strtod.c

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

The author of this software is David M. Gay.

Copyright (C) 1998-2001 by Lucent Technologies
All Rights Reserved

Permission to use, copy, modify, and distribute this software and
its documentation for any purpose and without fee is hereby
granted, provided that the above copyright notice appear in all
copies and that both that the copyright notice and this
permission notice and warranty disclaimer appear in supporting
documentation, and that the name of Lucent or any of its entities
not be used in advertising or publicity pertaining to
distribution of the software without specific, written prior
permission.

LUCENT DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE,
INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS.
IN NO EVENT SHALL LUCENT OR ANY OF ITS ENTITIES BE LIABLE FOR ANY
SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER
IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION,
ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF
THIS SOFTWARE.

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

/* Please send bug reports to David M. Gay (dmg at acm dot org,
 * with " at " changed at "@" and " dot " changed to ".").  */

#include "gdtoaimp.h"
#include <float.h>
#include <math.h>
#include <stdint.h>
#ifndef NO_FENV_H
#include <fenv.h>
#endif

#ifdef USE_LOCALE
#include "locale.h"
#endif

#ifdef IEEE_Arith
#ifndef NO_IEEE_Scale
#define Avoid_Underflow
#undef tinytens
/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
/* flag unnecessarily.  It leads to a song and dance at the end of strtod. */
static CONST double tinytens[] = {1e-16, 1e-32, 1e-64, 1e-128, 9007199254740992.e-256};
#endif
#endif

#ifdef Honor_FLT_ROUNDS
#define Rounding rounding
#undef Check_FLT_ROUNDS
#define Check_FLT_ROUNDS
#else
#define Rounding Flt_Rounds
#endif

double strtod
#ifdef KR_headers
    (s00, se) CONST char* s00;
CONST char** se;
#else
    (CONST char* s00, char** se)
#endif
{
#ifdef Avoid_Underflow
    int scale;
#endif
    int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, decpt, dsign, e, e1, esign, i, j, k, nd, nd0, nf,
        nz, nz0, sign;
    CONST char *s, *s0, *s1;
    double aadj, aadj1, adj, rv, rv0;
    Long L;
    ULong y, z;
    Bigint *bb = NULL, *bb1 = NULL, *bd = NULL, *bd0 = NULL, *bs = NULL, *delta = NULL;
#ifdef SET_INEXACT
    int inexact, oldinexact;
#endif
#ifdef Honor_FLT_ROUNDS
    int rounding;
#endif

    sign = nz0 = nz = decpt = 0;
    dval(rv) = 0.;
    for(s = s00;; s++)
    {
        switch(*s)
        {
            case '-':
                sign = 1;
                /* no break */
            case '+':
                if(*++s)
                {
                    goto break2;
                }
                /* no break */
            case 0:
                goto ret0;
            case '\t':
            case '\n':
            case '\v':
            case '\f':
            case '\r':
            case ' ':
                continue;
            default:
                goto break2;
        }
    }
break2:
    if(*s == '0')
    {
#ifndef NO_HEX_FP
        {
            static FPI fpi = {53, 1 - 1023 - 53 + 1, 2046 - 1023 - 53 + 1, 1, SI};
            Long exp;
            ULong bits[2];
            switch(s[1])
            {
                case 'x':
                case 'X':
                {
#if defined(FE_DOWNWARD) && defined(FE_TONEAREST) && defined(FE_TOWARDZERO) && defined(FE_UPWARD)
                    FPI fpi1 = fpi;
                    switch(fegetround())
                    {
                        case FE_TOWARDZERO:
                            fpi1.rounding = 0;
                            break;
                        case FE_UPWARD:
                            fpi1.rounding = 2;
                            break;
                        case FE_DOWNWARD:
                            fpi1.rounding = 3;
                    }
#else
#define fpi1 fpi
#endif
                    switch((i = gethex(&s, &fpi1, &exp, &bb, sign)) & STRTOG_Retmask)
                    {
                        case STRTOG_NoNumber:
                            s = s00;
                            sign = 0;
                        case STRTOG_Zero:
                            break;
                        default:
                            if(bb)
                            {
                                copybits(bits, fpi.nbits, bb);
                                Bfree(bb);
                            }
                            ULtod(((U*)&rv)->L, bits, exp, i);
                    }
                }
                    goto ret;
            }
        }
#endif
        nz0 = 1;
        while(*++s == '0')
        {
        }

