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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" > fft.h< / div > < / div >
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< a href = "backend_2metal_2kernels_2fft_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" > // Metal FFT using Stockham' s algorithm< / 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" > // References:< / span > < / div >
< div class = "line" > < a id = "l00006" name = "l00006" > < / a > < span class = "lineno" > 6< / span > < span class = "comment" > // - VkFFT (https://github.com/DTolm/VkFFT)< / span > < / div >
< div class = "line" > < a id = "l00007" name = "l00007" > < / a > < span class = "lineno" > 7< / span > < span class = "comment" > // - Eric Bainville' s excellent page (http://www.bealto.com/gpu-fft.html)< / span > < / 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 = "preprocessor" > #include < metal_common> < / span > < / div >
< div class = "line" > < a id = "l00010" name = "l00010" > < / a > < span class = "lineno" > 10< / span > < / div >
< div class = "line" > < a id = "l00011" name = "l00011" > < / a > < span class = "lineno" > 11< / span > < span class = "preprocessor" > #include " < a class = "code" href = "radix_8h.html" > mlx/backend/metal/kernels/fft/radix.h< / a > " < / span > < / div >
< div class = "line" > < a id = "l00012" name = "l00012" > < / a > < span class = "lineno" > 12< / span > < span class = "preprocessor" > #include " < a class = "code" href = "readwrite_8h.html" > mlx/backend/metal/kernels/fft/readwrite.h< / a > " < / span > < / div >
< div class = "line" > < a id = "l00013" name = "l00013" > < / a > < span class = "lineno" > 13< / 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 = "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 = "keyword" > using namespace < / span > < a class = "code hl_namespace" href = "namespacemetal.html" > metal< / a > ;< / div >
< div class = "line" > < a id = "l00016" name = "l00016" > < / a > < span class = "lineno" > 16< / span > < / div >
< div class = "line" > < a id = "l00017" name = "l00017" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#a7b6e56afa21f022c5e754b000955735a" > 17< / a > < / span > < span class = "preprocessor" > #define MAX_RADIX 13< / span > < / div >
< div class = "line" > < a id = "l00018" name = "l00018" > < / a > < span class = "lineno" > 18< / span > < span class = "comment" > // Reached when elems_per_thread_ = 6, max_radix = 13< / span > < / div >
< div class = "line" > < a id = "l00019" name = "l00019" > < / a > < span class = "lineno" > 19< / span > < span class = "comment" > // and some threads have to do 3 radix 6s requiring 18 float2s.< / span > < / div >
< div class = "line" > < a id = "l00020" name = "l00020" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#a28d683cf067736d76f867f30c066317e" > 20< / a > < / span > < span class = "preprocessor" > #define MAX_OUTPUT_SIZE 18< / span > < / div >
< div class = "line" > < a id = "l00021" name = "l00021" > < / a > < span class = "lineno" > 21< / span > < / div >
< div class = "line" > < a id = "l00022" name = "l00022" > < / a > < span class = "lineno" > 22< / span > < span class = "comment" > // Specialize for a particular value of N at runtime< / span > < / div >
< div class = "line" > < a id = "l00023" name = "l00023" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#a7a83318497519ff3ff0141b7d511ed38" > 23< / a > < / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b" > STEEL_CONST< / a > < span class = "keywordtype" > bool< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a7a83318497519ff3ff0141b7d511ed38" > inv_< / a > [[function_constant(0)]];< / div >
< div class = "line" > < a id = "l00024" name = "l00024" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#a2a4df90e329b84ee6c1890ba7c265c9c" > 24< / a > < / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b" > STEEL_CONST< / a > < span class = "keywordtype" > bool< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a2a4df90e329b84ee6c1890ba7c265c9c" > is_power_of_2_< / a > [[function_constant(1)]];< / div >
< div class = "line" > < a id = "l00025" name = "l00025" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3" > 25< / a > < / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b" > STEEL_CONST< / a > < span class = "keywordtype" > int< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3" > elems_per_thread_< / a > [[function_constant(2)]];< / div >
< div class = "line" > < a id = "l00026" name = "l00026" > < / a > < span class = "lineno" > 26< / span > < span class = "comment" > // rader_m = n / rader_n< / span > < / div >
< div class = "line" > < a id = "l00027" name = "l00027" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#ac309c77ef775a3ef13850c5287a86480" > 27< / a > < / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b" > STEEL_CONST< / a > < span class = "keywordtype" > int< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#ac309c77ef775a3ef13850c5287a86480" > rader_m_< / a > [[function_constant(3)]];< / div >
< div class = "line" > < a id = "l00028" name = "l00028" > < / a > < span class = "lineno" > 28< / span > < span class = "comment" > // Stockham steps< / span > < / div >
< div class = "line" > < a id = "l00029" name = "l00029" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#abb079b86e89ca88ce13a179d9ec566af" > 29< / a > < / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b" > STEEL_CONST< / a > < span class = "keywordtype" > int< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#abb079b86e89ca88ce13a179d9ec566af" > radix_13_steps_< / a > [[function_constant(4)]];< / div >
< div class = "line" > < a id = "l00030" name = "l00030" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#a7cd17bff8bc567f71d4789ee31fa07f2" > 30< / a > < / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b" > STEEL_CONST< / a > < span class = "keywordtype" > int< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a7cd17bff8bc567f71d4789ee31fa07f2" > radix_11_steps_< / a > [[function_constant(5)]];< / div >
< div class = "line" > < a id = "l00031" name = "l00031" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#a3cb03a97a209ba1346375e720ee76177" > 31< / a > < / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b" > STEEL_CONST< / a > < span class = "keywordtype" > int< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a3cb03a97a209ba1346375e720ee76177" > radix_8_steps_< / a > [[function_constant(6)]];< / div >
< div class = "line" > < a id = "l00032" name = "l00032" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#a2145cc8ab4d07583a735317b3cf60d55" > 32< / a > < / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b" > STEEL_CONST< / a > < span class = "keywordtype" > int< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a2145cc8ab4d07583a735317b3cf60d55" > radix_7_steps_< / a > [[function_constant(7)]];< / div >
< div class = "line" > < a id = "l00033" name = "l00033" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#a2f7f7cc2423cfcd4998d1a2a0363c3e2" > 33< / a > < / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b" > STEEL_CONST< / a > < span class = "keywordtype" > int< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a2f7f7cc2423cfcd4998d1a2a0363c3e2" > radix_6_steps_< / a > [[function_constant(8)]];< / div >
< div class = "line" > < a id = "l00034" name = "l00034" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#a903d5239b5f73577c559e97ff910892d" > 34< / a > < / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b" > STEEL_CONST< / a > < span class = "keywordtype" > int< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a903d5239b5f73577c559e97ff910892d" > radix_5_steps_< / a > [[function_constant(9)]];< / div >
< div class = "line" > < a id = "l00035" name = "l00035" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#a12d99a846c3686806bab6c42148e1039" > 35< / a > < / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b" > STEEL_CONST< / a > < span class = "keywordtype" > int< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a12d99a846c3686806bab6c42148e1039" > radix_4_steps_< / a > [[function_constant(10)]];< / div >
< div class = "line" > < a id = "l00036" name = "l00036" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#a579123b7be825f08f3076287dded08e3" > 36< / a > < / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b" > STEEL_CONST< / a > < span class = "keywordtype" > int< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a579123b7be825f08f3076287dded08e3" > radix_3_steps_< / a > [[function_constant(11)]];< / div >
< div class = "line" > < a id = "l00037" name = "l00037" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#a53fdc660e99e6b5db6808bbd596cd374" > 37< / a > < / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b" > STEEL_CONST< / a > < span class = "keywordtype" > int< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a53fdc660e99e6b5db6808bbd596cd374" > radix_2_steps_< / a > [[function_constant(12)]];< / div >
< div class = "line" > < a id = "l00038" name = "l00038" > < / a > < span class = "lineno" > 38< / span > < span class = "comment" > // Rader steps< / span > < / div >
< div class = "line" > < a id = "l00039" name = "l00039" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#a20d24f3e040d3d226a70d4dd7c9ac6a9" > 39< / a > < / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b" > STEEL_CONST< / a > < span class = "keywordtype" > int< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a20d24f3e040d3d226a70d4dd7c9ac6a9" > rader_13_steps_< / a > [[function_constant(13)]];< / div >
< div class = "line" > < a id = "l00040" name = "l00040" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#a1f3c377d05da52429172e64132dba750" > 40< / a > < / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b" > STEEL_CONST< / a > < span class = "keywordtype" > int< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a1f3c377d05da52429172e64132dba750" > rader_11_steps_< / a > [[function_constant(14)]];< / div >
< div class = "line" > < a id = "l00041" name = "l00041" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#ac6123e111816dd62a11ccb86b66fa3e9" > 41< / a > < / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b" > STEEL_CONST< / a > < span class = "keywordtype" > int< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#ac6123e111816dd62a11ccb86b66fa3e9" > rader_8_steps_< / a > [[function_constant(15)]];< / div >
< div class = "line" > < a id = "l00042" name = "l00042" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#a0d437aef17faf8d9707ae7ffe68fdb30" > 42< / a > < / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b" > STEEL_CONST< / a > < span class = "keywordtype" > int< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a0d437aef17faf8d9707ae7ffe68fdb30" > rader_7_steps_< / a > [[function_constant(16)]];< / div >
< div class = "line" > < a id = "l00043" name = "l00043" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#a020469d1aca557ff1b49414f121dedbb" > 43< / a > < / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b" > STEEL_CONST< / a > < span class = "keywordtype" > int< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a020469d1aca557ff1b49414f121dedbb" > rader_6_steps_< / a > [[function_constant(17)]];< / div >
< div class = "line" > < a id = "l00044" name = "l00044" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#afea05e9a7105bafbaafca25042f4d1b4" > 44< / a > < / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b" > STEEL_CONST< / a > < span class = "keywordtype" > int< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#afea05e9a7105bafbaafca25042f4d1b4" > rader_5_steps_< / a > [[function_constant(18)]];< / div >
< div class = "line" > < a id = "l00045" name = "l00045" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#ac7c58404df0434d4f861db62d3471870" > 45< / a > < / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b" > STEEL_CONST< / a > < span class = "keywordtype" > int< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#ac7c58404df0434d4f861db62d3471870" > rader_4_steps_< / a > [[function_constant(19)]];< / div >
< div class = "line" > < a id = "l00046" name = "l00046" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#adb129cc3808c08fd95af9795bfc7ae63" > 46< / a > < / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b" > STEEL_CONST< / a > < span class = "keywordtype" > int< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#adb129cc3808c08fd95af9795bfc7ae63" > rader_3_steps_< / a > [[function_constant(20)]];< / div >
< div class = "line" > < a id = "l00047" name = "l00047" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#a2d725bfd4c30be4c605b5c4559a62892" > 47< / a > < / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b" > STEEL_CONST< / a > < span class = "keywordtype" > int< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a2d725bfd4c30be4c605b5c4559a62892" > rader_2_steps_< / a > [[function_constant(21)]];< / 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 = "comment" > // See " radix.h" for radix codelets< / span > < / div >
< div class = "line" > < a id = "l00050" name = "l00050" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#a6ba62eabfd5428644aabf89ddaa0128d" > 50< / a > < / span > < span class = "keyword" > typedef< / span > void (*< a class = "code hl_typedef" href = "backend_2metal_2kernels_2fft_8h.html#a6ba62eabfd5428644aabf89ddaa0128d" > RadixFunc< / a > )(thread float2*, thread float2*);< / 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 > < span class = "comment" > // Perform a single radix n butterfly with appropriate twiddles< / span > < / div >
< div class = "line" > < a id = "l00053" name = "l00053" > < / a > < span class = "lineno" > 53< / span > < span class = "keyword" > template< / span > < < span class = "keywordtype" > int< / span > radix, RadixFunc radix_func> < / div >
