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blis/frame/base/noopt/bli_dlamch.c
Devin Matthews 372eef0b6c Fixed most conflicts after hack-n-slash ofr bli_f2c.h, cleanup in 
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2016-02-25 12:01:58 -06:00

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/* dlamch.f -- translated by f2c (version 19991025).
You must link the resulting object file with the libraries:
-lf2c -lm (in that order)
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "blis.h"
double bli_pow_di( bla_double* a, bla_integer* n );
/* Table of constant values */
//static bla_integer c__1 = 1;
static bla_double c_b32 = 0.;
double bli_pow_di(bla_double *ap, bla_integer *bp)
{
double pow, x;
bla_integer n;
unsigned long u;
pow = 1;
x = *ap;
n = *bp;
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;
}
bla_double bli_dlamch(bla_character *cmach, ftnlen cmach_len)
{
/* Initialized data */
static bla_logical first = TRUE_;
/* System generated locals */
bla_integer i__1;
bla_double ret_val;
/* Builtin functions */
double bli_pow_di(bla_double *, bla_integer *);
/* Local variables */
static bla_double base;
static bla_integer beta;
static bla_double emin, prec, emax;
static bla_integer imin, imax;
static bla_logical lrnd;
static bla_double rmin, rmax, t, rmach;
extern bla_logical bli_lsame(bla_character *, bla_character *, ftnlen, ftnlen);
static bla_double smnum, sfmin;
extern /* Subroutine */ int bli_dlamc2(bla_integer *, bla_integer *, bla_logical *,
bla_double *, bla_integer *, bla_double *, bla_integer *, bla_double *);
static bla_integer it;
static bla_double rnd, eps;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLAMCH determines double precision machine parameters. */
/* Arguments */
/* ========= */
/* CMACH (input) CHARACTER*1 */
/* Specifies the value to be returned by DLAMCH: */
/* = 'E' or 'e', DLAMCH := eps */
/* = 'S' or 's , DLAMCH := sfmin */
/* = 'B' or 'b', DLAMCH := base */
/* = 'P' or 'p', DLAMCH := eps*base */
/* = 'N' or 'n', DLAMCH := t */
/* = 'R' or 'r', DLAMCH := rnd */
/* = 'M' or 'm', DLAMCH := emin */
/* = 'U' or 'u', DLAMCH := rmin */
/* = 'L' or 'l', DLAMCH := emax */
/* = 'O' or 'o', DLAMCH := rmax */
/* where */
/* eps = relative machine precision */
/* sfmin = safe minimum, such that 1/sfmin does not overflow */
/* base = base of the machine */
/* prec = eps*base */
/* t = number of (base) digits in the mantissa */
/* rnd = 1.0 when rounding occurs in addition, 0.0 otherwise */
/* emin = minimum exponent before (gradual) underflow */
/* rmin = underflow threshold - base**(emin-1) */
/* emax = largest exponent before overflow */
/* rmax = overflow threshold - (base**emax)*(1-eps) */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Save statement .. */
/* .. */
/* .. Data statements .. */
/* .. */
/* .. Executable Statements .. */
if (first) {
bli_dlamc2(&beta, &it, &lrnd, &eps, &imin, &rmin, &imax, &rmax);
base = (bla_double) beta;
t = (bla_double) it;
if (lrnd) {
rnd = 1.;
i__1 = 1 - it;
eps = bli_pow_di(&base, &i__1) / 2;
} else {
rnd = 0.;
i__1 = 1 - it;
eps = bli_pow_di(&base, &i__1);
}
prec = eps * base;
emin = (bla_double) imin;
emax = (bla_double) imax;
sfmin = rmin;
smnum = 1. / rmax;
if (smnum >= sfmin) {
