#include <math.h>

#include <stdlib.h>

#include <string.h>

#include <stdio.h>

#include <complex.h>

#ifdef complex

#undef complex

#endif

#ifdef I

#undef I

#endif

#if defined(_WIN64)

typedef long long BLASLONG;

typedef unsigned long long BLASULONG;

#else

typedef long BLASLONG;

typedef unsigned long BLASULONG;

#endif

#ifdef LAPACK_ILP64

typedef BLASLONG blasint;

#if defined(_WIN64)

#define blasabs(x) llabs(x)

#else

#define blasabs(x) labs(x)

#endif

#else

typedef int blasint;

#define blasabs(x) abs(x)

#endif

typedef blasint integer;

typedef unsigned int uinteger;

typedef char *address;

typedef short int shortint;

typedef float real;

typedef double doublereal;

typedef struct { real r, i; } complex;

typedef struct { doublereal r, i; } doublecomplex;

#ifdef _MSC_VER

static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}

static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}

static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}

static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}

#else

static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}

static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}

static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}

static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}

#endif

#define pCf(z) (*_pCf(z))

#define pCd(z) (*_pCd(z))

typedef blasint logical;

typedef char logical1;

typedef char integer1;

#define TRUE_ (1)

#define FALSE_ (0)

/* Extern is for use with -E */

#ifndef Extern

#define Extern extern

#endif

/* I/O stuff */

typedef int flag;

typedef int ftnlen;

typedef int ftnint;

/*external read, write*/

typedef struct

{ flag cierr;

  ftnint ciunit;

  flag ciend;

  char *cifmt;

  ftnint cirec;

} cilist;

/*internal read, write*/

typedef struct

{ flag icierr;

  char *iciunit;

  flag iciend;

  char *icifmt;

  ftnint icirlen;

  ftnint icirnum;

} icilist;

/*open*/

typedef struct

{ flag oerr;

  ftnint ounit;

  char *ofnm;

  ftnlen ofnmlen;

  char *osta;

  char *oacc;

  char *ofm;

  ftnint orl;

  char *oblnk;

} olist;

/*close*/

typedef struct

{ flag cerr;

  ftnint cunit;

  char *csta;

} cllist;

/*rewind, backspace, endfile*/

typedef struct

{ flag aerr;

  ftnint aunit;

} alist;

/* inquire */

typedef struct

{ flag inerr;

  ftnint inunit;

  char *infile;

  ftnlen infilen;

  ftnint  *inex;  /*parameters in standard's order*/

  ftnint  *inopen;

  ftnint  *innum;

  ftnint  *innamed;

  char  *inname;

  ftnlen  innamlen;

  char  *inacc;

  ftnlen  inacclen;

  char  *inseq;

  ftnlen  inseqlen;

  char  *indir;

  ftnlen  indirlen;

  char  *infmt;

  ftnlen  infmtlen;

  char  *inform;

  ftnint  informlen;

  char  *inunf;

  ftnlen  inunflen;

  ftnint  *inrecl;

  ftnint  *innrec;

  char  *inblank;

  ftnlen  inblanklen;

} inlist;

#define VOID void

union Multitype { /* for multiple entry points */

  integer1 g;

  shortint h;

  integer i;

  /* longint j; */

  real r;

  doublereal d;

  complex c;

  doublecomplex z;

  };

typedef union Multitype Multitype;

struct Vardesc {  /* for Namelist */

  char *name;

  char *addr;

  ftnlen *dims;

  int  type;

  };

typedef struct Vardesc Vardesc;

struct Namelist {

  char *name;

  Vardesc **vars;

  int nvars;

  };

typedef struct Namelist Namelist;

#define abs(x) ((x) >= 0 ? (x) : -(x))

#define dabs(x) (fabs(x))

#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))

#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))

#define dmin(a,b) (f2cmin(a,b))

#define dmax(a,b) (f2cmax(a,b))

#define bit_test(a,b) ((a) >> (b) & 1)

#define bit_clear(a,b)  ((a) & ~((uinteger)1 << (b)))

#define bit_set(a,b)  ((a) |  ((uinteger)1 << (b)))

#define abort_() { sig_die("Fortran abort routine called", 1); }

#define c_abs(z) (cabsf(Cf(z)))

#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }

#ifdef _MSC_VER

#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}

#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}

#else

#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}

#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}

#endif

#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}

#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}

#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}

//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}

#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}

#define d_abs(x) (fabs(*(x)))

#define d_acos(x) (acos(*(x)))

#define d_asin(x) (asin(*(x)))