< div class = "foldopen" id = "foldopen00054" data-start = "{" data-end = "}" >
< div class = "line" > < a id = "l00054" name = "l00054" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#a278d980ed397e6841ce0af44b9aa4396" > 54< / a > < / span > METAL_FUNC < span class = "keywordtype" > void< / span > < a class = "code hl_function" href = "backend_2metal_2kernels_2fft_8h.html#a278d980ed397e6841ce0af44b9aa4396" > radix_butterfly< / a > (< / div >
< div class = "line" > < a id = "l00055" name = "l00055" > < / a > < span class = "lineno" > 55< / span > < span class = "keywordtype" > int< / span > i,< / div >
< div class = "line" > < a id = "l00056" name = "l00056" > < / a > < span class = "lineno" > 56< / span > < span class = "keywordtype" > int< / span > p,< / div >
< div class = "line" > < a id = "l00057" name = "l00057" > < / a > < span class = "lineno" > 57< / span > thread float2* x,< / div >
< div class = "line" > < a id = "l00058" name = "l00058" > < / a > < span class = "lineno" > 58< / span > thread < span class = "keywordtype" > short< / span > * indices,< / div >
< div class = "line" > < a id = "l00059" name = "l00059" > < / a > < span class = "lineno" > 59< / span > thread float2* y) {< / div >
< div class = "line" > < a id = "l00060" name = "l00060" > < / a > < span class = "lineno" > 60< / span > < span class = "comment" > // i: the index in the overall DFT that we' re processing.< / span > < / div >
< div class = "line" > < a id = "l00061" name = "l00061" > < / a > < span class = "lineno" > 61< / span > < span class = "comment" > // p: the size of the DFTs we' re merging at this step.< / span > < / div >
< div class = "line" > < a id = "l00062" name = "l00062" > < / a > < span class = "lineno" > 62< / span > < span class = "comment" > // m: how many threads are working on this DFT.< / span > < / div >
< div class = "line" > < a id = "l00063" name = "l00063" > < / a > < span class = "lineno" > 63< / span > < span class = "keywordtype" > int< / span > k, j;< / div >
< div class = "line" > < a id = "l00064" name = "l00064" > < / a > < span class = "lineno" > 64< / span > < / div >
< div class = "line" > < a id = "l00065" name = "l00065" > < / a > < span class = "lineno" > 65< / span > < span class = "comment" > // Use faster bitwise operations when working with powers of two< / span > < / div >
< div class = "line" > < a id = "l00066" name = "l00066" > < / a > < span class = "lineno" > 66< / span > < span class = "keyword" > constexpr< / span > < span class = "keywordtype" > bool< / span > radix_p_2 = (radix & (radix - 1)) == 0;< / div >
< div class = "line" > < a id = "l00067" name = "l00067" > < / a > < span class = "lineno" > 67< / span > < span class = "keywordflow" > if< / span > (radix_p_2 & & < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a2a4df90e329b84ee6c1890ba7c265c9c" > is_power_of_2_< / a > ) {< / div >
< div class = "line" > < a id = "l00068" name = "l00068" > < / a > < span class = "lineno" > 68< / span > < span class = "keyword" > constexpr< / span > < span class = "keywordtype" > short< / span > power = __builtin_ctz(radix);< / div >
< div class = "line" > < a id = "l00069" name = "l00069" > < / a > < span class = "lineno" > 69< / span > k = i & (p - 1);< / div >
< div class = "line" > < a id = "l00070" name = "l00070" > < / a > < span class = "lineno" > 70< / span > j = ((i - k) < < power) + k;< / div >
< div class = "line" > < a id = "l00071" name = "l00071" > < / a > < span class = "lineno" > 71< / span > } < span class = "keywordflow" > else< / span > {< / div >
< div class = "line" > < a id = "l00072" name = "l00072" > < / a > < span class = "lineno" > 72< / span > k = i % p;< / div >
< div class = "line" > < a id = "l00073" name = "l00073" > < / a > < span class = "lineno" > 73< / span > j = (i / p) * radix * p + k;< / div >
< div class = "line" > < a id = "l00074" name = "l00074" > < / a > < span class = "lineno" > 74< / span > }< / div >
< div class = "line" > < a id = "l00075" name = "l00075" > < / a > < span class = "lineno" > 75< / span > < / div >
< div class = "line" > < a id = "l00076" name = "l00076" > < / a > < span class = "lineno" > 76< / span > < span class = "comment" > // Apply twiddles< / span > < / div >
< div class = "line" > < a id = "l00077" name = "l00077" > < / a > < span class = "lineno" > 77< / span > < span class = "keywordflow" > if< / span > (p > 1) {< / div >
< div class = "line" > < a id = "l00078" name = "l00078" > < / a > < span class = "lineno" > 78< / span > float2 twiddle_1 = < a class = "code hl_function" href = "radix_8h.html#ac5cf950316b9445296ee9ecfc56a56bd" > get_twiddle< / a > (k, radix * p);< / div >
< div class = "line" > < a id = "l00079" name = "l00079" > < / a > < span class = "lineno" > 79< / span > float2 twiddle = twiddle_1;< / div >
< div class = "line" > < a id = "l00080" name = "l00080" > < / a > < span class = "lineno" > 80< / span > x[1] = < a class = "code hl_function" href = "radix_8h.html#a5bfc53b531214c9ce277bebc18aa67d6" > complex_mul< / a > (x[1], twiddle);< / div >
< div class = "line" > < a id = "l00081" name = "l00081" > < / a > < span class = "lineno" > 81< / span > < / div >
< div class = "line" > < a id = "l00082" name = "l00082" > < / a > < span class = "lineno" > 82< / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6" > STEEL_PRAGMA_UNROLL< / a > < / div >
< div class = "line" > < a id = "l00083" name = "l00083" > < / a > < span class = "lineno" > 83< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > t = 2; t < radix; t++) {< / div >
< div class = "line" > < a id = "l00084" name = "l00084" > < / a > < span class = "lineno" > 84< / span > twiddle = < a class = "code hl_function" href = "radix_8h.html#a5bfc53b531214c9ce277bebc18aa67d6" > complex_mul< / a > (twiddle, twiddle_1);< / div >
< div class = "line" > < a id = "l00085" name = "l00085" > < / a > < span class = "lineno" > 85< / span > x[t] = < a class = "code hl_function" href = "radix_8h.html#a5bfc53b531214c9ce277bebc18aa67d6" > complex_mul< / a > (x[t], twiddle);< / div >
< div class = "line" > < a id = "l00086" name = "l00086" > < / a > < span class = "lineno" > 86< / span > }< / div >
< div class = "line" > < a id = "l00087" name = "l00087" > < / a > < span class = "lineno" > 87< / span > }< / 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 > < a class = "code hl_function" href = "metal_2kernels_2hadamard_8h.html#a590e5366adc78bab4fe44e37885d413f" > radix_func< / a > (x, y);< / div >
< div class = "line" > < a id = "l00090" name = "l00090" > < / a > < span class = "lineno" > 90< / span > < / div >
< div class = "line" > < a id = "l00091" name = "l00091" > < / a > < span class = "lineno" > 91< / span > < a class = "code hl_define" href = "steel_2defines_8h.html#a5a5c3095b132a7589bc19cd5cb80e2c6" > STEEL_PRAGMA_UNROLL< / a > < / div >
< div class = "line" > < a id = "l00092" name = "l00092" > < / a > < span class = "lineno" > 92< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > t = 0; t < radix; t++) {< / div >
< div class = "line" > < a id = "l00093" name = "l00093" > < / a > < span class = "lineno" > 93< / span > indices[t] = j + t * p;< / div >
< div class = "line" > < a id = "l00094" name = "l00094" > < / a > < span class = "lineno" > 94< / span > }< / div >
< div class = "line" > < a id = "l00095" name = "l00095" > < / a > < span class = "lineno" > 95< / span > }< / div >
< / div >
< div class = "line" > < a id = "l00096" name = "l00096" > < / a > < span class = "lineno" > 96< / span > < / div >
< div class = "line" > < a id = "l00097" name = "l00097" > < / a > < span class = "lineno" > 97< / span > < span class = "comment" > // Perform all the radix steps required for a< / span > < / div >
< div class = "line" > < a id = "l00098" name = "l00098" > < / a > < span class = "lineno" > 98< / span > < span class = "comment" > // particular radix size n.< / span > < / div >
< div class = "line" > < a id = "l00099" name = "l00099" > < / a > < span class = "lineno" > 99< / span > < span class = "keyword" > template< / span > < < span class = "keywordtype" > int< / span > radix, RadixFunc radix_func> < / div >
< div class = "foldopen" id = "foldopen00100" data-start = "{" data-end = "}" >
< div class = "line" > < a id = "l00100" name = "l00100" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#aba8d32e0911499671df93678f39da08b" > 100< / a > < / span > METAL_FUNC < span class = "keywordtype" > void< / span > < a class = "code hl_function" href = "backend_2metal_2kernels_2fft_8h.html#aba8d32e0911499671df93678f39da08b" > radix_n_steps< / a > (< / div >
< div class = "line" > < a id = "l00101" name = "l00101" > < / a > < span class = "lineno" > 101< / span > < span class = "keywordtype" > int< / span > i,< / div >
< div class = "line" > < a id = "l00102" name = "l00102" > < / a > < span class = "lineno" > 102< / span > thread < span class = "keywordtype" > int< / span > * p,< / div >
< div class = "line" > < a id = "l00103" name = "l00103" > < / a > < span class = "lineno" > 103< / span > < span class = "keywordtype" > int< / span > m,< / div >
< div class = "line" > < a id = "l00104" name = "l00104" > < / a > < span class = "lineno" > 104< / span > < span class = "keywordtype" > int< / span > n,< / div >
< div class = "line" > < a id = "l00105" name = "l00105" > < / a > < span class = "lineno" > 105< / span > < span class = "keywordtype" > int< / span > num_steps,< / div >
< div class = "line" > < a id = "l00106" name = "l00106" > < / a > < span class = "lineno" > 106< / span > thread float2* inputs,< / div >
< div class = "line" > < a id = "l00107" name = "l00107" > < / a > < span class = "lineno" > 107< / span > thread < span class = "keywordtype" > short< / span > * indices,< / div >
< div class = "line" > < a id = "l00108" name = "l00108" > < / a > < span class = "lineno" > 108< / span > thread float2* values,< / div >
< div class = "line" > < a id = "l00109" name = "l00109" > < / a > < span class = "lineno" > 109< / span > threadgroup float2* < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > ) {< / div >
< div class = "line" > < a id = "l00110" name = "l00110" > < / a > < span class = "lineno" > 110< / span > < span class = "keywordtype" > int< / span > m_r = n / radix;< / div >
< div class = "line" > < a id = "l00111" name = "l00111" > < / a > < span class = "lineno" > 111< / span > < span class = "comment" > // When combining different sized radices, we have to do< / span > < / div >
< div class = "line" > < a id = "l00112" name = "l00112" > < / a > < span class = "lineno" > 112< / span > < span class = "comment" > // multiple butterflies in a single thread.< / span > < / div >
< div class = "line" > < a id = "l00113" name = "l00113" > < / a > < span class = "lineno" > 113< / span > < span class = "comment" > // E.g. n = 28 = 4 * 7< / span > < / div >
< div class = "line" > < a id = "l00114" name = "l00114" > < / a > < span class = "lineno" > 114< / span > < span class = "comment" > // 4 threads, 7 elems_per_thread< / span > < / div >
< div class = "line" > < a id = "l00115" name = "l00115" > < / a > < span class = "lineno" > 115< / span > < span class = "comment" > // All threads do 1 radix7 butterfly.< / span > < / div >
< div class = "line" > < a id = "l00116" name = "l00116" > < / a > < span class = "lineno" > 116< / span > < span class = "comment" > // 3 threads do 2 radix4 butterflies.< / span > < / div >
< div class = "line" > < a id = "l00117" name = "l00117" > < / a > < span class = "lineno" > 117< / span > < span class = "comment" > // 1 thread does 1 radix4 butterfly.< / span > < / div >
< div class = "line" > < a id = "l00118" name = "l00118" > < / a > < span class = "lineno" > 118< / span > < span class = "keywordtype" > int< / span > max_radices_per_thread = (< a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3" > elems_per_thread_< / a > + radix - 1) / radix;< / div >
< div class = "line" > < a id = "l00119" name = "l00119" > < / a > < span class = "lineno" > 119< / span > < / div >
< div class = "line" > < a id = "l00120" name = "l00120" > < / a > < span class = "lineno" > 120< / span > < span class = "keywordtype" > int< / span > index = 0;< / div >
< div class = "line" > < a id = "l00121" name = "l00121" > < / a > < span class = "lineno" > 121< / span > < span class = "keywordtype" > int< / span > r_index = 0;< / div >
< div class = "line" > < a id = "l00122" name = "l00122" > < / a > < span class = "lineno" > 122< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > s = 0; s < num_steps; s++) {< / div >
< div class = "line" > < a id = "l00123" name = "l00123" > < / a > < span class = "lineno" > 123< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > t = 0; t < max_radices_per_thread; t++) {< / div >
< div class = "line" > < a id = "l00124" name = "l00124" > < / a > < span class = "lineno" > 124< / span > index = i + t * m;< / div >
< div class = "line" > < a id = "l00125" name = "l00125" > < / a > < span class = "lineno" > 125< / span > < span class = "keywordflow" > if< / span > (index < m_r) {< / div >
< div class = "line" > < a id = "l00126" name = "l00126" > < / a > < span class = "lineno" > 126< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > r = 0; r < radix; r++) {< / div >
< div class = "line" > < a id = "l00127" name = "l00127" > < / a > < span class = "lineno" > 127< / span > inputs[r] = < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > [index + r * m_r];< / div >
< div class = "line" > < a id = "l00128" name = "l00128" > < / a > < span class = "lineno" > 128< / span > }< / div >
< div class = "line" > < a id = "l00129" name = "l00129" > < / a > < span class = "lineno" > 129< / span > < a class = "code hl_function" href = "backend_2metal_2kernels_2fft_8h.html#a278d980ed397e6841ce0af44b9aa4396" > radix_butterfly< radix, radix_func> < / a > (< / div >
