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1//===-- Implementation header for exp2f -------------------------*- 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_EXP2F_H10#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP2F_H11 12#include "exp10f_utils.h"13#include "src/__support/FPUtil/FEnvImpl.h"14#include "src/__support/FPUtil/FPBits.h"15#include "src/__support/FPUtil/PolyEval.h"16#include "src/__support/FPUtil/except_value_utils.h"17#include "src/__support/FPUtil/multiply_add.h"18#include "src/__support/FPUtil/nearest_integer.h"19#include "src/__support/FPUtil/rounding_mode.h"20#include "src/__support/common.h"21#include "src/__support/macros/config.h"22#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY23#include "src/__support/macros/properties/cpu_features.h"24 25namespace LIBC_NAMESPACE_DECL {26 27namespace math {28 29LIBC_INLINE static constexpr float exp2f(float x) {30 using FPBits = typename fputil::FPBits<float>;31 FPBits xbits(x);32 33 uint32_t x_u = xbits.uintval();34 uint32_t x_abs = x_u & 0x7fff'ffffU;35 36 // When |x| >= 128, or x is nan, or |x| <= 2^-537 if (LIBC_UNLIKELY(x_abs >= 0x4300'0000U || x_abs <= 0x3d00'0000U)) {38 // |x| <= 2^-539 if (x_abs <= 0x3d00'0000) {40 // |x| < 2^-2541 if (LIBC_UNLIKELY(x_abs <= 0x3280'0000U)) {42 return 1.0f + x;43 }44 45#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS46 constexpr uint32_t EXVAL1 = 0x3b42'9d37U;47 constexpr uint32_t EXVAL2 = 0xbcf3'a937U;48 constexpr uint32_t EXVAL_MASK = EXVAL1 & EXVAL2;49 50 // Check exceptional values.51 if (LIBC_UNLIKELY((x_u & EXVAL_MASK) == EXVAL_MASK)) {52 if (LIBC_UNLIKELY(x_u == EXVAL1)) { // x = 0x1.853a6ep-9f53 return fputil::round_result_slightly_down(0x1.00870ap+0f);54 } else if (LIBC_UNLIKELY(x_u == EXVAL2)) { // x = -0x1.e7526ep-6f55 return fputil::round_result_slightly_down(0x1.f58d62p-1f);56 }57 }58#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS59 60 // Minimax polynomial generated by Sollya with:61 // > P = fpminimax((2^x - 1)/x, 5, [|D...|], [-2^-5, 2^-5]);62 constexpr double COEFFS[] = {63 0x1.62e42fefa39f3p-1, 0x1.ebfbdff82c57bp-3, 0x1.c6b08d6f2d7aap-5,64 0x1.3b2ab6fc92f5dp-7, 0x1.5d897cfe27125p-10, 0x1.43090e61e6af1p-13};65 double xd = static_cast<double>(x);66 double xsq = xd * xd;67 double c0 = fputil::multiply_add(xd, COEFFS[1], COEFFS[0]);68 double c1 = fputil::multiply_add(xd, COEFFS[3], COEFFS[2]);69 double c2 = fputil::multiply_add(xd, COEFFS[5], COEFFS[4]);70 double p = fputil::polyeval(xsq, c0, c1, c2);71 double r = fputil::multiply_add(p, xd, 1.0);72 return static_cast<float>(r);73 }74 75 // x >= 12876 if (xbits.is_pos()) {77 // x is finite78 if (x_u < 0x7f80'0000U) {79 int rounding = fputil::quick_get_round();80 if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)81 return FPBits::max_normal().get_val();82 83 fputil::set_errno_if_required(ERANGE);84 fputil::raise_except_if_required(FE_OVERFLOW);85 }86 // x is +inf or nan87 return x + FPBits::inf().get_val();88 }89 // x <= -15090 if (x_u >= 0xc316'0000U) {91 // exp(-Inf) = 092 if (xbits.is_inf())93 return 0.0f;94 // exp(nan) = nan95 if (xbits.is_nan())96 return x;97 if (fputil::fenv_is_round_up())98 return FPBits::min_subnormal().get_val();99 if (x != 0.0f) {100 fputil::set_errno_if_required(ERANGE);101 fputil::raise_except_if_required(FE_UNDERFLOW);102 }103 return 0.0f;104 }105 }106 107 // For -150 < x < 128, to compute 2^x, we perform the following range108 // reduction: find hi, mid, lo such that:109 // x = hi + mid + lo, in which110 // hi is an integer,111 // 0 <= mid * 2^5 < 32 is an integer112 // -2^(-6) <= lo <= 2^-6.113 // In particular,114 // hi + mid = round(x * 2^5) * 2^(-5).115 // Then,116 // 2^x = 2^(hi + mid + lo) = 2^hi * 2^mid * 2^lo.117 // 2^mid is stored in the lookup table of 32 elements.118 // 2^lo is computed using a degree-5 minimax polynomial119 // generated by Sollya.120 // We perform 2^hi * 2^mid by simply add hi to the exponent field121 // of 2^mid.122 123 // kf = (hi + mid) * 2^5 = round(x * 2^5)124 float kf = 0;125 int k = 0;126#ifdef LIBC_TARGET_CPU_HAS_NEAREST_INT127 kf = fputil::nearest_integer(x * 32.0f);128 k = static_cast<int>(kf);129#else130 constexpr float HALF[2] = {0.5f, -0.5f};131 k = static_cast<int>(fputil::multiply_add(x, 32.0f, HALF[x < 0.0f]));132 kf = static_cast<float>(k);133#endif // LIBC_TARGET_CPU_HAS_NEAREST_INT134 135 // dx = lo = x - (hi + mid) = x - kf * 2^(-5)136 double dx = fputil::multiply_add(-0x1.0p-5f, kf, x);137 138 // hi = floor(kf * 2^(-4))139 // exp_hi = shift hi to the exponent field of double precision.140 int64_t exp_hi =141 static_cast<int64_t>(static_cast<uint64_t>(k >> ExpBase::MID_BITS)142 << fputil::FPBits<double>::FRACTION_LEN);143 // mh = 2^hi * 2^mid144 // mh_bits = bit field of mh145 int64_t mh_bits = ExpBase::EXP_2_MID[k & ExpBase::MID_MASK] + exp_hi;146 double mh = fputil::FPBits<double>(uint64_t(mh_bits)).get_val();147 148 // Degree-5 polynomial approximating (2^x - 1)/x generating by Sollya with:149 // > P = fpminimax((2^x - 1)/x, 5, [|D...|], [-1/32. 1/32]);150 constexpr double COEFFS[5] = {0x1.62e42fefa39efp-1, 0x1.ebfbdff8131c4p-3,151 0x1.c6b08d7061695p-5, 0x1.3b2b1bee74b2ap-7,152 0x1.5d88091198529p-10};153 double dx_sq = dx * dx;154 double c1 = fputil::multiply_add(dx, COEFFS[0], 1.0);155 double c2 = fputil::multiply_add(dx, COEFFS[2], COEFFS[1]);156 double c3 = fputil::multiply_add(dx, COEFFS[4], COEFFS[3]);157 double p = fputil::multiply_add(dx_sq, c3, c2);158 // 2^x = 2^(hi + mid + lo)159 // = 2^(hi + mid) * 2^lo160 // ~ mh * (1 + lo * P(lo))161 // = mh + (mh*lo) * P(lo)162 return static_cast<float>(fputil::multiply_add(p, dx_sq * mh, c1 * mh));163}164 165} // namespace math166 167} // namespace LIBC_NAMESPACE_DECL168 169#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP2F_H170