freebsd-dev/sbin/ft/ftecc.c

/*
 *  ftecc.c  10/30/93 v0.3
 *  Handle error correction for floppy tape drives.
 *
 *  File contents are copyrighted by David L. Brown and falls under the
 *  terms of the GPL version 2 or greater.  See his original release for
 *  the specific terms.
 *
 *  Steve Gerakines
 *  steve2@genesis.nred.ma.us
 *  Modified slightly to fit with my tape driver.  I'm not at all happy
 *  with this module and will have it replaced with a more functional one
 *  in the next release(/RSN).  I am close, but progress will continue to
 *  be slow until I can find a book on the subject where the translator
 *  understands both the to and from languages. :-(  For now it will
 *  suffice.
 */
#include <sys/ftape.h>

/*
 *  In order to speed up the correction and adjustment, we can compute
 *  a matrix of coefficients for the multiplication.
 */
struct inv_mat {
  UCHAR log_denom;      /* The log z of the denominator. */
  UCHAR zs[3][3];       /* The coefficients for the adjustment matrix. */
};

/* This array is a table of powers of x, from 0 to 254. */
static UCHAR alpha_power[] = {
  0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80,
  0x87, 0x89, 0x95, 0xad, 0xdd, 0x3d, 0x7a, 0xf4,
  0x6f, 0xde, 0x3b, 0x76, 0xec, 0x5f, 0xbe, 0xfb,
  0x71, 0xe2, 0x43, 0x86, 0x8b, 0x91, 0xa5, 0xcd,
  0x1d, 0x3a, 0x74, 0xe8, 0x57, 0xae, 0xdb, 0x31,
  0x62, 0xc4, 0x0f, 0x1e, 0x3c, 0x78, 0xf0, 0x67,
  0xce, 0x1b, 0x36, 0x6c, 0xd8, 0x37, 0x6e, 0xdc,
  0x3f, 0x7e, 0xfc, 0x7f, 0xfe, 0x7b, 0xf6, 0x6b,
  0xd6, 0x2b, 0x56, 0xac, 0xdf, 0x39, 0x72, 0xe4,
  0x4f, 0x9e, 0xbb, 0xf1, 0x65, 0xca, 0x13, 0x26,
  0x4c, 0x98, 0xb7, 0xe9, 0x55, 0xaa, 0xd3, 0x21,
  0x42, 0x84, 0x8f, 0x99, 0xb5, 0xed, 0x5d, 0xba,
  0xf3, 0x61, 0xc2, 0x03, 0x06, 0x0c, 0x18, 0x30,
  0x60, 0xc0, 0x07, 0x0e, 0x1c, 0x38, 0x70, 0xe0,
  0x47, 0x8e, 0x9b, 0xb1, 0xe5, 0x4d, 0x9a, 0xb3,
  0xe1, 0x45, 0x8a, 0x93, 0xa1, 0xc5, 0x0d, 0x1a,
  0x34, 0x68, 0xd0, 0x27, 0x4e, 0x9c, 0xbf, 0xf9,
  0x75, 0xea, 0x53, 0xa6, 0xcb, 0x11, 0x22, 0x44,
  0x88, 0x97, 0xa9, 0xd5, 0x2d, 0x5a, 0xb4, 0xef,
  0x59, 0xb2, 0xe3, 0x41, 0x82, 0x83, 0x81, 0x85,
  0x8d, 0x9d, 0xbd, 0xfd, 0x7d, 0xfa, 0x73, 0xe6,
  0x4b, 0x96, 0xab, 0xd1, 0x25, 0x4a, 0x94, 0xaf,
  0xd9, 0x35, 0x6a, 0xd4, 0x2f, 0x5e, 0xbc, 0xff,
  0x79, 0xf2, 0x63, 0xc6, 0x0b, 0x16, 0x2c, 0x58,
  0xb0, 0xe7, 0x49, 0x92, 0xa3, 0xc1, 0x05, 0x0a,
  0x14, 0x28, 0x50, 0xa0, 0xc7, 0x09, 0x12, 0x24,
  0x48, 0x90, 0xa7, 0xc9, 0x15, 0x2a, 0x54, 0xa8,
  0xd7, 0x29, 0x52, 0xa4, 0xcf, 0x19, 0x32, 0x64,
  0xc8, 0x17, 0x2e, 0x5c, 0xb8, 0xf7, 0x69, 0xd2,
  0x23, 0x46, 0x8c, 0x9f, 0xb9, 0xf5, 0x6d, 0xda,
  0x33, 0x66, 0xcc, 0x1f, 0x3e, 0x7c, 0xf8, 0x77,
  0xee, 0x5b, 0xb6, 0xeb, 0x51, 0xa2, 0xc3
};

