dlamch.c

Go to the documentation of this file.

/* DLAMCH.F -- translated by f2c (version 19941215).
   You must link the resulting object file with the libraries:
        -lf2c -lm   (in that order)
*/

#include "f2c.h"

/* Table of constant values */

static doublereal c_b31 = 0.;

doublereal dlamch_(cmach, cmach_len)
char *cmach;
ftnlen cmach_len;
{
    /* Initialized data */

    static logical first = TRUE_;

    /* System generated locals */
    integer i__1;
    doublereal ret_val;

    /* Builtin functions */
    double pow_di();

    /* Local variables */
    static doublereal base;
    static integer beta;
    static doublereal emin, prec, emax;
    static integer imin, imax;
    static logical lrnd;
    static doublereal rmin, rmax, t, rmach;
    extern logical lsame_();
    static doublereal small, sfmin;
    extern /* Subroutine */ int dlamc2_();
    static integer it;
    static doublereal rnd, eps;


/*  -- LAPACK auxiliary routine (version 1.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/*     Courant Institute, Argonne National Lab, and Rice University */
/*     October 31, 1992 */

/*     .. 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) {
        first = FALSE_;
        dlamc2_(&beta, &it, &lrnd, &eps, &imin, &rmin, &imax, &rmax);
        base = (doublereal) beta;
        t = (doublereal) it;
        if (lrnd) {
            rnd = 1.;
            i__1 = 1 - it;
            eps = pow_di(&base, &i__1) / 2;
        } else {
            rnd = 0.;
            i__1 = 1 - it;
            eps = pow_di(&base, &i__1);
        }
        prec = eps * base;
        emin = (doublereal) imin;
        emax = (doublereal) imax;
        sfmin = rmin;
        small = 1. / rmax;
        if (small >= sfmin) {

/*           Use SMALL plus a bit, to avoid the possibility of rou
nding */
/*           causing overflow when computing  1/sfmin. */

            sfmin = small * (eps + 1.);
        }
    }

    if (lsame_(cmach, "E", 1L, 1L)) {
        rmach = eps;
    } else if (lsame_(cmach, "S", 1L, 1L)) {
        rmach = sfmin;
    } else if (lsame_(cmach, "B", 1L, 1L)) {
        rmach = base;
    } else if (lsame_(cmach, "P", 1L, 1L)) {
        rmach = prec;
    } else if (lsame_(cmach, "N", 1L, 1L)) {
        rmach = t;
    } else if (lsame_(cmach, "R", 1L, 1L)) {
        rmach = rnd;
    } else if (lsame_(cmach, "M", 1L, 1L)) {
        rmach = emin;
    } else if (lsame_(cmach, "U", 1L, 1L)) {
        rmach = rmin;
    } else if (lsame_(cmach, "L", 1L, 1L)) {
        rmach = emax;
    } else if (lsame_(cmach, "O", 1L, 1L)) {
        rmach = rmax;
    }

    ret_val = rmach;
    return ret_val;

/*     End of DLAMCH */

} /* dlamch_ */


/* *********************************************************************** */

/* Subroutine */ int dlamc1_(beta, t, rnd, ieee1)
integer *beta, *t;
logical *rnd, *ieee1;
{
    /* Initialized data */

    static logical first = TRUE_;

    /* System generated locals */
    doublereal d__1, d__2;

    /* Local variables */
    static logical lrnd;
    static doublereal a, b, c, f;
    static integer lbeta;
    static doublereal savec;
    extern doublereal dlamc3_();
    static logical lieee1;
    static doublereal t1, t2;
    static integer lt;
    static doublereal one, qtr;


/*  -- LAPACK auxiliary routine (version 1.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/*     Courant Institute, Argonne National Lab, and Rice University */
/*     October 31, 1992 */

/*     .. 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) {
        first = FALSE_;
        one = 1.;

/*        LBETA,  LIEEE1,  LT and  LRND  are the  local values  of  BE
TA, */
/*        IEEE1, T and RND. */

/*        Throughout this routine  we use the function  DLAMC3  to ens
ure */
/*        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 integer m s
uch */
/*        that */

/*           fl( a + 1.0 ) = a. */

        a = 1.;
        c = 1.;

/* +       WHILE( C.EQ.ONE )LOOP */
L10:
        if (c == one) {
            a *= 2;
            c = dlamc3_(&a, &one);
            d__1 = -a;
            c = dlamc3_(&c, &d__1);
            goto L10;
        }
/* +       END WHILE */

/*        Now compute  b = 2.0**m  with the smallest positive integer 
m */
/*        such that */

/*           fl( a + b ) .gt. a. */

        b = 1.;
        c = dlamc3_(&a, &b);

/* +       WHILE( C.EQ.A )LOOP */
L20:
        if (c == a) {
            b *= 2;
            c = dlamc3_(&a, &b);
            goto L20;
        }
/* +       END WHILE */

/*        Now compute the base.  a and c  are neighbouring floating po
int */
/*        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 = dlamc3_(&c, &d__1);
        lbeta = (integer) (c + qtr);

