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Diffstat (limited to 'sbin/i386/ft/ftecc.c')
-rw-r--r-- | sbin/i386/ft/ftecc.c | 479 |
1 files changed, 479 insertions, 0 deletions
diff --git a/sbin/i386/ft/ftecc.c b/sbin/i386/ft/ftecc.c new file mode 100644 index 0000000..95de073 --- /dev/null +++ b/sbin/i386/ft/ftecc.c @@ -0,0 +1,479 @@ +/* + * Copyright (c) 1994 Steve Gerakines + * + * This is freely redistributable software. You may do anything you + * wish with it, so long as the above notice stays intact. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR(S) ``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 AUTHOR(S) 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. + * + * ftecc.c - QIC-40/80 Reed-Solomon error correction + * 05/30/94 v1.0 ++sg + * Did some minor optimization. The multiply by 0xc0 was a dog so it + * was replaced with a table lookup. Fixed a couple of places where + * bad sectors could go unnoticed. Moved to release. + * + * 03/22/94 v0.4 + * Major re-write. It can handle everything required by QIC now. + * + * 09/14/93 v0.2 pl01 + * Modified slightly to fit with my driver. Based entirely upon David + * L. Brown's package. + */ +#include <sys/ftape.h> + +/* Inverse matrix */ +struct inv_mat { + UCHAR log_denom; /* Log of the denominator */ + UCHAR zs[3][3]; /* The matrix */ +}; + + +/* + * Powers of x, modulo 255. + */ +static const 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, 0x01 +}; + + +/* + * Log table, modulo 255 + 1. + */ +static const 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 +}; + + +/* + * Multiplication table for 0xc0. + */ +static const UCHAR mult_c0[] = { + 0x00, 0xc0, 0x07, 0xc7, 0x0e, 0xce, 0x09, 0xc9, + 0x1c, 0xdc, 0x1b, 0xdb, 0x12, 0xd2, 0x15, 0xd5, + 0x38, 0xf8, 0x3f, 0xff, 0x36, 0xf6, 0x31, 0xf1, + 0x24, 0xe4, 0x23, 0xe3, 0x2a, 0xea, 0x2d, 0xed, + 0x70, 0xb0, 0x77, 0xb7, 0x7e, 0xbe, 0x79, 0xb9, + 0x6c, 0xac, 0x6b, 0xab, 0x62, 0xa2, 0x65, 0xa5, + 0x48, 0x88, 0x4f, 0x8f, 0x46, 0x86, 0x41, 0x81, + 0x54, 0x94, 0x53, 0x93, 0x5a, 0x9a, 0x5d, 0x9d, + 0xe0, 0x20, 0xe7, 0x27, 0xee, 0x2e, 0xe9, 0x29, + 0xfc, 0x3c, 0xfb, 0x3b, 0xf2, 0x32, 0xf5, 0x35, + 0xd8, 0x18, 0xdf, 0x1f, 0xd6, 0x16, 0xd1, 0x11, + 0xc4, 0x04, 0xc3, 0x03, 0xca, 0x0a, 0xcd, 0x0d, + 0x90, 0x50, 0x97, 0x57, 0x9e, 0x5e, 0x99, 0x59, + 0x8c, 0x4c, 0x8b, 0x4b, 0x82, 0x42, 0x85, 0x45, + 0xa8, 0x68, 0xaf, 0x6f, 0xa6, 0x66, 0xa1, 0x61, + 0xb4, 0x74, 0xb3, 0x73, 0xba, 0x7a, 0xbd, 0x7d, + 0x47, 0x87, 0x40, 0x80, 0x49, 0x89, 0x4e, 0x8e, + 0x5b, 0x9b, 0x5c, 0x9c, 0x55, 0x95, 0x52, 0x92, + 0x7f, 0xbf, 0x78, 0xb8, 0x71, 0xb1, 0x76, 0xb6, + 0x63, 0xa3, 0x64, 0xa4, 0x6d, 0xad, 0x6a, 0xaa, + 0x37, 0xf7, 0x30, 0xf0, 0x39, 0xf9, 0x3e, 0xfe, + 0x2b, 0xeb, 0x2c, 0xec, 0x25, 0xe5, 0x22, 0xe2, + 0x0f, 0xcf, 0x08, 0xc8, 0x01, 0xc1, 0x06, 0xc6, + 0x13, 0xd3, 0x14, 0xd4, 0x1d, 0xdd, 0x1a, 0xda, + 0xa7, 0x67, 0xa0, 0x60, 0xa9, 0x69, 0xae, 0x6e, + 0xbb, 0x7b, 0xbc, 0x7c, 0xb5, 0x75, 0xb2, 0x72, + 0x9f, 0x5f, 0x98, 0x58, 0x91, 0x51, 0x96, 0x56, + 0x83, 0x43, 0x84, 0x44, 0x8d, 0x4d, 0x8a, 0x4a, + 0xd7, 0x17, 0xd0, 0x10, 0xd9, 0x19, 0xde, 0x1e, + 0xcb, 0x0b, 