1*71db0c75SAndroid Build Coastguard Worker //===-- Single-precision 10^x function ------------------------------------===//
2*71db0c75SAndroid Build Coastguard Worker //
3*71db0c75SAndroid Build Coastguard Worker // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4*71db0c75SAndroid Build Coastguard Worker // See https://llvm.org/LICENSE.txt for license information.
5*71db0c75SAndroid Build Coastguard Worker // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6*71db0c75SAndroid Build Coastguard Worker //
7*71db0c75SAndroid Build Coastguard Worker //===----------------------------------------------------------------------===//
8*71db0c75SAndroid Build Coastguard Worker
9*71db0c75SAndroid Build Coastguard Worker #ifndef LLVM_LIBC_SRC_MATH_GENERIC_EXP10F_IMPL_H
10*71db0c75SAndroid Build Coastguard Worker #define LLVM_LIBC_SRC_MATH_GENERIC_EXP10F_IMPL_H
11*71db0c75SAndroid Build Coastguard Worker
12*71db0c75SAndroid Build Coastguard Worker #include "explogxf.h"
13*71db0c75SAndroid Build Coastguard Worker #include "src/__support/FPUtil/BasicOperations.h"
14*71db0c75SAndroid Build Coastguard Worker #include "src/__support/FPUtil/FEnvImpl.h"
15*71db0c75SAndroid Build Coastguard Worker #include "src/__support/FPUtil/FPBits.h"
16*71db0c75SAndroid Build Coastguard Worker #include "src/__support/FPUtil/PolyEval.h"
17*71db0c75SAndroid Build Coastguard Worker #include "src/__support/FPUtil/multiply_add.h"
18*71db0c75SAndroid Build Coastguard Worker #include "src/__support/FPUtil/nearest_integer.h"
19*71db0c75SAndroid Build Coastguard Worker #include "src/__support/FPUtil/rounding_mode.h"
20*71db0c75SAndroid Build Coastguard Worker #include "src/__support/common.h"
21*71db0c75SAndroid Build Coastguard Worker #include "src/__support/macros/config.h"
22*71db0c75SAndroid Build Coastguard Worker #include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
23*71db0c75SAndroid Build Coastguard Worker
24*71db0c75SAndroid Build Coastguard Worker namespace LIBC_NAMESPACE_DECL {
25*71db0c75SAndroid Build Coastguard Worker namespace generic {
26*71db0c75SAndroid Build Coastguard Worker
exp10f(float x)27*71db0c75SAndroid Build Coastguard Worker LIBC_INLINE float exp10f(float x) {
28*71db0c75SAndroid Build Coastguard Worker using FPBits = typename fputil::FPBits<float>;
29*71db0c75SAndroid Build Coastguard Worker FPBits xbits(x);
30*71db0c75SAndroid Build Coastguard Worker
31*71db0c75SAndroid Build Coastguard Worker uint32_t x_u = xbits.uintval();
32*71db0c75SAndroid Build Coastguard Worker uint32_t x_abs = x_u & 0x7fff'ffffU;
33*71db0c75SAndroid Build Coastguard Worker
34*71db0c75SAndroid Build Coastguard Worker // When |x| >= log10(2^128), or x is nan
35*71db0c75SAndroid Build Coastguard Worker if (LIBC_UNLIKELY(x_abs >= 0x421a'209bU)) {
36*71db0c75SAndroid Build Coastguard Worker // When x < log10(2^-150) or nan
37*71db0c75SAndroid Build Coastguard Worker if (x_u > 0xc234'9e35U) {
38*71db0c75SAndroid Build Coastguard Worker // exp(-Inf) = 0
39*71db0c75SAndroid Build Coastguard Worker if (xbits.is_inf())
40*71db0c75SAndroid Build Coastguard Worker return 0.0f;
41*71db0c75SAndroid Build Coastguard Worker // exp(nan) = nan
