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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 > < li class = "navelem" > < a class = "el" href = "dir_8c751ccfa9f494753d976761a9d60a84.html" > fft< / a > < / li > < / ul >
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< div class = "headertitle" > < div class = "title" > radix.h< / div > < / div >
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< a href = "radix_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 > < / div >
< div class = "line" > < a id = "l00003" name = "l00003" > < / a > < span class = "lineno" > 3< / span > < span class = "comment" > /* Radix kernels< / span > < / div >
< div class = "line" > < a id = "l00004" name = "l00004" > < / a > < span class = "lineno" > 4< / span > < span class = "comment" > < / span > < / div >
< div class = "line" > < a id = "l00005" name = "l00005" > < / a > < span class = "lineno" > 5< / span > < span class = "comment" > We provide optimized, single threaded Radix codelets< / span > < / div >
< div class = "line" > < a id = "l00006" name = "l00006" > < / a > < span class = "lineno" > 6< / span > < span class = "comment" > for n=2,3,4,5,6,7,8,10,11,12,13.< / span > < / div >
< div class = "line" > < a id = "l00007" name = "l00007" > < / a > < span class = "lineno" > 7< / span > < span class = "comment" > < / span > < / div >
< div class = "line" > < a id = "l00008" name = "l00008" > < / a > < span class = "lineno" > 8< / span > < span class = "comment" > For n=2,3,4,5,6 we hand write the codelets.< / span > < / div >
< div class = "line" > < a id = "l00009" name = "l00009" > < / a > < span class = "lineno" > 9< / span > < span class = "comment" > For n=8,10,12 we combine smaller codelets.< / span > < / div >
< div class = "line" > < a id = "l00010" name = "l00010" > < / a > < span class = "lineno" > 10< / span > < span class = "comment" > For n=7,11,13 we use Rader' s algorithm which decomposes< / span > < / div >
< div class = "line" > < a id = "l00011" name = "l00011" > < / a > < span class = "lineno" > 11< / span > < span class = "comment" > them into (n-1)=6,10,12 codelets. */< / span > < / div >
< div class = "line" > < a id = "l00012" name = "l00012" > < / a > < span class = "lineno" > 12< / span > < / div >
< div class = "line" > < a id = "l00013" name = "l00013" > < / a > < span class = "lineno" > 13< / span > < span class = "preprocessor" > #pragma once< / span > < / div >
< div class = "line" > < a id = "l00014" name = "l00014" > < / a > < span class = "lineno" > 14< / span > < / div >
< div class = "line" > < a id = "l00015" name = "l00015" > < / a > < span class = "lineno" > 15< / span > < span class = "preprocessor" > #include < metal_common> < / span > < / div >
< div class = "line" > < a id = "l00016" name = "l00016" > < / a > < span class = "lineno" > 16< / span > < span class = "preprocessor" > #include < metal_math> < / span > < / div >
< div class = "line" > < a id = "l00017" name = "l00017" > < / a > < span class = "lineno" > 17< / span > < span class = "preprocessor" > #include < metal_stdlib> < / span > < / div >
< div class = "line" > < a id = "l00018" name = "l00018" > < / a > < span class = "lineno" > 18< / span > < / div >
< div class = "foldopen" id = "foldopen00019" data-start = "{" data-end = "}" >
< div class = "line" > < a id = "l00019" name = "l00019" > < / a > < span class = "lineno" > < a class = "line" href = "radix_8h.html#a5bfc53b531214c9ce277bebc18aa67d6" > 19< / a > < / span > METAL_FUNC float2 < a class = "code hl_function" href = "radix_8h.html#a5bfc53b531214c9ce277bebc18aa67d6" > complex_mul< / a > (float2 a, float2 b) {< / div >
< div class = "line" > < a id = "l00020" name = "l00020" > < / a > < span class = "lineno" > 20< / span > < span class = "keywordflow" > return< / span > float2(a.x * b.x - a.y * b.y, a.x * b.y + a.y * b.x);< / div >
< div class = "line" > < a id = "l00021" name = "l00021" > < / a > < span class = "lineno" > 21< / span > }< / div >
< / div >
< div class = "line" > < a id = "l00022" name = "l00022" > < / a > < span class = "lineno" > 22< / span > < / div >
< div class = "line" > < a id = "l00023" name = "l00023" > < / a > < span class = "lineno" > 23< / span > < span class = "comment" > // Complex mul followed by conjugate< / span > < / div >
< div class = "foldopen" id = "foldopen00024" data-start = "{" data-end = "}" >
< div class = "line" > < a id = "l00024" name = "l00024" > < / a > < span class = "lineno" > < a class = "line" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > 24< / a > < / span > METAL_FUNC float2 < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (float2 a, float2 b) {< / div >
< div class = "line" > < a id = "l00025" name = "l00025" > < / a > < span class = "lineno" > 25< / span > < span class = "keywordflow" > return< / span > float2(a.x * b.x - a.y * b.y, -a.x * b.y - a.y * b.x);< / div >
< div class = "line" > < a id = "l00026" name = "l00026" > < / a > < span class = "lineno" > 26< / span > }< / div >
< / div >
< div class = "line" > < a id = "l00027" name = "l00027" > < / a > < span class = "lineno" > 27< / span > < / div >
< div class = "line" > < a id = "l00028" name = "l00028" > < / a > < span class = "lineno" > 28< / span > < span class = "comment" > // Compute an FFT twiddle factor< / span > < / div >
< div class = "foldopen" id = "foldopen00029" data-start = "{" data-end = "}" >
< div class = "line" > < a id = "l00029" name = "l00029" > < / a > < span class = "lineno" > < a class = "line" href = "radix_8h.html#ac5cf950316b9445296ee9ecfc56a56bd" > 29< / a > < / span > METAL_FUNC float2 < a class = "code hl_function" href = "radix_8h.html#ac5cf950316b9445296ee9ecfc56a56bd" > get_twiddle< / a > (< span class = "keywordtype" > int< / span > k, < span class = "keywordtype" > int< / span > p) {< / div >
< div class = "line" > < a id = "l00030" name = "l00030" > < / a > < span class = "lineno" > 30< / span > < span class = "keywordtype" > float< / span > theta = -2.0f * k * M_PI_F / p;< / div >
< div class = "line" > < a id = "l00031" name = "l00031" > < / a > < span class = "lineno" > 31< / span > < / div >
< div class = "line" > < a id = "l00032" name = "l00032" > < / a > < span class = "lineno" > 32< / span > float2 twiddle = {< a class = "code hl_function" href = "namespacemetal_1_1fast.html#a75b6bb32fa3870eda46a7bfc9f481f88" > metal::fast::cos< / a > (theta), < a class = "code hl_function" href = "namespacemetal_1_1fast.html#a3af771cfe7a135104f9d063147dba270" > metal::fast::sin< / a > (theta)};< / div >
< div class = "line" > < a id = "l00033" name = "l00033" > < / a > < span class = "lineno" > 33< / span > < span class = "keywordflow" > return< / span > twiddle;< / div >
< div class = "line" > < a id = "l00034" name = "l00034" > < / a > < span class = "lineno" > 34< / span > }< / div >
< / div >
< div class = "line" > < a id = "l00035" name = "l00035" > < / a > < span class = "lineno" > 35< / span > < / div >
< div class = "foldopen" id = "foldopen00036" data-start = "{" data-end = "}" >
< div class = "line" > < a id = "l00036" name = "l00036" > < / a > < span class = "lineno" > < a class = "line" href = "radix_8h.html#a745e50244f1470bba233d8b6b993729c" > 36< / a > < / span > METAL_FUNC < span class = "keywordtype" > void< / span > < a class = "code hl_function" href = "radix_8h.html#a745e50244f1470bba233d8b6b993729c" > radix2< / a > (thread float2* x, thread float2* y) {< / div >
