1//===-- Single-precision tanh 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/tanhf.h"
10#include "src/__support/FPUtil/FPBits.h"
11#include "src/__support/FPUtil/PolyEval.h"
12#include "src/__support/FPUtil/multiply_add.h"
13#include "src/__support/FPUtil/nearest_integer.h"
14#include "src/__support/macros/config.h"
15#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
16#include "src/__support/macros/properties/cpu_features.h"
17#include "src/math/generic/explogxf.h"
18
19namespace LIBC_NAMESPACE_DECL {
20
21// 2^6 * log2(e)
22constexpr double LOG2_E_EXP2_6 = ExpBase::LOG2_B * 2.0;
23
24LLVM_LIBC_FUNCTION(float, tanhf, (float x)) {
25 using FPBits = typename fputil::FPBits<float>;
26 FPBits xbits(x);
27 uint32_t x_abs = xbits.abs().uintval();
28
29 const int sign_index = xbits.is_neg() ? 1 : 0;
30
31 // When |x| >= 15, or x is inf or nan, or |x| <= 0.078125
32 if (LIBC_UNLIKELY((x_abs >= 0x4170'0000U) || (x_abs <= 0x3da0'0000U))) {
33 if (x_abs <= 0x3da0'0000U) {
34 // |x| <= 0.078125
35 if (LIBC_UNLIKELY(x_abs <= 0x3280'0000U)) {
36 // |x| <= 2^-26
37 return (x_abs != 0)
38 ? static_cast<float>(x - 0x1.5555555555555p-2 * x * x * x)
39 : x;
40 }
41
42 const double TAYLOR[] = {-0x1.5555555555555p-2, 0x1.1111111111111p-3,
43 -0x1.ba1ba1ba1ba1cp-5, 0x1.664f4882c10fap-6,
44 -0x1.226e355e6c23dp-7};
45 double xdbl = x;
46 double x2 = xdbl * xdbl;
47 // Taylor polynomial.
48 double x4 = x2 * x2;
49 double c0 = x2 * TAYLOR[0];
50 double c1 = fputil::multiply_add(x2, TAYLOR[2], TAYLOR[1]);
51 double c2 = fputil::multiply_add(x2, TAYLOR[4], TAYLOR[3]);
52 double pe = fputil::polyeval(x4, c0, c1, c2);
53
54 return static_cast<float>(fputil::multiply_add(xdbl, pe, xdbl));
55 }
56
57 // |x| >= 15
58 if (LIBC_UNLIKELY(xbits.is_nan()))
59 return x + 1.0f; // sNaN to qNaN + signal
60
61 constexpr float SIGNS[2][2] = {{1.0f, -0x1.0p-25f}, {-1.0f, 0x1.0p-25f}};
62
63 if (LIBC_UNLIKELY(xbits.is_inf()))
64 return SIGNS[sign_index][0];
65
66 return SIGNS[sign_index][0] + SIGNS[sign_index][1];
67 }
68
69 // Range reduction: e^(2x) = 2^(hi + mid) * e^lo
70 // Let k = round( x * 2^6 * log2(e)),
71 // So k = (hi + mid) * 2^5
72 // Then lo = 2x - (hi + mid) * log(2) = 2x - k * 2^-5 * log(2).
73
74 double xd = static_cast<double>(x);
75 // k = round( x* 2^6 * log2(e) )
76 double k;
77 // mk = -k
78 int mk;
79#ifdef LIBC_TARGET_CPU_HAS_NEAREST_INT
80 k = fputil::nearest_integer(xd * LOG2_E_EXP2_6);
81 mk = -static_cast<int>(k);
82#else
83 constexpr double HALF_WAY[2] = {-0.5, 0.5};
84
85 mk = static_cast<int>(
86 fputil::multiply_add(xd, -LOG2_E_EXP2_6, HALF_WAY[sign_index]));
87 k = static_cast<double>(-mk);
88#endif // LIBC_TARGET_CPU_HAS_NEAREST_INT
89 // -hi = floor(-k * 2^(-MID_BITS))
90 // exp_mhi = shift -hi to the exponent field of double precision.
91 int64_t exp_mhi = static_cast<int64_t>(mk >> ExpBase::MID_BITS)
92 << fputil::FPBits<double>::FRACTION_LEN;
93 // mh = 2^(-hi - mid)
94 int64_t mh_bits = ExpBase::EXP_2_MID[mk & ExpBase::MID_MASK] + exp_mhi;
95 double mh = fputil::FPBits<double>(uint64_t(mh_bits)).get_val();
96 // dx = lo/2 = x - (hi + mid) * log(2)/2 = x - k * 2^-6 * log(2)
97 double dx = fputil::multiply_add(
98 k, ExpBase::M_LOGB_2_LO * 0.5,
99 fputil::multiply_add(k, ExpBase::M_LOGB_2_HI * 0.5, xd));
100
101 // > P = fpminimax(expm1(2*x)/x, 4, [|D...|], [-log(2)/128, log(2)/128]);
102 constexpr double COEFFS[] = {0x1.ffffffffe5bc8p0, 0x1.555555555cd67p0,
103 0x1.5555c2a9b48b4p-1, 0x1.11112a0e34bdbp-2};
104
105 double dx2 = dx * dx;
106 double c0 = fputil::multiply_add(dx, 2.0, 1.0);
107 double c1 = fputil::multiply_add(dx, COEFFS[1], COEFFS[0]);
108 double c2 = fputil::multiply_add(dx, COEFFS[3], COEFFS[2]);
109 double r = fputil::polyeval(dx2, c0, c1, c2);
110
111 // tanh(x) = sinh(x) / cosh(x)
112 // = (e^x - e^(-x)) / (e^x + e^(-x))
113 // = (e^(2x) - 1) / (e^(2x) + 1)
114 // = (2^(hi + mid) * e^lo - 1) / (2^(hi + mid) * e^lo + 1)
115 // = (e^lo - 2^(-hi - mid)) / (e^lo + 2^(-hi - mid))
116 // = (r - mh) / (r + mh)
117 return static_cast<float>((r - mh) / (r + mh));
118}
119
120} // namespace LIBC_NAMESPACE_DECL
121

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