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1//===-- Implementation header for asinf -------------------------*- C++ -*-===//2//3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.4// See https://llvm.org/LICENSE.txt for license information.5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception6//7//===----------------------------------------------------------------------===//8 9#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_ASINHF_H10#define LLVM_LIBC_SRC___SUPPORT_MATH_ASINHF_H11 12#include "acoshf_utils.h"13#include "src/__support/FPUtil/FPBits.h"14#include "src/__support/FPUtil/PolyEval.h"15#include "src/__support/FPUtil/multiply_add.h"16#include "src/__support/FPUtil/sqrt.h"17#include "src/__support/macros/config.h"18#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY19 20namespace LIBC_NAMESPACE_DECL {21 22namespace math {23 24LIBC_INLINE static constexpr float asinhf(float x) {25 using namespace acoshf_internal;26 using FPBits_t = typename fputil::FPBits<float>;27 FPBits_t xbits(x);28 uint32_t x_u = xbits.uintval();29 uint32_t x_abs = xbits.abs().uintval();30 31 // |x| <= 2^-332 if (LIBC_UNLIKELY(x_abs <= 0x3e80'0000U)) {33 // |x| <= 2^-2634 if (LIBC_UNLIKELY(x_abs <= 0x3280'0000U)) {35 return static_cast<float>(LIBC_UNLIKELY(x_abs == 0)36 ? x37 : (x - 0x1.5555555555555p-3 * x * x * x));38 }39 40 double x_d = x;41 double x_sq = x_d * x_d;42 // Generated by Sollya with:43 // > P = fpminimax(asinh(x)/x, [|0, 2, 4, 6, 8, 10, 12, 14, 16|], [|D...|],44 // [0, 2^-2]);45 double p = fputil::polyeval(46 x_sq, 0.0, -0x1.555555555551ep-3, 0x1.3333333325495p-4,47 -0x1.6db6db5a7622bp-5, 0x1.f1c70f82928c6p-6, -0x1.6e893934266b7p-6,48 0x1.1c0b41d3fbe78p-6, -0x1.c0f47810b3c4fp-7, 0x1.2c8602690143dp-7);49 return static_cast<float>(fputil::multiply_add(x_d, p, x_d));50 }51 52 const double SIGN[2] = {1.0, -1.0};53 double x_sign = SIGN[x_u >> 31];54 double x_d = x;55 56#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS57 // Helper functions to set results for exceptional cases.58 auto round_result_slightly_down = [x_sign](float r) -> float {59 return fputil::multiply_add(static_cast<float>(x_sign), r,60 static_cast<float>(x_sign) * (-0x1.0p-24f));61 };62 auto round_result_slightly_up = [x_sign](float r) -> float {63 return fputil::multiply_add(static_cast<float>(x_sign), r,64 static_cast<float>(x_sign) * 0x1.0p-24f);65 };66 67 if (LIBC_UNLIKELY(x_abs >= 0x4bdd'65a5U)) {68 if (LIBC_UNLIKELY(xbits.is_inf_or_nan())) {69 if (xbits.is_signaling_nan()) {70 fputil::raise_except_if_required(FE_INVALID);71 return FPBits_t::quiet_nan().get_val();72 }73 74 return x;75 }76 77 // Exceptional cases when x > 2^24.78 switch (x_abs) {79 case 0x4bdd65a5: // |x| = 0x1.bacb4ap24f80 return round_result_slightly_down(0x1.1e0696p4f);81 case 0x4c803f2c: // |x| = 0x1.007e58p26f82 return round_result_slightly_down(0x1.2b786cp4f);83 case 0x4f8ffb03: // |x| = 0x1.1ff606p32f84 return round_result_slightly_up(0x1.6fdd34p4f);85 case 0x5c569e88: // |x| = 0x1.ad3d1p57f86 return round_result_slightly_up(0x1.45c146p5f);87 case 0x5e68984e: // |x| = 0x1.d1309cp61f88 return round_result_slightly_up(0x1.5c9442p5f);89 case 0x655890d3: // |x| = 0x1.b121a6p75f90 return round_result_slightly_down(0x1.a9a3f2p5f);91 case 0x65de7ca6: // |x| = 0x1.bcf94cp76f92 return round_result_slightly_up(0x1.af66cp5f);93 case 0x6eb1a8ec: // |x| = 0x1.6351d8p94f94 return round_result_slightly_down(0x1.08b512p6f);95 case 0x7997f30a: // |x| = 0x1.2fe614p116f96 return round_result_slightly_up(0x1.451436p6f);97 }98 } else {99 // Exceptional cases when x < 2^24.100 if (LIBC_UNLIKELY(x_abs == 0x45abaf26)) {101 // |x| = 0x1.575e4cp12f102 return round_result_slightly_down(0x1.29becap3f);103 }104 if (LIBC_UNLIKELY(x_abs == 0x49d29048)) {105 // |x| = 0x1.a5209p20f106 return round_result_slightly_down(0x1.e1b92p3f);107 }108 }109#else110 if (LIBC_UNLIKELY(xbits.is_inf_or_nan()))111 return x;112#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS113 114 // asinh(x) = log(x + sqrt(x^2 + 1))115 return static_cast<float>(116 x_sign * log_eval(fputil::multiply_add(117 x_d, x_sign,118 fputil::sqrt<double>(fputil::multiply_add(x_d, x_d, 1.0)))));119}120 121} // namespace math122 123} // namespace LIBC_NAMESPACE_DECL124 125#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ASINHF_H126