floatconv.c

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                        si = *sx++;
                        ys = (si & 0xffff) + carry;
                        zs = (si >> 16) + (ys >> 16);
                        carry = zs >> 16;
                        y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
                        borrow = y >> 16;
                        Sign_Extend(borrow, y);
                        z = (*bx >> 16) - (zs & 0xffff) + borrow;
                        borrow = z >> 16;
                        Sign_Extend(borrow, z);
                        Storeinc(bx, z, y);
                        }
                        while(sx <= sxe);
                bx = b->x;
                bxe = bx + n;
                if (!*bxe) {
                        while(--bxe > bx && !*bxe)
                                --n;
                        b->wds = n;
                        }
                }
        return q;
        }

/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
 *
 * Inspired by "How to Print Floating-Point Numbers Accurately" by
 * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
 *
 * Modifications:
 *      1. Rather than iterating, we use a simple numeric overestimate
 *         to determine k = floor(log10(d)).  We scale relevant
 *         quantities using O(log2(k)) rather than O(k) multiplications.
 *      2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
 *         try to generate digits strictly left to right.  Instead, we
 *         compute with fewer bits and propagate the carry if necessary
 *         when rounding the final digit up.  This is often faster.
 *      3. Under the assumption that input will be rounded nearest,
 *         mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
 *         That is, we allow equality in stopping tests when the
 *         round-nearest rule will give the same floating-point value
 *         as would satisfaction of the stopping test with strict
 *         inequality.
 *      4. We remove common factors of powers of 2 from relevant
 *         quantities.
 *      5. When converting floating-point integers less than 1e16,
 *         we use floating-point arithmetic rather than resorting
 *         to multiple-precision integers.
 *      6. When asked to produce fewer than 15 digits, we first try
 *         to get by with floating-point arithmetic; we resort to
 *         multiple-precision integer arithmetic only if we cannot
 *         guarantee that the floating-point calculation has given
 *         the correctly rounded result.  For k requested digits and
 *         "uniformly" distributed input, the probability is
 *         something like 10^(k-15) that we must resort to the long
 *         calculation.
 */

 char *
_IO_dtoa
#ifdef KR_headers
        (d, mode, ndigits, decpt, sign, rve)
        double d; int mode, ndigits, *decpt, *sign; char **rve;
#else
        (double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
#endif
{
 /*     Arguments ndigits, decpt, sign are similar to those
        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.
        */

        _G_int32_t bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
                j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
                spec_case, try_quick;
        _G_int32_t L;
#ifndef Sudden_Underflow
        int denorm;
#endif
	Bigint _b_avail, _b, _mhi, _mlo, _S;
	Bigint *b_avail = Binit(&_b_avail);
	Bigint *b = Binit(&_b);
	Bigint *S = Binit(&_S);
	/* mhi and mlo are only set and used if leftright. */
        Bigint *mhi = NULL, *mlo = NULL;
        double d2, ds, eps;
        char *s, *s0;
        static Bigint *result = NULL;
        static int result_k;

	TEST_ENDIANNESS;
        if (result) {
		/* result is contains a string, so its fields (interpreted
		   as a Bigint have been trashed.  Restore them.
		   This is a really ugly interface - result should
		   not be static, since that is not thread-safe.  FIXME. */
                result->k = result_k;
                result->maxwds = 1 << result_k;
                result->on_stack = 0;
                }

        if (word0(d) & Sign_bit) {
                /* set sign for everything, including 0's and NaNs */
                *sign = 1;
                setword0(d, word0(d) & ~Sign_bit);  /* clear sign bit */
                }
        else
                *sign = 0;

#if defined(IEEE_Arith) + defined(VAX)
#ifdef IEEE_Arith
        if ((word0(d) & Exp_mask) == Exp_mask)
#else
        if (word0(d)  == 0x8000)
#endif
                {
                /* Infinity or NaN */
                *decpt = 9999;
#ifdef IEEE_Arith
		if (!word1(d) && !(word0(d) & 0xfffff))
		  {
		    s = "Infinity";
		    if (rve)
		      *rve = s + 8;
		  }
		else
#endif
		  {
		    s = "NaN";
		    if (rve)
		      *rve = s +3;
		  }
                return s;
                }
#endif
#ifdef IBM
        d += 0; /* normalize */
#endif
        if (!d) {
                *decpt = 1;
                s = "0";
                if (rve)
                        *rve = s + 1;
                return s;
                }

