1//===----------------------------------------------------------------------===//
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/// \file
10/// Double-precision implementation of exp10f.
11///
12//===----------------------------------------------------------------------===//
13
14#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_EXP10F_DOUBLE_EVAL_H
15#define LLVM_LIBC_SRC___SUPPORT_MATH_EXP10F_DOUBLE_EVAL_H
16
17#include "src/__support/FPUtil/FEnvImpl.h"
18#include "src/__support/FPUtil/FPBits.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/macros/config.h"
23#include "src/__support/macros/optimization.h"
24#include "src/__support/math/exp10f_utils.h"
25
26namespace LIBC_NAMESPACE_DECL {
27namespace math {
28namespace double_eval {
29
30LIBC_INLINE float exp10f(float x) {
31 using FPBits = fputil::FPBits<float>;
32 FPBits xbits(x);
33
34 uint32_t x_u = xbits.uintval();
35 uint32_t x_abs = x_u & 0x7fff'ffffU;
36
37 // When |x| >= log10(2^128), or x is nan
38 if (LIBC_UNLIKELY(x_abs >= 0x421a'209bU)) {
39 // When x < log10(2^-150) or nan
40 if (x_u > 0xc234'9e35U) {
41 // exp(-Inf) = 0
42 if (xbits.is_inf())
43 return 0.0f;
44 // exp(nan) = nan
45 if (xbits.is_nan())
46 return x;
47#ifndef LIBC_MATH_HAS_ASSUME_ROUND_NEAREST_ONLY
48 if (fputil::fenv_is_round_up())
49 return FPBits::min_subnormal().get_val();
50#endif // LIBC_MATH_HAS_ASSUME_ROUND_NEAREST_ONLY
51 fputil::set_errno_if_required(ERANGE);
52 fputil::raise_except_if_required(FE_UNDERFLOW);
53 return 0.0f;
54 }
55 // x >= log10(2^128) or nan
56 if (xbits.is_pos() && (x_u >= 0x421a'209bU)) {
57 // x is finite
58 if (x_u < 0x7f80'0000U) {
59#ifndef LIBC_MATH_HAS_ASSUME_ROUND_NEAREST_ONLY
60 int rounding = fputil::quick_get_round();
61 if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
62 return FPBits::max_normal().get_val();
63#endif // LIBC_MATH_HAS_ASSUME_ROUND_NEAREST_ONLY
64
65 fputil::set_errno_if_required(ERANGE);
66 fputil::raise_except_if_required(FE_OVERFLOW);
67 }
68 // x is +inf or nan
69 return x + FPBits::inf().get_val();
70 }
71 }
72
73 // When |x| <= log10(2)*2^-6
74 if (LIBC_UNLIKELY(x_abs <= 0x3b9a'209bU)) {
75 if (LIBC_UNLIKELY(x_u == 0xb25e'5bd9U)) { // x = -0x1.bcb7b2p-27f
76#ifdef LIBC_MATH_HAS_ASSUME_ROUND_NEAREST_ONLY
77 return 0x1.fffffep-1f;
78#else // !LIBC_MATH_HAS_ASSUME_ROUND_NEAREST_ONLY
79 if (fputil::fenv_is_round_to_nearest())
80 return 0x1.fffffep-1f;
81#endif // LIBC_MATH_HAS_ASSUME_ROUND_NEAREST_ONLY
82 }
83 // |x| < 2^-25
84 // 10^x ~ 1 + log(10) * x
85 if (LIBC_UNLIKELY(x_abs <= 0x3280'0000U)) {
86 return fputil::multiply_add(x, y: 0x1.26bb1cp+1f, z: 1.0f);
87 }
88
89 return static_cast<float>(Exp10Base::powb_lo(dx: x));
90 }
91
92 // Exceptional value.
93 if (LIBC_UNLIKELY(x_u == 0x3d14'd956U)) { // x = 0x1.29b2acp-5f
94#ifndef LIBC_MATH_HAS_ASSUME_ROUND_NEAREST_ONLY
95 if (fputil::fenv_is_round_up())
96 return 0x1.1657c4p+0f;
97#endif // LIBC_MATH_HAS_ASSUME_ROUND_NEAREST_ONLY
98 }
99
100 // Exact outputs when x = 1, 2, ..., 10.
101 // Quick check mask: 0x800f'ffffU = ~(bits of 1.0f | ... | bits of 10.0f)
102 if (LIBC_UNLIKELY((x_u & 0x800f'ffffU) == 0)) {
103 switch (x_u) {
104 case 0x3f800000U: // x = 1.0f
105 return 10.0f;
106 case 0x40000000U: // x = 2.0f
107 return 100.0f;
108 case 0x40400000U: // x = 3.0f
109 return 1'000.0f;
110 case 0x40800000U: // x = 4.0f
111 return 10'000.0f;
112 case 0x40a00000U: // x = 5.0f
113 return 100'000.0f;
114 case 0x40c00000U: // x = 6.0f
115 return 1'000'000.0f;
116 case 0x40e00000U: // x = 7.0f
117 return 10'000'000.0f;
118 case 0x41000000U: // x = 8.0f
119 return 100'000'000.0f;
120 case 0x41100000U: // x = 9.0f
121 return 1'000'000'000.0f;
122 case 0x41200000U: // x = 10.0f
123 return 10'000'000'000.0f;
124 }
125 }
126
127 // Range reduction: 10^x = 2^(mid + hi) * 10^lo
128 // rr = (2^(mid + hi), lo)
129 auto rr = exp_b_range_reduc<Exp10Base>(x);
130
131 // The low part is approximated by a degree-5 minimax polynomial.
132 // 10^lo ~ 1 + COEFFS[0] * lo + ... + COEFFS[4] * lo^5
133 using fputil::multiply_add;
134 double lo2 = rr.lo * rr.lo;
135 // c0 = 1 + COEFFS[0] * lo
136 double c0 = multiply_add(x: rr.lo, y: Exp10Base::COEFFS[0], z: 1.0);
137 // c1 = COEFFS[1] + COEFFS[2] * lo
138 double c1 = multiply_add(x: rr.lo, y: Exp10Base::COEFFS[2], z: Exp10Base::COEFFS[1]);
139 // c2 = COEFFS[3] + COEFFS[4] * lo
140 double c2 = multiply_add(x: rr.lo, y: Exp10Base::COEFFS[4], z: Exp10Base::COEFFS[3]);
141 // p = c1 + c2 * lo^2
142 // = COEFFS[1] + COEFFS[2] * lo + COEFFS[3] * lo^2 + COEFFS[4] * lo^3
143 double p = multiply_add(x: lo2, y: c2, z: c1);
144 // 10^lo ~ c0 + p * lo^2
145 // 10^x = 2^(mid + hi) * 10^lo
146 // ~ mh * (c0 + p * lo^2)
147 // = (mh * c0) + p * (mh * lo^2)
148 return static_cast<float>(multiply_add(x: p, y: lo2 * rr.mh, z: c0 * rr.mh));
149}
150
151} // namespace double_eval
152} // namespace math
153} // namespace LIBC_NAMESPACE_DECL
154
155#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXP10F_DOUBLE_EVAL_H
156