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/* Ergo, version 3.5, a program for linear scaling electronic structure
* calculations.
* Copyright (C) 2016 Elias Rudberg, Emanuel H. Rubensson, Pawel Salek,
* and Anastasia Kruchinina.
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU 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 General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*
* Primary academic reference:
* KohnâSham Density Functional Theory Electronic Structure Calculations
* with Linearly Scaling Computational Time and Memory Usage,
* Elias Rudberg, Emanuel H. Rubensson, and Pawel Salek,
* J. Chem. Theory Comput. 7, 340 (2011),
* <http://dx.doi.org/10.1021/ct100611z>
*
* For further information about Ergo, see <http://www.ergoscf.org>.
*/
/** @file basicmath_test.cc Tests some basic math functions
such as template_blas_sqrt() template_blas_log() etc to
see that they are working properly and that they deliver
the expected accuracy. */
#include <stdio.h>
#include <stdlib.h>
#include <limits>
#include "realtype.h"
#include "template_blas_common.h"
int main(int argc, char *argv[])
{
int failed = 0;
int verbose = getenv("VERBOSE") != NULL;
ergo_real machine_epsilon = std::numeric_limits<ergo_real>::epsilon();
printf("machine_epsilon = %g Run with env VERBOSE for more info.\n",
(double)machine_epsilon);
/* Test sqrt function for a set of random numbers. */
ergo_real maxabsdiff_sqrt = 0;
for(int i = 0; i < 7777; i++)
{
ergo_real x = (ergo_real)rand() / RAND_MAX;
ergo_real x2 = x * x;
ergo_real sqrt_of_x2 = template_blas_sqrt(x2);
ergo_real diff = sqrt_of_x2 - x;
ergo_real absdiff = diff;
if(absdiff < 0)
absdiff *= -1;
if(absdiff > maxabsdiff_sqrt)
maxabsdiff_sqrt = absdiff;
}
if(verbose)
printf("maxabsdiff for template_blas_sqrt: %g\n",
(double)maxabsdiff_sqrt);
ergo_real maxabsdiff_sqrt_requested = machine_epsilon;
if(maxabsdiff_sqrt > maxabsdiff_sqrt_requested)
{
printf("ERROR: template_blas_sqrt() not accurate enough!\n");
printf("maxabsdiff_sqrt: %g, requested: %g\n", (double)maxabsdiff_sqrt, (double)maxabsdiff_sqrt_requested);
failed++;
}
else {
if(verbose)
printf("template_blas_sqrt() accuracy OK.\n");
}
/* Test exp function by computing exp(a)*exp(b) and comparing to exp(a+b) for a list of random pairs (a,b) */
ergo_real maxabsdiff_exp = 0;
for(int i = 0; i < 7777; i++)
{
ergo_real a = (ergo_real)rand() / RAND_MAX;
ergo_real b = (ergo_real)rand() / RAND_MAX;
ergo_real product_of_exps = template_blas_exp(a) * template_blas_exp(b);
ergo_real exp_of_sum = template_blas_exp(a + b);
ergo_real diff = product_of_exps - exp_of_sum;
ergo_real absdiff = diff;
if(absdiff < 0)
absdiff *= -1;
if(absdiff > maxabsdiff_exp)
maxabsdiff_exp = absdiff;
}
if(verbose)
printf("maxabsdiff for template_blas_exp: %g\n", (double)maxabsdiff_exp);
ergo_real maxabsdiff_exp_requested = machine_epsilon * 15;
if(maxabsdiff_exp > maxabsdiff_exp_requested)
{
printf("ERROR: template_blas_exp() not accurate enough!\n");
printf("maxabsdiff_exp: %g, requested: %g\n", (double)maxabsdiff_exp, (double)maxabsdiff_exp_requested);
failed++;
}
else {
if(verbose)
printf("template_blas_exp() accuracy OK.\n");
}
/* Test log function by computing log(a) + log(b) and comparing to log(a*b) for a list of random pairs (a,b) */
