1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
|
//===-- Single-precision tanh function ------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
#include "src/math/tanhf.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
#include "src/math/generic/explogxf.h"
namespace __llvm_libc {
LLVM_LIBC_FUNCTION(float, tanhf, (float x)) {
using FPBits = typename fputil::FPBits<float>;
FPBits xbits(x);
bool sign = xbits.get_sign();
uint32_t x_abs = xbits.uintval() & FPBits::FloatProp::EXP_MANT_MASK;
// |x| <= 2^-26
if (LIBC_UNLIKELY(x_abs <= 0x3280'0000U)) {
return static_cast<float>(
LIBC_UNLIKELY(x_abs == 0) ? x : (x - 0x1.5555555555555p-2 * x * x * x));
}
// When |x| >= 15, or x is inf or nan
if (LIBC_UNLIKELY(x_abs >= 0x4170'0000U)) {
if (xbits.is_nan())
return x + 1.0f; // sNaN to qNaN + signal
if (xbits.is_inf())
return sign ? -1.0f : 1.0f;
if (sign) {
return -1.0f + opt_barrier(FPBits(FPBits::MIN_NORMAL).get_val());
} else
return 1.0f - opt_barrier(FPBits(FPBits::MIN_NORMAL).get_val());
}
// |x| <= 0.078125
if (LIBC_UNLIKELY(x_abs <= 0x3da0'0000U)) {
double xdbl = x;
double x2 = xdbl * xdbl;
// Pure Taylor series.
double pe = fputil::polyeval(x2, 0.0, -0x1.5555555555555p-2,
0x1.1111111111111p-3, -0x1.ba1ba1ba1ba1cp-5,
0x1.664f4882c10fap-6, -0x1.226e355e6c23dp-7);
return static_cast<float>(fputil::multiply_add(xdbl, pe, xdbl));
}
if (LIBC_UNLIKELY(xbits.bits == 0x4058'e0a3U)) {
if (fputil::get_round() == FE_DOWNWARD)
return FPBits(0x3f7f'6ad9U).get_val();
}
// Range reduction: e^(2x) = 2^(mid + hi) * e^lo
auto ep = exp_b_range_reduc<ExpBase>(2.0f * x); // exp(2 * x)
double r = ExpBase::powb_lo(ep.lo);
// tanh(x) = (exp(2x) - 1) / (exp(2x) + 1)
#if defined(LIBC_TARGET_CPU_HAS_FMA)
return static_cast<float>(fputil::multiply_add(ep.mh, r, -1.0) /
fputil::multiply_add(ep.mh, r, 1.0));
#else
double exp_x = ep.mh * r;
return static_cast<float>((exp_x - 1.0) / (exp_x + 1.0));
#endif // LIBC_TARGET_CPU_HAS_FMA
}
} // namespace __llvm_libc
|