< div class = "line" > < a id = "l00037" name = "l00037" > < / a > < span class = "lineno" > 37< / span > y[0] = x[0] + x[1];< / div >
< div class = "line" > < a id = "l00038" name = "l00038" > < / a > < span class = "lineno" > 38< / span > y[1] = x[0] - x[1];< / div >
< div class = "line" > < a id = "l00039" name = "l00039" > < / a > < span class = "lineno" > 39< / span > }< / div >
< / div >
< div class = "line" > < a id = "l00040" name = "l00040" > < / a > < span class = "lineno" > 40< / span > < / div >
< div class = "foldopen" id = "foldopen00041" data-start = "{" data-end = "}" >
< div class = "line" > < a id = "l00041" name = "l00041" > < / a > < span class = "lineno" > < a class = "line" href = "radix_8h.html#a497b31cfa28418e1c2fad53d09f7bc0b" > 41< / a > < / span > METAL_FUNC < span class = "keywordtype" > void< / span > < a class = "code hl_function" href = "radix_8h.html#a497b31cfa28418e1c2fad53d09f7bc0b" > radix3< / a > (thread float2* x, thread float2* y) {< / div >
< div class = "line" > < a id = "l00042" name = "l00042" > < / a > < span class = "lineno" > 42< / span > < span class = "keywordtype" > float< / span > pi_2_3 = -0.8660254037844387;< / div >
< div class = "line" > < a id = "l00043" name = "l00043" > < / a > < span class = "lineno" > 43< / span > < / div >
< div class = "line" > < a id = "l00044" name = "l00044" > < / a > < span class = "lineno" > 44< / span > float2 a_1 = x[1] + x[2];< / div >
< div class = "line" > < a id = "l00045" name = "l00045" > < / a > < span class = "lineno" > 45< / span > float2 a_2 = x[1] - x[2];< / div >
< div class = "line" > < a id = "l00046" name = "l00046" > < / a > < span class = "lineno" > 46< / span > < / div >
< div class = "line" > < a id = "l00047" name = "l00047" > < / a > < span class = "lineno" > 47< / span > y[0] = x[0] + a_1;< / div >
< div class = "line" > < a id = "l00048" name = "l00048" > < / a > < span class = "lineno" > 48< / span > float2 b_1 = x[0] - 0.5 * a_1;< / div >
< div class = "line" > < a id = "l00049" name = "l00049" > < / a > < span class = "lineno" > 49< / span > float2 b_2 = pi_2_3 * a_2;< / div >
< div class = "line" > < a id = "l00050" name = "l00050" > < / a > < span class = "lineno" > 50< / span > < / div >
< div class = "line" > < a id = "l00051" name = "l00051" > < / a > < span class = "lineno" > 51< / span > float2 b_2_j = {-b_2.y, b_2.x};< / div >
< div class = "line" > < a id = "l00052" name = "l00052" > < / a > < span class = "lineno" > 52< / span > y[1] = b_1 + b_2_j;< / div >
< div class = "line" > < a id = "l00053" name = "l00053" > < / a > < span class = "lineno" > 53< / span > y[2] = b_1 - b_2_j;< / div >
< div class = "line" > < a id = "l00054" name = "l00054" > < / a > < span class = "lineno" > 54< / span > }< / div >
< / div >
< div class = "line" > < a id = "l00055" name = "l00055" > < / a > < span class = "lineno" > 55< / span > < / div >
< div class = "foldopen" id = "foldopen00056" data-start = "{" data-end = "}" >
< div class = "line" > < a id = "l00056" name = "l00056" > < / a > < span class = "lineno" > < a class = "line" href = "radix_8h.html#a12cb26bd3ad635d16a195ccea750256d" > 56< / a > < / span > METAL_FUNC < span class = "keywordtype" > void< / span > < a class = "code hl_function" href = "radix_8h.html#a12cb26bd3ad635d16a195ccea750256d" > radix4< / a > (thread float2* x, thread float2* y) {< / div >
< div class = "line" > < a id = "l00057" name = "l00057" > < / a > < span class = "lineno" > 57< / span > float2 z_0 = x[0] + x[2];< / div >
< div class = "line" > < a id = "l00058" name = "l00058" > < / a > < span class = "lineno" > 58< / span > float2 z_1 = x[0] - x[2];< / div >
< div class = "line" > < a id = "l00059" name = "l00059" > < / a > < span class = "lineno" > 59< / span > float2 z_2 = x[1] + x[3];< / div >
< div class = "line" > < a id = "l00060" name = "l00060" > < / a > < span class = "lineno" > 60< / span > float2 z_3 = x[1] - x[3];< / div >
< div class = "line" > < a id = "l00061" name = "l00061" > < / a > < span class = "lineno" > 61< / span > float2 z_3_i = {z_3.y, -z_3.x};< / 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 > y[0] = z_0 + z_2;< / div >
< div class = "line" > < a id = "l00064" name = "l00064" > < / a > < span class = "lineno" > 64< / span > y[1] = z_1 + z_3_i;< / div >
< div class = "line" > < a id = "l00065" name = "l00065" > < / a > < span class = "lineno" > 65< / span > y[2] = z_0 - z_2;< / div >
< div class = "line" > < a id = "l00066" name = "l00066" > < / a > < span class = "lineno" > 66< / span > y[3] = z_1 - z_3_i;< / div >
< div class = "line" > < a id = "l00067" name = "l00067" > < / a > < span class = "lineno" > 67< / span > }< / div >
< / div >
< div class = "line" > < a id = "l00068" name = "l00068" > < / a > < span class = "lineno" > 68< / span > < / div >
< div class = "foldopen" id = "foldopen00069" data-start = "{" data-end = "}" >
< div class = "line" > < a id = "l00069" name = "l00069" > < / a > < span class = "lineno" > < a class = "line" href = "radix_8h.html#a026e6779e6d2ecdef39ff4aad186091e" > 69< / a > < / span > METAL_FUNC < span class = "keywordtype" > void< / span > < a class = "code hl_function" href = "radix_8h.html#a026e6779e6d2ecdef39ff4aad186091e" > radix5< / a > (thread float2* x, thread float2* y) {< / div >
< div class = "line" > < a id = "l00070" name = "l00070" > < / a > < span class = "lineno" > 70< / span > float2 root_5_4 = 0.5590169943749475;< / div >
< div class = "line" > < a id = "l00071" name = "l00071" > < / a > < span class = "lineno" > 71< / span > float2 sin_2pi_5 = 0.9510565162951535;< / div >
< div class = "line" > < a id = "l00072" name = "l00072" > < / a > < span class = "lineno" > 72< / span > float2 sin_1pi_5 = 0.5877852522924731;< / 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 > float2 a_1 = x[1] + x[4];< / div >
< div class = "line" > < a id = "l00075" name = "l00075" > < / a > < span class = "lineno" > 75< / span > float2 a_2 = x[2] + x[3];< / div >
< div class = "line" > < a id = "l00076" name = "l00076" > < / a > < span class = "lineno" > 76< / span > float2 a_3 = x[1] - x[4];< / div >
< div class = "line" > < a id = "l00077" name = "l00077" > < / a > < span class = "lineno" > 77< / span > float2 a_4 = x[2] - x[3];< / 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 > float2 a_5 = a_1 + a_2;< / div >
< div class = "line" > < a id = "l00080" name = "l00080" > < / a > < span class = "lineno" > 80< / span > float2 a_6 = root_5_4 * (a_1 - a_2);< / div >
< div class = "line" > < a id = "l00081" name = "l00081" > < / a > < span class = "lineno" > 81< / span > float2 a_7 = x[0] - a_5 / 4;< / div >
< div class = "line" > < a id = "l00082" name = "l00082" > < / a > < span class = "lineno" > 82< / span > float2 a_8 = a_7 + a_6;< / div >
< div class = "line" > < a id = "l00083" name = "l00083" > < / a > < span class = "lineno" > 83< / span > float2 a_9 = a_7 - a_6;< / div >
< div class = "line" > < a id = "l00084" name = "l00084" > < / a > < span class = "lineno" > 84< / span > float2 a_10 = sin_2pi_5 * a_3 + sin_1pi_5 * a_4;< / div >
< div class = "line" > < a id = "l00085" name = "l00085" > < / a > < span class = "lineno" > 85< / span > float2 a_11 = sin_1pi_5 * a_3 - sin_2pi_5 * a_4;< / div >
< div class = "line" > < a id = "l00086" name = "l00086" > < / a > < span class = "lineno" > 86< / span > float2 a_10_j = {a_10.y, -a_10.x};< / div >
< div class = "line" > < a id = "l00087" name = "l00087" > < / a > < span class = "lineno" > 87< / span > float2 a_11_j = {a_11.y, -a_11.x};< / 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 > y[0] = x[0] + a_5;< / div >
