Tools/WinSN5.0Ver.iso/NETSCAP.50/WIN1998.ZIP/ns/nsprpub/pr/src/misc/prdtoa.c

C/C++ Source or Header | 1998-04-08 | 67.2 KB | 3,190 lines

/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*- */

#include "primpl.h"

/****************************************************************
 *
 * The author of this software is David M. Gay.
 *
 * Copyright (c) 1991 by AT&T.
 *
 * Permission to use, copy, modify, and distribute this software for any
 * purpose without fee is hereby granted, provided that this entire notice
 * is included in all copies of any software which is or includes a copy
 * or modification of this software and in all copies of the supporting
 * documentation for such software.
 *
 * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
 * WARRANTY.  IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY
 * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
 * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
 *
 ***************************************************************/

/* Please send bug reports to
    David M. Gay
    AT&T Bell Laboratories, Room 2C-463
    600 Mountain Avenue
    Murray Hill, NJ 07974-2070
    U.S.A.
    [e-mail] or research!dmg
 */

/* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
 *
 * This strtod returns a nearest machine number to the input decimal
 * string (or sets errno to ERANGE).  With IEEE arithmetic, ties are
 * broken by the IEEE round-even rule.  Otherwise ties are broken by
 * biased rounding (add half and chop).
 *
 * Inspired loosely by William D. Clinger's paper "How to Read Floating
 * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
 *
 * Modifications:
 *
 *    1. We only require IEEE, IBM, or VAX double-precision
 *        arithmetic (not IEEE double-extended).
 *    2. We get by with floating-point arithmetic in a case that
 *        Clinger missed -- when we're computing d * 10^n
 *        for a small integer d and the integer n is not too
 *        much larger than 22 (the maximum integer k for which
 *        we can represent 10^k exactly), we may be able to
 *        compute (d*10^k) * 10^(e-k) with just one roundoff.
 *    3. Rather than a bit-at-a-time adjustment of the binary
 *        result in the hard case, we use floating-point
 *        arithmetic to determine the adjustment to within
 *        one bit; only in really hard cases do we need to
 *        compute a second residual.
 *    4. Because of 3., we don't need a large table of powers of 10
 *        for ten-to-e (just some small tables, e.g. of 10^k
 *        for 0 <= k <= 22).
 */

/*
 * #define IEEE_8087 for IEEE-arithmetic machines where the least
 *    significant byte has the lowest address.
 * #define IEEE_MC68k for IEEE-arithmetic machines where the most
 *    significant byte has the lowest address.
 * #define Long int on machines with 32-bit ints and 64-bit longs.
 * #define Sudden_Underflow for IEEE-format machines without gradual
 *    underflow (i.e., that flush to zero on underflow).
 * #define IBM for IBM mainframe-style floating-point arithmetic.
 * #define VAX for VAX-style floating-point arithmetic.
 * #define Unsigned_Shifts if >> does treats its left operand as unsigned.
 * #define No_leftright to omit left-right logic in fast floating-point
 *    computation of PR_dtoa.
 * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3.
 * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
 *    that use extended-precision instructions to compute rounded
 *    products and quotients) with IBM.
 * #define ROUND_BIASED for IEEE-format with biased rounding.
 * #define Inaccurate_Divide for IEEE-format with correctly rounded
 *    products but inaccurate quotients, e.g., for Intel i860.
 * #define Just_16 to store 16 bits per 32-bit Long when doing high-precision
 *    integer arithmetic.  Whether this speeds things up or slows things
 *    down depends on the machine and the number being converted.
 * #define KR_headers for old-style C function headers.
 * #define Bad_float_h if your system lacks a float.h or if it does not
 *    define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
 *    FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
 * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
 *    if memory is available and otherwise does something you deem
 *    appropriate.  If MALLOC is undefined, malloc will be invoked
 *    directly -- and assumed always to succeed.
 */
#if  defined(IS_LITTLE_ENDIAN)
#define IEEE_8087
#else
#define IEEE_MC68k
#endif

#ifndef Long
#if PR_BYTES_PER_LONG == 4
#define Long long
#elif PR_BYTES_PER_INT == 4
#define Long int
#else
#error "No suitable type for Long"
#endif
#endif

#ifdef DEBUG_DTOA
#include "stdio.h"
#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
#else
#define Bug(x)
#endif

#include "stdlib.h"
#include "string.h"

#ifdef MALLOC
extern void *MALLOC(size_t);
#else
#define MALLOC PR_MALLOC
#endif

#include "errno.h"
#ifdef Bad_float_h
#undef __STDC__
#ifdef IEEE_MC68k
#define IEEE_ARITHMETIC
#endif
#ifdef IEEE_8087
#define IEEE_ARITHMETIC
#endif

#ifdef IEEE_ARITHMETIC
#define DBL_DIG 15
#define DBL_MAX_10_EXP 308
#define DBL_MAX_EXP 1024
#define FLT_RADIX 2
#define FLT_ROUNDS 1
#define DBL_MAX 1.7976931348623157e+308
#endif

#ifdef IBM
#define DBL_DIG 16
#define DBL_MAX_10_EXP 75
#define DBL_MAX_EXP 63
#define FLT_RADIX 16
#define FLT_ROUNDS 0
#define DBL_MAX 7.2370055773322621e+75
#endif

#ifdef VAX
#define DBL_DIG 16
#define DBL_MAX_10_EXP 38
#define DBL_MAX_EXP 127
#define FLT_RADIX 2
#define FLT_ROUNDS 1
#define DBL_MAX 1.7014118346046923e+38
#endif

#ifndef LONG_MAX
#define LONG_MAX 2147483647
#endif
#else
#include "float.h"
#endif
#ifndef __MATH_H__
#include "math.h"
#endif

#ifndef CONST
#define CONST const
#endif

#ifdef Unsigned_Shifts
#define Sign_Extend(a,b) if (b < 0) a |= 0xffff0000;
#else
#define Sign_Extend(a,b) /*no-op*/
#endif

#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM)    != 1
Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
#endif

#ifdef IEEE_8087
#define word0(x) ((unsigned Long *)&x)[1]
#define word1(x) ((unsigned Long *)&x)[0]
#else
#define word0(x) ((unsigned Long *)&x)[0]
#define word1(x) ((unsigned Long *)&x)[1]
#endif

