1//===-- Double-precision sincos 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-exception
6//
7//===----------------------------------------------------------------------===//
8
9#include "src/math/sincos.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/except_value_utils.h"
16#include "src/__support/FPUtil/multiply_add.h"
17#include "src/__support/FPUtil/rounding_mode.h"
18#include "src/__support/common.h"
19#include "src/__support/macros/config.h"
20#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
21#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
22#include "src/math/generic/range_reduction_double_common.h"
23#include "src/math/generic/sincos_eval.h"
24
25#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
26#include "range_reduction_double_fma.h"
27#else
28#include "range_reduction_double_nofma.h"
29#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
30
31namespace LIBC_NAMESPACE_DECL {
32
33using DoubleDouble = fputil::DoubleDouble;
34using Float128 = typename fputil::DyadicFloat<128>;
35
36LLVM_LIBC_FUNCTION(void, sincos, (double x, double *sin_x, double *cos_x)) {
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| < 2^16
47 if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT)) {
48 // |x| < 2^-7
49 if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 7)) {
50 // |x| < 2^-27
51 if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 27)) {
52 // Signed zeros.
53 if (LIBC_UNLIKELY(x == 0.0)) {
54 *sin_x = x;
55 *cos_x = 1.0;
56 return;
57 }
58
59 // For |x| < 2^-27, max(|sin(x) - x|, |cos(x) - 1|) < ulp(x)/2.
60#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
61 *sin_x = fputil::multiply_add(x, -0x1.0p-54, x);
62 *cos_x = fputil::multiply_add(x, -x, 1.0);
63#else
64 *cos_x = fputil::round_result_slightly_down(1.0);
65
66 if (LIBC_UNLIKELY(x_e < 4)) {
67 int rounding_mode = fputil::quick_get_round();
68 if (rounding_mode == FE_TOWARDZERO ||
69 (xbits.sign() == Sign::POS && rounding_mode == FE_DOWNWARD) ||
70 (xbits.sign() == Sign::NEG && rounding_mode == FE_UPWARD))
71 *sin_x = FPBits(xbits.uintval() - 1).get_val();
72 }
73 *sin_x = fputil::multiply_add(x, -0x1.0p-54, x);
74#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
75 return;
76 }
77 // No range reduction needed.
78 k = 0;
79 y.lo = 0.0;
80 y.hi = x;
81 } else {
82 // Small range reduction.
83 k = range_reduction_small(x, y);
84 }
85 } else {
86 // Inf or NaN
87 if (LIBC_UNLIKELY(x_e > 2 * FPBits::EXP_BIAS)) {
88 if (xbits.is_signaling_nan()) {
89 fputil::raise_except_if_required(FE_INVALID);
90 *sin_x = *cos_x = FPBits::quiet_nan().get_val();
91 return;
92 }
93
94 // sin(+-Inf) = NaN
95 if (xbits.get_mantissa() == 0) {
96 fputil::set_errno_if_required(EDOM);
97 fputil::raise_except_if_required(FE_INVALID);
98 }
99 *sin_x = *cos_x = x + FPBits::quiet_nan().get_val();
100 return;
101 }
102
103 // Large range reduction.
104 k = range_reduction_large.fast(x, y);
105 }
106
107 DoubleDouble sin_y, cos_y;
108
109 [[maybe_unused]] double err = generic::sincos_eval(y, sin_y, cos_y);
110
111 // Look up sin(k * pi/128) and cos(k * pi/128)
112#ifdef LIBC_MATH_HAS_SMALL_TABLES
113 // Memory saving versions. Use 65-entry table.
114 auto get_idx_dd = [](unsigned kk) -> DoubleDouble {
115 unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);
116 DoubleDouble ans = SIN_K_PI_OVER_128[idx];
117 if (kk & 128) {
118 ans.hi = -ans.hi;
119 ans.lo = -ans.lo;
120 }
121 return ans;
122 };
123 DoubleDouble sin_k = get_idx_dd(k);
124 DoubleDouble cos_k = get_idx_dd(k + 64);
125#else
126 // Fast look up version, but needs 256-entry table.
127 // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).
128 DoubleDouble sin_k = SIN_K_PI_OVER_128[k & 255];
129 DoubleDouble cos_k = SIN_K_PI_OVER_128[(k + 64) & 255];
130#endif // LIBC_MATH_HAS_SMALL_TABLES
131
132 DoubleDouble msin_k{-sin_k.lo, -sin_k.hi};
133
134 // After range reduction, k = round(x * 128 / pi) and y = x - k * (pi / 128).
