text: /* number.c: Implements arbitrary precision numbers. */
  
  /*  This file is part of bc written for MINIX.
      Copyright (C) 1991, 1992 Free Software Foundation, Inc.
  
      This program is free software; you can redistribute it and/or modify
      it under the terms of the GNU General Public License as published by
      the Free Software Foundation; either version 2 of the License , or
      (at your option) any later version.
  
      This program 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 General Public License for more details.
  
      You should have received a copy of the GNU General Public License
      along with this program; see the file COPYING.  If not, write to
      the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA.
  
      You may contact the author by:
         e-mail:  phil@cs.wwu.edu
        us-mail:  Philip A. Nelson
                  Computer Science Department, 9062
                  Western Washington University
                  Bellingham, WA 98226-9062
         
  *************************************************************************/
  
  #include "bcdefs.h"
  #include "proto.h"
  
  /* Storage used for special numbers. */
  bc_num _zero_;
  bc_num _one_;
  bc_num _two_;
  
  
  /* "Frees" a bc_num NUM.  Actually decreases reference count and only
     frees the storage if reference count is zero. */
  
  void
  free_num (bc_num * NONNULL num)
  {
    if (*num == NULL) return;
    (*num)->n_refs--; 
    if ((*num)->n_refs == 0) free(*num);
    *num = NULL;
  }
  
  
  /* new_num allocates a number and sets fields to known values. */
  
  bc_num
  new_num (int length, int scale)
  {
    bc_num temp;
  
    temp = (bc_struct *)malloc(sizeof(bc_struct)+length+scale);
    /* XXX if (temp == NULL) out_of_memory (); */
    temp->n_sign = PLUS;
    temp->n_len = length;
    temp->n_scale = scale;
    temp->n_refs = 1;
    temp->n_value[0] = 0;
    return temp;
  }
  
  
  /* Intitialize the number package! */
  
  void
  init_numbers (void)
  {
    _zero_ = new_num (1,0);
    _one_  = new_num (1,0);
    _one_->n_value[0] = 1;
    _two_  = new_num (1,0);
    _two_->n_value[0] = 2;
  }
  
  
  /* Make a copy of a number!  Just increments the reference count! */
  
  bc_num
  copy_num (bc_num num)
  {
    num->n_refs++;
    return num;
  }
  
  
  /* Initialize a number NUM by making it a copy of zero. */
  
  void
  init_num (bc_num * num)
  {
    *num = copy_num (_zero_);
  }
  
  
  /* Convert an integer  to a bc number NUM. */
  
  void
  int2num (bc_num * num, int val)
  {
    char buffer[30];
    char * bptr;
    char * vptr;
    int  ix = 1;
    char neg = 0;
    ;
    
    /* Sign. */
    if (val < 0)
      {
        neg = 1;
        val = -val;
      }
    
    /* Get things going. */
    bptr = &buffer[0];
    *bptr++ = val % 10;
    val = val / 10;
    
    /* Extract remaining digits. */
    while (val != 0)
      {
        *bptr++ = val % 10;
        val = val / 10;
        ix++; 		/* Count the digits. */
      }
    
    /* Make the number. */
    free_num (num);
    *num = new_num (ix, 0);
    if (neg) (*num)->n_sign = MINUS;
    
    /* Assign the digits. */
    vptr = &((*num)->n_value[0]);
    while (ix-- > 0)
      *vptr++ = *--bptr;
    ;
  }
  
  
  /* Convert a number NUM to a long.  The function returns only the integer 
     part of the number.  For numbers that are too large to represent as
     a long, this function returns a zero.  This can be detected by checking
     the NUM for zero after having a zero returned. */
  
  long
  num2long (bc_num num)
  {
    long val;
    char * nptr;
    int  index;
    ;
  
    /* Extract the int value, ignore the fraction. */
    val = 0;
    nptr = &num->n_value[0];
    for (index=num->n_len; (index>0) && (val<=(LONG_MAX/10)); index--)
      val = val*10 + *nptr++;
    
    /* Check for overflow.  If overflow, return zero. */
    if (index>0) val = 0;
    if (val < 0) val = 0;
   
    /* Return the value. */
    if (num->n_sign == PLUS) {
      ;
      return (val);
    }
    else {
      ;
      return (-val);
    }
  }
  
  
  /* The following are some math routines for numbers. */
  _PROTOTYPE(static int _do_compare, (bc_num n1, bc_num n2, int use_sign,
  				    int ignore_last));
  _PROTOTYPE(static void _rm_leading_zeros, (bc_num num));
  _PROTOTYPE(static bc_num _do_add, (bc_num n1, bc_num n2));
  _PROTOTYPE(static bc_num _do_sub, (bc_num n1, bc_num n2));
  