/* The following definition of Storeinc is appropriate for MIPS processors.
 * An alternative that might be better on some machines is
 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
 */
#if defined(IEEE_8087) + defined(VAX)
#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
((unsigned short *)a)[0] = (unsigned short)c, a++)
#else
#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
((unsigned short *)a)[1] = (unsigned short)c, a++)
#endif

/* #define P DBL_MANT_DIG */
/* Ten_pmax = floor(P*log(2)/log(5)) */
/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */

#if defined(IEEE_8087) + defined(IEEE_MC68k)
#define Exp_shift  20
#define Exp_shift1 20
#define Exp_msk1    0x100000
#define Exp_msk11   0x100000
#define Exp_mask  0x7ff00000
#define P 53
#define Bias 1023
#define IEEE_Arith
#define Emin (-1022)
#define Exp_1  0x3ff00000
#define Exp_11 0x3ff00000
#define Ebits 11
#define Frac_mask  0xfffff
#define Frac_mask1 0xfffff
#define Ten_pmax 22
#define Bletch 0x10
#define Bndry_mask  0xfffff
#define Bndry_mask1 0xfffff
#define LSB 1
#define Sign_bit 0x80000000
#define Log2P 1
#define Tiny0 0
#define Tiny1 1
#define Quick_max 14
#define Int_max 14
#define Infinite(x) (word0(x) == 0x7ff00000) /* sufficient test for here */
#else
#undef  Sudden_Underflow
#define Sudden_Underflow
#ifdef IBM
#define Exp_shift  24
#define Exp_shift1 24
#define Exp_msk1   0x1000000
#define Exp_msk11  0x1000000
#define Exp_mask  0x7f000000
#define P 14
#define Bias 65
#define Exp_1  0x41000000
#define Exp_11 0x41000000
#define Ebits 8    /* exponent has 7 bits, but 8 is the right value in b2d */
#define Frac_mask  0xffffff
#define Frac_mask1 0xffffff
#define Bletch 4
#define Ten_pmax 22
#define Bndry_mask  0xefffff
#define Bndry_mask1 0xffffff
#define LSB 1
#define Sign_bit 0x80000000
#define Log2P 4
#define Tiny0 0x100000
#define Tiny1 0
#define Quick_max 14
#define Int_max 15
#else /* VAX */
#define Exp_shift  23
#define Exp_shift1 7
#define Exp_msk1    0x80
#define Exp_msk11   0x800000
#define Exp_mask  0x7f80
#define P 56
#define Bias 129
#define Exp_1  0x40800000
#define Exp_11 0x4080
#define Ebits 8
#define Frac_mask  0x7fffff
#define Frac_mask1 0xffff007f
#define Ten_pmax 24
#define Bletch 2
#define Bndry_mask  0xffff007f
#define Bndry_mask1 0xffff007f
#define LSB 0x10000
#define Sign_bit 0x8000
#define Log2P 1
#define Tiny0 0x80
#define Tiny1 0
#define Quick_max 15
#define Int_max 15
#endif
#endif

#ifndef IEEE_Arith
#define ROUND_BIASED
#endif

#ifdef RND_PRODQUOT
#define rounded_product(a,b) a = rnd_prod(a, b)
#define rounded_quotient(a,b) a = rnd_quot(a, b)
extern double rnd_prod(double, double), rnd_quot(double, double);
#else
#define rounded_product(a,b) a *= b
#define rounded_quotient(a,b) a /= b
#endif

#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
#define Big1 0xffffffff

#ifndef Just_16
/* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
 * This makes some inner loops simpler and sometimes saves work
 * during multiplications, but it often seems to make things slightly
 * slower.  Hence the default is now to store 32 bits per Long.
 */
#ifndef Pack_32
#define Pack_32
#endif
#endif

#define Kmax 15

/*
 * Note: if you ever change struct Bigint, make sure that the
 * definition of the Bcopy(x,y) macro is still correct.
 */
struct Bigint {
    struct Bigint *next;
    PRInt32 k, maxwds, sign, wds;
    unsigned Long x[1];
};

typedef struct Bigint Bigint;

static Bigint *freelist[Kmax+1];

static PRLock *freelist_lock;

static Bigint *Balloc(PRInt32 k)
{
    PRInt32 x;
    Bigint *rv;

    PR_Lock(freelist_lock);
    if ((rv = freelist[k]) != NULL) {
        freelist[k] = rv->next;
    }
    PR_Unlock(freelist_lock);
    if (rv == NULL) {
        x = 1 << k;
        rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(Long));
        rv->k = k;
        rv->maxwds = x;
    }
    rv->sign = rv->wds = 0;
    return rv;
}

static void Bfree (Bigint *v)
{
    if (v) {
        PR_Lock(freelist_lock);
        v->next = freelist[v->k];
        freelist[v->k] = v;
        PR_Unlock(freelist_lock);
    }
}

/*
 * The definition of the Bcopy macro is highly dependent on the
 * ordering of members in struct Bigint.
 */
#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
                          y->wds*sizeof(Long) + 2*sizeof(PRInt32))

static Bigint *multadd(Bigint *b, PRInt32 m, PRInt32 a)    /* multiply by m and add a */
{
    PRInt32 i, wds;
    unsigned Long *x, y;
#ifdef Pack_32
    unsigned Long xi, z;
#endif
    Bigint *b1;

    wds = b->wds;
    x = b->x;
    i = 0;
    do {
#ifdef Pack_32
        xi = *x;
        y = (xi & 0xffff) * m + a;
        z = (xi >> 16) * m + (y >> 16);
        a = (PRInt32)(z >> 16);
        *x++ = (z << 16) + (y & 0xffff);
#else
        y = *x * m + a;
        a = (PRInt32)(y >> 16);
        *x++ = y & 0xffff;
#endif
    }
    while(++i < wds);
    if (a) {
        if (wds >= b->maxwds) {
            b1 = Balloc(b->k+1);
            Bcopy(b1, b);
            Bfree(b);
            b = b1;
        }
        b->x[wds++] = a;
        b->wds = wds;
    }
    return b;
}

static Bigint *s2b(CONST char *s, PRInt32 nd0, PRInt32 nd, unsigned Long y9)
{
    Bigint *b;
    PRInt32 i, k;
    Long x, y;

    x = (nd + 8) / 9;
    for(k = 0, y = 1; x > y; y <<= 1, k++) ;
#ifdef Pack_32
    b = Balloc(k);
    b->x[0] = y9;
    b->wds = 1;
#else
    b = Balloc(k+1);
    b->x[0] = y9 & 0xffff;
    b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
#endif