135 // So k is an integer and -pi / 256 <= y <= pi / 256.
136 // Then sin(x) = sin((k * pi/128 + y)
137 // = sin(y) * cos(k*pi/128) + cos(y) * sin(k*pi/128)
138 DoubleDouble sin_k_cos_y = fputil::quick_mult(cos_y, sin_k);
139 DoubleDouble cos_k_sin_y = fputil::quick_mult(sin_y, cos_k);
140 // cos(x) = cos((k * pi/128 + y)
141 // = cos(y) * cos(k*pi/128) - sin(y) * sin(k*pi/128)
142 DoubleDouble cos_k_cos_y = fputil::quick_mult(cos_y, cos_k);
143 DoubleDouble msin_k_sin_y = fputil::quick_mult(sin_y, msin_k);
144
145 DoubleDouble sin_dd =
146 fputil::exact_add<false>(sin_k_cos_y.hi, cos_k_sin_y.hi);
147 DoubleDouble cos_dd =
148 fputil::exact_add<false>(cos_k_cos_y.hi, msin_k_sin_y.hi);
149 sin_dd.lo += sin_k_cos_y.lo + cos_k_sin_y.lo;
150 cos_dd.lo += msin_k_sin_y.lo + cos_k_cos_y.lo;
151
152#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
153 *sin_x = sin_dd.hi + sin_dd.lo;
154 *cos_x = cos_dd.hi + cos_dd.lo;
155 return;
156#else
157 // Accurate test and pass for correctly rounded implementation.
158
159 double sin_lp = sin_dd.lo + err;
160 double sin_lm = sin_dd.lo - err;
161 double cos_lp = cos_dd.lo + err;
162 double cos_lm = cos_dd.lo - err;
163
164 double sin_upper = sin_dd.hi + sin_lp;
165 double sin_lower = sin_dd.hi + sin_lm;
166 double cos_upper = cos_dd.hi + cos_lp;
167 double cos_lower = cos_dd.hi + cos_lm;
168
169 // Ziv's rounding test.
170 if (LIBC_LIKELY(sin_upper == sin_lower && cos_upper == cos_lower)) {
171 *sin_x = sin_upper;
172 *cos_x = cos_upper;
173 return;
174 }
175
176 Float128 u_f128, sin_u, cos_u;
177 if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT))
178 u_f128 = range_reduction_small_f128(x);
179 else
180 u_f128 = range_reduction_large.accurate();
181
182 generic::sincos_eval(u_f128, sin_u, cos_u);
183
184 auto get_sin_k = [](unsigned kk) -> Float128 {
185 unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);
186 Float128 ans = SIN_K_PI_OVER_128_F128[idx];
187 if (kk & 128)
188 ans.sign = Sign::NEG;
189 return ans;
190 };
191
192 // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).
193 Float128 sin_k_f128 = get_sin_k(k);
194 Float128 cos_k_f128 = get_sin_k(k + 64);
195 Float128 msin_k_f128 = get_sin_k(k + 128);
196
197 // TODO: Add assertion if Ziv's accuracy tests fail in debug mode.
198 // https://github.com/llvm/llvm-project/issues/96452.
199
200 if (sin_upper == sin_lower)
201 *sin_x = sin_upper;
202 else
203 // sin(x) = sin((k * pi/128 + u)
204 // = sin(u) * cos(k*pi/128) + cos(u) * sin(k*pi/128)
205 *sin_x = static_cast<double>(
206 fputil::quick_add(fputil::quick_mul(sin_k_f128, cos_u),
207 fputil::quick_mul(cos_k_f128, sin_u)));
208
209 if (cos_upper == cos_lower)
210 *cos_x = cos_upper;
211 else
212 // cos(x) = cos((k * pi/128 + u)
213 // = cos(u) * cos(k*pi/128) - sin(u) * sin(k*pi/128)
214 *cos_x = static_cast<double>(
215 fputil::quick_add(fputil::quick_mul(cos_k_f128, cos_u),
216 fputil::quick_mul(msin_k_f128, sin_u)));
217
218#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
219}
220
221} // namespace LIBC_NAMESPACE_DECL
222

source code of libc/src/math/generic/sincos.cpp