  /* It seems that sometimes there is some room before the result */
  _PROTOTYPE(static void _one_mult,
             (char * COUNT(size)  num, int size, 
              int digit, char * BND(__this - extra_first,
                                    __this + size) result,
              int extra_first));
  
  
  
  /* Compare two bc numbers.  Return value is 0 if equal, -1 if N1 is less
     than N2 and +1 if N1 is greater than N2.  If USE_SIGN is false, just
     compare the magnitudes. */
  
  static int
  _do_compare (bc_num n1, bc_num n2, int use_sign, int ignore_last)
  {
    char * n1ptr;
    char * n2ptr;
    int  count;
    
    /* First, compare signs. */
    if (use_sign && n1->n_sign != n2->n_sign)
      {
        if (n1->n_sign == PLUS)
  	return (1);	/* Positive N1 > Negative N2 */
        else
  	return (-1);	/* Negative N1 < Positive N1 */
      }
    
    /* Now compare the magnitude. */
    if (n1->n_len != n2->n_len)
      {
        if (n1->n_len > n2->n_len)
  	{
  	  /* Magnitude of n1 > n2. */
  	  if (!use_sign || n1->n_sign == PLUS)
  	    return (1);
  	  else
  	    return (-1);
  	}
        else
  	{
  	  /* Magnitude of n1 < n2. */
  	  if (!use_sign || n1->n_sign == PLUS)
  	    return (-1);
  	  else
  	    return (1);
  	}
      }
  
    /* If we get here, they have the same number of integer digits.
       check the integer part and the equal length part of the fraction. */
    count = n1->n_len + MIN (n1->n_scale, n2->n_scale);
    n1ptr = &n1->n_value[0];
    n2ptr = &n2->n_value[0];
  
    while ((count > 0) && (*n1ptr == *n2ptr))
      {
        n1ptr++;
        n2ptr++;
        count--;
      }
    if (ignore_last && count == 1 && n1->n_scale == n2->n_scale)
      return (0);
    if (count != 0)
      {
        if (*n1ptr > *n2ptr)
  	{
  	  /* Magnitude of n1 > n2. */
  	  if (!use_sign || n1->n_sign == PLUS)
  	    return (1);
  	  else
  	    return (-1);
  	}
        else
  	{
  	  /* Magnitude of n1 < n2. */
  	  if (!use_sign || n1->n_sign == PLUS)
  	    return (-1);
  	  else
  	    return (1);
  	}
      }
  
    /* They are equal up to the last part of the equal part of the fraction. */
    if (n1->n_scale != n2->n_scale) 
      if (n1->n_scale > n2->n_scale)
        {
  	for (count = n1->n_scale-n2->n_scale; count>0; count--)
  	  if (*n1ptr++ != 0)
  	    {
  	      /* Magnitude of n1 > n2. */
  	      if (!use_sign || n1->n_sign == PLUS)
  		return (1);
  	      else
  		return (-1);
  	    }
        }
      else
        {
  	for (count = n2->n_scale-n1->n_scale; count>0; count--)
  	  if (*n2ptr++ != 0)
  	    {
  	      /* Magnitude of n1 < n2. */
  	      if (!use_sign || n1->n_sign == PLUS)
  		return (-1);
  	      else
  		return (1);
  	    }
        }
    
    /* They must be equal! */
    return (0);
  }
  
  
  /* This is the "user callable" routine to compare numbers N1 and N2. */
  
  int
  bc_compare (bc_num n1, bc_num n2)
  {
    return _do_compare (n1, n2, TRUE, FALSE);
  }
  
  
  /* In some places we need to check if the number NUM is zero. */
  
  char
  is_zero (bc_num num)
  {
    int  count;
    char * nptr;
  
    /* Quick check. */
    if (num == _zero_) return TRUE;
  
    /* Initialize */
    count = num->n_len + num->n_scale;
    nptr = &num->n_value[0];
  
    /* The check */
    while ((count > 0) && (*nptr++ == 0)) count--;
  
    if (count != 0)
      return FALSE;
    else 
      return TRUE;
  }
  
  
  /* In some places we need to check if the number is negative. */
  
  char
  is_neg (bc_num num)
  {
    return num->n_sign == MINUS;
  }
  
  
  /* For many things, we may have leading zeros in a number NUM.
     _rm_leading_zeros just moves the data to the correct
     place and adjusts the length. */
  
  static void
  _rm_leading_zeros (bc_num num)
  {
    int bytes;
    char * dst;
    char * src;
  
    /* Do a quick check to see if we need to do it. */
    /* if ((*num)->n_value != (void *)0) return; */
  