42*71db0c75SAndroid Build Coastguard Worker if (xbits.is_nan())
43*71db0c75SAndroid Build Coastguard Worker return x;
44*71db0c75SAndroid Build Coastguard Worker if (fputil::fenv_is_round_up())
45*71db0c75SAndroid Build Coastguard Worker return FPBits::min_subnormal().get_val();
46*71db0c75SAndroid Build Coastguard Worker fputil::set_errno_if_required(ERANGE);
47*71db0c75SAndroid Build Coastguard Worker fputil::raise_except_if_required(FE_UNDERFLOW);
48*71db0c75SAndroid Build Coastguard Worker return 0.0f;
49*71db0c75SAndroid Build Coastguard Worker }
50*71db0c75SAndroid Build Coastguard Worker // x >= log10(2^128) or nan
51*71db0c75SAndroid Build Coastguard Worker if (xbits.is_pos() && (x_u >= 0x421a'209bU)) {
52*71db0c75SAndroid Build Coastguard Worker // x is finite
53*71db0c75SAndroid Build Coastguard Worker if (x_u < 0x7f80'0000U) {
54*71db0c75SAndroid Build Coastguard Worker int rounding = fputil::quick_get_round();
55*71db0c75SAndroid Build Coastguard Worker if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
56*71db0c75SAndroid Build Coastguard Worker return FPBits::max_normal().get_val();
57*71db0c75SAndroid Build Coastguard Worker
58*71db0c75SAndroid Build Coastguard Worker fputil::set_errno_if_required(ERANGE);
59*71db0c75SAndroid Build Coastguard Worker fputil::raise_except_if_required(FE_OVERFLOW);
60*71db0c75SAndroid Build Coastguard Worker }
61*71db0c75SAndroid Build Coastguard Worker // x is +inf or nan
62*71db0c75SAndroid Build Coastguard Worker return x + FPBits::inf().get_val();
63*71db0c75SAndroid Build Coastguard Worker }
64*71db0c75SAndroid Build Coastguard Worker }
65*71db0c75SAndroid Build Coastguard Worker
66*71db0c75SAndroid Build Coastguard Worker // When |x| <= log10(2)*2^-6
67*71db0c75SAndroid Build Coastguard Worker if (LIBC_UNLIKELY(x_abs <= 0x3b9a'209bU)) {
68*71db0c75SAndroid Build Coastguard Worker if (LIBC_UNLIKELY(x_u == 0xb25e'5bd9U)) { // x = -0x1.bcb7b2p-27f
69*71db0c75SAndroid Build Coastguard Worker if (fputil::fenv_is_round_to_nearest())
70*71db0c75SAndroid Build Coastguard Worker return 0x1.fffffep-1f;
71*71db0c75SAndroid Build Coastguard Worker }
72*71db0c75SAndroid Build Coastguard Worker // |x| < 2^-25
73*71db0c75SAndroid Build Coastguard Worker // 10^x ~ 1 + log(10) * x
74*71db0c75SAndroid Build Coastguard Worker if (LIBC_UNLIKELY(x_abs <= 0x3280'0000U)) {
75*71db0c75SAndroid Build Coastguard Worker return fputil::multiply_add(x, 0x1.26bb1cp+1f, 1.0f);
76*71db0c75SAndroid Build Coastguard Worker }
77*71db0c75SAndroid Build Coastguard Worker
78*71db0c75SAndroid Build Coastguard Worker return static_cast<float>(Exp10Base::powb_lo(x));
79*71db0c75SAndroid Build Coastguard Worker }
80*71db0c75SAndroid Build Coastguard Worker
81*71db0c75SAndroid Build Coastguard Worker // Exceptional value.
82*71db0c75SAndroid Build Coastguard Worker if (LIBC_UNLIKELY(x_u == 0x3d14'd956U)) { // x = 0x1.29b2acp-5f
83*71db0c75SAndroid Build Coastguard Worker if (fputil::fenv_is_round_up())
84*71db0c75SAndroid Build Coastguard Worker return 0x1.1657c4p+0f;
85*71db0c75SAndroid Build Coastguard Worker }
86*71db0c75SAndroid Build Coastguard Worker
87*71db0c75SAndroid Build Coastguard Worker // Exact outputs when x = 1, 2, ..., 10.
