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/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
15
16 #if defined(LIBC_TARGET_CPU_HAS_FMA)
17 #include "range_reduction_fma.h"
18 // using namespace LIBC_NAMESPACE::fma;
19 using LIBC_NAMESPACE::fma::FAST_PASS_BOUND;
20 using LIBC_NAMESPACE::fma::large_range_reduction;
21 using LIBC_NAMESPACE::fma::small_range_reduction;
22 #else
23 #include "range_reduction.h"
24 // using namespace LIBC_NAMESPACE::generic;
25 using LIBC_NAMESPACE::generic::FAST_PASS_BOUND;
26 using LIBC_NAMESPACE::generic::large_range_reduction;
27 using LIBC_NAMESPACE::generic::small_range_reduction;
28 #endif // LIBC_TARGET_CPU_HAS_FMA
29
30 namespace LIBC_NAMESPACE {
31
32 // Lookup table for sin(k * pi / 32) with k = 0, ..., 63.
33 // Table is generated with Sollya as follow:
34 // > display = hexadecimal;
35 // > for k from 0 to 63 do { D(sin(k * pi/32)); };
36 const double SIN_K_PI_OVER_32[64] = {
37 0x0.0000000000000p+0, 0x1.917a6bc29b42cp-4, 0x1.8f8b83c69a60bp-3,
38 0x1.294062ed59f06p-2, 0x1.87de2a6aea963p-2, 0x1.e2b5d3806f63bp-2,
39 0x1.1c73b39ae68c8p-1, 0x1.44cf325091dd6p-1, 0x1.6a09e667f3bcdp-1,
40 0x1.8bc806b151741p-1, 0x1.a9b66290ea1a3p-1, 0x1.c38b2f180bdb1p-1,
41 0x1.d906bcf328d46p-1, 0x1.e9f4156c62ddap-1, 0x1.f6297cff75cbp-1,
42 0x1.fd88da3d12526p-1, 0x1.0000000000000p+0, 0x1.fd88da3d12526p-1,
43 0x1.f6297cff75cbp-1, 0x1.e9f4156c62ddap-1, 0x1.d906bcf328d46p-1,
44 0x1.c38b2f180bdb1p-1, 0x1.a9b66290ea1a3p-1, 0x1.8bc806b151741p-1,
45 0x1.6a09e667f3bcdp-1, 0x1.44cf325091dd6p-1, 0x1.1c73b39ae68c8p-1,
46 0x1.e2b5d3806f63bp-2, 0x1.87de2a6aea963p-2, 0x1.294062ed59f06p-2,
47 0x1.8f8b83c69a60bp-3, 0x1.917a6bc29b42cp-4, 0x0.0000000000000p+0,
48 -0x1.917a6bc29b42cp-4, -0x1.8f8b83c69a60bp-3, -0x1.294062ed59f06p-2,
49 -0x1.87de2a6aea963p-2, -0x1.e2b5d3806f63bp-2, -0x1.1c73b39ae68c8p-1,
50 -0x1.44cf325091dd6p-1, -0x1.6a09e667f3bcdp-1, -0x1.8bc806b151741p-1,
51 -0x1.a9b66290ea1a3p-1, -0x1.c38b2f180bdb1p-1, -0x1.d906bcf328d46p-1,
52 -0x1.e9f4156c62ddap-1, -0x1.f6297cff75cbp-1, -0x1.fd88da3d12526p-1,
53 -0x1.0000000000000p+0, -0x1.fd88da3d12526p-1, -0x1.f6297cff75cbp-1,
54 -0x1.e9f4156c62ddap-1, -0x1.d906bcf328d46p-1, -0x1.c38b2f180bdb1p-1,
55 -0x1.a9b66290ea1a3p-1, -0x1.8bc806b151741p-1, -0x1.6a09e667f3bcdp-1,
56 -0x1.44cf325091dd6p-1, -0x1.1c73b39ae68c8p-1, -0x1.e2b5d3806f63bp-2,
57 -0x1.87de2a6aea963p-2, -0x1.294062ed59f06p-2, -0x1.8f8b83c69a60bp-3,
58 -0x1.917a6bc29b42cp-4,
59 };
60
sincosf_eval(double xd,uint32_t x_abs,double & sin_k,double & cos_k,double & sin_y,double & cosm1_y)61 LIBC_INLINE void sincosf_eval(double xd, uint32_t x_abs, double &sin_k,
62 double &cos_k, double &sin_y, double &cosm1_y) {
63 int64_t k;
64 double y;
65
66 if (LIBC_LIKELY(x_abs < FAST_PASS_BOUND)) {
67 k = small_range_reduction(xd, y);
68 } else {
69 fputil::FPBits<float> x_bits(x_abs);
70 k = large_range_reduction(xd, x_bits.get_exponent(), y);
71 }
72
73 // After range reduction, k = round(x * 32 / pi) and y = (x * 32 / pi) - k.
74 // So k is an integer and -0.5 <= y <= 0.5.
75 // Then sin(x) = sin((k + y)*pi/32)
76 // = sin(y*pi/32) * cos(k*pi/32) + cos(y*pi/32) * sin(k*pi/32)
77
78 sin_k = SIN_K_PI_OVER_32[k & 63];
79 // cos(k * pi/32) = sin(k * pi/32 + pi/2) = sin((k + 16) * pi/32).
80 // cos_k = cos(k * pi/32)
81 cos_k = SIN_K_PI_OVER_32[(k + 16) & 63];
82
83 double ysq = y * y;
84
85 // Degree-6 minimax even polynomial for sin(y*pi/32)/y generated by Sollya
86 // with:
87 // > Q = fpminimax(sin(y*pi/32)/y, [|0, 2, 4, 6|], [|D...|], [0, 0.5]);
88 sin_y =
89 y * fputil::polyeval(ysq, 0x1.921fb54442d18p-4, -0x1.4abbce625abb1p-13,
90 0x1.466bc624f2776p-24, -0x1.32c3a619d4a7ep-36);
91 // Degree-6 minimax even polynomial for cos(y*pi/32) generated by Sollya with:
92 // > P = fpminimax(cos(x*pi/32), [|0, 2, 4, 6|], [|1, D...|], [0, 0.5]);
93 // Note that cosm1_y = cos(y*pi/32) - 1.
94 cosm1_y = ysq * fputil::polyeval(ysq, -0x1.3bd3cc9be430bp-8,
95 0x1.03c1f070c2e27p-18, -0x1.55cc84bd942p-30);
96 }
97
98 } // namespace LIBC_NAMESPACE
99
100 #endif // LLVM_LIBC_SRC_MATH_GENERIC_SINCOSF_UTILS_H
101