1//===-- Half-precision log10(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/log10f16.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_LOG10F16_EXCEPTS = 11;
29#else
30static constexpr size_t N_LOG10F16_EXCEPTS = 17;
31#endif
32
33static constexpr fputil::ExceptValues<float16, N_LOG10F16_EXCEPTS>
34 LOG10F16_EXCEPTS = {{
35 // (input, RZ output, RU offset, RD offset, RN offset)
36 // x = 0x1.e3cp-3, log10f16(x) = -0x1.40cp-1 (RZ)
37 {0x338fU, 0xb903U, 0U, 1U, 0U},
38 // x = 0x1.fep-3, log10f16(x) = -0x1.35p-1 (RZ)
39 {0x33f8U, 0xb8d4U, 0U, 1U, 1U},
40#ifndef LIBC_TARGET_CPU_HAS_FMA_FLOAT
41 // x = 0x1.394p-1, log10f16(x) = -0x1.b4cp-3 (RZ)
42 {0x38e5U, 0xb2d3U, 0U, 1U, 1U},
43#endif
44 // x = 0x1.ea8p-1, log10f16(x) = -0x1.31p-6 (RZ)
45 {0x3baaU, 0xa4c4U, 0U, 1U, 1U},
46 // x = 0x1.ebp-1, log10f16(x) = -0x1.29cp-6 (RZ)
47 {0x3bacU, 0xa4a7U, 0U, 1U, 1U},
48 // x = 0x1.f3p-1, log10f16(x) = -0x1.6dcp-7 (RZ)
49 {0x3bccU, 0xa1b7U, 0U, 1U, 1U},
50// x = 0x1.f38p-1, log10f16(x) = -0x1.5f8p-7 (RZ)
51#ifndef LIBC_TARGET_CPU_HAS_FMA_FLOAT
52 {0x3bceU, 0xa17eU, 0U, 1U, 1U},
53 // x = 0x1.fd8p-1, log10f16(x) = -0x1.168p-9 (RZ)
54 {0x3bf6U, 0x985aU, 0U, 1U, 1U},
55 // x = 0x1.ff8p-1, log10f16(x) = -0x1.bccp-12 (RZ)
56 {0x3bfeU, 0x8ef3U, 0U, 1U, 1U},
57 // x = 0x1.374p+0, log10f16(x) = 0x1.5b8p-4 (RZ)
58 {0x3cddU, 0x2d6eU, 1U, 0U, 1U},
59 // x = 0x1.3ecp+1, log10f16(x) = 0x1.958p-2 (RZ)
60 {0x40fbU, 0x3656U, 1U, 0U, 1U},
61#endif
62 // x = 0x1.4p+3, log10f16(x) = 0x1p+0 (RZ)
63 {0x4900U, 0x3c00U, 0U, 0U, 0U},
64 // x = 0x1.9p+6, log10f16(x) = 0x1p+1 (RZ)
65 {0x5640U, 0x4000U, 0U, 0U, 0U},
66 // x = 0x1.f84p+6, log10f16(x) = 0x1.0ccp+1 (RZ)
67 {0x57e1U, 0x4033U, 1U, 0U, 0U},
68 // x = 0x1.f4p+9, log10f16(x) = 0x1.8p+1 (RZ)
69 {0x63d0U, 0x4200U, 0U, 0U, 0U},
70 // x = 0x1.388p+13, log10f16(x) = 0x1p+2 (RZ)
71 {0x70e2U, 0x4400U, 0U, 0U, 0U},
72 // x = 0x1.674p+13, log10f16(x) = 0x1.03cp+2 (RZ)
73 {0x719dU, 0x440fU, 1U, 0U, 0U},
74 }};
75#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
76
77LLVM_LIBC_FUNCTION(float16, log10f16, (float16 x)) {
78 using FPBits = fputil::FPBits<float16>;
79 FPBits x_bits(x);
80
81 uint16_t x_u = x_bits.uintval();
82
83 // If x <= 0, or x is 1, or x is +inf, or x is NaN.
