1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851
|
/* -*- indent-tabs-mode: t; tab-width: 8; c-basic-offset: 8; -*- */
/* ts A91016 : libburn/ecma130ab.c is the replacement for old libburn/lec.c
Copyright 2009, Thomas Schmitt <scdbackup@gmx.net>, libburnia-project.org
Provided under GPL version 2 or later.
This code module implements the production of RSPC parity bytes (P- and Q-
parity) and the scrambling of raw CD-ROM sectors as specified in ECMA-130:
http://www.ecma-international.org/publications/files/ECMA-ST/Ecma-130.pdf
The following statements about Galois Fields have been learned mostly from
http://www.cs.utk.edu/~plank/plank/papers/CS-96-332.pdf
by James S. Plank after an e-mail exchange with Norbert Preining.
The output has been compared with the output of the old code of libburn
which was labeled "borrowed HEAVILY from cdrdao" and claimed by Joerg
Schilling to stem from code by Heiko Eissfeldt.
-------------------------------------------------------------------------
Note: In this text, "^" denotes exponentiation and not the binary exor
operation. Confusingly in the C code "^" is said exor.
Note: This is not C1, C2 which is rather mentioned in ECMA-130 Annex C and
always performed inside the drive.
-------------------------------------------------------------------------
RSPC resp. P- and Q-Parity
ECMA-130 Annex A prescribes to compute the parity bytes for P-columns and
Q-diagonals by RSPC based on a Galois Field GF(2^8) with enumerating
polynomials x^8+x^4+x^3+x^2+1 (i.e. 0x11d) and x^1 (i.e. 0x02).
Bytes 12 to 2075 of a audio-sized sector get ordered in two byte words
as 24 rows and 43 columns. Then this matrix is split into a LSB matrix
and a MSB matrix of the same layout. Parity bytes are to be computed
from these 8-bit values.
2 P-bytes cover each column of 24 bytes. They get appended to the matrix
as rows 24 and 25.
2 Q-bytes cover each the 26 diagonals of the extended matrix.
Both parity byte pairs have to be computed so that extended rows or
diagonals match this linear equation:
H x V = (0,0)
H is a 2-row matrix of size n matching the length of the V ectors
[ 1 1 ... 1 1 ]
[ x^(n-1) x^(n-2) x^1 1 ]
Vp represents a P-row. It is a byte vector consisting of row bytes at
position 0 to 23 and the two parity bytes which shall be determined
at position 24 and 25. So Hp has 26 columns.
Vq represents a Q-diagonal. It is a byte vector consisting of diagonal
bytes at position 0 to 42 and the two parity bytes at position 43 and 44.
So Hq has 45 columns. The Q-diagonals cover P-parity bytes.
By applying some high school algebra one gets the parity bytes b0, b1 of
vector V = (n_payload_bytes, b0 , b1) as
b0 = ( H[n] * SUM(n_payload_bytes) - H[0..(n-1)] x n_payload_bytes )
/ (H[n+1] - H[n])
b1 = - SUM(n_payload_bytes) - b0
H[i] is the i-the element of the second row of matrix H. E.g. H[0] = x^(n-1)
The result has to be computed by Galois field arithmetics. See below.
The P-parity bytes of each column get reunited as LSB and MSB of two words.
word1 gets written to positions 1032 to 1074, word0 to 1075 to 1117.
The Q-parity bytes of each diagonal get reunited too. word1 goes to 1118
to 1143, word0 to 1144 to 1169.
>>> I do not read this swap of word1 and word0 from ECMA-130 Annex A.
>>> But the new output matches the old output only if it is done that way.
>>> See correctness reservation below.
Algebra on Galois fields is the same as on Rational Numbers.
But arithmetics is defined by operations on polynomials rather than the
usual integer arithmetics on binary numbers.
Addition and subtraction are identical with the binary exor operator.
Multiplication and division would demand polynomial division, e.g. by the
euclidian algorithm. The computing path over logarithms and powers follows
algebra and allows to reduce the arithmetic task to table lookups, additions
modulo 255, and exor operations. Note that the logarithms are natural
numbers, not polynomials. They get added or subtracted by the usual addition
(not by exor) and their polynomial power depends on their value modulo 255.
Needed are a logarithm table and a power table (or inverse logarithm table)
for Galois Field GF(2^8) which will serve to perform the peculiar
multiplication and division operation of Galois fields.
The power table is simply an enumeration of x^n accorting to
GF-multiplication. It also serves as second line of matrix H for the parity
equations:
Hp[i] = gfpow[25-i] , i out of {0,..,25}
Hq[i] = gfpow[44-i] , i out of {0,..,44}
The logarithm table is the inverse permutation of the power table.
Some simplifications apply to the implementation:
In the world of Galois fields there is no difference between - and +.
The term (H[n+1] - H[n]) is constant: 3.
-------------------------------------------------------------------------
Scrambling
ECMA-130 Annex B prescribes to exor the byte stream of an audio-sized sector
with a sequence of pseudo random bytes. It mentions polynomial x^15+x+1 and
a 15-bit register.
It shows a diagram of a Feedback Shift Register with 16 bit boxes, though.
