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1//===-- Implementation header for expf16 ------------------------*- 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_EXPF16_H10#define LLVM_LIBC_SRC___SUPPORT_MATH_EXPF16_H11 12#include "include/llvm-libc-macros/float16-macros.h"13 14#ifdef LIBC_TYPES_HAS_FLOAT1615 16#include "hdr/errno_macros.h"17#include "hdr/fenv_macros.h"18#include "src/__support/FPUtil/FEnvImpl.h"19#include "src/__support/FPUtil/FPBits.h"20#include "src/__support/FPUtil/PolyEval.h"21#include "src/__support/FPUtil/cast.h"22#include "src/__support/FPUtil/except_value_utils.h"23#include "src/__support/FPUtil/rounding_mode.h"24#include "src/__support/common.h"25#include "src/__support/macros/config.h"26#include "src/__support/macros/optimization.h"27 28#include "expf16_utils.h"29 30namespace LIBC_NAMESPACE_DECL {31 32namespace math {33 34LIBC_INLINE static constexpr float16 expf16(float16 x) {35#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS36 constexpr fputil::ExceptValues<float16, 2> EXPF16_EXCEPTS_LO = {{37 // (input, RZ output, RU offset, RD offset, RN offset)38 // x = 0x1.de4p-8, expf16(x) = 0x1.01cp+0 (RZ)39 {0x1f79U, 0x3c07U, 1U, 0U, 0U},40 // x = 0x1.73cp-6, expf16(x) = 0x1.05cp+0 (RZ)41 {0x25cfU, 0x3c17U, 1U, 0U, 0U},42 }};43 44 constexpr fputil::ExceptValues<float16, 3> EXPF16_EXCEPTS_HI = {{45 // (input, RZ output, RU offset, RD offset, RN offset)46 // x = 0x1.c34p+0, expf16(x) = 0x1.74cp+2 (RZ)47 {0x3f0dU, 0x45d3U, 1U, 0U, 1U},48 // x = -0x1.488p-5, expf16(x) = 0x1.ebcp-1 (RZ)49 {0xa922U, 0x3bafU, 1U, 0U, 0U},50 // x = -0x1.55p-5, expf16(x) = 0x1.ebp-1 (RZ)51 {0xa954U, 0x3bacU, 1U, 0U, 0U},52 }};53#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS54 55 using FPBits = fputil::FPBits<float16>;56 FPBits x_bits(x);57 58 uint16_t x_u = x_bits.uintval();59 uint16_t x_abs = x_u & 0x7fffU;60 61 // When 0 < |x| <= 2^(-5), or |x| >= 12, or x is NaN.62 if (LIBC_UNLIKELY(x_abs <= 0x2800U || x_abs >= 0x4a00U)) {63 // exp(NaN) = NaN64 if (x_bits.is_nan()) {65 if (x_bits.is_signaling_nan()) {66 fputil::raise_except_if_required(FE_INVALID);67 return FPBits::quiet_nan().get_val();68 }69 70 return x;71 }72 73 // When x >= 12.74 if (x_bits.is_pos() && x_abs >= 0x4a00U) {75 // exp(+inf) = +inf76 if (x_bits.is_inf())77 return FPBits::inf().get_val();78 79 switch (fputil::quick_get_round()) {80 case FE_TONEAREST:81 case FE_UPWARD:82 fputil::set_errno_if_required(ERANGE);83 fputil::raise_except_if_required(FE_OVERFLOW);84 return FPBits::inf().get_val();85 default:86 return FPBits::max_normal().get_val();87 }88 }89 90 // When x <= -18.91 if (x_u >= 0xcc80U) {92 // exp(-inf) = +093 if (x_bits.is_inf())94 return FPBits::zero().get_val();95 96 fputil::set_errno_if_required(ERANGE);97 fputil::raise_except_if_required(FE_UNDERFLOW | FE_INEXACT);98 99 switch (fputil::quick_get_round()) {100 case FE_UPWARD:101 return FPBits::min_subnormal().get_val();102 default:103 return FPBits::zero().get_val();104 }105 }106 107 // When 0 < |x| <= 2^(-5).108 if (x_abs <= 0x2800U && !x_bits.is_zero()) {109#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS110 if (auto r = EXPF16_EXCEPTS_LO.lookup(x_u); LIBC_UNLIKELY(r.has_value()))111 return r.value();112#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS113 114 float xf = x;115 // Degree-3 minimax polynomial generated by Sollya with the following116 // commands:117 // > display = hexadecimal;118 // > P = fpminimax(expm1(x)/x, 2, [|SG...|], [-2^-5, 2^-5]);119 // > 1 + x * P;120 return fputil::cast<float16>(121 fputil::polyeval(xf, 0x1p+0f, 0x1p+0f, 0x1.0004p-1f, 0x1.555778p-3f));122 }123 }124 125#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS126 if (auto r = EXPF16_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value()))127 return r.value();128#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS129 130 // exp(x) = exp(hi + mid) * exp(lo)131 auto [exp_hi_mid, exp_lo] = exp_range_reduction(x);132 return fputil::cast<float16>(exp_hi_mid * exp_lo);133}134 135} // namespace math136 137} // namespace LIBC_NAMESPACE_DECL138 139#endif // LIBC_TYPES_HAS_FLOAT16140 141#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXPF16_H142