1*bb722a7dSDimitry Andric //===-- Implementation header for expf --------------------------*- C++ -*-===//
2*bb722a7dSDimitry Andric //
3*bb722a7dSDimitry Andric // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4*bb722a7dSDimitry Andric // See https://llvm.org/LICENSE.txt for license information.
5*bb722a7dSDimitry Andric // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6*bb722a7dSDimitry Andric //
7*bb722a7dSDimitry Andric //===----------------------------------------------------------------------===//
8*bb722a7dSDimitry Andric
9*bb722a7dSDimitry Andric #ifndef LLVM_LIBC_SRC___SUPPORT_MATH_EXPF_H
10*bb722a7dSDimitry Andric #define LLVM_LIBC_SRC___SUPPORT_MATH_EXPF_H
11*bb722a7dSDimitry Andric
12*bb722a7dSDimitry Andric #include "exp_float_constants.h" // Lookup tables EXP_M1 and EXP_M2.
13*bb722a7dSDimitry Andric #include "src/__support/FPUtil/FEnvImpl.h"
14*bb722a7dSDimitry Andric #include "src/__support/FPUtil/FPBits.h"
15*bb722a7dSDimitry Andric #include "src/__support/FPUtil/PolyEval.h"
16*bb722a7dSDimitry Andric #include "src/__support/FPUtil/multiply_add.h"
17*bb722a7dSDimitry Andric #include "src/__support/FPUtil/nearest_integer.h"
18*bb722a7dSDimitry Andric #include "src/__support/FPUtil/rounding_mode.h"
19*bb722a7dSDimitry Andric #include "src/__support/common.h"
20*bb722a7dSDimitry Andric #include "src/__support/macros/config.h"
21*bb722a7dSDimitry Andric #include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
22*bb722a7dSDimitry Andric
23*bb722a7dSDimitry Andric namespace LIBC_NAMESPACE_DECL {
24*bb722a7dSDimitry Andric
25*bb722a7dSDimitry Andric namespace math {
26*bb722a7dSDimitry Andric
expf(float x)27*bb722a7dSDimitry Andric static constexpr float expf(float x) {
28*bb722a7dSDimitry Andric using FPBits = typename fputil::FPBits<float>;
29*bb722a7dSDimitry Andric FPBits xbits(x);
30*bb722a7dSDimitry Andric
31*bb722a7dSDimitry Andric uint32_t x_u = xbits.uintval();
32*bb722a7dSDimitry Andric uint32_t x_abs = x_u & 0x7fff'ffffU;
33*bb722a7dSDimitry Andric
34*bb722a7dSDimitry Andric #ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
35*bb722a7dSDimitry Andric // Exceptional values
36*bb722a7dSDimitry Andric if (LIBC_UNLIKELY(x_u == 0xc236'bd8cU)) { // x = -0x1.6d7b18p+5f
37*bb722a7dSDimitry Andric return 0x1.108a58p-66f - x * 0x1.0p-95f;
38*bb722a7dSDimitry Andric }
39*bb722a7dSDimitry Andric #endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
40*bb722a7dSDimitry Andric
41*bb722a7dSDimitry Andric // When |x| >= 89, |x| < 2^-25, or x is nan
42*bb722a7dSDimitry Andric if (LIBC_UNLIKELY(x_abs >= 0x42b2'0000U || x_abs <= 0x3280'0000U)) {
43*bb722a7dSDimitry Andric // |x| < 2^-25
44*bb722a7dSDimitry Andric if (xbits.get_biased_exponent() <= 101) {
45*bb722a7dSDimitry Andric return 1.0f + x;
46*bb722a7dSDimitry Andric }
47*bb722a7dSDimitry Andric
48*bb722a7dSDimitry Andric // When x < log(2^-150) or nan
49*bb722a7dSDimitry Andric if (xbits.uintval() >= 0xc2cf'f1b5U) {
50*bb722a7dSDimitry Andric // exp(-Inf) = 0
51*bb722a7dSDimitry Andric if (xbits.is_inf())
52*bb722a7dSDimitry Andric return 0.0f;
53*bb722a7dSDimitry Andric // exp(nan) = nan
54*bb722a7dSDimitry Andric if (xbits.is_nan())
55*bb722a7dSDimitry Andric return x;
56*bb722a7dSDimitry Andric if (fputil::fenv_is_round_up())
57*bb722a7dSDimitry Andric return FPBits::min_subnormal().get_val();
58*bb722a7dSDimitry Andric fputil::set_errno_if_required(ERANGE);