Comparing this with explanations in
http://www.newwaveinstruments.com/resources/articles/m_sequence_linear_feedback_shift_register_lfsr.htm
one can recognize the diagram as a Fibonacci Implementation. But there seems
really to be one bit box too many.
The difference of both lengths is expressed in function next_bit() by
the constants 0x3fff,0x4000 for 15 bit versus 0x7fff,0x8000 for 16 bits.
Comparing the output of both alternatives with the old scrambler output
lets 15 bit win for now.
So the prescription is to start with 15 bit value 1, to use the lowest bit
as output, to shift the bits down by one, to exor the output bit with the
next lowest bit, and to put that exor result into bit 14 of the register.
-------------------------------------------------------------------------
Correctness Reservation
In both cases, parity and scrambling, the goal for now is to replicate the
output of the dismissed old lec.c by output which is based on published
specs and own implementation code. Whether they comply to ECMA-130 is a
different question which can only be answered by real test cases for
raw CD recording.
Of course this implementation will be corrected so that it really complies
to ECMA-130 as soon as evidence emerges that it does not yet.
*/
/* ------------------------------------------------------------------------- */
/* Power and logarithm tables for GF(2^8), parity matrices for ECMA-130.
Generated by burn_rspc_setup_tables() and burn_rspc_print_tables().
The highest possible sum of gflog[] values is is 508. So the table gfpow[]
with period 255 was manually unrolled to 509 elements to avoid one modulo
255 operation in burn_rspc_mult().
Proposed by D. Hugh Redelmeier.
*/
static unsigned char gfpow[509] = {
1, 2, 4, 8, 16, 32, 64, 128, 29, 58,
116, 232, 205, 135, 19, 38, 76, 152, 45, 90,
180, 117, 234, 201, 143, 3, 6, 12, 24, 48,
96, 192, 157, 39, 78, 156, 37, 74, 148, 53,
106, 212, 181, 119, 238, 193, 159, 35, 70, 140,
5, 10, 20, 40, 80, 160, 93, 186, 105, 210,
185, 111, 222, 161, 95, 190, 97, 194, 153, 47,
94, 188, 101, 202, 137, 15, 30, 60, 120, 240,
253, 231, 211, 187, 107, 214, 177, 127, 254, 225,
223, 163, 91, 182, 113, 226, 217, 175, 67, 134,
17, 34, 68, 136, 13, 26, 52, 104, 208, 189,
103, 206, 129, 31, 62, 124, 248, 237, 199, 147,
59, 118, 236, 197, 151, 51, 102, 204, 133, 23,
46, 92, 184, 109, 218, 169, 79, 158, 33, 66,
132, 21, 42, 84, 168, 77, 154, 41, 82, 164,
85, 170, 73, 146, 57, 114, 228, 213, 183, 115,
230, 209, 191, 99, 198, 145, 63, 126, 252, 229,
215, 179, 123, 246, 241, 255, 227, 219, 171, 75,
150, 49, 98, 196, 149, 55, 110, 220, 165, 87,
174, 65, 130, 25, 50, 100, 200, 141, 7, 14,
28, 56, 112, 224, 221, 167, 83, 166, 81, 162,
89, 178, 121, 242, 249, 239, 195, 155, 43, 86,
172, 69, 138, 9, 18, 36, 72, 144, 61, 122,
244, 245, 247, 243, 251, 235, 203, 139, 11, 22,
44, 88, 176, 125, 250, 233, 207, 131, 27, 54,
108, 216, 173, 71, 142,
1, 2, 4, 8, 16, 32, 64, 128, 29, 58,
116, 232, 205, 135, 19, 38, 76, 152, 45, 90,
180, 117, 234, 201, 143, 3, 6, 12, 24, 48,
96, 192, 157, 39, 78, 156, 37, 74, 148, 53,
106, 212, 181, 119, 238, 193, 159, 35, 70, 140,
5, 10, 20, 40, 80, 160, 93, 186, 105, 210,
185, 111, 222, 161, 95, 190, 97, 194, 153, 47,
94, 188, 101, 202, 137, 15, 30, 60, 120, 240,
253, 231, 211, 187, 107, 214, 177, 127, 254, 225,
223, 163, 91, 182, 113, 226, 217, 175, 67, 134,
17, 34, 68, 136, 13, 26, 52, 104, 208, 189,
103, 206, 129, 31, 62, 124, 248, 237, 199, 147,
