gdtoa.c File Reference

#include "gdtoaimp.h"
#include <float.h>
#include <math.h>

Include dependency graph for gdtoa.c:

Go to the source code of this file.

Functions
static Bigint *	bitstob (ULong *bits, int nbits, int *bbits)
char *	gdtoa (FPI *fpi, int be, ULong *bits, int *kindp, int mode, int ndigits, int *decpt, char **rve)

Function Documentation

bitstob()

static Bigint* bitstob ( ULong *  bits, int  nbits, int *  bbits  )

static

Definition at line 42 of file gdtoa.c.

{
    int i, k;
    Bigint* b;
    ULong *be, *x, *x0;

    i = ULbits;
    k = 0;
    while(i < nbits)
    {
        i <<= 1;
        k++;
    }
#ifndef Pack_32
    if(!k)
        k = 1;
#endif
    b = Balloc(k);
    be = bits + ((nbits - 1) >> kshift);
    x = x0 = b->x;
    do
    {
        *x++ = *bits & ALL_ON;
#ifdef Pack_16
        *x++ = (*bits >> 16) & ALL_ON;
#endif
    } while(++bits <= be);
    i = (int)(x - x0); // TODO: can we fix types here?
    while(!x0[--i])
    {
        {
            if(!i)
            {
                b->wds = 0;
                *bbits = 0;
                goto ret;
            }
        }
    }
    b->wds = i + 1;
    *bbits = i * ULbits + 32 - hi0bits(b->x[i]);
ret:
    return b;
}

References ALL_ON, Balloc(), hi0bits, kshift, ULbits, Bigint::wds, and Bigint::x.

Referenced by gdtoa().

gdtoa()

char* gdtoa	(	FPI *	fpi,
		int	be,
		ULong *	bits,
		int *	kindp,
		int	mode,
		int	ndigits,
		int *	decpt,
		char **	rve
	)

Definition at line 130 of file gdtoa.c.

{
    /*  Arguments ndigits and decpt are similar to the second and third
       arguments of ecvt and fcvt; trailing zeros are suppressed from
       the returned string.  If not null, *rve is set to point
       to the end of the return value.  If d is +-Infinity or NaN,
       then *decpt is set to 9999.

       mode:
           0 ==> shortest string that yields d when read in
               and rounded to nearest.
           1 ==> like 0, but with Steele & White stopping rule;
               e.g. with IEEE P754 arithmetic , mode 0 gives
               1e23 whereas mode 1 gives 9.999999999999999e22.
           2 ==> max(1,ndigits) significant digits.  This gives a
               return value similar to that of ecvt, except
               that trailing zeros are suppressed.
           3 ==> through ndigits past the decimal point.  This
               gives a return value similar to that from fcvt,
               except that trailing zeros are suppressed, and
               ndigits can be negative.
           4-9 should give the same return values as 2-3, i.e.,
               4 <= mode <= 9 ==> same return as mode
               2 + (mode & 1).  These modes are mainly for
               debugging; often they run slower but sometimes
               faster than modes 2-3.
           4,5,8,9 ==> left-to-right digit generation.
           6-9 ==> don't try fast floating-point estimate
               (if applicable).

           Values of mode other than 0-9 are treated as mode 0.

           Sufficient space is allocated to the return value
           to hold the suppressed trailing zeros.
       */

    int bbits, b2, b5, be0, dig, i, ieps, ilim = 0, ilim0, ilim1 = 0, inex;
    int j, j1, k, k0, k_check, kind, leftright, m2, m5, nbits;
    int rdir, s2, s5, spec_case, try_quick;
    Long L;
    Bigint *b, *b1, *delta, *mlo = NULL, *mhi, *mhi1, *S;
    double d, d2, ds, eps;
    char *s, *s0;

#ifndef MULTIPLE_THREADS
    if(dtoa_result)
    {
        freedtoa(dtoa_result);
        dtoa_result = 0;
    }
#endif
    inex = 0;
    kind = *kindp &= ~STRTOG_Inexact;
    switch(kind & STRTOG_Retmask)
    {
        case STRTOG_Zero:
            goto ret_zero;
        case STRTOG_Normal:
        case STRTOG_Denormal:
            break;
        case STRTOG_Infinite:
            *decpt = -32768;
            return nrv_alloc("Infinity", rve, 8);
        case STRTOG_NaN:
            *decpt = -32768;
            return nrv_alloc("NaN", rve, 3);
        default:
            return 0;
    }
    b = bitstob(bits, nbits = fpi->nbits, &bbits);
    be0 = be;
    if((i = trailz(b)) != 0)
    {
        rshift(b, i);
        be += i;
        bbits -= i;
    }
    if(!b->wds)
    {
        Bfree(b);
    ret_zero:
        *decpt = 1;
        return nrv_alloc("0", rve, 1);
    }

    dval(d) = b2d(b, &i);
    i = be + bbits - 1;
    word0(d) &= Frac_mask1;
    word0(d) |= Exp_11;