< div class = "line" > < a id = "l00090" name = "l00090" > < / a > < span class = "lineno" > 90< / span > y[1] = a_8 + a_10_j;< / div >
< div class = "line" > < a id = "l00091" name = "l00091" > < / a > < span class = "lineno" > 91< / span > y[2] = a_9 + a_11_j;< / div >
< div class = "line" > < a id = "l00092" name = "l00092" > < / a > < span class = "lineno" > 92< / span > y[3] = a_9 - a_11_j;< / div >
< div class = "line" > < a id = "l00093" name = "l00093" > < / a > < span class = "lineno" > 93< / span > y[4] = a_8 - a_10_j;< / div >
< div class = "line" > < a id = "l00094" name = "l00094" > < / a > < span class = "lineno" > 94< / span > }< / div >
< / div >
< div class = "line" > < a id = "l00095" name = "l00095" > < / a > < span class = "lineno" > 95< / span > < / div >
< div class = "foldopen" id = "foldopen00096" data-start = "{" data-end = "}" >
< div class = "line" > < a id = "l00096" name = "l00096" > < / a > < span class = "lineno" > < a class = "line" href = "radix_8h.html#afaaa5de58a97f0a5e6a84fc0d598a884" > 96< / a > < / span > METAL_FUNC < span class = "keywordtype" > void< / span > < a class = "code hl_function" href = "radix_8h.html#afaaa5de58a97f0a5e6a84fc0d598a884" > radix6< / a > (thread float2* x, thread float2* y) {< / div >
< div class = "line" > < a id = "l00097" name = "l00097" > < / a > < span class = "lineno" > 97< / span > < span class = "keywordtype" > float< / span > sin_pi_3 = 0.8660254037844387;< / div >
< div class = "line" > < a id = "l00098" name = "l00098" > < / a > < span class = "lineno" > 98< / span > float2 a_1 = x[2] + x[4];< / div >
< div class = "line" > < a id = "l00099" name = "l00099" > < / a > < span class = "lineno" > 99< / span > float2 a_2 = x[0] - a_1 / 2;< / div >
< div class = "line" > < a id = "l00100" name = "l00100" > < / a > < span class = "lineno" > 100< / span > float2 a_3 = sin_pi_3 * (x[2] - x[4]);< / div >
< div class = "line" > < a id = "l00101" name = "l00101" > < / a > < span class = "lineno" > 101< / span > float2 a_4 = x[5] + x[1];< / div >
< div class = "line" > < a id = "l00102" name = "l00102" > < / a > < span class = "lineno" > 102< / span > float2 a_5 = x[3] - a_4 / 2;< / div >
< div class = "line" > < a id = "l00103" name = "l00103" > < / a > < span class = "lineno" > 103< / span > float2 a_6 = sin_pi_3 * (x[5] - x[1]);< / div >
< div class = "line" > < a id = "l00104" name = "l00104" > < / a > < span class = "lineno" > 104< / span > float2 a_7 = x[0] + a_1;< / div >
< div class = "line" > < a id = "l00105" name = "l00105" > < / a > < span class = "lineno" > 105< / span > < / div >
< div class = "line" > < a id = "l00106" name = "l00106" > < / a > < span class = "lineno" > 106< / span > float2 a_3_i = {a_3.y, -a_3.x};< / div >
< div class = "line" > < a id = "l00107" name = "l00107" > < / a > < span class = "lineno" > 107< / span > float2 a_6_i = {a_6.y, -a_6.x};< / div >
< div class = "line" > < a id = "l00108" name = "l00108" > < / a > < span class = "lineno" > 108< / span > float2 a_8 = a_2 + a_3_i;< / div >
< div class = "line" > < a id = "l00109" name = "l00109" > < / a > < span class = "lineno" > 109< / span > float2 a_9 = a_2 - a_3_i;< / div >
< div class = "line" > < a id = "l00110" name = "l00110" > < / a > < span class = "lineno" > 110< / span > float2 a_10 = x[3] + a_4;< / div >
< div class = "line" > < a id = "l00111" name = "l00111" > < / a > < span class = "lineno" > 111< / span > float2 a_11 = a_5 + a_6_i;< / div >
< div class = "line" > < a id = "l00112" name = "l00112" > < / a > < span class = "lineno" > 112< / span > float2 a_12 = a_5 - a_6_i;< / 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 > y[0] = a_7 + a_10;< / div >
< div class = "line" > < a id = "l00115" name = "l00115" > < / a > < span class = "lineno" > 115< / span > y[1] = a_8 - a_11;< / div >
< div class = "line" > < a id = "l00116" name = "l00116" > < / a > < span class = "lineno" > 116< / span > y[2] = a_9 + a_12;< / div >
< div class = "line" > < a id = "l00117" name = "l00117" > < / a > < span class = "lineno" > 117< / span > y[3] = a_7 - a_10;< / div >
< div class = "line" > < a id = "l00118" name = "l00118" > < / a > < span class = "lineno" > 118< / span > y[4] = a_8 + a_11;< / div >
< div class = "line" > < a id = "l00119" name = "l00119" > < / a > < span class = "lineno" > 119< / span > y[5] = a_9 - a_12;< / div >
< div class = "line" > < a id = "l00120" name = "l00120" > < / a > < span class = "lineno" > 120< / span > }< / div >
< / div >
< div class = "line" > < a id = "l00121" name = "l00121" > < / a > < span class = "lineno" > 121< / span > < / div >
< div class = "foldopen" id = "foldopen00122" data-start = "{" data-end = "}" >
< div class = "line" > < a id = "l00122" name = "l00122" > < / a > < span class = "lineno" > < a class = "line" href = "radix_8h.html#a6d37e483d806c550deefabf56caf4ec8" > 122< / a > < / span > METAL_FUNC < span class = "keywordtype" > void< / span > < a class = "code hl_function" href = "radix_8h.html#a6d37e483d806c550deefabf56caf4ec8" > radix7< / a > (thread float2* x, thread float2* y) {< / div >
< div class = "line" > < a id = "l00123" name = "l00123" > < / a > < span class = "lineno" > 123< / span > < span class = "comment" > // Rader' s algorithm< / span > < / div >
< div class = "line" > < a id = "l00124" name = "l00124" > < / a > < span class = "lineno" > 124< / span > float2 inv = {1 / 6.0, -1 / 6.0};< / 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 = "comment" > // fft< / span > < / div >
< div class = "line" > < a id = "l00127" name = "l00127" > < / a > < span class = "lineno" > 127< / span > float2 in1[6] = {x[1], x[3], x[2], x[6], x[4], x[5]};< / div >
< div class = "line" > < a id = "l00128" name = "l00128" > < / a > < span class = "lineno" > 128< / span > < a class = "code hl_function" href = "radix_8h.html#afaaa5de58a97f0a5e6a84fc0d598a884" > radix6< / a > (in1, y + 1);< / div >
< div class = "line" > < a id = "l00129" name = "l00129" > < / a > < span class = "lineno" > 129< / span > < / div >
< div class = "line" > < a id = "l00130" name = "l00130" > < / a > < span class = "lineno" > 130< / span > y[0] = y[1] + x[0];< / div >
< div class = "line" > < a id = "l00131" name = "l00131" > < / a > < span class = "lineno" > 131< / span > < / div >
< div class = "line" > < a id = "l00132" name = "l00132" > < / a > < span class = "lineno" > 132< / span > < span class = "comment" > // b_q< / span > < / div >
< div class = "line" > < a id = "l00133" name = "l00133" > < / a > < span class = "lineno" > 133< / span > y[1] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[1], float2(-1, 0));< / div >
< div class = "line" > < a id = "l00134" name = "l00134" > < / a > < span class = "lineno" > 134< / span > y[2] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[2], float2(2.44013336, -1.02261879));< / div >
< div class = "line" > < a id = "l00135" name = "l00135" > < / a > < span class = "lineno" > 135< / span > y[3] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[3], float2(2.37046941, -1.17510629));< / div >
< div class = "line" > < a id = "l00136" name = "l00136" > < / a > < span class = "lineno" > 136< / span > y[4] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[4], float2(0, -2.64575131));< / div >
< div class = "line" > < a id = "l00137" name = "l00137" > < / a > < span class = "lineno" > 137< / span > y[5] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[5], float2(2.37046941, 1.17510629));< / div >