    /* The first digit is 0, find the first non-zero digit in the 10's or
       greater place. */
    bytes = num->n_len;
    src = &num->n_value[0];
    while (bytes > 1 && *src == 0) src++, bytes--;
    num->n_len = bytes;
    bytes += num->n_scale;
    dst = &num->n_value[0];
    while (bytes-- > 0) *dst++ = *src++;
    
  }
  
  
  /* Perform addition: N1 is added to N2 and the value is
     returned.  The signs of N1 and N2 are ignored. */
  
  static bc_num
  _do_add (bc_num n1, bc_num n2)
  {
    bc_num sum;
    int sum_scale, sum_digits;
    char * n1ptr;
    char * n2ptr;
    char * sumptr;
    int carry, n1bytes, n2bytes;
  
    /* Prepare sum. */
    sum_scale = MAX (n1->n_scale, n2->n_scale);
    sum_digits = MAX (n1->n_len, n2->n_len) + 1;
    sum = new_num (sum_digits,sum_scale);
  
    /* Start with the fraction part.  Initialize the pointers. */
    n1bytes = n1->n_scale;
    n2bytes = n2->n_scale;
    n1ptr = &n1->n_value[0] + n1->n_len + n1bytes - 1;
    n2ptr = &n2->n_value[0] + n2->n_len + n2bytes - 1;
    sumptr = &sum->n_value[0] + sum_scale + sum_digits - 1;
  
    /* Add the fraction part.  First copy the longer fraction.*/
    if (n1bytes != n2bytes)
      {
        if (n1bytes > n2bytes)
  	while (n1bytes>n2bytes)
  	  { *sumptr-- = *n1ptr--; n1bytes--;}
        else
  	while (n2bytes>n1bytes)
  	  { *sumptr-- = *n2ptr--; n2bytes--;}
      }
  
    /* Now add the remaining fraction part and equal size integer parts. */
    n1bytes += n1->n_len;
    n2bytes += n2->n_len;
    carry = 0;
    while ((n1bytes > 0) && (n2bytes > 0))
      {
        *sumptr = *n1ptr + *n2ptr + carry;
        if(n1bytes - 1 > 0) n1ptr --; // For Deputy
        if(n2bytes - 1 > 0) n2ptr --; // For Deputy
        if (*sumptr > 9)
  	{
  	   carry = 1;
  	   *sumptr -= 10;
  	}
        else
  	carry = 0;
        sumptr--;
        n1bytes--;
        n2bytes--;
      }
  
    /* Now add carry the longer integer part. */
    if (n1bytes == 0)
      { n1bytes = n2bytes; n1ptr = n2ptr; }
    while (n1bytes-- > 0)
      {
        *sumptr = *n1ptr + carry;
        if (*sumptr > 9)
  	{
  	   carry = 1;
  	   *sumptr -= 10;
  	 }
        else
  	carry = 0;
        sumptr--;
        // Deferred decrement for Deputy
        if(n1bytes > 0) { n1ptr --; }
      }
  
    /* Set final carry. */
    if (carry == 1)
      *sumptr += 1;
    
    /* Adjust sum and return. */
    _rm_leading_zeros (sum);
    return sum;  
  }
  
  
  /* Perform subtraction: N2 is subtracted from N1 and the value is
     returned.  The signs of N1 and N2 are ignored.  Also, N1 is
     assumed to be larger than N2.  */
  
  static bc_num
  _do_sub (bc_num n1, bc_num n2)
  {
    bc_num diff;
    int diff_scale, diff_len;
    int min_scale, min_len;
    char * n1ptr;
    char * n2ptr;
    char * diffptr;
    int borrow, count, val;
  
    /* Allocate temporary storage. */
    diff_len = MAX (n1->n_len, n2->n_len);
    diff_scale = MAX (n1->n_scale, n2->n_scale);
    min_len = MIN  (n1->n_len, n2->n_len);
    min_scale = MIN (n1->n_scale, n2->n_scale);
    diff = new_num (diff_len, diff_scale);
  
    /* Initialize the subtract. */
    n1ptr = &n1->n_value[0] + n1->n_len + n1->n_scale -1;
    n2ptr = &n2->n_value[0] + n2->n_len + n2->n_scale -1;
    diffptr = &diff->n_value[0] + diff_len + diff_scale -1;
  
    /* Subtract the numbers. */
    borrow = 0;
    
    /* Take care of the longer scaled number. */
    if (n1->n_scale != min_scale)
      {
        /* n1 has the longer scale */
        for (count = n1->n_scale - min_scale; count > 0; count--)
  	*diffptr-- = *n1ptr--;
      }
    else
      {
        /* n2 has the longer scale */
        for (count = n2->n_scale - min_scale; count > 0; count--)
  	{
  	  val = - *n2ptr-- - borrow;
  	  if (val < 0)
  	    {
  	      val += 10;
  	      borrow = 1;
  	    }
  	  else
  	    borrow = 0;
  	  *diffptr-- = val;
  	}
      }
    
