Improve analysis section.

[storin] / matrix.c

/* -*-c-*-
 *
 * $Id: matrix.c,v 1.1 2000/05/21 11:28:30 mdw Exp $
 *
 * Matrix arithmetic mod %$2^{24}$%
 *
 * (c) 2000 Mark Wooding
 */

/*----- Licensing notice --------------------------------------------------* 
 *
 * Copyright (c) 2000 Mark Wooding
 * All rights reserved.
 * 
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are
 * met:
 * 
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 
 * 2, Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 
 * 3. The name of the authors may not be used to endorse or promote
 *    products derived from this software without specific prior written
 *    permission.
 * 
 * THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESS OR IMPLIED
 * WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
 * MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.  IN
 * NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT,
 * INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
 * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
 * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 * POSSIBILITY OF SUCH DAMAGE.
 * 
 * Instead of accepting the above terms, you may redistribute and/or modify
 * this software under the terms of either the GNU General Public License,
 * or the GNU Library General Public License, published by the Free
 * Software Foundation; either version 2 of the License, or (at your
 * option) any later version.
 */

/*----- Revision history --------------------------------------------------* 
 *
 * $Log: matrix.c,v $
 * Revision 1.1  2000/05/21 11:28:30  mdw
 * Initial check-in.
 *
 */

/*----- Header files ------------------------------------------------------*/

#include <assert.h>
#include <stdio.h>
#include <stdlib.h>

#include "arith24.h"
#include "bits.h"
#include "matrix.h"

/*----- Main code ---------------------------------------------------------*/

/* --- @matmul@ --- *
 *
 * Arguments:	@uint24 *d@ = pointer to destination matrix
 *		@uint24 *a, *b@ = pointer to operand matrices
 *		@unsigned x, y, z@ = dimensions of the operand matrices
 *
 * Returns:	---
 *
 * Use:		Performs matrix multiplication mod %$2^{24}$%.  The matrix
 *		@d@ may not overlap either operand matrix.
 */

void matmul(uint24 *d, const uint24 *a, const uint24 *b,
	    unsigned x, unsigned y, unsigned z)
{
  unsigned i, j, k;

  for (i = 0; i < x; i++) {
    const uint24 *bb = b;
    for (j = 0; j < z; j++) {
      uint24 n = 0;
      for (k = 0; k < y; k++)
	n += a[k] * bb[k * z];
      *d++ = U24(n);
      bb++;
    }
    a += y;
  }
}

/* --- @matinv@ --- *
 *
 * Arguments:	@uint24 *d@ = pointer to destination matrix
 *		@uint24 *a@ = pointer to operand matrix
 *		@unsigned x, y@ = dimensions of operand matrix
 *
 * Returns:	Zero if the matrix was successfully inverted, %$-1$% if the
 *		matrix is singular.
 *
 * Use:		Computes the mod %$2^{24}$% inverse of a square matrix.
 */

int matinv(uint24 *d, uint24 *a, unsigned x, unsigned y)
{
  unsigned i, j, k;
  uint24 *aa;
  uint32 *p, *q, *r, *s;

  assert(x == y);

  aa = malloc(sizeof(uint24) * x * y);
  if (!aa) {
    fprintf(stderr, "unable to allocate memory\n");
    exit(EXIT_FAILURE);
  }
  memcpy(aa, a, sizeof(uint24) * x * y);

  p = d;
  for (i = 0; i < x; i++) {
    for (j = 0; j < y; j++)
      *p++ = i == j;
  }

  for (i = 0; i < x; i++) {
    uint24 c = inv24(aa[(x + 1) * i]);
    if (!c)
      goto fail;
    r = aa + y * i;
    s = d + y * i;
    for (j = 0; j < y; j++) {
      r[j] = U24(r[j] * c);
      s[j] = U24(s[j] * c);
    }
    for (j = 0; j < x; j++) {
      if (j == i)
	continue;
      p = aa + y * j;
      q = d + y * j;
      c = p[i];
      for (k = 0; k < y; k++) {
	p[k] = U24(p[k] - c * r[k]);
	q[k] = U24(q[k] - c * s[k]);
      }
    }
  }

  free(aa);
  return (0);

fail:
  free(aa);
  return (-1);
}

/*----- That's all, folks -------------------------------------------------*/