    /* log(x)   ~=~ log(1.5) + (x-1.5)/1.5
     * log10(x)  =  log(x) / log(10)
     *      ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
     * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
     *
     * This suggests computing an approximation k to log10(d) by
     *
     * k = (i - Bias)*0.301029995663981
     *  + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
     *
     * We want k to be too large rather than too small.
     * The error in the first-order Taylor series approximation
     * is in our favor, so we just round up the constant enough
     * to compensate for any error in the multiplication of
     * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
     * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
     * adding 1e-13 to the constant term more than suffices.
     * Hence we adjust the constant term to 0.1760912590558.
     * (We could get a more accurate k by invoking log10,
     *  but this is probably not worthwhile.)
     */
    ds = (dval(d) - 1.5) * 0.289529654602168 + 0.1760912590558 + i * 0.301029995663981;

    /* correct assumption about exponent range */
    if((j = i) < 0)
    {
        j = -j;
    }
    if((j -= 1077) > 0)
    {
        ds += j * 7e-17;
    }

    k = (int)ds;
    if(ds < 0. && (fabs(ds - k) > DBL_EPSILON))
    {
        k--; /* want k = floor(ds) */
    }
    k_check = 1;
    word0(d) += (unsigned)((be + bbits - 1) << Exp_shift);
    if(k >= 0 && k <= Ten_pmax)
    {
        if(dval(d) < tens[k])
        {
            k--;
        }
        k_check = 0;
    }
    j = bbits - i - 1;
    if(j >= 0)
    {
        b2 = 0;
        s2 = j;
    }
    else
    {
        b2 = -j;
        s2 = 0;
    }
    if(k >= 0)
    {
        b5 = 0;
        s5 = k;
        s2 += k;
    }
    else
    {
        b2 -= k;
        b5 = -k;
        s5 = 0;
    }
    if(mode < 0 || mode > 9)
    {
        mode = 0;
    }
    try_quick = 1;
    if(mode > 5)
    {
        mode -= 4;
        try_quick = 0;
    }
    leftright = 1;
    switch(mode)
    {
        case 0:
        case 1:
            ilim = ilim1 = -1;
            i = (int)(nbits * .30103) + 3;
            ndigits = 0;
            break;
        case 2:
            leftright = 0;
            /* no break */
        case 4:
            if(ndigits <= 0)
            {
                {
                    ndigits = 1;
                }
            }
            ilim = ilim1 = i = ndigits;
            break;
        case 3:
            leftright = 0;
            /* no break */
        case 5:
            i = ndigits + k + 1;
            ilim = i;
            ilim1 = i - 1;
            if(i <= 0)
            {
                {
                    i = 1;
                }
            }
    }
    s = s0 = rv_alloc(i);

    if((rdir = fpi->rounding - 1) != 0)
    {
        if(rdir < 0)
        {
            {
                rdir = 2;
            }
        }
        if(kind & STRTOG_Neg)
        {
            {
                rdir = 3 - rdir;
            }
        }
    }

    /* Now rdir = 0 ==> round near, 1 ==> round up, 2 ==> round down. */

    if(ilim >= 0 && ilim <= Quick_max && try_quick && !rdir
#ifndef IMPRECISE_INEXACT
       && k == 0
#endif
    )
    {
        /* Try to get by with floating-point arithmetic. */

