zlartg.c

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/* zlartg.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 zlartg_(doublecomplex *f, doublecomplex *g, doublereal *
        cs, doublecomplex *sn, doublecomplex *r__)
{
    /* System generated locals */
    integer i__1;
    doublereal d__1, d__2, d__3, d__4, d__5, d__6, d__7, d__8, d__9, d__10;
    doublecomplex z__1, z__2, z__3;

    /* Builtin functions */
    double log(doublereal), pow_di(doublereal *, integer *), d_imag(
            doublecomplex *), sqrt(doublereal);
    void d_cnjg(doublecomplex *, doublecomplex *);

    /* Local variables */
    doublereal d__;
    integer i__;
    doublereal f2, g2;
    doublecomplex ff;
    doublereal di, dr;
    doublecomplex fs, gs;
    doublereal f2s, g2s, eps, scale;
    integer count;
    doublereal safmn2;
    extern doublereal dlapy2_(doublereal *, doublereal *);
    doublereal safmx2;
    extern doublereal dlamch_(char *);
    doublereal safmin;


/*  -- LAPACK auxiliary routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  ZLARTG 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 ZROTG, 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*16 */
/*          The first component of vector to be rotated. */

/*  G       (input) COMPLEX*16 */
/*          The second component of vector to be rotated. */

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

/*  SN      (output) COMPLEX*16 */
/*          The sine of the rotation. */

/*  R       (output) COMPLEX*16 */
/*          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 = dlamch_("S");
    eps = dlamch_("E");
    d__1 = dlamch_("B");
    i__1 = (integer) (log(safmin / eps) / log(dlamch_("B")) / 2.);
    safmn2 = pow_di(&d__1, &i__1);
    safmx2 = 1. / safmn2;
/*        FIRST = .FALSE. */
/*     END IF */
/* Computing MAX */
/* Computing MAX */
    d__7 = (d__1 = f->r, abs(d__1)), d__8 = (d__2 = d_imag(f), abs(d__2));
/* Computing MAX */
    d__9 = (d__3 = g->r, abs(d__3)), d__10 = (d__4 = d_imag(g), abs(d__4));
    d__5 = max(d__7,d__8), d__6 = max(d__9,d__10);
    scale = max(d__5,d__6);
    fs.r = f->r, fs.i = f->i;
    gs.r = g->r, gs.i = g->i;
    count = 0;
    if (scale >= safmx2) {
L10:
        ++count;
        z__1.r = safmn2 * fs.r, z__1.i = safmn2 * fs.i;
        fs.r = z__1.r, fs.i = z__1.i;
        z__1.r = safmn2 * gs.r, z__1.i = safmn2 * gs.i;
        gs.r = z__1.r, gs.i = z__1.i;
        scale *= safmn2;
        if (scale >= safmx2) {
            goto L10;
        }
    } else if (scale <= safmn2) {
        if (g->r == 0. && g->i == 0.) {
            *cs = 1.;
            sn->r = 0., sn->i = 0.;
            r__->r = f->r, r__->i = f->i;
            return 0;
        }
L20:
        --count;
        z__1.r = safmx2 * fs.r, z__1.i = safmx2 * fs.i;
        fs.r = z__1.r, fs.i = z__1.i;
        z__1.r = safmx2 * gs.r, z__1.i = safmx2 * gs.i;
        gs.r = z__1.r, gs.i = z__1.i;
        scale *= safmx2;
        if (scale <= safmn2) {
            goto L20;
        }
    }
/* Computing 2nd power */
    d__1 = fs.r;
/* Computing 2nd power */
    d__2 = d_imag(&fs);
    f2 = d__1 * d__1 + d__2 * d__2;
/* Computing 2nd power */
    d__1 = gs.r;
/* Computing 2nd power */
    d__2 = d_imag(&gs);
    g2 = d__1 * d__1 + d__2 * d__2;
    if (f2 <= max(g2,1.) * safmin) {

