slamch.c

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/* slamch.f -- translated by f2c (version 20061008).
   You must link the resulting object file with libf2c:
        on Microsoft Windows system, link with libf2c.lib;
        on Linux or Unix systems, link with .../path/to/libf2c.a -lm
        or, if you install libf2c.a in a standard place, with -lf2c -lm
        -- in that order, at the end of the command line, as in
                cc *.o -lf2c -lm
        Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,

                http://www.netlib.org/f2c/libf2c.zip
*/

#include "f2c.h"
#include "blaswrap.h"

/* Table of constant values */

static integer c__1 = 1;
static real c_b32 = 0.f;

doublereal slamch_(char *cmach)
{
    /* Initialized data */

    static logical first = TRUE_;

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

    /* Builtin functions */
    double pow_ri(real *, integer *);

    /* Local variables */
    static real t;
    integer it;
    static real rnd, eps, base;
    integer beta;
    static real emin, prec, emax;
    integer imin, imax;
    logical lrnd;
    static real rmin, rmax;
    real rmach;
    extern logical lsame_(char *, char *);
    real small;
    static real sfmin;
    extern /* Subroutine */ int slamc2_(integer *, integer *, logical *, real 
            *, integer *, real *, integer *, real *);


/*  -- LAPACK auxiliary routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

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

/*  SLAMCH determines single precision machine parameters. */

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

/*  CMACH   (input) CHARACTER*1 */
/*          Specifies the value to be returned by SLAMCH: */
/*          = 'E' or 'e',   SLAMCH := eps */
/*          = 'S' or 's ,   SLAMCH := sfmin */
/*          = 'B' or 'b',   SLAMCH := base */
/*          = 'P' or 'p',   SLAMCH := eps*base */
/*          = 'N' or 'n',   SLAMCH := t */
/*          = 'R' or 'r',   SLAMCH := rnd */
/*          = 'M' or 'm',   SLAMCH := emin */
/*          = 'U' or 'u',   SLAMCH := rmin */
/*          = 'L' or 'l',   SLAMCH := emax */
/*          = 'O' or 'o',   SLAMCH := 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) {
        slamc2_(&beta, &it, &lrnd, &eps, &imin, &rmin, &imax, &rmax);
        base = (real) beta;
        t = (real) it;
        if (lrnd) {
            rnd = 1.f;
            i__1 = 1 - it;
            eps = pow_ri(&base, &i__1) / 2;
        } else {
            rnd = 0.f;
            i__1 = 1 - it;
            eps = pow_ri(&base, &i__1);
        }
        prec = eps * base;
        emin = (real) imin;
        emax = (real) imax;
        sfmin = rmin;
        small = 1.f / rmax;
        if (small >= sfmin) {

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

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

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

    ret_val = rmach;
    first = FALSE_;
    return ret_val;

/*     End of SLAMCH */

} /* slamch_ */


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

/* Subroutine */ int slamc1_(integer *beta, integer *t, logical *rnd, logical 
        *ieee1)
{
    /* Initialized data */

    static logical first = TRUE_;

    /* System generated locals */
    real r__1, r__2;

    /* Local variables */
    real a, b, c__, f, t1, t2;
    static integer lt;
    real one, qtr;
    static logical lrnd;
    static integer lbeta;
    real savec;
    static logical lieee1;
    extern doublereal slamc3_(real *, real *);


/*  -- LAPACK auxiliary routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

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

/*  SLAMC1 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.f;

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

/*        Throughout this routine  we use the function  SLAMC3  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 integer m such */
/*        that */

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

        a = 1.f;
        c__ = 1.f;

/* +       WHILE( C.EQ.ONE )LOOP */
L10:
        if (c__ == one) {
            a *= 2;
            c__ = slamc3_(&a, &one);
            r__1 = -a;
            c__ = slamc3_(&c__, &r__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.f;
        c__ = slamc3_(&a, &b);

/* +       WHILE( C.EQ.A )LOOP */
L20:
        if (c__ == a) {
            b *= 2;
            c__ = slamc3_(&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__;
        r__1 = -a;
        c__ = slamc3_(&c__, &r__1);
        lbeta = 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 = (real) lbeta;
        r__1 = b / 2;
        r__2 = -b / 100;
        f = slamc3_(&r__1, &r__2);
        c__ = slamc3_(&f, &a);
        if (c__ == a) {
            lrnd = TRUE_;
        } else {
            lrnd = FALSE_;
        }
        r__1 = b / 2;
        r__2 = b / 100;
        f = slamc3_(&r__1, &r__2);
        c__ = slamc3_(&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. */

        r__1 = b / 2;
        t1 = slamc3_(&r__1, &a);
        r__1 = b / 2;
        t2 = slamc3_(&r__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.f;
        c__ = 1.f;

