galois.c

/* Galois.c
 * James S. Plank
 * April, 2007

Galois.tar - Fast Galois Field Arithmetic Library in C/C++
Copright (C) 2007 James S. Plank

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 2.1 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.

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., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA

James S. Plank
Department of Electrical Engineering and Computer Science
University of Tennessee
Knoxville, TN 37996
plank@cs.utk.edu

 */

/*
 * Part of jerasure: 
 * $Revision: 1.2 $
 * $Date: 2008/08/19 17:40:58 $
 */

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

#include "galois.h"

#define NONE (10)
#define TABLE (11)
#define SHIFT (12)
#define LOGS (13)
#define SPLITW8 (14)

static int prim_poly[33] = 
{ 0, 
/*  1 */     1, 
/*  2 */    07,
/*  3 */    013,
/*  4 */    023,
/*  5 */    045,
/*  6 */    0103,
/*  7 */    0211,
/*  8 */    0435,
/*  9 */    01021,
/* 10 */    02011,
/* 11 */    04005,
/* 12 */    010123,
/* 13 */    020033,
/* 14 */    042103,
/* 15 */    0100003,
/* 16 */    0210013,
/* 17 */    0400011,
/* 18 */    01000201,
/* 19 */    02000047,
/* 20 */    04000011,
/* 21 */    010000005,
/* 22 */    020000003,
/* 23 */    040000041,
/* 24 */    0100000207,
/* 25 */    0200000011,
/* 26 */    0400000107,
/* 27 */    01000000047,
/* 28 */    02000000011,
/* 29 */    04000000005,
/* 30 */    010040000007,
/* 31 */    020000000011, 
/* 32 */    00020000007 };  /* Really 40020000007, but we're omitting the high order bit */

static int mult_type[33] = 
{ NONE, 
/*  1 */   TABLE, 
/*  2 */   TABLE,
/*  3 */   TABLE,
/*  4 */   TABLE,
/*  5 */   TABLE,
/*  6 */   TABLE,
/*  7 */   TABLE,
/*  8 */   TABLE,
/*  9 */   TABLE,
/* 10 */   LOGS,
/* 11 */   LOGS,
/* 12 */   LOGS,
/* 13 */   LOGS,
/* 14 */   LOGS,
/* 15 */   LOGS,
/* 16 */   LOGS,
/* 17 */   LOGS,
/* 18 */   LOGS,
/* 19 */   LOGS,
/* 20 */   LOGS,
/* 21 */   LOGS,
/* 22 */   LOGS,
/* 23 */   SHIFT,
/* 24 */   SHIFT,
/* 25 */   SHIFT,
/* 26 */   SHIFT,
/* 27 */   SHIFT,
/* 28 */   SHIFT,
/* 29 */   SHIFT,
/* 30 */   SHIFT,
/* 31 */   SHIFT,
/* 32 */   SPLITW8 };

static int nw[33] = { 0, (1 << 1), (1 << 2), (1 << 3), (1 << 4), 
(1 << 5), (1 << 6), (1 << 7), (1 << 8), (1 << 9), (1 << 10),
(1 << 11), (1 << 12), (1 << 13), (1 << 14), (1 << 15), (1 << 16),
(1 << 17), (1 << 18), (1 << 19), (1 << 20), (1 << 21), (1 << 22),
(1 << 23), (1 << 24), (1 << 25), (1 << 26), (1 << 27), (1 << 28),
(1 << 29), (1 << 30), (1 << 31), -1 };

static int nwm1[33] = { 0, (1 << 1)-1, (1 << 2)-1, (1 << 3)-1, (1 << 4)-1, 
(1 << 5)-1, (1 << 6)-1, (1 << 7)-1, (1 << 8)-1, (1 << 9)-1, (1 << 10)-1,
(1 << 11)-1, (1 << 12)-1, (1 << 13)-1, (1 << 14)-1, (1 << 15)-1, (1 << 16)-1,
(1 << 17)-1, (1 << 18)-1, (1 << 19)-1, (1 << 20)-1, (1 << 21)-1, (1 << 22)-1,
(1 << 23)-1, (1 << 24)-1, (1 << 25)-1, (1 << 26)-1, (1 << 27)-1, (1 << 28)-1,
(1 << 29)-1, (1 << 30)-1, 0x7fffffff, 0xffffffff };
   
static int *galois_log_tables[33] = { NULL, NULL, NULL, NULL, NULL, NULL, NULL,
NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,
NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL };

static int *galois_ilog_tables[33] = { NULL, NULL, NULL, NULL, NULL, NULL, NULL,
NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,
NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL };

static int *galois_mult_tables[33] = { NULL, NULL, NULL, NULL, NULL, NULL, NULL,
NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,
NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL };

static int *galois_div_tables[33] = { NULL, NULL, NULL, NULL, NULL, NULL, NULL,
NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,
NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL };

/* Special case for w = 32 */

static int *galois_split_w8[7] = { NULL, NULL, NULL, NULL, NULL, NULL, NULL };

int galois_create_log_tables(int w)
{
  int j, b;

  if (w > 30) return -1;
  if (galois_log_tables[w] != NULL) return 0;
  galois_log_tables[w] = (int *) malloc(sizeof(int)*nw[w]);
  if (galois_log_tables[w] == NULL) return -1; 
  
  galois_ilog_tables[w] = (int *) malloc(sizeof(int)*nw[w]*3);
  if (galois_ilog_tables[w] == NULL) { 
    free(galois_log_tables[w]);
    galois_log_tables[w] = NULL;
    return -1;
  }
  
  for (j = 0; j < nw[w]; j++) {
    galois_log_tables[w][j] = nwm1[w];
    galois_ilog_tables[w][j] = 0;
  } 
  
  b = 1;
  for (j = 0; j < nwm1[w]; j++) {
    if (galois_log_tables[w][b] != nwm1[w]) {
      fprintf(stderr, "Galois_create_log_tables Error: j=%d, b=%d, B->J[b]=%d, J->B[j]=%d (0%o)\n",
              j, b, galois_log_tables[w][b], galois_ilog_tables[w][j], (b << 1) ^ prim_poly[w]);
      exit(1);
    }
    galois_log_tables[w][b] = j;
    galois_ilog_tables[w][j] = b;
    b = b << 1;
    if (b & nw[w]) b = (b ^ prim_poly[w]) & nwm1[w];
  }
  for (j = 0; j < nwm1[w]; j++) {
    galois_ilog_tables[w][j+nwm1[w]] = galois_ilog_tables[w][j];
    galois_ilog_tables[w][j+nwm1[w]*2] = galois_ilog_tables[w][j];
  } 
  galois_ilog_tables[w] += nwm1[w];
  return 0;
}

int galois_logtable_multiply(int x, int y, int w)
{
  int sum_j;

  if (x == 0 || y == 0) return 0;
  
  sum_j = galois_log_tables[w][x] + galois_log_tables[w][y];
  /* if (sum_j >= nwm1[w]) sum_j -= nwm1[w];    Don't need to do this, 
                                   because we replicate the ilog table twice.  */
  return galois_ilog_tables[w][sum_j];
}

int galois_logtable_divide(int x, int y, int w)
{
  int sum_j;
  int z;

  if (y == 0) return -1;
  if (x == 0) return 0; 
  sum_j = galois_log_tables[w][x] - galois_log_tables[w][y];
  /* if (sum_j < 0) sum_j += nwm1[w];   Don't need to do this, because we replicate the ilog table twice.   */
  z = galois_ilog_tables[w][sum_j];
  return z;
}

int galois_create_mult_tables(int w)
{
  int j, x, y, logx;

  if (w >= 14) return -1;

  if (galois_mult_tables[w] != NULL) return 0;
  galois_mult_tables[w] = (int *) malloc(sizeof(int) * nw[w] * nw[w]);
  if (galois_mult_tables[w] == NULL) return -1;
  
  galois_div_tables[w] = (int *) malloc(sizeof(int) * nw[w] * nw[w]);
  if (galois_div_tables[w] == NULL) {
    free(galois_mult_tables[w]);
    galois_mult_tables[w] = NULL;
    return -1;
  }
  if (galois_log_tables[w] == NULL) {
    if (galois_create_log_tables(w) < 0) {
      free(galois_mult_tables[w]);
      free(galois_div_tables[w]);
      galois_mult_tables[w] = NULL;
      galois_div_tables[w] = NULL;
      return -1;
    }
  }

