > Definition< / b > bf16.h:265< / div > < / div >
< div class = "ttc" id = "asteel_2defines_8h_html" > < div class = "ttname" > < a href = "steel_2defines_8h.html" > defines.h< / a > < / div > < / div >
< div class = "ttc" id = "asteel_2defines_8h_html_a5a5c3095b132a7589bc19cd5cb80e2c6" > < div class = "ttname" > < a href = "steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6" > STEEL_PRAGMA_UNROLL< / a > < / div > < div class = "ttdeci" > #define STEEL_PRAGMA_UNROLL< / div > < div class = "ttdef" > < b > Definition< / b > defines.h:4< / div > < / div >
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