/* +       WHILE( C.EQ.ONE )LOOP */
L30:
        if (c__ == one) {
            ++lt;
            a *= lbeta;
            c__ = slamc3_(&a, &one);
            r__1 = -a;
            c__ = slamc3_(&c__, &r__1);
            goto L30;
        }
/* +       END WHILE */

    }

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

/*     End of SLAMC1 */

} /* slamc1_ */


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

/* Subroutine */ int slamc2_(integer *beta, integer *t, logical *rnd, real *
        eps, integer *emin, real *rmin, integer *emax, real *rmax)
{
    /* Initialized data */

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

    /* Format strings */
    static char fmt_9999[] = "(//\002 WARNING. The value EMIN may be incorre"
            "ct:-\002,\002  EMIN = \002,i8,/\002 If, after inspection, the va"
            "lue EMIN looks\002,\002 acceptable please comment out \002,/\002"
            " the IF block as marked within the code of routine\002,\002 SLAM"
            "C2,\002,/\002 otherwise supply EMIN explicitly.\002,/)";

    /* System generated locals */
    integer i__1;
    real r__1, r__2, r__3, r__4, r__5;

    /* Builtin functions */
    double pow_ri(real *, integer *);
    integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);

    /* Local variables */
    real a, b, c__;
    integer i__;
    static integer lt;
    real one, two;
    logical ieee;
    real half;
    logical lrnd;
    static real leps;
    real zero;
    static integer lbeta;
    real rbase;
    static integer lemin, lemax;
    integer gnmin;
    real small;
    integer gpmin;
    real third;
    static real lrmin, lrmax;
    real sixth;
    logical lieee1;
    extern /* Subroutine */ int slamc1_(integer *, integer *, logical *, 
            logical *);
    extern doublereal slamc3_(real *, real *);
    extern /* Subroutine */ int slamc4_(integer *, real *, integer *), 
            slamc5_(integer *, integer *, integer *, logical *, integer *, 
            real *);
    integer ngnmin, ngpmin;

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

/*  SLAMC2 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) REAL */
/*          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) REAL */
/*          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) REAL */
/*          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.f;
        one = 1.f;
        two = 2.f;

/*        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  SLAMC3  to ensure */
/*        that relevant values are stored  and not held in registers,  or */
/*        are not affected by optimizers. */

/*        SLAMC1 returns the parameters  LBETA, LT, LRND and LIEEE1. */

        slamc1_(&lbeta, &lt, &lrnd, &lieee1);

/*        Start to find EPS. */

        b = (real) lbeta;
        i__1 = -lt;
        a = pow_ri(&b, &i__1);
        leps = a;

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

        b = two / 3;
        half = one / 2;
        r__1 = -half;
        sixth = slamc3_(&b, &r__1);
        third = slamc3_(&sixth, &sixth);
        r__1 = -half;
        b = slamc3_(&third, &r__1);
        b = slamc3_(&b, &sixth);
        b = dabs(b);
        if (b < leps) {
            b = leps;
        }

        leps = 1.f;

/* +       WHILE( ( LEPS.GT.B ).AND.( B.GT.ZERO ) )LOOP */
L10:
        if (leps > b && b > zero) {
            leps = b;
            r__1 = half * leps;
/* Computing 5th power */
            r__3 = two, r__4 = r__3, r__3 *= r__3;
/* Computing 2nd power */
            r__5 = leps;
            r__2 = r__4 * (r__3 * r__3) * (r__5 * r__5);
            c__ = slamc3_(&r__1, &r__2);
            r__1 = -c__;
            c__ = slamc3_(&half, &r__1);
            b = slamc3_(&half, &c__);
            r__1 = -b;
            c__ = slamc3_(&half, &r__1);
            b = slamc3_(&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;
        small = one;
        for (i__ = 1; i__ <= 3; ++i__) {
            r__1 = small * rbase;
            small = slamc3_(&r__1, &zero);
/* L20: */
        }
        a = slamc3_(&one, &small);
        slamc4_(&ngpmin, &one, &lbeta);
        r__1 = -one;
        slamc4_(&ngnmin, &r__1, &lbeta);
        slamc4_(&gpmin, &a, &lbeta);
        r__1 = -a;
        slamc4_(&gnmin, &r__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 = 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 underflow; */
/*              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_;
        }
        first = FALSE_;
/* ** */
/* Comment out this if block if EMIN is ok */
        if (iwarn) {
            first = TRUE_;
            s_wsfe(&io___58);
            do_fio(&c__1, (char *)&lemin, (ftnlen)sizeof(integer));
            e_wsfe();
        }
/* ** */