59*bb722a7dSDimitry Andric fputil::raise_except_if_required(FE_UNDERFLOW);
60*bb722a7dSDimitry Andric return 0.0f;
61*bb722a7dSDimitry Andric }
62*bb722a7dSDimitry Andric // x >= 89 or nan
63*bb722a7dSDimitry Andric if (xbits.is_pos() && (xbits.uintval() >= 0x42b2'0000)) {
64*bb722a7dSDimitry Andric // x is finite
65*bb722a7dSDimitry Andric if (xbits.uintval() < 0x7f80'0000U) {
66*bb722a7dSDimitry Andric int rounding = fputil::quick_get_round();
67*bb722a7dSDimitry Andric if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
68*bb722a7dSDimitry Andric return FPBits::max_normal().get_val();
69*bb722a7dSDimitry Andric
70*bb722a7dSDimitry Andric fputil::set_errno_if_required(ERANGE);
71*bb722a7dSDimitry Andric fputil::raise_except_if_required(FE_OVERFLOW);
72*bb722a7dSDimitry Andric }
73*bb722a7dSDimitry Andric // x is +inf or nan
74*bb722a7dSDimitry Andric return x + FPBits::inf().get_val();
75*bb722a7dSDimitry Andric }
76*bb722a7dSDimitry Andric }
77*bb722a7dSDimitry Andric // For -104 < x < 89, to compute exp(x), we perform the following range
78*bb722a7dSDimitry Andric // reduction: find hi, mid, lo such that:
79*bb722a7dSDimitry Andric // x = hi + mid + lo, in which
80*bb722a7dSDimitry Andric // hi is an integer,
81*bb722a7dSDimitry Andric // mid * 2^7 is an integer
82*bb722a7dSDimitry Andric // -2^(-8) <= lo < 2^-8.
83*bb722a7dSDimitry Andric // In particular,
84*bb722a7dSDimitry Andric // hi + mid = round(x * 2^7) * 2^(-7).
85*bb722a7dSDimitry Andric // Then,
86*bb722a7dSDimitry Andric // exp(x) = exp(hi + mid + lo) = exp(hi) * exp(mid) * exp(lo).
87*bb722a7dSDimitry Andric // We store exp(hi) and exp(mid) in the lookup tables EXP_M1 and EXP_M2
88*bb722a7dSDimitry Andric // respectively. exp(lo) is computed using a degree-4 minimax polynomial
89*bb722a7dSDimitry Andric // generated by Sollya.
90*bb722a7dSDimitry Andric
91*bb722a7dSDimitry Andric // x_hi = (hi + mid) * 2^7 = round(x * 2^7).
92*bb722a7dSDimitry Andric float kf = fputil::nearest_integer(x * 0x1.0p7f);
93*bb722a7dSDimitry Andric // Subtract (hi + mid) from x to get lo.
94*bb722a7dSDimitry Andric double xd = static_cast<double>(fputil::multiply_add(kf, -0x1.0p-7f, x));
95*bb722a7dSDimitry Andric int x_hi = static_cast<int>(kf);
96*bb722a7dSDimitry Andric x_hi += 104 << 7;
97*bb722a7dSDimitry Andric // hi = x_hi >> 7
98*bb722a7dSDimitry Andric double exp_hi = EXP_M1[x_hi >> 7];
99*bb722a7dSDimitry Andric // mid * 2^7 = x_hi & 0x0000'007fU;
100*bb722a7dSDimitry Andric double exp_mid = EXP_M2[x_hi & 0x7f];
101*bb722a7dSDimitry Andric // Degree-4 minimax polynomial generated by Sollya with the following
102*bb722a7dSDimitry Andric // commands:
103*bb722a7dSDimitry Andric // > display = hexadecimal;
104*bb722a7dSDimitry Andric // > Q = fpminimax(expm1(x)/x, 3, [|D...|], [-2^-8, 2^-8]);
105*bb722a7dSDimitry Andric // > Q;
106*bb722a7dSDimitry Andric double exp_lo =
107*bb722a7dSDimitry Andric fputil::polyeval(xd, 0x1p0, 0x1.ffffffffff777p-1, 0x1.000000000071cp-1,
108*bb722a7dSDimitry Andric 0x1.555566668e5e7p-3, 0x1.55555555ef243p-5);
109*bb722a7dSDimitry Andric return static_cast<float>(exp_hi * exp_mid * exp_lo);
110*bb722a7dSDimitry Andric }
111*bb722a7dSDimitry Andric
112*bb722a7dSDimitry Andric } // namespace math
113*bb722a7dSDimitry Andric
114*bb722a7dSDimitry Andric } // namespace LIBC_NAMESPACE_DECL
115*bb722a7dSDimitry Andric
116*bb722a7dSDimitry Andric #endif // LLVM_LIBC_SRC___SUPPORT_MATH_EXPF_H
117