#define d_atan(x) (atan(*(x)))

#define d_atn2(x, y) (atan2(*(x),*(y)))

#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }

#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }

#define d_cos(x) (cos(*(x)))

#define d_cosh(x) (cosh(*(x)))

#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )

#define d_exp(x) (exp(*(x)))

#define d_imag(z) (cimag(Cd(z)))

#define r_imag(z) (cimagf(Cf(z)))

#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))

#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))

#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )

#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )

#define d_log(x) (log(*(x)))

#define d_mod(x, y) (fmod(*(x), *(y)))

#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))

#define d_nint(x) u_nint(*(x))

#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))

#define d_sign(a,b) u_sign(*(a),*(b))

#define r_sign(a,b) u_sign(*(a),*(b))

#define d_sin(x) (sin(*(x)))

#define d_sinh(x) (sinh(*(x)))

#define d_sqrt(x) (sqrt(*(x)))

#define d_tan(x) (tan(*(x)))

#define d_tanh(x) (tanh(*(x)))

#define i_abs(x) abs(*(x))

#define i_dnnt(x) ((integer)u_nint(*(x)))

#define i_len(s, n) (n)

#define i_nint(x) ((integer)u_nint(*(x)))

#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))

#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))

#define pow_si(B,E) spow_ui(*(B),*(E))

#define pow_ri(B,E) spow_ui(*(B),*(E))

#define pow_di(B,E) dpow_ui(*(B),*(E))

#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}

#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}

#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}

#define s_cat(lpp, rpp, rnp, np, llp) {   ftnlen i, nc, ll; char *f__rp, *lp;   ll = (llp); lp = (lpp);   for(i=0; i < (int)*(np); ++i) {           nc = ll;          if((rnp)[i] < nc) nc = (rnp)[i];          ll -= nc;           f__rp = (rpp)[i];           while(--nc >= 0) *lp++ = *(f__rp)++;         }  while(--ll >= 0) *lp++ = ' '; }

#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))

#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }

#define sig_die(s, kill) { exit(1); }

#define s_stop(s, n) {exit(0);}

static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";

#define z_abs(z) (cabs(Cd(z)))

#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}

#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}

#define myexit_() break;

#define mycycle() continue;

#define myceiling(w) {ceil(w)}

#define myhuge(w) {HUGE_VAL}

//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}

#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}

/* procedure parameter types for -A and -C++ */

#ifdef __cplusplus

typedef logical (*L_fp)(...);

#else

typedef logical (*L_fp)();

#endif

static float spow_ui(float x, integer n) {

  float pow=1.0; unsigned long int u;

  if(n != 0) {

    if(n < 0) n = -n, x = 1/x;

    for(u = n; ; ) {

      if(u & 01) pow *= x;

      if(u >>= 1) x *= x;

      else break;

    }

  }

  return pow;

}

static double dpow_ui(double x, integer n) {

  double pow=1.0; unsigned long int u;

  if(n != 0) {

    if(n < 0) n = -n, x = 1/x;

    for(u = n; ; ) {

      if(u & 01) pow *= x;

      if(u >>= 1) x *= x;

      else break;

    }

  }

  return pow;

}

#ifdef _MSC_VER

static _Fcomplex cpow_ui(complex x, integer n) {

  complex pow={1.0,0.0}; unsigned long int u;

    if(n != 0) {

    if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;

    for(u = n; ; ) {

      if(u & 01) pow.r *= x.r, pow.i *= x.i;

      if(u >>= 1) x.r *= x.r, x.i *= x.i;

      else break;

    }

  }

  _Fcomplex p={pow.r, pow.i};

  return p;

}

#else

static _Complex float cpow_ui(_Complex float x, integer n) {

  _Complex float pow=1.0; unsigned long int u;

  if(n != 0) {

    if(n < 0) n = -n, x = 1/x;

    for(u = n; ; ) {

      if(u & 01) pow *= x;

      if(u >>= 1) x *= x;

      else break;

    }

  }

  return pow;

}

#endif

#ifdef _MSC_VER

static _Dcomplex zpow_ui(_Dcomplex x, integer n) {

  _Dcomplex pow={1.0,0.0}; unsigned long int u;

  if(n != 0) {

    if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];

    for(u = n; ; ) {

      if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];

      if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];

      else break;

    }

  }

  _Dcomplex p = {pow._Val[0], pow._Val[1]};

  return p;

