1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
|
//===-- Half-precision tanpif function ------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
#include "src/math/tanpif16.h"
#include "hdr/errno_macros.h"
#include "hdr/fenv_macros.h"
#include "sincosf16_utils.h"
#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/cast.h"
#include "src/__support/FPUtil/except_value_utils.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/macros/optimization.h"
namespace LIBC_NAMESPACE_DECL {
#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
constexpr size_t N_EXCEPTS = 21;
constexpr fputil::ExceptValues<float16, N_EXCEPTS> TANPIF16_EXCEPTS{{
// (input, RZ output, RU offset, RD offset, RN offset)
{0x07f2, 0x0e3d, 1, 0, 0}, {0x086a, 0x0eee, 1, 0, 1},
{0x08db, 0x0fa0, 1, 0, 0}, {0x094c, 0x1029, 1, 0, 0},
{0x0b10, 0x118c, 1, 0, 0}, {0x1ce0, 0x23a8, 1, 0, 1},
{0x1235, 0x18e0, 1, 0, 0}, {0x2579, 0x2c4e, 1, 0, 0},
{0x28b2, 0x2f68, 1, 0, 1}, {0x2a43, 0x30f4, 1, 0, 1},
{0x31b7, 0x3907, 1, 0, 0}, {0x329d, 0x3a12, 1, 0, 1},
{0x34f1, 0x3dd7, 1, 0, 0}, {0x3658, 0x41ee, 1, 0, 0},
{0x38d4, 0xc1ee, 0, 1, 0}, {0x3d96, 0x41ee, 1, 0, 0},
{0x3e6a, 0xc1ee, 0, 1, 0}, {0x40cb, 0x41ee, 1, 0, 0},
{0x4135, 0xc1ee, 0, 1, 0}, {0x42cb, 0x41ee, 1, 0, 0},
{0x4335, 0xc1ee, 0, 1, 0},
}};
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
LLVM_LIBC_FUNCTION(float16, tanpif16, (float16 x)) {
using FPBits = typename fputil::FPBits<float16>;
FPBits xbits(x);
uint16_t x_u = xbits.uintval();
uint16_t x_abs = x_u & 0x7fff;
// Handle exceptional values
if (LIBC_UNLIKELY(x_abs <= 0x4335)) {
if (LIBC_UNLIKELY(x_abs == 0U))
return x;
#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
bool x_sign = x_u >> 15;
if (auto r = TANPIF16_EXCEPTS.lookup_odd(x_abs, x_sign);
LIBC_UNLIKELY(r.has_value()))
return r.value();
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
}
// Numbers greater or equal to 2^10 are integers, or infinity, or NaN
if (LIBC_UNLIKELY(x_abs >= 0x6400)) {
// Check for NaN or infinity values
if (LIBC_UNLIKELY(x_abs >= 0x7c00)) {
if (xbits.is_signaling_nan()) {
fputil::raise_except_if_required(FE_INVALID);
return FPBits::quiet_nan().get_val();
}
// is inf
if (x_abs == 0x7c00) {
fputil::set_errno_if_required(EDOM);
fputil::raise_except_if_required(FE_INVALID);
}
return x + FPBits::quiet_nan().get_val();
}
return FPBits::zero(xbits.sign()).get_val();
}
// Range reduction:
// For |x| > 1/32, we perform range reduction as follows:
// Find k and y such that:
// x = (k + y) * 1/32
// k is an integer
// |y| < 0.5
//
// This is done by performing:
// k = round(x * 32)
// y = x * 32 - k
//
// Once k and y are computed, we then deduce the answer by the formula:
// tan(x) = sin(x) / cos(x)
// = (sin_y * cos_k + cos_y * sin_k) / (cos_y * cos_k - sin_y * sin_k)
float xf = x;
float sin_k, cos_k, sin_y, cosm1_y;
sincospif16_eval(xf, sin_k, cos_k, sin_y, cosm1_y);
if (LIBC_UNLIKELY(sin_y == 0 && cos_k == 0)) {
fputil::set_errno_if_required(EDOM);
fputil::raise_except_if_required(FE_DIVBYZERO);
int16_t x_mp5_u = static_cast<int16_t>(x - 0.5);
return ((x_mp5_u & 0x1) ? -1 : 1) * FPBits::inf().get_val();
}
using fputil::multiply_add;
return fputil::cast<float16>(
multiply_add(sin_y, cos_k, multiply_add(cosm1_y, sin_k, sin_k)) /
multiply_add(sin_y, -sin_k, multiply_add(cosm1_y, cos_k, cos_k)));
}
} // namespace LIBC_NAMESPACE_DECL
|