/*        Now determine whether rounding or chopping occurs,  by addin
g a */
/*        bit  less  than  beta/2  and a  bit  more  than  beta/2  to 
 a. */

        b = (doublereal) lbeta;
        d__1 = b / 2;
        d__2 = -b / 100;
        f = dlamc3_(&d__1, &d__2);
        c = dlamc3_(&f, &a);
        if (c == a) {
            lrnd = TRUE_;
        } else {
            lrnd = FALSE_;
        }
        d__1 = b / 2;
        d__2 = b / 100;
        f = dlamc3_(&d__1, &d__2);
        c = 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  cha
nge */
/*        A, but adding B/2 to SAVEC should change SAVEC. */

        d__1 = b / 2;
        t1 = dlamc3_(&d__1, &a);
        d__1 = b / 2;
        t2 = dlamc3_(&d__1, &savec);
        lieee1 = t1 == a && t2 > savec && lrnd;

/*        Now find  the  mantissa, t.  It should  be the  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 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 = dlamc3_(&a, &one);
            d__1 = -a;
            c = dlamc3_(&c, &d__1);
            goto L30;
        }
/* +       END WHILE */

    }

    *beta = lbeta;
    *t = lt;
    *rnd = lrnd;
    *ieee1 = lieee1;
    return 0;

/*     End of DLAMC1 */

} /* dlamc1_ */


/* *********************************************************************** */

/* Subroutine */ int dlamc2_(beta, t, rnd, eps, emin, rmin, emax, rmax)
integer *beta, *t;
logical *rnd;
doublereal *eps;
integer *emin;
doublereal *rmin;
integer *emax;
doublereal *rmax;
{
    /* Initialized data */

    static logical first = TRUE_;
    static logical iwarn = FALSE_;

    /* System generated locals */
    integer i__1;
    doublereal d__1, d__2, d__3, d__4, d__5;

    /* Builtin functions */
    double pow_di();

    /* Local variables */
    static logical ieee;
    static doublereal half;
    static logical lrnd;
    static doublereal leps, zero, a, b, c;
    static integer i, lbeta;
    static doublereal rbase;
    static integer lemin, lemax, gnmin;
    static doublereal small;
    static integer gpmin;
    static doublereal third, lrmin, lrmax, sixth;
    extern /* Subroutine */ int dlamc1_();
    extern doublereal dlamc3_();
    static logical lieee1;
    extern /* Subroutine */ int dlamc4_(), dlamc5_();
    static integer lt, ngnmin, ngpmin;
    static doublereal one, two;


/*  -- LAPACK auxiliary routine (version 1.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/*     Courant Institute, Argonne National Lab, and Rice University */
/*     October 31, 1992 */

/*     .. 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) {
        first = FALSE_;
        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 ens
ure */
/*        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. 
*/

        dlamc1_(&lbeta, &lt, &lrnd, &lieee1);

/*        Start to find EPS. */

        b = (doublereal) lbeta;
        i__1 = -lt;
        a = pow_di(&b, &i__1);
        leps = a;

/*        Try some tricks to see whether or not this is the correct  E
PS. */

        b = two / 3;
        half = one / 2;
        d__1 = -half;
        sixth = dlamc3_(&b, &d__1);
        third = dlamc3_(&sixth, &sixth);
        d__1 = -half;
        b = dlamc3_(&third, &d__1);
        b = dlamc3_(&b, &sixth);
        b = 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 = dlamc3_(&d__1, &d__2);
            d__1 = -c;
            c = dlamc3_(&half, &d__1);
            b = dlamc3_(&half, &c);
            d__1 = -b;
            c = dlamc3_(&half, &d__1);
            b = 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. T
his */
/*        is detected when we cannot recover the previous A. */

        rbase = one / lbeta;
        small = one;
        for (i = 1; i <= 3; ++i) {
            d__1 = small * rbase;
            small = dlamc3_(&d__1, &zero);
/* L20: */
        }
        a = dlamc3_(&one, &small);
        dlamc4_(&ngpmin, &one, &lbeta);
        d__1 = -one;
        dlamc4_(&ngnmin, &d__1, &lbeta);
        dlamc4_(&gpmin, &a, &lbeta);
        d__1 = -a;
        dlamc4_(&gnmin, &d__1, &lbeta);
        ieee = FALSE_;

        if (ngpmin == ngnmin && gpmin == gnmin) {
            if (ngpmin == gpmin) {
                lemin = ngpmin;
/*            ( Non twos-complement machines, no gradual under
flow; */
/*              e.g.,  VAX ) */
            } else if (gpmin - ngpmin == 3) {
                lemin = ngpmin - 1 + lt;
                ieee = TRUE_;
/*            ( Non twos-complement machines, with gradual und
erflow; */
/*              e.g., IEEE standard followers ) */
            } else {
                lemin = min(ngpmin,gpmin);
/*            ( A guess; no known machine ) */
                iwarn = TRUE_;
            }

        } else if (ngpmin == gpmin && ngnmin == gnmin) {
            if ((i__1 = ngpmin - ngnmin, abs(i__1)) == 1) {
                lemin = max(ngpmin,ngnmin);
/*            ( Twos-complement machines, no gradual underflow
; */
/*              e.g., CYBER 205 ) */
            } else {
                lemin = min(ngpmin,ngnmin);
/*            ( A guess; no known machine ) */
                iwarn = TRUE_;
            }