    i = 9;
    if (9 < nd0) {
        s += 9;
        do b = multadd(b, 10, *s++ - '0');
        while(++i < nd0);
        s++;
    }
    else
        s += 10;
    for(; i < nd; i++)
        b = multadd(b, 10, *s++ - '0');
    return b;
}

static PRInt32 hi0bits(register unsigned Long x)
{
    register PRInt32 k = 0;

    if (!(x & 0xffff0000)) {
        k = 16;
        x <<= 16;
    }
    if (!(x & 0xff000000)) {
        k += 8;
        x <<= 8;
    }
    if (!(x & 0xf0000000)) {
        k += 4;
        x <<= 4;
    }
    if (!(x & 0xc0000000)) {
        k += 2;
        x <<= 2;
    }
    if (!(x & 0x80000000)) {
        k++;
        if (!(x & 0x40000000))
            return 32;
    }
    return k;
}

static PRInt32 lo0bits(unsigned Long *y)
{
    register PRInt32 k;
    register unsigned Long x = *y;

    if (x & 7) {
        if (x & 1)
            return 0;
        if (x & 2) {
            *y = x >> 1;
            return 1;
        }
        *y = x >> 2;
        return 2;
    }
    k = 0;
    if (!(x & 0xffff)) {
        k = 16;
        x >>= 16;
    }
    if (!(x & 0xff)) {
        k += 8;
        x >>= 8;
    }
    if (!(x & 0xf)) {
        k += 4;
        x >>= 4;
    }
    if (!(x & 0x3)) {
        k += 2;
        x >>= 2;
    }
    if (!(x & 1)) {
        k++;
        x >>= 1;
        if (!x & 1)
            return 32;
    }
    *y = x;
    return k;
}

static Bigint *i2b(PRInt32 i)
{
    Bigint *b;

    b = Balloc(1);
    b->x[0] = i;
    b->wds = 1;
    return b;
}

static Bigint *mult(CONST Bigint *a, CONST Bigint *b)
{
    CONST Bigint *t;
    Bigint *c;
    PRInt32 k, wa, wb, wc;
    unsigned Long carry, y, z;
    unsigned Long *xc, *xc0, *xce;
    CONST unsigned Long *x, *xa, *xae, *xb, *xbe;
#ifdef Pack_32
    unsigned Long z2;
#endif

    if (a->wds < b->wds) {
        t = a;
        a = b;
        b = t;
    }
    k = a->k;
    wa = a->wds;
    wb = b->wds;
    wc = wa + wb;
    if (wc > a->maxwds)
        k++;
    c = Balloc(k);
    for(xc = c->x, xce = xc + wc; xc < xce; xc++)
        *xc = 0;
    xa = a->x;
    xae = xa + wa;
    xb = b->x;
    xbe = xb + wb;
    xc0 = c->x;
#ifdef Pack_32
    for(; xb < xbe; xb++, xc0++) {
        if ((y = *xb & 0xffff) != 0) {
            x = xa;
            xc = xc0;
            carry = 0;
            do {
                z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
                carry = z >> 16;
                z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
                carry = z2 >> 16;
                Storeinc(xc, z2, z);
            }
            while(x < xae);
            *xc = carry;
        }
        if ((y = *xb >> 16) != 0) {
            x = xa;
            xc = xc0;
            carry = 0;
            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
    for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
    c->wds = wc;
    return c;
}

/*
 * 'p5s' points to a linked list of Bigints that are powers of 5.
 * This list grows on demand, and it can only grow: it won't change
 * in any other way.  So if we read 'p5s' or the 'next' field of
 * some Bigint on the list, and it is not NULL, we know it won't
 * change to NULL or some other value.  Only when the value of
 * 'p5s' or 'next' is NULL do we need to acquire the lock and add
 * a new Bigint to the list.
 */

static Bigint *p5s;

static PRLock *p5s_lock;

static Bigint *pow5mult(Bigint *b, PRInt32 k)
{
    Bigint *b1, *p5, *p51;
    PRInt32 i;
    static CONST PRInt32 p05[3] = { 5, 25, 125 };

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

    if (!(k >>= 2))
        return b;
    if (!(p5 = p5s)) {
        /*
         * We take great care to not call i2b() and Bfree()
         * while holding the lock.
         */
        Bigint *wasted_effort = NULL;
        p5 = i2b(625);
        /* lock and check again */
        PR_Lock(p5s_lock);
        if (!p5s) {
            /* first time */
            p5s = p5;
            p5->next = 0;
        } else {
            /* some other thread just beat us */
            wasted_effort = p5;
            p5 = p5s;
        }
        PR_Unlock(p5s_lock);
        if (wasted_effort) {
            Bfree(wasted_effort);
        }
    }
    for(;;) {
        if (k & 1) {
            b1 = mult(b, p5);
            Bfree(b);
            b = b1;
        }
        if (!(k >>= 1))
            break;
        if (!(p51 = p5->next)) {
            Bigint *wasted_effort = NULL;
            p51 = mult(p5, p5);
            PR_Lock(p5s_lock);
            if (!p5->next) {
                p5->next = p51;
                p51->next = 0;
            } else {
                wasted_effort = p51;
                p51 = p5->next;
            }
            PR_Unlock(p5s_lock);
            if (wasted_effort) {
                Bfree(wasted_effort);
            }
        }
        p5 = p51;
    }
    return b;
}

static Bigint *lshift(Bigint *b, PRInt32 k)
{
    PRInt32 i, k1, n, n1;
    Bigint *b1;
    unsigned Long *x, *x1, *xe, z;