59, 118, 236, 197, 151, 51, 102, 204, 133, 23,
46, 92, 184, 109, 218, 169, 79, 158, 33, 66,
132, 21, 42, 84, 168, 77, 154, 41, 82, 164,
85, 170, 73, 146, 57, 114, 228, 213, 183, 115,
230, 209, 191, 99, 198, 145, 63, 126, 252, 229,
215, 179, 123, 246, 241, 255, 227, 219, 171, 75,
150, 49, 98, 196, 149, 55, 110, 220, 165, 87,
174, 65, 130, 25, 50, 100, 200, 141, 7, 14,
28, 56, 112, 224, 221, 167, 83, 166, 81, 162,
89, 178, 121, 242, 249, 239, 195, 155, 43, 86,
172, 69, 138, 9, 18, 36, 72, 144, 61, 122,
244, 245, 247, 243, 251, 235, 203, 139, 11, 22,
44, 88, 176, 125, 250, 233, 207, 131, 27, 54,
108, 216, 173, 71,
};
static unsigned char gflog[256] = {
0, 0, 1, 25, 2, 50, 26, 198, 3, 223,
51, 238, 27, 104, 199, 75, 4, 100, 224, 14,
52, 141, 239, 129, 28, 193, 105, 248, 200, 8,
76, 113, 5, 138, 101, 47, 225, 36, 15, 33,
53, 147, 142, 218, 240, 18, 130, 69, 29, 181,
194, 125, 106, 39, 249, 185, 201, 154, 9, 120,
77, 228, 114, 166, 6, 191, 139, 98, 102, 221,
48, 253, 226, 152, 37, 179, 16, 145, 34, 136,
54, 208, 148, 206, 143, 150, 219, 189, 241, 210,
19, 92, 131, 56, 70, 64, 30, 66, 182, 163,
195, 72, 126, 110, 107, 58, 40, 84, 250, 133,
186, 61, 202, 94, 155, 159, 10, 21, 121, 43,
78, 212, 229, 172, 115, 243, 167, 87, 7, 112,
192, 247, 140, 128, 99, 13, 103, 74, 222, 237,
49, 197, 254, 24, 227, 165, 153, 119, 38, 184,
180, 124, 17, 68, 146, 217, 35, 32, 137, 46,
55, 63, 209, 91, 149, 188, 207, 205, 144, 135,
151, 178, 220, 252, 190, 97, 242, 86, 211, 171,
20, 42, 93, 158, 132, 60, 57, 83, 71, 109,
65, 162, 31, 45, 67, 216, 183, 123, 164, 118,
196, 23, 73, 236, 127, 12, 111, 246, 108, 161,
59, 82, 41, 157, 85, 170, 251, 96, 134, 177,
187, 204, 62, 90, 203, 89, 95, 176, 156, 169,
160, 81, 11, 245, 22, 235, 122, 117, 44, 215,
79, 174, 213, 233, 230, 231, 173, 232, 116, 214,
244, 234, 168, 80, 88, 175
};
#define Libburn_use_h_matriceS 1
#ifdef Libburn_use_h_matriceS
/* On my AMD 2x64 bit 3000 MHz processor h[i] costs about 7 % more time
than using gfpow[25-i] resp. gfpow[44-1]. I blame this on the more
condensed data representation which slightly increases the rate of cache
hits.
Nevertheless this effect is very likely depending on the exact cache
size and architecture. In general, using h[] saves more than 8000
subtractions per sector.
*/
/* Parity matrices H as prescribed by ECMA-130 Annex A.
Actually just reverted order start pieces of gfpow[].
*/
static unsigned char h26[26] = {
3, 143, 201, 234, 117, 180, 90, 45, 152, 76,
38, 19, 135, 205, 232, 116, 58, 29, 128, 64,
32, 16, 8, 4, 2, 1,
};
static unsigned char h45[45] = {
238, 119, 181, 212, 106, 53, 148, 74, 37, 156,
78, 39, 157, 192, 96, 48, 24, 12, 6, 3,
143, 201, 234, 117, 180, 90, 45, 152, 76, 38,
19, 135, 205, 232, 116, 58, 29, 128, 64, 32,
16, 8, 4, 2, 1,
};
#endif /* Libburn_use_h_matriceS */
/* Pseudo-random bytes which of course are exactly the same as with the
previously used code.
Generated by function print_ecma_130_scrambler().
*/
static unsigned char ecma_130_annex_b[2340] = {
1, 128, 0, 96, 0, 40, 0, 30, 128, 8,
96, 6, 168, 2, 254, 129, 128, 96, 96, 40,
40, 30, 158, 136, 104, 102, 174, 170, 252, 127,
1, 224, 0, 72, 0, 54, 128, 22, 224, 14,
200, 4, 86, 131, 126, 225, 224, 72, 72, 54,
182, 150, 246, 238, 198, 204, 82, 213, 253, 159,
1, 168, 0, 126, 128, 32, 96, 24, 40, 10,
158, 135, 40, 98, 158, 169, 168, 126, 254, 160,
64, 120, 48, 34, 148, 25, 175, 74, 252, 55,
1, 214, 128, 94, 224, 56, 72, 18, 182, 141,
182, 229, 182, 203, 54, 215, 86, 222, 190, 216,