 /* Set mult/div tables for x = 0 */
  j = 0;
  galois_mult_tables[w][j] = 0;   /* y = 0 */
  galois_div_tables[w][j] = -1;
  j++;
  for (y = 1; y < nw[w]; y++) {   /* y > 0 */
    galois_mult_tables[w][j] = 0;
    galois_div_tables[w][j] = 0;
    j++;
  }
  
  for (x = 1; x < nw[w]; x++) {  /* x > 0 */
    galois_mult_tables[w][j] = 0; /* y = 0 */
    galois_div_tables[w][j] = -1;
    j++;
    logx = galois_log_tables[w][x];
    for (y = 1; y < nw[w]; y++) {  /* y > 0 */
      galois_mult_tables[w][j] = galois_ilog_tables[w][logx+galois_log_tables[w][y]]; 
      galois_div_tables[w][j] = galois_ilog_tables[w][logx-galois_log_tables[w][y]]; 
      j++;
    }
  }
  return 0;
}

int galois_ilog(int value, int w)
{
  if (galois_ilog_tables[w] == NULL) {
    if (galois_create_log_tables(w) < 0) {
      fprintf(stderr, "Error: galois_ilog - w is too big.  Sorry\n");
      exit(1);
    }
  }
  return galois_ilog_tables[w][value];
}

int galois_log(int value, int w)
{
  if (galois_log_tables[w] == NULL) {
    if (galois_create_log_tables(w) < 0) {
      fprintf(stderr, "Error: galois_log - w is too big.  Sorry\n");
      exit(1);
    }
  }
  return galois_log_tables[w][value];
}


int galois_shift_multiply(int x, int y, int w)
{
  int prod;
  int i, j, ind;
  int k;
  int scratch[33];

  prod = 0;
  for (i = 0; i < w; i++) {
    scratch[i] = y;
    if (y & (1 << (w-1))) {
      y = y << 1;
      y = (y ^ prim_poly[w]) & nwm1[w];
    } else {
      y = y << 1;
    }
  }
  for (i = 0; i < w; i++) {
    ind = (1 << i);
    if (ind & x) {
      j = 1;
      for (k = 0; k < w; k++) {
        prod = prod ^ (j & scratch[i]);
        j = (j << 1);
      }
    }
  }
  return prod;
}

int galois_single_multiply(int x, int y, int w)
{
  int sum_j;
  int z;

  if (x == 0 || y == 0) return 0;
  
  if (mult_type[w] == TABLE) {
    if (galois_mult_tables[w] == NULL) {
      if (galois_create_mult_tables(w) < 0) {
        fprintf(stderr, "ERROR -- cannot make multiplication tables for w=%d\n", w);
        exit(1);
      }
    }
    return galois_mult_tables[w][(x<<w)|y];
  } else if (mult_type[w] == LOGS) {
    if (galois_log_tables[w] == NULL) {
      if (galois_create_log_tables(w) < 0) {
        fprintf(stderr, "ERROR -- cannot make log tables for w=%d\n", w);
        exit(1);
      }
    }
    sum_j = galois_log_tables[w][x] + galois_log_tables[w][y];
    z = galois_ilog_tables[w][sum_j];
    return z;
  } else if (mult_type[w] == SPLITW8) {
    if (galois_split_w8[0] == NULL) {
      if (galois_create_split_w8_tables() < 0) {
        fprintf(stderr, "ERROR -- cannot make log split_w8_tables for w=%d\n", w);
        exit(1);
      }
    }
    return galois_split_w8_multiply(x, y);
  } else if (mult_type[w] == SHIFT) {
    return galois_shift_multiply(x, y, w);
  }
  fprintf(stderr, "Galois_single_multiply - no implementation for w=%d\n", w);
  exit(1);
}

int galois_multtable_multiply(int x, int y, int w)
{
  return galois_mult_tables[w][(x<<w)|y];
}

int galois_single_divide(int a, int b, int w)
{
  int sum_j;