< div class = "line" > < a id = "l00130" name = "l00130" > < / a > < span class = "lineno" > 130< / span > index, *p, inputs, indices + t * radix, values + t * radix);< / 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 > }< / div >
< div class = "line" > < a id = "l00133" name = "l00133" > < / a > < span class = "lineno" > 133< / span > < / div >
< div class = "line" > < a id = "l00134" name = "l00134" > < / a > < span class = "lineno" > 134< / span > < span class = "comment" > // Wait until all threads have read their inputs into thread local mem< / span > < / div >
< div class = "line" > < a id = "l00135" name = "l00135" > < / a > < span class = "lineno" > 135< / span > threadgroup_barrier(mem_flags::mem_threadgroup);< / div >
< div class = "line" > < a id = "l00136" name = "l00136" > < / a > < span class = "lineno" > 136< / span > < / div >
< div class = "line" > < a id = "l00137" name = "l00137" > < / a > < span class = "lineno" > 137< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > t = 0; t < max_radices_per_thread; t++) {< / div >
< div class = "line" > < a id = "l00138" name = "l00138" > < / a > < span class = "lineno" > 138< / span > index = i + t * m;< / div >
< div class = "line" > < a id = "l00139" name = "l00139" > < / a > < span class = "lineno" > 139< / span > < span class = "keywordflow" > if< / span > (index < m_r) {< / div >
< div class = "line" > < a id = "l00140" name = "l00140" > < / a > < span class = "lineno" > 140< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > r = 0; r < radix; r++) {< / div >
< div class = "line" > < a id = "l00141" name = "l00141" > < / a > < span class = "lineno" > 141< / span > r_index = t * radix + r;< / div >
< div class = "line" > < a id = "l00142" name = "l00142" > < / a > < span class = "lineno" > 142< / span > < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > [indices[r_index]] = values[r_index];< / div >
< div class = "line" > < a id = "l00143" name = "l00143" > < / a > < span class = "lineno" > 143< / span > }< / div >
< div class = "line" > < a id = "l00144" name = "l00144" > < / a > < span class = "lineno" > 144< / span > }< / div >
< div class = "line" > < a id = "l00145" name = "l00145" > < / a > < span class = "lineno" > 145< / span > }< / div >
< div class = "line" > < a id = "l00146" name = "l00146" > < / a > < span class = "lineno" > 146< / span > < / div >
< div class = "line" > < a id = "l00147" name = "l00147" > < / a > < span class = "lineno" > 147< / span > < span class = "comment" > // Wait until all threads have written back to threadgroup mem< / span > < / div >
< div class = "line" > < a id = "l00148" name = "l00148" > < / a > < span class = "lineno" > 148< / span > threadgroup_barrier(mem_flags::mem_threadgroup);< / div >
< div class = "line" > < a id = "l00149" name = "l00149" > < / a > < span class = "lineno" > 149< / span > *p *= radix;< / 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 >
< div class = "line" > < a id = "l00152" name = "l00152" > < / a > < span class = "lineno" > 152< / span > < / div >
< div class = "foldopen" id = "foldopen00153" data-start = "" data-end = "" >
< div class = "line" > < a id = "l00153" name = "l00153" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#a794032d3a9acff0e31c77c69d0007f10" > 153< / a > < / span > < span class = "preprocessor" > #define RADIX_STEP(radix, radix_func, num_steps) \< / span > < / div >
< div class = "line" > < a id = "l00154" name = "l00154" > < / a > < span class = "lineno" > 154< / span > < span class = "preprocessor" > radix_n_steps< radix, radix_func> ( \< / span > < / div >
< div class = "line" > < a id = "l00155" name = "l00155" > < / a > < span class = "lineno" > 155< / span > < span class = "preprocessor" > fft_idx, p, m, n, num_steps, inputs, indices, values, buf);< / span > < / div >
< / div >
< div class = "line" > < a id = "l00156" name = "l00156" > < / a > < span class = "lineno" > 156< / span > < / div >
< div class = "line" > < a id = "l00157" name = "l00157" > < / a > < span class = "lineno" > 157< / span > < span class = "keyword" > template< / span > < < span class = "keywordtype" > bool< / span > rader = false> < / div >
< div class = "line" > < a id = "l00158" name = "l00158" > < / a > < span class = "lineno" > 158< / span > METAL_FUNC < span class = "keywordtype" > void< / span > < / div >
< div class = "foldopen" id = "foldopen00159" data-start = "{" data-end = "}" >
< div class = "line" > < a id = "l00159" name = "l00159" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#a050ead8fa5cacdaec13d68ca3c0dcb81" > 159< / a > < / span > < a class = "code hl_function" href = "backend_2metal_2kernels_2fft_8h.html#a050ead8fa5cacdaec13d68ca3c0dcb81" > perform_fft< / a > (< span class = "keywordtype" > int< / span > fft_idx, thread < span class = "keywordtype" > int< / span > * p, < span class = "keywordtype" > int< / span > m, < span class = "keywordtype" > int< / span > n, threadgroup float2* < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > ) {< / div >
< div class = "line" > < a id = "l00160" name = "l00160" > < / a > < span class = "lineno" > 160< / span > float2 inputs[< a class = "code hl_define" href = "backend_2metal_2kernels_2fft_8h.html#a7b6e56afa21f022c5e754b000955735a" > MAX_RADIX< / a > ];< / div >
< div class = "line" > < a id = "l00161" name = "l00161" > < / a > < span class = "lineno" > 161< / span > < span class = "keywordtype" > short< / span > indices[< a class = "code hl_define" href = "backend_2metal_2kernels_2fft_8h.html#a28d683cf067736d76f867f30c066317e" > MAX_OUTPUT_SIZE< / a > ];< / div >
< div class = "line" > < a id = "l00162" name = "l00162" > < / a > < span class = "lineno" > 162< / span > float2 values[< a class = "code hl_define" href = "backend_2metal_2kernels_2fft_8h.html#a28d683cf067736d76f867f30c066317e" > MAX_OUTPUT_SIZE< / a > ];< / div >
< div class = "line" > < a id = "l00163" name = "l00163" > < / a > < span class = "lineno" > 163< / span > < / div >
< div class = "line" > < a id = "l00164" name = "l00164" > < / a > < span class = "lineno" > 164< / span > < a class = "code hl_define" href = "backend_2metal_2kernels_2fft_8h.html#a794032d3a9acff0e31c77c69d0007f10" > RADIX_STEP< / a > (2, < a class = "code hl_function" href = "radix_8h.html#a745e50244f1470bba233d8b6b993729c" > radix2< / a > , rader ? < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a2d725bfd4c30be4c605b5c4559a62892" > rader_2_steps_< / a > : < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a53fdc660e99e6b5db6808bbd596cd374" > radix_2_steps_< / a > );< / div >
< div class = "line" > < a id = "l00165" name = "l00165" > < / a > < span class = "lineno" > 165< / span > < a class = "code hl_define" href = "backend_2metal_2kernels_2fft_8h.html#a794032d3a9acff0e31c77c69d0007f10" > RADIX_STEP< / a > (3, < a class = "code hl_function" href = "radix_8h.html#a497b31cfa28418e1c2fad53d09f7bc0b" > radix3< / a > , rader ? < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#adb129cc3808c08fd95af9795bfc7ae63" > rader_3_steps_< / a > : < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a579123b7be825f08f3076287dded08e3" > radix_3_steps_< / a > );< / div >
< div class = "line" > < a id = "l00166" name = "l00166" > < / a > < span class = "lineno" > 166< / span > < a class = "code hl_define" href = "backend_2metal_2kernels_2fft_8h.html#a794032d3a9acff0e31c77c69d0007f10" > RADIX_STEP< / a > (4, < a class = "code hl_function" href = "radix_8h.html#a12cb26bd3ad635d16a195ccea750256d" > radix4< / a > , rader ? < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#ac7c58404df0434d4f861db62d3471870" > rader_4_steps_< / a > : < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a12d99a846c3686806bab6c42148e1039" > radix_4_steps_< / a > );< / div >
< div class = "line" > < a id = "l00167" name = "l00167" > < / a > < span class = "lineno" > 167< / span > < a class = "code hl_define" href = "backend_2metal_2kernels_2fft_8h.html#a794032d3a9acff0e31c77c69d0007f10" > RADIX_STEP< / a > (5, < a class = "code hl_function" href = "radix_8h.html#a026e6779e6d2ecdef39ff4aad186091e" > radix5< / a > , rader ? < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#afea05e9a7105bafbaafca25042f4d1b4" > rader_5_steps_< / a > : < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a903d5239b5f73577c559e97ff910892d" > radix_5_steps_< / a > );< / div >
< div class = "line" > < a id = "l00168" name = "l00168" > < / a > < span class = "lineno" > 168< / span > < a class = "code hl_define" href = "backend_2metal_2kernels_2fft_8h.html#a794032d3a9acff0e31c77c69d0007f10" > RADIX_STEP< / a > (6, < a class = "code hl_function" href = "radix_8h.html#afaaa5de58a97f0a5e6a84fc0d598a884" > radix6< / a > , rader ? < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a020469d1aca557ff1b49414f121dedbb" > rader_6_steps_< / a > : < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a2f7f7cc2423cfcd4998d1a2a0363c3e2" > radix_6_steps_< / a > );< / div >
< div class = "line" > < a id = "l00169" name = "l00169" > < / a > < span class = "lineno" > 169< / span > < a class = "code hl_define" href = "backend_2metal_2kernels_2fft_8h.html#a794032d3a9acff0e31c77c69d0007f10" > RADIX_STEP< / a > (7, < a class = "code hl_function" href = "radix_8h.html#a6d37e483d806c550deefabf56caf4ec8" > radix7< / a > , rader ? < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a0d437aef17faf8d9707ae7ffe68fdb30" > rader_7_steps_< / a > : < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a2145cc8ab4d07583a735317b3cf60d55" > radix_7_steps_< / a > );< / div >
< div class = "line" > < a id = "l00170" name = "l00170" > < / a > < span class = "lineno" > 170< / span > < a class = "code hl_define" href = "backend_2metal_2kernels_2fft_8h.html#a794032d3a9acff0e31c77c69d0007f10" > RADIX_STEP< / a > (8, < a class = "code hl_function" href = "radix_8h.html#a6b306e1afe1c5b6af4cd80aa02adb138" > radix8< / a > , rader ? < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#ac6123e111816dd62a11ccb86b66fa3e9" > rader_8_steps_< / a > : < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a3cb03a97a209ba1346375e720ee76177" > radix_8_steps_< / a > );< / div >
< div class = "line" > < a id = "l00171" name = "l00171" > < / a > < span class = "lineno" > 171< / span > < a class = "code hl_define" href = "backend_2metal_2kernels_2fft_8h.html#a794032d3a9acff0e31c77c69d0007f10" > RADIX_STEP< / a > (11, < a class = "code hl_function" href = "radix_8h.html#a34f7dcefd29f8a7f6bddf9a17609a8a7" > radix11< / a > , rader ? < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a1f3c377d05da52429172e64132dba750" > rader_11_steps_< / a > : < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a7cd17bff8bc567f71d4789ee31fa07f2" > radix_11_steps_< / a > );< / div >
< div class = "line" > < a id = "l00172" name = "l00172" > < / a > < span class = "lineno" > 172< / span > < a class = "code hl_define" href = "backend_2metal_2kernels_2fft_8h.html#a794032d3a9acff0e31c77c69d0007f10" > RADIX_STEP< / a > (13, < a class = "code hl_function" href = "radix_8h.html#a833b7b31facbd62f6971bb108c54d1db" > radix13< / a > , rader ? < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a20d24f3e040d3d226a70d4dd7c9ac6a9" > rader_13_steps_< / a > : < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#abb079b86e89ca88ce13a179d9ec566af" > radix_13_steps_< / a > );< / div >
< div class = "line" > < a id = "l00173" name = "l00173" > < / a > < span class = "lineno" > 173< / span > }< / div >
< / div >
< div class = "line" > < a id = "l00174" name = "l00174" > < / a > < span class = "lineno" > 174< / span > < / div >
< div class = "line" > < a id = "l00175" name = "l00175" > < / a > < span class = "lineno" > 175< / span > < span class = "comment" > // Each FFT is computed entirely in shared GPU memory.< / span > < / div >
< div class = "line" > < a id = "l00176" name = "l00176" > < / a > < span class = "lineno" > 176< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00177" name = "l00177" > < / a > < span class = "lineno" > 177< / span > < span class = "comment" > // N is decomposed into radix-n DFTs:< / span > < / div >
< div class = "line" > < a id = "l00178" name = "l00178" > < / a > < span class = "lineno" > 178< / span > < span class = "comment" > // e.g. 128 = 2 * 4 * 4 * 4< / span > < / div >
< div class = "line" > < a id = "l00179" name = "l00179" > < / a > < span class = "lineno" > 179< / span > < span class = "keyword" > template< / span > < < span class = "keywordtype" > int< / span > tg_mem_size, < span class = "keyword" > typename< / span > in_T, < span class = "keyword" > typename< / span > out_T> < / div >
< div class = "foldopen" id = "foldopen00180" data-start = "{" data-end = "}" >
< div class = "line" > < a id = "l00180" name = "l00180" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#a4010b0e151e5f01e610e9c32234458c7" > 180< / a > < / span > [[kernel]] < span class = "keywordtype" > void< / span > < a class = "code hl_function" href = "backend_2metal_2kernels_2fft_8h.html#a4010b0e151e5f01e610e9c32234458c7" > fft< / a > (< / div >
< div class = "line" > < a id = "l00181" name = "l00181" > < / a > < span class = "lineno" > 181< / span > < span class = "keyword" > const< / span > device in_T* in [[buffer(0)]],< / div >
< div class = "line" > < a id = "l00182" name = "l00182" > < / a > < span class = "lineno" > 182< / span > device out_T* out [[buffer(1)]],< / div >
< div class = "line" > < a id = "l00183" name = "l00183" > < / a > < span class = "lineno" > 183< / span > constant < span class = "keyword" > const< / span > < span class = "keywordtype" > int< / span > & n,< / div >
< div class = "line" > < a id = "l00184" name = "l00184" > < / a > < span class = "lineno" > 184< / span > constant < span class = "keyword" > const< / span > < span class = "keywordtype" > int< / span > & batch_size,< / div >