    /* Now do the equal length scale and integer parts. */
    
    for (count = 0; count < min_len + min_scale; count++)
      {
        val = *n1ptr - *n2ptr - borrow;
        if (val < 0)
  	{
  	  val += 10;
  	  borrow = 1;
  	}
        else
  	borrow = 0;
        *diffptr = val;
        // Now do the decrements for Deputy, if we stay in the loop
        if(count + 1 < min_len + min_scale) {
          n2ptr --; n1ptr --; diffptr --;
        } 
      }
  
    /* If n1 has more digits then n2, we now do that subtract. */
    if (diff_len != min_len)
      {
        // Do the decrements that we missed above
        n1ptr --; diffptr --;
        for (count = diff_len - min_len; count > 0; count--)
  	{
  	  val = *n1ptr - borrow;
  	  if (val < 0)
  	    {
  	      val += 10;
  	      borrow = 1;
  	    }
  	  else
  	    borrow = 0;
  	  *diffptr = val;
            // Deferred decrement for Deputy
            if(count - 1 > 0) { n1ptr --; diffptr --; } 
  	}
      }
  
    /* Clean up and return. */
    _rm_leading_zeros (diff);
    return diff;
  }
  
  
  /* Here is the full add routine that takes care of negative numbers.
     N1 is added to N2 and the result placed into RESULT. */
  
  void
  bc_add ( bc_num n1, bc_num n2, bc_num * result)
  {
    bc_num sum;
    int cmp_res;
    sum = 0; //Deputy wants us to initialize sum because it doesn't know
             //know that do_compare always returns -1, 0, or 1.
  
    if (n1->n_sign == n2->n_sign)
      {
        sum = _do_add (n1, n2);
        sum->n_sign = n1->n_sign;
      }
    else
      {
        /* subtraction must be done. */
        cmp_res = _do_compare (n1, n2, FALSE, FALSE);  /* Compare magnitudes. */
        switch (cmp_res)
  	{
  	case -1:
  	  /* n1 is less than n2, subtract n1 from n2. */
  	  sum = _do_sub (n2, n1);
  	  sum->n_sign = n2->n_sign;
  	  break;
  	case  0:
  	  /* They are equal! return zero! */
  	  sum = copy_num (_zero_);   
  	  break;
  	case  1:
  	  /* n2 is less than n1, subtract n2 from n1. */
  	  sum = _do_sub (n1, n2);
  	  sum->n_sign = n1->n_sign;
  	}
      }
  
    /* Clean up and return. */
    free_num (result);
    *result = sum;
  }
  
  
  /* Here is the full subtract routine that takes care of negative numbers.
     N2 is subtracted from N1 and the result placed in RESULT. */
  
  void
  bc_sub ( bc_num n1, bc_num n2, bc_num * result)
  {
    bc_num diff = 0;
    int cmp_res;
  
    if (n1->n_sign != n2->n_sign)
      {
        diff = _do_add (n1, n2);
        diff->n_sign = n1->n_sign;
      }
    else
      {
        /* subtraction must be done. */
        cmp_res = _do_compare (n1, n2, FALSE, FALSE);  /* Compare magnitudes. */
        switch (cmp_res)
  	{
  	case -1:
  	  /* n1 is less than n2, subtract n1 from n2. */
  	  diff = _do_sub (n2, n1);
  	  diff->n_sign = (n2->n_sign == PLUS ? MINUS : PLUS);
  	  break;
  	case  0:
  	  /* They are equal! return zero! */
  	  diff = copy_num (_zero_);   
  	  break;
  	case  1:
  	  /* n2 is less than n1, subtract n2 from n1. */
  	  diff = _do_sub (n1, n2);
  	  diff->n_sign = n1->n_sign;
  	  break;
  	}
      }
    
    /* Clean up and return. */
    free_num (result);
    *result = diff;
  }
  
  
  /* The multiply routine.  N2 time N1 is put int PROD with the scale of
     the result being MIN(N2 scale+N1 scale, MAX (SCALE, N2 scale, N1 scale)).
     */
  
  void
  bc_multiply (bc_num n1, bc_num n2, bc_num * prod, int scale)
  {
    bc_num pval;			/* For the working storage. */
    char * n1ptr;
    char * n2ptr;
    char * pvptr;			/* Work pointers. */
    char * n1end;
    char * n2end;		/* To the end of n1 and n2. */
  
    int indx;
    int len1, len2, total_digits;
    long sum;
    int full_scale, prod_scale;
    int toss;
    int tmpI;
  
