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/* clartg.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Subroutine */ int clartg_(complex *f, complex *g, real *cs, complex *sn,
complex *r__)
{
/* System generated locals */
integer i__1;
real r__1, r__2, r__3, r__4, r__5, r__6, r__7, r__8, r__9, r__10;
complex q__1, q__2, q__3;
/* Builtin functions */
double log(doublereal), pow_ri(real *, integer *), r_imag(complex *),
sqrt(doublereal);
void r_cnjg(complex *, complex *);
/* Local variables */
real d__;
integer i__;
real f2, g2;
complex ff;
real di, dr;
complex fs, gs;
real f2s, g2s, eps, scale;
integer count;
real safmn2, safmx2;
extern doublereal slapy2_(real *, real *), slamch_(char *);
real safmin;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CLARTG generates a plane rotation so that */
/* [ CS SN ] [ F ] [ R ] */
/* [ __ ] . [ ] = [ ] where CS**2 + |SN|**2 = 1. */
/* [ -SN CS ] [ G ] [ 0 ] */
/* This is a faster version of the BLAS1 routine CROTG, except for */
/* the following differences: */
/* F and G are unchanged on return. */
/* If G=0, then CS=1 and SN=0. */
/* If F=0, then CS=0 and SN is chosen so that R is real. */
/* Arguments */
/* ========= */
/* F (input) COMPLEX */
/* The first component of vector to be rotated. */
/* G (input) COMPLEX */
/* The second component of vector to be rotated. */
/* CS (output) REAL */
/* The cosine of the rotation. */
/* SN (output) COMPLEX */
/* The sine of the rotation. */
/* R (output) COMPLEX */
/* The nonzero component of the rotated vector. */
/* Further Details */
/* ======= ======= */
/* 3-5-96 - Modified with a new algorithm by W. Kahan and J. Demmel */
/* This version has a few statements commented out for thread safety */
/* (machine parameters are computed on each entry). 10 feb 03, SJH. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* LOGICAL FIRST */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Save statement .. */
/* SAVE FIRST, SAFMX2, SAFMIN, SAFMN2 */
/* .. */
/* .. Data statements .. */
/* DATA FIRST / .TRUE. / */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* IF( FIRST ) THEN */
safmin = slamch_("S");
eps = slamch_("E");
r__1 = slamch_("B");
i__1 = (integer) (log(safmin / eps) / log(slamch_("B")) / 2.f);
safmn2 = pow_ri(&r__1, &i__1);
safmx2 = 1.f / safmn2;
/* FIRST = .FALSE. */
/* END IF */
/* Computing MAX */
/* Computing MAX */
r__7 = (r__1 = f->r, dabs(r__1)), r__8 = (r__2 = r_imag(f), dabs(r__2));
/* Computing MAX */
r__9 = (r__3 = g->r, dabs(r__3)), r__10 = (r__4 = r_imag(g), dabs(r__4));
r__5 = dmax(r__7,r__8), r__6 = dmax(r__9,r__10);
scale = dmax(r__5,r__6);
fs.r = f->r, fs.i = f->i;
gs.r = g->r, gs.i = g->i;
count = 0;
if (scale >= safmx2) {
L10:
++count;
q__1.r = safmn2 * fs.r, q__1.i = safmn2 * fs.i;
fs.r = q__1.r, fs.i = q__1.i;
q__1.r = safmn2 * gs.r, q__1.i = safmn2 * gs.i;
gs.r = q__1.r, gs.i = q__1.i;
scale *= safmn2;
if (scale >= safmx2) {
goto L10;
}
} else if (scale <= safmn2) {
if (g->r == 0.f && g->i == 0.f) {
*cs = 1.f;
sn->r = 0.f, sn->i = 0.f;
r__->r = f->r, r__->i = f->i;
return 0;
}
L20:
--count;
q__1.r = safmx2 * fs.r, q__1.i = safmx2 * fs.i;
fs.r = q__1.r, fs.i = q__1.i;
q__1.r = safmx2 * gs.r, q__1.i = safmx2 * gs.i;
gs.r = q__1.r, gs.i = q__1.i;
scale *= safmx2;
if (scale <= safmn2) {
goto L20;
}
}