        i = 0;
        d2 = dval(d);
        k0 = k;
        ilim0 = ilim;
        ieps = 2; /* conservative */
        if(k > 0)
        {
            ds = tens[k & 0xf];
            j = k >> 4;
            if(j & Bletch)
            {
                /* prevent overflows */
                j &= Bletch - 1;
                dval(d) /= bigtens[n_bigtens - 1];
                ieps++;
            }
            for(; j; j >>= 1, i++)
            {
                {
                    if(j & 1)
                    {
                        ieps++;
                        ds *= bigtens[i];
                    }
                }
            }
        }
        else
        {
            ds = 1.;
            if((j1 = -k) != 0)
            {
                dval(d) *= tens[j1 & 0xf];
                for(j = j1 >> 4; j; j >>= 1, i++)
                {
                    {
                        if(j & 1)
                        {
                            ieps++;
                            dval(d) *= bigtens[i];
                        }
                    }
                }
            }
        }
        if(k_check && dval(d) < 1. && ilim > 0)
        {
            if(ilim1 <= 0)
            {
                {
                    goto fast_failed;
                }
            }
            ilim = ilim1;
            k--;
            dval(d) *= 10.;
            ieps++;
        }
        dval(eps) = ieps * dval(d) + 7.;
        word0(eps) -= (P - 1) * Exp_msk1;
        if(ilim == 0)
        {
            S = mhi = 0;
            dval(d) -= 5.;
            if(dval(d) > dval(eps))
            {
                {
                    goto one_digit;
                }
            }
            if(dval(d) < -dval(eps))
            {
                {
                    goto no_digits;
                }
            }
            goto fast_failed;
        }
#ifndef No_leftright
        if(leftright)
        {
            /* Use Steele & White method of only
             * generating digits needed.
             */
            dval(eps) = ds * 0.5 / tens[ilim - 1] - dval(eps);
            for(i = 0;;)
            {
                L = (Long)(dval(d) / ds);
                dval(d) -= L * ds;
                *s++ = (char)('0' + (int)L);
                if(dval(d) < dval(eps))
                {
                    if(dval(d) > 0.0)
                    {
                        inex = STRTOG_Inexlo;
                    }
                    goto ret1;
                }
                if(ds - dval(d) < dval(eps))
                {
                    goto bump_up;
                }
                if(++i >= ilim)
                {
                    break;
                }
                dval(eps) *= 10.;
                dval(d) *= 10.;
            }
        }
        else
        {
#endif
            /* Generate ilim digits, then fix them up. */
            dval(eps) *= tens[ilim - 1];
            for(i = 1;; i++, dval(d) *= 10.)
            {
                if((L = (Long)(dval(d) / ds)) != 0)
                {
                    dval(d) -= L * ds;
                }
                *s++ = (char)('0' + (int)L);
                if(i == ilim)
                {
                    ds *= 0.5;
                    if(dval(d) > ds + dval(eps))
                    {
                        goto bump_up;
                    }
                    else if(dval(d) < ds - dval(eps))
                    {
                        while(*--s == '0')
                        {
                        }
                        s++;
                        if(dval(d) > 0.0)
                        {
                            inex = STRTOG_Inexlo;
                        }
                        goto ret1;
                    }
                    break;
                }
            }
#ifndef No_leftright
        }
#endif
    fast_failed:
        s = s0;
        dval(d) = d2;
        k = k0;
        ilim = ilim0;
    }

    /* Do we have a "small" integer? */

    if(be >= 0 && k <= Int_max)
    {
        /* Yes. */
        ds = tens[k];
        if(ndigits < 0 && ilim <= 0)
        {
            S = mhi = 0;
            if(ilim < 0 || dval(d) <= 5 * ds)
            {
                {
                    goto no_digits;
                }
            }
            goto one_digit;
        }
        for(i = 1;; i++, dval(d) *= 10.)
        {
            L = (int)(dval(d) / ds);
            dval(d) -= L * ds;
#ifdef Check_FLT_ROUNDS
            /* If FLT_ROUNDS == 2, L will usually be high by 1 */
            if(dval(d) < 0)
            {
                L--;
                dval(d) += ds;
            }
#endif
            *s++ = (char)('0' + (int)L);
            if(dval(d) == 0.)
            {
                {
                    break;
                }
            }
            if(i == ilim)
            {
                if(rdir)
                {
                    if(rdir == 1)
                    {
                        {
                            goto bump_up;
                        }
                    }
                    inex = STRTOG_Inexlo;
                    goto ret1;
                }
                dval(d) += dval(d);
                if((dval(d) > ds) || ((fabs(dval(d) - ds) <= DBL_EPSILON) && (L & 1)))
                {
                bump_up:
                    inex = STRTOG_Inexhi;
                    while(*--s == '9')
                    {
                        {
                            if(s == s0)
                            {
                                k++;
                                *s = '0';
                                break;
                            }
                        }
                    }
                    ++*s++;
                }
                else
                {
                    {
                        inex = STRTOG_Inexlo;
                    }
                }
                break;
            }
        }
        goto ret1;
    }