    /* Initialize things. */
    len1 = n1->n_len + n1->n_scale;
    len2 = n2->n_len + n2->n_scale;
    total_digits = len1 + len2;
    full_scale = n1->n_scale + n2->n_scale;
    prod_scale = MIN(full_scale,MAX(scale,MAX(n1->n_scale,n2->n_scale)));
    toss = full_scale - prod_scale;
    pval =  new_num (total_digits-full_scale, prod_scale);
    pval->n_sign = ( n1->n_sign == n2->n_sign ? PLUS : MINUS );
    n1end = &n1->n_value[0] + len1 - 1;
    n2end = &n2->n_value[0] + len2 - 1;
    tmpI = total_digits - toss - 1;
    pvptr = pval->n_value + tmpI;
    sum = 0;
  
    /* Here are the loops... */
    for (indx = 0; indx < toss; indx++)
      {
        n1ptr = n1end - MAX(0, indx-len2+1);
        n2ptr = n2end - MIN(indx, len2-1);
        while ((n1ptr >= n1->n_value) && (n2ptr <= n2end)) {
  	sum += *n1ptr-- * *n2ptr++;
          //if(n1ptr > n1->n_value) n1ptr --; // conditional for Deputy
        }
        sum = sum / 10;
      }
    for ( ; indx < total_digits-1; indx++)
      { // To make Deputy happy we cannot decrement the pointer before the area
        // So, we add another termination flag
        int done = 0;
        n1ptr = n1end - MAX(0, indx-len2+1);
        n2ptr = n2end - MIN(indx, len2-1);
        
        while (!done && (n1ptr >= n1->n_value) && (n2ptr <= n2end)) {
  	sum += *n1ptr * *n2ptr++;
          if(n1ptr > n1->n_value) {
            n1ptr --;
          } else
            done = 1;
        }
        *pvptr-- = sum % 10;
        sum = sum / 10;
      }
    *pvptr = sum; // Minor bug: was pvptr --
  
    /* Assign to prod and clean up the number. */
    free_num (prod);
    *prod = pval;
    _rm_leading_zeros (*prod);
    if (is_zero (*prod)) 
      (*prod)->n_sign = PLUS;
  }
  
  
  /* 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.  */
  
  /* Deputy: It seems that sometimes there is some extra room before result */
  static void
  _one_mult (char * COUNT(size) num, int size,
             int digit,
  	   char * BND(__this - extra_first, __this + size) result,
             int extra_first)
  {
    int carry, value;
    char * nptr;
    char * rptr;
    
    if (digit == 0)
      memset (result, 0, size);
    else
      {
        if (digit == 1)
  	memcpy (result, num, size);
        else
  	{
            int sizec = size; // Make a copy for Deputy
  	  /* Initialize */
  	  nptr = num+sizec-1;
  	  rptr = result+sizec-1;
  	  carry = 0;
  
  	  while (sizec-- > 0)
  	    {
  	      value = *nptr * digit + carry;
  	      *rptr = value % 10;
  	      carry = value / 10;
                if(sizec > 0) { nptr --; rptr --; } // For Deputy
  	    }
            
  	  if (carry != 0) * --rptr = carry; // To account for missing -- above
  	}
      }
  }
  
  
  /* 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;
    char * num1;
    char * num2;
    char * ptr1;
    char * ptr2;
    char * n2ptr;
    char * qptr;
    int  scale1, val;
    unsigned int  len1, len2, scale2, qdigits, extra, count;
    unsigned int  qdig, qguess, borrow, carry;
    char * mval;
    char zero;
    unsigned int  norm;
  
    /* Test for divide by zero. */
    if (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[0] == 1)
  	{
  	  qval = 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));
  	  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 = &n2->n_value[0] + 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 = (char *)malloc(n1->n_len+n1->n_scale+extra+2);
    /* XXX if (num1 == NULL) out_of_memory(); */
    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 = (char *)malloc(len2+1);
    /* XXX if (num2 == NULL) out_of_memory(); */
    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 = new_num (qdigits-scale,scale);
    memset (qval->n_value, 0, qdigits);
  
    /* Allocate storage for the temporary storage mval. */
    mval = (char *)malloc(len2+1);
    /* XXX if (mval == NULL) out_of_memory (); */
  
    /* 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, 0);
  	  _one_mult (n2ptr, len2, norm, n2ptr, 0);
  	}
  
        /* Initialize divide loop. */
        qdig = 0;
        if (len2 > len1)
  	qptr = (char *)&qval->n_value[0] +len2-len1;
        else
  	qptr = (char *)&qval->n_value[0];
  