#ifdef Pack_32
    n = k >> 5;
#else
    n = k >> 4;
#endif
    k1 = b->k;
    n1 = n + b->wds + 1;
    for(i = b->maxwds; n1 > i; i <<= 1)
        k1++;
    b1 = Balloc(k1);
    x1 = b1->x;
    for(i = 0; i < n; i++)
        *x1++ = 0;
    x = b->x;
    xe = x + b->wds;
#ifdef Pack_32
    if (k &= 0x1f) {
        k1 = 32 - k;
        z = 0;
        do {
            *x1++ = *x << k | z;
            z = *x++ >> k1;
        }
        while(x < xe);
        if ((*x1 = z) != 0)
            ++n1;
    }
#else
    if (k &= 0xf) {
        k1 = 16 - k;
        z = 0;
        do {
            *x1++ = *x << k  & 0xffff | z;
            z = *x++ >> k1;
        }
        while(x < xe);
        if ((*x1 = z) != 0)
            ++n1;
    }
#endif
    else do
        *x1++ = *x++;
         while(x < xe);
    b1->wds = n1 - 1;
    Bfree(b);
    return b1;
}

static PRInt32 cmp(Bigint *a, Bigint *b)
{
    unsigned Long *xa, *xa0, *xb, *xb0;
    PRInt32 i, j;

    i = a->wds;
    j = b->wds;
#ifdef DEBUG_DTOA
    if ((i > 1 && !a->x[i-1]))
        Bug("cmp called with a->x[a->wds-1] == 0");
    if ((j > 1 && !b->x[j-1]))
        Bug("cmp called with b->x[b->wds-1] == 0");
#endif
    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;
    PRInt32 i, wa, wb;
    Long borrow, y;    /* We need signed shifts here. */
    unsigned Long *xa, *xae, *xb, *xbe, *xc;
#ifdef Pack_32
    Long z;
#endif

    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;
    borrow = 0;
#ifdef Pack_32
    do {
        y = (long)((*xa & 0xffff) - (*xb & 0xffff) + borrow);
        borrow = y >> 16;
        Sign_Extend(borrow, y);
        z = (long)((*xa++ >> 16) - (*xb++ >> 16) + borrow);
        borrow = z >> 16;
        Sign_Extend(borrow, z);
        Storeinc(xc, z, y);
    }
    while(xb < xbe);
    while(xa < xae) {
        y = (long)((*xa & 0xffff) + borrow);
        borrow = y >> 16;
        Sign_Extend(borrow, y);
        z = (long)((*xa++ >> 16) + borrow);
        borrow = z >> 16;
        Sign_Extend(borrow, z);
        Storeinc(xc, z, y);
    }
#else
    do {
        y = *xa++ - *xb++ + borrow;
        borrow = y >> 16;
        Sign_Extend(borrow, y);
        *xc++ = y & 0xffff;
    }
    while(xb < xbe);
    while(xa < xae) {
        y = *xa++ + borrow;
        borrow = y >> 16;
        Sign_Extend(borrow, y);
        *xc++ = y & 0xffff;
    }
#endif
    while(!*--xc)
        wa--;
    c->wds = wa;
    return c;
}

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

    L = (long)((word0(x) & Exp_mask) - (P-1)*Exp_msk1);
#ifndef Sudden_Underflow
    if (L > 0) {
#endif
#ifdef IBM
        L |= Exp_msk1 >> 4;
#endif
        word0(a) = L;
        word1(a) = 0;
#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
    return a;
}

static double
b2d
#ifdef KR_headers
(a, e) Bigint *a; PRInt32 *e;
#else
(Bigint *a, PRInt32 *e)
#endif
{
    unsigned Long *xa, *xa0, w, y, z;
    PRInt32 k;
    double d;
#ifdef VAX
    unsigned Long d0, d1;
#else
#define d0 word0(d)
#define d1 word1(d)
#endif

    xa0 = a->x;
    xa = xa0 + a->wds;
    y = *--xa;
#ifdef DEBUG_DTOA
    if (!y) Bug("zero y in b2d");
#endif
    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:
#ifdef VAX
    word0(d) = d0 >> 16 | d0 << 16;
    word1(d) = d1 >> 16 | d1 << 16;
#else
#undef d0
#undef d1
#endif
    return d;
}

static Bigint *
d2b
#ifdef KR_headers
(d, e, bits) double d; PRInt32 *e, *bits;
#else
(double d, PRInt32 *e, PRInt32 *bits)
#endif
{
    Bigint *b;
    PRInt32 de, i, k;
    unsigned Long *x, y, z;
#ifdef VAX
    unsigned Long d0, d1;
    d0 = word0(d) >> 16 | word0(d) << 16;
    d1 = word1(d) >> 16 | word1(d) << 16;
#else
#define d0 word0(d)
#define d1 word1(d)
#endif

#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 = (PRInt32)(d0 >> Exp_shift);
#ifndef IBM
    z |= Exp_msk11;
#endif
#else
    if ((de = (PRInt32)(d0 >> Exp_shift)) != 0)
        z |= Exp_msk1;
#endif
#ifdef Pack_32
    if ((y = d1) != 0) {
        if ((k = lo0bits(&y)) != 0) {
            x[0] = y | z << (32 - k);
            z >>= k;
        }
        else
            x[0] = y;
        i = b->wds = (x[1] = z) ? 2 : 1;
    }
    else {
#ifdef DEBUG_DTOA
        if (!z)
            Bug("Zero passed to d2b");
#endif
        k = lo0bits(&z);
        x[0] = z;
        i = b->wds = 1;
        k += 32;
    }
#else
    if ((y = d1) != 0) {
        if ((k = lo0bits(&y)) != 0)
            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 {
#ifdef DEBUG_DTOA
        if (!z)
            Bug("Zero passed to d2b");
#endif
        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
#ifdef IBM
        *e = (de - Bias - (P-1) << 2) + k;
        *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
#else
        *e = de - Bias - (P-1) + k;
        *bits = P - k;
#endif
#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
#ifdef KR_headers
(a, b) Bigint *a, *b;
#else
(Bigint *a, Bigint *b)
#endif
{
    double da, db;
    PRInt32 k, ka, kb;

    da = b2d(a, &ka);
    db = b2d(b, &kb);
#ifdef Pack_32
    k = ka - kb + 32*(a->wds - b->wds);
#else
    k = ka - kb + 16*(a->wds - b->wds);
#endif
#ifdef IBM
    if (k > 0) {
        word0(da) += (k >> 2)*Exp_msk1;
        if (k &= 3)
            da *= 1 << k;
    }
    else {
        k = -k;
        word0(db) += (k >> 2)*Exp_msk1;
        if (k &= 3)
            db *= 1 << k;
    }
#else
    if (k > 0)
        word0(da) += k*Exp_msk1;
    else {
        k = -k;
        word0(db) += k*Exp_msk1;
    }
#endif
    return da / db;
}

static CONST double
tens[] = {
    1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
    1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
    1e20, 1e21, 1e22
#ifdef VAX
    , 1e23, 1e24
#endif
};

static CONST double
#ifdef IEEE_Arith
bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 1e-256 };
#define n_bigtens 5
#else
#ifdef IBM
bigtens[] = { 1e16, 1e32, 1e64 };
static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
#define n_bigtens 3
#else
bigtens[] = { 1e16, 1e32 };
static CONST double tinytens[] = { 1e-16, 1e-32 };
#define n_bigtens 2
#endif
#endif

void _PR_InitDtoa(void)
{
    freelist_lock = PR_NewLock();
    p5s_lock = PR_NewLock();
}

