1//===-- Half-precision log(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/logf16.h"
10#include "expxf16.h"
11#include "hdr/errno_macros.h"
12#include "hdr/fenv_macros.h"
13#include "src/__support/FPUtil/FEnvImpl.h"
14#include "src/__support/FPUtil/FPBits.h"
15#include "src/__support/FPUtil/PolyEval.h"
16#include "src/__support/FPUtil/cast.h"
17#include "src/__support/FPUtil/except_value_utils.h"
18#include "src/__support/FPUtil/multiply_add.h"
19#include "src/__support/common.h"
20#include "src/__support/macros/config.h"
21#include "src/__support/macros/optimization.h"
22#include "src/__support/macros/properties/cpu_features.h"
23
24namespace LIBC_NAMESPACE_DECL {
25
26#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
27#ifdef LIBC_TARGET_CPU_HAS_FMA_FLOAT
28static constexpr size_t N_LOGF16_EXCEPTS = 5;
29#else
30static constexpr size_t N_LOGF16_EXCEPTS = 11;
31#endif
32
33static constexpr fputil::ExceptValues<float16, N_LOGF16_EXCEPTS>
34 LOGF16_EXCEPTS = {{
35// (input, RZ output, RU offset, RD offset, RN offset)
36#ifndef LIBC_TARGET_CPU_HAS_FMA_FLOAT
37 // x = 0x1.61cp-13, logf16(x) = -0x1.16p+3 (RZ)
38 {0x0987U, 0xc858U, 0U, 1U, 0U},
39 // x = 0x1.f2p-12, logf16(x) = -0x1.e98p+2 (RZ)
40 {0x0fc8U, 0xc7a6U, 0U, 1U, 1U},
41#endif
42 // x = 0x1.4d4p-9, logf16(x) = -0x1.7e4p+2 (RZ)
43 {0x1935U, 0xc5f9U, 0U, 1U, 0U},
44 // x = 0x1.5ep-8, logf16(x) = -0x1.4ecp+2 (RZ)
45 {0x1d78U, 0xc53bU, 0U, 1U, 0U},
46#ifndef LIBC_TARGET_CPU_HAS_FMA_FLOAT
47 // x = 0x1.fdp-1, logf16(x) = -0x1.81p-8 (RZ)
48 {0x3bf4U, 0x9e04U, 0U, 1U, 1U},
49 // x = 0x1.fep-1, logf16(x) = -0x1.008p-8 (RZ)
50 {0x3bf8U, 0x9c02U, 0U, 1U, 0U},
51#endif
52 // x = 0x1.ffp-1, logf16(x) = -0x1.004p-9 (RZ)
53 {0x3bfcU, 0x9801U, 0U, 1U, 0U},
54 // x = 0x1.ff8p-1, logf16(x) = -0x1p-10 (RZ)
55 {0x3bfeU, 0x9400U, 0U, 1U, 1U},
56#ifdef LIBC_TARGET_CPU_HAS_FMA_FLOAT
57 // x = 0x1.4c4p+1, logf16(x) = 0x1.e84p-1 (RZ)
58 {0x4131U, 0x3ba1U, 1U, 0U, 1U},
59#else
60 // x = 0x1.75p+2, logf16(x) = 0x1.c34p+0 (RZ)
61 {0x45d4U, 0x3f0dU, 1U, 0U, 0U},
62 // x = 0x1.75p+2, logf16(x) = 0x1.c34p+0 (RZ)
63 {0x45d4U, 0x3f0dU, 1U, 0U, 0U},
64 // x = 0x1.d5p+9, logf16(x) = 0x1.b5cp+2 (RZ)
65 {0x6354U, 0x46d7U, 1U, 0U, 1U},
66#endif
67 }};
68#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
69
70LLVM_LIBC_FUNCTION(float16, logf16, (float16 x)) {
71 using FPBits = fputil::FPBits<float16>;
72 FPBits x_bits(x);
73
74 uint16_t x_u = x_bits.uintval();
75
76 // If x <= 0, or x is 1, or x is +inf, or x is NaN.