        if(!*s)
        {
            goto ret;
        }
    }
    s0 = s;
    y = z = 0;
    for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
    {
        if(nd < 9)
        {
            y = 10 * y + (unsigned)c - '0';
        }
        else if(nd < 16)
        {
            z = 10 * z + (unsigned)c - '0';
        }
    }
    nd0 = nd;
#ifdef USE_LOCALE
    if(c == *localeconv()->decimal_point)
#else
    if(c == '.')
#endif
    {
        decpt = 1;
        c = *++s;
        if(!nd)
        {
            for(; c == '0'; c = *++s)
            {
                nz++;
            }
            if(c > '0' && c <= '9')
            {
                s0 = s;
                nf += nz;
                nz = 0;
                goto have_dig;
            }
            goto dig_done;
        }
        for(; c >= '0' && c <= '9'; c = *++s)
        {
        have_dig:
            nz++;
            if(c -= '0')
            {
                nf += nz;
                for(i = 1; i < nz; i++)
                {
                    if(nd++ < 9)
                    {
                        y *= 10;
                    }
                    else if(nd <= DBL_DIG + 1)
                    {
                        z *= 10;
                    }
                }
                if(nd++ < 9)
                {
                    y = 10 * y + (unsigned)c;
                }
                else if(nd <= DBL_DIG + 1)
                {
                    z = 10 * z + (unsigned)c;
                }
                nz = 0;
            }
        }
    }
dig_done:
    e = 0;
    if(c == 'e' || c == 'E')
    {
        if(!nd && !nz && !nz0)
        {
            goto ret0;
        }
        s00 = s;
        esign = 0;
        switch(c = *++s)
        {
            case '-':
                esign = 1;
            case '+':
                c = *++s;
        }
        if(c >= '0' && c <= '9')
        {
            while(c == '0')
            {
                c = *++s;
            }
            if(c > '0' && c <= '9')
            {
                L = c - '0';
                s1 = s;
                while((c = *++s) >= '0' && c <= '9')
                {
                    L = 10 * L + c - '0';
                }
                if(s - s1 > 8 || L > 19999)
                {
                    /* Avoid confusion from exponents
                     * so large that e might overflow.
                     */
                    e = 19999; /* safe for 16 bit ints */
                }
                else
                {
                    e = (int)L;
                }
                if(esign)
                {
                    e = -e;
                }
            }
            else
            {
                e = 0;
            }
        }
        else
        {
            s = s00;
        }
    }
    if(!nd)
    {
        if(!nz && !nz0)
        {
#ifdef INFNAN_CHECK
            /* Check for Nan and Infinity */
            ULong bits[2];
            static FPI fpinan = /* only 52 explicit bits */
                {52, 1 - 1023 - 53 + 1, 2046 - 1023 - 53 + 1, 1, SI};
            if(!decpt)
                switch(c)
                {
                    case 'i':
                    case 'I':
                        if(match(&s, "nf"))
                        {
                            --s;
                            if(!match(&s, "inity"))
                                ++s;
                            word0(rv) = 0x7ff00000;
                            word1(rv) = 0;
                            goto ret;
                        }
                        break;
                    case 'n':
                    case 'N':
                        if(match(&s, "an"))
                        {
#ifndef No_Hex_NaN
                            if(*s == '(' /*)*/
                               && hexnan(&s, &fpinan, bits) == STRTOG_NaNbits)
                            {
                                word0(rv) = 0x7ff00000 | bits[1];
                                word1(rv) = bits[0];
                            }
                            else
                            {
#endif
                                word0(rv) = NAN_WORD0;
                                word1(rv) = NAN_WORD1;
#ifndef No_Hex_NaN
                            }
#endif
                            goto ret;
                        }
                }
#endif /* INFNAN_CHECK */
        ret0:
            s = s00;
            sign = 0;
        }
        goto ret;
    }
    e1 = e -= nf;

