dtoa.cpp

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    xc0 = c->x;
#ifdef USE_LONG_LONG
    for (; xb < xbe; xc0++) {
        if ((y = *xb++)) {
            x = xa;
            xc = xc0;
            carry = 0;
            do {
                z = *x++ * (unsigned long long)y + *xc + carry;
                carry = z >> 32;
                *xc++ = (uint32_t)z & 0xffffffffUL;
            } while (x < xae);
            *xc = (uint32_t)carry;
        }
    }
#else
#ifdef Pack_32
    for (; xb < xbe; xb++, xc0++) {
        if ((y = *xb & 0xffff)) {
            x = xa;
            xc = xc0;
            carry = 0;
            do {
                z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
                carry = z >> 16;
                uint32_t z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
                carry = z2 >> 16;
                Storeinc(xc, z2, z);
            } while (x < xae);
            *xc = carry;
        }
        if ((y = *xb >> 16)) {
            x = xa;
            xc = xc0;
            carry = 0;
            uint32_t z2 = *xc;
            do {
                z = (*x & 0xffff) * y + (*xc >> 16) + carry;
                carry = z >> 16;
                Storeinc(xc, z, z2);
                z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
                carry = z2 >> 16;
            } while (x < xae);
            *xc = z2;
        }
    }
#else
    for(; xb < xbe; xc0++) {
        if ((y = *xb++)) {
            x = xa;
            xc = xc0;
            carry = 0;
            do {
                z = *x++ * y + *xc + carry;
                carry = z >> 16;
                *xc++ = z & 0xffff;
            } while (x < xae);
            *xc = carry;
        }
    }
#endif
#endif
    for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) { }
    c->wds = wc;
    return c;
}

static Bigint* p5s;
static int p5s_count;

static Bigint* pow5mult(Bigint* b, int k)
{
    static int p05[3] = { 5, 25, 125 };

    if (int i = k & 3)
        b = multadd(b, p05[i - 1], 0);

    if (!(k >>= 2))
        return b;

#if ENABLE(JSC_MULTIPLE_THREADS)
    s_dtoaP5Mutex->lock();
#endif
    Bigint* p5 = p5s;
    if (!p5) {
        /* first time */
        p5 = p5s = i2b(625);
        p5s_count = 1;
    }
    int p5s_count_local = p5s_count;
#if ENABLE(JSC_MULTIPLE_THREADS)
    s_dtoaP5Mutex->unlock();
#endif
    int p5s_used = 0;

    for (;;) {
        if (k & 1) {
            Bigint* b1 = mult(b, p5);
            Bfree(b);
            b = b1;
        }
        if (!(k >>= 1))
            break;

        if (++p5s_used == p5s_count_local) {
#if ENABLE(JSC_MULTIPLE_THREADS)
            s_dtoaP5Mutex->lock();
#endif
            if (p5s_used == p5s_count) {
                ASSERT(!p5->next);
                p5->next = mult(p5, p5);
                ++p5s_count;
            }
            
            p5s_count_local = p5s_count;
#if ENABLE(JSC_MULTIPLE_THREADS)
            s_dtoaP5Mutex->unlock();
#endif
        }
        p5 = p5->next;
    }

    return b;
}

static Bigint* lshift(Bigint* b, int k)
{
    Bigint* result = b;

#ifdef Pack_32
    int n = k >> 5;
#else
    int n = k >> 4;
#endif

    int k1 = b->k;
    int n1 = n + b->wds + 1;
    for (int i = b->maxwds; n1 > i; i <<= 1)
        k1++;
    if (b->k < k1)
        result = Balloc(k1);

    const uint32_t* srcStart = b->x;
    uint32_t* dstStart = result->x;
    const uint32_t* src = srcStart + b->wds - 1;
    uint32_t* dst = dstStart + n1 - 1;
#ifdef Pack_32
    if (k &= 0x1f) {
        uint32_t hiSubword = 0;
        int s = 32 - k;
        for (; src >= srcStart; --src) {
            *dst-- = hiSubword | *src >> s;
            hiSubword = *src << k;
        }
        *dst = hiSubword;
        ASSERT(dst == dstStart + n);
        result->wds = b->wds + n + (result->x[n1 - 1] != 0);
    }
#else
    if (k &= 0xf) {
        uint32_t hiSubword = 0;
        int s = 16 - k;
        for (; src >= srcStart; --src) {
            *dst-- = hiSubword | *src >> s;
            hiSubword = (*src << k) & 0xffff;
        }
        *dst = hiSubword;
        ASSERT(dst == dstStart + n);
        result->wds = b->wds + n + (result->x[n1 - 1] != 0);
     }
 #endif
    else {
        do {
            *--dst = *src--;
        } while (src >= srcStart);
        result->wds = b->wds + n;
    }
    for (dst = dstStart + n; dst != dstStart; )
        *--dst = 0;