  if (mult_type[w] == TABLE) {
    if (galois_div_tables[w] == NULL) {
      if (galois_create_mult_tables(w) < 0) {
        fprintf(stderr, "ERROR -- cannot make multiplication tables for w=%d\n", w);
        exit(1);
      }
    }
    return galois_div_tables[w][(a<<w)|b];
  } else if (mult_type[w] == LOGS) {
    if (b == 0) return -1;
    if (a == 0) return 0;
    if (galois_log_tables[w] == NULL) {
      if (galois_create_log_tables(w) < 0) {
        fprintf(stderr, "ERROR -- cannot make log tables for w=%d\n", w);
        exit(1);
      }
    }
    sum_j = galois_log_tables[w][a] - galois_log_tables[w][b];
    return galois_ilog_tables[w][sum_j];
  } else {
    if (b == 0) return -1;
    if (a == 0) return 0;
    sum_j = galois_inverse(b, w);
    return galois_single_multiply(a, sum_j, w);
  }
  fprintf(stderr, "Galois_single_divide - no implementation for w=%d\n", w);
  exit(1);
}

int galois_shift_divide(int a, int b, int w)
{
  int inverse;

  if (b == 0) return -1;
  if (a == 0) return 0;
  inverse = galois_shift_inverse(b, w);
  return galois_shift_multiply(a, inverse, w);
}

int galois_multtable_divide(int x, int y, int w)
{
  return galois_div_tables[w][(x<<w)|y];
}

void galois_w08_region_multiply(char *region,      /* Region to multiply */
                                  int multby,       /* Number to multiply by */
                                  int nbytes,        /* Number of bytes in region */
                                  char *r2,          /* If r2 != NULL, products go here */
                                  int add)
{
  unsigned char *ur1, *ur2, *cp;
  unsigned char prod;
  int i, srow, j;
  unsigned long l, *lp2;
  unsigned char *lp;
  int sol;

  ur1 = (unsigned char *) region;
  ur2 = (r2 == NULL) ? ur1 : (unsigned char *) r2;

/* This is used to test its performance with respect to just calling galois_single_multiply 
  if (r2 == NULL || !add) {
    for (i = 0; i < nbytes; i++) ur2[i] = galois_single_multiply(ur1[i], multby, 8);
  } else {
    for (i = 0; i < nbytes; i++) {
      ur2[i] = (ur2[i]^galois_single_multiply(ur1[i], multby, 8));
    }
  }
 */

  if (galois_mult_tables[8] == NULL) {
    if (galois_create_mult_tables(8) < 0) {
      fprintf(stderr, "galois_08_region_multiply -- couldn't make multiplication tables\n");
      exit(1);
    }
  }
  srow = multby * nw[8];
  if (r2 == NULL || !add) {
    for (i = 0; i < nbytes; i++) {
      prod = galois_mult_tables[8][srow+ur1[i]];
      ur2[i] = prod;
    }
  } else {
    sol = sizeof(long);
    lp2 = &l;
    lp = (unsigned char *) lp2;
    for (i = 0; i < nbytes; i += sol) {
      cp = ur2+i;
      lp2 = (unsigned long *) cp;
      for (j = 0; j < sol; j++) {
        prod = galois_mult_tables[8][srow+ur1[i+j]];
        lp[j] = prod;
      }
      *lp2 = (*lp2) ^ l;
    }
  }
  return;
}

void galois_w16_region_multiply(char *region,      /* Region to multiply */
                                  int multby,       /* Number to multiply by */
                                  int nbytes,        /* Number of bytes in region */
                                  char *r2,          /* If r2 != NULL, products go here */
                                  int add)
{
  unsigned short *ur1, *ur2, *cp;
  int prod;
  int i, log1, j, log2;
  unsigned long l, *lp2, *lptop;
  unsigned short *lp;
  int sol;

  ur1 = (unsigned short *) region;
  ur2 = (r2 == NULL) ? ur1 : (unsigned short *) r2;
  nbytes /= 2;


/* This is used to test its performance with respect to just calling galois_single_multiply */
/*
  if (r2 == NULL || !add) {
    for (i = 0; i < nbytes; i++) ur2[i] = galois_single_multiply(ur1[i], multby, 16);
  } else {
    for (i = 0; i < nbytes; i++) {
      ur2[i] = (ur2[i]^galois_single_multiply(ur1[i], multby, 16));
    }
  }
  return;
  */

  if (multby == 0) {
    if (!add) {
      lp2 = (unsigned long *) ur2;
      ur2 += nbytes;
      lptop = (unsigned long *) ur2;
      while (lp2 < lptop) { *lp2 = 0; lp2++; }
    }
    return;
  }
    
  if (galois_log_tables[16] == NULL) {
    if (galois_create_log_tables(16) < 0) {
      fprintf(stderr, "galois_16_region_multiply -- couldn't make log tables\n");
      exit(1);
    }
  }
  log1 = galois_log_tables[16][multby];