88*71db0c75SAndroid Build Coastguard Worker // Quick check mask: 0x800f'ffffU = ~(bits of 1.0f | ... | bits of 10.0f)
89*71db0c75SAndroid Build Coastguard Worker if (LIBC_UNLIKELY((x_u & 0x800f'ffffU) == 0)) {
90*71db0c75SAndroid Build Coastguard Worker switch (x_u) {
91*71db0c75SAndroid Build Coastguard Worker case 0x3f800000U: // x = 1.0f
92*71db0c75SAndroid Build Coastguard Worker return 10.0f;
93*71db0c75SAndroid Build Coastguard Worker case 0x40000000U: // x = 2.0f
94*71db0c75SAndroid Build Coastguard Worker return 100.0f;
95*71db0c75SAndroid Build Coastguard Worker case 0x40400000U: // x = 3.0f
96*71db0c75SAndroid Build Coastguard Worker return 1'000.0f;
97*71db0c75SAndroid Build Coastguard Worker case 0x40800000U: // x = 4.0f
98*71db0c75SAndroid Build Coastguard Worker return 10'000.0f;
99*71db0c75SAndroid Build Coastguard Worker case 0x40a00000U: // x = 5.0f
100*71db0c75SAndroid Build Coastguard Worker return 100'000.0f;
101*71db0c75SAndroid Build Coastguard Worker case 0x40c00000U: // x = 6.0f
102*71db0c75SAndroid Build Coastguard Worker return 1'000'000.0f;
103*71db0c75SAndroid Build Coastguard Worker case 0x40e00000U: // x = 7.0f
104*71db0c75SAndroid Build Coastguard Worker return 10'000'000.0f;
105*71db0c75SAndroid Build Coastguard Worker case 0x41000000U: // x = 8.0f
106*71db0c75SAndroid Build Coastguard Worker return 100'000'000.0f;
107*71db0c75SAndroid Build Coastguard Worker case 0x41100000U: // x = 9.0f
108*71db0c75SAndroid Build Coastguard Worker return 1'000'000'000.0f;
109*71db0c75SAndroid Build Coastguard Worker case 0x41200000U: // x = 10.0f
110*71db0c75SAndroid Build Coastguard Worker return 10'000'000'000.0f;
111*71db0c75SAndroid Build Coastguard Worker }
112*71db0c75SAndroid Build Coastguard Worker }
113*71db0c75SAndroid Build Coastguard Worker
114*71db0c75SAndroid Build Coastguard Worker // Range reduction: 10^x = 2^(mid + hi) * 10^lo
115*71db0c75SAndroid Build Coastguard Worker // rr = (2^(mid + hi), lo)
116*71db0c75SAndroid Build Coastguard Worker auto rr = exp_b_range_reduc<Exp10Base>(x);
117*71db0c75SAndroid Build Coastguard Worker
118*71db0c75SAndroid Build Coastguard Worker // The low part is approximated by a degree-5 minimax polynomial.
119*71db0c75SAndroid Build Coastguard Worker // 10^lo ~ 1 + COEFFS[0] * lo + ... + COEFFS[4] * lo^5
120*71db0c75SAndroid Build Coastguard Worker using fputil::multiply_add;
121*71db0c75SAndroid Build Coastguard Worker double lo2 = rr.lo * rr.lo;
122*71db0c75SAndroid Build Coastguard Worker // c0 = 1 + COEFFS[0] * lo
123*71db0c75SAndroid Build Coastguard Worker double c0 = multiply_add(rr.lo, Exp10Base::COEFFS[0], 1.0);
124*71db0c75SAndroid Build Coastguard Worker // c1 = COEFFS[1] + COEFFS[2] * lo
125*71db0c75SAndroid Build Coastguard Worker double c1 = multiply_add(rr.lo, Exp10Base::COEFFS[2], Exp10Base::COEFFS[1]);
126*71db0c75SAndroid Build Coastguard Worker // c2 = COEFFS[3] + COEFFS[4] * lo
127*71db0c75SAndroid Build Coastguard Worker double c2 = multiply_add(rr.lo, Exp10Base::COEFFS[4], Exp10Base::COEFFS[3]);
128*71db0c75SAndroid Build Coastguard Worker // p = c1 + c2 * lo^2
129*71db0c75SAndroid Build Coastguard Worker // = COEFFS[1] + COEFFS[2] * lo + COEFFS[3] * lo^2 + COEFFS[4] * lo^3
130*71db0c75SAndroid Build Coastguard Worker double p = multiply_add(lo2, c2, c1);
131*71db0c75SAndroid Build Coastguard Worker // 10^lo ~ c0 + p * lo^2
132*71db0c75SAndroid Build Coastguard Worker // 10^x = 2^(mid + hi) * 10^lo
133*71db0c75SAndroid Build Coastguard Worker // ~ mh * (c0 + p * lo^2)
134*71db0c75SAndroid Build Coastguard Worker // = (mh * c0) + p * (mh * lo^2)
135*71db0c75SAndroid Build Coastguard Worker return static_cast<float>(multiply_add(p, lo2 * rr.mh, c0 * rr.mh));
136*71db0c75SAndroid Build Coastguard Worker }
137*71db0c75SAndroid Build Coastguard Worker
138*71db0c75SAndroid Build Coastguard Worker } // namespace generic
139*71db0c75SAndroid Build Coastguard Worker } // namespace LIBC_NAMESPACE_DECL
140*71db0c75SAndroid Build Coastguard Worker
141*71db0c75SAndroid Build Coastguard Worker #endif // LLVM_LIBC_SRC_MATH_GENERIC_EXP10F_IMPL_H
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