recmul.c

/* recmul.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"

/* Recursive vs non-recursive multiply crossover ranges. */
#if defined(MULDIGITS)
#include "muldigits.h"
#else
#define MUL_BASE_DIGITS 80
#endif

int mul_base_digits = MUL_BASE_DIGITS;
#define MUL_SMALL_DIGITS mul_base_digits/4

/* Multiply utility routines */

static bc_num
new_sub_num (length, scale, value)
     int length, scale;
     char *value;
{
  bc_num temp;

#ifdef SANDER_0
  if (_bc_Free_list != NULL) {
    temp = _bc_Free_list;
    _bc_Free_list = temp->n_next;
  } else {
#endif
    temp = (bc_num) emalloc (sizeof(bc_struct));
#ifdef SANDER_0
    if (temp == NULL) bc_out_of_memory ();
  }
#endif
  temp->n_sign = PLUS;
  temp->n_len = length;
  temp->n_scale = scale;
  temp->n_refs = 1;
  temp->n_ptr = NULL;
  temp->n_value = value;
  return temp;
}

static void
_bc_simp_mul (bc_num n1, int n1len, bc_num n2, int n2len, bc_num *prod,
	      int full_scale)
{
  char *n1ptr, *n2ptr, *pvptr;
  char *n1end, *n2end;		/* To the end of n1 and n2. */
  int indx, sum, prodlen;

  prodlen = n1len+n2len+1;

  *prod = bc_new_num (prodlen, 0);

  n1end = (char *) (n1->n_value + n1len - 1);
  n2end = (char *) (n2->n_value + n2len - 1);
  pvptr = (char *) ((*prod)->n_value + prodlen - 1);
  sum = 0;

  /* Here is the loop... */
  for (indx = 0; indx < prodlen-1; indx++)
    {
      n1ptr = (char *) (n1end - MAX(0, indx-n2len+1));
      n2ptr = (char *) (n2end - MIN(indx, n2len-1));
      while ((n1ptr >= n1->n_value) && (n2ptr <= n2end))
	sum += *n1ptr-- * *n2ptr++;
      *pvptr-- = sum % BASE;
      sum = sum / BASE;
    }
  *pvptr = sum;
}


/* A special adder/subtractor for the recursive divide and conquer
   multiply algorithm.  Note: if sub is called, accum must
   be larger that what is being subtracted.  Also, accum and val
   must have n_scale = 0.  (e.g. they must look like integers. *) */
static void
_bc_shift_addsub (bc_num accum, bc_num val, int shift, int sub)
{
  signed char *accp, *valp;
  int  count, carry;

  count = val->n_len;
  if (val->n_value[0] == 0)
    count--;
  assert (accum->n_len+accum->n_scale >= shift+count);

  /* Set up pointers and others */
  accp = (signed char *)(accum->n_value +
			 accum->n_len + accum->n_scale - shift - 1);
  valp = (signed char *)(val->n_value + val->n_len - 1);
  carry = 0;

  if (sub) {
    /* Subtraction, carry is really borrow. */
    while (count--) {
      *accp -= *valp-- + carry;
      if (*accp < 0) {
	carry = 1;
        *accp-- += BASE;
      } else {
	carry = 0;
	accp--;
      }
    }
    while (carry) {
      *accp -= carry;
      if (*accp < 0)
	*accp-- += BASE;
      else
	carry = 0;
    }
  } else {
    /* Addition */
    while (count--) {
      *accp += *valp-- + carry;
      if (*accp > (BASE-1)) {
	carry = 1;
        *accp-- -= BASE;
      } else {
	carry = 0;
	accp--;
      }
    }
    while (carry) {
      *accp += carry;
      if (*accp > (BASE-1))
	*accp-- -= BASE;
      else
	carry = 0;
    }
  }
}

/* Recursive divide and conquer multiply algorithm.
   Based on
   Let u = u0 + u1*(b^n)
   Let v = v0 + v1*(b^n)
   Then uv = (B^2n+B^n)*u1*v1 + B^n*(u1-u0)*(v0-v1) + (B^n+1)*u0*v0

   B is the base of storage, number of digits in u1,u0 close to equal.
*/
static void
_bc_rec_mul (bc_num u, int ulen, bc_num v, int vlen, bc_num *prod,
	     int full_scale)
{
  bc_num u0, u1, v0, v1;
  bc_num m1, m2, m3, d1, d2;
  int n, prodlen, m1zero;
  int d1len, d2len;

