/*******************************************************************************
* This file is part of SWIFT.
* Copyright (C) 2020 Matthieu Schaller (schaller@strw.leidenuniv.nl)
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published
* by the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program. If not, see .
*
******************************************************************************/
#include
/* Local includes. */
#include "swift.h"
/* Standard includes */
#include
#include
/**
* Compute erfcf(u) using eq. 7.1.26 of
* Abramowitz & Stegun, 1972.
*
* This has a *relative* error of less than 3.4e-3 over
* the range of interest (0 < x < 5)
*/
float optimized_erfcf(const float x) {
const float x2 = x * x;
const float exp_x2 = expf(-x2);
const float t = 1.f / (1.f + 0.3275911f * x);
const float a1 = 0.254829592f;
const float a2 = -0.284496736f;
const float a3 = 1.421413741f;
const float a4 = -1.453152027;
const float a5 = 1.061405429f;
/* a1 * t + a2 * t^2 + a3 * t^3 + a4 * t^4 + a5 * t^5 */
float a = a5 * t + a4;
a = a * t + a3;
a = a * t + a2;
a = a * t + a1;
a = a * t;
return a * exp_x2;
}
/**
* @brief Check that a and b are consistent (up to some relative error)
*
* @param a First value
* @param b Second value
* @param rel_tol Relative tolerance
* @param abs_tol Absolute tolerance
* @param x Value for which we tested the function (for error messages)
*/
void check_value(const double a, const double b, const double rel_tol,
const double abs_tol, const double x) {
if (fabs(a - b) / fabs(a + b) > rel_tol)
error("Values are inconsistent: %12.15e %12.15e rel=%e (for x=%e).", a, b,
fabs(a - b) / fabs(a + b), x);
if (fabs(a - b) > abs_tol)
error("Values are inconsistent: %12.15e %12.15e abs=%e (for x=%e).", a, b,
fabs(a - b), x);
}
int main(int argc, char* argv[]) {
/* Initialize CPU frequency, this also starts time. */
unsigned long long cpufreq = 0;
clocks_set_cpufreq(cpufreq);
/* Choke on FPEs */
#ifdef HAVE_FE_ENABLE_EXCEPT
feenableexcept(FE_DIVBYZERO | FE_INVALID | FE_OVERFLOW);
#endif
/* Loop over some values */
for (float x = 0.f; x < 5.f; x += 0.000001f) {
const double exact = erfc(x);
const double swift_erfcf = optimized_erfcf(x);
check_value(exact, swift_erfcf, 3.358e-3, 6.1e-7, x);
}
return 0;
}