  if (r2 == NULL || !add) {
    for (i = 0; i < nbytes; i++) {
      if (ur1[i] == 0) {
        ur2[i] = 0;
      } else {
        prod = galois_log_tables[16][ur1[i]] + log1;
        ur2[i] = galois_ilog_tables[16][prod];
      }
    }
  } else {
    sol = sizeof(long)/2;
    lp2 = &l;
    lp = (unsigned short *) lp2;
    for (i = 0; i < nbytes; i += sol) {
      cp = ur2+i;
      lp2 = (unsigned long *) cp;
      for (j = 0; j < sol; j++) {
        if (ur1[i+j] == 0) {
          lp[j] = 0;
        } else {
          log2 = galois_log_tables[16][ur1[i+j]];
          prod = log2 + log1;
          lp[j] = galois_ilog_tables[16][prod];
        }
      }
      *lp2 = (*lp2) ^ l;
    }
  }
  return; 
}

/* This will destroy mat, by the way */

void galois_invert_binary_matrix(int *mat, int *inv, int rows)
{
  int cols, i, j, k;
  int tmp;
 
  cols = rows;

  for (i = 0; i < rows; i++) inv[i] = (1 << i);

  /* First -- convert into upper triangular */

  for (i = 0; i < cols; i++) {

    /* Swap rows if we ave a zero i,i element.  If we can't swap, then the 
       matrix was not invertible */

    if ((mat[i] & (1 << i)) == 0) { 
      for (j = i+1; j < rows && (mat[j] & (1 << i)) == 0; j++) ;
      if (j == rows) {
        fprintf(stderr, "galois_invert_matrix: Matrix not invertible!!\n");
        exit(1);
      }
      tmp = mat[i]; mat[i] = mat[j]; mat[j] = tmp;
      tmp = inv[i]; inv[i] = inv[j]; inv[j] = tmp;
    }
 
    /* Now for each j>i, add A_ji*Ai to Aj */
    for (j = i+1; j != rows; j++) {
      if ((mat[j] & (1 << i)) != 0) {
        mat[j] ^= mat[i]; 
        inv[j] ^= inv[i];
      }
    }
  }

  /* Now the matrix is upper triangular.  Start at the top and multiply down */

  for (i = rows-1; i >= 0; i--) {
    for (j = 0; j < i; j++) {
      if (mat[j] & (1 << i)) {
/*        mat[j] ^= mat[i]; */
        inv[j] ^= inv[i];
      }
    }
  } 
}

int galois_inverse(int y, int w)
{

  if (y == 0) return -1;
  if (mult_type[w] == SHIFT || mult_type[w] == SPLITW8) return galois_shift_inverse(y, w);
  return galois_single_divide(1, y, w);
}

int galois_shift_inverse(int y, int w)
{
  int mat[1024], mat2[32];
  int inv[1024], inv2[32];
  int ind, i, j, k, prod;
 
  for (i = 0; i < w; i++) {
    mat2[i] = y;

    if (y & nw[w-1]) {
      y = y << 1;
      y = (y ^ prim_poly[w]) & nwm1[w];
    } else {
      y = y << 1;
    }
  }

  galois_invert_binary_matrix(mat2, inv2, w);

  return inv2[0]; 
}

int *galois_get_mult_table(int w)
{
  if (galois_mult_tables[w] == NULL) {
    if (galois_create_mult_tables(w)) {
      return NULL;
    }
  }
  return galois_mult_tables[w];
}

int *galois_get_div_table(int w) 
{
  if (galois_mult_tables[w] == NULL) {
    if (galois_create_mult_tables(w)) {
      return NULL;
    }
  }
  return galois_div_tables[w];
}

int *galois_get_log_table(int w)
{
  if (galois_log_tables[w] == NULL) {
    if (galois_create_log_tables(w)) {
      return NULL;
    }
  }
  return galois_log_tables[w];
}

int *galois_get_ilog_table(int w)
{
  if (galois_ilog_tables[w] == NULL) {
    if (galois_create_log_tables(w)) {
      return NULL;
    }
  }
  return galois_ilog_tables[w];
}

