1//===-- Half-precision sin(x) 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/sinf16.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/except_value_utils.h"
17#include "src/__support/FPUtil/multiply_add.h"
18#include "src/__support/macros/optimization.h"
19
20namespace LIBC_NAMESPACE_DECL {
21
22#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
23constexpr size_t N_EXCEPTS = 4;
24
25constexpr fputil::ExceptValues<float16, N_EXCEPTS> SINF16_EXCEPTS{{
26 // (input, RZ output, RU offset, RD offset, RN offset)
27 {0x2b45, 0x2b43, 1, 0, 1},
28 {0x585c, 0x3ba3, 1, 0, 1},
29 {0x5cb0, 0xbbff, 0, 1, 0},
30 {0x51f5, 0xb80f, 0, 1, 0},
31}};
32#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
33
34LLVM_LIBC_FUNCTION(float16, sinf16, (float16 x)) {
35 using FPBits = fputil::FPBits<float16>;
36 FPBits xbits(x);
37
38 uint16_t x_u = xbits.uintval();
39 uint16_t x_abs = x_u & 0x7fff;
40 float xf = x;
41
42 // Range reduction:
43 // For |x| > pi/32, we perform range reduction as follows:
44 // Find k and y such that:
45 // x = (k + y) * pi/32
46 // k is an integer, |y| < 0.5
47 //
48 // This is done by performing:
49 // k = round(x * 32/pi)
50 // y = x * 32/pi - k
51 //
52 // Once k and y are computed, we then deduce the answer by the sine of sum
53 // formula:
54 // sin(x) = sin((k + y) * pi/32)
55 // = sin(k * pi/32) * cos(y * pi/32) +
56 // sin(y * pi/32) * cos(k * pi/32)
57
58#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
59 // Handle exceptional values
60 bool x_sign = x_u >> 15;
61
62 if (auto r = SINF16_EXCEPTS.lookup_odd(x_abs, x_sign);
63 LIBC_UNLIKELY(r.has_value()))
64 return r.value();
65#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
66
67 int rounding = fputil::quick_get_round();
68
69 // Exhaustive tests show that for |x| <= 0x1.f4p-11, 1ULP rounding errors
70 // occur. To fix this, the following apply:
71 if (LIBC_UNLIKELY(x_abs <= 0x13d0)) {
72 // sin(+/-0) = +/-0
73 if (LIBC_UNLIKELY(x_abs == 0U))
74 return x;
75
76 // When x > 0, and rounding upward, sin(x) == x.
77 // When x < 0, and rounding downward, sin(x) == x.
78 if ((rounding == FE_UPWARD && xbits.is_pos()) ||
79 (rounding == FE_DOWNWARD && xbits.is_neg()))
80 return x;
81
82 // When x < 0, and rounding upward, sin(x) == (x - 1ULP)
83 if (rounding == FE_UPWARD && xbits.is_neg()) {
84 x_u--;
85 return FPBits(x_u).get_val();
86 }
87 }
88
89 if (xbits.is_inf_or_nan()) {
90 if (xbits.is_signaling_nan()) {
91 fputil::raise_except_if_required(FE_INVALID);
92 return FPBits::quiet_nan().get_val();
93 }
94
95 if (xbits.is_inf()) {
96 fputil::set_errno_if_required(EDOM);
97 fputil::raise_except_if_required(FE_INVALID);
98 }
99
100 return x + FPBits::quiet_nan().get_val();
101 }
102
103 float sin_k, cos_k, sin_y, cosm1_y;
104 sincosf16_eval(xf, sin_k, cos_k, sin_y, cosm1_y);
105
106 if (LIBC_UNLIKELY(sin_y == 0 && sin_k == 0))
107 return FPBits::zero(xbits.sign()).get_val();
108
109 // Since, cosm1_y = cos_y - 1, therefore:
110 // sin(x) = cos_k * sin_y + sin_k + (cosm1_y * sin_k)
111 return fputil::cast<float16>(fputil::multiply_add(
112 sin_y, cos_k, fputil::multiply_add(cosm1_y, sin_k, sin_k)));
113}
114
115} // namespace LIBC_NAMESPACE_DECL
116

source code of libc/src/math/generic/sinf16.cpp