File: template_lapack_lartg.h

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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_LAPACK_LARTG_HEADER
#define TEMPLATE_LAPACK_LARTG_HEADER


template<class Treal>
int template_lapack_lartg(const Treal *f, const Treal *g, Treal *cs, 
	Treal *sn, Treal *r__)
{
/*  -- LAPACK auxiliary routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       September 30, 1994   


    Purpose   
    =======   

    DLARTG generate a plane rotation so that   

       [  CS  SN  ]  .  [ F ]  =  [ R ]   where CS**2 + SN**2 = 1.   
       [ -SN  CS  ]     [ G ]     [ 0 ]   

    This is a slower, more accurate version of the BLAS1 routine DROTG,   
    with the following other differences:   
       F and G are unchanged on return.   
       If G=0, then CS=1 and SN=0.   
       If F=0 and (G .ne. 0), then CS=0 and SN=1 without doing any   
          floating point operations (saves work in DBDSQR when   
          there are zeros on the diagonal).   

    If F exceeds G in magnitude, CS will be positive.   

    Arguments   
    =========   

    F       (input) DOUBLE PRECISION   
            The first component of vector to be rotated.   

    G       (input) DOUBLE PRECISION   
            The second component of vector to be rotated.   

    CS      (output) DOUBLE PRECISION   
            The cosine of the rotation.   

    SN      (output) DOUBLE PRECISION   
            The sine of the rotation.   

    R       (output) DOUBLE PRECISION   
            The nonzero component of the rotated vector.   

    ===================================================================== */
    /* Initialized data */
     logical first = TRUE_;
    /* System generated locals */
    integer i__1;
    Treal d__1, d__2;
    /* Local variables */
     integer i__;
     Treal scale;
     integer count;
     Treal f1, g1, safmn2, safmx2;
     Treal safmin, eps;



    if (first) {
	first = FALSE_;
	safmin = template_lapack_lamch("S", (Treal)0);
	eps = template_lapack_lamch("E", (Treal)0);
	d__1 = template_lapack_lamch("B", (Treal)0);
	i__1 = (integer) (template_blas_log(safmin / eps) / template_blas_log(template_lapack_lamch("B", (Treal)0)) / 
		2.);
	safmn2 = template_lapack_pow_di(&d__1, &i__1);
	safmx2 = 1. / safmn2;
    }
    if (*g == 0.) {
	*cs = 1.;
	*sn = 0.;
	*r__ = *f;
    } else if (*f == 0.) {
	*cs = 0.;
	*sn = 1.;
	*r__ = *g;
    } else {
	f1 = *f;
	g1 = *g;
/* Computing MAX */
	d__1 = absMACRO(f1), d__2 = absMACRO(g1);
	scale = maxMACRO(d__1,d__2);
	if (scale >= safmx2) {
	    count = 0;
L10:
	    ++count;
	    f1 *= safmn2;
	    g1 *= safmn2;
/* Computing MAX */
	    d__1 = absMACRO(f1), d__2 = absMACRO(g1);
	    scale = maxMACRO(d__1,d__2);
	    if (scale >= safmx2) {
		goto L10;
	    }
/* Computing 2nd power */
	    d__1 = f1;
/* Computing 2nd power */
	    d__2 = g1;
	    *r__ = template_blas_sqrt(d__1 * d__1 + d__2 * d__2);
	    *cs = f1 / *r__;
	    *sn = g1 / *r__;
	    i__1 = count;
	    for (i__ = 1; i__ <= i__1; ++i__) {
		*r__ *= safmx2;
/* L20: */
	    }
	} else if (scale <= safmn2) {
	    count = 0;
L30:
	    ++count;
	    f1 *= safmx2;
	    g1 *= safmx2;
/* Computing MAX */
	    d__1 = absMACRO(f1), d__2 = absMACRO(g1);
	    scale = maxMACRO(d__1,d__2);
	    if (scale <= safmn2) {
		goto L30;
	    }
/* Computing 2nd power */
	    d__1 = f1;
/* Computing 2nd power */
	    d__2 = g1;
	    *r__ = template_blas_sqrt(d__1 * d__1 + d__2 * d__2);
	    *cs = f1 / *r__;
	    *sn = g1 / *r__;
	    i__1 = count;
	    for (i__ = 1; i__ <= i__1; ++i__) {
		*r__ *= safmn2;
/* L40: */
	    }
	} else {
/* Computing 2nd power */
	    d__1 = f1;
/* Computing 2nd power */
	    d__2 = g1;
	    *r__ = template_blas_sqrt(d__1 * d__1 + d__2 * d__2);
	    *cs = f1 / *r__;
	    *sn = g1 / *r__;
	}
	if (absMACRO(*f) > absMACRO(*g) && *cs < 0.) {
	    *cs = -(*cs);
	    *sn = -(*sn);
	    *r__ = -(*r__);
	}
    }
    return 0;

/*     End of DLARTG */

} /* dlartg_ */

#endif