        /* 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, 1);
  	      ptr1 = num1+qdig+len2;
  	      ptr2 = mval+len2;
  	      for (count = 0; count < len2+1; count++)
  		{
  		  val = (int) *ptr1 - (int) *ptr2 - borrow;
                    if(count + 1 < len2 + 1) ptr2 --; // For Deputy
  		  if (val < 0)
  		    {
  		      val += 10;
  		      borrow = 1;
  		    }
  		  else
  		    borrow = 0;
  		  *ptr1 = val;
                    if(count + 1 < len2 +1) ptr1 --; // For Deputy
  		}
  	    }
  
  	  /* Test for negative result. */
  	  if (borrow == 1)
  	    {
  	      qguess--;
  	      ptr1 = num1+qdig+len2;
  	      ptr2 = 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;
                    // Do the deferred decrement
                    if(count + 1 < len2) { ptr2 --; }
  		}
  	      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 (is_zero (qval)) qval->n_sign = PLUS;
    _rm_leading_zeros (qval);
    free_num (quot);
    *quot = qval;
  
    /* Clean up temporary storage. */
    free(mval);
    free(num1);
    free(num2);
  
    return 0;	/* Everything is OK. */
  }
  
  
  /* Modulo for numbers.  This computes NUM1 % NUM2  and puts the
     result in RESULT.   */
  
  int
  bc_modulo (bc_num num1, bc_num num2, bc_num * result, int scale)
  {
    bc_num temp;
    int rscale;
    ;
  
    /* Check for correct numbers. */
    if (is_zero (num2)) return -1;
  
    /* Calculate final scale. */
    rscale = MAX (num1->n_scale, num2->n_scale+scale);
    init_num (&temp);
    
    /* Calculate it. */
    bc_divide (num1, num2, &temp, scale);
    bc_multiply (temp, num2, &temp, rscale);
    bc_sub (num1, temp, result);
    free_num (&temp);
  
    ;
    return 0;	/* Everything is OK. */
  }
  
  
  /* Raise NUM1 to the NUM2 power.  The result is placed in RESULT.
     Maximum exponent is LONG_MAX.  If a NUM2 is not an integer,
     only the integer part is used.  */
  
  void
  bc_raise (bc_num num1, bc_num num2, bc_num * result, int scale)
  {
     bc_num temp, power; // So that we can take address-of
     long exponent;
     int rscale;
     char neg;
     ;
  
     /* Check the exponent for scale digits and convert to a long. */
     if (num2->n_scale != 0)
       rt_warn ("non-zero scale in exponent");
     exponent = num2long (num2);
     if (exponent == 0 && (num2->n_len > 1 || num2->n_value[0] != 0))
         rt_error ("exponent too large in raise");
  
     /* Special case if exponent is a zero. */
     if (exponent == 0)
       {
         free_num (result);
         *result = copy_num (_one_);
         ;
         return;
       }
  
     /* Other initializations. */
     if (exponent < 0)
       {
         neg = TRUE;
         exponent = -exponent;
         rscale = scale;
       }
     else
       {
         neg = FALSE;
         rscale = MIN (num1->n_scale*exponent, MAX(scale, num1->n_scale));
       }
     temp = copy_num (_one_);
     power = copy_num (num1);
  
     /* Do the calculation. */
     while (exponent != 0)
       {
         if (exponent & 1 != 0) 
  	 bc_multiply (temp, power, &temp, rscale);
         bc_multiply (power, power, &power, rscale);
         exponent = exponent >> 1;
       }
     
     /* Assign the value. */
     if (neg)
       {
         bc_divide (_one_, temp, result, rscale);
         free_num (&temp);
       }
     else
       {
         free_num (result);
         *result = temp;
       }
     free_num (&power);
     ;
  }
  
  
  /* Take the square root NUM and return it in NUM with SCALE digits
     after the decimal place. */
  
  int 
  bc_sqrt (bc_num * num, int scale)
  {
    int rscale, cmp_res, done;
    int cscale;
    bc_num guess, guess1, point5; // To take the address
    ;
  
    /* Initial checks. */
    cmp_res = bc_compare (*num, _zero_);
    if (cmp_res < 0) {
      ;
      return 0;		/* error */
    }
    else
      {
        if (cmp_res == 0)
  	{
  	  free_num (num);
  	  *num = copy_num (_zero_);
            ;
  	  return 1;
  	}
      }
    cmp_res = bc_compare (*num, _one_);
    if (cmp_res == 0)
      {
        free_num (num);
        *num = copy_num (_one_);
        ;
        return 1;
      }
  
    /* Initialize the variables. */
    rscale = MAX (scale, (*num)->n_scale);
    cscale = rscale + 2;
    init_num (&guess);
    init_num (&guess1);
    point5 = new_num (1,1);
    point5->n_value[1] = 5;
    
