1//===-- Half-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/sinpif16.h"
10#include "hdr/errno_macros.h"
11#include "hdr/fenv_macros.h"
12#include "sincosf16_utils.h"
13#include "src/__support/FPUtil/FEnvImpl.h"
14#include "src/__support/FPUtil/FPBits.h"
15#include "src/__support/FPUtil/cast.h"
16#include "src/__support/FPUtil/multiply_add.h"
17
18namespace LIBC_NAMESPACE_DECL {
19
20LLVM_LIBC_FUNCTION(float16, sinpif16, (float16 x)) {
21 using FPBits = typename fputil::FPBits<float16>;
22 FPBits xbits(x);
23
24 uint16_t x_u = xbits.uintval();
25 uint16_t x_abs = x_u & 0x7fff;
26 float xf = x;
27
28 // Range reduction:
29 // For |x| > 1/32, we perform range reduction as follows:
30 // Find k and y such that:
31 // x = (k + y) * 1/32
32 // k is an integer
33 // |y| < 0.5
34 //
35 // This is done by performing:
36 // k = round(x * 32)
37 // y = x * 32 - k
38 //
39 // Once k and y are computed, we then deduce the answer by the sine of sum
40 // formula:
41 // sin(x * pi) = sin((k + y) * pi/32)
42 // = sin(k * pi/32) * cos(y * pi/32) +
43 // sin(y * pi/32) * cos(k * pi/32)
44
45 // For signed zeros
46 if (LIBC_UNLIKELY(x_abs == 0U))
47 return x;
48
49 // Numbers greater or equal to 2^10 are integers, or infinity, or NaN
50 if (LIBC_UNLIKELY(x_abs >= 0x6400)) {
51 // Check for NaN or infinity values
52 if (LIBC_UNLIKELY(x_abs >= 0x7c00)) {
53 if (xbits.is_signaling_nan()) {
54 fputil::raise_except_if_required(FE_INVALID);
55 return FPBits::quiet_nan().get_val();
56 }
57 // If value is equal to infinity
58 if (x_abs == 0x7c00) {
59 fputil::set_errno_if_required(EDOM);
60 fputil::raise_except_if_required(FE_INVALID);
61 }
62
63 return x + FPBits::quiet_nan().get_val();
64 }
65 return FPBits::zero(xbits.sign()).get_val();
66 }
67
68 float sin_k, cos_k, sin_y, cosm1_y;
69 sincospif16_eval(xf, sin_k, cos_k, sin_y, cosm1_y);
70
71 if (LIBC_UNLIKELY(sin_y == 0 && sin_k == 0))
72 return FPBits::zero(xbits.sign()).get_val();
73
74 // Since, cosm1_y = cos_y - 1, therefore:
75 // sin(x * pi) = cos_k * sin_y + sin_k + (cosm1_y * sin_k)
76 return fputil::cast<float16>(fputil::multiply_add(
77 sin_y, cos_k, fputil::multiply_add(cosm1_y, sin_k, sin_k)));
78}
79
80} // namespace LIBC_NAMESPACE_DECL
81

source code of libc/src/math/generic/sinpif16.cpp