        } else if ((i__1 = ngpmin - ngnmin, abs(i__1)) == 1 && gpmin == gnmin)
                 {
            if (gpmin - min(ngpmin,ngnmin) == 3) {
                lemin = max(ngpmin,ngnmin) - 1 + lt;
/*            ( Twos-complement machines with gradual underflo
w; */
/*              no known machine ) */
            } else {
                lemin = min(ngpmin,ngnmin);
/*            ( A guess; no known machine ) */
                iwarn = TRUE_;
            }

        } else {
/* Computing MIN */
            i__1 = min(ngpmin,ngnmin), i__1 = min(i__1,gpmin);
            lemin = min(i__1,gnmin);
/*         ( A guess; no known machine ) */
            iwarn = TRUE_;
        }
/* ** */
/* Comment out this if block if EMIN is ok */
/*         IF( IWARN ) THEN */
/*            FIRST = .TRUE. */
/*            WRITE( 6, FMT = 9999 )LEMIN */
/*         END IF */
/* ** */

/*        Assume IEEE arithmetic if we found denormalised  numbers abo
ve, */
/*        or if arithmetic seems to round in the  IEEE style,  determi
ned */
/*        in routine DLAMC1. A true IEEE machine should have both  thi
ngs */
/*        true; however, faulty machines may have one or the other. */

        ieee = ieee || lieee1;

/*        Compute  RMIN by successive division by  BETA. We could comp
ute */
/*        RMIN as BASE**( EMIN - 1 ),  but some machines underflow dur
ing */
/*        this computation. */

        lrmin = 1.;
        i__1 = 1 - lemin;
        for (i = 1; i <= i__1; ++i) {
            d__1 = lrmin * rbase;
            lrmin = dlamc3_(&d__1, &zero);
/* L30: */
        }

/*        Finally, call DLAMC5 to compute EMAX and RMAX. */

        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;

/* L9999: */

/*     End of DLAMC2 */

} /* dlamc2_ */


/* *********************************************************************** */

doublereal dlamc3_(a, b)
doublereal *a, *b;
{
    /* System generated locals */
    doublereal ret_val;


/*  -- LAPACK auxiliary routine (version 1.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/*     Courant Institute, Argonne National Lab, and Rice University */
/*     October 31, 1992 */

/*     .. 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, B    (input) DOUBLE PRECISION */
/*          The values A and B. */

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

/*     .. Executable Statements .. */

    ret_val = *a + *b;

    return ret_val;

/*     End of DLAMC3 */

} /* dlamc3_ */


/* *********************************************************************** */

/* Subroutine */ int dlamc4_(emin, start, base)
integer *emin;
doublereal *start;
integer *base;
{
    /* System generated locals */
    integer i__1;
    doublereal d__1;

    /* Local variables */
    static doublereal zero, a;
    static integer i;
    static doublereal rbase, b1, b2, c1, c2, d1, d2;
    extern doublereal dlamc3_();
    static doublereal one;


/*  -- LAPACK auxiliary routine (version 1.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/*     Courant Institute, Argonne National Lab, and Rice University */
/*     October 31, 1992 */

/*     .. Scalar Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  DLAMC4 is a service routine for DLAMC2. */

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

/*  EMIN    (output) EMIN */
/*          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 = 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 = dlamc3_(&d__1, &zero);
        d__1 = b1 * *base;
        c1 = dlamc3_(&d__1, &zero);
        d1 = zero;
        i__1 = *base;
        for (i = 1; i <= i__1; ++i) {
            d1 += b1;
/* L20: */
        }
        d__1 = a * rbase;
        b2 = dlamc3_(&d__1, &zero);
        d__1 = b2 / rbase;
        c2 = 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 */

} /* dlamc4_ */


/* *********************************************************************** */

/* Subroutine */ int dlamc5_(beta, p, emin, ieee, emax, rmax)
integer *beta, *p, *emin;
logical *ieee;
integer *emax;
doublereal *rmax;
{
    /* System generated locals */
    integer i__1;
    doublereal d__1;

    /* Local variables */
    static integer lexp;
    static doublereal oldy;
    static integer uexp, i;
    static doublereal y, z;
    static integer nbits;
    extern doublereal dlamc3_();
    static doublereal recbas;
    static integer exbits, expsum, try__;


/*  -- LAPACK auxiliary routine (version 1.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/*     Courant Institute, Argonne National Lab, and Rice University */
/*     October 31, 1992 */

/*     .. Scalar Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  DLAMC5 attempts to compute RMAX, the largest machine floating-point */
/*  number, without overflow.  It assumes that EMAX + 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 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 */
/*     abs(EMIN). We then assume that EMAX + abs(EMIN) will sum */
/*     approximately to the bound that is closest to 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-b
it */
/*        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 = 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 = dlamc3_(&d__1, &c_b31);
/* L30: */
    }

    *rmax = y;
    return 0;

/*     End of DLAMC5 */

} /* dlamc5_ */

---