/* Use SMALL plus a bit, to avoid the possibility of rounding */
/* causing overflow when computing 1/sfmin. */
sfmin = smnum * (eps + 1.);
}
}
if (bli_lsame(cmach, "E", (ftnlen)1, (ftnlen)1)) {
rmach = eps;
} else if (bli_lsame(cmach, "S", (ftnlen)1, (ftnlen)1)) {
rmach = sfmin;
} else if (bli_lsame(cmach, "B", (ftnlen)1, (ftnlen)1)) {
rmach = base;
} else if (bli_lsame(cmach, "P", (ftnlen)1, (ftnlen)1)) {
rmach = prec;
} else if (bli_lsame(cmach, "N", (ftnlen)1, (ftnlen)1)) {
rmach = t;
} else if (bli_lsame(cmach, "R", (ftnlen)1, (ftnlen)1)) {
rmach = rnd;
} else if (bli_lsame(cmach, "M", (ftnlen)1, (ftnlen)1)) {
rmach = emin;
} else if (bli_lsame(cmach, "U", (ftnlen)1, (ftnlen)1)) {
rmach = rmin;
} else if (bli_lsame(cmach, "L", (ftnlen)1, (ftnlen)1)) {
rmach = emax;
} else if (bli_lsame(cmach, "O", (ftnlen)1, (ftnlen)1)) {
rmach = rmax;
}
ret_val = rmach;
first = FALSE_;
return ret_val;
/* End of DLAMCH */
} /* bli_dlamch_ */
/* *********************************************************************** */
/* Subroutine */ int bli_dlamc1(bla_integer *beta, bla_integer *t, bla_logical *rnd, bla_logical
*ieee1)
{
/* Initialized data */
static bla_logical first = TRUE_;
/* System generated locals */
bla_double d__1, d__2;
/* Local variables */
static bla_logical lrnd;
static bla_double a, b, c__, f;
static bla_integer lbeta;
static bla_double savec;
extern bla_double bli_dlamc3(bla_double *, bla_double *);
static bla_logical lieee1;
static bla_double t1, t2;
static bla_integer lt;
static bla_double one, qtr;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLAMC1 determines the machine parameters given by BETA, T, RND, and */
/* IEEE1. */
/* Arguments */
/* ========= */
/* BETA (output) INTEGER */
/* The base of the machine. */
/* T (output) INTEGER */
/* The number of ( BETA ) digits in the mantissa. */
/* RND (output) LOGICAL */
/* Specifies whether proper rounding ( RND = .TRUE. ) or */
/* chopping ( RND = .FALSE. ) occurs in addition. This may not */
/* be a reliable guide to the way in which the machine performs */
/* its arithmetic. */
/* IEEE1 (output) LOGICAL */
/* Specifies whether rounding appears to be done in the IEEE */
/* 'round to nearest' style. */
/* Further Details */
/* =============== */
/* The routine is based on the routine ENVRON by Malcolm and */
/* incorporates suggestions by Gentleman and Marovich. See */
/* Malcolm M. A. (1972) Algorithms to reveal properties of */
/* floating-point arithmetic. Comms. of the ACM, 15, 949-951. */
/* Gentleman W. M. and Marovich S. B. (1974) More on algorithms */
/* that reveal properties of floating point arithmetic units. */
/* Comms. of the ACM, 17, 276-277. */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Save statement .. */
/* .. */
/* .. Data statements .. */
/* .. */
/* .. Executable Statements .. */
if (first) {
one = 1.;
/* LBETA, LIEEE1, LT and LRND are the local values of BETA, */
/* IEEE1, T and RND. */
/* Throughout this routine we use the function DLAMC3 to ensure */
/* that relevant values are stored and not held in registers, or */
/* are not affected by optimizers. */
/* Compute a = 2.0**m with the smallest positive bla_integer m such */
/* that */
/* fl( a + 1.0 ) = a. */
a = 1.;
c__ = 1.;
/* + WHILE( C.EQ.ONE )LOOP */
L10:
if (c__ == one) {
