text: #include "f2c.h"
  #include "blaswrap.h"
  
  /* Subroutine */ int slazq3_(integer *i0, integer *n0, real *z__, integer *pp, 
  	 real *dmin__, real *sigma, real *desig, real *qmax, integer *nfail, 
  	integer *iter, integer *ndiv, logical *ieee, integer *ttype, real *
  	dmin1, real *dmin2, real *dn, real *dn1, real *dn2, real *tau)
  {
      /* System generated locals */
      integer i__1;
      real r__1, r__2;
  
      /* Builtin functions */
      double sqrt(doublereal);
  
      /* Local variables */
      real g, s, t;
      integer j4, nn;
      real eps, tol;
      integer n0in, ipn4;
      real tol2, temp;
      extern /* Subroutine */ int slasq5_(integer *, integer *, real *, integer 
  	    *, real *, real *, real *, real *, real *, real *, real *, 
  	    logical *), slasq6_(integer *, integer *, real *, integer *, real 
  	    *, real *, real *, real *, real *, real *), slazq4_(integer *, 
  	    integer *, real *, integer *, integer *, real *, real *, real *, 
  	    real *, real *, real *, real *, integer *, real *);
      extern doublereal slamch_(char *);
      real safmin;
  
  
  /*  -- LAPACK auxiliary routine (version 3.1) -- */
  /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
  /*     November 2006 */
  
  /*     .. Scalar Arguments .. */
  /*     .. */
  /*     .. Array Arguments .. */
  /*     .. */
  
  /*  Purpose */
  /*  ======= */
  
  /*  SLAZQ3 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) REAL array, dimension ( 4*N ) */
  /*         Z holds the qd array. */
  
  /*  PP     (input) INTEGER */
  /*         PP=0 for ping, PP=1 for pong. */
  
  /*  DMIN   (output) REAL */
  /*         Minimum value of d. */
  
  /*  SIGMA  (output) REAL */
  /*         Sum of shifts used in current segment. */
  
  /*  DESIG  (input/output) REAL */
  /*         Lower order part of SIGMA */
  
  /*  QMAX   (input) REAL */
  /*         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. */
  
  /*  IEEE   (input) LOGICAL */
  /*         Flag for IEEE or non IEEE arithmetic (passed to SLASQ5). */
  
  /*  TTYPE  (input/output) INTEGER */
  /*         Shift type.  TTYPE is passed as an argument in order to save */
  /*         its value between calls to SLAZQ3 */
  
  /*  DMIN1  (input/output) REAL */
  /*  DMIN2  (input/output) REAL */
  /*  DN     (input/output) REAL */
  /*  DN1    (input/output) REAL */
  /*  DN2    (input/output) REAL */
  /*  TAU    (input/output) REAL */
  /*         These are passed as arguments in order to save their values */
  /*         between calls to SLAZQ3 */
  
  /*  This is a thread safe version of SLASQ3, which passes TTYPE, DMIN1, */
  /*  DMIN2, DN, DN1. DN2 and TAU through the argument list in place of */
  /*  declaring them in a SAVE statment. */
  
  /*  ===================================================================== */
  
  /*     .. Parameters .. */
  /*     .. */
  /*     .. Local Scalars .. */
  /*     .. */
  /*     .. External Subroutines .. */
  /*     .. */
  /*     .. External Function .. */
  /*     .. */
  /*     .. Intrinsic Functions .. */
  /*     .. */
  /*     .. Executable Statements .. */
  
      /* Parameter adjustments */
      --z__;
  
      /* Function Body */
      n0in = *n0;
      eps = slamch_("Precision");
      safmin = slamch_("Safe minimum");
      tol = eps * 100.f;
  /* Computing 2nd power */
      r__1 = tol;
      tol2 = r__1 * r__1;
      g = 0.f;
  
