1//===-- Collection of utils for sinf/cosf/sincosf ---------------*- 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-exception
6//
7//===----------------------------------------------------------------------===//
8
9#ifndef LLVM_LIBC_SRC_MATH_GENERIC_SINCOSF_UTILS_H
10#define LLVM_LIBC_SRC_MATH_GENERIC_SINCOSF_UTILS_H
11
12#include "src/__support/FPUtil/FPBits.h"
13#include "src/__support/FPUtil/PolyEval.h"
14#include "src/__support/macros/config.h"
15#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
16
17#if defined(LIBC_TARGET_CPU_HAS_FMA_DOUBLE)
18#include "range_reduction_fma.h"
19// using namespace LIBC_NAMESPACE::fma;
20using LIBC_NAMESPACE::fma::FAST_PASS_BOUND;
21using LIBC_NAMESPACE::fma::large_range_reduction;
22using LIBC_NAMESPACE::fma::small_range_reduction;
23
24#else
25#include "range_reduction.h"
26// using namespace LIBC_NAMESPACE::generic;
27using LIBC_NAMESPACE::generic::FAST_PASS_BOUND;
28using LIBC_NAMESPACE::generic::large_range_reduction;
29using LIBC_NAMESPACE::generic::small_range_reduction;
30#endif // LIBC_TARGET_CPU_HAS_FMA_DOUBLE
31
32namespace LIBC_NAMESPACE_DECL {
33
34// Lookup table for sin(k * pi / 32) with k = 0, ..., 63.
35// Table is generated with Sollya as follow:
36// > display = hexadecimal;
37// > for k from 0 to 63 do { D(sin(k * pi/32)); };
38const double SIN_K_PI_OVER_32[64] = {
39 0x0.0000000000000p+0, 0x1.917a6bc29b42cp-4, 0x1.8f8b83c69a60bp-3,
40 0x1.294062ed59f06p-2, 0x1.87de2a6aea963p-2, 0x1.e2b5d3806f63bp-2,
41 0x1.1c73b39ae68c8p-1, 0x1.44cf325091dd6p-1, 0x1.6a09e667f3bcdp-1,
42 0x1.8bc806b151741p-1, 0x1.a9b66290ea1a3p-1, 0x1.c38b2f180bdb1p-1,
43 0x1.d906bcf328d46p-1, 0x1.e9f4156c62ddap-1, 0x1.f6297cff75cbp-1,
44 0x1.fd88da3d12526p-1, 0x1.0000000000000p+0, 0x1.fd88da3d12526p-1,
45 0x1.f6297cff75cbp-1, 0x1.e9f4156c62ddap-1, 0x1.d906bcf328d46p-1,
46 0x1.c38b2f180bdb1p-1, 0x1.a9b66290ea1a3p-1, 0x1.8bc806b151741p-1,
47 0x1.6a09e667f3bcdp-1, 0x1.44cf325091dd6p-1, 0x1.1c73b39ae68c8p-1,
48 0x1.e2b5d3806f63bp-2, 0x1.87de2a6aea963p-2, 0x1.294062ed59f06p-2,
49 0x1.8f8b83c69a60bp-3, 0x1.917a6bc29b42cp-4, 0x0.0000000000000p+0,
50 -0x1.917a6bc29b42cp-4, -0x1.8f8b83c69a60bp-3, -0x1.294062ed59f06p-2,
51 -0x1.87de2a6aea963p-2, -0x1.e2b5d3806f63bp-2, -0x1.1c73b39ae68c8p-1,
52 -0x1.44cf325091dd6p-1, -0x1.6a09e667f3bcdp-1, -0x1.8bc806b151741p-1,
53 -0x1.a9b66290ea1a3p-1, -0x1.c38b2f180bdb1p-1, -0x1.d906bcf328d46p-1,
54 -0x1.e9f4156c62ddap-1, -0x1.f6297cff75cbp-1, -0x1.fd88da3d12526p-1,
55 -0x1.0000000000000p+0, -0x1.fd88da3d12526p-1, -0x1.f6297cff75cbp-1,
56 -0x1.e9f4156c62ddap-1, -0x1.d906bcf328d46p-1, -0x1.c38b2f180bdb1p-1,
57 -0x1.a9b66290ea1a3p-1, -0x1.8bc806b151741p-1, -0x1.6a09e667f3bcdp-1,
58 -0x1.44cf325091dd6p-1, -0x1.1c73b39ae68c8p-1, -0x1.e2b5d3806f63bp-2,
59 -0x1.87de2a6aea963p-2, -0x1.294062ed59f06p-2, -0x1.8f8b83c69a60bp-3,
60 -0x1.917a6bc29b42cp-4,
61};
62
63static LIBC_INLINE void sincosf_poly_eval(int64_t k, double y, double &sin_k,
64 double &cos_k, double &sin_y,
65 double &cosm1_y) {
66 // After range reduction, k = round(x * 32 / pi) and y = (x * 32 / pi) - k.