< div class = "line" > < a id = "l00185" name = "l00185" > < / a > < span class = "lineno" > 185< / span > uint3 elem [[thread_position_in_grid]],< / div >
< div class = "line" > < a id = "l00186" name = "l00186" > < / a > < span class = "lineno" > 186< / span > uint3 grid [[threads_per_grid]]) {< / div >
< div class = "line" > < a id = "l00187" name = "l00187" > < / a > < span class = "lineno" > 187< / span > threadgroup float2 shared_in[tg_mem_size];< / div >
< div class = "line" > < a id = "l00188" name = "l00188" > < / a > < span class = "lineno" > 188< / span > < / div >
< div class = "line" > < a id = "l00189" name = "l00189" > < / a > < span class = "lineno" > 189< / span > thread < a class = "code hl_struct" href = "struct_read_writer.html" > ReadWriter< in_T, out_T> < / a > read_writer = < a class = "code hl_struct" href = "struct_read_writer.html" > ReadWriter< in_T, out_T> < / a > (< / div >
< div class = "line" > < a id = "l00190" name = "l00190" > < / a > < span class = "lineno" > 190< / span > in,< / div >
< div class = "line" > < a id = "l00191" name = "l00191" > < / a > < span class = "lineno" > 191< / span > & shared_in[0],< / div >
< div class = "line" > < a id = "l00192" name = "l00192" > < / a > < span class = "lineno" > 192< / span > out,< / div >
< div class = "line" > < a id = "l00193" name = "l00193" > < / a > < span class = "lineno" > 193< / span > n,< / div >
< div class = "line" > < a id = "l00194" name = "l00194" > < / a > < span class = "lineno" > 194< / span > batch_size,< / div >
< div class = "line" > < a id = "l00195" name = "l00195" > < / a > < span class = "lineno" > 195< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3" > elems_per_thread_< / a > ,< / div >
< div class = "line" > < a id = "l00196" name = "l00196" > < / a > < span class = "lineno" > 196< / span > elem,< / div >
< div class = "line" > < a id = "l00197" name = "l00197" > < / a > < span class = "lineno" > 197< / span > grid,< / div >
< div class = "line" > < a id = "l00198" name = "l00198" > < / a > < span class = "lineno" > 198< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a7a83318497519ff3ff0141b7d511ed38" > inv_< / a > );< / div >
< div class = "line" > < a id = "l00199" name = "l00199" > < / a > < span class = "lineno" > 199< / span > < / div >
< div class = "line" > < a id = "l00200" name = "l00200" > < / a > < span class = "lineno" > 200< / span > < span class = "keywordflow" > if< / span > (read_writer.out_of_bounds()) {< / div >
< div class = "line" > < a id = "l00201" name = "l00201" > < / a > < span class = "lineno" > 201< / span > < span class = "keywordflow" > return< / span > ;< / div >
< div class = "line" > < a id = "l00202" name = "l00202" > < / a > < span class = "lineno" > 202< / span > };< / div >
< div class = "line" > < a id = "l00203" name = "l00203" > < / a > < span class = "lineno" > 203< / span > read_writer.load();< / 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 > threadgroup_barrier(mem_flags::mem_threadgroup);< / div >
< div class = "line" > < a id = "l00206" name = "l00206" > < / a > < span class = "lineno" > 206< / span > < / div >
< div class = "line" > < a id = "l00207" name = "l00207" > < / a > < span class = "lineno" > 207< / span > < span class = "keywordtype" > int< / span > p = 1;< / div >
< div class = "line" > < a id = "l00208" name = "l00208" > < / a > < span class = "lineno" > 208< / span > < span class = "keywordtype" > int< / span > fft_idx = elem.z; < span class = "comment" > // Thread index in DFT< / span > < / div >
< div class = "line" > < a id = "l00209" name = "l00209" > < / a > < span class = "lineno" > 209< / span > < span class = "keywordtype" > int< / span > m = grid.z; < span class = "comment" > // Threads per DFT< / span > < / div >
< div class = "line" > < a id = "l00210" name = "l00210" > < / a > < span class = "lineno" > 210< / span > < span class = "keywordtype" > int< / span > tg_idx = elem.y * n; < span class = "comment" > // Index of this DFT in threadgroup< / span > < / div >
< div class = "line" > < a id = "l00211" name = "l00211" > < / a > < span class = "lineno" > 211< / span > threadgroup float2* < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > = & shared_in[tg_idx];< / div >
< div class = "line" > < a id = "l00212" name = "l00212" > < / a > < span class = "lineno" > 212< / span > < / div >
< div class = "line" > < a id = "l00213" name = "l00213" > < / a > < span class = "lineno" > 213< / span > < a class = "code hl_function" href = "backend_2metal_2kernels_2fft_8h.html#a050ead8fa5cacdaec13d68ca3c0dcb81" > perform_fft< / a > (fft_idx, & p, m, n, < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > );< / div >
< div class = "line" > < a id = "l00214" name = "l00214" > < / a > < span class = "lineno" > 214< / span > < / div >
< div class = "line" > < a id = "l00215" name = "l00215" > < / a > < span class = "lineno" > 215< / span > read_writer.write();< / div >
< div class = "line" > < a id = "l00216" name = "l00216" > < / a > < span class = "lineno" > 216< / span > }< / div >
< / div >
< div class = "line" > < a id = "l00217" name = "l00217" > < / a > < span class = "lineno" > 217< / span > < / div >
< div class = "line" > < a id = "l00218" name = "l00218" > < / a > < span class = "lineno" > 218< / span > < span class = "keyword" > template< / span > < < span class = "keywordtype" > int< / span > tg_mem_size, < span class = "keyword" > typename< / span > in_T, < span class = "keyword" > typename< / span > out_T> < / div >
< div class = "foldopen" id = "foldopen00219" data-start = "{" data-end = "}" >
< div class = "line" > < a id = "l00219" name = "l00219" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#ad123452303f6415904f3592f660769b8" > 219< / a > < / span > [[kernel]] < span class = "keywordtype" > void< / span > < a class = "code hl_function" href = "backend_2metal_2kernels_2fft_8h.html#ad123452303f6415904f3592f660769b8" > rader_fft< / a > (< / div >
< div class = "line" > < a id = "l00220" name = "l00220" > < / a > < span class = "lineno" > 220< / span > < span class = "keyword" > const< / span > device in_T* in [[buffer(0)]],< / div >
< div class = "line" > < a id = "l00221" name = "l00221" > < / a > < span class = "lineno" > 221< / span > device out_T* out [[buffer(1)]],< / div >
< div class = "line" > < a id = "l00222" name = "l00222" > < / a > < span class = "lineno" > 222< / span > < span class = "keyword" > const< / span > device float2* raders_b_q [[buffer(2)]],< / div >
< div class = "line" > < a id = "l00223" name = "l00223" > < / a > < span class = "lineno" > 223< / span > < span class = "keyword" > const< / span > device < span class = "keywordtype" > short< / span > * raders_g_q [[buffer(3)]],< / div >
< div class = "line" > < a id = "l00224" name = "l00224" > < / a > < span class = "lineno" > 224< / span > < span class = "keyword" > const< / span > device < span class = "keywordtype" > short< / span > * raders_g_minus_q [[buffer(4)]],< / div >
< div class = "line" > < a id = "l00225" name = "l00225" > < / a > < span class = "lineno" > 225< / span > constant < span class = "keyword" > const< / span > < span class = "keywordtype" > int< / span > & n,< / div >
< div class = "line" > < a id = "l00226" name = "l00226" > < / a > < span class = "lineno" > 226< / span > constant < span class = "keyword" > const< / span > < span class = "keywordtype" > int< / span > & batch_size,< / div >
< div class = "line" > < a id = "l00227" name = "l00227" > < / a > < span class = "lineno" > 227< / span > constant < span class = "keyword" > const< / span > < span class = "keywordtype" > int< / span > & rader_n,< / div >
< div class = "line" > < a id = "l00228" name = "l00228" > < / a > < span class = "lineno" > 228< / span > uint3 elem [[thread_position_in_grid]],< / div >
< div class = "line" > < a id = "l00229" name = "l00229" > < / a > < span class = "lineno" > 229< / span > uint3 grid [[threads_per_grid]]) {< / div >
< div class = "line" > < a id = "l00230" name = "l00230" > < / a > < span class = "lineno" > 230< / span > < span class = "comment" > // Use Rader' s algorithm to compute fast FFTs< / span > < / div >
< div class = "line" > < a id = "l00231" name = "l00231" > < / a > < span class = "lineno" > 231< / span > < span class = "comment" > // when a prime factor `p` of `n` is greater than 13 but< / span > < / div >
< div class = "line" > < a id = "l00232" name = "l00232" > < / a > < span class = "lineno" > 232< / span > < span class = "comment" > // has `p - 1` Stockham decomposable into to prime factors < = 13.< / span > < / div >
< div class = "line" > < a id = "l00233" name = "l00233" > < / a > < span class = "lineno" > 233< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00234" name = "l00234" > < / a > < span class = "lineno" > 234< / span > < span class = "comment" > // E.g. n = 102< / span > < / div >
< div class = "line" > < a id = "l00235" name = "l00235" > < / a > < span class = "lineno" > 235< / span > < span class = "comment" > // = 2 * 3 * 17< / span > < / div >
< div class = "line" > < a id = "l00236" name = "l00236" > < / a > < span class = "lineno" > 236< / span > < span class = "comment" > // . = 2 * 3 * RADER(16)< / span > < / div >
< div class = "line" > < a id = "l00237" name = "l00237" > < / a > < span class = "lineno" > 237< / span > < span class = "comment" > // . = 2 * 3 * RADER(4 * 4)< / span > < / div >
< div class = "line" > < a id = "l00238" name = "l00238" > < / a > < span class = "lineno" > 238< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00239" name = "l00239" > < / a > < span class = "lineno" > 239< / span > < span class = "comment" > // In numpy:< / span > < / div >
< div class = "line" > < a id = "l00240" name = "l00240" > < / a > < span class = "lineno" > 240< / span > < span class = "comment" > // x_perm = x[g_q]< / span > < / div >
< div class = "line" > < a id = "l00241" name = "l00241" > < / a > < span class = "lineno" > 241< / span > < span class = "comment" > // y = np.fft.fft(x_perm) * b_q< / span > < / div >
< div class = "line" > < a id = "l00242" name = "l00242" > < / a > < span class = "lineno" > 242< / span > < span class = "comment" > // z = np.fft.ifft(y) + x[0]< / span > < / div >
< div class = "line" > < a id = "l00243" name = "l00243" > < / a > < span class = "lineno" > 243< / span > < span class = "comment" > // out = z[g_minus_q]< / span > < / div >
< div class = "line" > < a id = "l00244" name = "l00244" > < / a > < span class = "lineno" > 244< / span > < span class = "comment" > // out[0] = x[1:].sum()< / span > < / div >
< div class = "line" > < a id = "l00245" name = "l00245" > < / a > < span class = "lineno" > 245< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00246" name = "l00246" > < / a > < span class = "lineno" > 246< / span > < span class = "comment" > // Where the g_q and g_minus_q are permutations formed< / span > < / div >
< div class = "line" > < a id = "l00247" name = "l00247" > < / a > < span class = "lineno" > 247< / span > < span class = "comment" > // by the group under multiplicative modulo N using the< / span > < / div >
< div class = "line" > < a id = "l00248" name = "l00248" > < / a > < span class = "lineno" > 248< / span > < span class = "comment" > // primitive root of N and b_q is a constant.< / span > < / div >
< div class = "line" > < a id = "l00249" name = "l00249" > < / a > < span class = "lineno" > 249< / span > < span class = "comment" > // See https://en.wikipedia.org/wiki/Rader%27s_FFT_algorithm< / span > < / div >
< div class = "line" > < a id = "l00250" name = "l00250" > < / a > < span class = "lineno" > 250< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00251" name = "l00251" > < / a > < span class = "lineno" > 251< / span > < span class = "comment" > // Rader' s uses fewer operations than Bluestein' s and so< / span > < / div >
< div class = "line" > < a id = "l00252" name = "l00252" > < / a > < span class = "lineno" > 252< / span > < span class = "comment" > // is more accurate. It' s also faster in most cases.< / span > < / div >
< div class = "line" > < a id = "l00253" name = "l00253" > < / a > < span class = "lineno" > 253< / span > threadgroup float2 shared_in[tg_mem_size];< / div >
< div class = "line" > < a id = "l00254" name = "l00254" > < / a > < span class = "lineno" > 254< / span > < / div >
< div class = "line" > < a id = "l00255" name = "l00255" > < / a > < span class = "lineno" > 255< / span > thread < a class = "code hl_struct" href = "struct_read_writer.html" > ReadWriter< in_T, out_T> < / a > read_writer = < a class = "code hl_struct" href = "struct_read_writer.html" > ReadWriter< in_T, out_T> < / a > (< / div >
< div class = "line" > < a id = "l00256" name = "l00256" > < / a > < span class = "lineno" > 256< / span > in,< / div >
< div class = "line" > < a id = "l00257" name = "l00257" > < / a > < span class = "lineno" > 257< / span > & shared_in[0],< / div >
< div class = "line" > < a id = "l00258" name = "l00258" > < / a > < span class = "lineno" > 258< / span > out,< / div >
< div class = "line" > < a id = "l00259" name = "l00259" > < / a > < span class = "lineno" > 259< / span > n,< / div >
< div class = "line" > < a id = "l00260" name = "l00260" > < / a > < span class = "lineno" > 260< / span > batch_size,< / div >
< div class = "line" > < a id = "l00261" name = "l00261" > < / a > < span class = "lineno" > 261< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3" > elems_per_thread_< / a > ,< / div >
< div class = "line" > < a id = "l00262" name = "l00262" > < / a > < span class = "lineno" > 262< / span > elem,< / div >
< div class = "line" > < a id = "l00263" name = "l00263" > < / a > < span class = "lineno" > 263< / span > grid,< / div >