  /*     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]) * .5f;
  	s = z__[nn - 3] * (z__[nn - 5] / t);
  	if (s <= t) {
  	    s = z__[nn - 3] * (z__[nn - 5] / (t * (sqrt(s / t + 1.f) + 1.f)));
  	} 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.f || *n0 < n0in) {
  	if (z__[(*i0 << 2) + *pp - 3] * 1.5f < 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 */
  	    r__1 = *dmin2, r__2 = z__[(*n0 << 2) + *pp - 1];
  	    *dmin2 = dmin(r__1,r__2);
  /* Computing MIN */
  	    r__1 = z__[(*n0 << 2) + *pp - 1], r__2 = z__[(*i0 << 2) + *pp - 1]
  		    , r__1 = min(r__1,r__2), r__2 = z__[(*i0 << 2) + *pp + 3];
  	    z__[(*n0 << 2) + *pp - 1] = dmin(r__1,r__2);
  /* Computing MIN */
  	    r__1 = z__[(*n0 << 2) - *pp], r__2 = z__[(*i0 << 2) - *pp], r__1 =
  		     min(r__1,r__2), r__2 = z__[(*i0 << 2) - *pp + 4];
  	    z__[(*n0 << 2) - *pp] = dmin(r__1,r__2);
  /* Computing MAX */
  	    r__1 = *qmax, r__2 = z__[(*i0 << 2) + *pp - 3], r__1 = max(r__1,
  		    r__2), r__2 = z__[(*i0 << 2) + *pp + 1];
  	    *qmax = dmax(r__1,r__2);
  	    *dmin__ = -0.f;
  	}
      }
  
  /* Computing MIN */
      r__1 = z__[(*n0 << 2) + *pp - 1], r__2 = z__[(*n0 << 2) + *pp - 9], r__1 =
  	     min(r__1,r__2), r__2 = *dmin2 + z__[(*n0 << 2) - *pp];
      if (*dmin__ < 0.f || safmin * *qmax < dmin(r__1,r__2)) {
  
  /*        Choose a shift. */
  
  	slazq4_(i0, n0, &z__[1], pp, &n0in, dmin__, dmin1, dmin2, dn, dn1, 
  		dn2, tau, ttype, &g);
  
  /*        Call dqds until DMIN > 0. */
  
  L80:
  
  	slasq5_(i0, n0, &z__[1], pp, tau, dmin__, dmin1, dmin2, dn, dn1, dn2, 
  		ieee);
  
  	*ndiv += *n0 - *i0 + 2;
  	++(*iter);
  
  /*        Check status. */
  
  	if (*dmin__ >= 0.f && *dmin1 > 0.f) {
  
  /*           Success. */
  
  	    goto L100;
  
  	} else if (*dmin__ < 0.f && *dmin1 > 0.f && z__[(*n0 - 1 << 2) - *pp] 
  		< tol * (*sigma + *dn1) && dabs(*dn) < tol * *sigma) {
  
  /*           Convergence hidden by negative DN. */
  
  	    z__[(*n0 - 1 << 2) - *pp + 2] = 0.f;
  	    *dmin__ = 0.f;
  	    goto L100;
  	} else if (*dmin__ < 0.f) {
  
  /*           TAU too big. Select new TAU and try again. */
  
  	    ++(*nfail);
  	    if (*ttype < -22) {
  
  /*              Failed twice. Play it safe. */
  
  		*tau = 0.f;
  	    } else if (*dmin1 > 0.f) {
  
  /*              Late failure. Gives excellent shift. */
  
  		*tau = (*tau + *dmin__) * (1.f - eps * 2.f);
  		*ttype += -11;
  	    } else {
  
  /*              Early failure. Divide by 4. */
  
  		*tau *= .25f;
  		*ttype += -12;
  	    }
  	    goto L80;
  	} else if (*dmin__ != *dmin__) {
  
  /*           NaN. */
  
  	    *tau = 0.f;
  	    goto L80;
  	} else {
  
  /*           Possible underflow. Play it safe. */
  
  	    goto L90;
  	}
      }
  
  /*     Risk of underflow. */
  
  L90:
      slasq6_(i0, n0, &z__[1], pp, dmin__, dmin1, dmin2, dn, dn1, dn2);
      *ndiv += *n0 - *i0 + 2;
      ++(*iter);
      *tau = 0.f;
  
  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 SLAZQ3 */
  
  } /* slazq3_ */
  