div.c

/* div.c: bcmath library file. */
/*
    Copyright (C) 1991, 1992, 1993, 1994, 1997 Free Software Foundation, Inc.
    Copyright (C) 2000 Philip A. Nelson

    This library is free software; you can redistribute it and/or
    modify it under the terms of the GNU Lesser General Public
    License as published by the Free Software Foundation; either
    version 2 of the License, or (at your option) any later version.

    This library is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
    Lesser General Public License for more details.  (COPYING.LIB)

    You should have received a copy of the GNU Lesser General Public
    License along with this library; if not, write to:

      The Free Software Foundation, Inc.
      59 Temple Place, Suite 330
      Boston, MA 02111-1307 USA.

    You may contact the author by:
       e-mail:  philnelson@acm.org
      us-mail:  Philip A. Nelson
                Computer Science Department, 9062
                Western Washington University
                Bellingham, WA 98226-9062

*************************************************************************/

#include <config.h>
#include <stdio.h>
#include <assert.h>
#include <stdlib.h>
#include <ctype.h>
#include <stdarg.h>
#include "bcmath.h"
#include "private.h"


/* Some utility routines for the divide:  First a one digit multiply.
   NUM (with SIZE digits) is multiplied by DIGIT and the result is
   placed into RESULT.  It is written so that NUM and RESULT can be
   the same pointers.  */

static void
_one_mult (num, size, digit, result)
     unsigned char *num;
     int size, digit;
     unsigned char *result;
{
  int carry, value;
  unsigned char *nptr, *rptr;

  if (digit == 0)
    memset (result, 0, size);
  else
    {
      if (digit == 1)
	memcpy (result, num, size);
      else
	{
	  /* Initialize */
	  nptr = (unsigned char *) (num+size-1);
	  rptr = (unsigned char *) (result+size-1);
	  carry = 0;

	  while (size-- > 0)
	    {
	      value = *nptr-- * digit + carry;
	      *rptr-- = value % BASE;
	      carry = value / BASE;
	    }

	  if (carry != 0) *rptr = carry;
	}
    }
}


/* The full division routine. This computes N1 / N2.  It returns
   0 if the division is ok and the result is in QUOT.  The number of
   digits after the decimal point is SCALE. It returns -1 if division
   by zero is tried.  The algorithm is found in Knuth Vol 2. p237. */

int
bc_divide (bc_num n1, bc_num n2, bc_num *quot, int scale)
{
  bc_num qval;
  unsigned char *num1, *num2;
  unsigned char *ptr1, *ptr2, *n2ptr, *qptr;
  int  scale1, val;
  unsigned int  len1, len2, scale2, qdigits, extra, count;
  unsigned int  qdig, qguess, borrow, carry;
  unsigned char *mval;
  char zero;
  unsigned int  norm;

  /* Test for divide by zero. */
  if (bc_is_zero (n2)) return -1;

  /* Test for divide by 1.  If it is we must truncate. */
  if (n2->n_scale == 0)
    {
      if (n2->n_len == 1 && *n2->n_value == 1)
	{
	  qval = bc_new_num (n1->n_len, scale);
	  qval->n_sign = (n1->n_sign == n2->n_sign ? PLUS : MINUS);
	  memset (&qval->n_value[n1->n_len],0,scale);
	  memcpy (qval->n_value, n1->n_value,
		  n1->n_len + MIN(n1->n_scale,scale));
	  bc_free_num (quot);
	  *quot = qval;
	}
    }

  /* Set up the divide.  Move the decimal point on n1 by n2's scale.
     Remember, zeros on the end of num2 are wasted effort for dividing. */
  scale2 = n2->n_scale;
  n2ptr = (unsigned char *) n2->n_value+n2->n_len+scale2-1;
  while ((scale2 > 0) && (*n2ptr-- == 0)) scale2--;

  len1 = n1->n_len + scale2;
  scale1 = n1->n_scale - scale2;
  if (scale1 < scale)
    extra = scale - scale1;
  else
    extra = 0;
  num1 = (unsigned char *) safe_emalloc (1, n1->n_len+n1->n_scale, extra+2);
  memset (num1, 0, n1->n_len+n1->n_scale+extra+2);
  memcpy (num1+1, n1->n_value, n1->n_len+n1->n_scale);

  len2 = n2->n_len + scale2;
  num2 = (unsigned char *) safe_emalloc (1, len2, 1);
  memcpy (num2, n2->n_value, len2);
  *(num2+len2) = 0;
  n2ptr = num2;
  while (*n2ptr == 0)
    {
      n2ptr++;
      len2--;
    }

