1//===-- Half-precision log2(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/log2f16.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_LOG2F16_EXCEPTS = 2;
29#else
30static constexpr size_t N_LOG2F16_EXCEPTS = 9;
31#endif
32
33static constexpr fputil::ExceptValues<float16, N_LOG2F16_EXCEPTS>
34 LOG2F16_EXCEPTS = {{
35// (input, RZ output, RU offset, RD offset, RN offset)
36#ifndef LIBC_TARGET_CPU_HAS_FMA_FLOAT
37 // x = 0x1.224p-1, log2f16(x) = -0x1.a34p-1 (RZ)
38 {0x3889U, 0xba8dU, 0U, 1U, 0U},
39 // x = 0x1.e34p-1, log2f16(x) = -0x1.558p-4 (RZ)
40 {0x3b8dU, 0xad56U, 0U, 1U, 0U},
41#endif
42 // x = 0x1.e8cp-1, log2f16(x) = -0x1.128p-4 (RZ)
43 {0x3ba3U, 0xac4aU, 0U, 1U, 0U},
44#ifndef LIBC_TARGET_CPU_HAS_FMA_FLOAT
45 // x = 0x1.f98p-1, log2f16(x) = -0x1.2ep-6 (RZ)
46 {0x3be6U, 0xa4b8U, 0U, 1U, 0U},
47 // x = 0x1.facp-1, log2f16(x) = -0x1.e7p-7 (RZ)
48 {0x3bebU, 0xa39cU, 0U, 1U, 1U},
49#endif
50 // x = 0x1.fb4p-1, log2f16(x) = -0x1.b88p-7 (RZ)
51 {0x3bedU, 0xa2e2U, 0U, 1U, 1U},
52#ifndef LIBC_TARGET_CPU_HAS_FMA_FLOAT
53 // x = 0x1.fecp-1, log2f16(x) = -0x1.cep-9 (RZ)
54 {0x3bfbU, 0x9b38U, 0U, 1U, 1U},
55 // x = 0x1.ffcp-1, log2f16(x) = -0x1.714p-11 (RZ)
56 {0x3bffU, 0x91c5U, 0U, 1U, 1U},
57 // x = 0x1.224p+0, log2f16(x) = 0x1.72cp-3 (RZ)
58 {0x3c89U, 0x31cbU, 1U, 0U, 1U},
59#endif
60 }};
61#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
62
63LLVM_LIBC_FUNCTION(float16, log2f16, (float16 x)) {
64 using FPBits = fputil::FPBits<float16>;
65 FPBits x_bits(x);
66
67 uint16_t x_u = x_bits.uintval();
68
69 // If x <= 0, or x is 1, or x is +inf, or x is NaN.
70 if (LIBC_UNLIKELY(x_u == 0U || x_u == 0x3c00U || x_u >= 0x7c00U)) {
71 // log2(NaN) = NaN
72 if (x_bits.is_nan()) {
73 if (x_bits.is_signaling_nan()) {
74 fputil::raise_except_if_required(FE_INVALID);
75 return FPBits::quiet_nan().get_val();
76 }
77
78 return x;
79 }
80
81 // log2(+/-0) = −inf
82 if ((x_u & 0x7fffU) == 0U) {
83 fputil::raise_except_if_required(FE_DIVBYZERO);
84 return FPBits::inf(Sign::NEG).get_val();
85 }
86
87 if (x_u == 0x3c00U)
88 return FPBits::zero().get_val();
89
90 // When x < 0.
91 if (x_u > 0x8000U) {
92 fputil::set_errno_if_required(EDOM);
93 fputil::raise_except_if_required(FE_INVALID);
94 return FPBits::quiet_nan().get_val();
95 }
96
97 // log2(+inf) = +inf
98 return FPBits::inf().get_val();
99 }
100
101#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
102 if (auto r = LOG2F16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
103 return r.value();
104#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
105
106 // To compute log2(x), we perform the following range reduction:
107 // x = 2^m * 1.mant,
108 // log2(x) = m + log2(1.mant).
109 // To compute log2(1.mant), let f be the highest 6 bits including the hidden
110 // bit, and d be the difference (1.mant - f), i.e., the remaining 5 bits of
111 // the mantissa, then:
112 // log2(1.mant) = log2(f) + log2(1.mant / f)
113 // = log2(f) + log2(1 + d/f)
114 // since d/f is sufficiently small.
115 // We store log2(f) and 1/f in the lookup tables LOG2F_F and ONE_OVER_F_F
116 // respectively.
117
118 int m = -FPBits::EXP_BIAS;
119
120 // When x is subnormal, normalize it.
121 if ((x_u & FPBits::EXP_MASK) == 0U) {
122 // Can't pass an integer to fputil::cast directly.
123 constexpr float NORMALIZE_EXP = 1U << FPBits::FRACTION_LEN;
124 x_bits = FPBits(x_bits.get_val() * fputil::cast<float16>(NORMALIZE_EXP));
125 x_u = x_bits.uintval();
126 m -= FPBits::FRACTION_LEN;
127 }
128
129 uint16_t mant = x_bits.get_mantissa();
130 // Leading 10 - 5 = 5 bits of the mantissa.
131 int f = mant >> 5;
132 // Unbiased exponent.
133 m += x_u >> FPBits::FRACTION_LEN;
134
135 // Set bits to 1.mant instead of 2^m * 1.mant.
136 x_bits.set_biased_exponent(FPBits::EXP_BIAS);
137 float mant_f = x_bits.get_val();
138 // v = 1.mant * 1/f - 1 = d/f
139 float v = fputil::multiply_add(mant_f, ONE_OVER_F_F[f], -1.0f);
140
141 // Degree-3 minimax polynomial generated by Sollya with the following
142 // commands:
143 // > display = hexadecimal;
144 // > P = fpminimax(log2(1 + x)/x, 2, [|SG...|], [-2^-5, 2^-5]);
145 // > x * P;
146 float log2p1_d_over_f =
147 v * fputil::polyeval(v, 0x1.715476p+0f, -0x1.71771ap-1f, 0x1.ecb38ep-2f);
148 // log2(1.mant) = log2(f) + log2(1 + d/f)
149 float log2_1_mant = LOG2F_F[f] + log2p1_d_over_f;
150 return fputil::cast<float16>(static_cast<float>(m) + log2_1_mant);
151}
152
153} // namespace LIBC_NAMESPACE_DECL
154

source code of libc/src/math/generic/log2f16.cpp