/* Computing 2nd power */
r__1 = fs.r;
/* Computing 2nd power */
r__2 = r_imag(&fs);
f2 = r__1 * r__1 + r__2 * r__2;
/* Computing 2nd power */
r__1 = gs.r;
/* Computing 2nd power */
r__2 = r_imag(&gs);
g2 = r__1 * r__1 + r__2 * r__2;
if (f2 <= dmax(g2,1.f) * safmin) {
/* This is a rare case: F is very small. */
if (f->r == 0.f && f->i == 0.f) {
*cs = 0.f;
r__2 = g->r;
r__3 = r_imag(g);
r__1 = slapy2_(&r__2, &r__3);
r__->r = r__1, r__->i = 0.f;
/* Do complex/real division explicitly with two real divisions */
r__1 = gs.r;
r__2 = r_imag(&gs);
d__ = slapy2_(&r__1, &r__2);
r__1 = gs.r / d__;
r__2 = -r_imag(&gs) / d__;
q__1.r = r__1, q__1.i = r__2;
sn->r = q__1.r, sn->i = q__1.i;
return 0;
}
r__1 = fs.r;
r__2 = r_imag(&fs);
f2s = slapy2_(&r__1, &r__2);
/* G2 and G2S are accurate */
/* G2 is at least SAFMIN, and G2S is at least SAFMN2 */
g2s = sqrt(g2);
/* Error in CS from underflow in F2S is at most */
/* UNFL / SAFMN2 .lt. sqrt(UNFL*EPS) .lt. EPS */
/* If MAX(G2,ONE)=G2, then F2 .lt. G2*SAFMIN, */
/* and so CS .lt. sqrt(SAFMIN) */
/* If MAX(G2,ONE)=ONE, then F2 .lt. SAFMIN */
/* and so CS .lt. sqrt(SAFMIN)/SAFMN2 = sqrt(EPS) */
/* Therefore, CS = F2S/G2S / sqrt( 1 + (F2S/G2S)**2 ) = F2S/G2S */
*cs = f2s / g2s;
/* Make sure abs(FF) = 1 */
/* Do complex/real division explicitly with 2 real divisions */
/* Computing MAX */
r__3 = (r__1 = f->r, dabs(r__1)), r__4 = (r__2 = r_imag(f), dabs(r__2)
);
if (dmax(r__3,r__4) > 1.f) {
r__1 = f->r;
r__2 = r_imag(f);
d__ = slapy2_(&r__1, &r__2);
r__1 = f->r / d__;
r__2 = r_imag(f) / d__;
q__1.r = r__1, q__1.i = r__2;
ff.r = q__1.r, ff.i = q__1.i;
} else {
dr = safmx2 * f->r;
di = safmx2 * r_imag(f);
d__ = slapy2_(&dr, &di);
r__1 = dr / d__;
r__2 = di / d__;
q__1.r = r__1, q__1.i = r__2;
ff.r = q__1.r, ff.i = q__1.i;
}
r__1 = gs.r / g2s;
r__2 = -r_imag(&gs) / g2s;
q__2.r = r__1, q__2.i = r__2;
q__1.r = ff.r * q__2.r - ff.i * q__2.i, q__1.i = ff.r * q__2.i + ff.i
* q__2.r;
sn->r = q__1.r, sn->i = q__1.i;
q__2.r = *cs * f->r, q__2.i = *cs * f->i;
q__3.r = sn->r * g->r - sn->i * g->i, q__3.i = sn->r * g->i + sn->i *
g->r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
r__->r = q__1.r, r__->i = q__1.i;
} else {
/* This is the most common case. */
/* Neither F2 nor F2/G2 are less than SAFMIN */
/* F2S cannot overflow, and it is accurate */
f2s = sqrt(g2 / f2 + 1.f);
/* Do the F2S(real)*FS(complex) multiply with two real multiplies */
r__1 = f2s * fs.r;
r__2 = f2s * r_imag(&fs);
q__1.r = r__1, q__1.i = r__2;
r__->r = q__1.r, r__->i = q__1.i;
*cs = 1.f / f2s;
d__ = f2 + g2;
/* Do complex/real division explicitly with two real divisions */
r__1 = r__->r / d__;
r__2 = r_imag(r__) / d__;
q__1.r = r__1, q__1.i = r__2;
sn->r = q__1.r, sn->i = q__1.i;
r_cnjg(&q__2, &gs);
q__1.r = sn->r * q__2.r - sn->i * q__2.i, q__1.i = sn->r * q__2.i +
sn->i * q__2.r;
sn->r = q__1.r, sn->i = q__1.i;
if (count != 0) {
if (count > 0) {
i__1 = count;
for (i__ = 1; i__ <= i__1; ++i__) {
q__1.r = safmx2 * r__->r, q__1.i = safmx2 * r__->i;
r__->r = q__1.r, r__->i = q__1.i;
/* L30: */
}
} else {
i__1 = -count;
for (i__ = 1; i__ <= i__1; ++i__) {
q__1.r = safmn2 * r__->r, q__1.i = safmn2 * r__->i;
r__->r = q__1.r, r__->i = q__1.i;
/* L40: */
}
}
}
}
return 0;
/* End of CLARTG */
} /* clartg_ */
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