112, 90, 164, 59, 59, 83, 83, 125, 253, 225,
129, 136, 96, 102, 168, 42, 254, 159, 0, 104,
0, 46, 128, 28, 96, 9, 232, 6, 206, 130,
212, 97, 159, 104, 104, 46, 174, 156, 124, 105,
225, 238, 200, 76, 86, 181, 254, 247, 0, 70,
128, 50, 224, 21, 136, 15, 38, 132, 26, 227,
75, 9, 247, 70, 198, 178, 210, 245, 157, 135,
41, 162, 158, 249, 168, 66, 254, 177, 128, 116,
96, 39, 104, 26, 174, 139, 60, 103, 81, 234,
188, 79, 49, 244, 20, 71, 79, 114, 180, 37,
183, 91, 54, 187, 86, 243, 126, 197, 224, 83,
8, 61, 198, 145, 146, 236, 109, 141, 237, 165,
141, 187, 37, 179, 91, 53, 251, 87, 3, 126,
129, 224, 96, 72, 40, 54, 158, 150, 232, 110,
206, 172, 84, 125, 255, 97, 128, 40, 96, 30,
168, 8, 126, 134, 160, 98, 248, 41, 130, 158,
225, 168, 72, 126, 182, 160, 118, 248, 38, 194,
154, 209, 171, 28, 127, 73, 224, 54, 200, 22,
214, 142, 222, 228, 88, 75, 122, 183, 99, 54,
169, 214, 254, 222, 192, 88, 80, 58, 188, 19,
49, 205, 212, 85, 159, 127, 40, 32, 30, 152,
8, 106, 134, 175, 34, 252, 25, 129, 202, 224,
87, 8, 62, 134, 144, 98, 236, 41, 141, 222,
229, 152, 75, 42, 183, 95, 54, 184, 22, 242,
142, 197, 164, 83, 59, 125, 211, 97, 157, 232,
105, 142, 174, 228, 124, 75, 97, 247, 104, 70,
174, 178, 252, 117, 129, 231, 32, 74, 152, 55,
42, 150, 159, 46, 232, 28, 78, 137, 244, 102,
199, 106, 210, 175, 29, 188, 9, 177, 198, 244,
82, 199, 125, 146, 161, 173, 184, 125, 178, 161,
181, 184, 119, 50, 166, 149, 186, 239, 51, 12,
21, 197, 207, 19, 20, 13, 207, 69, 148, 51,
47, 85, 220, 63, 25, 208, 10, 220, 7, 25,
194, 138, 209, 167, 28, 122, 137, 227, 38, 201,
218, 214, 219, 30, 219, 72, 91, 118, 187, 102,
243, 106, 197, 239, 19, 12, 13, 197, 197, 147,
19, 45, 205, 221, 149, 153, 175, 42, 252, 31,
1, 200, 0, 86, 128, 62, 224, 16, 72, 12,
54, 133, 214, 227, 30, 201, 200, 86, 214, 190,
222, 240, 88, 68, 58, 179, 83, 53, 253, 215,
1, 158, 128, 104, 96, 46, 168, 28, 126, 137,
224, 102, 200, 42, 214, 159, 30, 232, 8, 78,
134, 180, 98, 247, 105, 134, 174, 226, 252, 73,
129, 246, 224, 70, 200, 50, 214, 149, 158, 239,
40, 76, 30, 181, 200, 119, 22, 166, 142, 250,
228, 67, 11, 113, 199, 100, 82, 171, 125, 191,
97, 176, 40, 116, 30, 167, 72, 122, 182, 163,
54, 249, 214, 194, 222, 209, 152, 92, 106, 185,
239, 50, 204, 21, 149, 207, 47, 20, 28, 15,
73, 196, 54, 211, 86, 221, 254, 217, 128, 90,
224, 59, 8, 19, 70, 141, 242, 229, 133, 139,
35, 39, 89, 218, 186, 219, 51, 27, 85, 203,
127, 23, 96, 14, 168, 4, 126, 131, 96, 97,
232, 40, 78, 158, 180, 104, 119, 110, 166, 172,
122, 253, 227, 1, 137, 192, 102, 208, 42, 220,
31, 25, 200, 10, 214, 135, 30, 226, 136, 73,
166, 182, 250, 246, 195, 6, 209, 194, 220, 81,
153, 252, 106, 193, 239, 16, 76, 12, 53, 197,
215, 19, 30, 141, 200, 101, 150, 171, 46, 255,
92, 64, 57, 240, 18, 196, 13, 147, 69, 173,
243, 61, 133, 209, 163, 28, 121, 201, 226, 214,
201, 158, 214, 232, 94, 206, 184, 84, 114, 191,
101, 176, 43, 52, 31, 87, 72, 62, 182, 144,
118, 236, 38, 205, 218, 213, 155, 31, 43, 72,
31, 118, 136, 38, 230, 154, 202, 235, 23, 15,
78, 132, 52, 99, 87, 105, 254, 174, 192, 124,
80, 33, 252, 24, 65, 202, 176, 87, 52, 62,
151, 80, 110, 188, 44, 113, 221, 228, 89, 139,
122, 231, 99, 10, 169, 199, 62, 210, 144, 93,
172, 57, 189, 210, 241, 157, 132, 105, 163, 110,
249, 236, 66, 205, 241, 149, 132, 111, 35, 108,
25, 237, 202, 205, 151, 21, 174, 143, 60, 100,
17, 235, 76, 79, 117, 244, 39, 7, 90, 130,
187, 33, 179, 88, 117, 250, 167, 3, 58, 129,
211, 32, 93, 216, 57, 154, 146, 235, 45, 143,