#if defined(HAVE_WATCOM_BUG_1)
PRFloat64 __pascal __loadds  __export
#else
PR_IMPLEMENT(PRFloat64)
#endif
PR_strtod(CONST char *s00, char **se)
{
    PRInt32 bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
        e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
    CONST char *s, *s0, *s1;
    PRFloat64 aadj, aadj1, adj, rv, rv0;
    Long L;
    unsigned Long y, z;
    Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;


    if (!_pr_initialized) _PR_ImplicitInitialization();

    sign = nz0 = nz = 0;
    rv = 0.;
    for(s = s00;;s++) switch(*s) {
    case '-':
        sign = 1;
        /* no break */
    case '+':
        if (*++s)
            goto break2;
        /* no break */
    case 0:
        s = s00;
        goto ret;
    case '\t':
    case '\n':
    case '\v':
    case '\f':
    case '\r':
    case ' ':
        continue;
    default:
        goto break2;
    }
break2:
    if (*s == '0') {
        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 + c - '0';
        else if (nd < 16)
            z = 10*z + c - '0';
    nd0 = nd;
    if (c == '.') {
        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 + c;
                else if (nd <= DBL_DIG + 1)
                    z = 10*z + c;
                nz = 0;
            }
        }
    }
dig_done:
    e = 0;
    if (c == 'e' || c == 'E') {
        if (!nd && !nz && !nz0) {
            s = s00;
            goto ret;
        }
        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 = (PRInt32)L;
                if (esign)
                    e = -e;
            }
            else
                e = 0;
        }
        else
            s = s00;
    }
    if (!nd) {
        if (!nz && !nz0)
            s = s00;
        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;
    rv = y;
    if (k > 9)
        rv = tens[k - 9] * rv + z;
    bd0 = 0;
    if (nd <= DBL_DIG
#ifndef RND_PRODQUOT
        && FLT_ROUNDS == 1
#endif
        ) {
        if (!e)
            goto ret;
        if (e > 0) {
            if (e <= Ten_pmax) {
#ifdef VAX
                goto vax_ovfl_check;
#else
                /* rv = */ rounded_product(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.
                 */
                e -= i;
                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(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(rv, tens[e]);
#endif
                goto ret;
            }
        }
#ifndef Inaccurate_Divide
        else if (e >= -Ten_pmax) {
            /* rv = */ rounded_quotient(rv, tens[-e]);
            goto ret;
        }
#endif
    }
    e1 += nd - k;

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

    if (e1 > 0) {
        if ((i = e1 & 15) != 0)
            rv *= tens[i];
        if (e1 &= ~15) {
            if (e1 > DBL_MAX_10_EXP) {
            ovfl:
                errno = ERANGE;
#ifdef __STDC__
                rv = HUGE_VAL;
#else
                /* Can't trust HUGE_VAL */
#ifdef IEEE_Arith
                word0(rv) = Exp_mask;
                word1(rv) = 0;
#else
                word0(rv) = Big0;
                word1(rv) = Big1;
#endif
#endif
                if (bd0)
                    goto retfree;
                goto ret;
            }
            if (e1 >>= 4) {
                for(j = 0; e1 > 1; j++, e1 >>= 1)
                    if (e1 & 1)
                        rv *= bigtens[j];
                /* The last multiplication could overflow. */
                word0(rv) -= P*Exp_msk1;
                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)
            rv /= tens[i];
        if (e1 &= ~15) {
            e1 >>= 4;
            if (e1 >= 1 << n_bigtens)
                goto undfl;
            for(j = 0; e1 > 1; j++, e1 >>= 1)
                if (e1 & 1)
                    rv *= tinytens[j];
            /* The last multiplication could underflow. */
            rv0 = rv;
            rv *= tinytens[j];
            if (!rv) {
                rv = 2.*rv0;
                rv *= tinytens[j];
                if (!rv) {
                undfl:
                    rv = 0.;
                    errno = ERANGE;
                    if (bd0)
                        goto retfree;
                    goto ret;
                }
                word0(rv) = Tiny0;
                word1(rv) = Tiny1;
                /* The refinement below will clean
                 * this approximation up.
                 */
            }
        }
    }

    /* 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(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 Sudden_Underflow
#ifdef IBM
        j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
#else
        j = P + 1 - bbbits;
#endif
#else
        i = bbe + bbbits - 1;    /* logb(rv) */
        if (i < Emin)    /* denormal */
            j = bbe + (P-Emin);
        else
            j = P + 1 - bbbits;
#endif
        bb2 += j;
        bd2 += j;
        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);
        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)
                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) == 0xffffffff) {
                    /*boundary case -- increment exponent*/
                    word0(rv) = (word0(rv) & Exp_mask)
                        + Exp_msk1
#ifdef IBM
                        | Exp_msk1 >> 4
#endif
                        ;
                    word1(rv) = 0;
                    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
                    if (L <= Exp_msk1)
#endif
                        goto undfl;
                L -= Exp_msk1;
#else
                L = (long)((word0(rv) & Exp_mask) - Exp_msk1);
#endif
                word0(rv) = L | Bndry_mask1;
                word1(rv) = 0xffffffff;
#ifdef IBM
                goto cont;
#else
                break;
#endif
            }
#ifndef ROUND_BIASED
            if (!(word1(rv) & LSB))
                break;
#endif
            if (dsign)
                rv += ulp(rv);
#ifndef ROUND_BIASED
            else {
                rv -= ulp(rv);
#ifndef Sudden_Underflow
                if (!rv)
                    goto undfl;
#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(FLT_ROUNDS) {
            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
        }
        y = word0(rv) & Exp_mask;

