181 lines · cpp
1//===-- Double-precision sin 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/sin.h"10#include "hdr/errno_macros.h"11#include "src/__support/FPUtil/FEnvImpl.h"12#include "src/__support/FPUtil/FPBits.h"13#include "src/__support/FPUtil/double_double.h"14#include "src/__support/FPUtil/dyadic_float.h"15#include "src/__support/FPUtil/multiply_add.h"16#include "src/__support/FPUtil/rounding_mode.h"17#include "src/__support/common.h"18#include "src/__support/macros/config.h"19#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY20#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA21#include "src/__support/math/range_reduction_double_common.h"22#include "src/__support/math/sincos_eval.h"23 24#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE25#include "src/__support/math/range_reduction_double_fma.h"26#else27#include "src/__support/math/range_reduction_double_nofma.h"28#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE29 30namespace LIBC_NAMESPACE_DECL {31 32using DoubleDouble = fputil::DoubleDouble;33using Float128 = typename fputil::DyadicFloat<128>;34 35LLVM_LIBC_FUNCTION(double, sin, (double x)) {36 using namespace math::range_reduction_double_internal;37 using FPBits = typename fputil::FPBits<double>;38 FPBits xbits(x);39 40 uint16_t x_e = xbits.get_biased_exponent();41 42 DoubleDouble y;43 unsigned k;44 LargeRangeReduction range_reduction_large{};45 46 // |x| < 2^1647 if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT)) {48 // |x| < 2^-749 if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 7)) {50 // |x| < 2^-26, |sin(x) - x| < ulp(x)/2.51 if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 26)) {52 // Signed zeros.53 if (LIBC_UNLIKELY(x == 0.0))54 return x + x; // Make sure it works with FTZ/DAZ.55 56#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE57 return fputil::multiply_add(x, -0x1.0p-54, x);58#else59 if (LIBC_UNLIKELY(x_e < 4)) {60 int rounding_mode = fputil::quick_get_round();61 if (rounding_mode == FE_TOWARDZERO ||62 (xbits.sign() == Sign::POS && rounding_mode == FE_DOWNWARD) ||63 (xbits.sign() == Sign::NEG && rounding_mode == FE_UPWARD))64 return FPBits(xbits.uintval() - 1).get_val();65 }66 return fputil::multiply_add(x, -0x1.0p-54, x);67#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE68 }69 // No range reduction needed.70 k = 0;71 y.lo = 0.0;72 y.hi = x;73 } else {74 // Small range reduction.75 k = range_reduction_small(x, y);76 }77 } else {78 // Inf or NaN79 if (LIBC_UNLIKELY(x_e > 2 * FPBits::EXP_BIAS)) {80 // sin(+-Inf) = NaN81 if (xbits.is_signaling_nan()) {82 fputil::raise_except_if_required(FE_INVALID);83 return FPBits::quiet_nan().get_val();84 }85 86 if (xbits.get_mantissa() == 0) {87 fputil::set_errno_if_required(EDOM);88 fputil::raise_except_if_required(FE_INVALID);89 }90 return x + FPBits::quiet_nan().get_val();91 }92 93 // Large range reduction.94 k = range_reduction_large.fast(x, y);95 }96 97 DoubleDouble sin_y, cos_y;98 99 [[maybe_unused]] double err =100 math::sincos_eval_internal::sincos_eval(y, sin_y, cos_y);101 102 // Look up sin(k * pi/128) and cos(k * pi/128)103#ifdef LIBC_MATH_HAS_SMALL_TABLES104 // Memory saving versions. Use 65-entry table.105 auto get_idx_dd = [](unsigned kk) -> DoubleDouble {106 unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);107 DoubleDouble ans = SIN_K_PI_OVER_128[idx];108 if (kk & 128) {109 ans.hi = -ans.hi;110 ans.lo = -ans.lo;111 }112 return ans;113 };114 DoubleDouble sin_k = get_idx_dd(k);115 DoubleDouble cos_k = get_idx_dd(k + 64);116#else117 // Fast look up version, but needs 256-entry table.118 // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).119 DoubleDouble sin_k = SIN_K_PI_OVER_128[k & 255];120 DoubleDouble cos_k = SIN_K_PI_OVER_128[(k + 64) & 255];121#endif122 123 // After range reduction, k = round(x * 128 / pi) and y = x - k * (pi / 128).124 // So k is an integer and -pi / 256 <= y <= pi / 256.125 // Then sin(x) = sin((k * pi/128 + y)126 // = sin(y) * cos(k*pi/128) + cos(y) * sin(k*pi/128)127 DoubleDouble sin_k_cos_y = fputil::quick_mult(cos_y, sin_k);128 DoubleDouble cos_k_sin_y = fputil::quick_mult(sin_y, cos_k);129 130 DoubleDouble rr = fputil::exact_add<false>(sin_k_cos_y.hi, cos_k_sin_y.hi);131 rr.lo += sin_k_cos_y.lo + cos_k_sin_y.lo;132 133#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS134 return rr.hi + rr.lo;135#else136 // Accurate test and pass for correctly rounded implementation.137 138 double rlp = rr.lo + err;139 double rlm = rr.lo - err;140 141 double r_upper = rr.hi + rlp; // (rr.lo + ERR);142 double r_lower = rr.hi + rlm; // (rr.lo - ERR);143 144 // Ziv's rounding test.145 if (LIBC_LIKELY(r_upper == r_lower))146 return r_upper;147 148 Float128 u_f128, sin_u, cos_u;149 if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT))150 u_f128 = range_reduction_small_f128(x);151 else152 u_f128 = range_reduction_large.accurate();153 154 math::sincos_eval_internal::sincos_eval(u_f128, sin_u, cos_u);155 156 auto get_sin_k = [](unsigned kk) -> Float128 {157 unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);158 Float128 ans = SIN_K_PI_OVER_128_F128[idx];159 if (kk & 128)160 ans.sign = Sign::NEG;161 return ans;162 };163 164 // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).165 Float128 sin_k_f128 = get_sin_k(k);166 Float128 cos_k_f128 = get_sin_k(k + 64);167 168 // sin(x) = sin(k * pi/128 + u)169 // = sin(u) * cos(k*pi/128) + cos(u) * sin(k*pi/128)170 Float128 r = fputil::quick_add(fputil::quick_mul(sin_k_f128, cos_u),171 fputil::quick_mul(cos_k_f128, sin_u));172 173 // TODO: Add assertion if Ziv's accuracy tests fail in debug mode.174 // https://github.com/llvm/llvm-project/issues/96452.175 176 return static_cast<double>(r);177#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS178}179 180} // namespace LIBC_NAMESPACE_DECL181