< div class = "line" > < a id = "l00138" name = "l00138" > < / a > < span class = "lineno" > 138< / span > y[6] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[6], float2(-2.44013336, -1.02261879));< / div >
< div class = "line" > < a id = "l00139" name = "l00139" > < / a > < span class = "lineno" > 139< / span > < / div >
< div class = "line" > < a id = "l00140" name = "l00140" > < / a > < span class = "lineno" > 140< / span > < span class = "comment" > // ifft< / span > < / div >
< div class = "line" > < a id = "l00141" name = "l00141" > < / a > < span class = "lineno" > 141< / span > < a class = "code hl_function" href = "radix_8h.html#afaaa5de58a97f0a5e6a84fc0d598a884" > radix6< / a > (y + 1, x + 1);< / 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 > y[1] = x[1] * inv + x[0];< / div >
< div class = "line" > < a id = "l00144" name = "l00144" > < / a > < span class = "lineno" > 144< / span > y[5] = x[2] * inv + x[0];< / div >
< div class = "line" > < a id = "l00145" name = "l00145" > < / a > < span class = "lineno" > 145< / span > y[4] = x[3] * inv + x[0];< / div >
< div class = "line" > < a id = "l00146" name = "l00146" > < / a > < span class = "lineno" > 146< / span > y[6] = x[4] * inv + x[0];< / div >
< div class = "line" > < a id = "l00147" name = "l00147" > < / a > < span class = "lineno" > 147< / span > y[2] = x[5] * inv + x[0];< / div >
< div class = "line" > < a id = "l00148" name = "l00148" > < / a > < span class = "lineno" > 148< / span > y[3] = x[6] * inv + x[0];< / div >
< div class = "line" > < a id = "l00149" name = "l00149" > < / a > < span class = "lineno" > 149< / span > }< / div >
< / div >
< div class = "line" > < a id = "l00150" name = "l00150" > < / a > < span class = "lineno" > 150< / span > < / div >
< div class = "foldopen" id = "foldopen00151" data-start = "{" data-end = "}" >
< div class = "line" > < a id = "l00151" name = "l00151" > < / a > < span class = "lineno" > < a class = "line" href = "radix_8h.html#a6b306e1afe1c5b6af4cd80aa02adb138" > 151< / a > < / span > METAL_FUNC < span class = "keywordtype" > void< / span > < a class = "code hl_function" href = "radix_8h.html#a6b306e1afe1c5b6af4cd80aa02adb138" > radix8< / a > (thread float2* x, thread float2* y) {< / div >
< div class = "line" > < a id = "l00152" name = "l00152" > < / a > < span class = "lineno" > 152< / span > < span class = "keywordtype" > float< / span > cos_pi_4 = 0.7071067811865476;< / div >
< div class = "line" > < a id = "l00153" name = "l00153" > < / a > < span class = "lineno" > 153< / span > float2 w_0 = {cos_pi_4, -cos_pi_4};< / div >
< div class = "line" > < a id = "l00154" name = "l00154" > < / a > < span class = "lineno" > 154< / span > float2 w_1 = {-cos_pi_4, -cos_pi_4};< / div >
< div class = "line" > < a id = "l00155" name = "l00155" > < / a > < span class = "lineno" > 155< / span > float2 temp[8] = {x[0], x[2], x[4], x[6], x[1], x[3], x[5], x[7]};< / div >
< div class = "line" > < a id = "l00156" name = "l00156" > < / a > < span class = "lineno" > 156< / span > < a class = "code hl_function" href = "radix_8h.html#a12cb26bd3ad635d16a195ccea750256d" > radix4< / a > (temp, x);< / div >
< div class = "line" > < a id = "l00157" name = "l00157" > < / a > < span class = "lineno" > 157< / span > < a class = "code hl_function" href = "radix_8h.html#a12cb26bd3ad635d16a195ccea750256d" > radix4< / a > (temp + 4, x + 4);< / 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 > y[0] = x[0] + x[4];< / div >
< div class = "line" > < a id = "l00160" name = "l00160" > < / a > < span class = "lineno" > 160< / span > y[4] = x[0] - x[4];< / div >
< div class = "line" > < a id = "l00161" name = "l00161" > < / a > < span class = "lineno" > 161< / span > float2 x_5 = < a class = "code hl_function" href = "radix_8h.html#a5bfc53b531214c9ce277bebc18aa67d6" > complex_mul< / a > (x[5], w_0);< / div >
< div class = "line" > < a id = "l00162" name = "l00162" > < / a > < span class = "lineno" > 162< / span > y[1] = x[1] + x_5;< / div >
< div class = "line" > < a id = "l00163" name = "l00163" > < / a > < span class = "lineno" > 163< / span > y[5] = x[1] - x_5;< / div >
< div class = "line" > < a id = "l00164" name = "l00164" > < / a > < span class = "lineno" > 164< / span > float2 x_6 = {x[6].y, -x[6].x};< / div >
< div class = "line" > < a id = "l00165" name = "l00165" > < / a > < span class = "lineno" > 165< / span > y[2] = x[2] + x_6;< / div >
< div class = "line" > < a id = "l00166" name = "l00166" > < / a > < span class = "lineno" > 166< / span > y[6] = x[2] - x_6;< / div >
< div class = "line" > < a id = "l00167" name = "l00167" > < / a > < span class = "lineno" > 167< / span > float2 x_7 = < a class = "code hl_function" href = "radix_8h.html#a5bfc53b531214c9ce277bebc18aa67d6" > complex_mul< / a > (x[7], w_1);< / div >
< div class = "line" > < a id = "l00168" name = "l00168" > < / a > < span class = "lineno" > 168< / span > y[3] = x[3] + x_7;< / div >
< div class = "line" > < a id = "l00169" name = "l00169" > < / a > < span class = "lineno" > 169< / span > y[7] = x[3] - x_7;< / div >
< div class = "line" > < a id = "l00170" name = "l00170" > < / a > < span class = "lineno" > 170< / span > }< / div >
< / div >
< div class = "line" > < a id = "l00171" name = "l00171" > < / a > < span class = "lineno" > 171< / span > < / div >
< div class = "line" > < a id = "l00172" name = "l00172" > < / a > < span class = "lineno" > 172< / span > < span class = "keyword" > template< / span > < < span class = "keywordtype" > bool< / span > raders_perm> < / div >
< div class = "foldopen" id = "foldopen00173" data-start = "{" data-end = "}" >
< div class = "line" > < a id = "l00173" name = "l00173" > < / a > < span class = "lineno" > < a class = "line" href = "radix_8h.html#a27054992e148bfcd9f7a69c96d75d926" > 173< / a > < / span > METAL_FUNC < span class = "keywordtype" > void< / span > < a class = "code hl_function" href = "radix_8h.html#a27054992e148bfcd9f7a69c96d75d926" > radix10< / a > (thread float2* x, thread float2* y) {< / div >
< div class = "line" > < a id = "l00174" name = "l00174" > < / a > < span class = "lineno" > 174< / span > float2 w[4];< / div >
< div class = "line" > < a id = "l00175" name = "l00175" > < / a > < span class = "lineno" > 175< / span > w[0] = {0.8090169943749475, -0.5877852522924731};< / div >
< div class = "line" > < a id = "l00176" name = "l00176" > < / a > < span class = "lineno" > 176< / span > w[1] = {0.30901699437494745, -0.9510565162951535};< / div >
< div class = "line" > < a id = "l00177" name = "l00177" > < / a > < span class = "lineno" > 177< / span > w[2] = {-w[1].x, w[1].y};< / div >
< div class = "line" > < a id = "l00178" name = "l00178" > < / a > < span class = "lineno" > 178< / span > w[3] = {-w[0].x, w[0].y};< / div >
< div class = "line" > < a id = "l00179" name = "l00179" > < / a > < span class = "lineno" > 179< / span > < / div >
< div class = "line" > < a id = "l00180" name = "l00180" > < / a > < span class = "lineno" > 180< / span > < span class = "keywordflow" > if< / span > (raders_perm) {< / div >
< div class = "line" > < a id = "l00181" name = "l00181" > < / a > < span class = "lineno" > 181< / span > float2 temp[10] = {< / div >
< div class = "line" > < a id = "l00182" name = "l00182" > < / a > < span class = "lineno" > 182< / span > x[0], x[3], x[4], x[8], x[2], x[1], x[7], x[9], x[6], x[5]};< / div >