        /* Check for overflow */

        if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
            rv0 = rv;
            word0(rv) -= P*Exp_msk1;
            adj = aadj1 * ulp(rv);
            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 Sudden_Underflow
            if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
                rv0 = rv;
                word0(rv) += P*Exp_msk1;
                adj = aadj1 * ulp(rv);
                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(rv);
                rv += adj;
            }
#else
            /* 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)(PRInt32)(aadj + 0.5);
                if (!dsign)
                    aadj1 = -aadj1;
            }
            adj = aadj1 * ulp(rv);
            rv += adj;
#endif
        }
        z = word0(rv) & Exp_mask;
        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;
        }
    cont:
        Bfree(bb);
        Bfree(bd);
        Bfree(bs);
        Bfree(delta);
    }
retfree:
    Bfree(bb);
    Bfree(bd);
    Bfree(bs);
    Bfree(bd0);
    Bfree(delta);
ret:
    if (se)
        *se = (char *)s;
    return sign ? -rv : rv;
}

static PRInt32
quorem(Bigint *b, Bigint *S)
{
    PRInt32 n;
    Long borrow, y;
    unsigned Long carry, q, ys;
    unsigned Long *bx, *bxe, *sx, *sxe;
#ifdef Pack_32
    Long z;
    unsigned Long si, zs;
#endif

    n = S->wds;
#ifdef DEBUG_DTOA
    /*debug*/ if (b->wds > n)
        /*debug*/    Bug("oversize b in quorem");
#endif
    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 */
#ifdef DEBUG_DTOA
    /*debug*/ if (q > 9)
        /*debug*/    Bug("oversized quotient in quorem");
#endif
    if (q) {
        borrow = 0;
        carry = 0;
        do {
#ifdef Pack_32
            si = *sx++;
            ys = (si & 0xffff) * q + carry;
            zs = (si >> 16) * q + (ys >> 16);
            carry = zs >> 16;
            y = (long)((*bx & 0xffff) - (ys & 0xffff) + borrow);
            borrow = y >> 16;
            Sign_Extend(borrow, y);
            z = (long)((*bx >> 16) - (zs & 0xffff) + borrow);
            borrow = z >> 16;
            Sign_Extend(borrow, z);
            Storeinc(bx, z, y);
#else
            ys = *sx++ * q + carry;
            carry = ys >> 16;
            y = *bx - (ys & 0xffff) + borrow;
            borrow = y >> 16;
            Sign_Extend(borrow, y);
            *bx++ = y & 0xffff;
#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 Pack_32
            si = *sx++;
            ys = (si & 0xffff) + carry;
            zs = (si >> 16) + (ys >> 16);
            carry = zs >> 16;
            y = (long)((*bx & 0xffff) - (ys & 0xffff) + borrow);
            borrow = y >> 16;
            Sign_Extend(borrow, y);
            z = (long)((*bx >> 16) - (zs & 0xffff) + borrow);
            borrow = z >> 16;
            Sign_Extend(borrow, z);
            Storeinc(bx, z, y);
#else
            ys = *sx++ + carry;
            carry = ys >> 16;
            y = *bx - (ys & 0xffff) + borrow;
            borrow = y >> 16;
            Sign_Extend(borrow, y);
            *bx++ = y & 0xffff;
#endif
        }
        while(sx <= sxe);
        bx = b->x;
        bxe = bx + n;
        if (!*bxe) {
            while(--bxe > bx && !*bxe)
                --n;
            b->wds = n;
        }
    }
    return (int)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.
 */

PR_IMPLEMENT(char *)
PR_dtoa(double d, int mode, 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.

        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.
    */

    PRInt32 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;
    Long L;
#ifndef Sudden_Underflow
    PRInt32 denorm;
    unsigned Long x;
#endif
    Bigint *b, *b1, *delta, *mlo, *mhi, *S;
    double d2, ds, eps;
    char *s, *s0;
    static Bigint *result;
    static PRInt32 result_k;

    if (!_pr_initialized) _PR_ImplicitInitialization();

    if (result) {
        result->k = result_k;
        result->maxwds = 1 << result_k;
        Bfree(result);
        result = 0;
    }

    if (word0(d) & Sign_bit) {
        /* set sign for everything, including 0's and NaNs */
        *sign = 1;
        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;
                s =
#ifdef IEEE_Arith
                    !word1(d) && !(word0(d) & 0xfffff) ? "Infinity" :
#endif
                    "NaN";
                if (rve)
                    *rve =
#ifdef IEEE_Arith
                        s[3] ? s + 8 :
#endif
                    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(d, &be, &bbits);
#ifdef Sudden_Underflow
    i = (PRInt32)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
#else
    if ((i = (PRInt32)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) != 0) {
#endif
        d2 = d;
        word0(d2) &= Frac_mask1;
        word0(d2) |= Exp_11;
#ifdef IBM
        if (j = 11 - hi0bits(word0(d2) & Frac_mask))
            d2 /= 1 << j;
#endif

        /* 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.)
         */

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

        i = bbits + be + (Bias + (P-1) - 1);
        x = i > 32  ? word0(d) << (64 - i) | word1(d) >> (i - 32)
            : word1(d) << (32 - i);
        d2 = x;
        word0(d2) -= 31*Exp_msk1; /* adjust exponent */
        i -= (Bias + (P-1) - 1) + 1;
        denorm = 1;
    }
#endif
    ds = (d2-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
    k = (PRInt32)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;
    }
    j = sizeof(unsigned Long);
    for(result_k = 0; sizeof(Bigint) - sizeof(unsigned Long) <= i - j;
        j <<= 1) result_k++;
    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) != 0) {
            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.;
        word0(eps) -= (P-1)*Exp_msk1;
        if (ilim == 0) {
            S = mhi = 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 = (Long) d;
                d -= L;
                *s++ = '0' + (PRInt32)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 = (Long) d;
                d -= L;
                *s++ = '0' + (PRInt32)L;
                if (i == ilim) {
                    if (d > 0.5 + eps)
                        goto bump_up;
                    else if (d < 0.5 - eps) {
                        while(*--s == '0'){} /* just count -- nothing to execute */
                        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) {
            S = mhi = 0;
            if (ilim < 0 || d <= 5*ds)
                goto no_digits;
            goto one_digit;
        }
        for(i = 1;; i++) {
            L = (Long) (d / ds);
            d -= L*ds;
#ifdef Check_FLT_ROUNDS
            /* If FLT_ROUNDS == 2, L will usually be high by 1 */
            if (d < 0) {
                L--;
                d += ds;
            }
#endif
            *s++ = '0' + (PRInt32)L;
            if (i == ilim) {
                d += d;
                if ((d > ds) || (d == ds && L & 1)) {
                bump_up:
                    while(*--s == '9')
                        if (s == s0) {
                            k++;
                            *s = '0';
                            break;
                        }
                    ++*s++;
                }
                break;
            }
            if (!(d *= 10.))
                break;
        }
        goto ret1;
    }

