mlx/mlx/backend/common/erf.cpp
2023-11-30 11:12:53 -08:00

41 lines
1.5 KiB
C++

// Copyright © 2023 Apple Inc.
#include <cmath>
namespace mlx::core {
/* Approximation to the inverse error function.
* Based on code from:
* https://stackoverflow.com/questions/27229371/inverse-error-function-in-c#answer-49743348
*/
float erfinv(float a) {
auto t = std::fma(a, 0.0f - a, 1.0f);
t = std::log(t);
float p;
if (std::abs(t) > 6.125f) { // maximum ulp error = 2.35793
p = 3.03697567e-10f; // 0x1.4deb44p-32
p = std::fma(p, t, 2.93243101e-8f); // 0x1.f7c9aep-26
p = std::fma(p, t, 1.22150334e-6f); // 0x1.47e512p-20
p = std::fma(p, t, 2.84108955e-5f); // 0x1.dca7dep-16
p = std::fma(p, t, 3.93552968e-4f); // 0x1.9cab92p-12
p = std::fma(p, t, 3.02698812e-3f); // 0x1.8cc0dep-9
p = std::fma(p, t, 4.83185798e-3f); // 0x1.3ca920p-8
p = std::fma(p, t, -2.64646143e-1f); // -0x1.0eff66p-2
p = std::fma(p, t, 8.40016484e-1f); // 0x1.ae16a4p-1
} else { // maximum ulp error = 2.35002
p = 5.43877832e-9f; // 0x1.75c000p-28
p = std::fma(p, t, 1.43285448e-7f); // 0x1.33b402p-23
p = std::fma(p, t, 1.22774793e-6f); // 0x1.499232p-20
p = std::fma(p, t, 1.12963626e-7f); // 0x1.e52cd2p-24
p = std::fma(p, t, -5.61530760e-5f); // -0x1.d70bd0p-15
p = std::fma(p, t, -1.47697632e-4f); // -0x1.35be90p-13
p = std::fma(p, t, 2.31468678e-3f); // 0x1.2f6400p-9
p = std::fma(p, t, 1.15392581e-2f); // 0x1.7a1e50p-7
p = std::fma(p, t, -2.32015476e-1f); // -0x1.db2aeep-3
p = std::fma(p, t, 8.86226892e-1f); // 0x1.c5bf88p-1
}
return a * p;
}
} // namespace mlx::core