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//===-- 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/FPUtil/PolyEval.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/FPUtil/nearest_integer.h"
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
#include "src/__support/macros/properties/cpu_features.h"
#include "src/math/generic/explogxf.h"
namespace LIBC_NAMESPACE_DECL {
// 2^6 * log2(e)
constexpr double LOG2_E_EXP2_6 = ExpBase::LOG2_B * 2.0;
LLVM_LIBC_FUNCTION(float, tanhf, (float x)) {
using FPBits = typename fputil::FPBits<float>;
FPBits xbits(x);
uint32_t x_abs = xbits.abs().uintval();
const int sign_index = xbits.is_neg() ? 1 : 0;
// When |x| >= 15, or x is inf or nan, or |x| <= 0.078125
if (LIBC_UNLIKELY((x_abs >= 0x4170'0000U) || (x_abs <= 0x3da0'0000U))) {
if (x_abs <= 0x3da0'0000U) {
// |x| <= 0.078125
if (LIBC_UNLIKELY(x_abs <= 0x3280'0000U)) {
// |x| <= 2^-26
return (x_abs != 0)
? static_cast<float>(x - 0x1.5555555555555p-2 * x * x * x)
: x;
}
const double TAYLOR[] = {-0x1.5555555555555p-2, 0x1.1111111111111p-3,
-0x1.ba1ba1ba1ba1cp-5, 0x1.664f4882c10fap-6,
-0x1.226e355e6c23dp-7};
double xdbl = x;
double x2 = xdbl * xdbl;
// Taylor polynomial.
double x4 = x2 * x2;
double c0 = x2 * TAYLOR[0];
double c1 = fputil::multiply_add(x2, TAYLOR[2], TAYLOR[1]);
double c2 = fputil::multiply_add(x2, TAYLOR[4], TAYLOR[3]);
double pe = fputil::polyeval(x4, c0, c1, c2);
return static_cast<float>(fputil::multiply_add(xdbl, pe, xdbl));
}
// |x| >= 15
if (LIBC_UNLIKELY(xbits.is_nan()))
return x + 1.0f; // sNaN to qNaN + signal
constexpr float SIGNS[2][2] = {{1.0f, -0x1.0p-25f}, {-1.0f, 0x1.0p-25f}};
if (LIBC_UNLIKELY(xbits.is_inf()))
return SIGNS[sign_index][0];
return SIGNS[sign_index][0] + SIGNS[sign_index][1];
}
// Range reduction: e^(2x) = 2^(hi + mid) * e^lo
// Let k = round( x * 2^6 * log2(e)),
// So k = (hi + mid) * 2^5
// Then lo = 2x - (hi + mid) * log(2) = 2x - k * 2^-5 * log(2).
double xd = static_cast<double>(x);
// k = round( x* 2^6 * log2(e) )
double k;
// mk = -k
int mk;
#ifdef LIBC_TARGET_CPU_HAS_NEAREST_INT
k = fputil::nearest_integer(xd * LOG2_E_EXP2_6);
mk = -static_cast<int>(k);
#else
constexpr double HALF_WAY[2] = {-0.5, 0.5};
mk = static_cast<int>(
fputil::multiply_add(xd, -LOG2_E_EXP2_6, HALF_WAY[sign_index]));
k = static_cast<double>(-mk);
#endif // LIBC_TARGET_CPU_HAS_NEAREST_INT
// -hi = floor(-k * 2^(-MID_BITS))
// exp_mhi = shift -hi to the exponent field of double precision.
int64_t exp_mhi = static_cast<int64_t>(mk >> ExpBase::MID_BITS)
<< fputil::FPBits<double>::FRACTION_LEN;
// mh = 2^(-hi - mid)
int64_t mh_bits = ExpBase::EXP_2_MID[mk & ExpBase::MID_MASK] + exp_mhi;
double mh = fputil::FPBits<double>(uint64_t(mh_bits)).get_val();
// dx = lo/2 = x - (hi + mid) * log(2)/2 = x - k * 2^-6 * log(2)
double dx = fputil::multiply_add(
k, ExpBase::M_LOGB_2_LO * 0.5,
fputil::multiply_add(k, ExpBase::M_LOGB_2_HI * 0.5, xd));
// > P = fpminimax(expm1(2*x)/x, 4, [|D...|], [-log(2)/128, log(2)/128]);
constexpr double COEFFS[] = {0x1.ffffffffe5bc8p0, 0x1.555555555cd67p0,
0x1.5555c2a9b48b4p-1, 0x1.11112a0e34bdbp-2};
double dx2 = dx * dx;
double c0 = fputil::multiply_add(dx, 2.0, 1.0);
double c1 = fputil::multiply_add(dx, COEFFS[1], COEFFS[0]);
double c2 = fputil::multiply_add(dx, COEFFS[3], COEFFS[2]);
double r = fputil::polyeval(dx2, c0, c1, c2);
// tanh(x) = sinh(x) / cosh(x)
// = (e^x - e^(-x)) / (e^x + e^(-x))
// = (e^(2x) - 1) / (e^(2x) + 1)
// = (2^(hi + mid) * e^lo - 1) / (2^(hi + mid) * e^lo + 1)
// = (e^lo - 2^(-hi - mid)) / (e^lo + 2^(-hi - mid))
// = (r - mh) / (r + mh)
return static_cast<float>((r - mh) / (r + mh));
}
} // namespace LIBC_NAMESPACE_DECL
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