< div class = "line" > < a id = "l00183" name = "l00183" > < / a > < span class = "lineno" > 183< / span > < a class = "code hl_function" href = "radix_8h.html#a026e6779e6d2ecdef39ff4aad186091e" > radix5< / a > (temp, x);< / div >
< div class = "line" > < a id = "l00184" name = "l00184" > < / a > < span class = "lineno" > 184< / span > < a class = "code hl_function" href = "radix_8h.html#a026e6779e6d2ecdef39ff4aad186091e" > radix5< / a > (temp + 5, x + 5);< / div >
< div class = "line" > < a id = "l00185" name = "l00185" > < / a > < span class = "lineno" > 185< / span > } < span class = "keywordflow" > else< / span > {< / div >
< div class = "line" > < a id = "l00186" name = "l00186" > < / a > < span class = "lineno" > 186< / span > float2 temp[10] = {< / div >
< div class = "line" > < a id = "l00187" name = "l00187" > < / a > < span class = "lineno" > 187< / span > x[0], x[2], x[4], x[6], x[8], x[1], x[3], x[5], x[7], x[9]};< / div >
< div class = "line" > < a id = "l00188" name = "l00188" > < / a > < span class = "lineno" > 188< / span > < a class = "code hl_function" href = "radix_8h.html#a026e6779e6d2ecdef39ff4aad186091e" > radix5< / a > (temp, x);< / div >
< div class = "line" > < a id = "l00189" name = "l00189" > < / a > < span class = "lineno" > 189< / span > < a class = "code hl_function" href = "radix_8h.html#a026e6779e6d2ecdef39ff4aad186091e" > radix5< / a > (temp + 5, x + 5);< / div >
< div class = "line" > < a id = "l00190" name = "l00190" > < / a > < span class = "lineno" > 190< / span > }< / div >
< div class = "line" > < a id = "l00191" name = "l00191" > < / a > < span class = "lineno" > 191< / span > < / div >
< div class = "line" > < a id = "l00192" name = "l00192" > < / a > < span class = "lineno" > 192< / span > y[0] = x[0] + x[5];< / div >
< div class = "line" > < a id = "l00193" name = "l00193" > < / a > < span class = "lineno" > 193< / span > y[5] = x[0] - x[5];< / div >
< div class = "line" > < a id = "l00194" name = "l00194" > < / a > < span class = "lineno" > 194< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > t = 1; t < 5; t++) {< / div >
< div class = "line" > < a id = "l00195" name = "l00195" > < / a > < span class = "lineno" > 195< / span > float2 a = < a class = "code hl_function" href = "radix_8h.html#a5bfc53b531214c9ce277bebc18aa67d6" > complex_mul< / a > (x[t + 5], w[t - 1]);< / div >
< div class = "line" > < a id = "l00196" name = "l00196" > < / a > < span class = "lineno" > 196< / span > y[t] = x[t] + a;< / div >
< div class = "line" > < a id = "l00197" name = "l00197" > < / a > < span class = "lineno" > 197< / span > y[t + 5] = x[t] - a;< / div >
< div class = "line" > < a id = "l00198" name = "l00198" > < / a > < span class = "lineno" > 198< / span > }< / div >
< div class = "line" > < a id = "l00199" name = "l00199" > < / a > < span class = "lineno" > 199< / span > }< / div >
< / div >
< div class = "line" > < a id = "l00200" name = "l00200" > < / a > < span class = "lineno" > 200< / span > < / div >
< div class = "foldopen" id = "foldopen00201" data-start = "{" data-end = "}" >
< div class = "line" > < a id = "l00201" name = "l00201" > < / a > < span class = "lineno" > < a class = "line" href = "radix_8h.html#a34f7dcefd29f8a7f6bddf9a17609a8a7" > 201< / a > < / span > METAL_FUNC < span class = "keywordtype" > void< / span > < a class = "code hl_function" href = "radix_8h.html#a34f7dcefd29f8a7f6bddf9a17609a8a7" > radix11< / a > (thread float2* x, thread float2* y) {< / div >
< div class = "line" > < a id = "l00202" name = "l00202" > < / a > < span class = "lineno" > 202< / span > < span class = "comment" > // Raders Algorithm< / span > < / div >
< div class = "line" > < a id = "l00203" name = "l00203" > < / a > < span class = "lineno" > 203< / span > float2 inv = {1 / 10.0, -1 / 10.0};< / div >
< div class = "line" > < a id = "l00204" name = "l00204" > < / a > < span class = "lineno" > 204< / span > < / div >
< div class = "line" > < a id = "l00205" name = "l00205" > < / a > < span class = "lineno" > 205< / span > < span class = "comment" > // fft< / span > < / div >
< div class = "line" > < a id = "l00206" name = "l00206" > < / a > < span class = "lineno" > 206< / span > < a class = "code hl_function" href = "radix_8h.html#a27054992e148bfcd9f7a69c96d75d926" > radix10< true> < / a > (x + 1, y + 1);< / div >
< div class = "line" > < a id = "l00207" name = "l00207" > < / a > < span class = "lineno" > 207< / span > < / div >
< div class = "line" > < a id = "l00208" name = "l00208" > < / a > < span class = "lineno" > 208< / span > y[0] = y[1] + x[0];< / div >
< div class = "line" > < a id = "l00209" name = "l00209" > < / a > < span class = "lineno" > 209< / span > < / div >
< div class = "line" > < a id = "l00210" name = "l00210" > < / a > < span class = "lineno" > 210< / span > < span class = "comment" > // b_q< / span > < / div >
< div class = "line" > < a id = "l00211" name = "l00211" > < / a > < span class = "lineno" > 211< / span > y[1] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[1], float2(-1, 0));< / div >
< div class = "line" > < a id = "l00212" name = "l00212" > < / a > < span class = "lineno" > 212< / span > y[2] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[2], float2(0.955301878, -3.17606649));< / div >
< div class = "line" > < a id = "l00213" name = "l00213" > < / a > < span class = "lineno" > 213< / span > y[3] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[3], float2(2.63610556, 2.01269656));< / div >
< div class = "line" > < a id = "l00214" name = "l00214" > < / a > < span class = "lineno" > 214< / span > y[4] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[4], float2(2.54127802, 2.13117479));< / div >
< div class = "line" > < a id = "l00215" name = "l00215" > < / a > < span class = "lineno" > 215< / span > y[5] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[5], float2(2.07016210, 2.59122150));< / div >
< div class = "line" > < a id = "l00216" name = "l00216" > < / a > < span class = "lineno" > 216< / span > y[6] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[6], float2(0, -3.31662479));< / div >
< div class = "line" > < a id = "l00217" name = "l00217" > < / a > < span class = "lineno" > 217< / span > y[7] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[7], float2(2.07016210, -2.59122150));< / div >
< div class = "line" > < a id = "l00218" name = "l00218" > < / a > < span class = "lineno" > 218< / span > y[8] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[8], float2(-2.54127802, 2.13117479));< / div >
< div class = "line" > < a id = "l00219" name = "l00219" > < / a > < span class = "lineno" > 219< / span > y[9] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[9], float2(2.63610556, -2.01269656));< / div >
< div class = "line" > < a id = "l00220" name = "l00220" > < / a > < span class = "lineno" > 220< / span > y[10] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[10], float2(-0.955301878, -3.17606649));< / div >
< div class = "line" > < a id = "l00221" name = "l00221" > < / a > < span class = "lineno" > 221< / span > < / div >
< div class = "line" > < a id = "l00222" name = "l00222" > < / a > < span class = "lineno" > 222< / span > < span class = "comment" > // ifft< / span > < / div >
< div class = "line" > < a id = "l00223" name = "l00223" > < / a > < span class = "lineno" > 223< / span > < a class = "code hl_function" href = "radix_8h.html#a27054992e148bfcd9f7a69c96d75d926" > radix10< false> < / a > (y + 1, x + 1);< / div >
< div class = "line" > < a id = "l00224" name = "l00224" > < / a > < span class = "lineno" > 224< / span > < / div >