    /* Now we have nd0 digits, starting at s0, followed by a
     * decimal point, followed by nd-nd0 digits.  The number we're
     * after is the integer represented by those digits times
     * 10**e */

    if(!nd0)
    {
        nd0 = nd;
    }
    k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
    dval(rv) = y;
    if(k > 9)
    {
#ifdef SET_INEXACT
        if(k > DBL_DIG)
            oldinexact = get_inexact();
#endif
        dval(rv) = tens[k - 9] * dval(rv) + z;
    }
    bd0 = 0;
    if(nd <= DBL_DIG
#ifndef RND_PRODQUOT
#ifndef Honor_FLT_ROUNDS
       && Flt_Rounds == 1
#endif
#endif
    )
    {
        if(!e)
        {
            goto ret;
        }
        if(e > 0)
        {
            if(e <= Ten_pmax)
            {
#ifdef VAX
                goto vax_ovfl_check;
#else
#ifdef Honor_FLT_ROUNDS
                /* round correctly FLT_ROUNDS = 2 or 3 */
                if(sign)
                {
                    rv = -rv;
                    sign = 0;
                }
#endif
                /* rv = */ rounded_product(dval(rv), tens[e]);
                goto ret;
#endif
            }
            i = DBL_DIG - nd;
            if(e <= Ten_pmax + i)
            {
                /* A fancier test would sometimes let us do
                 * this for larger i values.
                 */
#ifdef Honor_FLT_ROUNDS
                /* round correctly FLT_ROUNDS = 2 or 3 */
                if(sign)
                {
                    rv = -rv;
                    sign = 0;
                }
#endif
                e -= i;
                dval(rv) *= tens[i];
#ifdef VAX
                /* VAX exponent range is so narrow we must
                 * worry about overflow here...
                 */
            vax_ovfl_check:
                word0(rv) -= P * Exp_msk1;
                /* rv = */ rounded_product(dval(rv), tens[e]);
                if((word0(rv) & Exp_mask) > Exp_msk1 * (DBL_MAX_EXP + Bias - 1 - P))
                {
                    goto ovfl;
                }
                word0(rv) += P * Exp_msk1;
#else
                /* rv = */ rounded_product(dval(rv), tens[e]);
#endif
                goto ret;
            }
        }
#ifndef Inaccurate_Divide
        else if(e >= -Ten_pmax)
        {
#ifdef Honor_FLT_ROUNDS
            /* round correctly FLT_ROUNDS = 2 or 3 */
            if(sign)
            {
                rv = -rv;
                sign = 0;
            }
#endif
            /* rv = */ rounded_quotient(dval(rv), tens[-e]);
            goto ret;
        }
#endif
    }
    e1 += nd - k;

#ifdef IEEE_Arith
#ifdef SET_INEXACT
    inexact = 1;
    if(k <= DBL_DIG)
    {
        oldinexact = get_inexact();
    }
#endif
#ifdef Avoid_Underflow
    scale = 0;
#endif
#ifdef Honor_FLT_ROUNDS
    if((rounding = Flt_Rounds) >= 2)
    {
        if(sign)
        {
            rounding = rounding == 2 ? 0 : 2;
        }
        else if(rounding != 2)
        {
            rounding = 0;
        }
    }
#endif
#endif /*IEEE_Arith*/

