clartg.c

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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_ */