1//===-- Double-precision cos 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/cos.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/common.h"
17#include "src/__support/macros/config.h"
18#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
19#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
20#include "src/math/generic/range_reduction_double_common.h"
21#include "src/math/generic/sincos_eval.h"
22
23#ifdef LIBC_TARGET_CPU_HAS_FMA_DOUBLE
24#include "range_reduction_double_fma.h"
25#else
26#include "range_reduction_double_nofma.h"
27#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
28
29namespace LIBC_NAMESPACE_DECL {
30
31using DoubleDouble = fputil::DoubleDouble;
32using Float128 = typename fputil::DyadicFloat<128>;
33
34LLVM_LIBC_FUNCTION(double, cos, (double x)) {
35 using FPBits = typename fputil::FPBits<double>;
36 FPBits xbits(x);
37
38 uint16_t x_e = xbits.get_biased_exponent();
39
40 DoubleDouble y;
41 unsigned k;
42 LargeRangeReduction range_reduction_large{};
43
44 // |x| < 2^16.
45 if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT)) {
46 // |x| < 2^-7
47 if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 7)) {
48 // |x| < 2^-27
49 if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 27)) {
50 // Signed zeros.
51 if (LIBC_UNLIKELY(x == 0.0))
52 return 1.0;
53
54 // For |x| < 2^-27, |cos(x) - 1| < |x|^2/2 < 2^-54 = ulp(1 - 2^-53)/2.
55 return fputil::round_result_slightly_down(1.0);
56 }
57 // No range reduction needed.
58 k = 0;
59 y.lo = 0.0;
60 y.hi = x;
61 } else {
62 // Small range reduction.
63 k = range_reduction_small(x, y);
64 }
65 } else {
66 // Inf or NaN
67 if (LIBC_UNLIKELY(x_e > 2 * FPBits::EXP_BIAS)) {
68 if (xbits.is_signaling_nan()) {
69 fputil::raise_except_if_required(FE_INVALID);
70 return FPBits::quiet_nan().get_val();
71 }
72 // cos(+-Inf) = NaN
73 if (xbits.get_mantissa() == 0) {
74 fputil::set_errno_if_required(EDOM);
75 fputil::raise_except_if_required(FE_INVALID);
76 }
77 return x + FPBits::quiet_nan().get_val();
78 }
79
80 // Large range reduction.
81 k = range_reduction_large.fast(x, y);
82 }
83
84 DoubleDouble sin_y, cos_y;
85
86 [[maybe_unused]] double err = generic::sincos_eval(y, sin_y, cos_y);
87
88 // Look up sin(k * pi/128) and cos(k * pi/128)
89#ifdef LIBC_MATH_HAS_SMALL_TABLES
90 // Memory saving versions. Use 65-entry table.
91 auto get_idx_dd = [](unsigned kk) -> DoubleDouble {
92 unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);
93 DoubleDouble ans = SIN_K_PI_OVER_128[idx];
94 if (kk & 128) {
95 ans.hi = -ans.hi;
96 ans.lo = -ans.lo;
97 }
98 return ans;
99 };
100 DoubleDouble msin_k = get_idx_dd(k + 128);
101 DoubleDouble cos_k = get_idx_dd(k + 64);
102#else
103 // Fast look up version, but needs 256-entry table.
104 // -sin(k * pi/128) = sin((k + 128) * pi/128)
105 // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).
106 DoubleDouble msin_k = SIN_K_PI_OVER_128[(k + 128) & 255];
107 DoubleDouble cos_k = SIN_K_PI_OVER_128[(k + 64) & 255];
108#endif // LIBC_MATH_HAS_SMALL_TABLES
109
110 // After range reduction, k = round(x * 128 / pi) and y = x - k * (pi / 128).
111 // So k is an integer and -pi / 256 <= y <= pi / 256.
112 // Then cos(x) = cos((k * pi/128 + y)
113 // = cos(y) * cos(k*pi/128) - sin(y) * sin(k*pi/128)
114 DoubleDouble cos_k_cos_y = fputil::quick_mult(cos_y, cos_k);
115 DoubleDouble msin_k_sin_y = fputil::quick_mult(sin_y, msin_k);
116
117 DoubleDouble rr = fputil::exact_add<false>(cos_k_cos_y.hi, msin_k_sin_y.hi);
118 rr.lo += msin_k_sin_y.lo + cos_k_cos_y.lo;
119
120#ifdef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
121 return rr.hi + rr.lo;
122#else
123
124 double rlp = rr.lo + err;
125 double rlm = rr.lo - err;
126
127 double r_upper = rr.hi + rlp; // (rr.lo + ERR);
128 double r_lower = rr.hi + rlm; // (rr.lo - ERR);
129
130 // Ziv's rounding test.
131 if (LIBC_LIKELY(r_upper == r_lower))
132 return r_upper;
133
134 Float128 u_f128, sin_u, cos_u;
135 if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + FAST_PASS_EXPONENT))
136 u_f128 = range_reduction_small_f128(x);
137 else
138 u_f128 = range_reduction_large.accurate();
139
140 generic::sincos_eval(u_f128, sin_u, cos_u);
141
142 auto get_sin_k = [](unsigned kk) -> Float128 {
143 unsigned idx = (kk & 64) ? 64 - (kk & 63) : (kk & 63);
144 Float128 ans = SIN_K_PI_OVER_128_F128[idx];
145 if (kk & 128)
146 ans.sign = Sign::NEG;
147 return ans;
148 };
149
150 // -sin(k * pi/128) = sin((k + 128) * pi/128)
151 // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).
152 Float128 msin_k_f128 = get_sin_k(k + 128);
153 Float128 cos_k_f128 = get_sin_k(k + 64);
154
155 // cos(x) = cos((k * pi/128 + u)
156 // = cos(u) * cos(k*pi/128) - sin(u) * sin(k*pi/128)
157 Float128 r = fputil::quick_add(fputil::quick_mul(cos_k_f128, cos_u),
158 fputil::quick_mul(msin_k_f128, sin_u));
159
160 // TODO: Add assertion if Ziv's accuracy tests fail in debug mode.
161 // https://github.com/llvm/llvm-project/issues/96452.
162
163 return static_cast<double>(r);
164#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
165}
166
167} // namespace LIBC_NAMESPACE_DECL
168

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