1//===-- Single-precision cospi 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/cospif.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/multiply_add.h"
14#include "src/__support/common.h"
15#include "src/__support/macros/config.h"
16#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
17#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
18
19namespace LIBC_NAMESPACE_DECL {
20
21LLVM_LIBC_FUNCTION(float, cospif, (float x)) {
22 using FPBits = typename fputil::FPBits<float>;
23
24 FPBits xbits(x);
25 xbits.set_sign(Sign::POS);
26
27 uint32_t x_abs = xbits.uintval();
28 double xd = static_cast<double>(xbits.get_val());
29
30 // Range reduction:
31 // For |x| > 1/32, we perform range reduction as follows:
32 // Find k and y such that:
33 // x = (k + y) * 1/32
34 // k is an integer
35 // |y| < 0.5
36 //
37 // This is done by performing:
38 // k = round(x * 32)
39 // y = x * 32 - k
40 //
41 // Once k and y are computed, we then deduce the answer by the cosine of sum
42 // formula:
43 // cospi(x) = cos((k + y)*pi/32)
44 // = cos(y*pi/32) * cos(k*pi/32) - sin(y*pi/32) * sin(k*pi/32)
45 // The values of sin(k*pi/32) and cos(k*pi/32) for k = 0..63 are precomputed
46 // and stored using a vector of 32 doubles. Sin(y*pi/32) and cos(y*pi/32) are
47 // computed using degree-7 and degree-6 minimax polynomials generated by
48 // Sollya respectively.
49
50 // The exhautive test passes for smaller values
51 if (LIBC_UNLIKELY(x_abs < 0x38A2'F984U)) {
52
53#if defined(LIBC_TARGET_CPU_HAS_FMA_FLOAT)
54 return fputil::multiply_add(xbits.get_val(), -0x1.0p-25f, 1.0f);
55#else
56 return static_cast<float>(fputil::multiply_add(xd, -0x1.0p-25, 1.0));
57#endif // LIBC_TARGET_CPU_HAS_FMA_FLOAT
58 }
59
60 // Numbers greater or equal to 2^23 are always integers or NaN
61 if (LIBC_UNLIKELY(x_abs >= 0x4B00'0000)) {
62
63 if (LIBC_UNLIKELY(x_abs < 0x4B80'0000)) {
64 return (x_abs & 0x1) ? -1.0f : 1.0f;
65 }
66
67 // x is inf or nan.
68 if (LIBC_UNLIKELY(x_abs >= 0x7f80'0000U)) {
69 if (xbits.is_signaling_nan()) {
70 fputil::raise_except_if_required(FE_INVALID);
71 return FPBits::quiet_nan().get_val();
72 }
73
74 if (x_abs == 0x7f80'0000U) {
75 fputil::set_errno_if_required(EDOM);
76 fputil::raise_except_if_required(FE_INVALID);
77 }
78 return x + FPBits::quiet_nan().get_val();
79 }
80
81 return 1.0f;
82 }
83
84 // Combine the results with the sine of sum formula:
85 // cos(pi * x) = cos((k + y)*pi/32)
86 // = cos(y*pi/32) * cos(k*pi/32) - sin(y*pi/32) * sin(k*pi/32)
87 // = (cosm1_y + 1) * cos_k - sin_y * sin_k
88 // = (cosm1_y * cos_k + cos_k) - sin_y * sin_k
89 double sin_k, cos_k, sin_y, cosm1_y;
90
91 sincospif_eval(xd, sin_k, cos_k, sin_y, cosm1_y);
92
93 if (LIBC_UNLIKELY(sin_y == 0 && cos_k == 0)) {
94 return 0.0f;
95 }
96
97 return static_cast<float>(fputil::multiply_add(
98 sin_y, -sin_k, fputil::multiply_add(cosm1_y, cos_k, cos_k)));
99}
100
101} // namespace LIBC_NAMESPACE_DECL
102

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