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< a href = "erf_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 © 2023 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 = "preprocessor" > #pragma once< / span > < / div >
< div class = "line" > < a id = "l00004" name = "l00004" > < / a > < span class = "lineno" > 4< / span > < span class = "preprocessor" > #include < metal_math> < / span > < / div >
< div class = "line" > < a id = "l00005" name = "l00005" > < / a > < span class = "lineno" > 5< / span > < / div >
< div class = "line" > < a id = "l00006" name = "l00006" > < / a > < span class = "lineno" > 6< / span > < span class = "comment" > /*< / span > < / div >
< div class = "line" > < a id = "l00007" name = "l00007" > < / a > < span class = "lineno" > 7< / span > < span class = "comment" > * Approximation to the error function.< / span > < / div >
< div class = "line" > < a id = "l00008" name = "l00008" > < / a > < span class = "lineno" > 8< / span > < span class = "comment" > * Based on code from:< / span > < / div >
< div class = "line" > < a id = "l00009" name = "l00009" > < / a > < span class = "lineno" > 9< / span > < span class = "comment" > * https://stackoverflow.com/questions/35148198/efficient-faithfully-rounded-implementation-of-error-function-erff#answer-35148199< / span > < / div >
< div class = "line" > < a id = "l00010" name = "l00010" > < / a > < span class = "lineno" > 10< / span > < span class = "comment" > */< / span > < / div >
< div class = "foldopen" id = "foldopen00011" data-start = "{" data-end = "}" >
< div class = "line" > < a id = "l00011" name = "l00011" > < / a > < span class = "lineno" > < a class = "line" href = "erf_8h.html#a6ce199ee56105c67adbf8c48c019a8b2" > 11< / a > < / span > < span class = "keywordtype" > float< / span > < a class = "code hl_function" href = "erf_8h.html#a6ce199ee56105c67adbf8c48c019a8b2" > erf< / a > (< span class = "keywordtype" > float< / span > a) {< / div >
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< div class = "line" > < a id = "l00012" name = "l00012" > < / a > < span class = "lineno" > 12< / span > < span class = "keywordtype" > float< / span > r, s, t, u;< / div >
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< div class = "line" > < a id = "l00013" name = "l00013" > < / a > < span class = "lineno" > 13< / span > t = < a class = "code hl_function" href = "namespacemetal.html#a87c5122c60f9a12afceb9925a5b78ffb" > metal::abs< / a > (a);< / div >
< div class = "line" > < a id = "l00014" name = "l00014" > < / a > < span class = "lineno" > 14< / span > s = a * a;< / div >
< div class = "line" > < a id = "l00015" name = "l00015" > < / a > < span class = "lineno" > 15< / span > < span class = "keywordflow" > if< / span > (t > 0.927734375f) {< / div >
< div class = "line" > < a id = "l00016" name = "l00016" > < / a > < span class = "lineno" > 16< / span > < span class = "comment" > // maximum error 0.99527 ulp< / span > < / div >
< div class = "line" > < a id = "l00017" name = "l00017" > < / a > < span class = "lineno" > 17< / span > r = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (< / div >
< div class = "line" > < a id = "l00018" name = "l00018" > < / a > < span class = "lineno" > 18< / span > -1.72853470e-5f, t, 3.83197126e-4f); < span class = "comment" > // -0x1.220000p-16,0x1.91cfb2p-12< / span > < / div >
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< div class = "line" > < a id = "l00019" name = "l00019" > < / a > < span class = "lineno" > 19< / span > u = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (< / div >
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< div class = "line" > < a id = "l00020" name = "l00020" > < / a > < span class = "lineno" > 20< / span > -3.88396438e-3f, t, 2.42546219e-2f); < span class = "comment" > // -0x1.fd1438p-9, 0x1.8d6342p-6< / span > < / div >
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< div class = "line" > < a id = "l00021" name = "l00021" > < / a > < span class = "lineno" > 21< / span > r = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (r, s, u);< / div >
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< div class = "line" > < a id = "l00022" name = "l00022" > < / a > < span class = "lineno" > 22< / span > r = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (r, t, -1.06777877e-1f); < span class = "comment" > // -0x1.b55cb8p-4< / span > < / div >