a *= 2;
c__ = bli_dlamc3(&a, &one);
d__1 = -a;
c__ = bli_dlamc3(&c__, &d__1);
goto L10;
}
/* + END WHILE */
/* Now compute b = 2.0**m with the smallest positive bla_integer m */
/* such that */
/* fl( a + b ) .gt. a. */
b = 1.;
c__ = bli_dlamc3(&a, &b);
/* + WHILE( C.EQ.A )LOOP */
L20:
if (c__ == a) {
b *= 2;
c__ = bli_dlamc3(&a, &b);
goto L20;
}
/* + END WHILE */
/* Now compute the base. a and c are neighbouring floating point */
/* numbers in the interval ( beta**t, beta**( t + 1 ) ) and so */
/* their difference is beta. Adding 0.25 to c is to ensure that it */
/* is truncated to beta and not ( beta - 1 ). */
qtr = one / 4;
savec = c__;
d__1 = -a;
c__ = bli_dlamc3(&c__, &d__1);
lbeta = (bla_integer) (c__ + qtr);
/* Now determine whether rounding or chopping occurs, by adding a */
/* bit less than beta/2 and a bit more than beta/2 to a. */
b = (bla_double) lbeta;
d__1 = b / 2;
d__2 = -b / 100;
f = bli_dlamc3(&d__1, &d__2);
c__ = bli_dlamc3(&f, &a);
if (c__ == a) {
lrnd = TRUE_;
} else {
lrnd = FALSE_;
}
d__1 = b / 2;
d__2 = b / 100;
f = bli_dlamc3(&d__1, &d__2);
c__ = bli_dlamc3(&f, &a);
if (lrnd && c__ == a) {
lrnd = FALSE_;
}
/* Try and decide whether rounding is done in the IEEE 'round to */
/* nearest' style. B/2 is half a unit in the last place of the two */
/* numbers A and SAVEC. Furthermore, A is even, i.e. has last bit */
/* zero, and SAVEC is odd. Thus adding B/2 to A should not change */
/* A, but adding B/2 to SAVEC should change SAVEC. */
d__1 = b / 2;
t1 = bli_dlamc3(&d__1, &a);
d__1 = b / 2;
t2 = bli_dlamc3(&d__1, &savec);
lieee1 = t1 == a && t2 > savec && lrnd;
/* Now find the mantissa, t. It should be the bla_integer part of */
/* log to the base beta of a, however it is safer to determine t */
/* by powering. So we find t as the smallest positive bla_integer for */
/* which */
/* fl( beta**t + 1.0 ) = 1.0. */
lt = 0;
a = 1.;
c__ = 1.;
/* + WHILE( C.EQ.ONE )LOOP */
L30:
if (c__ == one) {
++lt;
a *= lbeta;
c__ = bli_dlamc3(&a, &one);
d__1 = -a;
c__ = bli_dlamc3(&c__, &d__1);
goto L30;
}
/* + END WHILE */
}
*beta = lbeta;
*t = lt;
*rnd = lrnd;
*ieee1 = lieee1;
first = FALSE_;
return 0;
/* End of DLAMC1 */
} /* bli_dlamc1_ */
/* *********************************************************************** */
/* Subroutine */ int bli_dlamc2(bla_integer *beta, bla_integer *t, bla_logical *rnd,
bla_double *eps, bla_integer *emin, bla_double *rmin, bla_integer *emax,
bla_double *rmax)
{
/* Initialized data */
static bla_logical first = TRUE_;
static bla_logical iwarn = FALSE_;
/* Format strings */
static bla_character fmt_9999[] = "(//\002 WARNING. The value EMIN may be incorre\
ct:-\002,\002 EMIN = \002,i8,/\002 If, after inspection, the value EMIN loo\
ks\002,\002 acceptable please comment out \002,/\002 the IF block as marked \
within the code of routine\002,\002 DLAMC2,\002,/\002 otherwise supply EMIN \
explicitly.\002,/)";
/* System generated locals */
bla_integer i__1;
bla_double d__1, d__2, d__3, d__4, d__5;
/* Builtin functions */
double bli_pow_di(bla_double *, bla_integer *);
//bla_integer s_wsfe(cilist *), do_fio(bla_integer *, bla_character *, ftnlen), e_wsfe();
/* Local variables */
static bla_logical ieee;
static bla_double half;
static bla_logical lrnd;
static bla_double leps, zero, a, b, c__;