    if (result != b)
        Bfree(b);
    return result;
}

static int cmp(Bigint* a, Bigint* b)
{
    uint32_t *xa, *xa0, *xb, *xb0;
    int i, j;

    i = a->wds;
    j = b->wds;
    ASSERT(i <= 1 || a->x[i - 1]);
    ASSERT(j <= 1 || b->x[j - 1]);
    if (i -= j)
        return i;
    xa0 = a->x;
    xa = xa0 + j;
    xb0 = b->x;
    xb = xb0 + j;
    for (;;) {
        if (*--xa != *--xb)
            return *xa < *xb ? -1 : 1;
        if (xa <= xa0)
            break;
    }
    return 0;
}

static Bigint* diff(Bigint* a, Bigint* b)
{
    Bigint* c;
    int i, wa, wb;
    uint32_t *xa, *xae, *xb, *xbe, *xc;

    i = cmp(a,b);
    if (!i) {
        c = Balloc(0);
        c->wds = 1;
        c->x[0] = 0;
        return c;
    }
    if (i < 0) {
        c = a;
        a = b;
        b = c;
        i = 1;
    } else
        i = 0;
    c = Balloc(a->k);
    c->sign = i;
    wa = a->wds;
    xa = a->x;
    xae = xa + wa;
    wb = b->wds;
    xb = b->x;
    xbe = xb + wb;
    xc = c->x;
#ifdef USE_LONG_LONG
    unsigned long long borrow = 0;
    do {
        unsigned long long y = (unsigned long long)*xa++ - *xb++ - borrow;
        borrow = y >> 32 & (uint32_t)1;
        *xc++ = (uint32_t)y & 0xffffffffUL;
    } while (xb < xbe);
    while (xa < xae) {
        unsigned long long y = *xa++ - borrow;
        borrow = y >> 32 & (uint32_t)1;
        *xc++ = (uint32_t)y & 0xffffffffUL;
    }
#else
    uint32_t borrow = 0;
#ifdef Pack_32
    do {
        uint32_t y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
        borrow = (y & 0x10000) >> 16;
        uint32_t z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
        borrow = (z & 0x10000) >> 16;
        Storeinc(xc, z, y);
    } while (xb < xbe);
    while (xa < xae) {
        uint32_t y = (*xa & 0xffff) - borrow;
        borrow = (y & 0x10000) >> 16;
        uint32_t z = (*xa++ >> 16) - borrow;
        borrow = (z & 0x10000) >> 16;
        Storeinc(xc, z, y);
    }
#else
    do {
        uint32_t y = *xa++ - *xb++ - borrow;
        borrow = (y & 0x10000) >> 16;
        *xc++ = y & 0xffff;
    } while (xb < xbe);
    while (xa < xae) {
        uint32_t y = *xa++ - borrow;
        borrow = (y & 0x10000) >> 16;
        *xc++ = y & 0xffff;
    }
#endif
#endif
    while (!*--xc)
        wa--;
    c->wds = wa;
    return c;
}

static double ulp(double x)
{
    register int32_t L;
    double a;

    L = (word0(x) & Exp_mask) - (P - 1) * Exp_msk1;
#ifndef Avoid_Underflow
#ifndef Sudden_Underflow
    if (L > 0) {
#endif
#endif
        word0(a) = L;
        word1(a) = 0;
#ifndef Avoid_Underflow
#ifndef Sudden_Underflow
    } else {
        L = -L >> Exp_shift;
        if (L < Exp_shift) {
            word0(a) = 0x80000 >> L;
            word1(a) = 0;
        } else {
            word0(a) = 0;
            L -= Exp_shift;
            word1(a) = L >= 31 ? 1 : 1 << 31 - L;
        }
    }
#endif
#endif
    return dval(a);
}

static double b2d(Bigint* a, int* e)
{
    uint32_t* xa;
    uint32_t* xa0;
    uint32_t w;
    uint32_t y;
    uint32_t z;
    int k;
    double d;