    /* Get starting approximation = rv * 10**e1 */

    if(e1 > 0)
    {
        if((i = e1 & 15) != 0)
        {
            dval(rv) *= tens[i];
        }
        if(e1 &= ~15)
        {
            if(e1 > DBL_MAX_10_EXP)
            {
            ovfl:
#ifndef NO_ERRNO
                errno = ERANGE;
#endif
                /* Can't trust HUGE_VAL */
#ifdef IEEE_Arith
#ifdef Honor_FLT_ROUNDS
                switch(rounding)
                {
                    case 0: /* toward 0 */
                    case 3: /* toward -infinity */
                        word0(rv) = Big0;
                        word1(rv) = Big1;
                        break;
                    default:
                        word0(rv) = Exp_mask;
                        word1(rv) = 0;
                }
#else /*Honor_FLT_ROUNDS*/
                word0(rv) = Exp_mask;
                word1(rv) = 0;
#endif /*Honor_FLT_ROUNDS*/
#ifdef SET_INEXACT
                /* set overflow bit */
                dval(rv0) = 1e300;
                dval(rv0) *= dval(rv0);
#endif
#else /*IEEE_Arith*/
                word0(rv) = Big0;
                word1(rv) = Big1;
#endif /*IEEE_Arith*/
                if(bd0)
                {
                    goto retfree;
                }
                goto ret;
            }
            e1 >>= 4;
            for(j = 0; e1 > 1; j++, e1 >>= 1)
            {
                if(e1 & 1)
                {
                    dval(rv) *= bigtens[j];
                }
            }
            /* The last multiplication could overflow. */
            word0(rv) -= P * Exp_msk1;
            dval(rv) *= bigtens[j];
            if((z = word0(rv) & Exp_mask) > Exp_msk1 * (DBL_MAX_EXP + Bias - P))
            {
                goto ovfl;
            }
            if(z > Exp_msk1 * (DBL_MAX_EXP + Bias - 1 - P))
            {
                /* set to largest number */
                /* (Can't trust DBL_MAX) */
                word0(rv) = Big0;
                word1(rv) = Big1;
            }
            else
            {
                word0(rv) += P * Exp_msk1;
            }
        }
    }
    else if(e1 < 0)
    {
        e1 = -e1;
        if((i = e1 & 15) != 0)
        {
            dval(rv) /= tens[i];
        }
        if(e1 >>= 4)
        {
            if(e1 >= 1 << n_bigtens)
            {
                goto undfl;
            }
#ifdef Avoid_Underflow
            if(e1 & Scale_Bit)
            {
                scale = 2 * P;
            }
            for(j = 0; e1 > 0; j++, e1 >>= 1)
            {
                if(e1 & 1)
                {
                    dval(rv) *= tinytens[j];
                }
            }
            if(scale && (j = 2 * P + 1 - ((word0(rv) & Exp_mask) >> Exp_shift)) > 0)
            {
                /* scaled rv is denormal; zap j low bits */
                if(j >= 32)
                {
                    word1(rv) = 0;
                    if(j >= 53)
                    {
                        word0(rv) = (P + 2) * Exp_msk1;
                    }
                    else
                    {
                        word0(rv) &= 0xffffffff << (j - 32);
                    }
                }
                else
                {
                    word1(rv) &= 0xffffffff << j;
                }
            }
#else
            for(j = 0; e1 > 1; j++, e1 >>= 1)
            {
                if(e1 & 1)
                {
                    dval(rv) *= tinytens[j];
                }
            }
            /* The last multiplication could underflow. */
            dval(rv0) = dval(rv);
            dval(rv) *= tinytens[j];
            if(!dval(rv))
            {
                dval(rv) = 2. * dval(rv0);
                dval(rv) *= tinytens[j];
#endif
            if(fabs(dval(rv)) <= DBL_EPSILON)
            {
            undfl:
                dval(rv) = 0.;
#ifndef NO_ERRNO
                errno = ERANGE;
#endif
                if(bd0)
                {
                    goto retfree;
                }
                goto ret;
            }
#ifndef Avoid_Underflow
            word0(rv) = Tiny0;
            word1(rv) = Tiny1;
            /* The refinement below will clean
             * this approximation up.
             */
        }
#endif
    }
}