< div class = "line" > < a id = "l00225" name = "l00225" > < / a > < span class = "lineno" > 225< / span > y[1] = x[1] * inv + x[0];< / div >
< div class = "line" > < a id = "l00226" name = "l00226" > < / a > < span class = "lineno" > 226< / span > y[6] = x[2] * inv + x[0];< / div >
< div class = "line" > < a id = "l00227" name = "l00227" > < / a > < span class = "lineno" > 227< / span > y[3] = x[3] * inv + x[0];< / div >
< div class = "line" > < a id = "l00228" name = "l00228" > < / a > < span class = "lineno" > 228< / span > y[7] = x[4] * inv + x[0];< / div >
< div class = "line" > < a id = "l00229" name = "l00229" > < / a > < span class = "lineno" > 229< / span > y[9] = x[5] * inv + x[0];< / div >
< div class = "line" > < a id = "l00230" name = "l00230" > < / a > < span class = "lineno" > 230< / span > y[10] = x[6] * inv + x[0];< / div >
< div class = "line" > < a id = "l00231" name = "l00231" > < / a > < span class = "lineno" > 231< / span > y[5] = x[7] * inv + x[0];< / div >
< div class = "line" > < a id = "l00232" name = "l00232" > < / a > < span class = "lineno" > 232< / span > y[8] = x[8] * inv + x[0];< / div >
< div class = "line" > < a id = "l00233" name = "l00233" > < / a > < span class = "lineno" > 233< / span > y[4] = x[9] * inv + x[0];< / div >
< div class = "line" > < a id = "l00234" name = "l00234" > < / a > < span class = "lineno" > 234< / span > y[2] = x[10] * inv + x[0];< / div >
< div class = "line" > < a id = "l00235" name = "l00235" > < / a > < span class = "lineno" > 235< / span > }< / div >
< / div >
< div class = "line" > < a id = "l00236" name = "l00236" > < / a > < span class = "lineno" > 236< / span > < / div >
< div class = "line" > < a id = "l00237" name = "l00237" > < / a > < span class = "lineno" > 237< / span > < span class = "keyword" > template< / span > < < span class = "keywordtype" > bool< / span > raders_perm> < / div >
< div class = "foldopen" id = "foldopen00238" data-start = "{" data-end = "}" >
< div class = "line" > < a id = "l00238" name = "l00238" > < / a > < span class = "lineno" > < a class = "line" href = "radix_8h.html#a3c61aa04a4b38575722d864cc9ffd0b7" > 238< / a > < / span > METAL_FUNC < span class = "keywordtype" > void< / span > < a class = "code hl_function" href = "radix_8h.html#a3c61aa04a4b38575722d864cc9ffd0b7" > radix12< / a > (thread float2* x, thread float2* y) {< / div >
< div class = "line" > < a id = "l00239" name = "l00239" > < / a > < span class = "lineno" > 239< / span > float2 w[6];< / div >
< div class = "line" > < a id = "l00240" name = "l00240" > < / a > < span class = "lineno" > 240< / span > < span class = "keywordtype" > float< / span > sin_pi_3 = 0.8660254037844387;< / div >
< div class = "line" > < a id = "l00241" name = "l00241" > < / a > < span class = "lineno" > 241< / span > w[0] = {sin_pi_3, -0.5};< / div >
< div class = "line" > < a id = "l00242" name = "l00242" > < / a > < span class = "lineno" > 242< / span > w[1] = {0.5, -sin_pi_3};< / div >
< div class = "line" > < a id = "l00243" name = "l00243" > < / a > < span class = "lineno" > 243< / span > w[2] = {0, -1};< / div >
< div class = "line" > < a id = "l00244" name = "l00244" > < / a > < span class = "lineno" > 244< / span > w[3] = {-0.5, -sin_pi_3};< / div >
< div class = "line" > < a id = "l00245" name = "l00245" > < / a > < span class = "lineno" > 245< / span > w[4] = {-sin_pi_3, -0.5};< / div >
< div class = "line" > < a id = "l00246" name = "l00246" > < / a > < span class = "lineno" > 246< / span > < / div >
< div class = "line" > < a id = "l00247" name = "l00247" > < / a > < span class = "lineno" > 247< / span > < span class = "keywordflow" > if< / span > (raders_perm) {< / div >
< div class = "line" > < a id = "l00248" name = "l00248" > < / a > < span class = "lineno" > 248< / span > float2 temp[12] = {< / div >
< div class = "line" > < a id = "l00249" name = "l00249" > < / a > < span class = "lineno" > 249< / span > x[0],< / div >
< div class = "line" > < a id = "l00250" name = "l00250" > < / a > < span class = "lineno" > 250< / span > x[3],< / div >
< div class = "line" > < a id = "l00251" name = "l00251" > < / a > < span class = "lineno" > 251< / span > x[2],< / div >
< div class = "line" > < a id = "l00252" name = "l00252" > < / a > < span class = "lineno" > 252< / span > x[11],< / div >
< div class = "line" > < a id = "l00253" name = "l00253" > < / a > < span class = "lineno" > 253< / span > x[8],< / div >
< div class = "line" > < a id = "l00254" name = "l00254" > < / a > < span class = "lineno" > 254< / span > x[9],< / div >
< div class = "line" > < a id = "l00255" name = "l00255" > < / a > < span class = "lineno" > 255< / span > x[1],< / div >
< div class = "line" > < a id = "l00256" name = "l00256" > < / a > < span class = "lineno" > 256< / span > x[7],< / div >
< div class = "line" > < a id = "l00257" name = "l00257" > < / a > < span class = "lineno" > 257< / span > x[5],< / div >
< div class = "line" > < a id = "l00258" name = "l00258" > < / a > < span class = "lineno" > 258< / span > x[10],< / div >
< div class = "line" > < a id = "l00259" name = "l00259" > < / a > < span class = "lineno" > 259< / span > x[4],< / div >
< div class = "line" > < a id = "l00260" name = "l00260" > < / a > < span class = "lineno" > 260< / span > x[6]};< / div >
< div class = "line" > < a id = "l00261" name = "l00261" > < / a > < span class = "lineno" > 261< / span > < a class = "code hl_function" href = "radix_8h.html#afaaa5de58a97f0a5e6a84fc0d598a884" > radix6< / a > (temp, x);< / div >
< div class = "line" > < a id = "l00262" name = "l00262" > < / a > < span class = "lineno" > 262< / span > < a class = "code hl_function" href = "radix_8h.html#afaaa5de58a97f0a5e6a84fc0d598a884" > radix6< / a > (temp + 6, x + 6);< / div >
< div class = "line" > < a id = "l00263" name = "l00263" > < / a > < span class = "lineno" > 263< / span > } < span class = "keywordflow" > else< / span > {< / div >
< div class = "line" > < a id = "l00264" name = "l00264" > < / a > < span class = "lineno" > 264< / span > float2 temp[12] = {< / div >
< div class = "line" > < a id = "l00265" name = "l00265" > < / a > < span class = "lineno" > 265< / span > x[0],< / div >
< div class = "line" > < a id = "l00266" name = "l00266" > < / a > < span class = "lineno" > 266< / span > x[2],< / div >
< div class = "line" > < a id = "l00267" name = "l00267" > < / a > < span class = "lineno" > 267< / span > x[4],< / div >
< div class = "line" > < a id = "l00268" name = "l00268" > < / a > < span class = "lineno" > 268< / span > x[6],< / div >
< div class = "line" > < a id = "l00269" name = "l00269" > < / a > < span class = "lineno" > 269< / span > x[8],< / div >
< div class = "line" > < a id = "l00270" name = "l00270" > < / a > < span class = "lineno" > 270< / span > x[10],< / div >
< div class = "line" > < a id = "l00271" name = "l00271" > < / a > < span class = "lineno" > 271< / span > x[1],< / div >
< div class = "line" > < a id = "l00272" name = "l00272" > < / a > < span class = "lineno" > 272< / span > x[3],< / div >
< div class = "line" > < a id = "l00273" name = "l00273" > < / a > < span class = "lineno" > 273< / span > x[5],< / div >
< div class = "line" > < a id = "l00274" name = "l00274" > < / a > < span class = "lineno" > 274< / span > x[7],< / div >
< div class = "line" > < a id = "l00275" name = "l00275" > < / a > < span class = "lineno" > 275< / span > x[9],< / div >