< div class = "line" > < a id = "l00023" name = "l00023" > < / a > < span class = "lineno" > 23< / span > r = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (r, t, -6.34846687e-1f); < span class = "comment" > // -0x1.450aa0p-1< / span > < / div >
< div class = "line" > < a id = "l00024" name = "l00024" > < / a > < span class = "lineno" > 24< / span > r = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (r, t, -1.28717512e-1f); < span class = "comment" > // -0x1.079d0cp-3< / span > < / div >
< div class = "line" > < a id = "l00025" name = "l00025" > < / a > < span class = "lineno" > 25< / span > r = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (r, t, -t);< / div >
< div class = "line" > < a id = "l00026" name = "l00026" > < / a > < span class = "lineno" > 26< / span > < span class = "comment" > // TODO, replace with expm1 when implemented< / span > < / div >
< div class = "line" > < a id = "l00027" name = "l00027" > < / a > < span class = "lineno" > 27< / span > r = 1.0f - < a class = "code hl_function" href = "namespacemetal.html#ac2a0b3618d922ac014baac8189d44650" > metal::exp< / a > (r);< / div >
< div class = "line" > < a id = "l00028" name = "l00028" > < / a > < span class = "lineno" > 28< / span > r = metal::copysign(r, a);< / div >
< div class = "line" > < a id = "l00029" name = "l00029" > < / a > < span class = "lineno" > 29< / span > } < span class = "keywordflow" > else< / span > {< / div >
< div class = "line" > < a id = "l00030" name = "l00030" > < / a > < span class = "lineno" > 30< / span > < span class = "comment" > // maximum error 0.98929 ulp< / span > < / div >
< div class = "line" > < a id = "l00031" name = "l00031" > < / a > < span class = "lineno" > 31< / span > r = -5.96761703e-4f; < span class = "comment" > // -0x1.38e000p-11< / span > < / div >
< div class = "line" > < a id = "l00032" name = "l00032" > < / a > < span class = "lineno" > 32< / span > r = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (r, s, 4.99119423e-3f); < span class = "comment" > // 0x1.471a58p-8< / span > < / div >
< div class = "line" > < a id = "l00033" name = "l00033" > < / a > < span class = "lineno" > 33< / span > r = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (r, s, -2.67681349e-2f); < span class = "comment" > // -0x1.b691b2p-6< / span > < / div >
< div class = "line" > < a id = "l00034" name = "l00034" > < / a > < span class = "lineno" > 34< / span > r = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (r, s, 1.12819925e-1f); < span class = "comment" > // 0x1.ce1c44p-4< / span > < / div >
< div class = "line" > < a id = "l00035" name = "l00035" > < / a > < span class = "lineno" > 35< / span > r = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (r, s, -3.76125336e-1f); < span class = "comment" > // -0x1.812700p-2< / span > < / div >
< div class = "line" > < a id = "l00036" name = "l00036" > < / a > < span class = "lineno" > 36< / span > r = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (r, s, 1.28379166e-1f); < span class = "comment" > // 0x1.06eba8p-3< / span > < / div >
< div class = "line" > < a id = "l00037" name = "l00037" > < / a > < span class = "lineno" > 37< / span > r = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (r, a, a);< / div >
< div class = "line" > < a id = "l00038" name = "l00038" > < / a > < span class = "lineno" > 38< / span > }< / div >
< div class = "line" > < a id = "l00039" name = "l00039" > < / a > < span class = "lineno" > 39< / span > < span class = "keywordflow" > return< / span > r;< / div >
< div class = "line" > < a id = "l00040" name = "l00040" > < / a > < span class = "lineno" > 40< / span > }< / div >
< / div >
< div class = "line" > < a id = "l00041" name = "l00041" > < / a > < span class = "lineno" > 41< / span > < / div >
< div class = "foldopen" id = "foldopen00042" data-start = "{" data-end = "}" >
< div class = "line" > < a id = "l00042" name = "l00042" > < / a > < span class = "lineno" > < a class = "line" href = "erf_8h.html#a1846e0d683c7aff826bb32addcc3b885" > 42< / a > < / span > < span class = "keywordtype" > float< / span > < a class = "code hl_function" href = "erf_8h.html#a1846e0d683c7aff826bb32addcc3b885" > erfinv< / a > (< span class = "keywordtype" > float< / span > a) {< / div >
< div class = "line" > < a id = "l00043" name = "l00043" > < / a > < span class = "lineno" > 43< / span > < span class = "keyword" > auto< / span > t = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (a, 0.0f - a, 1.0f);< / div >