/*        Assume IEEE arithmetic if we found denormalised  numbers above, */
/*        or if arithmetic seems to round in the  IEEE style,  determined */
/*        in routine SLAMC1. 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.f;
        i__1 = 1 - lemin;
        for (i__ = 1; i__ <= i__1; ++i__) {
            r__1 = lrmin * rbase;
            lrmin = slamc3_(&r__1, &zero);
/* L30: */
        }

/*        Finally, call SLAMC5 to compute EMAX and RMAX. */

        slamc5_(&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 SLAMC2 */

} /* slamc2_ */


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

doublereal slamc3_(real *a, real *b)
{
    /* System generated locals */
    real ret_val;


/*  -- LAPACK auxiliary routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

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

/*  SLAMC3  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) REAL */
/*  B       (input) REAL */
/*          The values A and B. */

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

/*     .. Executable Statements .. */

    ret_val = *a + *b;

    return ret_val;

/*     End of SLAMC3 */

} /* slamc3_ */


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

/* Subroutine */ int slamc4_(integer *emin, real *start, integer *base)
{
    /* System generated locals */
    integer i__1;
    real r__1;

    /* Local variables */
    real a;
    integer i__;
    real b1, b2, c1, c2, d1, d2, one, zero, rbase;
    extern doublereal slamc3_(real *, real *);


/*  -- LAPACK auxiliary routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

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

/*  SLAMC4 is a service routine for SLAMC2. */

/*  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) REAL */
/*          The starting point for determining EMIN. */

/*  BASE    (input) INTEGER */
/*          The base of the machine. */

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

/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. Executable Statements .. */

    a = *start;
    one = 1.f;
    rbase = one / *base;
    zero = 0.f;
    *emin = 1;
    r__1 = a * rbase;
    b1 = slamc3_(&r__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;
        r__1 = a / *base;
        b1 = slamc3_(&r__1, &zero);
        r__1 = b1 * *base;
        c1 = slamc3_(&r__1, &zero);
        d1 = zero;
        i__1 = *base;
        for (i__ = 1; i__ <= i__1; ++i__) {
            d1 += b1;
/* L20: */
        }
        r__1 = a * rbase;
        b2 = slamc3_(&r__1, &zero);
        r__1 = b2 / rbase;
        c2 = slamc3_(&r__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 SLAMC4 */

} /* slamc4_ */


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

/* Subroutine */ int slamc5_(integer *beta, integer *p, integer *emin, 
        logical *ieee, integer *emax, real *rmax)
{
    /* System generated locals */
    integer i__1;
    real r__1;

    /* Local variables */
    integer i__;
    real y, z__;
    integer try__, lexp;
    real oldy;
    integer uexp, nbits;
    extern doublereal slamc3_(real *, real *);
    real recbas;
    integer exbits, expsum;


/*  -- LAPACK auxiliary routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

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

/*  SLAMC5 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) REAL */
/*          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-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.f / *beta;
    z__ = *beta - 1.f;
    y = 0.f;
    i__1 = *p;
    for (i__ = 1; i__ <= i__1; ++i__) {
        z__ *= recbas;
        if (y < 1.f) {
            oldy = y;
        }
        y = slamc3_(&y, &z__);
/* L20: */
    }
    if (y >= 1.f) {
        y = oldy;
    }

/*     Now multiply by BETA**EMAX to get RMAX. */

    i__1 = *emax;
    for (i__ = 1; i__ <= i__1; ++i__) {
        r__1 = y * *beta;
        y = slamc3_(&r__1, &c_b32);
/* L30: */
    }

    *rmax = y;
    return 0;

/*     End of SLAMC5 */

} /* slamc5_ */