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
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
|
//===-- Implementation header for logf16 ------------------------*- C++ -*-===//
//
// 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
//
//===----------------------------------------------------------------------===//
#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_LOGF16_H
#define LLVM_LIBC_SRC___SUPPORT_MATH_LOGF16_H
#include "include/llvm-libc-macros/float16-macros.h"
#ifdef LIBC_TYPES_HAS_FLOAT16
#include "expxf16_utils.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/common.h"
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h"
#include "src/__support/macros/properties/cpu_features.h"
namespace LIBC_NAMESPACE_DECL {
namespace math {
namespace logf16_internal {
#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
#ifdef LIBC_TARGET_CPU_HAS_FMA_FLOAT
LIBC_INLINE_VAR constexpr size_t N_LOGF16_EXCEPTS = 5;
#else
LIBC_INLINE_VAR constexpr size_t N_LOGF16_EXCEPTS = 11;
#endif
LIBC_INLINE_VAR constexpr fputil::ExceptValues<float16, N_LOGF16_EXCEPTS>
LOGF16_EXCEPTS = {{
// (input, RZ output, RU offset, RD offset, RN offset)
#ifndef LIBC_TARGET_CPU_HAS_FMA_FLOAT
// x = 0x1.61cp-13, logf16(x) = -0x1.16p+3 (RZ)
{0x0987U, 0xc858U, 0U, 1U, 0U},
// x = 0x1.f2p-12, logf16(x) = -0x1.e98p+2 (RZ)
{0x0fc8U, 0xc7a6U, 0U, 1U, 1U},
#endif
// x = 0x1.4d4p-9, logf16(x) = -0x1.7e4p+2 (RZ)
{0x1935U, 0xc5f9U, 0U, 1U, 0U},
// x = 0x1.5ep-8, logf16(x) = -0x1.4ecp+2 (RZ)
{0x1d78U, 0xc53bU, 0U, 1U, 0U},
#ifndef LIBC_TARGET_CPU_HAS_FMA_FLOAT
// x = 0x1.fdp-1, logf16(x) = -0x1.81p-8 (RZ)
{0x3bf4U, 0x9e04U, 0U, 1U, 1U},
// x = 0x1.fep-1, logf16(x) = -0x1.008p-8 (RZ)
{0x3bf8U, 0x9c02U, 0U, 1U, 0U},
#endif
// x = 0x1.ffp-1, logf16(x) = -0x1.004p-9 (RZ)
{0x3bfcU, 0x9801U, 0U, 1U, 0U},
// x = 0x1.ff8p-1, logf16(x) = -0x1p-10 (RZ)
{0x3bfeU, 0x9400U, 0U, 1U, 1U},
#ifdef LIBC_TARGET_CPU_HAS_FMA_FLOAT
// x = 0x1.4c4p+1, logf16(x) = 0x1.e84p-1 (RZ)
{0x4131U, 0x3ba1U, 1U, 0U, 1U},
#else
// x = 0x1.75p+2, logf16(x) = 0x1.c34p+0 (RZ)
{0x45d4U, 0x3f0dU, 1U, 0U, 0U},
// x = 0x1.75p+2, logf16(x) = 0x1.c34p+0 (RZ)
{0x45d4U, 0x3f0dU, 1U, 0U, 0U},
// x = 0x1.d5p+9, logf16(x) = 0x1.b5cp+2 (RZ)
{0x6354U, 0x46d7U, 1U, 0U, 1U},
#endif
}};
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
} // namespace logf16_internal
LIBC_INLINE float16 logf16(float16 x) {
using namespace math::expxf16_internal;
using namespace math::logf16_internal;
using FPBits = fputil::FPBits<float16>;
FPBits x_bits(x);
uint16_t x_u = x_bits.uintval();
// If x <= 0, or x is 1, or x is +inf, or x is NaN.
if (LIBC_UNLIKELY(x_u == 0U || x_u == 0x3c00U || x_u >= 0x7c00U)) {
// log(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;
}
// log(+/-0) = −inf
if ((x_u & 0x7fffU) == 0U) {
fputil::raise_except_if_required(FE_DIVBYZERO);
return FPBits::inf(Sign::NEG).get_val();
}
if (x_u == 0x3c00U)
return FPBits::zero().get_val();
// When x < 0.
if (x_u > 0x8000U) {
fputil::set_errno_if_required(EDOM);
fputil::raise_except_if_required(FE_INVALID);
return FPBits::quiet_nan().get_val();
}
// log(+inf) = +inf
return FPBits::inf().get_val();
}
#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
if (auto r = LOGF16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
return r.value();
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
// To compute log(x), we perform the following range reduction:
// x = 2^m * 1.mant,
// log(x) = m * log(2) + log(1.mant).
// To compute log(1.mant), let f be the highest 6 bits including the hidden
// bit, and d be the difference (1.mant - f), i.e., the remaining 5 bits of
// the mantissa, then:
// log(1.mant) = log(f) + log(1.mant / f)
// = log(f) + log(1 + d/f)
// since d/f is sufficiently small.
// We store log(f) and 1/f in the lookup tables LOGF_F and ONE_OVER_F_F
// respectively.
int m = -FPBits::EXP_BIAS;
// When x is subnormal, normalize it.
if ((x_u & FPBits::EXP_MASK) == 0U) {
// Can't pass an integer to fputil::cast directly.
constexpr float NORMALIZE_EXP = 1U << FPBits::FRACTION_LEN;
x_bits = FPBits(x_bits.get_val() * fputil::cast<float16>(NORMALIZE_EXP));
x_u = x_bits.uintval();
m -= FPBits::FRACTION_LEN;
}
uint16_t mant = x_bits.get_mantissa();
// Leading 10 - 5 = 5 bits of the mantissa.
int f = mant >> 5;
// Unbiased exponent.
m += x_u >> FPBits::FRACTION_LEN;
// Set bits to 1.mant instead of 2^m * 1.mant.
x_bits.set_biased_exponent(FPBits::EXP_BIAS);
float mant_f = x_bits.get_val();
// v = 1.mant * 1/f - 1 = d/f
float v = fputil::multiply_add(mant_f, ONE_OVER_F_F[f], -1.0f);
// Degree-3 minimax polynomial generated by Sollya with the following
// commands:
// > display = hexadecimal;
// > P = fpminimax(log(1 + x)/x, 2, [|SG...|], [-2^-5, 2^-5]);
// > x * P;
float log1p_d_over_f =
v * fputil::polyeval(v, 0x1p+0f, -0x1.001804p-1f, 0x1.557ef6p-2f);
// log(1.mant) = log(f) + log(1 + d/f)
float log_1_mant = LOGF_F[f] + log1p_d_over_f;
return fputil::cast<float16>(
fputil::multiply_add(static_cast<float>(m), LOGF_2, log_1_mant));
}
} // namespace math
} // namespace LIBC_NAMESPACE_DECL
#endif // LIBC_TYPES_HAS_FLOAT16
#endif // LLVM_LIBC_SRC___SUPPORT_MATH_LOGF16_H
|
