#include #include #include #include #include #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 int logical; typedef short int shortlogical; 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++ */ #define F2C_proc_par_types 1 #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 \brief \b SLAG2 computes the eigenvalues of a 2-by-2 generalized eigenvalue problem, with scaling as nece ssary to avoid over-/underflow. */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download SLAG2 + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE SLAG2( A, LDA, B, LDB, SAFMIN, SCALE1, SCALE2, WR1, */ /* WR2, WI ) */ /* INTEGER LDA, LDB */ /* REAL SAFMIN, SCALE1, SCALE2, WI, WR1, WR2 */ /* REAL A( LDA, * ), B( LDB, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > SLAG2 computes the eigenvalues of a 2 x 2 generalized eigenvalue */ /* > problem A - w B, with scaling as necessary to avoid over-/underflow. */ /* > */ /* > The scaling factor "s" results in a modified eigenvalue equation */ /* > */ /* > s A - w B */ /* > */ /* > where s is a non-negative scaling factor chosen so that w, w B, */ /* > and s A do not overflow and, if possible, do not underflow, either. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] A */ /* > \verbatim */ /* > A is REAL array, dimension (LDA, 2) */ /* > On entry, the 2 x 2 matrix A. It is assumed that its 1-norm */ /* > is less than 1/SAFMIN. Entries less than */ /* > sqrt(SAFMIN)*norm(A) are subject to being treated as zero. */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > The leading dimension of the array A. LDA >= 2. */ /* > \endverbatim */ /* > */ /* > \param[in] B */ /* > \verbatim */ /* > B is REAL array, dimension (LDB, 2) */ /* > On entry, the 2 x 2 upper triangular matrix B. It is */ /* > assumed that the one-norm of B is less than 1/SAFMIN. The */ /* > diagonals should be at least sqrt(SAFMIN) times the largest */ /* > element of B (in absolute value); if a diagonal is smaller */ /* > than that, then +/- sqrt(SAFMIN) will be used instead of */ /* > that diagonal. */ /* > \endverbatim */ /* > */ /* > \param[in] LDB */ /* > \verbatim */ /* > LDB is INTEGER */ /* > The leading dimension of the array B. LDB >= 2. */ /* > \endverbatim */ /* > */ /* > \param[in] SAFMIN */ /* > \verbatim */ /* > SAFMIN is REAL */ /* > The smallest positive number s.t. 1/SAFMIN does not */ /* > overflow. (This should always be SLAMCH('S') -- it is an */ /* > argument in order to avoid having to call SLAMCH frequently.) */ /* > \endverbatim */ /* > */ /* > \param[out] SCALE1 */ /* > \verbatim */ /* > SCALE1 is REAL */ /* > A scaling factor used to avoid over-/underflow in the */ /* > eigenvalue equation which defines the first eigenvalue. If */ /* > the eigenvalues are complex, then the eigenvalues are */ /* > ( WR1 +/- WI i ) / SCALE1 (which may lie outside the */ /* > exponent range of the machine), SCALE1=SCALE2, and SCALE1 */ /* > will always be positive. If the eigenvalues are real, then */ /* > the first (real) eigenvalue is WR1 / SCALE1 , but this may */ /* > overflow or underflow, and in fact, SCALE1 may be zero or */ /* > less than the underflow threshold if the exact eigenvalue */ /* > is sufficiently large. */ /* > \endverbatim */ /* > */ /* > \param[out] SCALE2 */ /* > \verbatim */ /* > SCALE2 is REAL */ /* > A scaling factor used to avoid over-/underflow in the */ /* > eigenvalue equation which defines the second eigenvalue. If */ /* > the eigenvalues are complex, then SCALE2=SCALE1. If the */ /* > eigenvalues are real, then the second (real) eigenvalue is */ /* > WR2 / SCALE2 , but this may overflow or underflow, and in */ /* > fact, SCALE2 may be zero or less than the underflow */ /* > threshold if the exact eigenvalue is sufficiently large. */ /* > \endverbatim */ /* > */ /* > \param[out] WR1 */ /* > \verbatim */ /* > WR1 is REAL */ /* > If the eigenvalue is real, then WR1 is SCALE1 times the */ /* > eigenvalue closest to the (2,2) element of A B**(-1). If the */ /* > eigenvalue is complex, then WR1=WR2 is SCALE1 times the real */ /* > part of the eigenvalues. */ /* > \endverbatim */ /* > */ /* > \param[out] WR2 */ /* > \verbatim */ /* > WR2 is REAL */ /* > If the eigenvalue is real, then WR2 is SCALE2 times the */ /* > other eigenvalue. If the eigenvalue is complex, then */ /* > WR1=WR2 is SCALE1 times the real part of the eigenvalues. */ /* > \endverbatim */ /* > */ /* > \param[out] WI */ /* > \verbatim */ /* > WI is REAL */ /* > If the eigenvalue is real, then WI is zero. If the */ /* > eigenvalue is complex, then WI is SCALE1 times the imaginary */ /* > part of the eigenvalues. WI will always be non-negative. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date June 2016 */ /* > \ingroup realOTHERauxiliary */ /* ===================================================================== */ /* Subroutine */ int slag2_(real *a, integer *lda, real *b, integer *ldb, real *safmin, real *scale1, real *scale2, real *wr1, real *wr2, real * wi) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset; real r__1, r__2, r__3, r__4, r__5, r__6; /* Local variables */ real diff, bmin, wbig, wabs, wdet, r__, binv11, binv22, discr, anorm, bnorm, bsize, shift, c1, c2, c3, c4, c5, rtmin, rtmax, wsize, s1, s2, a11, a12, a21, a22, b11, b12, b22, ascale, bscale, pp, qq, ss, wscale, safmax, wsmall, as11, as12, as22, sum, abi22; /* -- 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..-- */ /* June 2016 */ /* ===================================================================== */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; /* Function Body */ rtmin = sqrt(*safmin); rtmax = 1.f / rtmin; safmax = 1.f / *safmin; /* Scale A */ /* Computing MAX */ r__5 = (r__1 = a[a_dim1 + 1], abs(r__1)) + (r__2 = a[a_dim1 + 2], abs( r__2)), r__6 = (r__3 = a[(a_dim1 << 1) + 1], abs(r__3)) + (r__4 = a[(a_dim1 << 1) + 2], abs(r__4)), r__5 = f2cmax(r__5,r__6); anorm = f2cmax(r__5,*safmin); ascale = 1.f / anorm; a11 = ascale * a[a_dim1 + 1]; a21 = ascale * a[a_dim1 + 2]; a12 = ascale * a[(a_dim1 << 1) + 1]; a22 = ascale * a[(a_dim1 << 1) + 2]; /* Perturb B if necessary to insure non-singularity */ b11 = b[b_dim1 + 1]; b12 = b[(b_dim1 << 1) + 1]; b22 = b[(b_dim1 << 1) + 2]; /* Computing MAX */ r__1 = abs(b11), r__2 = abs(b12), r__1 = f2cmax(r__1,r__2), r__2 = abs(b22), r__1 = f2cmax(r__1,r__2); bmin = rtmin * f2cmax(r__1,rtmin); if (abs(b11) < bmin) { b11 = r_sign(&bmin, &b11); } if (abs(b22) < bmin) { b22 = r_sign(&bmin, &b22); } /* Scale B */ /* Computing MAX */ r__1 = abs(b11), r__2 = abs(b12) + abs(b22), r__1 = f2cmax(r__1,r__2); bnorm = f2cmax(r__1,*safmin); /* Computing MAX */ r__1 = abs(b11), r__2 = abs(b22); bsize = f2cmax(r__1,r__2); bscale = 1.f / bsize; b11 *= bscale; b12 *= bscale; b22 *= bscale; /* Compute larger eigenvalue by method described by C. van Loan */ /* ( AS is A shifted by -SHIFT*B ) */ binv11 = 1.f / b11; binv22 = 1.f / b22; s1 = a11 * binv11; s2 = a22 * binv22; if (abs(s1) <= abs(s2)) { as12 = a12 - s1 * b12; as22 = a22 - s1 * b22; ss = a21 * (binv11 * binv22); abi22 = as22 * binv22 - ss * b12; pp = abi22 * .5f; shift = s1; } else { as12 = a12 - s2 * b12; as11 = a11 - s2 * b11; ss = a21 * (binv11 * binv22); abi22 = -ss * b12; pp = (as11 * binv11 + abi22) * .5f; shift = s2; } qq = ss * as12; if ((r__1 = pp * rtmin, abs(r__1)) >= 1.f) { /* Computing 2nd power */ r__1 = rtmin * pp; discr = r__1 * r__1 + qq * *safmin; r__ = sqrt((abs(discr))) * rtmax; } else { /* Computing 2nd power */ r__1 = pp; if (r__1 * r__1 + abs(qq) <= *safmin) { /* Computing 2nd power */ r__1 = rtmax * pp; discr = r__1 * r__1 + qq * safmax; r__ = sqrt((abs(discr))) * rtmin; } else { /* Computing 2nd power */ r__1 = pp; discr = r__1 * r__1 + qq; r__ = sqrt((abs(discr))); } } /* Note: the test of R in the following IF is to cover the case when */ /* DISCR is small and negative and is flushed to zero during */ /* the calculation of R. On machines which have a consistent */ /* flush-to-zero threshold and handle numbers above that */ /* threshold correctly, it would not be necessary. */ if (discr >= 0.f || r__ == 0.f) { sum = pp + r_sign(&r__, &pp); diff = pp - r_sign(&r__, &pp); wbig = shift + sum; /* Compute smaller eigenvalue */ wsmall = shift + diff; /* Computing MAX */ r__1 = abs(wsmall); if (abs(wbig) * .5f > f2cmax(r__1,*safmin)) { wdet = (a11 * a22 - a12 * a21) * (binv11 * binv22); wsmall = wdet / wbig; } /* Choose (real) eigenvalue closest to 2,2 element of A*B**(-1) */ /* for WR1. */ if (pp > abi22) { *wr1 = f2cmin(wbig,wsmall); *wr2 = f2cmax(wbig,wsmall); } else { *wr1 = f2cmax(wbig,wsmall); *wr2 = f2cmin(wbig,wsmall); } *wi = 0.f; } else { /* Complex eigenvalues */ *wr1 = shift + pp; *wr2 = *wr1; *wi = r__; } /* Further scaling to avoid underflow and overflow in computing */ /* SCALE1 and overflow in computing w*B. */ /* This scale factor (WSCALE) is bounded from above using C1 and C2, */ /* and from below using C3 and C4. */ /* C1 implements the condition s A must never overflow. */ /* C2 implements the condition w B must never overflow. */ /* C3, with C2, */ /* implement the condition that s A - w B must never overflow. */ /* C4 implements the condition s should not underflow. */ /* C5 implements the condition f2cmax(s,|w|) should be at least 2. */ c1 = bsize * (*safmin * f2cmax(1.f,ascale)); c2 = *safmin * f2cmax(1.f,bnorm); c3 = bsize * *safmin; if (ascale <= 1.f && bsize <= 1.f) { /* Computing MIN */ r__1 = 1.f, r__2 = ascale / *safmin * bsize; c4 = f2cmin(r__1,r__2); } else { c4 = 1.f; } if (ascale <= 1.f || bsize <= 1.f) { /* Computing MIN */ r__1 = 1.f, r__2 = ascale * bsize; c5 = f2cmin(r__1,r__2); } else { c5 = 1.f; } /* Scale first eigenvalue */ wabs = abs(*wr1) + abs(*wi); /* Computing MAX */ /* Computing MIN */ r__3 = c4, r__4 = f2cmax(wabs,c5) * .5f; r__1 = f2cmax(*safmin,c1), r__2 = (wabs * c2 + c3) * 1.0000100000000001f, r__1 = f2cmax(r__1,r__2), r__2 = f2cmin(r__3,r__4); wsize = f2cmax(r__1,r__2); if (wsize != 1.f) { wscale = 1.f / wsize; if (wsize > 1.f) { *scale1 = f2cmax(ascale,bsize) * wscale * f2cmin(ascale,bsize); } else { *scale1 = f2cmin(ascale,bsize) * wscale * f2cmax(ascale,bsize); } *wr1 *= wscale; if (*wi != 0.f) { *wi *= wscale; *wr2 = *wr1; *scale2 = *scale1; } } else { *scale1 = ascale * bsize; *scale2 = *scale1; } /* Scale second eigenvalue (if real) */ if (*wi == 0.f) { /* Computing MAX */ /* Computing MIN */ /* Computing MAX */ r__5 = abs(*wr2); r__3 = c4, r__4 = f2cmax(r__5,c5) * .5f; r__1 = f2cmax(*safmin,c1), r__2 = (abs(*wr2) * c2 + c3) * 1.0000100000000001f, r__1 = f2cmax(r__1,r__2), r__2 = f2cmin(r__3, r__4); wsize = f2cmax(r__1,r__2); if (wsize != 1.f) { wscale = 1.f / wsize; if (wsize > 1.f) { *scale2 = f2cmax(ascale,bsize) * wscale * f2cmin(ascale,bsize); } else { *scale2 = f2cmin(ascale,bsize) * wscale * f2cmax(ascale,bsize); } *wr2 *= wscale; } else { *scale2 = ascale * bsize; } } /* End of SLAG2 */ return 0; } /* slag2_ */