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
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
|
//===-- Half-precision e^x - 1 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/expm1f16.h"
#include "expxf16.h"
#include "hdr/errno_macros.h"
#include "hdr/fenv_macros.h"
#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/PolyEval.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/FPUtil/rounding_mode.h"
#include "src/__support/common.h"
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h"
namespace LIBC_NAMESPACE_DECL {
#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
static constexpr fputil::ExceptValues<float16, 1> EXPM1F16_EXCEPTS_LO = {{
// (input, RZ output, RU offset, RD offset, RN offset)
// x = 0x1.564p-5, expm1f16(x) = 0x1.5d4p-5 (RZ)
{0x2959U, 0x2975U, 1U, 0U, 1U},
}};
#ifdef LIBC_TARGET_CPU_HAS_FMA_FLOAT
static constexpr size_t N_EXPM1F16_EXCEPTS_HI = 2;
#else
static constexpr size_t N_EXPM1F16_EXCEPTS_HI = 3;
#endif
static constexpr fputil::ExceptValues<float16, N_EXPM1F16_EXCEPTS_HI>
EXPM1F16_EXCEPTS_HI = {{
// (input, RZ output, RU offset, RD offset, RN offset)
// x = 0x1.c34p+0, expm1f16(x) = 0x1.34cp+2 (RZ)
{0x3f0dU, 0x44d3U, 1U, 0U, 1U},
// x = -0x1.e28p-3, expm1f16(x) = -0x1.adcp-3 (RZ)
{0xb38aU, 0xb2b7U, 0U, 1U, 1U},
#ifndef LIBC_TARGET_CPU_HAS_FMA_FLOAT
// x = 0x1.a08p-3, exp10m1f(x) = 0x1.cdcp-3 (RZ)
{0x3282U, 0x3337U, 1U, 0U, 0U},
#endif
}};
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
LLVM_LIBC_FUNCTION(float16, expm1f16, (float16 x)) {
using FPBits = fputil::FPBits<float16>;
FPBits x_bits(x);
uint16_t x_u = x_bits.uintval();
uint16_t x_abs = x_u & 0x7fffU;
// When |x| <= 2^(-3), or |x| >= -11 * log(2), or x is NaN.
if (LIBC_UNLIKELY(x_abs <= 0x3000U || x_abs >= 0x47a0U)) {
// expm1(NaN) = NaN
if (x_bits.is_nan()) {
if (x_bits.is_signaling_nan()) {
fputil::raise_except_if_required(FE_INVALID);
return FPBits::quiet_nan().get_val();
}
return x;
}
// expm1(+/-0) = +/-0
if (x_abs == 0)
return x;
// When x >= 16 * log(2).
if (x_bits.is_pos() && x_abs >= 0x498cU) {
// expm1(+inf) = +inf
if (x_bits.is_inf())
return FPBits::inf().get_val();
switch (fputil::quick_get_round()) {
case FE_TONEAREST:
case FE_UPWARD:
fputil::set_errno_if_required(ERANGE);
fputil::raise_except_if_required(FE_OVERFLOW | FE_INEXACT);
return FPBits::inf().get_val();
default:
return FPBits::max_normal().get_val();
}
}
// When x <= -11 * log(2).
if (x_u >= 0xc7a0U) {
// expm1(-inf) = -1
if (x_bits.is_inf())
return FPBits::one(Sign::NEG).get_val();
// When x > -0x1.0ap+3, round(expm1(x), HP, RN) = -1.
if (x_u > 0xc828U)
return fputil::round_result_slightly_up(
FPBits::one(Sign::NEG).get_val());
// When x <= -0x1.0ap+3, round(expm1(x), HP, RN) = -0x1.ffcp-1.
return fputil::round_result_slightly_down(
fputil::cast<float16>(-0x1.ffcp-1));
}
// When 0 < |x| <= 2^(-3).
if (x_abs <= 0x3000U && !x_bits.is_zero()) {
#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
if (auto r = EXPM1F16_EXCEPTS_LO.lookup(x_u);
LIBC_UNLIKELY(r.has_value()))
return r.value();
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
float xf = x;
// Degree-5 minimax polynomial generated by Sollya with the following
// commands:
// > display = hexadecimal;
// > P = fpminimax(expm1(x)/x, 4, [|SG...|], [-2^-3, 2^-3]);
// > x * P;
return fputil::cast<float16>(
xf * fputil::polyeval(xf, 0x1p+0f, 0x1.fffff8p-2f, 0x1.555556p-3f,
0x1.55905ep-5f, 0x1.1124c2p-7f));
}
}
#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
if (auto r = EXPM1F16_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
return r.value();
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
// exp(x) = exp(hi + mid) * exp(lo)
auto [exp_hi_mid, exp_lo] = exp_range_reduction(x);
// expm1(x) = exp(hi + mid) * exp(lo) - 1
return fputil::cast<float16>(fputil::multiply_add(exp_hi_mid, exp_lo, -1.0f));
}
} // namespace LIBC_NAMESPACE_DECL
|