    m2 = b2;
    m5 = b5;
    mhi = mlo = 0;
    if (leftright) {
        if (mode < 2) {
            i =
#ifndef Sudden_Underflow
                denorm ? be + (Bias + (P-1) - 1 + 1) :
#endif
#ifdef IBM
                1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
#else
            1 + P - bbits;
#endif
        }
        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. */

    if (mode < 2) {
        if (!word1(d) && !(word0(d) & Bndry_mask)
#ifndef Sudden_Underflow
            && word0(d) & Exp_mask
#endif
            ) {
            /* The special case */
            b2 += Log2P;
            s2 += Log2P;
            spec_case = 1;
        }
        else
            spec_case = 0;
    }

    /* 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)
        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;
            goto ret;
        }
    one_digit:
        *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, Log2P);
        }

        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 && !(word1(d) & 1)) {
                if (dig == '9')
                    goto round_9_up;
                if (j > 0)
                    dig++;
                *s++ = dig;
                goto ret;
            }
#endif
            if ((j < 0) || ((j == 0) && (!mode)
#ifndef ROUND_BIASED
                && (!(word1(d) & 1)))
#endif
                ) {
                if (j1 > 0) {
                    b = lshift(b, 1);
                    j1 = cmp(b, S);
                    if (((j1 > 0) || (j1 == 0 && dig & 1))
                        && (dig++ == '9'))
                        goto round_9_up;
                }
                *s++ = dig;
                goto ret;
            }
            if (j1 > 0) {
                if (dig == '9') { /* possible if i == 1 */
                round_9_up:
                    *s++ = '9';
                    goto roundoff;
                }
                *s++ = dig + 1;
                goto ret;
            }
            *s++ = 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++) {
            *s++ = dig = quorem(b,S) + '0';
            if (i >= ilim)
                break;
            b = multadd(b, 10, 0);
        }

    /* Round off last digit */

    b = lshift(b, 1);
    j = cmp(b, S);
    if ((j > 0) || (j == 0 && dig & 1)) {
    roundoff:
        while(*--s == '9')
            if (s == s0) {
                k++;
                *s++ = '1';
                goto ret;
            }
        ++*s++;
    }
    else {
        while(*--s == '0'){} /* just count -- nothing to execute */
        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;
    return s0;
}

/* 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.
 */

PR_IMPLEMENT(PRStatus)
PR_dtoa_r(double d, int mode, int ndigits,
    int *decpt, int *sign, char **rve, char *buf, PRSize bufsize)
{
    /*    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.
    */

    PRInt32 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;
    Long L;
#ifndef Sudden_Underflow
    PRInt32 denorm;
    unsigned Long x;
#endif
    Bigint *b, *b1, *delta, *mlo, *mhi, *S;
    double d2, ds, eps;
    char *s, *s0;
    Bigint *result = 0;
    PRInt32 result_k;
    PRStatus retval;
    PRSize strsize;

    if (!_pr_initialized) _PR_ImplicitInitialization();

    if (word0(d) & Sign_bit) {
        /* set sign for everything, including 0's and NaNs */
        *sign = 1;
        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;
                s =
#ifdef IEEE_Arith
                    !word1(d) && !(word0(d) & 0xfffff) ? "Infinity" :
#endif
                    "NaN";
                if ((s[0] == 'I' && bufsize < 9) || (s[0] == 'N' && bufsize < 4)) {
                    PR_SetError(PR_BUFFER_OVERFLOW_ERROR, 0);
                    return PR_FAILURE;
                }
                strcpy(buf, s);
                if (rve) {
                    *rve =
#ifdef IEEE_Arith
                        buf[3] ? buf + 8 :
#endif
                    buf + 3;
                    PR_ASSERT(**rve == '\0');
                }
                return PR_SUCCESS;
            }
#endif
#ifdef IBM
    d += 0; /* normalize */
#endif
    if (!d) {
        *decpt = 1;
        if (bufsize < 2) {
            PR_SetError(PR_BUFFER_OVERFLOW_ERROR, 0);
            return PR_FAILURE;
        }
        buf[0] = '0'; buf[1] = '\0';  /* copy "0" to buffer */
        if (rve) {
            *rve = buf + 1;
            PR_ASSERT(**rve == '\0');
        }
        return PR_SUCCESS;
    }

    b = d2b(d, &be, &bbits);
#ifdef Sudden_Underflow
    i = (PRInt32)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
#else
    if ((i = (PRInt32)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1))) != 0) {
#endif
        d2 = d;
        word0(d2) &= Frac_mask1;
        word0(d2) |= Exp_11;
#ifdef IBM
        if (j = 11 - hi0bits(word0(d2) & Frac_mask))
            d2 /= 1 << j;
#endif

        /* 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.)
         */

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

        i = bbits + be + (Bias + (P-1) - 1);
        x = i > 32  ? word0(d) << (64 - i) | word1(d) >> (i - 32)
            : word1(d) << (32 - i);
        d2 = x;
        word0(d2) -= 31*Exp_msk1; /* adjust exponent */
        i -= (Bias + (P-1) - 1) + 1;
        denorm = 1;
    }
#endif
    ds = (d2-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
    k = (PRInt32)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;
    }
    j = sizeof(unsigned Long);
    for(result_k = 0; sizeof(Bigint) - sizeof(unsigned Long) <= i - j;
        j <<= 1) result_k++;
    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) != 0) {
            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.;
        word0(eps) -= (P-1)*Exp_msk1;
        if (ilim == 0) {
            S = mhi = 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 = (Long) d;
                d -= L;
                *s++ = '0' + (PRInt32)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 = (Long) d;
                d -= L;
                *s++ = '0' + (PRInt32)L;
                if (i == ilim) {
                    if (d > 0.5 + eps)
                        goto bump_up;
                    else if (d < 0.5 - eps) {
                        while(*--s == '0'){} /* just count -- nothing to execute */
                        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) {
            S = mhi = 0;
            if (ilim < 0 || d <= 5*ds)
                goto no_digits;
            goto one_digit;
        }
        for(i = 1;; i++) {
            L = (Long) (d / ds);
            d -= L*ds;
#ifdef Check_FLT_ROUNDS
            /* If FLT_ROUNDS == 2, L will usually be high by 1 */
            if (d < 0) {
                L--;
                d += ds;
            }
#endif
            *s++ = '0' + (PRInt32)L;
            if (i == ilim) {
                d += d;
                if ((d > ds) || (d == ds && L & 1)) {
                bump_up:
                    while(*--s == '9')
                        if (s == s0) {
                            k++;
                            *s = '0';
                            break;
                        }
                    ++*s++;
                }
                break;
            }
            if (!(d *= 10.))
                break;
        }
        goto ret1;
    }

