1//===-- Single-precision sinpif 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/sinpif.h"
10#include "sincosf_utils.h"
11#include "src/__support/FPUtil/FEnvImpl.h"
12#include "src/__support/FPUtil/FPBits.h"
13#include "src/__support/FPUtil/PolyEval.h"
14#include "src/__support/FPUtil/multiply_add.h"
15#include "src/__support/common.h"
16#include "src/__support/macros/config.h"
17#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
18
19namespace LIBC_NAMESPACE_DECL {
20
21LLVM_LIBC_FUNCTION(float, sinpif, (float x)) {
22 using FPBits = typename fputil::FPBits<float>;
23 FPBits xbits(x);
24
25 uint32_t x_u = xbits.uintval();
26 uint32_t x_abs = x_u & 0x7fff'ffffU;
27 double xd = static_cast<double>(x);
28
29 // Range reduction:
30 // For |x| > 1/32, we perform range reduction as follows:
31 // Find k and y such that:
32 // x = (k + y) * 1/32
33 // k is an integer
34 // |y| < 0.5
35 //
36 // This is done by performing:
37 // k = round(x * 32)
38 // y = x * 32 - k
39 //
40 // Once k and y are computed, we then deduce the answer by the sine of sum
41 // formula:
42 // sin(x * pi) = sin((k + y)*pi/32)
43 // = sin(y*pi/32) * cos(k*pi/32) + cos(y*pi/32) * sin(k*pi/32)
44 // The values of sin(k*pi/32) and cos(k*pi/32) for k = 0..31 are precomputed
45 // and stored using a vector of 32 doubles. Sin(y*pi/32) and cos(y*pi/32) are
46 // computed using degree-7 and degree-6 minimax polynomials generated by
47 // Sollya respectively.
48
49 // |x| <= 1/16
50 if (LIBC_UNLIKELY(x_abs <= 0x3d80'0000U)) {
51
52 if (LIBC_UNLIKELY(x_abs < 0x33CD'01D7U)) {
53 if (LIBC_UNLIKELY(x_abs == 0U)) {
54 // For signed zeros.
55 return x;
56 }
57
58 // For very small values we can approximate sinpi(x) with x * pi
59 // An exhaustive test shows that this is accurate for |x| < 9.546391 ×
60 // 10-8
61 double xdpi = xd * 0x1.921fb54442d18p1;
62 return static_cast<float>(xdpi);
63 }
64
65 // |x| < 1/16.
66 double xsq = xd * xd;
67
68 // Degree-9 polynomial approximation:
69 // sinpi(x) ~ x + a_3 x^3 + a_5 x^5 + a_7 x^7 + a_9 x^9
70 // = x (1 + a_3 x^2 + ... + a_9 x^8)
71 // = x * P(x^2)
72 // generated by Sollya with the following commands:
73 // > display = hexadecimal;
74 // > Q = fpminimax(sin(pi * x)/x, [|0, 2, 4, 6, 8|], [|D...|], [0, 1/16]);
75 double result = fputil::polyeval(
76 xsq, 0x1.921fb54442d18p1, -0x1.4abbce625bbf2p2, 0x1.466bc675e116ap1,
77 -0x1.32d2c0b62d41cp-1, 0x1.501ec4497cb7dp-4);
78 return static_cast<float>(xd * result);
79 }
80
81 // Numbers greater or equal to 2^23 are always integers or NaN
82 if (LIBC_UNLIKELY(x_abs >= 0x4B00'0000)) {
83
84 // check for NaN values
85 if (LIBC_UNLIKELY(x_abs >= 0x7f80'0000U)) {
86 if (xbits.is_signaling_nan()) {
87 fputil::raise_except_if_required(FE_INVALID);
88 return FPBits::quiet_nan().get_val();
89 }
90
91 if (x_abs == 0x7f80'0000U) {
92 fputil::set_errno_if_required(EDOM);
93 fputil::raise_except_if_required(FE_INVALID);
94 }
95
96 return x + FPBits::quiet_nan().get_val();
97 }
98
99 return FPBits::zero(xbits.sign()).get_val();
100 }
101
102 // Combine the results with the sine of sum formula:
103 // sin(x * pi) = sin((k + y)*pi/32)
104 // = sin(y*pi/32) * cos(k*pi/32) + cos(y*pi/32) * sin(k*pi/32)
105 // = sin_y * cos_k + (1 + cosm1_y) * sin_k
106 // = sin_y * cos_k + (cosm1_y * sin_k + sin_k)
107 double sin_k, cos_k, sin_y, cosm1_y;
108 sincospif_eval(xd, sin_k, cos_k, sin_y, cosm1_y);
109
110 if (LIBC_UNLIKELY(sin_y == 0 && sin_k == 0))
111 return FPBits::zero(xbits.sign()).get_val();
112
113 return static_cast<float>(fputil::multiply_add(
114 sin_y, cos_k, fputil::multiply_add(cosm1_y, sin_k, sin_k)));
115}
116
117} // namespace LIBC_NAMESPACE_DECL
118

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