< div class = "line" > < a id = "l00044" name = "l00044" > < / a > < span class = "lineno" > 44< / span > t = < a class = "code hl_function" href = "namespacemetal.html#a423a9f4f2fc7ef5ec7eda061277b51b6" > metal::log< / a > (t);< / div >
< div class = "line" > < a id = "l00045" name = "l00045" > < / a > < span class = "lineno" > 45< / span > < span class = "keywordtype" > float< / span > p;< / div >
< div class = "line" > < a id = "l00046" name = "l00046" > < / a > < span class = "lineno" > 46< / span > < span class = "keywordflow" > if< / span > (< a class = "code hl_function" href = "namespacemetal.html#a87c5122c60f9a12afceb9925a5b78ffb" > metal::abs< / a > (t) > 6.125f) { < span class = "comment" > // maximum ulp error = 2.35793< / span > < / div >
< div class = "line" > < a id = "l00047" name = "l00047" > < / a > < span class = "lineno" > 47< / span > p = 3.03697567e-10f; < span class = "comment" > // 0x1.4deb44p-32< / span > < / div >
< div class = "line" > < a id = "l00048" name = "l00048" > < / a > < span class = "lineno" > 48< / span > p = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (p, t, 2.93243101e-8f); < span class = "comment" > // 0x1.f7c9aep-26< / span > < / div >
< div class = "line" > < a id = "l00049" name = "l00049" > < / a > < span class = "lineno" > 49< / span > p = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (p, t, 1.22150334e-6f); < span class = "comment" > // 0x1.47e512p-20< / span > < / div >
< div class = "line" > < a id = "l00050" name = "l00050" > < / a > < span class = "lineno" > 50< / span > p = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (p, t, 2.84108955e-5f); < span class = "comment" > // 0x1.dca7dep-16< / span > < / div >
< div class = "line" > < a id = "l00051" name = "l00051" > < / a > < span class = "lineno" > 51< / span > p = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (p, t, 3.93552968e-4f); < span class = "comment" > // 0x1.9cab92p-12< / span > < / div >
< div class = "line" > < a id = "l00052" name = "l00052" > < / a > < span class = "lineno" > 52< / span > p = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (p, t, 3.02698812e-3f); < span class = "comment" > // 0x1.8cc0dep-9< / span > < / div >
< div class = "line" > < a id = "l00053" name = "l00053" > < / a > < span class = "lineno" > 53< / span > p = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (p, t, 4.83185798e-3f); < span class = "comment" > // 0x1.3ca920p-8< / span > < / div >
< div class = "line" > < a id = "l00054" name = "l00054" > < / a > < span class = "lineno" > 54< / span > p = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (p, t, -2.64646143e-1f); < span class = "comment" > // -0x1.0eff66p-2< / span > < / div >
< div class = "line" > < a id = "l00055" name = "l00055" > < / a > < span class = "lineno" > 55< / span > p = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (p, t, 8.40016484e-1f); < span class = "comment" > // 0x1.ae16a4p-1< / span > < / div >
< div class = "line" > < a id = "l00056" name = "l00056" > < / a > < span class = "lineno" > 56< / span > } < span class = "keywordflow" > else< / span > { < span class = "comment" > // maximum ulp error = 2.35002< / span > < / div >
< div class = "line" > < a id = "l00057" name = "l00057" > < / a > < span class = "lineno" > 57< / span > p = 5.43877832e-9f; < span class = "comment" > // 0x1.75c000p-28< / span > < / div >
< div class = "line" > < a id = "l00058" name = "l00058" > < / a > < span class = "lineno" > 58< / span > p = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (p, t, 1.43285448e-7f); < span class = "comment" > // 0x1.33b402p-23< / span > < / div >
< div class = "line" > < a id = "l00059" name = "l00059" > < / a > < span class = "lineno" > 59< / span > p = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (p, t, 1.22774793e-6f); < span class = "comment" > // 0x1.499232p-20< / span > < / div >
< div class = "line" > < a id = "l00060" name = "l00060" > < / a > < span class = "lineno" > 60< / span > p = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (p, t, 1.12963626e-7f); < span class = "comment" > // 0x1.e52cd2p-24< / span > < / div >
< div class = "line" > < a id = "l00061" name = "l00061" > < / a > < span class = "lineno" > 61< / span > p = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (p, t, -5.61530760e-5f); < span class = "comment" > // -0x1.d70bd0p-15< / span > < / div >
< div class = "line" > < a id = "l00062" name = "l00062" > < / a > < span class = "lineno" > 62< / span > p = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (p, t, -1.47697632e-4f); < span class = "comment" > // -0x1.35be90p-13< / span > < / div >