/* Now the hard part -- adjusting rv to the correct value.*/

/* Put digits into bd: true value = bd * 10^e */

bd0 = s2b(s0, nd0, nd, y);

for(;;)
{
    bd = Balloc(bd0->k);
    Bcopy(bd, bd0);
    bb = d2b(dval(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */
    bs = i2b(1);

    if(e >= 0)
    {
        bb2 = bb5 = 0;
        bd2 = bd5 = e;
    }
    else
    {
        bb2 = bb5 = -e;
        bd2 = bd5 = 0;
    }
    if(bbe >= 0)
    {
        bb2 += bbe;
    }
    else
    {
        bd2 -= bbe;
    }
    bs2 = bb2;
#ifdef Honor_FLT_ROUNDS
    if(rounding != 1)
    {
        bs2++;
    }
#endif
#ifdef Avoid_Underflow
    j = bbe - scale;
    i = j + bbbits - 1; /* logb(rv) */
    if(i < Emin) /* denormal */
    {
        j += P - Emin;
    }
    else
    {
        j = P + 1 - bbbits;
    }
#else /*Avoid_Underflow*/
#ifdef Sudden_Underflow
#ifdef IBM
            j = 1 + 4 * P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
#else
            j = P + 1 - bbbits;
#endif
#else /*Sudden_Underflow*/
            j = bbe;
            i = j + bbbits - 1; /* logb(rv) */
            if(i < Emin) /* denormal */
            {
                j += P - Emin;
            }
            else
            {
                j = P + 1 - bbbits;
            }
#endif /*Sudden_Underflow*/
#endif /*Avoid_Underflow*/
    bb2 += j;
    bd2 += j;
#ifdef Avoid_Underflow
    bd2 += scale;
#endif
    i = bb2 < bd2 ? bb2 : bd2;
    if(i > bs2)
    {
        i = bs2;
    }
    if(i > 0)
    {
        bb2 -= i;
        bd2 -= i;
        bs2 -= i;
    }
    if(bb5 > 0)
    {
        bs = pow5mult(bs, bb5);
        bb1 = mult(bs, bb);
        Bfree(bb);
        bb = bb1;
    }
    if(bb2 > 0)
    {
        bb = lshift(bb, bb2);
    }
    if(bd5 > 0)
    {
        bd = pow5mult(bd, bd5);
    }
    if(bd2 > 0)
    {
        bd = lshift(bd, bd2);
    }
    if(bs2 > 0)
    {
        bs = lshift(bs, bs2);
    }
    delta = diff(bb, bd);
    dsign = delta->sign;
    delta->sign = 0;
    i = cmp(delta, bs);
#ifdef Honor_FLT_ROUNDS
    if(rounding != 1)
    {
        if(i < 0)
        {
            /* Error is less than an ulp */
            if(!delta->x[0] && delta->wds <= 1)
            {
                /* exact */
#ifdef SET_INEXACT
                inexact = 0;
#endif
                break;
            }
            if(rounding)
            {
                if(dsign)
                {
                    adj = 1.;
                    goto apply_adj;
                }
            }
            else if(!dsign)
            {
                adj = -1.;
                if(!word1(rv) && !(word0(rv) & Frac_mask))
                {
                    y = word0(rv) & Exp_mask;
#ifdef Avoid_Underflow
                    if(!scale || y > 2 * P * Exp_msk1)
#else
                    if(y)
#endif
                    {
                        delta = lshift(delta, Log2P);
                        if(cmp(delta, bs) <= 0)
                        {
                            adj = -0.5;
                        }
                    }
                }
            apply_adj:
#ifdef Avoid_Underflow
                if(scale && (y = word0(rv) & Exp_mask) <= 2 * P * Exp_msk1)
                {
                    word0(adj) += (2 * P + 1) * Exp_msk1 - y;
                }
#else
#ifdef Sudden_Underflow
                if((word0(rv) & Exp_mask) <= P * Exp_msk1)
                {
                    word0(rv) += P * Exp_msk1;
                    dval(rv) += adj * ulp(dval(rv));
                    word0(rv) -= P * Exp_msk1;
                }
                else
#endif /*Sudden_Underflow*/
#endif /*Avoid_Underflow*/
                dval(rv) += adj * ulp(dval(rv));
            }
            break;
        }
        adj = ratio(delta, bs);
        if(adj < 1.)
        {
            adj = 1.;
        }
        if(adj <= 0x7ffffffe)
        {
            /* adj = rounding ? ceil(adj) : floor(adj); */
            y = (ULong)adj;
            if(fabs(y - adj) > DBL_EPSILON)
            {
                if(!((rounding >> 1) ^ dsign))
                {
                    y++;
                }
                adj = y;
            }
        }
#ifdef Avoid_Underflow
        if(scale && (y = word0(rv) & Exp_mask) <= (2 * P * Exp_msk1))
        {
            word0(adj) += (2 * P + 1) * Exp_msk1 - y;
        }
#else
#ifdef Sudden_Underflow
        if((word0(rv) & Exp_mask) <= P * Exp_msk1)
        {
            word0(rv) += P * Exp_msk1;
            adj *= ulp(dval(rv));
            if(dsign)
            {
                dval(rv) += adj;
            }
            else
            {
                dval(rv) -= adj;
            }
            word0(rv) -= P * Exp_msk1;
            goto cont;
        }
#endif /*Sudden_Underflow*/
#endif /*Avoid_Underflow*/
        adj *= ulp(dval(rv));
        if(dsign)
        {
            dval(rv) += adj;
        }
        else
        {
            dval(rv) -= adj;
        }
        goto cont;
    }
#endif /*Honor_FLT_ROUNDS*/