void galois_w32_region_multiply(char *region,      /* Region to multiply */
                                  int multby,       /* Number to multiply by */
                                  int nbytes,        /* Number of bytes in region */
                                  char *r2,          /* If r2 != NULL, products go here */
                                  int add)
{
  unsigned int *ur1, *ur2, *cp, *ur2top;
  unsigned long *lp2, *lptop;
  int i, j, a, b, accumulator, i8, j8, k;
  int acache[4];

  ur1 = (unsigned int *) region;
  ur2 = (r2 == NULL) ? ur1 : (unsigned int *) r2;
  nbytes /= sizeof(int);
  ur2top = ur2 + nbytes;

  if (galois_split_w8[0]== NULL) {
    if (galois_create_split_w8_tables(8) < 0) {
      fprintf(stderr, "galois_32_region_multiply -- couldn't make split multiplication tables\n");
      exit(1);
    }
  }

  /* If we're overwriting r2, then we can't do better than just calling split_multiply.
     We'll inline it here to save on the procedure call overhead */

  i8 = 0;
  for (i = 0; i < 4; i++) {
    acache[i] = (((multby >> i8) & 255) << 8);
    i8 += 8;
  }
  if (!add) {
    for (k = 0; k < nbytes; k++) {
      accumulator = 0;
      for (i = 0; i < 4; i++) {
        a = acache[i];
        j8 = 0;
        for (j = 0; j < 4; j++) {
          b = ((ur1[k] >> j8) & 255);
          accumulator ^= galois_split_w8[i+j][a|b];
          j8 += 8;
        }
      }
      ur2[k] = accumulator;
    }
  } else {
    for (k = 0; k < nbytes; k++) {
      accumulator = 0;
      for (i = 0; i < 4; i++) {
        a = acache[i];
        j8 = 0;
        for (j = 0; j < 4; j++) {
          b = ((ur1[k] >> j8) & 255);
          accumulator ^= galois_split_w8[i+j][a|b];
          j8 += 8;
        }
      }
      ur2[k] = (ur2[k] ^ accumulator);
    }
  }
  return;

}

void galois_region_xor(           char *r1,         /* Region 1 */
                                  char *r2,         /* Region 2 */
                                  char *r3,         /* Sum region (r3 = r1 ^ r2) -- can be r1 or r2 */
                                  int nbytes)       /* Number of bytes in region */
{
  long *l1;
  long *l2;
  long *l3;
  long *ltop;
  char *ctop;
  
  ctop = r1 + nbytes;
  ltop = (long *) ctop;
  l1 = (long *) r1;
  l2 = (long *) r2;
  l3 = (long *) r3;
 
  while (l1 < ltop) {
    *l3 = ((*l1)  ^ (*l2));
    l1++;
    l2++;
    l3++;
  }
}

int galois_create_split_w8_tables()
{
  int p1, p2, i, j, p1elt, p2elt, index, ishift, jshift, *table;

  if (galois_split_w8[0] != NULL) return 0;

  if (galois_create_mult_tables(8) < 0) return -1;

  for (i = 0; i < 7; i++) {
    galois_split_w8[i] = (int *) malloc(sizeof(int) * (1 << 16));
    if (galois_split_w8[i] == NULL) {
      for (i--; i >= 0; i--) free(galois_split_w8[i]);
      return -1;
    }
  }

  for (i = 0; i < 4; i += 3) {
    ishift = i * 8;
    for (j = ((i == 0) ? 0 : 1) ; j < 4; j++) {
      jshift = j * 8;
      table = galois_split_w8[i+j];
      index = 0;
      for (p1 = 0; p1 < 256; p1++) {
        p1elt = (p1 << ishift);
        for (p2 = 0; p2 < 256; p2++) {
          p2elt = (p2 << jshift);
          table[index] = galois_shift_multiply(p1elt, p2elt, 32);
          index++;
        }
      }
    }
  }
  return 0;
}

int galois_split_w8_multiply(int x, int y)
{
  int i, j, a, b, accumulator, i8, j8;

  accumulator = 0;
  
  i8 = 0;
  for (i = 0; i < 4; i++) {
    a = (((x >> i8) & 255) << 8);
    j8 = 0;
    for (j = 0; j < 4; j++) {
      b = ((y >> j8) & 255);
      accumulator ^= galois_split_w8[i+j][a|b];
      j8 += 8;
    }
    i8 += 8;
  }
  return accumulator;
}