0xcc, 0x0c, 0xc5, 0x05, 0xc2, 0x02, + 0xef, 0x2f, 0xe8, 0x28, 0xe1, 0x21, 0xe6, 0x26, + 0xf3, 0x33, 0xf4, 0x34, 0xfd, 0x3d, 0xfa, 0x3a +}; + + +/* + * 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 inline UCHAR +multiply(UCHAR a, UCHAR b) +{ + int tmp; + + if (!a || !b) return(0); + tmp = alpha_log[a] + alpha_log[b]; + if (tmp > 254) tmp -= 255; + return(alpha_power[tmp]); +} + + +/* + * Multiply by an exponent. + */ +static inline UCHAR +multiply_out(UCHAR a, int b) +{ + int tmp; + + if (!a) return(0); + tmp = alpha_log[a] + b; + if (tmp > 254) tmp -= 255; + return(alpha_power[tmp]); +} + + +/* + * Divide two numbers. + */ +static inline UCHAR +divide(UCHAR a, UCHAR b) +{ + int tmp; + + if (!a || !b) return(0); + tmp = alpha_log[a] - alpha_log[b]; + if (tmp < 0) tmp += 255; + return (alpha_power[tmp]); +} + + +/* + * Divide using exponent. + */ +static inline UCHAR +divide_out(UCHAR a, UCHAR b) +{ + int tmp; + + if (!a) return 0; + tmp = alpha_log[a] - b; + if (tmp < 0) tmp += 255; + return (alpha_power[tmp]); +} + + +/* + * This returns the value z^{a-b}. + */ +static inline UCHAR +z_of_ab(UCHAR a, UCHAR b) +{ + int tmp = a - b; + + if (tmp < 0) tmp += 255; + return(alpha_power[tmp]); +} + + +/* + * Calculate the inverse matrix for two or three errors. Returns 0 + * if there is no inverse or 1 if successful. + */ +static inline int +calculate_inverse(int nerrs, 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; + UCHAR iv0, iv1, iv2; + + if (nerrs < 2) return(1); + if (nerrs > 3) return(0); + + i0 = pblk[0]; i1 = pblk[1]; i2 = pblk[2]; + if (nerrs == 2) { + /* 2 errs */ + z01 = alpha_power[255 - i0]; + z02 = alpha_power[255 - i1]; + inv->log_denom = (z01 ^ z02); + if (!inv->log_denom) return(0); + inv->log_denom = 255 - alpha_log[inv->log_denom]; + + inv->zs[0][0] = multiply_out( 1, inv->log_denom); + inv->zs[0][1] = multiply_out(z02, inv->log_denom); + inv->zs[1][0] = multiply_out( 1, inv->log_denom); + inv->zs[1][1] = multiply_out(z01, inv->log_denom); + } else { + /* 3 errs */ + 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) return(0); + inv->log_denom = 255 - alpha_log[inv->log_denom]; + + iv0 = alpha_power[255 - i0]; + iv1 = alpha_power[255 - i1]; + iv2 = alpha_power[255 - i2]; + i0 = alpha_power[i0]; + i1 = alpha_power[i1]; + i2 = alpha_power[i2]; + inv->zs[0][0] = multiply_out(i1 ^ i2, inv->log_denom); + inv->zs[0][1] = multiply_out(z21 ^ z12, inv->log_denom); + inv->zs[0][2] = multiply_out(iv1 ^ iv2, inv->log_denom); + inv->zs[1][0] = multiply_out(i0 ^ i2, inv->log_denom); + inv->zs[1][1] = multiply_out(z20 ^ z02, inv->log_denom); + inv->zs[1][2] = multiply_out(iv0 ^ iv2, inv->log_denom); + inv->zs[2][0] = multiply_out(i0 ^ i1, inv->log_denom); + inv->zs[2][1] = multiply_out(z10 ^ z01, inv->log_denom); + inv->zs[2][2] = multiply_out(iv0 ^ iv1, inv->log_denom); + } + return(1); +} + + +/* + * Determine the error magnitudes for a given matrix and syndromes. + */ +static inline void +determine(int nerrs, struct inv_mat *inv, UCHAR *ss, UCHAR *es) +{ + int i, j; + + for (i = 0; i < nerrs; i++) { + es[i] = 0; + for (j = 0; j < nerrs; j++) + es[i] ^= multiply(ss[j], inv->zs[i][j]); + } +} + + +/* + * Compute the 3 syndrome values. + */ +static inline int +compute_syndromes(UCHAR *data, int nblks, int col, UCHAR *ss) +{ + UCHAR r0, r1, r2, t1, t2; + UCHAR *rptr; + + rptr = data + col; + data += nblks << 10; + r0 = r1 = r2 = 0; + while (rptr < data) { + t1 = *rptr ^ r0; + t2 = mult_c0[t1]; + r0 = t2 ^ r1; + r1 = t2 ^ r2; + r2 = t1; + rptr += QCV_BLKSIZE; + } + if (r0 || r1 || r2) { + ss[0] = divide_out(r0 ^ divide_out(r1 ^ divide_out(r2, 1), 1), nblks); + ss[1] = r0 ^ r1 ^ r2; + ss[2] = multiply_out(r0 ^ multiply_out(r1 ^ multiply_out(r2, 1), 1), nblks); + return(0); + } + return(1); +} + + +/* + * Calculate the parity bytes for a segment, returns 0 on success (always). + */ +int +set_parity (UCHAR *data, ULONG badmap) +{ + UCHAR r0, r1, r2, t1, t2; + UCHAR *rptr; + int max, row, col; + + max = sect_count(badmap) - 3; + col = QCV_BLKSIZE; + while (col--) { + rptr = data; + r0 = r1 = r2 = 0; + row = max; + while (row--) { + t1 = *rptr ^ r0; + t2 = mult_c0[t1]; + r0 = t2 ^ r1; + r1 = t2 ^ r2; + r2 = t1; + rptr += QCV_BLKSIZE; + } + *rptr = r0; rptr += QCV_BLKSIZE; + *rptr = r1; rptr += QCV_BLKSIZE; + *rptr = r2; + data++; + } + 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 crcerrs, eblk[3]; + int col; + int i, nblks; + UCHAR ss[3], es[3]; + int i1, i2; + struct inv_mat inv; + + nblks = sect_count(badmap); + + /* Count the number of CRC errors and note their locations. */ + crcerrs = 0; + if (crcmap) { + for (i = 0; i < nblks; i++) { + if (crcmap & (1 << i)) { + if (crcerrs == 3) return(1); + eblk[crcerrs++] = i; + } + } + } + + /* Calculate the inverse matrix */ + if (!calculate_inverse(crcerrs, eblk, &inv)) return(1); + + /* Scan each column for problems and attempt to correct. */ + for (col = 0; col < QCV_BLKSIZE; col++) { + if (compute_syndromes(data, nblks, col, ss)) continue; + es[0] = es[1] = es[2] = 0; + + /* Analyze the error situation. */ + switch (crcerrs) { + case 0: /* 0 errors >0 failures */ + if (!ss[0]) return(1); + eblk[crcerrs] = alpha_log[divide(ss[1], ss[0])]; + if (eblk[crcerrs] >= nblks) return(1); + es[0] = ss[1]; + if (++crcerrs > 3) return(1); + break; + + case 1: /* 1 error (+ possible failures) */ + i1 = ss[2] ^ multiply_out(ss[1], eblk[0]); + i2 = ss[1] ^ multiply_out(ss[0], eblk[0]); + if (!i1 && !i2) { /* only 1 error */ + inv.zs[0][0] = alpha_power[eblk[0]]; + inv.log_denom = 0; + } else if (!i1 || !i2) { /* too many errors */ + return(1); + } else { /* add failure */ + eblk[crcerrs] = alpha_log[divide(i1, i2)]; + if (eblk[crcerrs] >= nblks) return(1); + if (++crcerrs > 3) return(1); + if (!calculate_inverse(crcerrs, eblk, &inv)) return(1); + } + determine(crcerrs, &inv, ss, es); + break; + + case 2: /* 2 errors */ + case 3: /* 3 errors */ + determine(crcerrs, &inv, ss, es); + break; + + default: + return(1); + } + + /* Make corrections. */ + for (i = 0; i < crcerrs; i++) { + data[(eblk[i] << 10) | col] ^= es[i]; + ss[0] ^= divide_out(es[i], eblk[i]); + ss[1] ^= es[i]; + ss[2] ^= multiply_out(es[i], eblk[i]); + } + if (ss[0] || ss[1] || ss[2]) return(1); + } + return(0); +} |