< div class = "line" > < a id = "l00264" name = "l00264" > < / a > < span class = "lineno" > 264< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a7a83318497519ff3ff0141b7d511ed38" > inv_< / a > );< / div >
< div class = "line" > < a id = "l00265" name = "l00265" > < / a > < span class = "lineno" > 265< / span > < / div >
< div class = "line" > < a id = "l00266" name = "l00266" > < / a > < span class = "lineno" > 266< / span > < span class = "keywordflow" > if< / span > (read_writer.out_of_bounds()) {< / div >
< div class = "line" > < a id = "l00267" name = "l00267" > < / a > < span class = "lineno" > 267< / span > < span class = "keywordflow" > return< / span > ;< / div >
< div class = "line" > < a id = "l00268" name = "l00268" > < / a > < span class = "lineno" > 268< / span > };< / div >
< div class = "line" > < a id = "l00269" name = "l00269" > < / a > < span class = "lineno" > 269< / span > read_writer.load();< / div >
< div class = "line" > < a id = "l00270" name = "l00270" > < / a > < span class = "lineno" > 270< / span > < / div >
< div class = "line" > < a id = "l00271" name = "l00271" > < / a > < span class = "lineno" > 271< / span > threadgroup_barrier(mem_flags::mem_threadgroup);< / div >
< div class = "line" > < a id = "l00272" name = "l00272" > < / a > < span class = "lineno" > 272< / span > < / div >
< div class = "line" > < a id = "l00273" name = "l00273" > < / a > < span class = "lineno" > 273< / span > < span class = "comment" > // The number of the threads we' re using for each DFT< / span > < / div >
< div class = "line" > < a id = "l00274" name = "l00274" > < / a > < span class = "lineno" > 274< / span > < span class = "keywordtype" > int< / span > m = grid.z;< / div >
< div class = "line" > < a id = "l00275" name = "l00275" > < / a > < span class = "lineno" > 275< / span > < / div >
< div class = "line" > < a id = "l00276" name = "l00276" > < / a > < span class = "lineno" > 276< / span > < span class = "keywordtype" > int< / span > fft_idx = elem.z;< / div >
< div class = "line" > < a id = "l00277" name = "l00277" > < / a > < span class = "lineno" > 277< / span > < span class = "keywordtype" > int< / span > tg_idx = elem.y * n;< / div >
< div class = "line" > < a id = "l00278" name = "l00278" > < / a > < span class = "lineno" > 278< / span > threadgroup float2* < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > = & shared_in[tg_idx];< / 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 > < span class = "comment" > // rader_m = n / rader_n;< / span > < / div >
< div class = "line" > < a id = "l00281" name = "l00281" > < / a > < span class = "lineno" > 281< / span > < span class = "keywordtype" > int< / span > rader_m = < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#ac309c77ef775a3ef13850c5287a86480" > rader_m_< / a > ;< / div >
< div class = "line" > < a id = "l00282" name = "l00282" > < / a > < span class = "lineno" > 282< / span > < / div >
< div class = "line" > < a id = "l00283" name = "l00283" > < / a > < span class = "lineno" > 283< / span > < span class = "comment" > // We have to load two x_0s for each thread since sometimes< / span > < / div >
< div class = "line" > < a id = "l00284" name = "l00284" > < / a > < span class = "lineno" > 284< / span > < span class = "comment" > // elems_per_thread_ crosses a boundary.< / span > < / div >
< div class = "line" > < a id = "l00285" name = "l00285" > < / a > < span class = "lineno" > 285< / span > < span class = "comment" > // E.g. with n = 34, rader_n = 17, elems_per_thread_ = 4< / span > < / div >
< div class = "line" > < a id = "l00286" name = "l00286" > < / a > < span class = "lineno" > 286< / span > < span class = "comment" > // 0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8< / span > < / div >
< div class = "line" > < a id = "l00287" name = "l00287" > < / a > < span class = "lineno" > 287< / span > < span class = "comment" > // 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1< / span > < / div >
< div class = "line" > < a id = "l00288" name = "l00288" > < / a > < span class = "lineno" > 288< / span > < span class = "keywordtype" > short< / span > x_0_index =< / div >
< div class = "line" > < a id = "l00289" name = "l00289" > < / a > < span class = "lineno" > 289< / span > < a class = "code hl_function" href = "namespacemetal.html#a6653b28c9473087141eddce39878d4d3" > metal::min< / a > (fft_idx * < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3" > elems_per_thread_< / a > / (rader_n - 1), rader_m - 1);< / div >
< div class = "line" > < a id = "l00290" name = "l00290" > < / a > < span class = "lineno" > 290< / span > float2 x_0[2] = {< a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > [x_0_index], < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > [x_0_index + 1]};< / div >
< div class = "line" > < a id = "l00291" name = "l00291" > < / a > < span class = "lineno" > 291< / span > < / div >
< div class = "line" > < a id = "l00292" name = "l00292" > < / a > < span class = "lineno" > 292< / span > < span class = "comment" > // Do the Rader permutation in shared memory< / span > < / div >
< div class = "line" > < a id = "l00293" name = "l00293" > < / a > < span class = "lineno" > 293< / span > float2 temp[< a class = "code hl_define" href = "backend_2metal_2kernels_2fft_8h.html#a7b6e56afa21f022c5e754b000955735a" > MAX_RADIX< / a > ];< / div >
< div class = "line" > < a id = "l00294" name = "l00294" > < / a > < span class = "lineno" > 294< / span > < span class = "keywordtype" > int< / span > max_index = n - rader_m - 1;< / div >
< div class = "line" > < a id = "l00295" name = "l00295" > < / a > < span class = "lineno" > 295< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > e = 0; e < < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3" > elems_per_thread_< / a > ; e++) {< / div >
< div class = "line" > < a id = "l00296" name = "l00296" > < / a > < span class = "lineno" > 296< / span > < span class = "keywordtype" > short< / span > index = < a class = "code hl_function" href = "namespacemetal.html#a6653b28c9473087141eddce39878d4d3" > metal::min< / a > (fft_idx * < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3" > elems_per_thread_< / a > + e, max_index);< / div >
< div class = "line" > < a id = "l00297" name = "l00297" > < / a > < span class = "lineno" > 297< / span > < span class = "keywordtype" > short< / span > g_q = raders_g_q[index / rader_m];< / div >
< div class = "line" > < a id = "l00298" name = "l00298" > < / a > < span class = "lineno" > 298< / span > temp[e] = < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > [rader_m + (g_q - 1) * rader_m + index % rader_m];< / div >
< div class = "line" > < a id = "l00299" name = "l00299" > < / a > < span class = "lineno" > 299< / span > }< / div >
< div class = "line" > < a id = "l00300" name = "l00300" > < / a > < span class = "lineno" > 300< / span > < / div >
< div class = "line" > < a id = "l00301" name = "l00301" > < / a > < span class = "lineno" > 301< / span > threadgroup_barrier(mem_flags::mem_threadgroup);< / div >
< div class = "line" > < a id = "l00302" name = "l00302" > < / a > < span class = "lineno" > 302< / span > < / div >
< div class = "line" > < a id = "l00303" name = "l00303" > < / a > < span class = "lineno" > 303< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > e = 0; e < < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3" > elems_per_thread_< / a > ; e++) {< / div >
< div class = "line" > < a id = "l00304" name = "l00304" > < / a > < span class = "lineno" > 304< / span > < span class = "keywordtype" > short< / span > index = < a class = "code hl_function" href = "namespacemetal.html#a6653b28c9473087141eddce39878d4d3" > metal::min< / a > (fft_idx * < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3" > elems_per_thread_< / a > + e, max_index);< / div >
< div class = "line" > < a id = "l00305" name = "l00305" > < / a > < span class = "lineno" > 305< / span > < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > [index + rader_m] = temp[e];< / div >
< div class = "line" > < a id = "l00306" name = "l00306" > < / a > < span class = "lineno" > 306< / span > }< / div >
< div class = "line" > < a id = "l00307" name = "l00307" > < / a > < span class = "lineno" > 307< / span > < / div >
< div class = "line" > < a id = "l00308" name = "l00308" > < / a > < span class = "lineno" > 308< / span > threadgroup_barrier(mem_flags::mem_threadgroup);< / div >
< div class = "line" > < a id = "l00309" name = "l00309" > < / a > < span class = "lineno" > 309< / span > < / div >
< div class = "line" > < a id = "l00310" name = "l00310" > < / a > < span class = "lineno" > 310< / span > < span class = "comment" > // Rader FFT on x[rader_m:]< / span > < / div >
< div class = "line" > < a id = "l00311" name = "l00311" > < / a > < span class = "lineno" > 311< / span > < span class = "keywordtype" > int< / span > p = 1;< / div >
< div class = "line" > < a id = "l00312" name = "l00312" > < / a > < span class = "lineno" > 312< / span > < a class = "code hl_function" href = "backend_2metal_2kernels_2fft_8h.html#a050ead8fa5cacdaec13d68ca3c0dcb81" > perform_fft< / a > < < span class = "comment" > /*rader=*/< / span > < span class = "keyword" > true< / span > > (fft_idx, & p, m, n - rader_m, < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > + rader_m);< / div >
< div class = "line" > < a id = "l00313" name = "l00313" > < / a > < span class = "lineno" > 313< / span > < / div >
< div class = "line" > < a id = "l00314" name = "l00314" > < / a > < span class = "lineno" > 314< / span > < span class = "comment" > // x_1 + ... + x_n is computed for us in the first FFT step so< / span > < / div >
< div class = "line" > < a id = "l00315" name = "l00315" > < / a > < span class = "lineno" > 315< / span > < span class = "comment" > // we save it in the first rader_m indices of the array for later.< / span > < / div >
< div class = "line" > < a id = "l00316" name = "l00316" > < / a > < span class = "lineno" > 316< / span > < span class = "keywordtype" > int< / span > x_sum_index = < a class = "code hl_function" href = "namespacemetal.html#a6653b28c9473087141eddce39878d4d3" > metal::min< / a > (fft_idx, rader_m - 1);< / div >
< div class = "line" > < a id = "l00317" name = "l00317" > < / a > < span class = "lineno" > 317< / span > < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > [x_sum_index] = < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > [rader_m + x_sum_index * (rader_n - 1)];< / div >
< div class = "line" > < a id = "l00318" name = "l00318" > < / a > < span class = "lineno" > 318< / span > < / div >
< div class = "line" > < a id = "l00319" name = "l00319" > < / a > < span class = "lineno" > 319< / span > float2 inv = {1.0f, -1.0f};< / div >
< div class = "line" > < a id = "l00320" name = "l00320" > < / a > < span class = "lineno" > 320< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > e = 0; e < < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3" > elems_per_thread_< / a > ; e++) {< / div >
< div class = "line" > < a id = "l00321" name = "l00321" > < / a > < span class = "lineno" > 321< / span > < span class = "keywordtype" > short< / span > index = < a class = "code hl_function" href = "namespacemetal.html#a6653b28c9473087141eddce39878d4d3" > metal::min< / a > (fft_idx * < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3" > elems_per_thread_< / a > + e, max_index);< / div >
< div class = "line" > < a id = "l00322" name = "l00322" > < / a > < span class = "lineno" > 322< / span > < span class = "keywordtype" > short< / span > interleaved_index =< / div >
< div class = "line" > < a id = "l00323" name = "l00323" > < / a > < span class = "lineno" > 323< / span > index / rader_m + (index % rader_m) * (rader_n - 1);< / div >
< div class = "line" > < a id = "l00324" name = "l00324" > < / a > < span class = "lineno" > 324< / span > temp[e] = < a class = "code hl_function" href = "radix_8h.html#a5bfc53b531214c9ce277bebc18aa67d6" > complex_mul< / a > (< / div >
< div class = "line" > < a id = "l00325" name = "l00325" > < / a > < span class = "lineno" > 325< / span > < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > [rader_m + interleaved_index],< / div >
< div class = "line" > < a id = "l00326" name = "l00326" > < / a > < span class = "lineno" > 326< / span > raders_b_q[interleaved_index % (rader_n - 1)]);< / div >
< div class = "line" > < a id = "l00327" name = "l00327" > < / a > < span class = "lineno" > 327< / span > }< / div >
< div class = "line" > < a id = "l00328" name = "l00328" > < / a > < span class = "lineno" > 328< / span > < / div >
< div class = "line" > < a id = "l00329" name = "l00329" > < / a > < span class = "lineno" > 329< / span > threadgroup_barrier(mem_flags::mem_threadgroup);< / div >
< div class = "line" > < a id = "l00330" name = "l00330" > < / a > < span class = "lineno" > 330< / span > < / div >
< div class = "line" > < a id = "l00331" name = "l00331" > < / a > < span class = "lineno" > 331< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > e = 0; e < < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3" > elems_per_thread_< / a > ; e++) {< / div >
< div class = "line" > < a id = "l00332" name = "l00332" > < / a > < span class = "lineno" > 332< / span > < span class = "keywordtype" > short< / span > index = < a class = "code hl_function" href = "namespacemetal.html#a6653b28c9473087141eddce39878d4d3" > metal::min< / a > (fft_idx * < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3" > elems_per_thread_< / a > + e, max_index);< / div >
< div class = "line" > < a id = "l00333" name = "l00333" > < / a > < span class = "lineno" > 333< / span > < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > [rader_m + index] = temp[e] * inv;< / div >
< div class = "line" > < a id = "l00334" name = "l00334" > < / a > < span class = "lineno" > 334< / span > }< / div >