84 if (LIBC_UNLIKELY(x_u == 0U || x_u == 0x3c00U || x_u >= 0x7c00U)) {
85 // log10(NaN) = NaN
86 if (x_bits.is_nan()) {
87 if (x_bits.is_signaling_nan()) {
88 fputil::raise_except_if_required(FE_INVALID);
89 return FPBits::quiet_nan().get_val();
90 }
91
92 return x;
93 }
94
95 // log10(+/-0) = −inf
96 if ((x_u & 0x7fffU) == 0U) {
97 fputil::raise_except_if_required(FE_DIVBYZERO);
98 return FPBits::inf(Sign::NEG).get_val();
99 }
100
101 if (x_u == 0x3c00U)
102 return FPBits::zero().get_val();
103
104 // When x < 0.
105 if (x_u > 0x8000U) {
106 fputil::set_errno_if_required(EDOM);
107 fputil::raise_except_if_required(FE_INVALID);
108 return FPBits::quiet_nan().get_val();
109 }
110
111 // log10(+inf) = +inf
112 return FPBits::inf().get_val();
113 }
114
115#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
116 if (auto r = LOG10F16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
117 return r.value();
118#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
119
120 // To compute log10(x), we perform the following range reduction:
121 // x = 2^m * 1.mant,
122 // log10(x) = m * log10(2) + log10(1.mant).
123 // To compute log10(1.mant), let f be the highest 6 bits including the hidden
124 // bit, and d be the difference (1.mant - f), i.e., the remaining 5 bits of
125 // the mantissa, then:
126 // log10(1.mant) = log10(f) + log10(1.mant / f)
127 // = log10(f) + log10(1 + d/f)
128 // since d/f is sufficiently small.
129 // We store log10(f) and 1/f in the lookup tables LOG10F_F and ONE_OVER_F_F
130 // respectively.
131
132 int m = -FPBits::EXP_BIAS;
133
134 // When x is subnormal, normalize it.
135 if ((x_u & FPBits::EXP_MASK) == 0U) {
136 // Can't pass an integer to fputil::cast directly.
137 constexpr float NORMALIZE_EXP = 1U << FPBits::FRACTION_LEN;
138 x_bits = FPBits(x_bits.get_val() * fputil::cast<float16>(NORMALIZE_EXP));
139 x_u = x_bits.uintval();
140 m -= FPBits::FRACTION_LEN;
141 }
142
143 uint16_t mant = x_bits.get_mantissa();
144 // Leading 10 - 5 = 5 bits of the mantissa.
145 int f = mant >> 5;
146 // Unbiased exponent.
147 m += x_u >> FPBits::FRACTION_LEN;
148
149 // Set bits to 1.mant instead of 2^m * 1.mant.
150 x_bits.set_biased_exponent(FPBits::EXP_BIAS);
151 float mant_f = x_bits.get_val();
152 // v = 1.mant * 1/f - 1 = d/f
153 float v = fputil::multiply_add(mant_f, ONE_OVER_F_F[f], -1.0f);
154
155 // Degree-3 minimax polynomial generated by Sollya with the following
156 // commands:
157 // > display = hexadecimal;
158 // > P = fpminimax(log10(1 + x)/x, 2, [|SG...|], [-2^-5, 2^-5]);
159 // > x * P;
160 float log10p1_d_over_f =
161 v * fputil::polyeval(v, 0x1.bcb7bp-2f, -0x1.bce168p-3f, 0x1.28acb8p-3f);
162 // log10(1.mant) = log10(f) + log10(1 + d/f)
163 float log10_1_mant = LOG10F_F[f] + log10p1_d_over_f;
164 return fputil::cast<float16>(
165 fputil::multiply_add(static_cast<float>(m), LOG10F_2, log10_1_mant));
166}
167
168} // namespace LIBC_NAMESPACE_DECL
169

source code of libc/src/math/generic/log10f16.cpp