    if(i < 0)
    {
        /* Error is less than half an ulp -- check for
         * special case of mantissa a power of two.
         */
        if(dsign || word1(rv) || word0(rv) & Bndry_mask
#ifdef IEEE_Arith
#ifdef Avoid_Underflow
           || (word0(rv) & Exp_mask) <= (2 * P + 1) * Exp_msk1
#else
           || (word0(rv) & Exp_mask) <= Exp_msk1
#endif
#endif
        )
        {
#ifdef SET_INEXACT
            if(!delta->x[0] && delta->wds <= 1)
            {
                inexact = 0;
            }
#endif
            break;
        }
        if(!delta->x[0] && delta->wds <= 1)
        {
            /* exact result */
#ifdef SET_INEXACT
            inexact = 0;
#endif
            break;
        }
        delta = lshift(delta, Log2P);
        if(cmp(delta, bs) > 0)
        {
            goto drop_down;
        }
        break;
    }
    if(i == 0)
    {
        /* exactly half-way between */
        if(dsign)
        {
            if((word0(rv) & Bndry_mask1) == Bndry_mask1 &&
               word1(rv) == (
#ifdef Avoid_Underflow
                                (scale && (y = word0(rv) & Exp_mask) <= 2 * P * Exp_msk1)
                                    ? (0xffffffff & (0xffffffff << (2 * P + 1 - (y >> Exp_shift))))
                                    :
#endif
                                    0xffffffff))
            {
                /*boundary case -- increment exponent*/
                word0(rv) = (word0(rv) & Exp_mask) + Exp_msk1
#ifdef IBM
                            | Exp_msk1 >> 4
#endif
                    ;
                word1(rv) = 0;
#ifdef Avoid_Underflow
                dsign = 0;
#endif
                break;
            }
        }
        else if(!(word0(rv) & Bndry_mask) && !word1(rv))
        {
        drop_down:
            /* boundary case -- decrement exponent */
#ifdef Sudden_Underflow /*{{*/
            L = word0(rv) & Exp_mask;
#ifdef IBM
            if(L < Exp_msk1)
#else
#ifdef Avoid_Underflow
            if(L <= (scale ? (2 * P + 1) * Exp_msk1 : Exp_msk1))
#else
            if(L <= Exp_msk1)
#endif /*Avoid_Underflow*/
#endif /*IBM*/
                goto undfl;
            L -= Exp_msk1;
#else /*Sudden_Underflow}{*/
#ifdef Avoid_Underflow
                    if(scale)
                    {
                        L = word0(rv) & Exp_mask;
                        if(L <= (2 * P + 1) * Exp_msk1)
                        {
                            if(L > (P + 2) * Exp_msk1)
                            {
                                /* round even ==> */
                                /* accept rv */
                                break;
                            }
                            /* rv = smallest denormal */
                            goto undfl;
                        }
                    }
#endif /*Avoid_Underflow*/
                    L = (word0(rv) & Exp_mask) - Exp_msk1;
#endif /*Sudden_Underflow}*/
            word0(rv) = (ULong)(L | Bndry_mask1);
            word1(rv) = 0xffffffff;
#ifdef IBM
            goto cont;
#else
                    break;
#endif
        }
#ifndef ROUND_BIASED
        if(!(word1(rv) & LSB))
        {
            break;
        }
#endif
        if(dsign)
        {
            dval(rv) += ulp(dval(rv));
        }
#ifndef ROUND_BIASED
        else
        {
            dval(rv) -= ulp(dval(rv));
#ifndef Sudden_Underflow
            if(fabs(dval(rv)) <= DBL_EPSILON)
            {
                goto undfl;
            }
#endif
        }
#ifdef Avoid_Underflow
        dsign = 1 - dsign;
#endif
#endif
        break;
    }
    if((aadj = ratio(delta, bs)) <= 2.)
    {
        if(dsign)
        {
            aadj = aadj1 = 1.;
        }
        else if(word1(rv) || word0(rv) & Bndry_mask)
        {
#ifndef Sudden_Underflow
            if(word1(rv) == Tiny1 && !word0(rv))
            {
                goto undfl;
            }
#endif
            aadj = 1.;
            aadj1 = -1.;
        }
        else
        {
            /* special case -- power of FLT_RADIX to be */
            /* rounded down... */