< div class = "line" > < a id = "l00335" name = "l00335" > < / a > < span class = "lineno" > 335< / span > < / div >
< div class = "line" > < a id = "l00336" name = "l00336" > < / a > < span class = "lineno" > 336< / span > threadgroup_barrier(mem_flags::mem_threadgroup);< / div >
< div class = "line" > < a id = "l00337" name = "l00337" > < / a > < span class = "lineno" > 337< / span > < / div >
< div class = "line" > < a id = "l00338" name = "l00338" > < / a > < span class = "lineno" > 338< / span > < span class = "comment" > // Rader IFFT on x[rader_m:]< / span > < / div >
< div class = "line" > < a id = "l00339" name = "l00339" > < / a > < span class = "lineno" > 339< / span > p = 1;< / div >
< div class = "line" > < a id = "l00340" name = "l00340" > < / a > < span class = "lineno" > 340< / span > < a class = "code hl_function" href = "backend_2metal_2kernels_2fft_8h.html#a050ead8fa5cacdaec13d68ca3c0dcb81" > perform_fft< / a > < < span class = "comment" > /*rader=*/< / span > < span class = "keyword" > true< / span > > (fft_idx, & p, m, n - rader_m, < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > + rader_m);< / div >
< div class = "line" > < a id = "l00341" name = "l00341" > < / a > < span class = "lineno" > 341< / span > < / div >
< div class = "line" > < a id = "l00342" name = "l00342" > < / a > < span class = "lineno" > 342< / span > float2 rader_inv_factor = {1.0f / (rader_n - 1), -1.0f / (rader_n - 1)};< / div >
< div class = "line" > < a id = "l00343" name = "l00343" > < / a > < span class = "lineno" > 343< / span > < / div >
< div class = "line" > < a id = "l00344" name = "l00344" > < / a > < span class = "lineno" > 344< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > e = 0; e < < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3" > elems_per_thread_< / a > ; e++) {< / div >
< div class = "line" > < a id = "l00345" name = "l00345" > < / a > < span class = "lineno" > 345< / span > < span class = "keywordtype" > short< / span > index = < a class = "code hl_function" href = "namespacemetal.html#a6653b28c9473087141eddce39878d4d3" > metal::min< / a > (fft_idx * < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3" > elems_per_thread_< / a > + e, n - rader_m - 1);< / div >
< div class = "line" > < a id = "l00346" name = "l00346" > < / a > < span class = "lineno" > 346< / span > < span class = "keywordtype" > short< / span > diff_index = index / (rader_n - 1) - x_0_index;< / div >
< div class = "line" > < a id = "l00347" name = "l00347" > < / a > < span class = "lineno" > 347< / span > temp[e] = < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > [rader_m + index] * rader_inv_factor + x_0[diff_index];< / div >
< div class = "line" > < a id = "l00348" name = "l00348" > < / a > < span class = "lineno" > 348< / span > }< / div >
< div class = "line" > < a id = "l00349" name = "l00349" > < / a > < span class = "lineno" > 349< / span > < / div >
< div class = "line" > < a id = "l00350" name = "l00350" > < / a > < span class = "lineno" > 350< / span > < span class = "comment" > // Use the sum of elements that was computed in the first FFT< / span > < / div >
< div class = "line" > < a id = "l00351" name = "l00351" > < / a > < span class = "lineno" > 351< / span > float2 x_sum = < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > [x_0_index] + x_0[0];< / div >
< div class = "line" > < a id = "l00352" name = "l00352" > < / a > < span class = "lineno" > 352< / span > < / div >
< div class = "line" > < a id = "l00353" name = "l00353" > < / a > < span class = "lineno" > 353< / span > threadgroup_barrier(mem_flags::mem_threadgroup);< / div >
< div class = "line" > < a id = "l00354" name = "l00354" > < / a > < span class = "lineno" > 354< / span > < / div >
< div class = "line" > < a id = "l00355" name = "l00355" > < / a > < span class = "lineno" > 355< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > e = 0; e < < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3" > elems_per_thread_< / a > ; e++) {< / div >
< div class = "line" > < a id = "l00356" name = "l00356" > < / a > < span class = "lineno" > 356< / span > < span class = "keywordtype" > short< / span > index = < a class = "code hl_function" href = "namespacemetal.html#a6653b28c9473087141eddce39878d4d3" > metal::min< / a > (fft_idx * < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3" > elems_per_thread_< / a > + e, max_index);< / div >
< div class = "line" > < a id = "l00357" name = "l00357" > < / a > < span class = "lineno" > 357< / span > < span class = "keywordtype" > short< / span > g_q_index = index % (rader_n - 1);< / div >
< div class = "line" > < a id = "l00358" name = "l00358" > < / a > < span class = "lineno" > 358< / span > < span class = "keywordtype" > short< / span > g_q = raders_g_minus_q[g_q_index];< / div >
< div class = "line" > < a id = "l00359" name = "l00359" > < / a > < span class = "lineno" > 359< / span > < span class = "keywordtype" > short< / span > out_index = index - g_q_index + g_q + (index / (rader_n - 1));< / div >
< div class = "line" > < a id = "l00360" name = "l00360" > < / a > < span class = "lineno" > 360< / span > < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > [out_index] = temp[e];< / div >
< div class = "line" > < a id = "l00361" name = "l00361" > < / a > < span class = "lineno" > 361< / span > }< / div >
< div class = "line" > < a id = "l00362" name = "l00362" > < / a > < span class = "lineno" > 362< / span > < / div >
< div class = "line" > < a id = "l00363" name = "l00363" > < / a > < span class = "lineno" > 363< / span > < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > [x_0_index * rader_n] = x_sum;< / div >
< div class = "line" > < a id = "l00364" name = "l00364" > < / a > < span class = "lineno" > 364< / span > < / div >
< div class = "line" > < a id = "l00365" name = "l00365" > < / a > < span class = "lineno" > 365< / span > threadgroup_barrier(mem_flags::mem_threadgroup);< / div >
< div class = "line" > < a id = "l00366" name = "l00366" > < / a > < span class = "lineno" > 366< / span > < / div >
< div class = "line" > < a id = "l00367" name = "l00367" > < / a > < span class = "lineno" > 367< / span > p = rader_n;< / div >
< div class = "line" > < a id = "l00368" name = "l00368" > < / a > < span class = "lineno" > 368< / span > < a class = "code hl_function" href = "backend_2metal_2kernels_2fft_8h.html#a050ead8fa5cacdaec13d68ca3c0dcb81" > perform_fft< / a > (fft_idx, & p, m, n, < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > );< / div >
< div class = "line" > < a id = "l00369" name = "l00369" > < / a > < span class = "lineno" > 369< / span > < / div >
< div class = "line" > < a id = "l00370" name = "l00370" > < / a > < span class = "lineno" > 370< / span > read_writer.write();< / div >
< div class = "line" > < a id = "l00371" name = "l00371" > < / a > < span class = "lineno" > 371< / span > }< / div >
< / div >
< div class = "line" > < a id = "l00372" name = "l00372" > < / a > < span class = "lineno" > 372< / span > < / div >
< div class = "line" > < a id = "l00373" name = "l00373" > < / a > < span class = "lineno" > 373< / span > < span class = "keyword" > template< / span > < < span class = "keywordtype" > int< / span > tg_mem_size, < span class = "keyword" > typename< / span > in_T, < span class = "keyword" > typename< / span > out_T> < / div >
< div class = "foldopen" id = "foldopen00374" data-start = "{" data-end = "}" >
< div class = "line" > < a id = "l00374" name = "l00374" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#a0abc609e9756475800e996775a96a87e" > 374< / a > < / span > [[kernel]] < span class = "keywordtype" > void< / span > < a class = "code hl_function" href = "backend_2metal_2kernels_2fft_8h.html#a0abc609e9756475800e996775a96a87e" > bluestein_fft< / a > (< / div >
< div class = "line" > < a id = "l00375" name = "l00375" > < / a > < span class = "lineno" > 375< / span > < span class = "keyword" > const< / span > device in_T* in [[buffer(0)]],< / div >
< div class = "line" > < a id = "l00376" name = "l00376" > < / a > < span class = "lineno" > 376< / span > device out_T* out [[buffer(1)]],< / div >
< div class = "line" > < a id = "l00377" name = "l00377" > < / a > < span class = "lineno" > 377< / span > < span class = "keyword" > const< / span > device float2* w_q [[buffer(2)]],< / div >
< div class = "line" > < a id = "l00378" name = "l00378" > < / a > < span class = "lineno" > 378< / span > < span class = "keyword" > const< / span > device float2* w_k [[buffer(3)]],< / div >
< div class = "line" > < a id = "l00379" name = "l00379" > < / a > < span class = "lineno" > 379< / span > constant < span class = "keyword" > const< / span > < span class = "keywordtype" > int< / span > & length,< / div >
< div class = "line" > < a id = "l00380" name = "l00380" > < / a > < span class = "lineno" > 380< / span > constant < span class = "keyword" > const< / span > < span class = "keywordtype" > int< / span > & n,< / div >
< div class = "line" > < a id = "l00381" name = "l00381" > < / a > < span class = "lineno" > 381< / span > constant < span class = "keyword" > const< / span > < span class = "keywordtype" > int< / span > & batch_size,< / div >
< div class = "line" > < a id = "l00382" name = "l00382" > < / a > < span class = "lineno" > 382< / span > uint3 elem [[thread_position_in_grid]],< / div >
< div class = "line" > < a id = "l00383" name = "l00383" > < / a > < span class = "lineno" > 383< / span > uint3 grid [[threads_per_grid]]) {< / div >
< div class = "line" > < a id = "l00384" name = "l00384" > < / a > < span class = "lineno" > 384< / span > < span class = "comment" > // Computes arbitrary length FFTs with Bluestein' s algorithm< / span > < / div >
< div class = "line" > < a id = "l00385" name = "l00385" > < / a > < span class = "lineno" > 385< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00386" name = "l00386" > < / a > < span class = "lineno" > 386< / span > < span class = "comment" > // In numpy:< / span > < / div >
< div class = "line" > < a id = "l00387" name = "l00387" > < / a > < span class = "lineno" > 387< / span > < span class = "comment" > // bluestein_n = next_power_of_2(2*n - 1)< / span > < / div >
< div class = "line" > < a id = "l00388" name = "l00388" > < / a > < span class = "lineno" > 388< / span > < span class = "comment" > // out = w_k * np.fft.ifft(np.fft.fft(w_k * in, bluestein_n) * w_q)< / span > < / div >
< div class = "line" > < a id = "l00389" name = "l00389" > < / a > < span class = "lineno" > 389< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00390" name = "l00390" > < / a > < span class = "lineno" > 390< / span > < span class = "comment" > // Where w_k and w_q are precomputed on CPU in high precision as:< / span > < / div >
< div class = "line" > < a id = "l00391" name = "l00391" > < / a > < span class = "lineno" > 391< / span > < span class = "comment" > // w_k = np.exp(-1j * np.pi / n * (np.arange(-n + 1, n) ** 2))< / span > < / div >
< div class = "line" > < a id = "l00392" name = "l00392" > < / a > < span class = "lineno" > 392< / span > < span class = "comment" > // w_q = np.fft.fft(1/w_k[-n:])< / span > < / div >
< div class = "line" > < a id = "l00393" name = "l00393" > < / a > < span class = "lineno" > 393< / span > threadgroup float2 shared_in[tg_mem_size];< / div >
< div class = "line" > < a id = "l00394" name = "l00394" > < / a > < span class = "lineno" > 394< / span > < / div >
< div class = "line" > < a id = "l00395" name = "l00395" > < / a > < span class = "lineno" > 395< / span > thread < a class = "code hl_struct" href = "struct_read_writer.html" > ReadWriter< in_T, out_T> < / a > read_writer = < a class = "code hl_struct" href = "struct_read_writer.html" > ReadWriter< in_T, out_T> < / a > (< / div >
< div class = "line" > < a id = "l00396" name = "l00396" > < / a > < span class = "lineno" > 396< / span > in,< / div >
< div class = "line" > < a id = "l00397" name = "l00397" > < / a > < span class = "lineno" > 397< / span > & shared_in[0],< / div >
< div class = "line" > < a id = "l00398" name = "l00398" > < / a > < span class = "lineno" > 398< / span > out,< / div >
< div class = "line" > < a id = "l00399" name = "l00399" > < / a > < span class = "lineno" > 399< / span > n,< / div >
< div class = "line" > < a id = "l00400" name = "l00400" > < / a > < span class = "lineno" > 400< / span > batch_size,< / div >
< div class = "line" > < a id = "l00401" name = "l00401" > < / a > < span class = "lineno" > 401< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3" > elems_per_thread_< / a > ,< / div >
< div class = "line" > < a id = "l00402" name = "l00402" > < / a > < span class = "lineno" > 402< / span > elem,< / div >
< div class = "line" > < a id = "l00403" name = "l00403" > < / a > < span class = "lineno" > 403< / span > grid,< / div >
< div class = "line" > < a id = "l00404" name = "l00404" > < / a > < span class = "lineno" > 404< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a7a83318497519ff3ff0141b7d511ed38" > inv_< / a > );< / div >
< div class = "line" > < a id = "l00405" name = "l00405" > < / a > < span class = "lineno" > 405< / span > < / div >
< div class = "line" > < a id = "l00406" name = "l00406" > < / a > < span class = "lineno" > 406< / span > < span class = "keywordflow" > if< / span > (read_writer.out_of_bounds()) {< / div >
< div class = "line" > < a id = "l00407" name = "l00407" > < / a > < span class = "lineno" > 407< / span > < span class = "keywordflow" > return< / span > ;< / div >
< div class = "line" > < a id = "l00408" name = "l00408" > < / a > < span class = "lineno" > 408< / span > };< / div >
< div class = "line" > < a id = "l00409" name = "l00409" > < / a > < span class = "lineno" > 409< / span > read_writer.load_padded(length, w_k);< / div >