< div class = "line" > < a id = "l00276" name = "l00276" > < / a > < span class = "lineno" > 276< / span > x[11]};< / div >
< div class = "line" > < a id = "l00277" name = "l00277" > < / a > < span class = "lineno" > 277< / span > < a class = "code hl_function" href = "radix_8h.html#afaaa5de58a97f0a5e6a84fc0d598a884" > radix6< / a > (temp, x);< / div >
< div class = "line" > < a id = "l00278" name = "l00278" > < / a > < span class = "lineno" > 278< / span > < a class = "code hl_function" href = "radix_8h.html#afaaa5de58a97f0a5e6a84fc0d598a884" > radix6< / a > (temp + 6, x + 6);< / div >
< div class = "line" > < a id = "l00279" name = "l00279" > < / a > < span class = "lineno" > 279< / span > }< / div >
< div class = "line" > < a id = "l00280" name = "l00280" > < / a > < span class = "lineno" > 280< / span > < / div >
< div class = "line" > < a id = "l00281" name = "l00281" > < / a > < span class = "lineno" > 281< / span > y[0] = x[0] + x[6];< / div >
< div class = "line" > < a id = "l00282" name = "l00282" > < / a > < span class = "lineno" > 282< / span > y[6] = x[0] - x[6];< / div >
< div class = "line" > < a id = "l00283" name = "l00283" > < / a > < span class = "lineno" > 283< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > t = 1; t < 6; t++) {< / div >
< div class = "line" > < a id = "l00284" name = "l00284" > < / a > < span class = "lineno" > 284< / span > float2 a = < a class = "code hl_function" href = "radix_8h.html#a5bfc53b531214c9ce277bebc18aa67d6" > complex_mul< / a > (x[t + 6], w[t - 1]);< / div >
< div class = "line" > < a id = "l00285" name = "l00285" > < / a > < span class = "lineno" > 285< / span > y[t] = x[t] + a;< / div >
< div class = "line" > < a id = "l00286" name = "l00286" > < / a > < span class = "lineno" > 286< / span > y[t + 6] = x[t] - a;< / div >
< div class = "line" > < a id = "l00287" name = "l00287" > < / a > < span class = "lineno" > 287< / span > }< / div >
< div class = "line" > < a id = "l00288" name = "l00288" > < / a > < span class = "lineno" > 288< / span > }< / div >
< / div >
< div class = "line" > < a id = "l00289" name = "l00289" > < / a > < span class = "lineno" > 289< / span > < / div >
< div class = "foldopen" id = "foldopen00290" data-start = "{" data-end = "}" >
< div class = "line" > < a id = "l00290" name = "l00290" > < / a > < span class = "lineno" > < a class = "line" href = "radix_8h.html#a833b7b31facbd62f6971bb108c54d1db" > 290< / a > < / span > METAL_FUNC < span class = "keywordtype" > void< / span > < a class = "code hl_function" href = "radix_8h.html#a833b7b31facbd62f6971bb108c54d1db" > radix13< / a > (thread float2* x, thread float2* y) {< / div >
< div class = "line" > < a id = "l00291" name = "l00291" > < / a > < span class = "lineno" > 291< / span > < span class = "comment" > // Raders Algorithm< / span > < / div >
< div class = "line" > < a id = "l00292" name = "l00292" > < / a > < span class = "lineno" > 292< / span > float2 inv = {1 / 12.0, -1 / 12.0};< / div >
< div class = "line" > < a id = "l00293" name = "l00293" > < / a > < span class = "lineno" > 293< / span > < / div >
< div class = "line" > < a id = "l00294" name = "l00294" > < / a > < span class = "lineno" > 294< / span > < span class = "comment" > // fft< / span > < / div >
< div class = "line" > < a id = "l00295" name = "l00295" > < / a > < span class = "lineno" > 295< / span > < a class = "code hl_function" href = "radix_8h.html#a3c61aa04a4b38575722d864cc9ffd0b7" > radix12< true> < / a > (x + 1, y + 1);< / div >
< div class = "line" > < a id = "l00296" name = "l00296" > < / a > < span class = "lineno" > 296< / span > < / div >
< div class = "line" > < a id = "l00297" name = "l00297" > < / a > < span class = "lineno" > 297< / span > y[0] = y[1] + x[0];< / div >
< div class = "line" > < a id = "l00298" name = "l00298" > < / a > < span class = "lineno" > 298< / span > < / div >
< div class = "line" > < a id = "l00299" name = "l00299" > < / a > < span class = "lineno" > 299< / span > < span class = "comment" > // b_q< / span > < / div >
< div class = "line" > < a id = "l00300" name = "l00300" > < / a > < span class = "lineno" > 300< / span > y[1] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[1], float2(-1, 0));< / div >
< div class = "line" > < a id = "l00301" name = "l00301" > < / a > < span class = "lineno" > 301< / span > y[2] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[2], float2(3.07497206, -1.88269669));< / div >
< div class = "line" > < a id = "l00302" name = "l00302" > < / a > < span class = "lineno" > 302< / span > y[3] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[3], float2(3.09912468, 1.84266823));< / div >
< div class = "line" > < a id = "l00303" name = "l00303" > < / a > < span class = "lineno" > 303< / span > y[4] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[4], float2(3.45084438, -1.04483161));< / div >
< div class = "line" > < a id = "l00304" name = "l00304" > < / a > < span class = "lineno" > 304< / span > y[5] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[5], float2(0.91083583, 3.48860690));< / div >
< div class = "line" > < a id = "l00305" name = "l00305" > < / a > < span class = "lineno" > 305< / span > y[6] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[6], float2(-3.60286363, 0.139189267));< / div >
< div class = "line" > < a id = "l00306" name = "l00306" > < / a > < span class = "lineno" > 306< / span > y[7] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[7], float2(3.60555128, 0));< / div >
< div class = "line" > < a id = "l00307" name = "l00307" > < / a > < span class = "lineno" > 307< / span > y[8] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[8], float2(3.60286363, 0.139189267));< / div >
< div class = "line" > < a id = "l00308" name = "l00308" > < / a > < span class = "lineno" > 308< / span > y[9] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[9], float2(0.91083583, -3.48860690));< / div >
< div class = "line" > < a id = "l00309" name = "l00309" > < / a > < span class = "lineno" > 309< / span > y[10] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[10], float2(-3.45084438, -1.04483161));< / div >
< div class = "line" > < a id = "l00310" name = "l00310" > < / a > < span class = "lineno" > 310< / span > y[11] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[11], float2(3.09912468, -1.84266823));< / div >
< div class = "line" > < a id = "l00311" name = "l00311" > < / a > < span class = "lineno" > 311< / span > y[12] = < a class = "code hl_function" href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > (y[12], float2(-3.07497206, -1.88269669));< / div >
< div class = "line" > < a id = "l00312" name = "l00312" > < / a > < span class = "lineno" > 312< / span > < / div >
< div class = "line" > < a id = "l00313" name = "l00313" > < / a > < span class = "lineno" > 313< / span > < span class = "comment" > // ifft< / span > < / div >
< div class = "line" > < a id = "l00314" name = "l00314" > < / a > < span class = "lineno" > 314< / span > < a class = "code hl_function" href = "radix_8h.html#a3c61aa04a4b38575722d864cc9ffd0b7" > radix12< false> < / a > (y + 1, x + 1);< / div >
< div class = "line" > < a id = "l00315" name = "l00315" > < / a > < span class = "lineno" > 315< / span > < / div >
< div class = "line" > < a id = "l00316" name = "l00316" > < / a > < span class = "lineno" > 316< / span > y[1] = x[1] * inv + x[0];< / div >
< div class = "line" > < a id = "l00317" name = "l00317" > < / a > < span class = "lineno" > 317< / span > y[7] = x[2] * inv + x[0];< / div >
