/* Copyright (c) 1992-2008 The University of Tennessee.  All rights reserved.
 * See file COPYING in this directory for details. */

#ifdef __cplusplus
extern "C" {
#endif

#include "f2c.h"
#include "hypre_lapack.h"

/* Subroutine */ integer dlasq3_(integer *i0, integer *n0, doublereal *z__,
	integer *pp, doublereal *dmin__, doublereal *sigma, doublereal *desig,
	 doublereal *qmax, integer *nfail, integer *iter, integer *ndiv,
	logical *ieee)
{
/*  -- LAPACK auxiliary routine (version 3.0) --
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
       Courant Institute, Argonne National Lab, and Rice University
       May 17, 2000


    Purpose
    =======

    DLASQ3 checks for deflation, computes a shift (TAU) and calls dqds.
    In case of failure it changes shifts, and tries again until output
    is positive.

    Arguments
    =========

    I0     (input) INTEGER
           First index.

    N0     (input) INTEGER
           Last index.

    Z      (input) DOUBLE PRECISION array, dimension ( 4*N )
           Z holds the qd array.

    PP     (input) INTEGER
           PP=0 for ping, PP=1 for pong.

    DMIN   (output) DOUBLE PRECISION
           Minimum value of d.

    SIGMA  (output) DOUBLE PRECISION
           Sum of shifts used in current segment.

    DESIG  (input/output) DOUBLE PRECISION
           Lower order part of SIGMA

    QMAX   (input) DOUBLE PRECISION
           Maximum value of q.

    NFAIL  (output) INTEGER
           Number of times shift was too big.

    ITER   (output) INTEGER
           Number of iterations.

    NDIV   (output) INTEGER
           Number of divisions.

    TTYPE  (output) INTEGER
           Shift type.

    IEEE   (input) LOGICAL
           Flag for IEEE or non IEEE arithmetic (passed to DLASQ5).

    =====================================================================

       Parameter adjustments */
    /* Initialized data */
    integer ttype = 0;
    doublereal dmin1 = 0.;
    doublereal dmin2 = 0.;
    doublereal dn = 0.;
    doublereal dn1 = 0.;
    doublereal dn2 = 0.;
    doublereal tau = 0.;
    /* System generated locals */
    integer i__1;
    doublereal d__1, d__2;
    /* Local variables */
    doublereal temp, s, t;
    integer j4;
    extern /* Subroutine */ integer dlasq4_(integer *, integer *, doublereal *,
	    integer *, integer *, doublereal *, doublereal *, doublereal *,
	    doublereal *, doublereal *, doublereal *, doublereal *, integer *)
	    , dlasq5_(integer *, integer *, doublereal *, integer *,
	    doublereal *, doublereal *, doublereal *, doublereal *,
	    doublereal *, doublereal *, doublereal *, logical *), dlasq6_(
	    integer *, integer *, doublereal *, integer *, doublereal *,
	    doublereal *, doublereal *, doublereal *, doublereal *,
	    doublereal *);
    extern doublereal dlamch_(const char *);
    integer nn;
    doublereal safmin, eps, tol;
    integer n0in, ipn4;
    doublereal tol2;

    --z__;

    /* Function Body */

    n0in = *n0;
    eps = dlamch_("Precision");
    safmin = dlamch_("Safe minimum");
    tol = eps * 100.;
/* Computing 2nd power */
    d__1 = tol;
    tol2 = d__1 * d__1;

/*     Check for deflation. */

L10:

    if (*n0 < *i0) {
	return 0;
    }
    if (*n0 == *i0) {
	goto L20;
    }
    nn = (*n0 << 2) + *pp;
    if (*n0 == *i0 + 1) {
	goto L40;
    }

/*     Check whether E(N0-1) is negligible, 1 eigenvalue. */

    if (z__[nn - 5] > tol2 * (*sigma + z__[nn - 3]) && z__[nn - (*pp << 1) -
	    4] > tol2 * z__[nn - 7]) {
	goto L30;
    }

L20:

    z__[(*n0 << 2) - 3] = z__[(*n0 << 2) + *pp - 3] + *sigma;
    --(*n0);
    goto L10;

/*     Check  whether E(N0-2) is negligible, 2 eigenvalues. */

L30:

    if (z__[nn - 9] > tol2 * *sigma && z__[nn - (*pp << 1) - 8] > tol2 * z__[
	    nn - 11]) {
	goto L50;
    }

L40:

    if (z__[nn - 3] > z__[nn - 7]) {
	s = z__[nn - 3];
	z__[nn - 3] = z__[nn - 7];
	z__[nn - 7] = s;
    }
    if (z__[nn - 5] > z__[nn - 3] * tol2) {
	t = (z__[nn - 7] - z__[nn - 3] + z__[nn - 5]) * .5;
	s = z__[nn - 3] * (z__[nn - 5] / t);
	if (s <= t) {
	    s = z__[nn - 3] * (z__[nn - 5] / (t * (sqrt(s / t + 1.) + 1.)));
	} else {
	    s = z__[nn - 3] * (z__[nn - 5] / (t + sqrt(t) * sqrt(t + s)));
	}
	t = z__[nn - 7] + (s + z__[nn - 5]);
	z__[nn - 3] *= z__[nn - 7] / t;
	z__[nn - 7] = t;
    }
    z__[(*n0 << 2) - 7] = z__[nn - 7] + *sigma;
    z__[(*n0 << 2) - 3] = z__[nn - 3] + *sigma;
    *n0 += -2;
    goto L10;

