1//===-- Half-precision 10^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/exp10f16.h"
10#include "expxf16.h"
11#include "hdr/errno_macros.h"
12#include "hdr/fenv_macros.h"
13#include "src/__support/CPP/array.h"
14#include "src/__support/FPUtil/FEnvImpl.h"
15#include "src/__support/FPUtil/FPBits.h"
16#include "src/__support/FPUtil/PolyEval.h"
17#include "src/__support/FPUtil/cast.h"
18#include "src/__support/FPUtil/except_value_utils.h"
19#include "src/__support/FPUtil/multiply_add.h"
20#include "src/__support/FPUtil/nearest_integer.h"
21#include "src/__support/FPUtil/rounding_mode.h"
22#include "src/__support/common.h"
23#include "src/__support/macros/config.h"
24#include "src/__support/macros/optimization.h"
25#include "src/__support/macros/properties/cpu_features.h"
26
27namespace LIBC_NAMESPACE_DECL {
28
29#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
30#ifdef LIBC_TARGET_CPU_HAS_FMA_FLOAT
31static constexpr size_t N_EXP10F16_EXCEPTS = 5;
32#else
33static constexpr size_t N_EXP10F16_EXCEPTS = 8;
34#endif
35
36static constexpr fputil::ExceptValues<float16, N_EXP10F16_EXCEPTS>
37 EXP10F16_EXCEPTS = {{
38 // x = 0x1.8f4p-2, exp10f16(x) = 0x1.3ap+1 (RZ)
39 {0x363dU, 0x40e8U, 1U, 0U, 1U},
40 // x = 0x1.95cp-2, exp10f16(x) = 0x1.3ecp+1 (RZ)
41 {0x3657U, 0x40fbU, 1U, 0U, 0U},
42 // x = -0x1.018p-4, exp10f16(x) = 0x1.bbp-1 (RZ)
43 {0xac06U, 0x3aecU, 1U, 0U, 0U},
44 // x = -0x1.c28p+0, exp10f16(x) = 0x1.1ccp-6 (RZ)
45 {0xbf0aU, 0x2473U, 1U, 0U, 0U},
46 // x = -0x1.e1cp+1, exp10f16(x) = 0x1.694p-13 (RZ)
47 {0xc387U, 0x09a5U, 1U, 0U, 0U},
48#ifndef LIBC_TARGET_CPU_HAS_FMA_FLOAT
49 // x = 0x1.0cp+1, exp10f16(x) = 0x1.f04p+6 (RZ)
50 {0x4030U, 0x57c1U, 1U, 0U, 1U},
51 // x = 0x1.1b8p+1, exp10f16(x) = 0x1.47cp+7 (RZ)
52 {0x406eU, 0x591fU, 1U, 0U, 1U},
53 // x = 0x1.1b8p+2, exp10f16(x) = 0x1.a4p+14 (RZ)
54 {0x446eU, 0x7690U, 1U, 0U, 1U},
55#endif
56 }};
57#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
58
59LLVM_LIBC_FUNCTION(float16, exp10f16, (float16 x)) {
60 using FPBits = fputil::FPBits<float16>;
61 FPBits x_bits(x);
62
63 uint16_t x_u = x_bits.uintval();
64 uint16_t x_abs = x_u & 0x7fffU;
65
66 // When |x| >= 5, or x is NaN.
67 if (LIBC_UNLIKELY(x_abs >= 0x4500U)) {
68 // exp10(NaN) = NaN
69 if (x_bits.is_nan()) {
70 if (x_bits.is_signaling_nan()) {
71 fputil::raise_except_if_required(FE_INVALID);
72 return FPBits::quiet_nan().get_val();
73 }
74
75 return x;
76 }
77
78 // When x >= 5.
79 if (x_bits.is_pos()) {
80 // exp10(+inf) = +inf
81 if (x_bits.is_inf())
82 return FPBits::inf().get_val();
83
84 switch (fputil::quick_get_round()) {
85 case FE_TONEAREST:
86 case FE_UPWARD:
87 fputil::set_errno_if_required(ERANGE);
88 fputil::raise_except_if_required(FE_OVERFLOW);
89 return FPBits::inf().get_val();
90 default:
91 return FPBits::max_normal().get_val();
92 }
93 }
94
95 // When x <= -8.
96 if (x_u >= 0xc800U) {
97 // exp10(-inf) = +0
98 if (x_bits.is_inf())
99 return FPBits::zero().get_val();
100
101 fputil::set_errno_if_required(ERANGE);
102 fputil::raise_except_if_required(FE_UNDERFLOW | FE_INEXACT);
103
104 if (fputil::fenv_is_round_up())
105 return FPBits::min_subnormal().get_val();
106 return FPBits::zero().get_val();
107 }
108 }
109
110 // When x is 1, 2, 3, or 4. These are hard-to-round cases with exact results.
111 if (LIBC_UNLIKELY((x_u & ~(0x3c00U | 0x4000U | 0x4200U | 0x4400U)) == 0)) {
112 switch (x_u) {
113 case 0x3c00U: // x = 1.0f16
114 return fputil::cast<float16>(10.0);
115 case 0x4000U: // x = 2.0f16
116 return fputil::cast<float16>(100.0);
117 case 0x4200U: // x = 3.0f16
118 return fputil::cast<float16>(1'000.0);
119 case 0x4400U: // x = 4.0f16
120 return fputil::cast<float16>(10'000.0);
121 }
122 }
123
124#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
125 if (auto r = EXP10F16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
126 return r.value();
127#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
128
129 // 10^x = 2^((hi + mid) * log2(10)) * 10^lo
130 auto [exp2_hi_mid, exp10_lo] = exp10_range_reduction(x);
131 return fputil::cast<float16>(exp2_hi_mid * exp10_lo);
132}
133
134} // namespace LIBC_NAMESPACE_DECL
135

source code of libc/src/math/generic/exp10f16.cpp