mprec.c

this gcc-g++-3.3.1.tar.gz is a source file of gcc, you can learn more about gcc through this codes f

/****************************************************************
 *
 * 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 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.
 */

#include <stdlib.h>
#include <string.h>
#include <java-assert.h>
#include "mprec.h"

/* reent.c knows this value */
#define _Kmax 15
#include <stdio.h>

_Jv_Bigint *
_DEFUN (Balloc, (ptr, k), struct _Jv_reent *ptr _AND int k)
{
  _Jv_Bigint *rv = NULL;

  int i = 0;
  int j = 1;

  JvAssert ((1 << k) < MAX_BIGNUM_WDS);

  while ((ptr->_allocation_map & j) && i < MAX_BIGNUMS)
    i++, j <<= 1;

  JvAssert (i < MAX_BIGNUMS);

  if (i >= MAX_BIGNUMS) 
    return NULL;

  ptr->_allocation_map |= j;
  rv = &ptr->_freelist[i];
      
  rv->_k = k;
  rv->_maxwds = 32;

  return rv;
}


void
_DEFUN (Bfree, (ptr, v), struct _Jv_reent *ptr _AND _Jv_Bigint * v)
{
  long i;

  i = v - ptr->_freelist;

  JvAssert (i >= 0 && i < MAX_BIGNUMS);

  if (i >= 0 && i < MAX_BIGNUMS)
    ptr->_allocation_map &= ~ (1 << i);
}


_Jv_Bigint *
_DEFUN (multadd, (ptr, b, m, a),
	struct _Jv_reent *ptr _AND
	_Jv_Bigint * b _AND
	int m _AND
	int a)
{
  int i, wds;
  unsigned long *x, y;
#ifdef Pack_32
  unsigned long xi, z;
#endif
  _Jv_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 (ptr, b->_k + 1);
	  Bcopy (b1, b);
	  Bfree (ptr, b);
	  b = b1;
	}
      b->_x[wds++] = a;
      b->_wds = wds;
    }
  return b;
}

_Jv_Bigint *
_DEFUN (s2b, (ptr, s, nd0, nd, y9),
	struct _Jv_reent * ptr _AND
	_CONST char *s _AND
	int nd0 _AND
	int nd _AND
	unsigned long y9)
{
  _Jv_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 (ptr, k);
  b->_x[0] = y9;
  b->_wds = 1;
#else
  b = Balloc (ptr, 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 (ptr, b, 10, *s++ - '0');
      while (++i < nd0);
      s++;
    }
  else
    s += 10;
  for (; i < nd; i++)
    b = multadd (ptr, b, 10, *s++ - '0');
  return b;
}

int
_DEFUN (hi0bits,
	(x), 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;
}

int
_DEFUN (lo0bits, (y), 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;
}

_Jv_Bigint *
_DEFUN (i2b, (ptr, i), struct _Jv_reent * ptr _AND int i)
{
  _Jv_Bigint *b;

  b = Balloc (ptr, 1);
  b->_x[0] = i;
  b->_wds = 1;
  return b;
}

_Jv_Bigint *
_DEFUN (mult, (ptr, a, b), struct _Jv_reent * ptr _AND _Jv_Bigint * a _AND _Jv_Bigint * b)
{
  _Jv_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 (ptr, 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;
}

_Jv_Bigint *
_DEFUN (pow5mult,
	(ptr, b, k), struct _Jv_reent * ptr _AND _Jv_Bigint * b _AND int k)
{
  _Jv_Bigint *b1, *p5, *p51;
  int i;
  static _CONST int p05[3] = {5, 25, 125};

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

  if (!(k >>= 2))
    return b;
  if (!(p5 = ptr->_p5s))
    {
      /* first time */
      p5 = ptr->_p5s = i2b (ptr, 625);
      p5->_next = 0;
    }
  for (;;)
    {
      if (k & 1)
	{
	  b1 = mult (ptr, b, p5);
	  Bfree (ptr, b);
	  b = b1;
	}
      if (!(k >>= 1))
	break;
      if (!(p51 = p5->_next))
	{
	  p51 = p5->_next = mult (ptr, p5, p5);
	  p51->_next = 0;
	}
      p5 = p51;
    }
  return b;
}

_Jv_Bigint *
_DEFUN (lshift, (ptr, b, k), struct _Jv_reent * ptr _AND _Jv_Bigint * b _AND int k)
{
  int i, k1, n, n1;
  _Jv_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 (ptr, 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);