lib_dtoa.c

/****************************************************************************
 * lib/lib_dtoa.c
 *
 * This file was ported to NuttX by Yolande Cates.
 *
 * Copyright (c) 1990, 1993
 *      The Regents of the University of California.  All rights reserved.
 *
 * This code is derived from software contributed to Berkeley by
 * Chris Torek.
 *
 * 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.
 *
 ****************************************************************************/

/****************************************************************************
 * Included Files
 ****************************************************************************/

#include <nuttx/config.h>

#include <stdlib.h>
#include <stdint.h>
#include <string.h>

/****************************************************************************
 * Pre-processor Definitions
 ****************************************************************************/

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

#ifdef CONFIG_ENDIAN_BIG
#  define word0(x) ((uint32_t *)&x)[0]
#  define word1(x) ((uint32_t *)&x)[1]
#else
#  define word0(x) ((uint32_t *)&x)[1]
#  define word1(x) ((uint32_t *)&x)[0]
#endif

#ifdef CONFIG_ENDIAN_BIG
#  define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
                         ((unsigned short *)a)[1] = (unsigned short)c, a++)
#else
#  define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
                         ((unsigned short *)a)[0] = (unsigned short)c, a++)
#endif

#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 */

#define Kmax 15

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

/****************************************************************************
 * Private Type Definitions
 ****************************************************************************/

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

typedef struct Bigint Bigint;

/****************************************************************************
 * Private Data
 ****************************************************************************/

static Bigint *freelist[Kmax + 1];

/****************************************************************************
 * Private Functions
 ****************************************************************************/

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

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

/* multiply by m and add a */

static Bigint *multadd(Bigint * b, int m, int 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 int hi0bits(unsigned long x)
{
  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)
{
  int k;
  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
  uint32_t 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 };

  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 CONFIG_DEBUG_LIB
  if (i > 1 && !a->x[i - 1])
   {
    ldbg("cmp called with a->x[a->wds-1] == 0\n");
   }
  if (j > 1 && !b->x[j - 1])
   {
    ldbg("cmp called with b->x[b->wds-1] == 0\n");
   }
#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
  int32_t 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 Bigint *d2b(double d, int *e, int *bits)
{
  Bigint *b;
  int de, i, k;
  unsigned long *x, y, z;

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

  z = word0(d) & Frac_mask;
  word0(d) &= 0x7fffffff;       /* clear sign bit, which we ignore */
  if ((de = (int)(word0(d) >> Exp_shift)))
    z |= Exp_msk1;
#ifdef Pack_32
  if ((y = word1(d)))
    {
      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 CONFIG_DEBUG_LIB
      if (!z)
        {
          ldbg("Zero passed to d2b\n");
        }
#endif
      k = lo0bits(&z);
      x[0] = z;
      i = b->wds = 1;
      k += 32;
    }
#else
  if ((y = word1(d)))
    {
      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 CONFIG_DEBUG_LIB
      if (!z)
        {
          ldbg("Zero passed to d2b\n");
        }
#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
  if (de)
    {
      *e = de - Bias - (P - 1) + k;
      *bits = P - k;
    }
  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
    }
  return b;
}

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 IEEE_Arith
static const double 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
static const double bigtens[] = { 1e16, 1e32 };
static const double tinytens[] = { 1e-16, 1e-32 };

#  define n_bigtens 2
#endif

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
  int32_t z;
  uint32_t si, zs;
#endif

  n = S->wds;
#ifdef CONFIG_DEBUG_LIB
  if (b->wds > n)
    {
      ldbg("oversize b in quorem\n");
    }
#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 CONFIG_DEBUG_LIB
  if (q > 9)
   {
     ldbg("oversized quotient in quorem\n");
   }
#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;
}

/****************************************************************************
 * Public Functions
 ****************************************************************************/

/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
 *
 * Inspired by "How to Print Floating-Point Numbers Accurately" by
 * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
 *
 * Modifications:
 *      1. Rather than iterating, we use a simple numeric overestimate
 *         to determine k = floor(log10(d)).  We scale relevant
 *         quantities using O(log2(k)) rather than O(k) multiplications.
 *      2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
 *         try to generate digits strictly left to right.  Instead, we
 *         compute with fewer bits and propagate the carry if necessary
 *         when rounding the final digit up.  This is often faster.
 *      3. Under the assumption that input will be rounded nearest,
 *         mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
 *         That is, we allow equality in stopping tests when the
 *         round-nearest rule will give the same floating-point value
 *         as would satisfaction of the stopping test with strict
 *         inequality.
 *      4. We remove common factors of powers of 2 from relevant
 *         quantities.
 *      5. When converting floating-point integers less than 1e16,
 *         we use floating-point arithmetic rather than resorting
 *         to multiple-precision integers.
 *      6. When asked to produce fewer than 15 digits, we first try
 *         to get by with floating-point arithmetic; we resort to
 *         multiple-precision integer arithmetic only if we cannot
 *         guarantee that the floating-point calculation has given
 *         the correctly rounded result.  For k requested digits and
 *         "uniformly" distributed input, the probability is
 *         something like 10^(k-15) that we must resort to the int32_t
 *         calculation.
 */

char *__dtoa(double d, int 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, j_1, k, k0, k_check, leftright, m2, m5, s2, s5, spec_case = 0, try_quick;
  long L;
  int denorm;
  unsigned long x;
  Bigint *b, *b1, *delta, *mlo = NULL, *mhi, *S;
  double d2, ds, eps;
  char *s, *s0;
  static Bigint *result;
  static int result_k;

  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)
#  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
  if (!d)
    {
      *decpt = 1;
      s = "0";