77 if (LIBC_UNLIKELY(x_u == 0U || x_u == 0x3c00U || x_u >= 0x7c00U)) {
78 // log(NaN) = NaN
79 if (x_bits.is_nan()) {
80 if (x_bits.is_signaling_nan()) {
81 fputil::raise_except_if_required(FE_INVALID);
82 return FPBits::quiet_nan().get_val();
83 }
84
85 return x;
86 }
87
88 // log(+/-0) = −inf
89 if ((x_u & 0x7fffU) == 0U) {
90 fputil::raise_except_if_required(FE_DIVBYZERO);
91 return FPBits::inf(Sign::NEG).get_val();
92 }
93
94 if (x_u == 0x3c00U)
95 return FPBits::zero().get_val();
96
97 // When x < 0.
98 if (x_u > 0x8000U) {
99 fputil::set_errno_if_required(EDOM);
100 fputil::raise_except_if_required(FE_INVALID);
101 return FPBits::quiet_nan().get_val();
102 }
103
104 // log(+inf) = +inf
105 return FPBits::inf().get_val();
106 }
107
108#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
109 if (auto r = LOGF16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
110 return r.value();
111#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
112
113 // To compute log(x), we perform the following range reduction:
114 // x = 2^m * 1.mant,
115 // log(x) = m * log(2) + log(1.mant).
116 // To compute log(1.mant), let f be the highest 6 bits including the hidden
117 // bit, and d be the difference (1.mant - f), i.e., the remaining 5 bits of
118 // the mantissa, then:
119 // log(1.mant) = log(f) + log(1.mant / f)
120 // = log(f) + log(1 + d/f)
121 // since d/f is sufficiently small.
122 // We store log(f) and 1/f in the lookup tables LOGF_F and ONE_OVER_F_F
123 // respectively.
124
125 int m = -FPBits::EXP_BIAS;
126
127 // When x is subnormal, normalize it.
128 if ((x_u & FPBits::EXP_MASK) == 0U) {
129 // Can't pass an integer to fputil::cast directly.
130 constexpr float NORMALIZE_EXP = 1U << FPBits::FRACTION_LEN;
131 x_bits = FPBits(x_bits.get_val() * fputil::cast<float16>(NORMALIZE_EXP));
132 x_u = x_bits.uintval();
133 m -= FPBits::FRACTION_LEN;
134 }
135
136 uint16_t mant = x_bits.get_mantissa();
137 // Leading 10 - 5 = 5 bits of the mantissa.
138 int f = mant >> 5;
139 // Unbiased exponent.
140 m += x_u >> FPBits::FRACTION_LEN;
141
142 // Set bits to 1.mant instead of 2^m * 1.mant.
143 x_bits.set_biased_exponent(FPBits::EXP_BIAS);
144 float mant_f = x_bits.get_val();
145 // v = 1.mant * 1/f - 1 = d/f
146 float v = fputil::multiply_add(mant_f, ONE_OVER_F_F[f], -1.0f);
147
148 // Degree-3 minimax polynomial generated by Sollya with the following
149 // commands:
150 // > display = hexadecimal;
151 // > P = fpminimax(log(1 + x)/x, 2, [|SG...|], [-2^-5, 2^-5]);
152 // > x * P;
153 float log1p_d_over_f =
154 v * fputil::polyeval(v, 0x1p+0f, -0x1.001804p-1f, 0x1.557ef6p-2f);
155 // log(1.mant) = log(f) + log(1 + d/f)
156 float log_1_mant = LOGF_F[f] + log1p_d_over_f;
157 return fputil::cast<float16>(
158 fputil::multiply_add(static_cast<float>(m), LOGF_2, log_1_mant));
159}
160
161} // namespace LIBC_NAMESPACE_DECL
162

source code of libc/src/math/generic/logf16.cpp