    m2 = b2;
    m5 = b5;
    mhi = mlo = 0;
    if(leftright)
    {
        if(mode < 2)
        {
            i = nbits - bbits;
            if(be - i++ < fpi->emin)
            {
                {
                    /* denormal */
                    i = be - fpi->emin + 1;
                }
            }
        }
        else
        {
            j = ilim - 1;
            if(m5 >= j)
            {
                {
                    m5 -= j;
                }
            }
            else
            {
                s5 += j -= m5;
                b5 += j;
                m5 = 0;
            }
            if((i = ilim) < 0)
            {
                m2 -= i;
                i = 0;
            }
        }
        b2 += i;
        s2 += i;
        mhi = i2b(1);
    }
    if(m2 > 0 && s2 > 0)
    {
        i = m2 < s2 ? m2 : s2;
        b2 -= i;
        m2 -= i;
        s2 -= i;
    }
    if(b5 > 0)
    {
        if(leftright)
        {
            if(m5 > 0)
            {
                mhi = pow5mult(mhi, m5);
                b1 = mult(mhi, b);
                Bfree(b);
                b = b1;
            }
            if((j = b5 - m5) != 0)
            {
                {
                    b = pow5mult(b, j);
                }
            }
        }
        else
        {
            {
                b = pow5mult(b, b5);
            }
        }
    }
    S = i2b(1);
    if(s5 > 0)
    {
        {
            S = pow5mult(S, s5);
        }
    }

    /* Check for special case that d is a normalized power of 2. */

    spec_case = 0;
    if(mode < 2)
    {
        if(bbits == 1 && be0 > fpi->emin + 1)
        {
            /* The special case */
            b2++;
            s2++;
            spec_case = 1;
        }
    }

    /* Arrange for convenient computation of quotients:
     * shift left if necessary so divisor has 4 leading 0 bits.
     *
     * Perhaps we should just compute leading 28 bits of S once
     * and for all and pass them and a shift to quorem, so it
     * can do shifts and ors to compute the numerator for q.
     */
#ifdef Pack_32
    if((i = ((s5 ? 32 - hi0bits(S->x[S->wds - 1]) : 1) + s2) & 0x1f) != 0)
    {
        {
            i = 32 - i;
        }
    }
#else
    if((i = ((s5 ? 32 - hi0bits(S->x[S->wds - 1]) : 1) + s2) & 0xf) != 0)
        i = 16 - i;
#endif
    if(i > 4)
    {
        i -= 4;
        b2 += i;
        m2 += i;
        s2 += i;
    }
    else if(i < 4)
    {
        i += 28;
        b2 += i;
        m2 += i;
        s2 += i;
    }
    if(b2 > 0)
    {
        {
            b = lshift(b, b2);
        }
    }
    if(s2 > 0)
    {
        {
            S = lshift(S, s2);
        }
    }
    if(k_check)
    {
        if(cmp(b, S) < 0)
        {
            k--;
            b = multadd(b, 10, 0); /* we botched the k estimate */
            if(leftright)
            {
                {
                    mhi = multadd(mhi, 10, 0);
                }
            }
            ilim = ilim1;
        }
    }
    if(ilim <= 0 && mode > 2)
    {
        if(ilim < 0 || cmp(b, S = multadd(S, 5, 0)) <= 0)
        {
            /* no digits, fcvt style */
        no_digits:
            k = -1 - ndigits;
            inex = STRTOG_Inexlo;
            goto ret;
        }
    one_digit:
        inex = STRTOG_Inexhi;
        *s++ = '1';
        k++;
        goto ret;
    }
    if(leftright)
    {
        if(m2 > 0)
        {
            {
                mhi = lshift(mhi, m2);
            }
        }

        /* Compute mlo -- check for special case
         * that d is a normalized power of 2.
         */

        mlo = mhi;
        if(spec_case)
        {
            mhi = Balloc(mhi->k);
            Bcopy(mhi, mlo);
            mhi = lshift(mhi, 1);
        }