< div class = "line" > < a id = "l00410" name = "l00410" > < / a > < span class = "lineno" > 410< / span > < / div >
< div class = "line" > < a id = "l00411" name = "l00411" > < / a > < span class = "lineno" > 411< / span > threadgroup_barrier(mem_flags::mem_threadgroup);< / div >
< div class = "line" > < a id = "l00412" name = "l00412" > < / a > < span class = "lineno" > 412< / span > < / div >
< div class = "line" > < a id = "l00413" name = "l00413" > < / a > < span class = "lineno" > 413< / span > < span class = "keywordtype" > int< / span > p = 1;< / div >
< div class = "line" > < a id = "l00414" name = "l00414" > < / a > < span class = "lineno" > 414< / span > < span class = "keywordtype" > int< / span > fft_idx = elem.z; < span class = "comment" > // Thread index in DFT< / span > < / div >
< div class = "line" > < a id = "l00415" name = "l00415" > < / a > < span class = "lineno" > 415< / span > < span class = "keywordtype" > int< / span > m = grid.z; < span class = "comment" > // Threads per DFT< / span > < / div >
< div class = "line" > < a id = "l00416" name = "l00416" > < / a > < span class = "lineno" > 416< / span > < span class = "keywordtype" > int< / span > tg_idx = elem.y * n; < span class = "comment" > // Index of this DFT in threadgroup< / span > < / div >
< div class = "line" > < a id = "l00417" name = "l00417" > < / a > < span class = "lineno" > 417< / span > threadgroup float2* < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > = & shared_in[tg_idx];< / div >
< div class = "line" > < a id = "l00418" name = "l00418" > < / a > < span class = "lineno" > 418< / span > < / div >
< div class = "line" > < a id = "l00419" name = "l00419" > < / a > < span class = "lineno" > 419< / span > < span class = "comment" > // fft< / span > < / div >
< div class = "line" > < a id = "l00420" name = "l00420" > < / a > < span class = "lineno" > 420< / span > < a class = "code hl_function" href = "backend_2metal_2kernels_2fft_8h.html#a050ead8fa5cacdaec13d68ca3c0dcb81" > perform_fft< / a > (fft_idx, & p, m, n, < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > );< / div >
< div class = "line" > < a id = "l00421" name = "l00421" > < / a > < span class = "lineno" > 421< / span > < / div >
< div class = "line" > < a id = "l00422" name = "l00422" > < / a > < span class = "lineno" > 422< / span > float2 inv = float2(1.0f, -1.0f);< / div >
< div class = "line" > < a id = "l00423" name = "l00423" > < / a > < span class = "lineno" > 423< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > t = 0; t < < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3" > elems_per_thread_< / a > ; t++) {< / div >
< div class = "line" > < a id = "l00424" name = "l00424" > < / a > < span class = "lineno" > 424< / span > < span class = "keywordtype" > int< / span > index = fft_idx + t * m;< / div >
< div class = "line" > < a id = "l00425" name = "l00425" > < / a > < span class = "lineno" > 425< / span > < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > [index] = < a class = "code hl_function" href = "radix_8h.html#a5bfc53b531214c9ce277bebc18aa67d6" > complex_mul< / a > (< a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > [index], w_q[index]) * inv;< / div >
< div class = "line" > < a id = "l00426" name = "l00426" > < / a > < span class = "lineno" > 426< / span > }< / div >
< div class = "line" > < a id = "l00427" name = "l00427" > < / a > < span class = "lineno" > 427< / span > < / div >
< div class = "line" > < a id = "l00428" name = "l00428" > < / a > < span class = "lineno" > 428< / span > threadgroup_barrier(mem_flags::mem_threadgroup);< / div >
< div class = "line" > < a id = "l00429" name = "l00429" > < / a > < span class = "lineno" > 429< / span > < / div >
< div class = "line" > < a id = "l00430" name = "l00430" > < / a > < span class = "lineno" > 430< / span > < span class = "comment" > // ifft< / span > < / div >
< div class = "line" > < a id = "l00431" name = "l00431" > < / a > < span class = "lineno" > 431< / span > p = 1;< / div >
< div class = "line" > < a id = "l00432" name = "l00432" > < / a > < span class = "lineno" > 432< / span > < a class = "code hl_function" href = "backend_2metal_2kernels_2fft_8h.html#a050ead8fa5cacdaec13d68ca3c0dcb81" > perform_fft< / a > (fft_idx, & p, m, n, < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > );< / div >
< div class = "line" > < a id = "l00433" name = "l00433" > < / a > < span class = "lineno" > 433< / span > < / div >
< div class = "line" > < a id = "l00434" name = "l00434" > < / a > < span class = "lineno" > 434< / span > read_writer.write_padded(length, w_k);< / div >
< div class = "line" > < a id = "l00435" name = "l00435" > < / a > < span class = "lineno" > 435< / span > }< / div >
< / div >
< div class = "line" > < a id = "l00436" name = "l00436" > < / a > < span class = "lineno" > 436< / span > < / div >
< div class = "line" > < a id = "l00437" name = "l00437" > < / a > < span class = "lineno" > 437< / span > < span class = "keyword" > template< / span > < < / div >
< div class = "line" > < a id = "l00438" name = "l00438" > < / a > < span class = "lineno" > 438< / span > < span class = "keywordtype" > int< / span > tg_mem_size,< / div >
< div class = "line" > < a id = "l00439" name = "l00439" > < / a > < span class = "lineno" > 439< / span > < span class = "keyword" > typename< / span > in_T,< / div >
< div class = "line" > < a id = "l00440" name = "l00440" > < / a > < span class = "lineno" > 440< / span > < span class = "keyword" > typename< / span > out_T,< / div >
< div class = "line" > < a id = "l00441" name = "l00441" > < / a > < span class = "lineno" > 441< / span > < span class = "keywordtype" > int< / span > step,< / div >
2024-10-19 03:13:44 +08:00
< div class = "line" > < a id = "l00442" name = "l00442" > < / a > < span class = "lineno" > 442< / span > < span class = "keywordtype" > bool< / span > < a class = "code hl_function" href = "group__ops.html#gaf8913cabeb9fb193ba687aaeb2087764" > real< / a > = < span class = "keyword" > false< / span > > < / div >
2024-10-15 23:12:17 +08:00
< div class = "foldopen" id = "foldopen00443" data-start = "{" data-end = "}" >
< div class = "line" > < a id = "l00443" name = "l00443" > < / a > < span class = "lineno" > < a class = "line" href = "backend_2metal_2kernels_2fft_8h.html#a6558a8205ee4c3e4767bafa93f7606de" > 443< / a > < / span > [[kernel]] < span class = "keywordtype" > void< / span > < a class = "code hl_function" href = "backend_2metal_2kernels_2fft_8h.html#a6558a8205ee4c3e4767bafa93f7606de" > four_step_fft< / a > (< / div >
< div class = "line" > < a id = "l00444" name = "l00444" > < / a > < span class = "lineno" > 444< / span > < span class = "keyword" > const< / span > device in_T* in [[buffer(0)]],< / div >
< div class = "line" > < a id = "l00445" name = "l00445" > < / a > < span class = "lineno" > 445< / span > device out_T* out [[buffer(1)]],< / div >
< div class = "line" > < a id = "l00446" name = "l00446" > < / a > < span class = "lineno" > 446< / span > constant < span class = "keyword" > const< / span > < span class = "keywordtype" > int< / span > & n1,< / div >
< div class = "line" > < a id = "l00447" name = "l00447" > < / a > < span class = "lineno" > 447< / span > constant < span class = "keyword" > const< / span > < span class = "keywordtype" > int< / span > & n2,< / div >
< div class = "line" > < a id = "l00448" name = "l00448" > < / a > < span class = "lineno" > 448< / span > constant < span class = "keyword" > const< / span > < span class = "keywordtype" > int< / span > & batch_size,< / div >
< div class = "line" > < a id = "l00449" name = "l00449" > < / a > < span class = "lineno" > 449< / span > uint3 elem [[thread_position_in_grid]],< / div >
< div class = "line" > < a id = "l00450" name = "l00450" > < / a > < span class = "lineno" > 450< / span > uint3 grid [[threads_per_grid]]) {< / div >
< div class = "line" > < a id = "l00451" name = "l00451" > < / a > < span class = "lineno" > 451< / span > < span class = "comment" > // Fast four step FFT implementation for powers of 2.< / span > < / div >
< div class = "line" > < a id = "l00452" name = "l00452" > < / a > < span class = "lineno" > 452< / span > < span class = "keywordtype" > int< / span > overall_n = n1 * n2;< / div >
< div class = "line" > < a id = "l00453" name = "l00453" > < / a > < span class = "lineno" > 453< / span > < span class = "keywordtype" > int< / span > n = step == 0 ? n1 : n2;< / div >
< div class = "line" > < a id = "l00454" name = "l00454" > < / a > < span class = "lineno" > 454< / span > < span class = "keywordtype" > int< / span > stride = step == 0 ? n2 : n1;< / div >
< div class = "line" > < a id = "l00455" name = "l00455" > < / a > < span class = "lineno" > 455< / span > < / div >
< div class = "line" > < a id = "l00456" name = "l00456" > < / a > < span class = "lineno" > 456< / span > < span class = "comment" > // The number of the threads we' re using for each DFT< / span > < / div >
< div class = "line" > < a id = "l00457" name = "l00457" > < / a > < span class = "lineno" > 457< / span > < span class = "keywordtype" > int< / span > m = grid.z;< / div >
< div class = "line" > < a id = "l00458" name = "l00458" > < / a > < span class = "lineno" > 458< / span > < span class = "keywordtype" > int< / span > fft_idx = elem.z;< / div >
< div class = "line" > < a id = "l00459" name = "l00459" > < / a > < span class = "lineno" > 459< / span > < / div >
< div class = "line" > < a id = "l00460" name = "l00460" > < / a > < span class = "lineno" > 460< / span > threadgroup float2 shared_in[tg_mem_size];< / div >
< div class = "line" > < a id = "l00461" name = "l00461" > < / a > < span class = "lineno" > 461< / span > threadgroup float2* < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > = & shared_in[elem.y * n];< / div >
< div class = "line" > < a id = "l00462" name = "l00462" > < / a > < span class = "lineno" > 462< / span > < / div >
< div class = "line" > < a id = "l00463" name = "l00463" > < / a > < span class = "lineno" > 463< / span > < span class = "keyword" > using < / span > read_writer_t = < a class = "code hl_struct" href = "struct_read_writer.html" > ReadWriter< in_T, out_T, step, real> < / a > ;< / div >
< div class = "line" > < a id = "l00464" name = "l00464" > < / a > < span class = "lineno" > 464< / span > read_writer_t read_writer = read_writer_t(< / div >
< div class = "line" > < a id = "l00465" name = "l00465" > < / a > < span class = "lineno" > 465< / span > in,< / div >
< div class = "line" > < a id = "l00466" name = "l00466" > < / a > < span class = "lineno" > 466< / span > & shared_in[0],< / div >
< div class = "line" > < a id = "l00467" name = "l00467" > < / a > < span class = "lineno" > 467< / span > out,< / div >
< div class = "line" > < a id = "l00468" name = "l00468" > < / a > < span class = "lineno" > 468< / span > n,< / div >
< div class = "line" > < a id = "l00469" name = "l00469" > < / a > < span class = "lineno" > 469< / span > batch_size,< / div >
< div class = "line" > < a id = "l00470" name = "l00470" > < / a > < span class = "lineno" > 470< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3" > elems_per_thread_< / a > ,< / div >
< div class = "line" > < a id = "l00471" name = "l00471" > < / a > < span class = "lineno" > 471< / span > elem,< / div >
< div class = "line" > < a id = "l00472" name = "l00472" > < / a > < span class = "lineno" > 472< / span > grid,< / div >
< div class = "line" > < a id = "l00473" name = "l00473" > < / a > < span class = "lineno" > 473< / span > < a class = "code hl_variable" href = "backend_2metal_2kernels_2fft_8h.html#a7a83318497519ff3ff0141b7d511ed38" > inv_< / a > );< / div >
< div class = "line" > < a id = "l00474" name = "l00474" > < / a > < span class = "lineno" > 474< / span > < / div >
< div class = "line" > < a id = "l00475" name = "l00475" > < / a > < span class = "lineno" > 475< / span > < span class = "keywordflow" > if< / span > (read_writer.out_of_bounds()) {< / div >
< div class = "line" > < a id = "l00476" name = "l00476" > < / a > < span class = "lineno" > 476< / span > < span class = "keywordflow" > return< / span > ;< / div >
< div class = "line" > < a id = "l00477" name = "l00477" > < / a > < span class = "lineno" > 477< / span > };< / div >
< div class = "line" > < a id = "l00478" name = "l00478" > < / a > < span class = "lineno" > 478< / span > read_writer.load_strided(stride, overall_n);< / div >
< div class = "line" > < a id = "l00479" name = "l00479" > < / a > < span class = "lineno" > 479< / span > < / div >
< div class = "line" > < a id = "l00480" name = "l00480" > < / a > < span class = "lineno" > 480< / span > threadgroup_barrier(mem_flags::mem_threadgroup);< / div >
< div class = "line" > < a id = "l00481" name = "l00481" > < / a > < span class = "lineno" > 481< / span > < / div >
< div class = "line" > < a id = "l00482" name = "l00482" > < / a > < span class = "lineno" > 482< / span > < span class = "keywordtype" > int< / span > p = 1;< / div >
< div class = "line" > < a id = "l00483" name = "l00483" > < / a > < span class = "lineno" > 483< / span > < a class = "code hl_function" href = "backend_2metal_2kernels_2fft_8h.html#a050ead8fa5cacdaec13d68ca3c0dcb81" > perform_fft< / a > (fft_idx, & p, m, n, < a class = "code hl_variable" href = "backend_2metal_2allocator_8h.html#a15aa5cc1baf29be08d55cca88509e697" > buf< / a > );< / div >
< div class = "line" > < a id = "l00484" name = "l00484" > < / a > < span class = "lineno" > 484< / span > < / div >
< div class = "line" > < a id = "l00485" name = "l00485" > < / a > < span class = "lineno" > 485< / span > read_writer.write_strided(stride, overall_n);< / div >
< div class = "line" > < a id = "l00486" name = "l00486" > < / a > < span class = "lineno" > 486< / span > }< / div >
< / div >
2024-10-26 04:23:45 +08:00
