#include "blaswrap.h"
#include "f2c.h"

/* Subroutine */ int clartg_(complex *f, complex *g, real *cs, complex *sn, 
	complex *r__)
{
/*  -- LAPACK auxiliary routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       June 30, 1999   


    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   

    ===================================================================== */
    /* Initialized data */
    static logical first = TRUE_;
    /* 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 */
    static real d__;
    static integer i__;
    static real scale;
    static integer count;
    static real f2, g2, safmn2, safmx2;
    extern doublereal slapy2_(real *, real *);
    static complex ff;
    static real di, dr;
    static complex fs, gs;
    extern doublereal slamch_(char *);
    static real safmin, f2s, g2s, eps;



    if (first) {
	first = FALSE_;
	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;
    }
/* 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_ */