        for(i = 1;; i++)
        {
            dig = quorem(b, S) + '0';
            /* Do we yet have the shortest decimal string
             * that will round to d?
             */
            j = cmp(b, mlo);
            delta = diff(S, mhi);
            j1 = delta->sign ? 1 : cmp(b, delta);
            Bfree(delta);
#ifndef ROUND_BIASED
            if(j1 == 0 && !mode && !(bits[0] & 1) && !rdir)
            {
                if(dig == '9')
                {
                    {
                        goto round_9_up;
                    }
                }
                if(j <= 0)
                {
                    if(b->wds > 1 || b->x[0])
                    {
                        {
                            inex = STRTOG_Inexlo;
                        }
                    }
                }
                else
                {
                    dig++;
                    inex = STRTOG_Inexhi;
                }
                *s++ = (char)dig;
                goto ret;
            }
#endif
            if((j < 0) || ((j == 0) && !mode
#ifndef ROUND_BIASED
                           && !(bits[0] & 1)
#endif
                               ))
            {
                if(rdir && (b->wds > 1 || b->x[0]))
                {
                    if(rdir == 2)
                    {
                        inex = STRTOG_Inexlo;
                        goto accept;
                    }
                    while(cmp(S, mhi) > 0)
                    {
                        *s++ = (char)dig;
                        mhi1 = multadd(mhi, 10, 0);
                        if(mlo == mhi)
                        {
                            {
                                mlo = mhi1;
                            }
                        }
                        mhi = mhi1;
                        b = multadd(b, 10, 0);
                        dig = quorem(b, S) + '0';
                    }
                    if(dig++ == '9')
                    {
                        {
                            goto round_9_up;
                        }
                    }
                    inex = STRTOG_Inexhi;
                    goto accept;
                }
                if(j1 > 0)
                {
                    b = lshift(b, 1);
                    j1 = cmp(b, S);
                    if(((j1 > 0) || (j1 == 0 && dig & 1)) && (dig++ == '9'))
                    {
                        {
                            goto round_9_up;
                        }
                    }
                    inex = STRTOG_Inexhi;
                }
                if(b->wds > 1 || b->x[0])
                {
                    {
                        inex = STRTOG_Inexlo;
                    }
                }
            accept:
                *s++ = (char)dig;
                goto ret;
            }
            if(j1 > 0 && rdir != 2)
            {
                if(dig == '9')
                { /* possible if i == 1 */
                round_9_up:
                    *s++ = '9';
                    inex = STRTOG_Inexhi;
                    goto roundoff;
                }
                inex = STRTOG_Inexhi;
                *s++ = (char)(dig + 1);
                goto ret;
            }
            *s++ = (char)dig;
            if(i == ilim)
            {
                {
                    break;
                }
            }
            b = multadd(b, 10, 0);
            if(mlo == mhi)
            {
                {
                    mlo = mhi = multadd(mhi, 10, 0);
                }
            }
            else
            {
                mlo = multadd(mlo, 10, 0);
                mhi = multadd(mhi, 10, 0);
            }
        }
    }
    else
    {
        {
            for(i = 1;; i++)
            {
                dig = quorem(b, S) + '0';
                *s++ = (char)dig;
                if(i >= ilim)
                {
                    {
                        break;
                    }
                }
                b = multadd(b, 10, 0);
            }
        }
    }

    /* Round off last digit */

    if(rdir)
    {
        if((rdir == 2) || ((b->wds <= 1) && !b->x[0]))
        {
            {
                goto chopzeros;
            }
        }
        goto roundoff;
    }
    b = lshift(b, 1);
    j = cmp(b, S);
    if((j > 0) || ((j == 0) && (dig & 1)))
    {
    roundoff:
        inex = STRTOG_Inexhi;
        while(*--s == '9')
        {
            {
                if(s == s0)
                {
                    k++;
                    *s++ = '1';
                    goto ret;
                }
            }
        }
        ++*s++;
    }
    else
    {
    chopzeros:
        if(b->wds > 1 || b->x[0])
        {
            {
                inex = STRTOG_Inexlo;
            }
        }
        while(*--s == '0')
        {
        }
        s++;
    }
ret:
    Bfree(S);
    if(mhi)
    {
        if(mlo && mlo != mhi)
        {
            {
                Bfree(mlo);
            }
        }
        Bfree(mhi);
    }
ret1:
    Bfree(b);
    *s = 0;
    *decpt = k + 1;
    if(rve)
    {
        {
            *rve = s;
        }
    }
    *kindp |= inex;
    return s0;
}

References b2d(), Balloc(), Bcopy, Bfree(), bigtens, bitstob(), Bletch, cmp(), DBL_EPSILON, diff(), dtoa_result, dval, FPI::emin, Exp_11, Exp_msk1, Exp_shift, fabs(), Frac_mask1, freedtoa(), hi0bits, i2b(), Int_max, Long, lshift(), mult(), multadd(), FPI::nbits, nrv_alloc(), NULL, P, pow5mult(), Quick_max, quorem(), ROUND_BIASED, FPI::rounding, rshift(), rv_alloc(), Bigint::sign, STRTOG_Denormal, STRTOG_Inexact, STRTOG_Inexhi, STRTOG_Inexlo, STRTOG_Infinite, STRTOG_NaN, STRTOG_Neg, STRTOG_Normal, STRTOG_Retmask, STRTOG_Zero, Ten_pmax, tens, trailz(), Bigint::wds, word0, and Bigint::x.

Referenced by g_ddfmt(), g_dfmt(), g_ffmt(), g_Qfmt(), g_xfmt(), and g_xLfmt().