< 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:39< / div > < / div >
2024-10-15 23:12:17 +08:00
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_a020469d1aca557ff1b49414f121dedbb" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#a020469d1aca557ff1b49414f121dedbb" > rader_6_steps_< / a > < / div > < div class = "ttdeci" > static constant constexpr const int rader_6_steps_< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:43< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_a050ead8fa5cacdaec13d68ca3c0dcb81" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#a050ead8fa5cacdaec13d68ca3c0dcb81" > perform_fft< / a > < / div > < div class = "ttdeci" > METAL_FUNC void perform_fft(int fft_idx, thread int *p, int m, int n, threadgroup float2 *buf)< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:159< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_a0abc609e9756475800e996775a96a87e" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#a0abc609e9756475800e996775a96a87e" > bluestein_fft< / a > < / div > < div class = "ttdeci" > void bluestein_fft(const device in_T *in, device out_T *out, const device float2 *w_q, const device float2 *w_k, constant const int & length, constant const int & n, constant const int & batch_size, uint3 elem, uint3 grid)< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:374< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_a0d437aef17faf8d9707ae7ffe68fdb30" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#a0d437aef17faf8d9707ae7ffe68fdb30" > rader_7_steps_< / a > < / div > < div class = "ttdeci" > static constant constexpr const int rader_7_steps_< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:42< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_a12d99a846c3686806bab6c42148e1039" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#a12d99a846c3686806bab6c42148e1039" > radix_4_steps_< / a > < / div > < div class = "ttdeci" > static constant constexpr const int radix_4_steps_< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:35< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_a1f3c377d05da52429172e64132dba750" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#a1f3c377d05da52429172e64132dba750" > rader_11_steps_< / a > < / div > < div class = "ttdeci" > static constant constexpr const int rader_11_steps_< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:40< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_a20d24f3e040d3d226a70d4dd7c9ac6a9" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#a20d24f3e040d3d226a70d4dd7c9ac6a9" > rader_13_steps_< / a > < / div > < div class = "ttdeci" > static constant constexpr const int rader_13_steps_< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:39< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_a2145cc8ab4d07583a735317b3cf60d55" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#a2145cc8ab4d07583a735317b3cf60d55" > radix_7_steps_< / a > < / div > < div class = "ttdeci" > static constant constexpr const int radix_7_steps_< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:32< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_a278d980ed397e6841ce0af44b9aa4396" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#a278d980ed397e6841ce0af44b9aa4396" > radix_butterfly< / a > < / div > < div class = "ttdeci" > METAL_FUNC void radix_butterfly(int i, int p, thread float2 *x, thread short *indices, thread float2 *y)< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:54< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_a28d683cf067736d76f867f30c066317e" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#a28d683cf067736d76f867f30c066317e" > MAX_OUTPUT_SIZE< / a > < / div > < div class = "ttdeci" > #define MAX_OUTPUT_SIZE< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:20< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_a2a4df90e329b84ee6c1890ba7c265c9c" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#a2a4df90e329b84ee6c1890ba7c265c9c" > is_power_of_2_< / a > < / div > < div class = "ttdeci" > static constant constexpr const bool is_power_of_2_< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:24< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_a2d725bfd4c30be4c605b5c4559a62892" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#a2d725bfd4c30be4c605b5c4559a62892" > rader_2_steps_< / a > < / div > < div class = "ttdeci" > static constant constexpr const int rader_2_steps_< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:47< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_a2f7f7cc2423cfcd4998d1a2a0363c3e2" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#a2f7f7cc2423cfcd4998d1a2a0363c3e2" > radix_6_steps_< / a > < / div > < div class = "ttdeci" > static constant constexpr const int radix_6_steps_< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:33< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_a3cb03a97a209ba1346375e720ee76177" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#a3cb03a97a209ba1346375e720ee76177" > radix_8_steps_< / a > < / div > < div class = "ttdeci" > static constant constexpr const int radix_8_steps_< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:31< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_a4010b0e151e5f01e610e9c32234458c7" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#a4010b0e151e5f01e610e9c32234458c7" > fft< / a > < / div > < div class = "ttdeci" > void fft(const device in_T *in, device out_T *out, constant const int & n, constant const int & batch_size, uint3 elem, uint3 grid)< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:180< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_a53fdc660e99e6b5db6808bbd596cd374" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#a53fdc660e99e6b5db6808bbd596cd374" > radix_2_steps_< / a > < / div > < div class = "ttdeci" > static constant constexpr const int radix_2_steps_< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:37< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_a579123b7be825f08f3076287dded08e3" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#a579123b7be825f08f3076287dded08e3" > radix_3_steps_< / a > < / div > < div class = "ttdeci" > static constant constexpr const int radix_3_steps_< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:36< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_a6558a8205ee4c3e4767bafa93f7606de" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#a6558a8205ee4c3e4767bafa93f7606de" > four_step_fft< / a > < / div > < div class = "ttdeci" > void four_step_fft(const device in_T *in, device out_T *out, constant const int & n1, constant const int & n2, constant const int & batch_size, uint3 elem, uint3 grid)< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:443< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_a6ba62eabfd5428644aabf89ddaa0128d" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#a6ba62eabfd5428644aabf89ddaa0128d" > RadixFunc< / a > < / div > < div class = "ttdeci" > void(* RadixFunc)(thread float2 *, thread float2 *)< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:50< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_a794032d3a9acff0e31c77c69d0007f10" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#a794032d3a9acff0e31c77c69d0007f10" > RADIX_STEP< / a > < / div > < div class = "ttdeci" > #define RADIX_STEP(radix, radix_func, num_steps)< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:153< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_a7a83318497519ff3ff0141b7d511ed38" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#a7a83318497519ff3ff0141b7d511ed38" > inv_< / a > < / div > < div class = "ttdeci" > static constant constexpr const bool inv_< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:23< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_a7b6e56afa21f022c5e754b000955735a" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#a7b6e56afa21f022c5e754b000955735a" > MAX_RADIX< / a > < / div > < div class = "ttdeci" > #define MAX_RADIX< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:17< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_a7cd17bff8bc567f71d4789ee31fa07f2" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#a7cd17bff8bc567f71d4789ee31fa07f2" > radix_11_steps_< / a > < / div > < div class = "ttdeci" > static constant constexpr const int radix_11_steps_< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:30< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_a903d5239b5f73577c559e97ff910892d" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#a903d5239b5f73577c559e97ff910892d" > radix_5_steps_< / a > < / div > < div class = "ttdeci" > static constant constexpr const int radix_5_steps_< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:34< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_aba8d32e0911499671df93678f39da08b" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#aba8d32e0911499671df93678f39da08b" > radix_n_steps< / a > < / div > < div class = "ttdeci" > METAL_FUNC void radix_n_steps(int i, thread int *p, int m, int n, int num_steps, thread float2 *inputs, thread short *indices, thread float2 *values, threadgroup float2 *buf)< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:100< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_abb079b86e89ca88ce13a179d9ec566af" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#abb079b86e89ca88ce13a179d9ec566af" > radix_13_steps_< / a > < / div > < div class = "ttdeci" > static constant constexpr const int radix_13_steps_< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:29< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_ac309c77ef775a3ef13850c5287a86480" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#ac309c77ef775a3ef13850c5287a86480" > rader_m_< / a > < / div > < div class = "ttdeci" > static constant constexpr const int rader_m_< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:27< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_ac6123e111816dd62a11ccb86b66fa3e9" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#ac6123e111816dd62a11ccb86b66fa3e9" > rader_8_steps_< / a > < / div > < div class = "ttdeci" > static constant constexpr const int rader_8_steps_< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:41< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_ac7c58404df0434d4f861db62d3471870" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#ac7c58404df0434d4f861db62d3471870" > rader_4_steps_< / a > < / div > < div class = "ttdeci" > static constant constexpr const int rader_4_steps_< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:45< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_ad123452303f6415904f3592f660769b8" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#ad123452303f6415904f3592f660769b8" > rader_fft< / a > < / div > < div class = "ttdeci" > void rader_fft(const device in_T *in, device out_T *out, const device float2 *raders_b_q, const device short *raders_g_q, const device short *raders_g_minus_q, constant const int & n, constant const int & batch_size, constant const int & rader_n, uint3 elem, uint3 grid)< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:219< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_ad395c11e6f2aee72cd1928fba93a35a3" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#ad395c11e6f2aee72cd1928fba93a35a3" > elems_per_thread_< / a > < / div > < div class = "ttdeci" > static constant constexpr const int elems_per_thread_< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:25< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_adb129cc3808c08fd95af9795bfc7ae63" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#adb129cc3808c08fd95af9795bfc7ae63" > rader_3_steps_< / a > < / div > < div class = "ttdeci" > static constant constexpr const int rader_3_steps_< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:46< / div > < / div >
< div class = "ttc" id = "abackend_2metal_2kernels_2fft_8h_html_afea05e9a7105bafbaafca25042f4d1b4" > < div class = "ttname" > < a href = "backend_2metal_2kernels_2fft_8h.html#afea05e9a7105bafbaafca25042f4d1b4" > rader_5_steps_< / a > < / div > < div class = "ttdeci" > static constant constexpr const int rader_5_steps_< / div > < div class = "ttdef" > < b > Definition< / b > fft.h:44< / div > < / div >
2024-10-19 03:13:44 +08:00
< div class = "ttc" id = "agroup__ops_html_gaf8913cabeb9fb193ba687aaeb2087764" > < div class = "ttname" > < a href = "group__ops.html#gaf8913cabeb9fb193ba687aaeb2087764" > mlx::core::real< / a > < / div > < div class = "ttdeci" > array real(const array & a, StreamOrDevice s={})< / div > < / div >
2024-10-15 23:12:17 +08:00
< 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 = "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 = "anamespacemetal_html_a6653b28c9473087141eddce39878d4d3" > < div class = "ttname" > < a href = "namespacemetal.html#a6653b28c9473087141eddce39878d4d3" > metal::min< / a > < / div > < div class = "ttdeci" > METAL_FUNC bfloat16_t min(bfloat16_t x, bfloat16_t y)< / div > < div class = "ttdef" > < b > Definition< / b > bf16_math.h:234< / div > < / div >
< div class = "ttc" id = "aradix_8h_html" > < div class = "ttname" > < a href = "radix_8h.html" > radix.h< / a > < / div > < / div >
< 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_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_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_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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< div class = "ttc" id = "asteel_2defines_8h_html_a90b91c866313ffa46eff6d9cc944ad2b" > < div class = "ttname" > < a href = "steel_2defines_8h.html#a90b91c866313ffa46eff6d9cc944ad2b" > STEEL_CONST< / a > < / div > < div class = "ttdeci" > #define STEEL_CONST< / div > < div class = "ttdef" > < b > Definition< / b > defines.h:3< / div > < / div >
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