153 lines · cpp
1//===-- Half-precision tanh(x) function -----------------------------------===//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#include "src/math/tanhf16.h"10#include "hdr/fenv_macros.h"11#include "src/__support/CPP/array.h"12#include "src/__support/FPUtil/FEnvImpl.h"13#include "src/__support/FPUtil/FPBits.h"14#include "src/__support/FPUtil/PolyEval.h"15#include "src/__support/FPUtil/cast.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"23#include "src/__support/math/expxf16_utils.h"24 25namespace LIBC_NAMESPACE_DECL {26 27#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS28static constexpr fputil::ExceptValues<float16, 2> TANHF16_EXCEPTS = {{29 // x = 0x1.f54p+0, tanhf16(x) = 0x1.ecp-1 (RZ)30 {0x3fd5U, 0x3bb0U, 1U, 0U, 0U},31 // x = -0x1.f54p+0, tanhf16(x) = -0x1.ecp-1 (RZ)32 {0xbfd5U, 0xbbb0U, 0U, 1U, 0U},33}};34#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS35 36LLVM_LIBC_FUNCTION(float16, tanhf16, (float16 x)) {37 using namespace math::expxf16_internal;38 using FPBits = fputil::FPBits<float16>;39 FPBits x_bits(x);40 41 uint16_t x_u = x_bits.uintval();42 uint16_t x_abs = x_u & 0x7fffU;43 44 // When -2^(-14) <= x <= -2^(-9), or |x| <= 0x1.d2p-4,45 // or |x| >= atanh(1 - 2^(-11)), or x is NaN.46 if (LIBC_UNLIKELY(x_abs <= 0x2f48U || x_abs >= 0x4429U)) {47 // tanh(NaN) = NaN48 if (x_bits.is_nan()) {49 if (x_bits.is_signaling_nan()) {50 fputil::raise_except_if_required(FE_INVALID);51 return FPBits::quiet_nan().get_val();52 }53 54 return x;55 }56 57 // When -2^(-14) <= x <= -2^(-9).58 if (x_u >= 0x8400U && x_u <= 0x9800U) {59 switch (fputil::quick_get_round()) {60 case FE_TONEAREST:61 case FE_DOWNWARD:62 return x;63 default:64 return FPBits(static_cast<uint16_t>(x_u - 1U)).get_val();65 }66 }67 68 // When |x| <= 0x1.d2p-4.69 if (x_abs <= 0x2f48U) {70 if (LIBC_UNLIKELY(x_abs == 0))71 return x;72 73 float xf = x;74 float xf_sq = xf * xf;75 // Degree-7 Taylor expansion generated by Sollya with the following76 // commands:77 // > taylor(tanh(x), 7, 0);78 // > display = hexadecimal;79 // > // For each coefficient:80 // > round(/* put coefficient here */, SG, RN);81 return fputil::cast<float16>(82 xf * fputil::polyeval(xf_sq, 0x1p+0f, -0x1.555556p-2f, 0x1.111112p-3f,83 -0x1.ba1ba2p-5f));84 }85 86 // tanh(+/-inf) = +/-187 if (x_bits.is_inf())88 return FPBits::one(x_bits.sign()).get_val();89 90 // When |x| >= atanh(1 - 2^(-11)).91 fputil::raise_except_if_required(FE_INEXACT);92 93 int rounding_mode = fputil::quick_get_round();94 if ((rounding_mode == FE_TONEAREST && x_abs >= 0x4482U) ||95 (rounding_mode == FE_UPWARD && x_bits.is_pos()) ||96 (rounding_mode == FE_DOWNWARD && x_bits.is_neg())) {97 return FPBits::one(x_bits.sign()).get_val();98 }99 if (x_bits.is_pos())100 return fputil::cast<float16>(0x1.ffcp-1);101 return fputil::cast<float16>(-0x1.ffcp-1);102 }103 104#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS105 if (auto r = TANHF16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))106 return r.value();107#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS108 109 // For atanh(-1 + 2^(-11)) < x < atanh(1 - 2^(-11)), to compute tanh(x), we110 // perform the following range reduction: find hi, mid, lo, such that:111 // x = (hi + mid) * log(2) * 0.5 + lo, in which112 // hi is an integer,113 // mid * 2^5 is an integer,114 // -2^(-5) <= lo < 2^(-5).115 // In particular,116 // hi + mid = round(x * log2(e) * 2 * 2^5) * 2^(-5).117 // Then,118 // tanh(x) = sinh(x)/cosh(x)119 // = (e^x - e^(-x)) / (e^x + e^(-x))120 // = (e^(2x) - 1) / (e^(2x) + 1)121 // = (2^(hi + mid) * e^(2*lo) - 1) / (2^(hi + mid) * e^(2*lo) + 1)122 // = (e^(2*lo) - 2^(-hi - mid)) / (e^(2*lo) + 2^(-hi - mid))123 // We store 2^(-mid) in the lookup table EXP2_MID_5_BITS, and compute124 // 2^(-hi - mid) by adding -hi to the exponent field of 2^(-mid).125 // e^lo is computed using a degree-3 minimax polynomial generated by Sollya.126 127 float xf = x;128 float kf = fputil::nearest_integer(xf * (LOG2F_E * 2.0f * 0x1.0p+5f));129 int x_hi_mid = -static_cast<int>(kf);130 unsigned x_hi = static_cast<unsigned>(x_hi_mid) >> 5;131 unsigned x_mid = static_cast<unsigned>(x_hi_mid) & 0x1f;132 // lo = x - (hi + mid)133 // = round(x * log2(e) * 2 * 2^5) * log(2) * 0.5 * (-2^(-5)) + x134 float lo = fputil::multiply_add(kf, LOGF_2 * 0.5f * -0x1.0p-5f, xf);135 136 uint32_t exp2_hi_mid_bits =137 EXP2_MID_5_BITS[x_mid] +138 static_cast<uint32_t>(x_hi << fputil::FPBits<float>::FRACTION_LEN);139 // exp2_hi_mid = 2^(-hi - mid)140 float exp2_hi_mid = fputil::FPBits<float>(exp2_hi_mid_bits).get_val();141 // Degree-3 minimax polynomial generated by Sollya with the following142 // commands:143 // > display = hexadecimal;144 // > P = fpminimax(expm1(2*x)/x, 2, [|SG...|], [-2^-5, 2^-5]);145 // > 1 + x * P;146 float exp_2lo =147 fputil::polyeval(lo, 0x1p+0f, 0x1p+1f, 0x1.001p+1f, 0x1.555ddep+0f);148 return fputil::cast<float16>((exp_2lo - exp2_hi_mid) /149 (exp_2lo + exp2_hi_mid));150}151 152} // namespace LIBC_NAMESPACE_DECL153