  /* Calculate the number of quotient digits. */
  if (len2 > len1+scale)
    {
      qdigits = scale+1;
      zero = TRUE;
    }
  else
    {
      zero = FALSE;
      if (len2>len1)
	qdigits = scale+1;  	/* One for the zero integer part. */
      else
	qdigits = len1-len2+scale+1;
    }

  /* Allocate and zero the storage for the quotient. */
  qval = bc_new_num (qdigits-scale,scale);
  memset (qval->n_value, 0, qdigits);

  /* Allocate storage for the temporary storage mval. */
  mval = (unsigned char *) safe_emalloc (1, len2, 1);

  /* Now for the full divide algorithm. */
  if (!zero)
    {
      /* Normalize */
      norm =  10 / ((int)*n2ptr + 1);
      if (norm != 1)
	{
	  _one_mult (num1, len1+scale1+extra+1, norm, num1);
	  _one_mult (n2ptr, len2, norm, n2ptr);
	}

      /* Initialize divide loop. */
      qdig = 0;
      if (len2 > len1)
	qptr = (unsigned char *) qval->n_value+len2-len1;
      else
	qptr = (unsigned char *) qval->n_value;

      /* Loop */
      while (qdig <= len1+scale-len2)
	{
	  /* Calculate the quotient digit guess. */
	  if (*n2ptr == num1[qdig])
	    qguess = 9;
	  else
	    qguess = (num1[qdig]*10 + num1[qdig+1]) / *n2ptr;

	  /* Test qguess. */
	  if (n2ptr[1]*qguess >
	      (num1[qdig]*10 + num1[qdig+1] - *n2ptr*qguess)*10
	       + num1[qdig+2])
	    {
	      qguess--;
	      /* And again. */
	      if (n2ptr[1]*qguess >
		  (num1[qdig]*10 + num1[qdig+1] - *n2ptr*qguess)*10
		  + num1[qdig+2])
		qguess--;
	    }

	  /* Multiply and subtract. */
	  borrow = 0;
	  if (qguess != 0)
	    {
	      *mval = 0;
	      _one_mult (n2ptr, len2, qguess, mval+1);
	      ptr1 = (unsigned char *) num1+qdig+len2;
	      ptr2 = (unsigned char *) mval+len2;
	      for (count = 0; count < len2+1; count++)
		{
		  val = (int) *ptr1 - (int) *ptr2-- - borrow;
		  if (val < 0)
		    {
		      val += 10;
		      borrow = 1;
		    }
		  else
		    borrow = 0;
		  *ptr1-- = val;
		}
	    }

	  /* Test for negative result. */
	  if (borrow == 1)
	    {
	      qguess--;
	      ptr1 = (unsigned char *) num1+qdig+len2;
	      ptr2 = (unsigned char *) n2ptr+len2-1;
	      carry = 0;
	      for (count = 0; count < len2; count++)
		{
		  val = (int) *ptr1 + (int) *ptr2-- + carry;
		  if (val > 9)
		    {
		      val -= 10;
		      carry = 1;
		    }
		  else
		    carry = 0;
		  *ptr1-- = val;
		}
	      if (carry == 1) *ptr1 = (*ptr1 + 1) % 10;
	    }

	  /* We now know the quotient digit. */
	  *qptr++ =  qguess;
	  qdig++;
	}
    }

  /* Clean up and return the number. */
  qval->n_sign = ( n1->n_sign == n2->n_sign ? PLUS : MINUS );
  if (bc_is_zero (qval)) qval->n_sign = PLUS;
  _bc_rm_leading_zeros (qval);
  bc_free_num (quot);
  *quot = qval;

  /* Clean up temporary storage. */
  efree (mval);
  efree (num1);
  efree (num2);

  return 0;	/* Everything is OK. */
}