}

#else

static _Complex double zpow_ui(_Complex double x, integer n) {

  _Complex double pow=1.0; unsigned long int u;

  if(n != 0) {

    if(n < 0) n = -n, x = 1/x;

    for(u = n; ; ) {

      if(u & 01) pow *= x;

      if(u >>= 1) x *= x;

      else break;

    }

  }

  return pow;

}

#endif

static integer pow_ii(integer x, integer n) {

  integer pow; unsigned long int u;

  if (n <= 0) {

    if (n == 0 || x == 1) pow = 1;

    else if (x != -1) pow = x == 0 ? 1/x : 0;

    else n = -n;

  }

  if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {

    u = n;

    for(pow = 1; ; ) {

      if(u & 01) pow *= x;

      if(u >>= 1) x *= x;

      else break;

    }

  }

  return pow;

}

static integer dmaxloc_(double *w, integer s, integer e, integer *n)

{

  double m; integer i, mi;

  for(m=w[s-1], mi=s, i=s+1; i<=e; i++)

    if (w[i-1]>m) mi=i ,m=w[i-1];

  return mi-s+1;

}

static integer smaxloc_(float *w, integer s, integer e, integer *n)

{

  float m; integer i, mi;

  for(m=w[s-1], mi=s, i=s+1; i<=e; i++)

    if (w[i-1]>m) mi=i ,m=w[i-1];

  return mi-s+1;

}

static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {

  integer n = *n_, incx = *incx_, incy = *incy_, i;

#ifdef _MSC_VER

  _Fcomplex zdotc = {0.0, 0.0};

  if (incx == 1 && incy == 1) {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];

      zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];

    }

  } else {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];

      zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];

    }

  }

  pCf(z) = zdotc;

}

#else

  _Complex float zdotc = 0.0;

  if (incx == 1 && incy == 1) {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);

    }

  } else {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);

    }

  }

  pCf(z) = zdotc;

}

#endif

static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {

  integer n = *n_, incx = *incx_, incy = *incy_, i;

#ifdef _MSC_VER

  _Dcomplex zdotc = {0.0, 0.0};

  if (incx == 1 && incy == 1) {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];

      zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];

    }

  } else {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];

      zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];

    }

  }

  pCd(z) = zdotc;

}

#else

  _Complex double zdotc = 0.0;

  if (incx == 1 && incy == 1) {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc += conj(Cd(&x[i])) * Cd(&y[i]);

    }

  } else {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);

    }

  }

  pCd(z) = zdotc;

}

#endif  

static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {

  integer n = *n_, incx = *incx_, incy = *incy_, i;

#ifdef _MSC_VER

  _Fcomplex zdotc = {0.0, 0.0};

  if (incx == 1 && incy == 1) {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];

      zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];

    }

  } else {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];

      zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];

    }

  }

  pCf(z) = zdotc;

}

#else

  _Complex float zdotc = 0.0;

  if (incx == 1 && incy == 1) {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc += Cf(&x[i]) * Cf(&y[i]);

    }

  } else {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);

    }

  }

  pCf(z) = zdotc;

}

#endif

static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {

  integer n = *n_, incx = *incx_, incy = *incy_, i;

#ifdef _MSC_VER

  _Dcomplex zdotc = {0.0, 0.0};

  if (incx == 1 && incy == 1) {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];

      zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];

    }

  } else {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];

      zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];

    }

  }

  pCd(z) = zdotc;

}

#else

  _Complex double zdotc = 0.0;

  if (incx == 1 && incy == 1) {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc += Cd(&x[i]) * Cd(&y[i]);

    }

  } else {

    for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

      zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);

    }

  }

  pCd(z) = zdotc;

}

#endif

/*  -- translated by f2c (version 20000121).

   You must link the resulting object file with the libraries:

  -lf2c -lm   (in that order)

*/

/* > \brief \b DLASQ3 checks for deflation, computes a shift and calls dqds. Used by sbdsqr. */

/*  =========== DOCUMENTATION =========== */

/* Online html documentation available at */

/*            http://www.netlib.org/lapack/explore-html/ */

/* > \htmlonly */

/* > Download DLASQ3 + dependencies */

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq3.

f"> */

/* > [TGZ]</a> */

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasq3.

f"> */

/* > [ZIP]</a> */

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasq3.

f"> */

/* > [TXT]</a> */

/* > \endhtmlonly */

/*  Definition: */

/*  =========== */

/*       SUBROUTINE DLASQ3( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL, */

/*                          ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1, */

/*                          DN2, G, TAU ) */

/*       LOGICAL            IEEE */

/*       INTEGER            I0, ITER, N0, NDIV, NFAIL, PP */

/*       DOUBLE PRECISION   DESIG, DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, */