/*
 * This is the reverse lookup table.  There is no log of 0, so the
 * first element is not valid.
 */
static UCHAR alpha_log[] = {
  0xff, 0x00, 0x01, 0x63, 0x02, 0xc6, 0x64, 0x6a,
  0x03, 0xcd, 0xc7, 0xbc, 0x65, 0x7e, 0x6b, 0x2a,
  0x04, 0x8d, 0xce, 0x4e, 0xc8, 0xd4, 0xbd, 0xe1,
  0x66, 0xdd, 0x7f, 0x31, 0x6c, 0x20, 0x2b, 0xf3,
  0x05, 0x57, 0x8e, 0xe8, 0xcf, 0xac, 0x4f, 0x83,
  0xc9, 0xd9, 0xd5, 0x41, 0xbe, 0x94, 0xe2, 0xb4,
  0x67, 0x27, 0xde, 0xf0, 0x80, 0xb1, 0x32, 0x35,
  0x6d, 0x45, 0x21, 0x12, 0x2c, 0x0d, 0xf4, 0x38,
  0x06, 0x9b, 0x58, 0x1a, 0x8f, 0x79, 0xe9, 0x70,
  0xd0, 0xc2, 0xad, 0xa8, 0x50, 0x75, 0x84, 0x48,
  0xca, 0xfc, 0xda, 0x8a, 0xd6, 0x54, 0x42, 0x24,
  0xbf, 0x98, 0x95, 0xf9, 0xe3, 0x5e, 0xb5, 0x15,
  0x68, 0x61, 0x28, 0xba, 0xdf, 0x4c, 0xf1, 0x2f,
  0x81, 0xe6, 0xb2, 0x3f, 0x33, 0xee, 0x36, 0x10,
  0x6e, 0x18, 0x46, 0xa6, 0x22, 0x88, 0x13, 0xf7,
  0x2d, 0xb8, 0x0e, 0x3d, 0xf5, 0xa4, 0x39, 0x3b,
  0x07, 0x9e, 0x9c, 0x9d, 0x59, 0x9f, 0x1b, 0x08,
  0x90, 0x09, 0x7a, 0x1c, 0xea, 0xa0, 0x71, 0x5a,
  0xd1, 0x1d, 0xc3, 0x7b, 0xae, 0x0a, 0xa9, 0x91,
  0x51, 0x5b, 0x76, 0x72, 0x85, 0xa1, 0x49, 0xeb,
  0xcb, 0x7c, 0xfd, 0xc4, 0xdb, 0x1e, 0x8b, 0xd2,
  0xd7, 0x92, 0x55, 0xaa, 0x43, 0x0b, 0x25, 0xaf,
  0xc0, 0x73, 0x99, 0x77, 0x96, 0x5c, 0xfa, 0x52,
  0xe4, 0xec, 0x5f, 0x4a, 0xb6, 0xa2, 0x16, 0x86,
  0x69, 0xc5, 0x62, 0xfe, 0x29, 0x7d, 0xbb, 0xcc,
  0xe0, 0xd3, 0x4d, 0x8c, 0xf2, 0x1f, 0x30, 0xdc,
  0x82, 0xab, 0xe7, 0x56, 0xb3, 0x93, 0x40, 0xd8,
  0x34, 0xb0, 0xef, 0x26, 0x37, 0x0c, 0x11, 0x44,
  0x6f, 0x78, 0x19, 0x9a, 0x47, 0x74, 0xa7, 0xc1,
  0x23, 0x53, 0x89, 0xfb, 0x14, 0x5d, 0xf8, 0x97,
  0x2e, 0x4b, 0xb9, 0x60, 0x0f, 0xed, 0x3e, 0xe5,
  0xf6, 0x87, 0xa5, 0x17, 0x3a, 0xa3, 0x3c, 0xb7
};