  /* Base case? */
  if ((ulen+vlen) < mul_base_digits
      || ulen < MUL_SMALL_DIGITS
      || vlen < MUL_SMALL_DIGITS ) {
    _bc_simp_mul (u, ulen, v, vlen, prod, full_scale);
    return;
  }

  /* Calculate n -- the u and v split point in digits. */
  n = (MAX(ulen, vlen)+1) / 2;

  /* Split u and v. */
  if (ulen < n) {
    u1 = bc_copy_num (BCG(_zero_));
    u0 = new_sub_num (ulen,0, u->n_value);
  } else {
    u1 = new_sub_num (ulen-n, 0, u->n_value);
    u0 = new_sub_num (n, 0, u->n_value+ulen-n);
  }
  if (vlen < n) {
    v1 = bc_copy_num (BCG(_zero_));
    v0 = new_sub_num (vlen,0, v->n_value);
  } else {
    v1 = new_sub_num (vlen-n, 0, v->n_value);
    v0 = new_sub_num (n, 0, v->n_value+vlen-n);
    }
  _bc_rm_leading_zeros (u1);
  _bc_rm_leading_zeros (u0);
  _bc_rm_leading_zeros (v1);
  _bc_rm_leading_zeros (v0);

  m1zero = bc_is_zero(u1) || bc_is_zero(v1);

  /* Calculate sub results ... */

  bc_init_num(&d1);
  bc_init_num(&d2);
  bc_sub (u1, u0, &d1, 0);
  d1len = d1->n_len;
  bc_sub (v0, v1, &d2, 0);
  d2len = d2->n_len;


  /* Do recursive multiplies and shifted adds. */
  if (m1zero)
    m1 = bc_copy_num (BCG(_zero_));
  else
    _bc_rec_mul (u1, u1->n_len, v1, v1->n_len, &m1, 0);

  if (bc_is_zero(d1) || bc_is_zero(d2))
    m2 = bc_copy_num (BCG(_zero_));
  else
    _bc_rec_mul (d1, d1len, d2, d2len, &m2, 0);

  if (bc_is_zero(u0) || bc_is_zero(v0))
    m3 = bc_copy_num (BCG(_zero_));
  else
    _bc_rec_mul (u0, u0->n_len, v0, v0->n_len, &m3, 0);

  /* Initialize product */
  prodlen = ulen+vlen+1;
  *prod = bc_new_num(prodlen, 0);

  if (!m1zero) {
    _bc_shift_addsub (*prod, m1, 2*n, 0);
    _bc_shift_addsub (*prod, m1, n, 0);
  }
  _bc_shift_addsub (*prod, m3, n, 0);
  _bc_shift_addsub (*prod, m3, 0, 0);
  _bc_shift_addsub (*prod, m2, n, d1->n_sign != d2->n_sign);

  /* Now clean up! */
  bc_free_num (&u1);
  bc_free_num (&u0);
  bc_free_num (&v1);
  bc_free_num (&m1);
  bc_free_num (&v0);
  bc_free_num (&m2);
  bc_free_num (&m3);
  bc_free_num (&d1);
  bc_free_num (&d2);
}

/* The multiply routine.  N2 times 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;
  int len1, len2;
  int full_scale, prod_scale;

  /* Initialize things. */
  len1 = n1->n_len + n1->n_scale;
  len2 = n2->n_len + n2->n_scale;
  full_scale = n1->n_scale + n2->n_scale;
  prod_scale = MIN(full_scale,MAX(scale,MAX(n1->n_scale,n2->n_scale)));

  /* Do the multiply */
  _bc_rec_mul (n1, len1, n2, len2, &pval, full_scale);

  /* Assign to prod and clean up the number. */
  pval->n_sign = ( n1->n_sign == n2->n_sign ? PLUS : MINUS );
  pval->n_value = pval->n_ptr;
  pval->n_len = len2 + len1 + 1 - full_scale;
  pval->n_scale = prod_scale;
  _bc_rm_leading_zeros (pval);
  if (bc_is_zero (pval))
    pval->n_sign = PLUS;
  bc_free_num (prod);
  *prod = pval;
}