#define d0 word0(d)
#define d1 word1(d)

    xa0 = a->x;
    xa = xa0 + a->wds;
    y = *--xa;
    ASSERT(y);
    k = hi0bits(y);
    *e = 32 - k;
#ifdef Pack_32
    if (k < Ebits) {
        d0 = Exp_1 | y >> Ebits - k;
        w = xa > xa0 ? *--xa : 0;
        d1 = y << (32 - Ebits) + k | w >> Ebits - k;
        goto ret_d;
    }
    z = xa > xa0 ? *--xa : 0;
    if (k -= Ebits) {
        d0 = Exp_1 | y << k | z >> 32 - k;
        y = xa > xa0 ? *--xa : 0;
        d1 = z << k | y >> 32 - k;
    } else {
        d0 = Exp_1 | y;
        d1 = z;
    }
#else
    if (k < Ebits + 16) {
        z = xa > xa0 ? *--xa : 0;
        d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
        w = xa > xa0 ? *--xa : 0;
        y = xa > xa0 ? *--xa : 0;
        d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
        goto ret_d;
    }
    z = xa > xa0 ? *--xa : 0;
    w = xa > xa0 ? *--xa : 0;
    k -= Ebits + 16;
    d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
    y = xa > xa0 ? *--xa : 0;
    d1 = w << k + 16 | y << k;
#endif
ret_d:
#undef d0
#undef d1
    return dval(d);
}

static Bigint* d2b(double d, int* e, int* bits)
{
    Bigint* b;
    int de, k;
    uint32_t *x, y, z;
#ifndef Sudden_Underflow
    int i;
#endif
#define d0 word0(d)
#define d1 word1(d)

#ifdef Pack_32
    b = Balloc(1);
#else
    b = Balloc(2);
#endif
    x = b->x;

    z = d0 & Frac_mask;
    d0 &= 0x7fffffff;    /* clear sign bit, which we ignore */
#ifdef Sudden_Underflow
    de = (int)(d0 >> Exp_shift);
#else
    if ((de = (int)(d0 >> Exp_shift)))
        z |= Exp_msk1;
#endif
#ifdef Pack_32
    if ((y = d1)) {
        if ((k = lo0bits(&y))) {
            x[0] = y | z << 32 - k;
            z >>= k;
        } else
            x[0] = y;
#ifndef Sudden_Underflow
        i =
#endif
            b->wds = (x[1] = z) ? 2 : 1;
    } else {
        k = lo0bits(&z);
        x[0] = z;
#ifndef Sudden_Underflow
        i =
#endif
            b->wds = 1;
        k += 32;
    }
#else
    if ((y = d1)) {
        if ((k = lo0bits(&y))) {
            if (k >= 16) {
                x[0] = y | z << 32 - k & 0xffff;
                x[1] = z >> k - 16 & 0xffff;
                x[2] = z >> k;
                i = 2;
            } else {
                x[0] = y & 0xffff;
                x[1] = y >> 16 | z << 16 - k & 0xffff;
                x[2] = z >> k & 0xffff;
                x[3] = z >> k + 16;
                i = 3;
            }
        } else {
            x[0] = y & 0xffff;
            x[1] = y >> 16;
            x[2] = z & 0xffff;
            x[3] = z >> 16;
            i = 3;
        }
    } else {
        k = lo0bits(&z);
        if (k >= 16) {
            x[0] = z;
            i = 0;
        } else {
            x[0] = z & 0xffff;
            x[1] = z >> 16;
            i = 1;
        }
        k += 32;
    } while (!x[i])
        --i;
    b->wds = i + 1;
#endif
#ifndef Sudden_Underflow
    if (de) {
#endif
        *e = de - Bias - (P - 1) + k;
        *bits = P - k;
#ifndef Sudden_Underflow
    } else {
        *e = de - Bias - (P - 1) + 1 + k;
#ifdef Pack_32
        *bits = (32 * i) - hi0bits(x[i - 1]);
#else
        *bits = (i + 2) * 16 - hi0bits(x[i]);
#endif
    }
#endif
    return b;
}
#undef d0
#undef d1

static double ratio(Bigint* a, Bigint* b)
{
    double da, db;
    int k, ka, kb;

    dval(da) = b2d(a, &ka);
    dval(db) = b2d(b, &kb);
#ifdef Pack_32
    k = ka - kb + 32 * (a->wds - b->wds);
#else
    k = ka - kb + 16 * (a->wds - b->wds);