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

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