93, 164, 57, 187, 82, 243, 125, 133, 225, 163,
8, 121, 198, 162, 210, 249, 157, 130, 233, 161,
142, 248, 100, 66, 171, 113, 191, 100, 112, 43,
100, 31, 107, 72, 47, 118, 156, 38, 233, 218,
206, 219, 20, 91, 79, 123, 116, 35, 103, 89,
234, 186, 207, 51, 20, 21, 207, 79, 20, 52,
15, 87, 68, 62, 179, 80, 117, 252, 39, 1,
218, 128, 91, 32, 59, 88, 19, 122, 141, 227,
37, 137, 219, 38, 219, 90, 219, 123, 27, 99,
75, 105, 247, 110, 198, 172, 82, 253, 253, 129,
129, 160, 96, 120, 40, 34, 158, 153, 168, 106,
254, 175, 0, 124, 0, 33, 192, 24, 80, 10,
188, 7, 49, 194, 148, 81, 175, 124, 124, 33,
225, 216, 72, 90, 182, 187, 54, 243, 86, 197,
254, 211, 0, 93, 192, 57, 144, 18, 236, 13,
141, 197, 165, 147, 59, 45, 211, 93, 157, 249,
169, 130, 254, 225, 128, 72, 96, 54, 168, 22,
254, 142, 192, 100, 80, 43, 124, 31, 97, 200,
40, 86, 158, 190, 232, 112, 78, 164, 52, 123,
87, 99, 126, 169, 224, 126, 200, 32, 86, 152,
62, 234, 144, 79, 44, 52, 29, 215, 73, 158,
182, 232, 118, 206, 166, 212, 122, 223, 99, 24,
41, 202, 158, 215, 40, 94, 158, 184, 104, 114,
174, 165, 188, 123, 49, 227, 84, 73, 255, 118,
192, 38, 208, 26, 220, 11, 25, 199, 74, 210,
183, 29, 182, 137, 182, 230, 246, 202, 198, 215,
18, 222, 141, 152, 101, 170, 171, 63, 63, 80,
16, 60, 12, 17, 197, 204, 83, 21, 253, 207,
1, 148, 0, 111, 64, 44, 48, 29, 212, 9,
159, 70, 232, 50, 206, 149, 148, 111, 47, 108,
28, 45, 201, 221, 150, 217, 174, 218, 252, 91,
1, 251, 64, 67, 112, 49, 228, 20, 75, 79,
119, 116, 38, 167, 90, 250, 187, 3, 51, 65,
213, 240, 95, 4, 56, 3, 82, 129, 253, 160,
65, 184, 48, 114, 148, 37, 175, 91, 60, 59,
81, 211, 124, 93, 225, 249, 136, 66, 230, 177,
138, 244, 103, 7, 106, 130, 175, 33, 188, 24,
113, 202, 164, 87, 59, 126, 147, 96, 109, 232,
45, 142, 157, 164, 105, 187, 110, 243, 108, 69,
237, 243, 13, 133, 197, 163, 19, 57, 205, 210,
213, 157, 159, 41, 168, 30, 254, 136, 64, 102,
176, 42, 244, 31, 7, 72, 2, 182, 129, 182,
224, 118, 200, 38, 214, 154, 222, 235, 24, 79,
74, 180, 55, 55, 86, 150, 190, 238, 240, 76,
68, 53, 243, 87, 5, 254, 131, 0, 97, 192,
40, 80, 30, 188, 8, 113, 198, 164, 82, 251,
125, 131, 97, 161, 232, 120, 78, 162, 180, 121,
183, 98, 246, 169, 134, 254, 226, 192, 73, 144,
54, 236, 22, 205, 206, 213, 148, 95, 47, 120,
28, 34, 137, 217, 166, 218, 250, 219, 3, 27,
65, 203, 112, 87, 100, 62, 171, 80, 127, 124,
32, 33, 216, 24, 90, 138, 187, 39, 51, 90,
149, 251, 47, 3, 92, 1, 249, 192, 66, 208,
49, 156, 20, 105, 207, 110, 212, 44, 95, 93,
248, 57, 130, 146, 225, 173, 136, 125, 166, 161,
186, 248, 115, 2, 165, 193, 187, 16, 115, 76,
37, 245, 219, 7, 27, 66, 139, 113, 167, 100,
122, 171, 99, 63, 105, 208, 46, 220, 28, 89,
201, 250, 214, 195, 30, 209, 200, 92, 86, 185,
254, 242, 192, 69, 144, 51, 44, 21, 221, 207,
25, 148, 10, 239, 71, 12, 50, 133, 213, 163,
31, 57, 200, 18, 214, 141, 158, 229, 168, 75,
62, 183, 80, 118, 188, 38, 241, 218, 196, 91,
19, 123, 77, 227, 117, 137, 231, 38, 202, 154,
215, 43, 30, 159, 72, 104, 54, 174, 150, 252,
110, 193, 236, 80, 77, 252, 53, 129, 215, 32,
94, 152, 56, 106, 146, 175, 45, 188, 29, 177,
201, 180, 86, 247, 126, 198, 160, 82, 248, 61,
130, 145, 161, 172, 120, 125, 226, 161, 137, 184,
102, 242, 170, 197, 191, 19, 48, 13, 212, 5,
159, 67, 40, 49, 222, 148, 88, 111, 122, 172,
35, 61, 217, 209, 154, 220, 107, 25, 239, 74,
204, 55, 21, 214, 143, 30, 228, 8, 75, 70,
183, 114, 246, 165, 134, 251, 34, 195, 89, 145,
250, 236, 67, 13, 241, 197, 132, 83, 35, 125,
217, 225, 154, 200, 107, 22, 175, 78, 252, 52,