            if(aadj < 2. / FLT_RADIX)
            {
                aadj = 1. / FLT_RADIX;
            }
            else
            {
                aadj *= 0.5;
            }
            aadj1 = -aadj;
        }
    }
    else
    {
        aadj *= 0.5;
        aadj1 = dsign ? aadj : -aadj;
#ifdef Check_FLT_ROUNDS
        switch(Rounding)
        {
            case 2: /* towards +infinity */
                aadj1 -= 0.5;
                break;
            case 0: /* towards 0 */
            case 3: /* towards -infinity */
                aadj1 += 0.5;
        }
#else
                if(Flt_Rounds == 0)
                {
                    aadj1 += 0.5;
                }
#endif /*Check_FLT_ROUNDS*/
    }
    y = word0(rv) & Exp_mask;

    /* Check for overflow */

    if(y == Exp_msk1 * (DBL_MAX_EXP + Bias - 1))
    {
        dval(rv0) = dval(rv);
        word0(rv) -= P * Exp_msk1;
        adj = aadj1 * ulp(dval(rv));
        dval(rv) += adj;
        if((word0(rv) & Exp_mask) >= Exp_msk1 * (DBL_MAX_EXP + Bias - P))
        {
            if(word0(rv0) == Big0 && word1(rv0) == Big1)
            {
                goto ovfl;
            }
            word0(rv) = Big0;
            word1(rv) = Big1;
            goto cont;
        }
        else
        {
            word0(rv) += P * Exp_msk1;
        }
    }
    else
    {
#ifdef Avoid_Underflow
        if(scale && y <= 2 * P * Exp_msk1)
        {
            if(aadj <= 0x7fffffff)
            {
                z = (ULong)aadj;
                if(z <= 0)
                {
                    z = 1;
                }
                aadj = z;
                aadj1 = dsign ? aadj : -aadj;
            }
            word0(aadj1) += (2 * P + 1) * Exp_msk1 - y;
        }
        adj = aadj1 * ulp(dval(rv));
        dval(rv) += adj;
#else
#ifdef Sudden_Underflow
                if((word0(rv) & Exp_mask) <= P * Exp_msk1)
                {
                    dval(rv0) = dval(rv);
                    word0(rv) += P * Exp_msk1;
                    adj = aadj1 * ulp(dval(rv));
                    dval(rv) += adj;
#ifdef IBM
                    if((word0(rv) & Exp_mask) < P * Exp_msk1)
#else
                    if((word0(rv) & Exp_mask) <= P * Exp_msk1)
#endif
                    {
                        if(word0(rv0) == Tiny0 && word1(rv0) == Tiny1)
                        {
                            goto undfl;
                        }
                        word0(rv) = Tiny0;
                        word1(rv) = Tiny1;
                        goto cont;
                    }
                    else
                    {
                        word0(rv) -= P * Exp_msk1;