        b = d2b(b, d, &be, &bbits);
        i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
#ifndef Sudden_Underflow
        if (i) {
#endif
                d2 = d;
                setword0(d2, (word0(d2) & Frac_mask1) | Exp_11);
#ifdef IBM
                if (j = 11 - hi0bits(word0(d2) & Frac_mask))
                        d2 /= 1 << j;
#endif

                i -= Bias;
#ifdef IBM
                i <<= 2;
                i += j;
#endif
#ifndef Sudden_Underflow
                denorm = 0;
                }
        else {
                /* d is denormalized */
		unsigned32 x;

                i = bbits + be + (Bias + (P-1) - 1);
                x = i > 32  ? word0(d) << (64 - i) | word1(d) >> (i - 32)
                            : word1(d) << (32 - i);
                d2 = x;
                addword0(d2, - 31*Exp_msk1); /* adjust exponent */
                i -= (Bias + (P-1) - 1) + 1;
                denorm = 1;
                }
#endif

	/* Now i is the unbiased base-2 exponent. */

        /* 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*log(2)/log(10) + log10(d2)
         *
         * This suggests computing an approximation k to log10(d) by
         *
         * k = i*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) by 0.301029995663981; since |i| <= 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 = (d2-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
        k = (int)ds;
        if (ds < 0. && ds != k)
                k--;    /* want k = floor(ds) */
        k_check = 1;
        if (k >= 0 && k <= Ten_pmax) {
                if (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 = 18;
                        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;
                }
	/* i is now an upper bound of the number of digits to generate. */
        j = sizeof(unsigned32) * (1<<BIGINT_MINIMUM_K);
	/* The test is <= so as to allow room for the final '\0'. */
        for(result_k = BIGINT_MINIMUM_K; BIGINT_HEADER_SIZE + j <= i;
                j <<= 1) result_k++;
        if (!result || result_k > result->k)
        {
          Bfree (result);
          result = Balloc(result_k);
        }
        s = s0 = (char *)result;

        if (ilim >= 0 && ilim <= Quick_max && try_quick) {

                /* Try to get by with floating-point arithmetic. */

                i = 0;
                d2 = 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;
                                d /= bigtens[n_bigtens-1];
                                ieps++;
                                }
                        for(; j; j >>= 1, i++)
                                if (j & 1) {
                                        ieps++;
                                        ds *= bigtens[i];
                                        }
                        d /= ds;
                        }
                else if ((j1 = -k)) {
                        d *= tens[j1 & 0xf];
                        for(j = j1 >> 4; j; j >>= 1, i++)
                                if (j & 1) {
                                        ieps++;
                                        d *= bigtens[i];
                                        }
                        }
                if (k_check && d < 1. && ilim > 0) {
                        if (ilim1 <= 0)
                                goto fast_failed;
                        ilim = ilim1;
                        k--;
                        d *= 10.;
                        ieps++;
                        }
                eps = ieps*d + 7.;
                addword0(eps, - (P-1)*Exp_msk1);
                if (ilim == 0) {
                        d -= 5.;
                        if (d > eps)
                                goto one_digit;
                        if (d < -eps)
                                goto no_digits;
                        goto fast_failed;
                        }
#ifndef No_leftright
                if (leftright) {
                        /* Use Steele & White method of only
                         * generating digits needed.
                         */
                        eps = 0.5/tens[ilim-1] - eps;
                        for(i = 0;;) {
                                L = (_G_int32_t)d;
                                d -= L;
                                *s++ = '0' + (int)L;
                                if (d < eps)
                                        goto ret1;
                                if (1. - d < eps)
                                        goto bump_up;
                                if (++i >= ilim)
                                        break;
                                eps *= 10.;
                                d *= 10.;
                                }
                        }
                else {
#endif
                        /* Generate ilim digits, then fix them up. */
                        eps *= tens[ilim-1];
                        for(i = 1;; i++, d *= 10.) {
                                L = (_G_int32_t)d;
                                d -= L;
                                *s++ = '0' + (int)L;
                                if (i == ilim) {
                                        if (d > 0.5 + eps)
                                                goto bump_up;
                                        else if (d < 0.5 - eps) {
                                                while(*--s == '0');
                                                s++;
                                                goto ret1;
                                                }
                                        break;
                                        }
                                }
#ifndef No_leftright
                        }
#endif
 fast_failed:
                s = s0;
                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) {
                        if (ilim < 0 || d <= 5*ds)
                                goto no_digits;
                        goto one_digit;
                        }
                for(i = 1;; i++) {
                        L = (_G_int32_t)(d / ds);
                        d -= L*ds;
#ifdef Check_FLT_ROUNDS
                        /* If FLT_ROUNDS == 2, L will usually be high by 1 */
                        if (d < 0) {