< div class = "line" > < a id = "l00318" name = "l00318" > < / a > < span class = "lineno" > 318< / span > y[10] = x[3] * inv + x[0];< / div >
< div class = "line" > < a id = "l00319" name = "l00319" > < / a > < span class = "lineno" > 319< / span > y[5] = x[4] * inv + x[0];< / div >
< div class = "line" > < a id = "l00320" name = "l00320" > < / a > < span class = "lineno" > 320< / span > y[9] = x[5] * inv + x[0];< / div >
< div class = "line" > < a id = "l00321" name = "l00321" > < / a > < span class = "lineno" > 321< / span > y[11] = x[6] * inv + x[0];< / div >
< div class = "line" > < a id = "l00322" name = "l00322" > < / a > < span class = "lineno" > 322< / span > y[12] = x[7] * inv + x[0];< / div >
< div class = "line" > < a id = "l00323" name = "l00323" > < / a > < span class = "lineno" > 323< / span > y[6] = x[8] * inv + x[0];< / div >
< div class = "line" > < a id = "l00324" name = "l00324" > < / a > < span class = "lineno" > 324< / span > y[3] = x[9] * inv + x[0];< / div >
< div class = "line" > < a id = "l00325" name = "l00325" > < / a > < span class = "lineno" > 325< / span > y[8] = x[10] * inv + x[0];< / div >
< div class = "line" > < a id = "l00326" name = "l00326" > < / a > < span class = "lineno" > 326< / span > y[4] = x[11] * inv + x[0];< / div >
< div class = "line" > < a id = "l00327" name = "l00327" > < / a > < span class = "lineno" > 327< / span > y[2] = x[12] * inv + x[0];< / div >
< div class = "line" > < a id = "l00328" name = "l00328" > < / a > < span class = "lineno" > 328< / span > }< / div >
< / div >
2024-11-23 04:24:16 +08:00
< div class = "ttc" id = "anamespacemetal_1_1fast_html_a3af771cfe7a135104f9d063147dba270" > < div class = "ttname" > < a href = "namespacemetal_1_1fast.html#a3af771cfe7a135104f9d063147dba270" > metal::fast::sin< / a > < / div > < div class = "ttdeci" > METAL_FUNC bfloat16_t sin(bfloat16_t x)< / div > < div class = "ttdef" > < b > Definition< / b > bf16_math.h:240< / div > < / div >
< div class = "ttc" id = "anamespacemetal_1_1fast_html_a75b6bb32fa3870eda46a7bfc9f481f88" > < div class = "ttname" > < a href = "namespacemetal_1_1fast.html#a75b6bb32fa3870eda46a7bfc9f481f88" > metal::fast::cos< / a > < / div > < div class = "ttdeci" > METAL_FUNC bfloat16_t cos(bfloat16_t x)< / div > < div class = "ttdef" > < b > Definition< / b > bf16_math.h:240< / div > < / div >
2024-10-15 23:12:17 +08:00
< div class = "ttc" id = "aradix_8h_html_a026e6779e6d2ecdef39ff4aad186091e" > < div class = "ttname" > < a href = "radix_8h.html#a026e6779e6d2ecdef39ff4aad186091e" > radix5< / a > < / div > < div class = "ttdeci" > METAL_FUNC void radix5(thread float2 *x, thread float2 *y)< / div > < div class = "ttdef" > < b > Definition< / b > radix.h:69< / div > < / div >
< div class = "ttc" id = "aradix_8h_html_a0e2dfd3d1dda09f47ccc64eec35629f3" > < div class = "ttname" > < a href = "radix_8h.html#a0e2dfd3d1dda09f47ccc64eec35629f3" > complex_mul_conj< / a > < / div > < div class = "ttdeci" > METAL_FUNC float2 complex_mul_conj(float2 a, float2 b)< / div > < div class = "ttdef" > < b > Definition< / b > radix.h:24< / div > < / div >
< div class = "ttc" id = "aradix_8h_html_a12cb26bd3ad635d16a195ccea750256d" > < div class = "ttname" > < a href = "radix_8h.html#a12cb26bd3ad635d16a195ccea750256d" > radix4< / a > < / div > < div class = "ttdeci" > METAL_FUNC void radix4(thread float2 *x, thread float2 *y)< / div > < div class = "ttdef" > < b > Definition< / b > radix.h:56< / div > < / div >
< div class = "ttc" id = "aradix_8h_html_a27054992e148bfcd9f7a69c96d75d926" > < div class = "ttname" > < a href = "radix_8h.html#a27054992e148bfcd9f7a69c96d75d926" > radix10< / a > < / div > < div class = "ttdeci" > METAL_FUNC void radix10(thread float2 *x, thread float2 *y)< / div > < div class = "ttdef" > < b > Definition< / b > radix.h:173< / div > < / div >
< div class = "ttc" id = "aradix_8h_html_a34f7dcefd29f8a7f6bddf9a17609a8a7" > < div class = "ttname" > < a href = "radix_8h.html#a34f7dcefd29f8a7f6bddf9a17609a8a7" > radix11< / a > < / div > < div class = "ttdeci" > METAL_FUNC void radix11(thread float2 *x, thread float2 *y)< / div > < div class = "ttdef" > < b > Definition< / b > radix.h:201< / div > < / div >
< div class = "ttc" id = "aradix_8h_html_a3c61aa04a4b38575722d864cc9ffd0b7" > < div class = "ttname" > < a href = "radix_8h.html#a3c61aa04a4b38575722d864cc9ffd0b7" > radix12< / a > < / div > < div class = "ttdeci" > METAL_FUNC void radix12(thread float2 *x, thread float2 *y)< / div > < div class = "ttdef" > < b > Definition< / b > radix.h:238< / div > < / div >
< div class = "ttc" id = "aradix_8h_html_a497b31cfa28418e1c2fad53d09f7bc0b" > < div class = "ttname" > < a href = "radix_8h.html#a497b31cfa28418e1c2fad53d09f7bc0b" > radix3< / a > < / div > < div class = "ttdeci" > METAL_FUNC void radix3(thread float2 *x, thread float2 *y)< / div > < div class = "ttdef" > < b > Definition< / b > radix.h:41< / div > < / div >
< div class = "ttc" id = "aradix_8h_html_a5bfc53b531214c9ce277bebc18aa67d6" > < div class = "ttname" > < a href = "radix_8h.html#a5bfc53b531214c9ce277bebc18aa67d6" > complex_mul< / a > < / div > < div class = "ttdeci" > METAL_FUNC float2 complex_mul(float2 a, float2 b)< / div > < div class = "ttdef" > < b > Definition< / b > radix.h:19< / div > < / div >
< div class = "ttc" id = "aradix_8h_html_a6b306e1afe1c5b6af4cd80aa02adb138" > < div class = "ttname" > < a href = "radix_8h.html#a6b306e1afe1c5b6af4cd80aa02adb138" > radix8< / a > < / div > < div class = "ttdeci" > METAL_FUNC void radix8(thread float2 *x, thread float2 *y)< / div > < div class = "ttdef" > < b > Definition< / b > radix.h:151< / div > < / div >
< div class = "ttc" id = "aradix_8h_html_a6d37e483d806c550deefabf56caf4ec8" > < div class = "ttname" > < a href = "radix_8h.html#a6d37e483d806c550deefabf56caf4ec8" > radix7< / a > < / div > < div class = "ttdeci" > METAL_FUNC void radix7(thread float2 *x, thread float2 *y)< / div > < div class = "ttdef" > < b > Definition< / b > radix.h:122< / div > < / div >
< div class = "ttc" id = "aradix_8h_html_a745e50244f1470bba233d8b6b993729c" > < div class = "ttname" > < a href = "radix_8h.html#a745e50244f1470bba233d8b6b993729c" > radix2< / a > < / div > < div class = "ttdeci" > METAL_FUNC void radix2(thread float2 *x, thread float2 *y)< / div > < div class = "ttdef" > < b > Definition< / b > radix.h:36< / div > < / div >
< div class = "ttc" id = "aradix_8h_html_a833b7b31facbd62f6971bb108c54d1db" > < div class = "ttname" > < a href = "radix_8h.html#a833b7b31facbd62f6971bb108c54d1db" > radix13< / a > < / div > < div class = "ttdeci" > METAL_FUNC void radix13(thread float2 *x, thread float2 *y)< / div > < div class = "ttdef" > < b > Definition< / b > radix.h:290< / div > < / div >
< div class = "ttc" id = "aradix_8h_html_ac5cf950316b9445296ee9ecfc56a56bd" > < div class = "ttname" > < a href = "radix_8h.html#ac5cf950316b9445296ee9ecfc56a56bd" > get_twiddle< / a > < / div > < div class = "ttdeci" > METAL_FUNC float2 get_twiddle(int k, int p)< / div > < div class = "ttdef" > < b > Definition< / b > radix.h:29< / div > < / div >
< div class = "ttc" id = "aradix_8h_html_afaaa5de58a97f0a5e6a84fc0d598a884" > < div class = "ttname" > < a href = "radix_8h.html#afaaa5de58a97f0a5e6a84fc0d598a884" > radix6< / a > < / div > < div class = "ttdeci" > METAL_FUNC void radix6(thread float2 *x, thread float2 *y)< / div > < div class = "ttdef" > < b > Definition< / b > radix.h:96< / div > < / div >
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