                    }
                }
                else
                {
                    adj = aadj1 * ulp(dval(rv));
                    dval(rv) += adj;
                }
#else /*Sudden_Underflow*/
                /* Compute adj so that the IEEE rounding rules will
                 * correctly round rv + adj in some half-way cases.
                 * If rv * ulp(rv) is denormalized (i.e.,
                 * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
                 * trouble from bits lost to denormalization;
                 * example: 1.2e-307 .
                 */
                if(y <= (P - 1) * Exp_msk1 && aadj > 1.)
                {
                    aadj1 = (double)(int)(aadj + 0.5);
                    if(!dsign)
                    {
                        aadj1 = -aadj1;
                    }
                }
                adj = aadj1 * ulp(dval(rv));
                dval(rv) += adj;
#endif /*Sudden_Underflow*/
#endif /*Avoid_Underflow*/
    }
    z = word0(rv) & Exp_mask;
#ifndef SET_INEXACT
#ifdef Avoid_Underflow
    if(!scale)
    {
#endif
        if(y == z)
        {
            /* Can we stop now? */
            L = (Long)aadj;
            aadj -= L;
            /* The tolerances below are conservative. */
            if(dsign || word1(rv) || word0(rv) & Bndry_mask)
            {
                if(aadj < .4999999 || aadj > .5000001)
                {
                    break;
                }
            }
            else if(aadj < .4999999 / FLT_RADIX)
            {
                break;
            }
        }
#ifdef Avoid_Underflow
    }
#endif
#endif
cont:
    Bfree(bb);
    Bfree(bd);
    Bfree(bs);
    Bfree(delta);
}
#ifdef SET_INEXACT
if(inexact)
{
    if(!oldinexact)
    {
        word0(rv0) = Exp_1 + (70 << Exp_shift);
        word1(rv0) = 0;
        dval(rv0) += 1.;
    }
}
else if(!oldinexact)
{
    clear_inexact();
}
#endif
#ifdef Avoid_Underflow
if(scale)
{
    word0(rv0) = Exp_1 - 2 * P * Exp_msk1;
    word1(rv0) = 0;
    dval(rv) *= dval(rv0);
#ifndef NO_ERRNO
    /* try to avoid the bug of testing an 8087 register value */
    if(word0(rv) == 0 && word1(rv) == 0)
    {
        errno = ERANGE;
    }
#endif
}
#endif /* Avoid_Underflow */
#ifdef SET_INEXACT
if(inexact && !(word0(rv) & Exp_mask))
{
    /* set underflow bit */
    dval(rv0) = 1e-300;
    dval(rv0) *= dval(rv0);
}
#endif
retfree : if(bb)
{
    Bfree(bb);
}

if(bd)
{
    Bfree(bd);
}

if(bs)
{
    Bfree(bs);
}

if(bd0)
{
    Bfree(bd0);
}

if(delta)
{
    Bfree(delta);
}

ret : if(se)
{
    *se = (char*)(uintptr_t)s;
}
return sign ? -dval(rv) : dval(rv);
}