/****************************************************************************
 *
 * $Source: /usr/local/cvsroot/gccsdk/unixlib/source/strtod.c,v $
 * $Date: 2003/04/26 10:42:09 $
 * $Revision: 1.4 $
 * $State: Exp $
 * $Author: peter $
 *
 ***************************************************************************/

#ifdef EMBED_RCSID
static const char rcs_id[] = "$Id: strtod.c,v 1.4 2003/04/26 10:42:09 peter Exp $";
#endif

/*-
 * Copyright (c) 1993
 *	The Regents of the University of California.  All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. All advertising materials mentioning features or use of this software
 *    must display the following acknowledgement:
 *	This product includes software developed by the University of
 *	California, Berkeley and its contributors.
 * 4. Neither the name of the University nor the names of its contributors
 *    may be used to endorse or promote products derived from this software
 *    without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 */

#if defined(LIBC_SCCS) && !defined(lint)
static char sccsid[] = "@(#)strtod.c	8.1 (Berkeley) 6/4/93";
#endif /* LIBC_SCCS and not lint */

/****************************************************************
 *
 * 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.
   dmg@research.att.com 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 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 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.
 */

#include <sys/types.h>

#if defined(i386) || defined(mips) && defined(MIPSEL)
#define IEEE_8087
#else
#define IEEE_MC68k
#endif

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

#ifdef __cplusplus
#include "malloc.h"
#include "memory.h"
#else
#include "stdlib.h"
#include "string.h"
#endif

#include "errno.h"
#include <ctype.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

#include <pthread.h>

#ifdef __cplusplus
extern "C"
{
#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)
 */
#define Storeinc(a,b,c) (*a++ = (b << 16) | (c & 0xffff))


/* #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

#ifdef __cplusplus
  extern "C" double strtod (const char *s00, char **se);
  extern "C" char *__dtoa (double d, int mode, int ndigits,
			   int *decpt, int *sign, char **rve);
#endif

  struct
  Bigint
    {
      struct Bigint *next;
      int k, maxwds, sign, wds;
      unsigned long x[1];
    };

  typedef struct Bigint Bigint;

  static Bigint *freelist[Kmax + 1];

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

    PTHREAD_UNSAFE

    if ((rv = freelist[k]))
      {
	freelist[k] = rv->next;
      }
    else
      {
	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)
  {
    PTHREAD_UNSAFE

    if (v)
      {
	v->next = freelist[v->k];
	freelist[v->k] = v;
      }
  }

#define Bcopy(x,y) \
   memcpy((char *)&x->sign, (char *)&y->sign, y->wds*sizeof(long) + 2*sizeof(int))

  static Bigint *
    multadd
    (Bigint * b, int m, int a)	/* multiply by m and add a */
  {
    int 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 = (int) (z >> 16);
	*x++ = (z << 16) + (y & 0xffff);
#else
	y = *x * m + a;
	a = (int) (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, int nd0, int nd, unsigned long y9)
  {
    Bigint *b;
    int 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 int
    hi0bits
    (register unsigned long x)
  {
    register int 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 int
    lo0bits
    (unsigned long *y)
  {
    register int 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
    (int i)
  {
    Bigint *b;

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

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

    if (a->wds < b->wds)
      {
	c = a;
	a = b;
	b = c;
      }
    k = a->k;
    wa = a->wds;
    wb = b->wds;
    wc = wa + wb;
    if (wc > a->maxwds)
      k++;
    c = Balloc (k);
    for (x = c->x, xa = x + wc; x < xa; x++)
      *x = 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))
	  {
	    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))
	  {
	    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;
  }

  static Bigint *p5s;

