dtoa.cpp

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             * special case of mantissa a power of two.
             */
            if (dsign || word1(rv) || word0(rv) & Bndry_mask
#ifdef Avoid_Underflow
             || (word0(rv) & Exp_mask) <= (2 * P + 1) * Exp_msk1
#else
             || (word0(rv) & Exp_mask) <= Exp_msk1
#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;
                    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 Avoid_Underflow
                if (L <= (scale ? (2 * P + 1) * Exp_msk1 : Exp_msk1))
#else
                if (L <= Exp_msk1)
#endif /*Avoid_Underflow*/
                    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) = L | Bndry_mask1;
                word1(rv) = 0xffffffff;
                break;
            }
            if (!(word1(rv) & LSB))
                break;
            if (dsign)
                dval(rv) += ulp(dval(rv));
            else {
                dval(rv) -= ulp(dval(rv));
#ifndef Sudden_Underflow
                if (!dval(rv))
                    goto undfl;
#endif
            }
#ifdef Avoid_Underflow
            dsign = 1 - dsign;
#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) {
                    if ((z = (uint32_t)aadj) <= 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;
                if ((word0(rv) & Exp_mask) <= P * Exp_msk1)
                {
                    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 = (int32_t)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;
        }
#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:
    Bfree(bb);
    Bfree(bd);
    Bfree(bs);
    Bfree(bd0);
    Bfree(delta);
ret:
    if (se)
        *se = const_cast<char*>(s);
    return sign ? -dval(rv) : dval(rv);
}

static int quorem(Bigint* b, Bigint* S)
{
    int n;
    uint32_t *bx, *bxe, q, *sx, *sxe;
#ifdef USE_LONG_LONG
    unsigned long long borrow, carry, y, ys;
#else
    uint32_t borrow, carry, y, ys;
#ifdef Pack_32
    uint32_t si, z, zs;
#endif
#endif

    n = S->wds;
    ASSERT_WITH_MESSAGE(b->wds <= n, "oversize b in quorem");
    if (b->wds < n)
        return 0;
    sx = S->x;
    sxe = sx + --n;
    bx = b->x;
    bxe = bx + n;
    q = *bxe / (*sxe + 1);    /* ensure q <= true quotient */
    ASSERT_WITH_MESSAGE(q <= 9, "oversized quotient in quorem");
    if (q) {
        borrow = 0;
        carry = 0;
        do {
#ifdef USE_LONG_LONG
            ys = *sx++ * (unsigned long long)q + carry;
            carry = ys >> 32;
            y = *bx - (ys & 0xffffffffUL) - borrow;
            borrow = y >> 32 & (uint32_t)1;
            *bx++ = (uint32_t)y & 0xffffffffUL;
#else
#ifdef Pack_32
            si = *sx++;
            ys = (si & 0xffff) * q + carry;
            zs = (si >> 16) * q + (ys >> 16);
            carry = zs >> 16;
            y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
            borrow = (y & 0x10000) >> 16;
            z = (*bx >> 16) - (zs & 0xffff) - borrow;
            borrow = (z & 0x10000) >> 16;
            Storeinc(bx, z, y);
#else
            ys = *sx++ * q + carry;
            carry = ys >> 16;
            y = *bx - (ys & 0xffff) - borrow;
            borrow = (y & 0x10000) >> 16;
            *bx++ = y & 0xffff;
#endif
#endif
        } while (sx <= sxe);
        if (!*bxe) {
            bx = b->x;
            while (--bxe > bx && !*bxe)
                --n;
            b->wds = n;
        }
    }
    if (cmp(b, S) >= 0) {
        q++;
        borrow = 0;
        carry = 0;
        bx = b->x;
        sx = S->x;
        do {
#ifdef USE_LONG_LONG
            ys = *sx++ + carry;
            carry = ys >> 32;
            y = *bx - (ys & 0xffffffffUL) - borrow;
            borrow = y >> 32 & (uint32_t)1;
            *bx++ = (uint32_t)y & 0xffffffffUL;
#else
#ifdef Pack_32
            si = *sx++;
            ys = (si & 0xffff) + carry;
            zs = (si >> 16) + (ys >> 16);
            carry = zs >> 16;
            y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
            borrow = (y & 0x10000) >> 16;
            z = (*bx >> 16) - (zs & 0xffff) - borrow;
            borrow = (z & 0x10000) >> 16;
            Storeinc(bx, z, y);
#else
            ys = *sx++ + carry;
            carry = ys >> 16;
            y = *bx - (ys & 0xffff) - borrow;
            borrow = (y & 0x10000) >> 16;
            *bx++ = y & 0xffff;
#endif
#endif
        } while (sx <= sxe);
        bx = b->x;
        bxe = bx + n;
        if (!*bxe) {
            while (--bxe > bx && !*bxe)
                --n;
            b->wds = n;
        }
    }
    return q;
}

#if !ENABLE(JSC_MULTIPLE_THREADS)
static char* dtoa_result;
#endif

static char* rv_alloc(int i)
{
    int k;

    int j = sizeof(uint32_t);
    for (k = 0;
        sizeof(Bigint) - sizeof(uint32_t) - sizeof(int) + j <= (unsigned)i;
        j <<= 1)
            k++;
    int* r = (int*)Balloc(k);
    *r = k;
    return
#if !ENABLE(JSC_MULTIPLE_THREADS)
    dtoa_result =
#endif
        (char*)(r + 1);
}

static char* nrv_alloc(const char* s, char** rve, int n)
{
    char* rv = rv_alloc(n);
    char* t = rv;

    while ((*t = *s++))
        t++;
    if (rve)
        *rve = t;
    return rv;
}

/* freedtoa(s) must be used to free values s returned by dtoa
 * when MULTIPLE_THREADS is #defined.  It should be used in all cases,
 * but for consistency with earlier versions of dtoa, it is optional
 * when MULTIPLE_THREADS is not defined.
 */

void freedtoa(char* s)
{
    Bigint* b = (Bigint*)((int*)s - 1);
    b->maxwds = 1 << (b->k = *(int*)b);
    Bfree(b);
#if !ENABLE(JSC_MULTIPLE_THREADS)
    if (s == dtoa_result)
        dtoa_result = 0;
#endif
}

/* 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 int32_t
 *       calculation.
 */

char* dtoa(double d, int ndigits, int* decpt, int* sign, char** rve)
{
    /*
        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.

    */

    int bbits, b2, b5, be, dig, i, ieps, ilim = 0, ilim0, ilim1 = 0,
        j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
        spec_case, try_quick;
    int32_t L;
#ifndef Sudden_Underflow
    int denorm;
    uint32_t x;
#endif
    Bigint *b, *b1, *delta, *mlo = NULL, *mhi, *S;
    double d2, ds, eps;
    char *s, *s0;
#ifdef SET_INEXACT
    int inexact, oldinexact;
#endif

#if !ENABLE(JSC_MULTIPLE_THREADS)
    if (dtoa_result) {
        freedtoa(dtoa_result);
        dtoa_result = 0;
    }
#endif

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