/*        This is a rare case: F is very small. */

        if (f->r == 0. && f->i == 0.) {
            *cs = 0.;
            d__2 = g->r;
            d__3 = d_imag(g);
            d__1 = dlapy2_(&d__2, &d__3);
            r__->r = d__1, r__->i = 0.;
/*           Do complex/real division explicitly with two real divisions */
            d__1 = gs.r;
            d__2 = d_imag(&gs);
            d__ = dlapy2_(&d__1, &d__2);
            d__1 = gs.r / d__;
            d__2 = -d_imag(&gs) / d__;
            z__1.r = d__1, z__1.i = d__2;
            sn->r = z__1.r, sn->i = z__1.i;
            return 0;
        }
        d__1 = fs.r;
        d__2 = d_imag(&fs);
        f2s = dlapy2_(&d__1, &d__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 */
        d__3 = (d__1 = f->r, abs(d__1)), d__4 = (d__2 = d_imag(f), abs(d__2));
        if (max(d__3,d__4) > 1.) {
            d__1 = f->r;
            d__2 = d_imag(f);
            d__ = dlapy2_(&d__1, &d__2);
            d__1 = f->r / d__;
            d__2 = d_imag(f) / d__;
            z__1.r = d__1, z__1.i = d__2;
            ff.r = z__1.r, ff.i = z__1.i;
        } else {
            dr = safmx2 * f->r;
            di = safmx2 * d_imag(f);
            d__ = dlapy2_(&dr, &di);
            d__1 = dr / d__;
            d__2 = di / d__;
            z__1.r = d__1, z__1.i = d__2;
            ff.r = z__1.r, ff.i = z__1.i;
        }
        d__1 = gs.r / g2s;
        d__2 = -d_imag(&gs) / g2s;
        z__2.r = d__1, z__2.i = d__2;
        z__1.r = ff.r * z__2.r - ff.i * z__2.i, z__1.i = ff.r * z__2.i + ff.i 
                * z__2.r;
        sn->r = z__1.r, sn->i = z__1.i;
        z__2.r = *cs * f->r, z__2.i = *cs * f->i;
        z__3.r = sn->r * g->r - sn->i * g->i, z__3.i = sn->r * g->i + sn->i * 
                g->r;
        z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
        r__->r = z__1.r, r__->i = z__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.);
/*        Do the F2S(real)*FS(complex) multiply with two real multiplies */
        d__1 = f2s * fs.r;
        d__2 = f2s * d_imag(&fs);
        z__1.r = d__1, z__1.i = d__2;
        r__->r = z__1.r, r__->i = z__1.i;
        *cs = 1. / f2s;
        d__ = f2 + g2;
/*        Do complex/real division explicitly with two real divisions */
        d__1 = r__->r / d__;
        d__2 = d_imag(r__) / d__;
        z__1.r = d__1, z__1.i = d__2;
        sn->r = z__1.r, sn->i = z__1.i;
        d_cnjg(&z__2, &gs);
        z__1.r = sn->r * z__2.r - sn->i * z__2.i, z__1.i = sn->r * z__2.i + 
                sn->i * z__2.r;
        sn->r = z__1.r, sn->i = z__1.i;
        if (count != 0) {
            if (count > 0) {
                i__1 = count;
                for (i__ = 1; i__ <= i__1; ++i__) {
                    z__1.r = safmx2 * r__->r, z__1.i = safmx2 * r__->i;
                    r__->r = z__1.r, r__->i = z__1.i;
/* L30: */
                }
            } else {
                i__1 = -count;
                for (i__ = 1; i__ <= i__1; ++i__) {
                    z__1.r = safmn2 * r__->r, z__1.i = safmn2 * r__->i;
                    r__->r = z__1.r, r__->i = z__1.i;
/* L40: */
                }
            }
        }
    }
    return 0;

/*     End of ZLARTG */

} /* zlartg_ */