/*      $                   QMAX, SIGMA, TAU */

/*       DOUBLE PRECISION   Z( * ) */

/* > \par Purpose: */

/*  ============= */

/* > */

/* > \verbatim */

/* > */

/* > 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. */

/* > \endverbatim */

/*  Arguments: */

/*  ========== */

/* > \param[in] I0 */

/* > \verbatim */

/* >          I0 is INTEGER */

/* >         First index. */

/* > \endverbatim */

/* > */

/* > \param[in,out] N0 */

/* > \verbatim */

/* >          N0 is INTEGER */

/* >         Last index. */

/* > \endverbatim */

/* > */

/* > \param[in,out] Z */

/* > \verbatim */

/* >          Z is DOUBLE PRECISION array, dimension ( 4*N0 ) */

/* >         Z holds the qd array. */

/* > \endverbatim */

/* > */

/* > \param[in,out] PP */

/* > \verbatim */

/* >          PP is INTEGER */

/* >         PP=0 for ping, PP=1 for pong. */

/* >         PP=2 indicates that flipping was applied to the Z array */

/* >         and that the initial tests for deflation should not be */

/* >         performed. */

/* > \endverbatim */

/* > */

/* > \param[out] DMIN */

/* > \verbatim */

/* >          DMIN is DOUBLE PRECISION */

/* >         Minimum value of d. */

/* > \endverbatim */

/* > */

/* > \param[out] SIGMA */

/* > \verbatim */

/* >          SIGMA is DOUBLE PRECISION */

/* >         Sum of shifts used in current segment. */

/* > \endverbatim */

/* > */

/* > \param[in,out] DESIG */

/* > \verbatim */

/* >          DESIG is DOUBLE PRECISION */

/* >         Lower order part of SIGMA */

/* > \endverbatim */

/* > */

/* > \param[in] QMAX */

/* > \verbatim */

/* >          QMAX is DOUBLE PRECISION */

/* >         Maximum value of q. */

/* > \endverbatim */

/* > */

/* > \param[in,out] NFAIL */

/* > \verbatim */

/* >          NFAIL is INTEGER */

/* >         Increment NFAIL by 1 each time the shift was too big. */

/* > \endverbatim */

/* > */

/* > \param[in,out] ITER */

/* > \verbatim */

/* >          ITER is INTEGER */

/* >         Increment ITER by 1 for each iteration. */

/* > \endverbatim */

/* > */

/* > \param[in,out] NDIV */

/* > \verbatim */

/* >          NDIV is INTEGER */

/* >         Increment NDIV by 1 for each division. */

/* > \endverbatim */

/* > */

/* > \param[in] IEEE */

/* > \verbatim */

/* >          IEEE is LOGICAL */

/* >         Flag for IEEE or non IEEE arithmetic (passed to DLASQ5). */

/* > \endverbatim */

/* > */

/* > \param[in,out] TTYPE */

/* > \verbatim */

/* >          TTYPE is INTEGER */

/* >         Shift type. */

/* > \endverbatim */

/* > */

/* > \param[in,out] DMIN1 */

/* > \verbatim */

/* >          DMIN1 is DOUBLE PRECISION */

/* > \endverbatim */

/* > */

/* > \param[in,out] DMIN2 */

/* > \verbatim */

/* >          DMIN2 is DOUBLE PRECISION */

/* > \endverbatim */

/* > */

/* > \param[in,out] DN */

/* > \verbatim */

/* >          DN is DOUBLE PRECISION */

/* > \endverbatim */

/* > */

/* > \param[in,out] DN1 */

/* > \verbatim */

/* >          DN1 is DOUBLE PRECISION */

/* > \endverbatim */

/* > */

/* > \param[in,out] DN2 */

/* > \verbatim */

/* >          DN2 is DOUBLE PRECISION */

/* > \endverbatim */

/* > */

/* > \param[in,out] G */

/* > \verbatim */

/* >          G is DOUBLE PRECISION */

/* > \endverbatim */

/* > */

/* > \param[in,out] TAU */

/* > \verbatim */

/* >          TAU is DOUBLE PRECISION */

/* > */

/* >         These are passed as arguments in order to save their values */

/* >         between calls to DLASQ3. */

/* > \endverbatim */

/*  Authors: */

/*  ======== */

/* > \author Univ. of Tennessee */

/* > \author Univ. of California Berkeley */

/* > \author Univ. of Colorado Denver */

/* > \author NAG Ltd. */

/* > \date June 2016 */

/* > \ingroup auxOTHERcomputational */

/*  ===================================================================== */

/* Subroutine */ void 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, integer *ttype, doublereal *dmin1, doublereal *dmin2, 

  doublereal *dn, doublereal *dn1, doublereal *dn2, doublereal *g, 

  doublereal *tau)