/* Return number of sectors available in a segment. */
int sect_count(ULONG badmap)
{
  int i, amt;

  for (amt = QCV_BLKSEG, i = 0; i < QCV_BLKSEG; i++)
	if (badmap & (1 << i)) amt--;
  return(amt);
}

/* Return number of bytes available in a segment. */
int sect_bytes(ULONG badmap)
{
  int i, amt;

  for (amt = QCV_SEGSIZE, i = 0; i < QCV_BLKSEG; i++)
	if (badmap & (1 << i)) amt -= QCV_BLKSIZE;
  return(amt);
}

/* Multiply two numbers in the field. */
static UCHAR multiply(UCHAR a, UCHAR b)
{
  int tmp;

  if (a == 0 || b == 0) return(0);
  tmp = (alpha_log[a] + alpha_log[b]);
  if (tmp > 254) tmp -= 255;
  return (alpha_power[tmp]);
}

static UCHAR divide(UCHAR a, UCHAR b)
{
  int tmp;

  if (a == 0 || b == 0) return(0);
  tmp = (alpha_log[a] - alpha_log[b]);
  if (tmp < 0) tmp += 255;
  return (alpha_power[tmp]);
}

/*
 * This is just like divide, except we have already looked up the log
 * of the second number.
 */
static UCHAR divide_out(UCHAR a, UCHAR b)
{
  int tmp;

  if (a == 0) return 0;
  tmp = alpha_log[a] - b;
  if (tmp < 0) tmp += 255;
  return (alpha_power[tmp]);
}

/* This returns the value z^{a-b}. */
static UCHAR z_of_ab(UCHAR a, UCHAR b)
{
  int tmp = (int)a - (int)b;

  if (tmp < 0)
	tmp += 255;
  else if (tmp >= 255)
	tmp -= 255;
  return(alpha_power[tmp]);
}

/*  Calculate the inverse matrix.  Returns 1 if the matrix is valid, or
 *  zero if there is no inverse.  The i's are the indices of the bytes
 *  to be corrected.
 */
static int calculate_inverse (int *pblk, struct inv_mat *inv)
{
  /* First some variables to remember some of the results. */
  UCHAR z20, z10, z21, z12, z01, z02;
  UCHAR i0, i1, i2;

  i0 = pblk[0]; i1 = pblk[1]; i2 = pblk[2];

  z20 = z_of_ab (i2, i0); z10 = z_of_ab (i1, i0);
  z21 = z_of_ab (i2, i1); z12 = z_of_ab (i1, i2);
  z01 = z_of_ab (i0, i1); z02 = z_of_ab (i0, i2);
  inv->log_denom = (z20 ^ z10 ^ z21 ^ z12 ^ z01 ^ z02);
  if (inv->log_denom == 0) return 0;
  inv->log_denom = alpha_log[inv->log_denom];

  /* Calculate all of the coefficients on the top. */
  inv->zs[0][0] = alpha_power[i1] ^ alpha_power[i2];
  inv->zs[0][1] = z21 ^ z12;
  inv->zs[0][2] = alpha_power[255-i1] ^ alpha_power[255-i2];

  inv->zs[1][0] = alpha_power[i0] ^ alpha_power[i2];
  inv->zs[1][1] = z20 ^ z02;
  inv->zs[1][2] = alpha_power[255-i0] ^ alpha_power[255-i2];

  inv->zs[2][0] = alpha_power[i0] ^ alpha_power[i1];
  inv->zs[2][1] = z10 ^ z01;
  inv->zs[2][2] = alpha_power[255-i0] ^ alpha_power[255-i1];
  return(1);
}

