#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) {float nenn=crealf(_FCmulcc(Cf(b),conjf(Cf(b)))); _Fcomplex zaehl=_FCmulcc(Cf(a),conjf(Cf(b))); pCf(c)=_FCbuild(crealf(zaehl)/nenn,cimagf(zaehl)/nenn);}
#define z_div(c, a, b) {double nenn=creal(_Cmulcc(Cd(b),conj(Cd(b)))); _Dcomplex zaehl=_Cmulcc(Cd(a),conj(Cd(b))); pCd(c)=_Cbuild(creal(zaehl)/nenn,cimag(zaehl)/nenn);}
#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] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0]
				+ Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
			zdotc._Val[1] -= Cf(&x[i])._Val[1] * Cf(&y[i])._Val[0]
				- Cf(&x[i])._Val[0] * 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]
				+ Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
			zdotc._Val[1] -= Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1]
				- Cf(&x[i*incx])._Val[0] * 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]
				+ Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
			zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1]
				- Cd(&x[i])._Val[0] * 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]
				+ Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
			zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1]
				- Cd(&x[i*incx])._Val[0] * 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]
				- Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
			zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1]
				+ Cf(&x[i])._Val[0] * 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]
				- Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
			zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1]
				+ Cf(&x[i*incx])._Val[0] * 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]
				- Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
			zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1]
				+ Cd(&x[i])._Val[0] * 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]
				- Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
			zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1]
				+ Cd(&x[i*incx])._Val[0] * 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 CLARTG generates a plane rotation with real cosine and complex sine. */

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

/* Online html documentation available at */
/*            http://www.netlib.org/lapack/explore-html/ */

/* > \htmlonly */
/* > Download CLARTG + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clartg.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clartg.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clartg.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */

/*  Definition: */
/*  =========== */

/*       SUBROUTINE CLARTG( F, G, CS, SN, R ) */

/*       REAL               CS */
/*       COMPLEX            F, G, R, SN */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > 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. */
/* > \endverbatim */

/*  Arguments: */
/*  ========== */

/* > \param[in] F */
/* > \verbatim */
/* >          F is COMPLEX */
/* >          The first component of vector to be rotated. */
/* > \endverbatim */
/* > */
/* > \param[in] G */
/* > \verbatim */
/* >          G is COMPLEX */
/* >          The second component of vector to be rotated. */
/* > \endverbatim */
/* > */
/* > \param[out] CS */
/* > \verbatim */
/* >          CS is REAL */
/* >          The cosine of the rotation. */
/* > \endverbatim */
/* > */
/* > \param[out] SN */
/* > \verbatim */
/* >          SN is COMPLEX */
/* >          The sine of the rotation. */
/* > \endverbatim */
/* > */
/* > \param[out] R */
/* > \verbatim */
/* >          R is COMPLEX */
/* >          The nonzero component of the rotated vector. */
/* > \endverbatim */

/*  Authors: */
/*  ======== */

/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */

/* > \date December 2016 */

/* > \ingroup complexOTHERauxiliary */

/* > \par Further Details: */
/*  ===================== */
/* > */
/* > \verbatim */
/* > */
/* >  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. */
/* > \endverbatim */
/* > */
/*  ===================================================================== */
/* Subroutine */ void clartg_(complex *f, complex *g, real *cs, complex *sn, 
	complex *r__)
{
    /* System generated locals */
    integer i__1;
    real r__1=0., r__2=0., r__3=0., r__4=0., r__5=0., r__6=0., r__7=0., r__8=0., r__9=0., r__10=0.;
    complex q__1={0.,0.}, q__2={0.,0.}, q__3={0.,0.};

    /* Local variables */
    real d__;
    integer i__;
    real scale;
    integer count;
    real f2, g2, safmn2, safmx2;
    extern real slapy2_(real *, real *);
    complex ff;
    real di, dr;
    complex fs, gs;
    extern real slamch_(char *);
    real safmin;
    extern logical sisnan_(real *);
    real f2s, g2s, eps;


/*  -- LAPACK auxiliary 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..-- */
/*     December 2016 */


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

/*     LOGICAL            FIRST */

    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, abs(r__1)), r__8 = (r__2 = r_imag(f), abs(r__2));
/* Computing MAX */
    r__9 = (r__3 = g->r, abs(r__3)), r__10 = (r__4 = r_imag(g), abs(r__4));
    r__5 = f2cmax(r__7,r__8), r__6 = f2cmax(r__9,r__10);
    scale = f2cmax(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 && count < 20) {
	    goto L10;
	}
    } else if (scale <= safmn2) {
	r__1 = c_abs(g);
	if (g->r == 0.f && g->i == 0.f || sisnan_(&r__1)) {
	    *cs = 1.f;
	    sn->r = 0.f, sn->i = 0.f;
	    r__->r = f->r, r__->i = f->i;
	    return;
	}
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 <= f2cmax(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;
	}
	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, abs(r__1)), r__4 = (r__2 = r_imag(f), abs(r__2));
	if (f2cmax(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;

/*     End of CLARTG */

} /* clartg_ */