65, 215, 112, 94, 164, 56, 123, 82, 163, 125,
185, 225, 178, 200, 117, 150, 167, 46, 250, 156,
67, 41, 241, 222, 196, 88, 83, 122, 189, 227,
49, 137, 212, 102, 223, 106, 216, 47, 26, 156,
11, 41, 199, 94, 210, 184, 93, 178, 185, 181,
178, 247, 53, 134, 151, 34, 238, 153, 140, 106,
229, 239, 11, 12, 7, 69, 194, 179, 17, 181,
204, 119, 21, 230, 143, 10, 228, 7, 11, 66,
135, 113, 162, 164, 121, 187, 98, 243, 105, 133,
238, 227, 12, 73, 197, 246, 211, 6, 221, 194,
217, 145, 154, 236, 107, 13, 239, 69, 140, 51,
37, 213, 219, 31, 27, 72, 11, 118, 135, 102,
226, 170, 201, 191, 22, 240, 14, 196, 4, 83,
67, 125, 241, 225, 132, 72, 99, 118, 169, 230,
254, 202, 192, 87, 16, 62, 140, 16, 101, 204,
43, 21, 223, 79, 24, 52, 10, 151, 71, 46,
178, 156, 117, 169, 231, 62, 202, 144, 87, 44,
62, 157, 208, 105, 156, 46, 233, 220, 78, 217,
244, 90, 199, 123, 18, 163, 77, 185, 245, 178,
199, 53, 146, 151, 45, 174, 157, 188, 105, 177,
238, 244, 76, 71, 117, 242, 167, 5, 186, 131,
51, 33, 213, 216, 95, 26, 184, 11, 50, 135,
85, 162, 191, 57, 176, 18, 244, 13, 135, 69,
162, 179, 57, 181, 210, 247, 29, 134, 137, 162,
230, 249, 138, 194, 231, 17, 138, 140, 103, 37,
234, 155, 15, 43, 68, 31, 115, 72, 37, 246,
155, 6, 235, 66, 207, 113, 148, 36, 111, 91,
108, 59, 109, 211, 109, 157, 237, 169, 141, 190,
229, 176, 75, 52, 55, 87, 86, 190, 190, 240,
112, 68, 36, 51, 91, 85, 251, 127, 3, 96,
1, 232, 0, 78, 128, 52, 96, 23, 104, 14,
174, 132, 124, 99, 97, 233, 232, 78, 206, 180,
84, 119, 127, 102, 160, 42, 248, 31, 2, 136,
1, 166, 128, 122, 224, 35, 8, 25, 198, 138,
210, 231, 29, 138, 137, 167, 38, 250, 154, 195,
43, 17, 223, 76, 88, 53, 250, 151, 3, 46,
129, 220, 96, 89, 232, 58, 206, 147, 20, 109,
207, 109, 148, 45, 175, 93, 188, 57, 177, 210,
244, 93, 135, 121, 162, 162, 249, 185, 130, 242,
225, 133, 136, 99, 38, 169, 218, 254, 219, 0,
91, 64, 59, 112, 19, 100, 13, 235, 69, 143,
115, 36, 37, 219, 91, 27, 123, 75, 99, 119,
105, 230, 174, 202, 252, 87, 1, 254, 128, 64,
96, 48, 40, 20, 30, 143, 72, 100, 54, 171,
86, 255, 126, 192, 32, 80, 24, 60, 10, 145,
199, 44, 82, 157, 253, 169, 129, 190, 224, 112,
72, 36, 54, 155, 86, 235, 126, 207, 96, 84,
40, 63, 94, 144, 56, 108, 18, 173, 205, 189,
149, 177, 175, 52, 124, 23, 97, 206, 168, 84,
126, 191, 96, 112, 40, 36, 30, 155, 72, 107,
118, 175, 102, 252, 42, 193, 223, 16, 88, 12,
58, 133, 211, 35, 29, 217, 201, 154, 214, 235,
30, 207, 72, 84, 54, 191, 86, 240, 62, 196,
16, 83, 76, 61, 245, 209, 135, 28, 98, 137,
233, 166, 206, 250, 212, 67, 31, 113, 200, 36,
86, 155, 126, 235, 96, 79, 104, 52, 46, 151,
92, 110, 185, 236, 114, 205, 229, 149, 139, 47,
39, 92, 26, 185, 203, 50, 215, 85, 158, 191,
40, 112, 30, 164, 8, 123, 70, 163, 114, 249,
229, 130, 203, 33, 151, 88, 110, 186, 172, 115,
61, 229, 209, 139, 28, 103, 73, 234, 182, 207,
54, 212, 22, 223, 78, 216, 52, 90, 151, 123,
46, 163, 92, 121, 249, 226, 194, 201, 145, 150,
236, 110, 205, 236, 85, 141, 255, 37, 128, 27,
32, 11, 88, 7, 122, 130, 163, 33, 185, 216,
114, 218, 165, 155, 59, 43, 83, 95, 125, 248,
33, 130, 152, 97, 170, 168, 127, 62, 160, 16,
120, 12, 34, 133, 217, 163, 26, 249, 203, 2,
215, 65, 158, 176, 104, 116, 46, 167, 92, 122,
185, 227, 50, 201, 213, 150, 223, 46, 216, 28,
90, 137, 251, 38, 195, 90, 209, 251, 28, 67,
73, 241, 246, 196, 70, 211, 114, 221, 229, 153
};
/* ------------------------------------------------------------------------- */
/* This is the new implementation of P- and Q-parity generation.