    
    /* Calculate the initial guess. */
    if (cmp_res < 0)
      /* The number is between 0 and 1.  Guess should start at 1. */
      guess = copy_num (_one_);
    else
      {
        /* The number is greater than 1.  Guess should start at 10^(exp/2). */
        int2num (&guess,10);
        int2num (&guess1,(*num)->n_len);
        bc_multiply (guess1, point5, &guess1, rscale);
        guess1->n_scale = 0;
        bc_raise (guess, guess1, &guess, rscale);
        free_num (&guess1);
      }
    
    /* Find the square root using Newton's algorithm. */
    done = FALSE;
    while (!done)
      {
        free_num (&guess1);
        guess1 = copy_num (guess);
        bc_divide (*num,guess,&guess,cscale);
        bc_add (guess,guess1,&guess);
        bc_multiply (guess,point5,&guess,cscale);
        cmp_res = _do_compare (guess,guess1,FALSE,TRUE);
        if (cmp_res == 0) done = TRUE;
      }
    
    /* Assign the number and clean up. */
    free_num (num);
    bc_divide (guess,_one_,num,rscale);
    free_num (&guess);
    free_num (&guess1);
    free_num (&point5);
  
    ;
    return 1;
  }
  
  
  /* The following routines provide output for bcd numbers package
     using the rules of POSIX bc for output. */
  
  /* This structure is used for saving digits in the conversion process. */
  typedef struct stk_rec {
  	long  digit;
  	struct stk_rec * next;
  } stk_rec;
  
  /* The reference string for digits. */
  char ref_str[] = "0123456789ABCDEF";
  
  
  /* A special output routine for "multi-character digits."  Exactly
     SIZE characters must be output for the value .  If SPACE is
     non-zero, we must output one space before the number.  OUT_CHAR
     is the actual routine for writing the characters. */
  
  void
  out_long (long val, int size, int space, void (*out_char)(int))
  {
    char digits[40];
    int len, ix;
  
    if (space) (*out_char) (' ');
    sprintf (digits, "%ld", val);
    len = strlen (digits);
    while (size > len)
      {
        (*out_char) ('0');
        size--;
      }
    for (ix=0; ix < len; ix++)
      (*out_char) (digits[ix]);
  }
  
  /* Output of a bcd number.  NUM is written in base O_BASE using OUT_CHAR
     as the routine to do the actual output of the characters. */
  
  void
  out_num (bc_num num, int o_base, void (*out_char)(int))
  {
    char * nptr;
    int  index, fdigit, pre_space;
    stk_rec * digits;
    stk_rec * temp;
    bc_num int_part, frac_part, base, cur_dig, t_num, max_o_digit;
    ;
  
    /* The negative sign if needed. */
    if (num->n_sign == MINUS) (*out_char) ('-');
  
    /* Output the number. */
    if (is_zero (num))
      (*out_char) ('0');
    else
      if (o_base == 10)
        {
  	/* The number is in base 10, do it the fast way. */
  	nptr = &num->n_value[0];
  	if (num->n_len > 1 || *nptr != 0)
  	  for (index=num->n_len; index>0; index--)
  	    (*out_char) (BCD_CHAR(*nptr++));
  	else
  	  nptr++;
  	
  	/* Now the fraction. */
  	if (num->n_scale > 0)
  	  {
  	    (*out_char) ('.');
  	    for (index=0; index<num->n_scale; index++)
  	      (*out_char) (BCD_CHAR(*nptr++));
  	  }
        }
      else
        {
  	/* The number is some other base. */
  	digits = NULL;
  	init_num (&int_part);
  	bc_divide (num, _one_, &int_part, 0);
  	init_num (&frac_part);
  	init_num (&cur_dig);
  	init_num (&base);
  	bc_sub (num, int_part, &frac_part);
  	int2num (&base, o_base);
  	init_num (&max_o_digit);
  	int2num (&max_o_digit, o_base-1);
  
  
  	/* Get the digits of the integer part and push them on a stack. */
  	while (!is_zero (int_part))
  	  {
  	    bc_modulo (int_part, base, &cur_dig, 0);
  	    temp = (stk_rec *)malloc(sizeof(stk_rec));
  	    /* XXX if (temp == NULL) out_of_memory(); */
  	    temp->digit = num2long (cur_dig);
  	    temp->next = digits;
  	    digits = temp;
  	    bc_divide (int_part, base, &int_part, 0);
  	  }
  
  	/* Print the digits on the stack. */
  	if (digits != NULL)
  	  {
  	    /* Output the digits. */
  	    while (digits != NULL)
  	      {
  		temp = digits;
  		digits = digits->next;
  		if (o_base <= 16) 
  		  (*out_char) (ref_str[ (int) temp->digit]);
  		else
  		  out_long (temp->digit, max_o_digit->n_len, 1, out_char);
  		free(temp);
  	      }
  	  }
  