67 // So k is an integer and -0.5 <= y <= 0.5.
68 // Then sin(x) = sin((k + y)*pi/32)
69 // = sin(y*pi/32) * cos(k*pi/32) + cos(y*pi/32) * sin(k*pi/32)
70
71 sin_k = SIN_K_PI_OVER_32[k & 63];
72 // cos(k * pi/32) = sin(k * pi/32 + pi/2) = sin((k + 16) * pi/32).
73 // cos_k = cos(k * pi/32)
74 cos_k = SIN_K_PI_OVER_32[(k + 16) & 63];
75
76 double ysq = y * y;
77
78 // Degree-6 minimax even polynomial for sin(y*pi/32)/y generated by Sollya
79 // with:
80 // > Q = fpminimax(sin(y*pi/32)/y, [|0, 2, 4, 6|], [|D...|], [0, 0.5]);
81 sin_y =
82 y * fputil::polyeval(ysq, 0x1.921fb54442d18p-4, -0x1.4abbce625abb1p-13,
83 0x1.466bc624f2776p-24, -0x1.32c3a619d4a7ep-36);
84 // Degree-6 minimax even polynomial for cos(y*pi/32) generated by Sollya with:
85 // > P = fpminimax(cos(x*pi/32), [|0, 2, 4, 6|], [|1, D...|], [0, 0.5]);
86 // Note that cosm1_y = cos(y*pi/32) - 1.
87 cosm1_y = ysq * fputil::polyeval(ysq, -0x1.3bd3cc9be430bp-8,
88 0x1.03c1f070c2e27p-18, -0x1.55cc84bd942p-30);
89}
90
91LIBC_INLINE void sincosf_eval(double xd, uint32_t x_abs, double &sin_k,
92 double &cos_k, double &sin_y, double &cosm1_y) {
93 int64_t k;
94 double y;
95
96 if (LIBC_LIKELY(x_abs < FAST_PASS_BOUND)) {
97 k = small_range_reduction(xd, y);
98 } else {
99 fputil::FPBits<float> x_bits(x_abs);
100 k = large_range_reduction(xd, x_bits.get_exponent(), y);
101 }
102
103 sincosf_poly_eval(k, y, sin_k, cos_k, sin_y, cosm1_y);
104}
105
106// Return k and y, where
107// k = round(x * 32) and y = (x * 32) - k.
108// => pi * x = (k + y) * pi / 32
109static LIBC_INLINE int64_t range_reduction_sincospi(double x, double &y) {
110 double kd = fputil::nearest_integer(x * 32);
111 y = fputil::multiply_add(x, 32.0, -kd);
112
113 return static_cast<int64_t>(kd);
114}
115
116LIBC_INLINE void sincospif_eval(double xd, double &sin_k, double &cos_k,
117 double &sin_y, double &cosm1_y) {
118 double y;
119 int64_t k = range_reduction_sincospi(xd, y);
120 sincosf_poly_eval(k, y, sin_k, cos_k, sin_y, cosm1_y);
121}
122
123} // namespace LIBC_NAMESPACE_DECL
124
125#endif // LLVM_LIBC_SRC_MATH_GENERIC_SINCOSF_UTILS_H
126

source code of libc/src/math/generic/sincosf_utils.h