{

    /* System generated locals */

    integer i__1;

    doublereal d__1, d__2;

    /* Local variables */

    doublereal temp, s, t;

    integer j4;

    extern /* Subroutine */ void dlasq4_(integer *, integer *, doublereal *, 

      integer *, integer *, doublereal *, doublereal *, doublereal *, 

      doublereal *, doublereal *, doublereal *, doublereal *, integer *,

       doublereal *), dlasq5_(integer *, integer *, doublereal *, 

      integer *, doublereal *, doublereal *, doublereal *, doublereal *,

       doublereal *, doublereal *, doublereal *, doublereal *, logical *

      , doublereal *), dlasq6_(integer *, integer *, doublereal *, 

      integer *, doublereal *, doublereal *, doublereal *, doublereal *,

       doublereal *, doublereal *);

    extern doublereal dlamch_(char *);

    integer nn;

    extern logical disnan_(doublereal *);

    doublereal eps, tol;

    integer n0in, ipn4;

    doublereal tol2;

/*  -- LAPACK computational routine (version 3.7.0) -- */

/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */

/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */

/*     June 2016 */

/*  ===================================================================== */

    /* Parameter adjustments */

    --z__;

    /* Function Body */

    n0in = *n0;

    eps = dlamch_("Precision");

    tol = eps * 100.;

/* Computing 2nd power */

    d__1 = tol;

    tol2 = d__1 * d__1;

/*     Check for deflation. */

L10:

    if (*n0 < *i0) {

  return;

    }

    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;

    }

    t = (z__[nn - 7] - z__[nn - 3] + z__[nn - 5]) * .5;

    if (z__[nn - 5] > z__[nn - 3] * tol2 && t != 0.) {

  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:

    if (*pp == 2) {

  *pp = 0;

    }

/*     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 = f2cmin(d__1,d__2);

/* Computing MIN */

      d__1 = z__[(*n0 << 2) + *pp - 1], d__2 = z__[(*i0 << 2) + *pp - 1]

        , d__1 = f2cmin(d__1,d__2), d__2 = z__[(*i0 << 2) + *pp + 3];

      z__[(*n0 << 2) + *pp - 1] = f2cmin(d__1,d__2);

/* Computing MIN */

      d__1 = z__[(*n0 << 2) - *pp], d__2 = z__[(*i0 << 2) - *pp], d__1 =

         f2cmin(d__1,d__2), d__2 = z__[(*i0 << 2) - *pp + 4];

      z__[(*n0 << 2) - *pp] = f2cmin(d__1,d__2);

/* Computing MAX */

      d__1 = *qmax, d__2 = z__[(*i0 << 2) + *pp - 3], d__1 = f2cmax(d__1,

        d__2), d__2 = z__[(*i0 << 2) + *pp + 1];

      *qmax = f2cmax(d__1,d__2);

      *dmin__ = 0.;

  }

    }

/*     Choose a shift. */

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

      tau, ttype, g);

/*     Call dqds until DMIN > 0. */

L70:

    dlasq5_(i0, n0, &z__[1], pp, tau, sigma, dmin__, dmin1, dmin2, dn, dn1, 

      dn2, ieee, &eps);

    *ndiv += *n0 - *i0 + 2;

    ++(*iter);

/*     Check status. */

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

/*        Success. */

  goto L90;

    } 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 L90;

    } 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 L70;

    } else if (disnan_(dmin__)) {

/*        NaN. */

  if (*tau == 0.) {

      goto L80;

  } else {

      *tau = 0.;

      goto L70;

  }

    } else {

/*        Possible underflow. Play it safe. */

  goto L80;

    }

/*     Risk of underflow. */

L80:

    dlasq6_(i0, n0, &z__[1], pp, dmin__, dmin1, dmin2, dn, dn1, dn2);

    *ndiv += *n0 - *i0 + 2;

    ++(*iter);

    *tau = 0.;

L90:

    if (*tau < *sigma) {

  *desig += *tau;

  t = *sigma + *desig;

  *desig -= t - *sigma;

    } else {

  t = *sigma + *tau;

  *desig = *sigma - (t - *tau) + *desig;

    }

    *sigma = t;

    return;

/*     End of DLASQ3 */

} /* dlasq3_ */