1//===-- Implementation header for cospif16 ----------------------*- 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___SUPPORT_MATH_COSPIF16_H
10#define LLVM_LIBC_SRC___SUPPORT_MATH_COSPIF16_H
11
12#include "include/llvm-libc-macros/float16-macros.h"
13
14#ifdef LIBC_TYPES_HAS_FLOAT16
15
16#include "sincosf16_utils.h"
17#include "src/__support/FPUtil/FEnvImpl.h"
18#include "src/__support/FPUtil/FPBits.h"
19#include "src/__support/FPUtil/cast.h"
20#include "src/__support/FPUtil/multiply_add.h"
21#include "src/__support/macros/optimization.h"
22
23namespace LIBC_NAMESPACE_DECL {
24
25namespace math {
26
27LIBC_INLINE constexpr float16 cospif16(float16 x) {
28
29 using namespace sincosf16_internal;
30 using FPBits = typename fputil::FPBits<float16>;
31 FPBits xbits(x);
32
33 uint16_t x_u = xbits.uintval();
34 uint16_t x_abs = x_u & 0x7fff;
35 float xf = x;
36
37 // Range reduction:
38 // For |x| > 1/32, we perform range reduction as follows:
39 // Find k and y such that:
40 // x = (k + y) * 1/32
41 // k is an integer
42 // |y| < 0.5
43 //
44 // This is done by performing:
45 // k = round(x * 32)
46 // y = x * 32 - k
47 //
48 // Once k and y are computed, we then deduce the answer by the cosine of sum
49 // formula:
50 // cos(x * pi) = cos((k + y) * pi/32)
51 // = cos(k * pi/32) * cos(y * pi/32) +
52 // sin(y * pi/32) * sin(k * pi/32)
53
54 // For signed zeros
55 if (LIBC_UNLIKELY(x_abs == 0U))
56 return fputil::cast<float16>(x: 1.0f);
57
58 // Numbers greater or equal to 2^10 are integers, or infinity, or NaN
59 if (LIBC_UNLIKELY(x_abs >= 0x6400)) {
60 if (LIBC_UNLIKELY(x_abs <= 0x67FF))
61 return fputil::cast<float16>(x: (x_abs & 0x1) ? -1.0f : 1.0f);
62
63 // Check for NaN or infintiy values
64 if (LIBC_UNLIKELY(x_abs >= 0x7c00)) {
65 if (xbits.is_signaling_nan()) {
66 fputil::raise_except_if_required(FE_INVALID);
67 return FPBits::quiet_nan().get_val();
68 }
69 // If value is equal to infinity
70 if (x_abs == 0x7c00) {
71 fputil::set_errno_if_required(EDOM);
72 fputil::raise_except_if_required(FE_INVALID);
73 }
74
75 return x + FPBits::quiet_nan().get_val();
76 }
77
78 return fputil::cast<float16>(x: 1.0f);
79 }
80
81 float sin_k = 0, cos_k = 0, sin_y = 0, cosm1_y = 0;
82 sincospif16_eval(xf, sin_k, cos_k, sin_y, cosm1_y);
83
84 if (LIBC_UNLIKELY(sin_y == 0 && cos_k == 0))
85 return fputil::cast<float16>(x: 0.0f);
86
87 // Since, cosm1_y = cos_y - 1, therefore:
88 // cos(x * pi) = cos_k(cosm1_y) + cos_k - sin_k * sin_y
89 return fputil::cast<float16>(x: fputil::multiply_add(
90 x: cos_k, y: cosm1_y, z: fputil::multiply_add(x: -sin_k, y: sin_y, z: cos_k)));
91}
92
93} // namespace math
94
95} // namespace LIBC_NAMESPACE_DECL
96
97#endif // LIBC_TYPES_HAS_FLOAT16
98
99#endif // LLVM_LIBC_SRC___SUPPORT_MATH_COSPIF16_H
100