static bla_integer i__, lbeta;
static bla_double rbase;
static bla_integer lemin, lemax, gnmin;
static bla_double smnum;
static bla_integer gpmin;
static bla_double third, lrmin, lrmax, sixth;
extern /* Subroutine */ int bli_dlamc1(bla_integer *, bla_integer *, bla_logical *,
bla_logical *);
extern bla_double bli_dlamc3(bla_double *, bla_double *);
static bla_logical lieee1;
extern /* Subroutine */ int bli_dlamc4(bla_integer *, bla_double *, bla_integer *),
bli_dlamc5(bla_integer *, bla_integer *, bla_integer *, bla_logical *, bla_integer *,
bla_double *);
static bla_integer lt, ngnmin, ngpmin;
static bla_double one, two;
/* Fortran I/O blocks */
//static cilist io___58 = { 0, 6, 0, fmt_9999, 0 };
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLAMC2 determines the machine parameters specified in its argument */
/* list. */
/* Arguments */
/* ========= */
/* BETA (output) INTEGER */
/* The base of the machine. */
/* T (output) INTEGER */
/* The number of ( BETA ) digits in the mantissa. */
/* RND (output) LOGICAL */
/* Specifies whether proper rounding ( RND = .TRUE. ) or */
/* chopping ( RND = .FALSE. ) occurs in addition. This may not */
/* be a reliable guide to the way in which the machine performs */
/* its arithmetic. */
/* EPS (output) DOUBLE PRECISION */
/* The smallest positive number such that */
/* fl( 1.0 - EPS ) .LT. 1.0, */
/* where fl denotes the computed value. */
/* EMIN (output) INTEGER */
/* The minimum exponent before (gradual) underflow occurs. */
/* RMIN (output) DOUBLE PRECISION */
/* The smallest normalized number for the machine, given by */
/* BASE**( EMIN - 1 ), where BASE is the floating point value */
/* of BETA. */
/* EMAX (output) INTEGER */
/* The maximum exponent before overflow occurs. */
/* RMAX (output) DOUBLE PRECISION */
/* The largest positive number for the machine, given by */
/* BASE**EMAX * ( 1 - EPS ), where BASE is the floating point */
/* value of BETA. */
/* Further Details */
/* =============== */
/* The computation of EPS is based on a routine PARANOIA by */
/* W. Kahan of the University of California at Berkeley. */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Save statement .. */
/* .. */
/* .. Data statements .. */
/* .. */
/* .. Executable Statements .. */
if (first) {
zero = 0.;
one = 1.;
two = 2.;
/* LBETA, LT, LRND, LEPS, LEMIN and LRMIN are the local values of */
/* BETA, T, RND, EPS, EMIN and RMIN. */
/* Throughout this routine we use the function DLAMC3 to ensure */
/* that relevant values are stored and not held in registers, or */
/* are not affected by optimizers. */
/* DLAMC1 returns the parameters LBETA, LT, LRND and LIEEE1. */
bli_dlamc1(&lbeta, &lt, &lrnd, &lieee1);
/* Start to find EPS. */
b = (bla_double) lbeta;
i__1 = -lt;
a = bli_pow_di(&b, &i__1);
leps = a;
/* Try some tricks to see whether or not this is the correct EPS. */
b = two / 3;
half = one / 2;
d__1 = -half;
sixth = bli_dlamc3(&b, &d__1);
third = bli_dlamc3(&sixth, &sixth);
d__1 = -half;
b = bli_dlamc3(&third, &d__1);
b = bli_dlamc3(&b, &sixth);
b = f2c_abs(b);
if (b < leps) {
b = leps;
}
leps = 1.;
/* + WHILE( ( LEPS.GT.B ).AND.( B.GT.ZERO ) )LOOP */
L10:
if (leps > b && b > zero) {
leps = b;
d__1 = half * leps;
/* Computing 5th power */
