1//===-- Implementation header for expf --------------------------*- C++ -*-===//
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#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_EXPF_H
10#define LLVM_LIBC_SRC___SUPPORT_MATH_EXPF_H
11
12#include "exp_float_constants.h" // Lookup tables EXP_M1 and EXP_M2.
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/multiply_add.h"
17#include "src/__support/FPUtil/nearest_integer.h"
18#include "src/__support/FPUtil/rounding_mode.h"
19#include "src/__support/common.h"
20#include "src/__support/macros/config.h"
21#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
22
23namespace LIBC_NAMESPACE_DECL {
24
25namespace math {
26
27LIBC_INLINE float expf(float x) {
28 using FPBits = typename fputil::FPBits<float>;
29 FPBits xbits(x);
30
31 uint32_t x_u = xbits.uintval();
32 uint32_t x_abs = x_u & 0x7fff'ffffU;
33
34#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
35 // Exceptional values
36 if (LIBC_UNLIKELY(x_u == 0xc236'bd8cU)) { // x = -0x1.6d7b18p+5f
37 return 0x1.108a58p-66f - x * 0x1.0p-95f;
38 }
39#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
40
41 // When |x| >= 89, |x| < 2^-25, or x is nan
42 if (LIBC_UNLIKELY(x_abs >= 0x42b2'0000U || x_abs <= 0x3280'0000U)) {
43 // |x| < 2^-25
44 if (xbits.get_biased_exponent() <= 101) {
45 return 1.0f + x;
46 }
47
48 // When x < log(2^-150) or nan
49 if (xbits.uintval() >= 0xc2cf'f1b5U) {
50 // exp(-Inf) = 0
51 if (xbits.is_inf())
52 return 0.0f;
53 // exp(nan) = nan
54 if (xbits.is_nan())
55 return x;
56#ifndef LIBC_MATH_HAS_ASSUME_ROUND_NEAREST_ONLY
57 if (fputil::fenv_is_round_up())
58 return FPBits::min_subnormal().get_val();
59#endif
60 fputil::set_errno_if_required(ERANGE);
61 fputil::raise_except_if_required(FE_UNDERFLOW);
62 return 0.0f;
63 }
64 // x >= 89 or nan
65 if (xbits.is_pos() && (xbits.uintval() >= 0x42b2'0000)) {
66 // x is finite
67 if (xbits.uintval() < 0x7f80'0000U) {
68#ifndef LIBC_MATH_HAS_ASSUME_ROUND_NEAREST_ONLY
69 int rounding = fputil::quick_get_round();
70 if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
71 return FPBits::max_normal().get_val();
72#endif
73
74 fputil::set_errno_if_required(ERANGE);
75 fputil::raise_except_if_required(FE_OVERFLOW);
76 }
77 // x is +inf or nan
78 return x + FPBits::inf().get_val();
79 }
80 }
81 // For -104 < x < 89, to compute exp(x), we perform the following range
82 // reduction: find hi, mid, lo such that:
83 // x = hi + mid + lo, in which
84 // hi is an integer,
85 // mid * 2^7 is an integer
86 // -2^(-8) <= lo < 2^-8.
87 // In particular,
88 // hi + mid = round(x * 2^7) * 2^(-7).
89 // Then,
90 // exp(x) = exp(hi + mid + lo) = exp(hi) * exp(mid) * exp(lo).
91 // We store exp(hi) and exp(mid) in the lookup tables EXP_M1 and EXP_M2
92 // respectively. exp(lo) is computed using a degree-4 minimax polynomial
93 // generated by Sollya.
94
95 // x_hi = (hi + mid) * 2^7 = round(x * 2^7).
96 float kf = fputil::nearest_integer(x: x * 0x1.0p7f);
97 // Subtract (hi + mid) from x to get lo.
98 double xd = static_cast<double>(fputil::multiply_add(x: kf, y: -0x1.0p-7f, z: x));
99 int x_hi = static_cast<int>(kf);
100 x_hi += 104 << 7;
101 // hi = x_hi >> 7
102 double exp_hi = EXP_M1[x_hi >> 7];
103 // mid * 2^7 = x_hi & 0x0000'007fU;
104 double exp_mid = EXP_M2[x_hi & 0x7f];
105 // Degree-4 minimax polynomial generated by Sollya with the following
106 // commands:
107 // > display = hexadecimal;
108 // > Q = fpminimax(expm1(x)/x, 3, [|D...|], [-2^-8, 2^-8]);
109 // > Q;
110 double exp_lo =
111 fputil::polyeval(x: xd, a0: 0x1p0, a: 0x1.ffffffffff777p-1, a: 0x1.000000000071cp-1,
112 a: 0x1.555566668e5e7p-3, a: 0x1.55555555ef243p-5);
113 return static_cast<float>(exp_hi * exp_mid * exp_lo);
114}
115
116} // namespace math
117
118} // namespace LIBC_NAMESPACE_DECL
119
120#endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXPF_H
121