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 //===-- Implementation of expm1f function ---------------------------------===// // // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. // See https://llvm.org/LICENSE.txt for license information. // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception // //===----------------------------------------------------------------------===// #include "src/math/expm1f.h" #include "src/__support/FPUtil/BasicOperations.h" #include "src/__support/FPUtil/PolyEval.h" #include "src/__support/common.h" #include "src/math/expf.h" namespace __llvm_libc { // When |x| > Ln2, catastrophic cancellation does not occur with the // subtraction expf(x) - 1.0f, so we use it to compute expm1f(x). // // We divide [-Ln2; Ln2] into 3 subintervals [-Ln2; -1/8], [-1/8; 1/8], // [1/8; Ln2]. And we use a degree-6 polynomial to approximate exp(x) - 1 in // each interval. The coefficients were generated by Sollya's fpminmax. // // See libc/utils/mathtools/expm1f.sollya for more detail. LLVM_LIBC_FUNCTION(float, expm1f, (float x)) { const float Ln2 = 0.69314718055994530941723212145817656807550013436025f; // For C++17: // 0x1.62e'42ffp-1 float abs_x = __llvm_libc::fputil::abs(x); if (abs_x <= Ln2) { if (abs_x <= 0.125f) { return x * __llvm_libc::fputil::polyeval( x, 1.0f, 0.5f, 0.16666664183139801025390625f, 4.1666664183139801025390625e-2f, 8.3379410207271575927734375e-3f, 1.3894210569560527801513671875e-3f); } if (x > 0.125f) { return __llvm_libc::fputil::polyeval( x, 1.23142086749794543720781803131103515625e-7f, 0.9999969005584716796875f, 0.500031292438507080078125f, 0.16650259494781494140625f, 4.21491153538227081298828125e-2f, 7.53940828144550323486328125e-3f, 2.05591344274580478668212890625e-3f); } return __llvm_libc::fputil::polyeval( x, -6.899231408397099585272371768951416015625e-8f, 0.999998271465301513671875f, 0.4999825656414031982421875f, 0.16657467186450958251953125f, 4.1390590369701385498046875e-2f, 7.856394164264202117919921875e-3f, 9.380675037391483783721923828125e-4f); } return expf(x) - 1.0f; } } // namespace __llvm_libc