d__3 = two, d__4 = d__3, d__3 *= d__3;
/* Computing 2nd power */
d__5 = leps;
d__2 = d__4 * (d__3 * d__3) * (d__5 * d__5);
c__ = bli_dlamc3(&d__1, &d__2);
d__1 = -c__;
c__ = bli_dlamc3(&half, &d__1);
b = bli_dlamc3(&half, &c__);
d__1 = -b;
c__ = bli_dlamc3(&half, &d__1);
b = bli_dlamc3(&half, &c__);
goto L10;
}
/* + END WHILE */
if (a < leps) {
leps = a;
}
/* Computation of EPS complete. */
/* Now find EMIN. Let A = + or - 1, and + or - (1 + BASE**(-3)). */
/* Keep dividing A by BETA until (gradual) underflow occurs. This */
/* is detected when we cannot recover the previous A. */
rbase = one / lbeta;
smnum = one;
for (i__ = 1; i__ <= 3; ++i__) {
d__1 = smnum * rbase;
smnum = bli_dlamc3(&d__1, &zero);
/* L20: */
}
a = bli_dlamc3(&one, &smnum);
bli_dlamc4(&ngpmin, &one, &lbeta);
d__1 = -one;
bli_dlamc4(&ngnmin, &d__1, &lbeta);
bli_dlamc4(&gpmin, &a, &lbeta);
d__1 = -a;
bli_dlamc4(&gnmin, &d__1, &lbeta);
ieee = FALSE_;
if (ngpmin == ngnmin && gpmin == gnmin) {
if (ngpmin == gpmin) {
lemin = ngpmin;
/* ( Non twos-complement machines, no gradual underflow; */
/* e.g., VAX ) */
} else if (gpmin - ngpmin == 3) {
lemin = ngpmin - 1 + lt;
ieee = TRUE_;
/* ( Non twos-complement machines, with gradual underflow; */
/* e.g., IEEE standard followers ) */
} else {
lemin = f2c_min(ngpmin,gpmin);
/* ( A guess; no known machine ) */
iwarn = TRUE_;
}
} else if (ngpmin == gpmin && ngnmin == gnmin) {
if ((i__1 = ngpmin - ngnmin, f2c_abs(i__1)) == 1) {
lemin = f2c_max(ngpmin,ngnmin);
/* ( Twos-complement machines, no gradual underflow; */
/* e.g., CYBER 205 ) */
} else {
lemin = f2c_min(ngpmin,ngnmin);
/* ( A guess; no known machine ) */
iwarn = TRUE_;
}
} else if ((i__1 = ngpmin - ngnmin, f2c_abs(i__1)) == 1 && gpmin == gnmin)
{
if (gpmin - f2c_min(ngpmin,ngnmin) == 3) {
lemin = f2c_max(ngpmin,ngnmin) - 1 + lt;
/* ( Twos-complement machines with gradual underflow; */
/* no known machine ) */
} else {
lemin = f2c_min(ngpmin,ngnmin);
/* ( A guess; no known machine ) */
iwarn = TRUE_;
}
} else {
/* Computing MIN */
i__1 = f2c_min(ngpmin,ngnmin), i__1 = f2c_min(i__1,gpmin);
lemin = f2c_min(i__1,gnmin);
/* ( A guess; no known machine ) */
iwarn = TRUE_;
}
first = FALSE_;
/* ** */
/* Comment out this if block if EMIN is ok */
if (iwarn) {
first = TRUE_;
/*
s_wsfe(&io___58);
do_fio(&c__1, (bla_character *)&lemin, (ftnlen)sizeof(bla_integer));
e_wsfe();
*/
printf( "%s", fmt_9999 );
}
/* ** */
/* Assume IEEE arithmetic if we found denormalised numbers above, */
/* or if arithmetic seems to round in the IEEE style, determined */
/* in routine DLAMC1. A true IEEE machine should have both things */
/* true; however, faulty machines may have one or the other. */
ieee = ieee || lieee1;
/* Compute RMIN by successive division by BETA. We could compute */
/* RMIN as BASE**( EMIN - 1 ), but some machines underflow during */
/* this computation. */
lrmin = 1.;
i__1 = 1 - lemin;
for (i__ = 1; i__ <= i__1; ++i__) {
d__1 = lrmin * rbase;
lrmin = bli_dlamc3(&d__1, &zero);
/* L30: */
}
/* Finally, call DLAMC5 to compute EMAX and RMAX. */
bli_dlamc5(&lbeta, &lt, &lemin, &ieee, &lemax, &lrmax);
}
*beta = lbeta;
*t = lt;
*rnd = lrnd;
*eps = leps;
*emin = lemin;
*rmin = lrmin;
*emax = lemax;
*rmax = lrmax;
return 0;
/* End of DLAMC2 */
} /* bli_dlamc2_ */