It needs about the same computing time as the old implementation (both
with gcc -O2 on AMD 64 bit). Measurements indicate that about 280 MIPS
are needed for 48x CD speed (7.1 MB/s).
*/
static unsigned char burn_rspc_mult(unsigned char a, unsigned char b)
{
if (a == 0 || b == 0)
return 0;
/* Optimization of (a == 0 || b == 0) by D. Hugh Redelmeier
if((((int)a - 1) | ((int)b - 1)) < 0)
return 0;
*/
return gfpow[gflog[a] + gflog[b]];
/* % 255 not necessary because gfpow is unrolled up to index 510 */
}
/* Divide by polynomial 0x03. Derived from burn_rspc_div() and using the
unrolled size of the gfpow[] array.
*/
static unsigned char burn_rspc_div_3(unsigned char a)
{
if (a == 0)
return 0;
return gfpow[230 + gflog[a]];
}
static void burn_rspc_p0p1(unsigned char *sector, int col,
unsigned char *p0_lsb, unsigned char *p0_msb,
unsigned char *p1_lsb, unsigned char *p1_msb)
{
unsigned char *start, b;
unsigned int i, sum_v_lsb = 0, sum_v_msb = 0;
unsigned int hxv_lsb = 0, hxv_msb = 0;
start = sector + 12 + 2 * col;
for(i = 0; i < 24; i++) {
b = *start;
sum_v_lsb ^= b;
#ifdef Libburn_use_h_matriceS
hxv_lsb ^= burn_rspc_mult(b, h26[i]);
#else
hxv_lsb ^= burn_rspc_mult(b, gfpow[25 - i]);
#endif
b = *(start + 1);
sum_v_msb ^= b;
#ifdef Libburn_use_h_matriceS
hxv_msb ^= burn_rspc_mult(b, h26[i]);
#else
hxv_msb ^= burn_rspc_mult(b, gfpow[25 - i]);
#endif
start += 86;
}
/* 3 = gfpow[1] ^ gfpow[0] , 2 = gfpow[1] */
*p0_lsb = burn_rspc_div_3(burn_rspc_mult(2, sum_v_lsb) ^ hxv_lsb);
*p0_msb = burn_rspc_div_3(burn_rspc_mult(2, sum_v_msb) ^ hxv_msb);
*p1_lsb = sum_v_lsb ^ *p0_lsb;
*p1_msb = sum_v_msb ^ *p0_msb;
}
void burn_rspc_parity_p(unsigned char *sector)
{
int i;
unsigned char p0_lsb, p0_msb, p1_lsb, p1_msb;
/* Loop over P columns */
for(i = 0; i < 43; i++) {
burn_rspc_p0p1(sector, i, &p0_lsb, &p0_msb, &p1_lsb, &p1_msb);
sector[2162 + 2 * i] = p0_lsb;
sector[2162 + 2 * i + 1] = p0_msb;
sector[2076 + 2 * i] = p1_lsb;
sector[2076 + 2 * i + 1] = p1_msb;
#ifdef Libburn_with_lec_generatoR
if(verbous) {
printf("p %2d : %2.2X %2.2X ", i,
(unsigned int) p0_lsb, (unsigned int) p0_msb);
printf("%2.2X %2.2X ",
(unsigned int) p1_lsb, (unsigned int) p1_msb);
printf("-> %d,%d\n", 2162 + 2 * i, 2076 + 2 * i);
}
#endif /* Libburn_with_lec_generatoR */
}
}
static void burn_rspc_q0q1(unsigned char *sector, int diag,
unsigned char *q0_lsb, unsigned char *q0_msb,
unsigned char *q1_lsb, unsigned char *q1_msb)
{
unsigned char *start, b;
unsigned int i, idx, sum_v_lsb = 0, sum_v_msb = 0;
unsigned int hxv_lsb = 0, hxv_msb = 0;
start = sector + 12;
idx = 2 * 43 * diag;
for(i = 0; i < 43; i++) {
if (idx >= 2236)
idx -= 2236;
b = start[idx];
sum_v_lsb ^= b;
#ifdef Libburn_use_h_matriceS
hxv_lsb ^= burn_rspc_mult(b, h45[i]);
#else
hxv_lsb ^= burn_rspc_mult(b, gfpow[44 - i]);
#endif
b = start[idx + 1];
sum_v_msb ^= b;
#ifdef Libburn_use_h_matriceS
hxv_msb ^= burn_rspc_mult(b, h45[i]);
#else
hxv_msb ^= burn_rspc_mult(b, gfpow[44 - i]);
#endif
idx += 88;
}
/* 3 = gfpow[1] ^ gfpow[0] , 2 = gfpow[1] */
*q0_lsb = burn_rspc_div_3(burn_rspc_mult(2, sum_v_lsb) ^ hxv_lsb);
*q0_msb = burn_rspc_div_3(burn_rspc_mult(2, sum_v_msb) ^ hxv_msb);
*q1_lsb = sum_v_lsb ^ *q0_lsb;
*q1_msb = sum_v_msb ^ *q0_msb;
}
void burn_rspc_parity_q(unsigned char *sector)
{
int i;
unsigned char q0_lsb, q0_msb, q1_lsb, q1_msb;
/* Loop over Q diagonals */
for(i = 0; i < 26; i++) {
burn_rspc_q0q1(sector, i, &q0_lsb, &q0_msb, &q1_lsb, &q1_msb);
sector[2300 + 2 * i] = q0_lsb;
sector[2300 + 2 * i + 1] = q0_msb;
sector[2248 + 2 * i] = q1_lsb;
sector[2248 + 2 * i + 1] = q1_msb;
#ifdef Libburn_with_lec_generatoR
if(verbous) {
printf("q %2d : %2.2X %2.2X ", i,
(unsigned int) q0_lsb, (unsigned int) q0_msb);
printf("%2.2X %2.2X ",
(unsigned int) q1_lsb, (unsigned int) q1_msb);
printf("-> %d,%d\n", 2300 + 2 * i, 2248 + 2 * i);
}
#endif /* Libburn_with_lec_generatoR */
}
}
/* ------------------------------------------------------------------------- */
/* The new implementation of the ECMA-130 Annex B scrambler.
