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1//===-- Implementation header for cos ---------------------------*- 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 LIBC_SRC___SUPPORT_MATH_COS_H10#define LIBC_SRC___SUPPORT_MATH_COS_H11 12#include "range_reduction_double_common.h"13#include "sincos_eval.h"14#include "src/__support/FPUtil/FEnvImpl.h"15#include "src/__support/FPUtil/FPBits.h"16#include "src/__support/FPUtil/double_double.h"17#include "src/__support/FPUtil/dyadic_float.h"18#include "src/__support/FPUtil/except_value_utils.h"19#include "src/__support/macros/config.h"20#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY21#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA22 23#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE24#include "range_reduction_double_fma.h"25#else26#include "range_reduction_double_nofma.h"27#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE28 29namespace LIBC_NAMESPACE_DECL {30 31namespace math {32 33LIBC_INLINE static constexpr double cos(double x) {34 using namespace range_reduction_double_internal;35 using DoubleDouble = fputil::DoubleDouble;36 using FPBits = typename fputil::FPBits<double>;37 FPBits xbits(x);38 39 uint16_t x_e = xbits.get_biased_exponent();40 41 DoubleDouble y;42 unsigned k = 0;43 LargeRangeReduction range_reduction_large;44 45 // |x| < 2^16.46 if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT)) {47 // |x| < 2^-748 if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 7)) {49 // |x| < 2^-2750 if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 27)) {51 // Signed zeros.52 if (LIBC_UNLIKELY(x == 0.0))53 return 1.0;54 55 // For |x| < 2^-27, |cos(x) - 1| < |x|^2/2 < 2^-54 = ulp(1 - 2^-53)/2.56 return fputil::round_result_slightly_down(1.0);57 }58 // No range reduction needed.59 k = 0;60 y.lo = 0.0;61 y.hi = x;62 } else {63 // Small range reduction.64 k = range_reduction_small(x, y);65 }66 } else {67 // Inf or NaN68 if (LIBC_UNLIKELY(x_e > 2 * FPBits::EXP_BIAS)) {69 if (xbits.is_signaling_nan()) {70 fputil::raise_except_if_required(FE_INVALID);71 return FPBits::quiet_nan().get_val();72 }73 // cos(+-Inf) = NaN74 if (xbits.get_mantissa() == 0) {75 fputil::set_errno_if_required(EDOM);76 fputil::raise_except_if_required(FE_INVALID);77 }78 return x + FPBits::quiet_nan().get_val();79 }80 81 // Large range reduction.82 k = range_reduction_large.fast(x, y);83 }84 85 DoubleDouble sin_y, cos_y;86 87 [[maybe_unused]] double err =88 math::sincos_eval_internal::sincos_eval(y, sin_y, cos_y);89 90 // Look up sin(k * pi/128) and cos(k * pi/128)91#ifdef LIBC_MATH_HAS_SMALL_TABLES92 // Memory saving versions. Use 65-entry table.93 auto get_idx_dd = [](unsigned kk) -> DoubleDouble {94 unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);95 DoubleDouble ans = SIN_K_PI_OVER_128[idx];96 if (kk & 128) {97 ans.hi = -ans.hi;98 ans.lo = -ans.lo;99 }100 return ans;101 };102 DoubleDouble msin_k = get_idx_dd(k + 128);103 DoubleDouble cos_k = get_idx_dd(k + 64);104#else105 // Fast look up version, but needs 256-entry table.106 // -sin(k * pi/128) = sin((k + 128) * pi/128)107 // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).108 DoubleDouble msin_k = SIN_K_PI_OVER_128[(k + 128) & 255];109 DoubleDouble cos_k = SIN_K_PI_OVER_128[(k + 64) & 255];110#endif // LIBC_MATH_HAS_SMALL_TABLES111 112 // After range reduction, k = round(x * 128 / pi) and y = x - k * (pi / 128).113 // So k is an integer and -pi / 256 <= y <= pi / 256.114 // Then cos(x) = cos((k * pi/128 + y)115 // = cos(y) * cos(k*pi/128) - sin(y) * sin(k*pi/128)116 DoubleDouble cos_k_cos_y = fputil::quick_mult(cos_y, cos_k);117 DoubleDouble msin_k_sin_y = fputil::quick_mult(sin_y, msin_k);118 119 DoubleDouble rr = fputil::exact_add<false>(cos_k_cos_y.hi, msin_k_sin_y.hi);120 rr.lo += msin_k_sin_y.lo + cos_k_cos_y.lo;121 122#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS123 return rr.hi + rr.lo;124#else125 using Float128 = typename fputil::DyadicFloat<128>;126 double rlp = rr.lo + err;127 double rlm = rr.lo - err;128 129 double r_upper = rr.hi + rlp; // (rr.lo + ERR);130 double r_lower = rr.hi + rlm; // (rr.lo - ERR);131 132 // Ziv's rounding test.133 if (LIBC_LIKELY(r_upper == r_lower))134 return r_upper;135 136 Float128 u_f128, sin_u, cos_u;137 if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT))138 u_f128 = range_reduction_small_f128(x);139 else140 u_f128 = range_reduction_large.accurate();141 142 math::sincos_eval_internal::sincos_eval(u_f128, sin_u, cos_u);143 144 auto get_sin_k = [](unsigned kk) -> Float128 {145 unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);146 Float128 ans = SIN_K_PI_OVER_128_F128[idx];147 if (kk & 128)148 ans.sign = Sign::NEG;149 return ans;150 };151 152 // -sin(k * pi/128) = sin((k + 128) * pi/128)153 // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).154 Float128 msin_k_f128 = get_sin_k(k + 128);155 Float128 cos_k_f128 = get_sin_k(k + 64);156 157 // cos(x) = cos((k * pi/128 + u)158 // = cos(u) * cos(k*pi/128) - sin(u) * sin(k*pi/128)159 Float128 r = fputil::quick_add(fputil::quick_mul(cos_k_f128, cos_u),160 fputil::quick_mul(msin_k_f128, sin_u));161 162 // TODO: Add assertion if Ziv's accuracy tests fail in debug mode.163 // https://github.com/llvm/llvm-project/issues/96452.164 165 return static_cast<double>(r);166#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS167}168 169} // namespace math170 171} // namespace LIBC_NAMESPACE_DECL172 173#endif // LIBC_SRC___SUPPORT_MATH_COS_H174