  	/* Get and print the digits of the fraction part. */
  	if (num->n_scale > 0)
  	  {
  	    (*out_char) ('.');
  	    pre_space = 0;
  	    t_num = copy_num (_one_);
  	    while (t_num->n_len <= num->n_scale) {
  	      bc_multiply (frac_part, base, &frac_part, num->n_scale);
  	      fdigit = num2long (frac_part);
  	      int2num (&int_part, fdigit);
  	      bc_sub (frac_part, int_part, &frac_part);
  	      if (o_base <= 16)
  		(*out_char) (ref_str[fdigit]);
  	      else {
  		out_long (fdigit, max_o_digit->n_len, pre_space, out_char);
  		pre_space = 1;
  	      }
  	      bc_multiply (t_num, base, &t_num, 0);
  	    }
  	  }
      
  	/* Clean up. */
  	free_num (&int_part);
  	free_num (&frac_part);
  	free_num (&base);
  	free_num (&cur_dig);
        }
        ;
  }
  
  
  #if DEBUG > 0
  
  /* Debugging procedures.  Some are just so one can call them from the
     debugger.  */
  
  /* p_n prints the number NUM in base 10. */
  
  void
  p_n (bc_num num)
  {
    out_num (num, 10, out_char);
    return 0;
  }
  
  
  /* p_b prints a character array as if it was a string of bcd digits. */
  void
  p_v (char * name, unsigned char * num, int len)
  {
    int i;
    printf ("%s=", name);
    for (i=0; i<len; i++) printf ("%c",BCD_CHAR(num[i]));
    printf ("\n");
  }
  
  
  /* Convert strings to bc numbers.  Base 10 only.*/
  
  void
  str2num (bc_num * num, char * str, int scale)
  {
    int digits, strscale;
    char * ptr;
    char * nptr;
    char zero_int;
  
    /* Prepare num. */
    free_num (num);
  
    /* Check for valid number and count digits. */
    ptr = str;
    digits = 0;
    strscale = 0;
    zero_int = FALSE;
    if ( (*ptr == '+') || (*ptr == '-'))  ptr++;  /* Sign */
    while (*ptr == '0') ptr++;			/* Skip leading zeros. */
    while (isdigit(*ptr)) ptr++, digits++;	/* digits */
    if (*ptr == '.') ptr++;			/* decimal point */
    while (isdigit(*ptr)) ptr++, strscale++;	/* digits */
    if ((*ptr != '\0') || (digits+strscale == 0))
      {
        *num = copy_num (_zero_);
        return;
      }
  
    /* Adjust numbers and allocate storage and initialize fields. */
    strscale = MIN(strscale, scale);
    if (digits == 0)
      {
        zero_int = TRUE;
        digits = 1;
      }
    *num = new_num (digits, strscale);
  
    /* Build the whole number. */
    ptr = str;
    if (*ptr == '-')
      {
        (*num)->n_sign = MINUS;
        ptr++;
      }
    else
      {
        (*num)->n_sign = PLUS;
        if (*ptr == '+') ptr++;
      }
    while (*ptr == '0') ptr++;			/* Skip leading zeros. */
    nptr = (*num)->n_value;
    if (zero_int)
      {
        *nptr++ = 0;
        digits = 0;
      }
    for (;digits > 0; digits--)
      *nptr++ = CH_VAL(*ptr++);
  
    
    /* Build the fractional part. */
    if (strscale > 0)
      {
        ptr++;  /* skip the decimal point! */
        for (;strscale > 0; strscale--)
  	*nptr++ = CH_VAL(*ptr++);
      }
  }
  
  /* Convert a numbers to a string.  Base 10 only.*/
  
  char *
  num2str (bc_num num)
  {
    char * str;
    char * sptr;
    char * nptr;
    int  index, signch;
  
    /* Allocate the string memory. */
    signch = ( num->n_sign == PLUS ? 0 : 1 );  /* Number of sign chars. */
    if (num->n_scale > 0)
      str = (char *)malloc(num->n_len + num->n_scale + 2 + signch);
    else
      str = (char *)malloc(num->n_len + 1 + signch);
    /* XXX if (str == NULL) out_of_memory(); */
  
    /* The negative sign if needed. */
    sptr = str;
    if (signch) *sptr++ = '-';
  
    /* Load the whole number. */
    nptr = num->n_value;
    for (index=num->n_len; index>0; index--)
      *sptr++ = BCD_CHAR(*nptr++);
  
    /* Now the fraction. */
    if (num->n_scale > 0)
      {
        *sptr++ = '.';
        for (index=0; index<num->n_scale; index++)
  	*sptr++ = BCD_CHAR(*nptr++);
      }
  
    /* Terminate the string and return it! */
    *sptr = '\0';
    return (str);
  }
  #endif
  