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-exception
6//
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_UNLIKELY
20#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
21#include "src/math/generic/range_reduction_double_common.h"
22#include "src/math/generic/sincos_eval.h"
23
24#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
25#include "range_reduction_double_fma.h"
26#else
27#include "range_reduction_double_nofma.h"
28#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
29
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 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;
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^-7
48 if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 7)) {
49 // |x| < 2^-26, |sin(x) - x| < ulp(x)/2.
50 if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 26)) {
51 // Signed zeros.
52 if (LIBC_UNLIKELY(x == 0.0))
53 return x + x; // Make sure it works with FTZ/DAZ.
54
55#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
56 return fputil::multiply_add(x, -0x1.0p-54, x);
57#else
58 if (LIBC_UNLIKELY(x_e < 4)) {
59 int rounding_mode = fputil::quick_get_round();
60 if (rounding_mode == FE_TOWARDZERO ||
61 (xbits.sign() == Sign::POS && rounding_mode == FE_DOWNWARD) ||
62 (xbits.sign() == Sign::NEG && rounding_mode == FE_UPWARD))
63 return FPBits(xbits.uintval() - 1).get_val();
64 }
65 return fputil::multiply_add(x, -0x1.0p-54, x);
66#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
67 }
68 // No range reduction needed.
69 k = 0;
70 y.lo = 0.0;
71 y.hi = x;
72 } else {
73 // Small range reduction.
74 k = range_reduction_small(x, y);
75 }
76 } else {
77 // Inf or NaN
78 if (LIBC_UNLIKELY(x_e > 2 * FPBits::EXP_BIAS)) {
79 // sin(+-Inf) = NaN
80 if (xbits.is_signaling_nan()) {
81 fputil::raise_except_if_required(FE_INVALID);
82 return FPBits::quiet_nan().get_val();
83 }
84
85 if (xbits.get_mantissa() == 0) {
86 fputil::set_errno_if_required(EDOM);
87 fputil::raise_except_if_required(FE_INVALID);
88 }
89 return x + FPBits::quiet_nan().get_val();
90 }
91
92 // Large range reduction.
93 k = range_reduction_large.fast(x, y);
94 }
95
96 DoubleDouble sin_y, cos_y;
97
98 [[maybe_unused]] double err = generic::sincos_eval(y, sin_y, cos_y);
99
100 // Look up sin(k * pi/128) and cos(k * pi/128)
101#ifdef LIBC_MATH_HAS_SMALL_TABLES
102 // Memory saving versions. Use 65-entry table.
103 auto get_idx_dd = [](unsigned kk) -> DoubleDouble {
104 unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);
105 DoubleDouble ans = SIN_K_PI_OVER_128[idx];
106 if (kk & 128) {
107 ans.hi = -ans.hi;
108 ans.lo = -ans.lo;
109 }
110 return ans;
111 };
112 DoubleDouble sin_k = get_idx_dd(k);
113 DoubleDouble cos_k = get_idx_dd(k + 64);
114#else
115 // Fast look up version, but needs 256-entry table.
116 // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).
117 DoubleDouble sin_k = SIN_K_PI_OVER_128[k & 255];
118 DoubleDouble cos_k = SIN_K_PI_OVER_128[(k + 64) & 255];
119#endif
120
121 // After range reduction, k = round(x * 128 / pi) and y = x - k * (pi / 128).
122 // So k is an integer and -pi / 256 <= y <= pi / 256.
123 // Then sin(x) = sin((k * pi/128 + y)
124 // = sin(y) * cos(k*pi/128) + cos(y) * sin(k*pi/128)
125 DoubleDouble sin_k_cos_y = fputil::quick_mult(cos_y, sin_k);
126 DoubleDouble cos_k_sin_y = fputil::quick_mult(sin_y, cos_k);
127
128 DoubleDouble rr = fputil::exact_add<false>(sin_k_cos_y.hi, cos_k_sin_y.hi);
129 rr.lo += sin_k_cos_y.lo + cos_k_sin_y.lo;
130
131#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
132 return rr.hi + rr.lo;
133#else
134 // Accurate test and pass for correctly rounded implementation.
135
136 double rlp = rr.lo + err;
137 double rlm = rr.lo - err;
138
139 double r_upper = rr.hi + rlp; // (rr.lo + ERR);
140 double r_lower = rr.hi + rlm; // (rr.lo - ERR);
141
142 // Ziv's rounding test.
143 if (LIBC_LIKELY(r_upper == r_lower))
144 return r_upper;
145
146 Float128 u_f128, sin_u, cos_u;
147 if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT))
148 u_f128 = range_reduction_small_f128(x);
149 else
150 u_f128 = range_reduction_large.accurate();
151
152 generic::sincos_eval(u_f128, sin_u, cos_u);
153
154 auto get_sin_k = [](unsigned kk) -> Float128 {
155 unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);
156 Float128 ans = SIN_K_PI_OVER_128_F128[idx];
157 if (kk & 128)
158 ans.sign = Sign::NEG;
159 return ans;
160 };
161
162 // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).
163 Float128 sin_k_f128 = get_sin_k(k);
164 Float128 cos_k_f128 = get_sin_k(k + 64);
165
166 // sin(x) = sin(k * pi/128 + u)
167 // = sin(u) * cos(k*pi/128) + cos(u) * sin(k*pi/128)
168 Float128 r = fputil::quick_add(fputil::quick_mul(sin_k_f128, cos_u),
169 fputil::quick_mul(cos_k_f128, sin_u));
170
171 // TODO: Add assertion if Ziv's accuracy tests fail in debug mode.
172 // https://github.com/llvm/llvm-project/issues/96452.
173
174 return static_cast<double>(r);
175#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
176}
177
178} // namespace LIBC_NAMESPACE_DECL
179

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