L50:

/*     Reverse the qd-array, if warranted. */

    if (*dmin__ <= 0. || *n0 < n0in) {
	if (z__[(*i0 << 2) + *pp - 3] * 1.5 < z__[(*n0 << 2) + *pp - 3]) {
	    ipn4 = (*i0 + *n0) << 2;
	    i__1 = (*i0 + *n0 - 1) << 1;
	    for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) {
		temp = z__[j4 - 3];
		z__[j4 - 3] = z__[ipn4 - j4 - 3];
		z__[ipn4 - j4 - 3] = temp;
		temp = z__[j4 - 2];
		z__[j4 - 2] = z__[ipn4 - j4 - 2];
		z__[ipn4 - j4 - 2] = temp;
		temp = z__[j4 - 1];
		z__[j4 - 1] = z__[ipn4 - j4 - 5];
		z__[ipn4 - j4 - 5] = temp;
		temp = z__[j4];
		z__[j4] = z__[ipn4 - j4 - 4];
		z__[ipn4 - j4 - 4] = temp;
/* L60: */
	    }
	    if (*n0 - *i0 <= 4) {
		z__[(*n0 << 2) + *pp - 1] = z__[(*i0 << 2) + *pp - 1];
		z__[(*n0 << 2) - *pp] = z__[(*i0 << 2) - *pp];
	    }
/* Computing MIN */
	    d__1 = dmin2, d__2 = z__[(*n0 << 2) + *pp - 1];
	    dmin2 = min(d__1,d__2);
/* Computing MIN */
	    d__1 = z__[(*n0 << 2) + *pp - 1], d__2 = z__[(*i0 << 2) + *pp - 1]
		    , d__1 = min(d__1,d__2), d__2 = z__[(*i0 << 2) + *pp + 3];
	    z__[(*n0 << 2) + *pp - 1] = min(d__1,d__2);
/* Computing MIN */
	    d__1 = z__[(*n0 << 2) - *pp], d__2 = z__[(*i0 << 2) - *pp], d__1 =
		     min(d__1,d__2), d__2 = z__[(*i0 << 2) - *pp + 4];
	    z__[(*n0 << 2) - *pp] = min(d__1,d__2);
/* Computing MAX */
	    d__1 = *qmax, d__2 = z__[(*i0 << 2) + *pp - 3], d__1 = max(d__1,
		    d__2), d__2 = z__[(*i0 << 2) + *pp + 1];
	    *qmax = max(d__1,d__2);
	    *dmin__ = 0.;
	}
    }

/* L70:

   Computing MIN */
    d__1 = z__[(*n0 << 2) + *pp - 1], d__2 = z__[(*n0 << 2) + *pp - 9], d__1 =
	     min(d__1,d__2), d__2 = dmin2 + z__[(*n0 << 2) - *pp];
    if (*dmin__ < 0. || safmin * *qmax < min(d__1,d__2)) {

/*        Choose a shift. */

	dlasq4_(i0, n0, &z__[1], pp, &n0in, dmin__, &dmin1, &dmin2, &dn, &dn1,
		 &dn2, &tau, &ttype);

/*        Call dqds until DMIN > 0. */

L80:

	dlasq5_(i0, n0, &z__[1], pp, &tau, dmin__, &dmin1, &dmin2, &dn, &dn1,
		&dn2, ieee);

	*ndiv += *n0 - *i0 + 2;
	++(*iter);

/*        Check status. */

	if (*dmin__ >= 0. && dmin1 > 0.) {

/*           Success. */

	    goto L100;

	} else if (*dmin__ < 0. && dmin1 > 0. && z__[((*n0 - 1) << 2) - *pp] <
		tol * (*sigma + dn1) && abs(dn) < tol * *sigma) {

/*           Convergence hidden by negative DN. */

	    z__[((*n0 - 1) << 2) - *pp + 2] = 0.;
	    *dmin__ = 0.;
	    goto L100;
	} else if (*dmin__ < 0.) {

/*           TAU too big. Select new TAU and try again. */

	    ++(*nfail);
	    if (ttype < -22) {

/*              Failed twice. Play it safe. */

		tau = 0.;
	    } else if (dmin1 > 0.) {

/*              Late failure. Gives excellent shift. */

		tau = (tau + *dmin__) * (1. - eps * 2.);
		ttype += -11;
	    } else {

/*              Early failure. Divide by 4. */

		tau *= .25;
		ttype += -12;
	    }
	    goto L80;
	} else if (*dmin__ != *dmin__) {

/*           NaN. */

	    tau = 0.;
	    goto L80;
	} else {

/*           Possible underflow. Play it safe. */

	    goto L90;
	}
    }

/*     Risk of underflow. */

L90:
    dlasq6_(i0, n0, &z__[1], pp, dmin__, &dmin1, &dmin2, &dn, &dn1, &dn2);
    *ndiv += *n0 - *i0 + 2;
    ++(*iter);
    tau = 0.;

L100:
    if (tau < *sigma) {
	*desig += tau;
	t = *sigma + *desig;
	*desig -= t - *sigma;
    } else {
	t = *sigma + tau;
	*desig = *sigma - (t - tau) + *desig;
    }
    *sigma = t;

    return 0;

/*     End of DLASQ3 */

} /* dlasq3_ */

#ifdef __cplusplus
}
#endif
