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-/* 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 (n1, n2, quot, scale)
- bc_num n1, n2, *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 *) emalloc (n1->n_len+n1->n_scale+extra+2);
- if (num1 == NULL) bc_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 = (unsigned char *) emalloc (len2+1);
- if (num2 == NULL) bc_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 = bc_new_num (qdigits-scale,scale);
- memset (qval->n_value, 0, qdigits);
-
- /* Allocate storage for the temporary storage mval. */
- mval = (unsigned char *) emalloc (len2+1);
- if (mval == NULL) bc_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);
- _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. */
-}
-