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1//===-- Implementation header for asinhf16 ----------------------*- 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_ASINHF16_H10#define LLVM_LIBC_SRC___SUPPORT_MATH_ASINHF16_H11 12#include "include/llvm-libc-macros/float16-macros.h"13 14#ifdef LIBC_TYPES_HAS_FLOAT1615 16#include "acoshf_utils.h"17#include "src/__support/FPUtil/FEnvImpl.h"18#include "src/__support/FPUtil/FPBits.h"19#include "src/__support/FPUtil/PolyEval.h"20#include "src/__support/FPUtil/cast.h"21#include "src/__support/FPUtil/except_value_utils.h"22#include "src/__support/FPUtil/multiply_add.h"23#include "src/__support/FPUtil/rounding_mode.h"24#include "src/__support/FPUtil/sqrt.h"25#include "src/__support/macros/config.h"26#include "src/__support/macros/optimization.h"27 28namespace LIBC_NAMESPACE_DECL {29 30namespace math {31 32LIBC_INLINE static constexpr float16 asinhf16(float16 x) {33 34#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS35 constexpr size_t N_EXCEPTS = 8;36 37 constexpr fputil::ExceptValues<float16, N_EXCEPTS> ASINHF16_EXCEPTS{{38 // (input, RZ output, RU offset, RD offset, RN offset)39 40 // x = 0x1.da4p-2, asinhf16(x) = 0x1.ca8p-2 (RZ)41 {0x3769, 0x372a, 1, 0, 1},42 // x = 0x1.d6cp-1, asinhf16(x) = 0x1.a58p-1 (RZ)43 {0x3b5b, 0x3a96, 1, 0, 0},44 // x = 0x1.c7cp+3, asinhf16(x) = 0x1.accp+1 (RZ)45 {0x4b1f, 0x42b3, 1, 0, 0},46 // x = 0x1.26cp+4, asinhf16(x) = 0x1.cd8p+1 (RZ)47 {0x4c9b, 0x4336, 1, 0, 1},48 // x = -0x1.da4p-2, asinhf16(x) = -0x1.ca8p-2 (RZ)49 {0xb769, 0xb72a, 0, 1, 1},50 // x = -0x1.d6cp-1, asinhf16(x) = -0x1.a58p-1 (RZ)51 {0xbb5b, 0xba96, 0, 1, 0},52 // x = -0x1.c7cp+3, asinhf16(x) = -0x1.accp+1 (RZ)53 {0xcb1f, 0xc2b3, 0, 1, 0},54 // x = -0x1.26cp+4, asinhf16(x) = -0x1.cd8p+1 (RZ)55 {0xcc9b, 0xc336, 0, 1, 1},56 }};57#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS58 59 using namespace acoshf_internal;60 using FPBits = fputil::FPBits<float16>;61 FPBits xbits(x);62 63 uint16_t x_u = xbits.uintval();64 uint16_t x_abs = x_u & 0x7fff;65 66 if (LIBC_UNLIKELY(xbits.is_inf_or_nan())) {67 if (xbits.is_signaling_nan()) {68 fputil::raise_except_if_required(FE_INVALID);69 return FPBits::quiet_nan().get_val();70 }71 72 return x;73 }74 75#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS76 // Handle exceptional values77 if (auto r = ASINHF16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))78 return r.value();79#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS80 81 float xf = x;82 const float SIGN[2] = {1.0f, -1.0f};83 float x_sign = SIGN[x_u >> 15];84 85 // |x| <= 0.2586 if (LIBC_UNLIKELY(x_abs <= 0x3400)) {87 // when |x| < 0x1.718p-5, asinhf16(x) = x. Adjust by 1 ULP for certain88 // rounding types.89 if (LIBC_UNLIKELY(x_abs < 0x29c6)) {90 int rounding = fputil::quick_get_round();91 if ((rounding == FE_UPWARD || rounding == FE_TOWARDZERO) && xf < 0)92 return fputil::cast<float16>(xf + 0x1p-24f);93 if ((rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO) && xf > 0)94 return fputil::cast<float16>(xf - 0x1p-24f);95 return fputil::cast<float16>(xf);96 }97 98 float x_sq = xf * xf;99 // Generated by Sollya with:100 // > P = fpminimax(asinh(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 2^-2]);101 // The last coefficient 0x1.bd114ep-6f has been changed to 0x1.bd114ep-5f102 // for better accuracy.103 float p = fputil::polyeval(x_sq, 1.0f, -0x1.555552p-3f, 0x1.332f6ap-4f,104 -0x1.6c53dep-5f, 0x1.bd114ep-5f);105 106 return fputil::cast<float16>(xf * p);107 }108 109 // General case: asinh(x) = ln(x + sqrt(x^2 + 1))110 float sqrt_term = fputil::sqrt<float>(fputil::multiply_add(xf, xf, 1.0f));111 return fputil::cast<float16>(112 x_sign * log_eval(fputil::multiply_add(xf, x_sign, sqrt_term)));113}114 115} // namespace math116 117} // namespace LIBC_NAMESPACE_DECL118 119#endif // LIBC_TYPES_HAS_FLOAT16120 121#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ASINHF16_H122