/* *********************************************************************** */
bla_double bli_dlamc3(bla_double *a, bla_double *b)
{
/* System generated locals */
bla_double ret_val;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLAMC3 is intended to force A and B to be stored prior to doing */
/* the addition of A and B , for use in situations where optimizers */
/* might hold one of these in a register. */
/* Arguments */
/* ========= */
/* A (input) DOUBLE PRECISION */
/* B (input) DOUBLE PRECISION */
/* The values A and B. */
/* ===================================================================== */
/* .. Executable Statements .. */
ret_val = *a + *b;
return ret_val;
/* End of DLAMC3 */
} /* bli_dlamc3_ */
/* *********************************************************************** */
/* Subroutine */ int bli_dlamc4(bla_integer *emin, bla_double *start, bla_integer *base)
{
/* System generated locals */
bla_integer i__1;
bla_double d__1;
/* Local variables */
static bla_double zero, a;
static bla_integer i__;
static bla_double rbase, b1, b2, c1, c2, d1, d2;
extern bla_double bli_dlamc3(bla_double *, bla_double *);
static bla_double one;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLAMC4 is a service routine for DLAMC2. */
/* Arguments */
/* ========= */
/* EMIN (output) INTEGER */
/* The minimum exponent before (gradual) underflow, computed by */
/* setting A = START and dividing by BASE until the previous A */
/* can not be recovered. */
/* START (input) DOUBLE PRECISION */
/* The starting point for determining EMIN. */
/* BASE (input) INTEGER */
/* The base of the machine. */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
a = *start;
one = 1.;
rbase = one / *base;
zero = 0.;
*emin = 1;
d__1 = a * rbase;
b1 = bli_dlamc3(&d__1, &zero);
c1 = a;
c2 = a;
d1 = a;
d2 = a;
/* + WHILE( ( C1.EQ.A ).AND.( C2.EQ.A ).AND. */
/* $ ( D1.EQ.A ).AND.( D2.EQ.A ) )LOOP */
L10:
if (c1 == a && c2 == a && d1 == a && d2 == a) {
--(*emin);
a = b1;
d__1 = a / *base;
b1 = bli_dlamc3(&d__1, &zero);
d__1 = b1 * *base;
c1 = bli_dlamc3(&d__1, &zero);
d1 = zero;
i__1 = *base;
for (i__ = 1; i__ <= i__1; ++i__) {
d1 += b1;
/* L20: */
}
d__1 = a * rbase;
b2 = bli_dlamc3(&d__1, &zero);
d__1 = b2 / rbase;
c2 = bli_dlamc3(&d__1, &zero);
d2 = zero;
i__1 = *base;
for (i__ = 1; i__ <= i__1; ++i__) {
d2 += b2;
/* L30: */
}
goto L10;
}
/* + END WHILE */
return 0;
/* End of DLAMC4 */
} /* bli_dlamc4_ */
/* *********************************************************************** */
/* Subroutine */ int bli_dlamc5(bla_integer *beta, bla_integer *p, bla_integer *emin,
bla_logical *ieee, bla_integer *emax, bla_double *rmax)
{
/* System generated locals */
bla_integer i__1;
bla_double d__1;
/* Local variables */
static bla_integer lexp;
static bla_double oldy;
static bla_integer uexp, i__;
static bla_double y, z__;
static bla_integer nbits;
extern bla_double bli_dlamc3(bla_double *, bla_double *);
static bla_double recbas;
static bla_integer exbits, expsum, try__;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLAMC5 attempts to compute RMAX, the largest machine floating-point */
/* number, without overflow. It assumes that EMAX + f2c_abs(EMIN) sum */
/* approximately to a power of 2. It will fail on machines where this */
