1//===-- Collection of utils for sinf16/cosf16 -------------------*- 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_SINCOSF16_UTILS_H
10#define LLVM_LIBC_SRC_MATH_GENERIC_SINCOSF16_UTILS_H
11
12#include "src/__support/FPUtil/PolyEval.h"
13#include "src/__support/FPUtil/nearest_integer.h"
14#include "src/__support/common.h"
15#include "src/__support/macros/config.h"
16
17namespace LIBC_NAMESPACE_DECL {
18
19// Lookup table for sin(k * pi / 32) with k = 0, ..., 63.
20// Table is generated with Sollya as follows:
21// > display = hexadecimmal;
22// > for k from 0 to 63 do { round(sin(k * pi/32), SG, RN); };
23constexpr float SIN_K_PI_OVER_32[64] = {
24 0x0.0p0, 0x1.917a6cp-4, 0x1.8f8b84p-3, 0x1.294062p-2,
25 0x1.87de2ap-2, 0x1.e2b5d4p-2, 0x1.1c73b4p-1, 0x1.44cf32p-1,
26 0x1.6a09e6p-1, 0x1.8bc806p-1, 0x1.a9b662p-1, 0x1.c38b3p-1,
27 0x1.d906bcp-1, 0x1.e9f416p-1, 0x1.f6297cp-1, 0x1.fd88dap-1,
28 0x1p0, 0x1.fd88dap-1, 0x1.f6297cp-1, 0x1.e9f416p-1,
29 0x1.d906bcp-1, 0x1.c38b3p-1, 0x1.a9b662p-1, 0x1.8bc806p-1,
30 0x1.6a09e6p-1, 0x1.44cf32p-1, 0x1.1c73b4p-1, 0x1.e2b5d4p-2,
31 0x1.87de2ap-2, 0x1.294062p-2, 0x1.8f8b84p-3, 0x1.917a6cp-4,
32 0x0.0p0, -0x1.917a6cp-4, -0x1.8f8b84p-3, -0x1.294062p-2,
33 -0x1.87de2ap-2, -0x1.e2b5d4p-2, -0x1.1c73b4p-1, -0x1.44cf32p-1,
34 -0x1.6a09e6p-1, -0x1.8bc806p-1, -0x1.a9b662p-1, -0x1.c38b3p-1,
35 -0x1.d906bcp-1, -0x1.e9f416p-1, -0x1.f6297ep-1, -0x1.fd88dap-1,
36 -0x1p0, -0x1.fd88dap-1, -0x1.f6297cp-1, -0x1.e9f416p-1,
37 -0x1.d906bcp-1, -0x1.c38b3p-1, -0x1.a9b662p-1, -0x1.8bc806p-1,
38 -0x1.6a09e6p-1, -0x1.44cf32p-1, -0x1.1c73b4p-1, -0x1.e2b5d4p-2,
39 -0x1.87de2ap-2, -0x1.294062p-2, -0x1.8f8b84p-3, -0x1.917a6cp-4};
40
41LIBC_INLINE int32_t range_reduction_sincospif16(float x, float &y) {
42 float kf = fputil::nearest_integer(x * 32);
43 y = fputil::multiply_add(x, 32.0f, -kf);
44
45 return static_cast<int32_t>(kf);
46}
47
48// Recall, range reduction:
49// k = round(x * 32/pi)
50//
51// The precision choice of 'double' in the following function is to minimize
52// rounding errors in this initial scaling step,
53// preserving enough bits so errors accumulated while computing the subtraction:
54// y = x * 32/pi - round(x * 32/pi)
55// are beyond the least-significant bit of single-precision used during
56// further intermediate computation.
57LIBC_INLINE int32_t range_reduction_sincosf16(float x, float &y) {
58 // Generated by Sollya with:
59 // > D(32/pi);
60 constexpr double THIRTYTWO_OVER_PI = 0x1.45f306dc9c883p3;
61
62 double prod = x * THIRTYTWO_OVER_PI;
63 double kd = fputil::nearest_integer(prod);
64 y = static_cast<float>(prod - kd);
65
66 return static_cast<int32_t>(kd);
67}
68
69static LIBC_INLINE void sincosf16_poly_eval(int32_t k, float y, float &sin_k,
70 float &cos_k, float &sin_y,
71 float &cosm1_y) {
72
73 sin_k = SIN_K_PI_OVER_32[k & 63];
74 cos_k = SIN_K_PI_OVER_32[(k + 16) & 63];
75
76 // Recall, after range reduction, -0.5 <= y <= 0.5. For very small values of
77 // y, calculating sin(y * p/32) can be inaccurate. Generating a polynomial for
78 // sin(y * p/32)/y instead significantly reduces the relative errors.
79 float ysq = y * y;
80
81 // Degree-6 minimax even polynomial for sin(y*pi/32)/y generated by Sollya
82 // with:
83 // > Q = fpminimax(sin(y * pi/32)/y, [|0, 2, 4, 6|], [|SG...|], [0, 0.5]);
84 sin_y = y * fputil::polyeval(ysq, 0x1.921fb6p-4f, -0x1.4aeabcp-13f,
85 0x1.a03354p-21f, -0x1.ad02d2p-20f);
86
87 // Degree-6 minimax even polynomial for cos(y*pi/32) generated by Sollya
88 // with:
89 // > P = fpminimax(cos(y * pi/32), [|0, 2, 4, 6|],[|1, SG...|], [0, 0.5]);
90 cosm1_y = ysq * fputil::polyeval(ysq, -0x1.3bd3ccp-8f, 0x1.03a61ap-18f,
91 0x1.a6f7a2p-29f);
92}
93
94LIBC_INLINE void sincosf16_eval(float xf, float &sin_k, float &cos_k,
95 float &sin_y, float &cosm1_y) {
96 float y;
97 int32_t k = range_reduction_sincosf16(xf, y);
98
99 sincosf16_poly_eval(k, y, sin_k, cos_k, sin_y, cosm1_y);
100}
101
102LIBC_INLINE void sincospif16_eval(float xf, float &sin_k, float &cos_k,
103 float &sin_y, float &cosm1_y) {
104 float y;
105 int32_t k = range_reduction_sincospif16(xf, y);
106
107 sincosf16_poly_eval(k, y, sin_k, cos_k, sin_y, cosm1_y);
108}
109
110} // namespace LIBC_NAMESPACE_DECL
111
112#endif // LLVM_LIBC_SRC_MATH_GENERIC_SINCOSF16_UTILS_H
113

source code of libc/src/math/generic/sincosf16_utils.h