< div class = "line" > < a id = "l00063" name = "l00063" > < / a > < span class = "lineno" > 63< / span > p = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (p, t, 2.31468678e-3f); < span class = "comment" > // 0x1.2f6400p-9< / span > < / div >
< div class = "line" > < a id = "l00064" name = "l00064" > < / a > < span class = "lineno" > 64< / span > p = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (p, t, 1.15392581e-2f); < span class = "comment" > // 0x1.7a1e50p-7< / span > < / div >
< div class = "line" > < a id = "l00065" name = "l00065" > < / a > < span class = "lineno" > 65< / span > p = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (p, t, -2.32015476e-1f); < span class = "comment" > // -0x1.db2aeep-3< / span > < / div >
< div class = "line" > < a id = "l00066" name = "l00066" > < / a > < span class = "lineno" > 66< / span > p = < a class = "code hl_function" href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > (p, t, 8.86226892e-1f); < span class = "comment" > // 0x1.c5bf88p-1< / span > < / div >
< div class = "line" > < a id = "l00067" name = "l00067" > < / a > < span class = "lineno" > 67< / span > }< / div >
< div class = "line" > < a id = "l00068" name = "l00068" > < / a > < span class = "lineno" > 68< / span > < span class = "keywordflow" > return< / span > a * p;< / div >
< div class = "line" > < a id = "l00069" name = "l00069" > < / a > < span class = "lineno" > 69< / span > }< / div >
< / div >
< div class = "ttc" id = "aerf_8h_html_a1846e0d683c7aff826bb32addcc3b885" > < div class = "ttname" > < a href = "erf_8h.html#a1846e0d683c7aff826bb32addcc3b885" > erfinv< / a > < / div > < div class = "ttdeci" > float erfinv(float a)< / div > < div class = "ttdef" > < b > Definition< / b > erf.h:42< / div > < / div >
< div class = "ttc" id = "aerf_8h_html_a6ce199ee56105c67adbf8c48c019a8b2" > < div class = "ttname" > < a href = "erf_8h.html#a6ce199ee56105c67adbf8c48c019a8b2" > erf< / a > < / div > < div class = "ttdeci" > float erf(float a)< / div > < div class = "ttdef" > < b > Definition< / b > erf.h:11< / div > < / div >
2024-11-23 04:24:16 +08:00
< div class = "ttc" id = "anamespacemetal_html_a423a9f4f2fc7ef5ec7eda061277b51b6" > < div class = "ttname" > < a href = "namespacemetal.html#a423a9f4f2fc7ef5ec7eda061277b51b6" > metal::log< / a > < / div > < div class = "ttdeci" > METAL_FUNC bfloat16_t log(bfloat16_t x)< / div > < div class = "ttdef" > < b > Definition< / b > bf16_math.h:232< / div > < / div >
< div class = "ttc" id = "anamespacemetal_html_a6301a78d69ff14a06194ca85a0c7d326" > < div class = "ttname" > < a href = "namespacemetal.html#a6301a78d69ff14a06194ca85a0c7d326" > metal::fma< / a > < / div > < div class = "ttdeci" > METAL_FUNC bfloat16_t fma(bfloat16_t x, bfloat16_t y, bfloat16_t z)< / div > < div class = "ttdef" > < b > Definition< / b > bf16_math.h:232< / div > < / div >
< div class = "ttc" id = "anamespacemetal_html_a87c5122c60f9a12afceb9925a5b78ffb" > < div class = "ttname" > < a href = "namespacemetal.html#a87c5122c60f9a12afceb9925a5b78ffb" > metal::abs< / a > < / div > < div class = "ttdeci" > METAL_FUNC bfloat16_t abs(bfloat16_t x)< / div > < div class = "ttdef" > < b > Definition< / b > bf16_math.h:232< / div > < / div >
< div class = "ttc" id = "anamespacemetal_html_ac2a0b3618d922ac014baac8189d44650" > < div class = "ttname" > < a href = "namespacemetal.html#ac2a0b3618d922ac014baac8189d44650" > metal::exp< / a > < / div > < div class = "ttdeci" > METAL_FUNC bfloat16_t exp(bfloat16_t x)< / div > < div class = "ttdef" > < b > Definition< / b > bf16_math.h:232< / div > < / div >
2024-10-15 23:12:17 +08:00
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2025-01-10 05:56:20 +08:00
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< li class = "navelem" > < a class = "el" href = "dir_938ab0ecf10b8b860ff766c820f665fd.html" > mlx< / a > < / li > < li class = "navelem" > < a class = "el" href = "dir_1d446c9bd3c99228254c9484e0bc5c06.html" > backend< / a > < / li > < li class = "navelem" > < a class = "el" href = "dir_d0c977ea65824390717cdb7efc36c157.html" > metal< / a > < / li > < li class = "navelem" > < a class = "el" href = "dir_70a37effa88bcbd6b791977fa1e64356.html" > kernels< / a > < / li > < li class = "navelem" > < a class = "el" href = "erf_8h.html" > erf.h< / a > < / li >
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