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/* Ergo, version 3.8.2, a program for linear scaling electronic structure
* calculations.
* Copyright (C) 2023 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:
* Ergo: An open-source program for linear-scaling electronic structure
* calculations,
* Elias Rudberg, Emanuel H. Rubensson, Pawel Salek, and Anastasia
* Kruchinina,
* SoftwareX 7, 107 (2018),
* <http://dx.doi.org/10.1016/j.softx.2018.03.005>
*
* For further information about Ergo, see <http://www.ergoscf.org>.
*/
/* This file belongs to the template_lapack part of the Ergo source
* code. The source files in the template_lapack directory are modified
* versions of files originally distributed as CLAPACK, see the
* Copyright/license notice in the file template_lapack/COPYING.
*/
#ifndef TEMPLATE_BLAS_BASICMATH_HEADER
#define TEMPLATE_BLAS_BASICMATH_HEADER
#include "template_blas_num_limits.h"
template<class Treal>
Treal template_blas_fabs(Treal x);
template<class Treal>
Treal template_blas_sqrt(Treal x);
template<class Treal>
Treal template_blas_exp(Treal x);
template<class Treal>
Treal template_blas_log(Treal x);
template<class Treal>
Treal template_blas_log10(Treal x);
template<class Treal>
Treal template_blas_erf(Treal x);
template<class Treal>
Treal template_blas_erfc(Treal x);
template<class Treal>
Treal template_blas_sin(Treal x);
template<class Treal>
Treal template_blas_cos(Treal x);
template<class Treal>
Treal template_blas_pow(Treal x, Treal y);
/* template_blas_compute_pi_BBP
This routine computes the number pi up to the precision of Treal
using the BBP formula. */
template<class Treal>
Treal template_blas_compute_pi_BBP(Treal dummy)
{
Treal epsilon = template_blas_get_machine_epsilon<Treal>();
Treal one_over_16 = (Treal)1 / (Treal)16;
Treal one_over_16_to_pow_k = 1;
Treal sum = 0;
int k = 0;
do
{
Treal factor =
(Treal)4 / (Treal)(8*k + 1) -
(Treal)2 / (Treal)(8*k + 4) -
(Treal)1 / (Treal)(8*k + 5) -
(Treal)1 / (Treal)(8*k + 6);
sum += one_over_16_to_pow_k * factor;
k++;
one_over_16_to_pow_k *= one_over_16;
}
while(one_over_16_to_pow_k > epsilon);
return sum;
}
#endif
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