    m2 = b2;
    m5 = b5;
    mhi = mlo = 0;
    if (leftright) {
        if (mode < 2) {
            i =
#ifndef Sudden_Underflow
                denorm ? be + (Bias + (P-1) - 1 + 1) :
#endif
#ifdef IBM
                1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
#else
            1 + P - bbits;
#endif
        }
        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. */

    if (mode < 2) {
        if (!word1(d) && !(word0(d) & Bndry_mask)
#ifndef Sudden_Underflow
            && word0(d) & Exp_mask
#endif
            ) {
            /* The special case */
            b2 += Log2P;
            s2 += Log2P;
            spec_case = 1;
        }
        else
            spec_case = 0;
    }

    /* 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)
        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;
            goto ret;
        }
    one_digit:
        *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, Log2P);
        }

        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 && !(word1(d) & 1)) {
                if (dig == '9')
                    goto round_9_up;
                if (j > 0)
                    dig++;
                *s++ = dig;
                goto ret;
            }
#endif
            if ((j < 0) || ((j == 0) && (!mode)
#ifndef ROUND_BIASED
                && (!(word1(d) & 1)))
#endif
                ) {
                if (j1 > 0) {
                    b = lshift(b, 1);
                    j1 = cmp(b, S);
                    if (((j1 > 0) || (j1 == 0 && dig & 1))
                        && (dig++ == '9'))
                        goto round_9_up;
                }
                *s++ = dig;
                goto ret;
            }
            if (j1 > 0) {
                if (dig == '9') { /* possible if i == 1 */
                round_9_up:
                    *s++ = '9';
                    goto roundoff;
                }
                *s++ = dig + 1;
                goto ret;
            }
            *s++ = 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++) {
            *s++ = dig = quorem(b,S) + '0';
            if (i >= ilim)
                break;
            b = multadd(b, 10, 0);
        }

    /* Round off last digit */

    b = lshift(b, 1);
    j = cmp(b, S);
    if ((j > 0) || (j == 0 && dig & 1)) {
    roundoff:
        while(*--s == '9')
            if (s == s0) {
                k++;
                *s++ = '1';
                goto ret;
            }
        ++*s++;
    }
    else {
        while(*--s == '0'){} /* just count -- nothing to execute */
        s++;
    }
ret:
    Bfree(S);
    if (mhi) {
        if (mlo && mlo != mhi)
            Bfree(mlo);
        Bfree(mhi);
    }
ret1:
    Bfree(b);
    *s = 0;
    *decpt = k + 1;
    strsize = (s - s0) + 1;
    if (strsize <= bufsize) {
        retval = PR_SUCCESS;
        memcpy(buf, s0, strsize);
        if (rve) {
            *rve = buf + strsize - 1;
            PR_ASSERT(**rve == '\0');
        }
    } else {
        PR_SetError(PR_BUFFER_OVERFLOW_ERROR, 0);
        retval = PR_FAILURE;
    }

    /* cleanup */
    result->k = result_k;
    result->maxwds = 1 << result_k;
    Bfree(result);

    return retval;
}

/*
** conversion routines for floating point
** prcsn - number of digits of precision to generate floating
** point value.
** This should be reparameterized so that you can send in a
**   prcn for the positive and negative ranges.  For now,
**   conform to the ECMA JavaScript spec which says numbers
**   less than 1e-6 are in scientific notation.
** Also, the ECMA spec says that there should always be a
**   '+' or '-' after the 'e' in scientific notation
*/
PR_IMPLEMENT(void)
PR_cnvtf(char *buf,int bufsz, int prcsn,double fval)
{
    PRIntn decpt, sign, numdigits;
    char *num, *nump;
    char *bufp = buf;
    char *endnum;

    /* If anything fails, we store an empty string in 'buf' */
    num = (char*)PR_MALLOC(bufsz);
    if (num == NULL) {
        buf[0] = '\0';
        return;
    }
    /* XXX Why use mode 1? */
    if (PR_dtoa_r(fval,1,prcsn,&decpt,&sign,&endnum,num,bufsz)
            == PR_FAILURE) {
        buf[0] = '\0';
        goto done;
    }
    numdigits = endnum - num;
    nump = num;

    if (sign &&
        !(word0(fval) == Sign_bit && word1(fval) == 0) &&
        !((word0(fval) & Exp_mask) == Exp_mask &&
          (word1(fval) || (word0(fval) & 0xfffff)))) {
        *bufp++ = '-';
    }

    if(decpt == 9999){
        while((*bufp++ = *nump++) != 0){} /* nothing to execute */
        goto done;
    }

    if(decpt > (prcsn+1) || decpt < -(prcsn-1) || decpt < -5){
        *bufp++ = *nump++;
        if(numdigits != 1){
            *bufp++ = '.';
        }

        while(*nump != '\0'){
            *bufp++ = *nump++;
        }
        *bufp++ = 'e';
        PR_snprintf(bufp,bufsz - (bufp - buf), "%+d",decpt-1);
    }
    else if(decpt >= 0){
        while(decpt--){
            if(*nump != '\0'){
                *bufp++ = *nump++;
            }
            else {
                *bufp++ = '0';
            }
        }
        if(*nump != '\0'){
            *bufp++ = '.';
            while(*nump != '\0'){
                *bufp++ = *nump++;
            }
        }
        *bufp++ = '\0';
    }
    else if(decpt < 0){
        *bufp++ = '0';
        *bufp++ = '.';
        while(decpt++){
            *bufp++ = '0';
        }

        while(*nump != '\0'){
            *bufp++ = *nump++;
        }
        *bufp++ = '\0';
    }
done:
    PR_DELETE(num);
}