ergo_real maxabsdiff_log = 0;
for(int i = 0; i < 7777; i++)
{
ergo_real a = (ergo_real)rand() / RAND_MAX;
ergo_real b = (ergo_real)rand() / RAND_MAX;
ergo_real sum_of_logs = template_blas_log(a) + template_blas_log(b);
ergo_real log_of_product = template_blas_log(a * b);
ergo_real diff = sum_of_logs - log_of_product;
ergo_real absdiff = diff;
if(absdiff < 0)
absdiff *= -1;
if(absdiff > maxabsdiff_log)
maxabsdiff_log = absdiff;
}
if(verbose)
printf("maxabsdiff for template_blas_log: %g\n", (double)maxabsdiff_log);
ergo_real maxabsdiff_log_requested = machine_epsilon * 10;
if(maxabsdiff_log > maxabsdiff_log_requested)
{
printf("ERROR: template_blas_log() not accurate enough!\n");
printf("maxabsdiff_log: %g, requested: %g\n", (double)maxabsdiff_log, (double)maxabsdiff_log_requested);
failed++;
}
else {
if(verbose)
printf("template_blas_log() accuracy OK.\n");
}
/* Test erf function by comparing with a series expression */
ergo_real piBBP = template_blas_compute_pi_BBP((ergo_real)0);
ergo_real maxabsdiff_erf = 0;
for(int i = 0; i < 777; i++)
{
ergo_real x = (ergo_real)rand() / RAND_MAX;
ergo_real minus_1_to_pow_n = 1;
ergo_real n_factorial = 1;
ergo_real x_to_pow_2n_plus_1 = x;
int n = 0;
ergo_real sum = 0;
while(((ergo_real)1 / n_factorial) > machine_epsilon)
{
sum += (minus_1_to_pow_n / ( n_factorial * (ergo_real)( 2 * n + 1) )) * x_to_pow_2n_plus_1;
n++;
minus_1_to_pow_n *= -1;
n_factorial *= n;
x_to_pow_2n_plus_1 *= x * x;
}
ergo_real series_result = ((ergo_real)2 / template_blas_sqrt(piBBP)) * sum;
ergo_real erf_value = template_blas_erf(x);
ergo_real diff = series_result - erf_value;
ergo_real absdiff = diff;
if(absdiff < 0)
absdiff *= -1;
if(absdiff > maxabsdiff_erf)
maxabsdiff_erf = absdiff;
} // END FOR i
if(verbose)
printf("maxabsdiff for template_blas_erf: %g\n", (double)maxabsdiff_erf);
ergo_real maxabsdiff_erf_requested = machine_epsilon * 5;
if(maxabsdiff_erf > maxabsdiff_erf_requested)
{
printf("ERROR: template_blas_erf() not accurate enough!\n");
printf("maxabsdiff_erf: %g, requested: %g\n", (double)maxabsdiff_erf, (double)maxabsdiff_erf_requested);
failed++;
}
else {
if(verbose)
printf("template_blas_erf() accuracy OK.\n");
}
/* Test erfc function by computing erf(x) + erfc(x) and comparing to 1 */
ergo_real maxabsdiff_erfc = 0;
for(int i = 0; i < 777; i++)
{
ergo_real x = (ergo_real)rand() / RAND_MAX;
ergo_real erf_of_x = template_blas_erf(x);
ergo_real erfc_of_x = template_blas_erfc(x);
ergo_real sum = erf_of_x + erfc_of_x;
ergo_real diff = sum - (ergo_real)1.0;
ergo_real absdiff = diff;
if(absdiff < 0)
absdiff *= -1;
if(absdiff > maxabsdiff_erfc)
maxabsdiff_erfc = absdiff;
} // END FOR i
if(verbose)
printf("maxabsdiff for template_blas_erfc: %g\n", (double)maxabsdiff_erfc);
ergo_real maxabsdiff_erfc_requested = machine_epsilon * 1;
if(maxabsdiff_erfc > maxabsdiff_erfc_requested)
{
printf("ERROR: template_blas_erfc() not accurate enough!\n");
printf("maxabsdiff_erfc: %g, requested: %g\n", (double)maxabsdiff_erfc, (double)maxabsdiff_erfc_requested);
failed++;
}
else {
if(verbose)
printf("template_blas_erfc() accuracy OK.\n");
}
if (!failed)
puts("Basic math functions test succeeded.");
else
puts("Basic math functions test FAILED.");
return failed;
}
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