It is totally unoptimized. One should make use of larger word operations.
Measurements indicate that about 50 MIPS are needed for 48x CD speed.
*/
void burn_ecma130_scramble(unsigned char *sector)
{
int i;
unsigned char *s;
s = sector + 12;
for (i = 0; i < 2340; i++)
s[i] ^= ecma_130_annex_b[i];
}
/* ------------------------------------------------------------------------- */
/* The following code is not needed for libburn but rather documents the
origin of the tables above. In libburn it will not be compiled.
*/
#ifdef Libburn_with_lec_generatoR
/* This function produced the content of gflog[] and gfpow[]
*/
static int burn_rspc_setup_tables(void)
{
unsigned int b, l;
memset(gflog, 0, sizeof(gflog));
memset(gfpow, 0, sizeof(gfpow));
b = 1;
for (l = 0; l < 255; l++) {
gfpow[l] = (unsigned char) b;
gflog[b] = (unsigned char) l;
b = b << 1;
if (b & 256)
b = b ^ 0x11d;
}
return 0;
}
/* This function printed the content of gflog[] and gfpow[] as C code
and compared the content with the tables of the old implementation.
h26[] and h45[] are reverted order copies of gfpow[]
*/
static int burn_rspc_print_tables(void)
{
int i;
printf("static unsigned char gfpow[255] = {");
printf("\n\t");
for(i= 0; i < 255; i++) {
printf("%3u, ", gfpow[i]);
#ifdef Libburn_with_old_lec_comparisoN
if(gfpow[i] != gf8_ilog[i])
fprintf(stderr, "*** ILOG %d : %d != %d ***\n", i, gfpow[i], gf8_ilog[i]);
#endif
if((i % 10) == 9)
printf("\n\t");
}
printf("\n};\n\n");
printf("static unsigned char gflog[256] = {");
printf("\n\t");
for(i= 0; i < 256; i++) {
printf(" %3u,", gflog[i]);
#ifdef Libburn_with_old_lec_comparisoN
if(gflog[i] != gf8_log[i])
fprintf(stderr, "*** LOG %d : %d != %d ***\n", i, gflog[i], gf8_log[i]);
#endif
if((i % 10) == 9)
printf("\n\t");
}
printf("\n};\n\n");
printf("static unsigned char h26[26] = {");
printf("\n\t");
for(i= 0; i < 26; i++) {
printf(" %3u,", gfpow[25 - i]);
if((i % 10) == 9)
printf("\n\t");
}
printf("\n};\n\n");
printf("static unsigned char h45[45] = {");
printf("\n\t");
for(i= 0; i < 45; i++) {
printf(" %3u,",gfpow[44 - i]);
if((i % 10) == 9)
printf("\n\t");
}
printf("\n};\n\n");
return 0;
}
/* This code was used to generate the content of array ecma_130_annex_b[].
*/
static unsigned short ecma_130_fsr = 1;
static int next_bit(void)
{
int ret;
ret = ecma_130_fsr & 1;
ecma_130_fsr = (ecma_130_fsr >> 1) & 0x3fff;
if (ret ^ (ecma_130_fsr & 1))
ecma_130_fsr |= 0x4000;
return ret;
}
static int print_ecma_130_scrambler(void)
{
int i, j, b;
ecma_130_fsr = 1;
printf("static unsigned char ecma_130_annex_b[2340] = {");
printf("\n\t");
for (i = 0; i < 2340; i++) {
b = 0;
for (j = 0; j < 8; j++)
b |= next_bit() << j;
printf("%3u, ", b);
if ((i % 10) == 9)
printf("\n\t");
}
printf("\n};\n");
return 1;
}
#ifdef Libburn_with_general_rspc_diV
/* This is a general polynomial division function.
burn_rspc_div_3() has been derived from this by setting b to constant 3.
*/
static unsigned char burn_rspc_div(unsigned char a, unsigned char b)
{
int d;
if (a == 0)
return 0;
if (b == 0)
return -1;
d = gflog[a] - gflog[b];
if (d < 0)
d += 255;
return gfpow[d];
}
#endif /* Libburn_with_general_rspc_diV */
#endif /* Libburn_with_lec_generatoR */
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