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

    PTHREAD_UNSAFE

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

    if (!(k >>= 2))
        return b;
    if (!(p5 = p5s))
      {
	/* first time */
	p5 = p5s = i2b (625);
	p5->next = 0;
      }
    for (;;)
      {
	if (k & 1)
	  {
	    b1 = mult (b, p5);
	    Bfree (b);
	    b = b1;
	  }
	if (!(k >>= 1))
	  break;
	if (!(p51 = p5->next))
	  {
	    p51 = p5->next = mult (p5, p5);
	    p51->next = 0;
	  }
	p5 = p51;
      }
    return b;
  }

  static Bigint *
    lshift
    (Bigint * b, int k)
  {
    int 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))
	  ++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)
	  ++n1;
      }
#endif
    else
      do
	*x1++ = *x++;
      while (x < xe);
    b1->wds = n1 - 1;
    Bfree (b);
    return b1;
  }

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

      i = a->wds;
      j = b->wds;
#ifdef DEBUG
    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;
    int 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 = (*xa & 0xffff) - (*xb & 0xffff) + borrow;
	borrow = y >> 16;
	Sign_Extend (borrow, y);
	z = (*xa++ >> 16) - (*xb++ >> 16) + borrow;
	borrow = z >> 16;
	Sign_Extend (borrow, z);
	Storeinc (xc, z, y);
      }
    while (xb < xbe);
    while (xa < xae)
      {
	y = (*xa & 0xffff) + borrow;
	borrow = y >> 16;
	Sign_Extend (borrow, y);
	z = (*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 = (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
    (Bigint * a, int *e)
  {
    unsigned long *xa, *xa0, w, y, z;
    int 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
    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
    (double d, int *e, int *bits)
  {
    Bigint *b;
    int 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 = (int) (d0 >> Exp_shift);
#ifndef IBM
      z |= Exp_msk11;
#endif
#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;
	i = b->wds = (x[1] = z) ? 2 : 1;
      }
    else
      {
#ifdef DEBUG
	if (!z)
	  Bug ("Zero passed to d2b");
#endif
	k = lo0bits (&z);
	x[0] = z;
	i = 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
      {
#ifdef DEBUG
	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
    (Bigint * a, Bigint * b)
  {
    double da, db;
    int 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 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 double
#ifdef IEEE_Arith
    bigtens[] =
  {1e16, 1e32, 1e64, 1e128, 1e256};
  static double tinytens[] =
  {1e-16, 1e-32, 1e-64, 1e-128, 1e-256};
#define n_bigtens 5
#else
#ifdef IBM
    bigtens[] =
  {1e16, 1e32, 1e64};
  static double tinytens[] =
  {1e-16, 1e-32, 1e-64};
#define n_bigtens 3
#else
    bigtens[] =
  {1e16, 1e32};
  static double tinytens[] =
  {1e-16, 1e-32};
#define n_bigtens 2
#endif
#endif

#undef atof
  double
    atof(const char *string)
  {
    return strtod(string, NULL);
  }

  double
    strtod
    (CONST char *s00, char **se)
  {
    int 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;
    double aadj, aadj1, adj, rv, rv0;
    long L;
    unsigned long y, z;
    Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
      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;
	  default:
	  if (isspace ((unsigned char) *s))
	    continue;
	  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 = (int) 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;
    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))
	  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
		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))
	  rv /= tens[i];
	if ((e1 &= ~15))
	  {
	    e1 >>= 4;
	    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;
		    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 = (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) (int) (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 = 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);
      }
    Bfree (bb);
    Bfree (bd);
    Bfree (bs);
    Bfree (bd0);
    Bfree (delta);
  ret:
    if (se)
      *se = (char *) s;
    return sign ? -rv : rv;
  }

  static int
    quorem
    (Bigint * b, Bigint * S)
  {
    int 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
    /*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
    /*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 = (*bx & 0xffff) - (ys & 0xffff) + borrow;
	    borrow = y >> 16;
	    Sign_Extend (borrow, y);
	    z = (*bx >> 16) - (zs & 0xffff) + borrow;
	    borrow = z >> 16;
	    Sign_Extend (borrow, z);
	    Storeinc (bx, z, y);
#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 = (*bx & 0xffff) - (ys & 0xffff) + borrow;
	    borrow = y >> 16;
	    Sign_Extend (borrow, y);
	    z = (*bx >> 16) - (zs & 0xffff) + borrow;
	    borrow = z >> 16;
	    Sign_Extend (borrow, z);
	    Storeinc (bx, z, y);
#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 q;
  }

/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.