/* assumption does not hold, for example, the Cyber 205 (EMIN = -28625, */
/* EMAX = 28718). It will also fail if the value supplied for EMIN is */
/* too large (i.e. too close to zero), probably with overflow. */
/* Arguments */
/* ========= */
/* BETA (input) INTEGER */
/* The base of floating-point arithmetic. */
/* P (input) INTEGER */
/* The number of base BETA digits in the mantissa of a */
/* floating-point value. */
/* EMIN (input) INTEGER */
/* The minimum exponent before (gradual) underflow. */
/* IEEE (input) LOGICAL */
/* A bla_logical flag specifying whether or not the arithmetic */
/* system is thought to comply with the IEEE standard. */
/* EMAX (output) INTEGER */
/* The largest exponent before overflow */
/* RMAX (output) DOUBLE PRECISION */
/* The largest machine floating-point number. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* First compute LEXP and UEXP, two powers of 2 that bound */
/* f2c_abs(EMIN). We then assume that EMAX + f2c_abs(EMIN) will sum */
/* approximately to the bound that is closest to f2c_abs(EMIN). */
/* (EMAX is the exponent of the required number RMAX). */
lexp = 1;
exbits = 1;
L10:
try__ = lexp << 1;
if (try__ <= -(*emin)) {
lexp = try__;
++exbits;
goto L10;
}
if (lexp == -(*emin)) {
uexp = lexp;
} else {
uexp = try__;
++exbits;
}
/* Now -LEXP is less than or equal to EMIN, and -UEXP is greater */
/* than or equal to EMIN. EXBITS is the number of bits needed to */
/* store the exponent. */
if (uexp + *emin > -lexp - *emin) {
expsum = lexp << 1;
} else {
expsum = uexp << 1;
}
/* EXPSUM is the exponent range, approximately equal to */
/* EMAX - EMIN + 1 . */
*emax = expsum + *emin - 1;
nbits = exbits + 1 + *p;
/* NBITS is the total number of bits needed to store a */
/* floating-point number. */
if (nbits % 2 == 1 && *beta == 2) {
/* Either there are an odd number of bits used to store a */
/* floating-point number, which is unlikely, or some bits are */
/* not used in the representation of numbers, which is possible, */
/* (e.g. Cray machines) or the mantissa has an implicit bit, */
/* (e.g. IEEE machines, Dec Vax machines), which is perhaps the */
/* most likely. We have to assume the last alternative. */
/* If this is true, then we need to reduce EMAX by one because */
/* there must be some way of representing zero in an implicit-bit */
/* system. On machines like Cray, we are reducing EMAX by one */
/* unnecessarily. */
--(*emax);
}
if (*ieee) {
/* Assume we are on an IEEE machine which reserves one exponent */
/* for infinity and NaN. */
--(*emax);
}
/* Now create RMAX, the largest machine number, which should */
/* be equal to (1.0 - BETA**(-P)) * BETA**EMAX . */
/* First compute 1.0 - BETA**(-P), being careful that the */
/* result is less than 1.0 . */
recbas = 1. / *beta;
z__ = *beta - 1.;
y = 0.;
i__1 = *p;
for (i__ = 1; i__ <= i__1; ++i__) {
z__ *= recbas;
if (y < 1.) {
oldy = y;
}
y = bli_dlamc3(&y, &z__);
/* L20: */
}
if (y >= 1.) {
y = oldy;
}
/* Now multiply by BETA**EMAX to get RMAX. */
i__1 = *emax;
for (i__ = 1; i__ <= i__1; ++i__) {
d__1 = y * *beta;
y = bli_dlamc3(&d__1, &c_b32);
/* L30: */
}
*rmax = y;
return 0;
/* End of DLAMC5 */
} /* bli_dlamc5_ */
#ifdef __cplusplus
}
#endif
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