/*
 * Determine the error values for a given inverse matrix and syndromes.
 */
static void determine3(struct inv_mat *inv, UCHAR *es, UCHAR *ss)
{
  UCHAR tmp;
  int i, j;

  for (i = 0; i < 3; i++) {
	tmp = 0;
	for (j = 0; j < 3; j++) tmp ^= multiply (ss[j], inv->zs[i][j]);
	es[i] = divide_out(tmp, inv->log_denom);
  }
}


/*
 *  Compute the 3 syndrome values.  The data pointer should point to
 *  the offset within the first block of the column to calculate.  The
 *  count of blocks is in blocks.  The three bytes will be placed in
 *  ss[0], ss[1], and ss[2].
 */
static void compute_syndromes(UCHAR *data, int nblks, int col, UCHAR *ss)
{
  int i;
  UCHAR v;

  ss[0] = 0; ss[1] = 0; ss[2] = 0;
  for (i = (nblks-1)*QCV_BLKSIZE; i >= 0; i -= QCV_BLKSIZE) {
	v = data[i+col];
	if (ss[0] & 0x01) { ss[0] >>= 1; ss[0] ^= 0xc3;	} else ss[0] >>= 1;
	ss[0] ^= v;
	ss[1] ^= v;
	if (ss[2] & 0x80) { ss[2] <<= 1; ss[2] ^= 0x87; } else ss[2] <<= 1;
	ss[2] ^= v;
  }
}

/*
 *  Calculate the parity bytes for a segment.  Returns 0 on success.
 */
int set_parity (UCHAR *data, ULONG badmap)
{
  int col;
  struct inv_mat inv;
  UCHAR ss[3], es[3];
  int nblks, pblk[3];

  nblks = sect_count(badmap);
  pblk[0] = nblks-3; pblk[1] = nblks-2; pblk[2] = nblks-1;
  if (!calculate_inverse(pblk, &inv)) return(1);

  pblk[0] *= QCV_BLKSIZE; pblk[1] *= QCV_BLKSIZE; pblk[2] *= QCV_BLKSIZE;
  for (col = 0; col < QCV_BLKSIZE; col++) {
	compute_syndromes (data, nblks-3, col, ss);
	determine3(&inv, es, ss);
	data[pblk[0]+col] = es[0];
	data[pblk[1]+col] = es[1];
	data[pblk[2]+col] = es[2];
  }
  return(0);
}


/*
 *  Check and correct errors in a block.  Returns 0 on success,
 *  1 if failed.
 */
int check_parity(UCHAR *data, ULONG badmap, ULONG crcmap)
{
  int i, j, col, crcerrs, r, tries, nblks;
  struct inv_mat inv;
  UCHAR ss[3], es[3];
  int i1, i2, eblk[3];

  nblks = sect_count(badmap);
  crcerrs = 0;
  for (i = 0; crcerrs < 3 && i < nblks; i++)
	if (crcmap & (1 << i)) eblk[crcerrs++] = i;

  for (i = 1, j = crcerrs; j < 3 && i < nblks; i++)
	if ((crcmap & (1 << i)) == 0) eblk[j++] = i;

  if (!calculate_inverse (eblk, &inv)) return(1);

  eblk[0] *= QCV_BLKSIZE; eblk[1] *= QCV_BLKSIZE; eblk[2] *= QCV_BLKSIZE;
  r = 0;
  for (col = 0; col < QCV_BLKSIZE; col++) {
	compute_syndromes (data, nblks, col, ss);

	if (!ss[0] && !ss[1] && !ss[2]) continue;
	if (crcerrs) {
		determine3 (&inv, es, ss);
		for (j = 0; j < crcerrs; j++)
			data[eblk[j] + col] ^= es[j];
		compute_syndromes (data, nblks, col, ss);
		if (!ss[0] && !ss[1] && !ss[2]) {
			r = 1;
			continue;
		}
	}
	determine3 (&inv, es, ss);
	i1 = alpha_log[divide(ss[2], ss[1])];
	i2 = alpha_log[divide(ss[1], ss[0])];
	if (i1 != i2 || ((QCV_BLKSIZE * i1) + col) > QCV_SEGSIZE)
		r = 1;
	else
		data[QCV_BLKSIZE * i1 + col] ^= ss[1];
  }

  return(r);
}