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

  char *
    __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.
     */

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

    PTHREAD_UNSAFE

    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 = (int) (word0 (d) >> Exp_shift1 & (Exp_mask >> Exp_shift1));
#else
    if ((i = (int) ((word0 (d) >> Exp_shift1) & (Exp_mask >> Exp_shift1))))
      {
#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 = (int) ds;
    if (ds < 0. && ds != k)
      k--;			/* want k = floor(ds) */
    k_check = 1;
    if (k >= 0 && k <= Ten_pmax)
      {
	if (d < tens[k])
	  k--;
	k_check = 0;
      }
    j = bbits - i - 1;
    if (j >= 0)
      {
	b2 = 0;
	s2 = j;
      }
    else
      {
	b2 = -j;
	s2 = 0;
      }
    if (k >= 0)
      {
	b5 = 0;
	s5 = k;
	s2 += k;
      }
    else
      {
	b2 -= k;
	b5 = -k;
	s5 = 0;
      }
    if (mode < 0 || mode > 9)
      mode = 0;
    try_quick = 1;
    if (mode > 5)
      {
	mode -= 4;
	try_quick = 0;
      }
    leftright = 1;
    switch (mode)
      {
      case 0:
      case 1:
	ilim = ilim1 = -1;
	i = 18;
	ndigits = 0;
	break;
      case 2:
	leftright = 0;
	/* no break */
      case 4:
	if (ndigits <= 0)
	  ndigits = 1;
	ilim = ilim1 = i = ndigits;
	break;
      case 3:
	leftright = 0;
	/* no break */
      case 5:
	i = ndigits + k + 1;
	ilim = i;
	ilim1 = i - 1;
	if (i <= 0)
	  i = 1;
      }
    j = sizeof (unsigned long);
    for (result_k = 0; sizeof (Bigint) - sizeof (unsigned long) + j < i;
	 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))
	  {
	    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 = d;
		d -= L;
		*s++ = '0' + (int) L;
		if (d < eps)
		  goto ret1;
		if (1. - d < eps)
		  goto bump_up;
		if (++i >= ilim)
		  break;
		eps *= 10.;
		d *= 10.;
	      }
	  }
	else
	  {
#endif
	    /* Generate ilim digits, then fix them up. */
	    eps *= tens[ilim - 1];
	    for (i = 1;; i++, d *= 10.)
	      {
		L = d;
		d -= L;
		*s++ = '0' + (int) L;
		if (i == ilim)
		  {
		    if (d > 0.5 + eps)
		      goto bump_up;
		    else if (d < 0.5 - eps)
		      {
			while (*--s == '0');
			s++;
			goto ret1;
		      }
		    break;
		  }
	      }
#ifndef No_leftright
	  }
#endif
      fast_failed:
	s = s0;
	d = d2;
	k = k0;
	ilim = ilim0;
      }

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

    if (be >= 0 && k <= Int_max)
      {
	/* Yes. */
	ds = tens[k];
	if (ndigits < 0 && ilim <= 0)
	  {
	    S = mhi = 0;
	    if (ilim < 0 || d <= 5 * ds)
	      goto no_digits;
	    goto one_digit;
	  }
	for (i = 1;; i++)
	  {
	    L = 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' + (int) 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))
	      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))
      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');
	s++;
      }
  ret:
    Bfree (S);
    if (mhi)
      {
	if (mlo && mlo != mhi)
	  Bfree (mlo);
	Bfree (mhi);
      }
  ret1:
    Bfree (b);
    if (s == s0)
      {				/* don't return empty string */
	*s++ = '0';
	k = 0;
      }
    *s = 0;
    *decpt = k + 1;
    if (rve)
      *rve = s;
    return s0;
  }
#ifdef __cplusplus
}
#endif
