text: /* 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.  (LICENSE)
  
      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 <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 (unsigned char *num, int size, int 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. */
  }
  