/* -*- indent-tabs-mode: t; tab-width: 8; c-basic-offset: 8; -*- */ #ifdef HAVE_CONFIG_H #include "../config.h" #endif #include "crc.h" static unsigned short ccitt_table[256] = { 0x0000, 0x1021, 0x2042, 0x3063, 0x4084, 0x50A5, 0x60C6, 0x70E7, 0x8108, 0x9129, 0xA14A, 0xB16B, 0xC18C, 0xD1AD, 0xE1CE, 0xF1EF, 0x1231, 0x0210, 0x3273, 0x2252, 0x52B5, 0x4294, 0x72F7, 0x62D6, 0x9339, 0x8318, 0xB37B, 0xA35A, 0xD3BD, 0xC39C, 0xF3FF, 0xE3DE, 0x2462, 0x3443, 0x0420, 0x1401, 0x64E6, 0x74C7, 0x44A4, 0x5485, 0xA56A, 0xB54B, 0x8528, 0x9509, 0xE5EE, 0xF5CF, 0xC5AC, 0xD58D, 0x3653, 0x2672, 0x1611, 0x0630, 0x76D7, 0x66F6, 0x5695, 0x46B4, 0xB75B, 0xA77A, 0x9719, 0x8738, 0xF7DF, 0xE7FE, 0xD79D, 0xC7BC, 0x48C4, 0x58E5, 0x6886, 0x78A7, 0x0840, 0x1861, 0x2802, 0x3823, 0xC9CC, 0xD9ED, 0xE98E, 0xF9AF, 0x8948, 0x9969, 0xA90A, 0xB92B, 0x5AF5, 0x4AD4, 0x7AB7, 0x6A96, 0x1A71, 0x0A50, 0x3A33, 0x2A12, 0xDBFD, 0xCBDC, 0xFBBF, 0xEB9E, 0x9B79, 0x8B58, 0xBB3B, 0xAB1A, 0x6CA6, 0x7C87, 0x4CE4, 0x5CC5, 0x2C22, 0x3C03, 0x0C60, 0x1C41, 0xEDAE, 0xFD8F, 0xCDEC, 0xDDCD, 0xAD2A, 0xBD0B, 0x8D68, 0x9D49, 0x7E97, 0x6EB6, 0x5ED5, 0x4EF4, 0x3E13, 0x2E32, 0x1E51, 0x0E70, 0xFF9F, 0xEFBE, 0xDFDD, 0xCFFC, 0xBF1B, 0xAF3A, 0x9F59, 0x8F78, 0x9188, 0x81A9, 0xB1CA, 0xA1EB, 0xD10C, 0xC12D, 0xF14E, 0xE16F, 0x1080, 0x00A1, 0x30C2, 0x20E3, 0x5004, 0x4025, 0x7046, 0x6067, 0x83B9, 0x9398, 0xA3FB, 0xB3DA, 0xC33D, 0xD31C, 0xE37F, 0xF35E, 0x02B1, 0x1290, 0x22F3, 0x32D2, 0x4235, 0x5214, 0x6277, 0x7256, 0xB5EA, 0xA5CB, 0x95A8, 0x8589, 0xF56E, 0xE54F, 0xD52C, 0xC50D, 0x34E2, 0x24C3, 0x14A0, 0x0481, 0x7466, 0x6447, 0x5424, 0x4405, 0xA7DB, 0xB7FA, 0x8799, 0x97B8, 0xE75F, 0xF77E, 0xC71D, 0xD73C, 0x26D3, 0x36F2, 0x0691, 0x16B0, 0x6657, 0x7676, 0x4615, 0x5634, 0xD94C, 0xC96D, 0xF90E, 0xE92F, 0x99C8, 0x89E9, 0xB98A, 0xA9AB, 0x5844, 0x4865, 0x7806, 0x6827, 0x18C0, 0x08E1, 0x3882, 0x28A3, 0xCB7D, 0xDB5C, 0xEB3F, 0xFB1E, 0x8BF9, 0x9BD8, 0xABBB, 0xBB9A, 0x4A75, 0x5A54, 0x6A37, 0x7A16, 0x0AF1, 0x1AD0, 0x2AB3, 0x3A92, 0xFD2E, 0xED0F, 0xDD6C, 0xCD4D, 0xBDAA, 0xAD8B, 0x9DE8, 0x8DC9, 0x7C26, 0x6C07, 0x5C64, 0x4C45, 0x3CA2, 0x2C83, 0x1CE0, 0x0CC1, 0xEF1F, 0xFF3E, 0xCF5D, 0xDF7C, 0xAF9B, 0xBFBA, 0x8FD9, 0x9FF8, 0x6E17, 0x7E36, 0x4E55, 0x5E74, 0x2E93, 0x3EB2, 0x0ED1, 0x1EF0 }; unsigned long crc32_table[256] = { 0x00000000L, 0x90910101L, 0x91210201L, 0x01B00300L, 0x92410401L, 0x02D00500L, 0x03600600L, 0x93F10701L, 0x94810801L, 0x04100900L, 0x05A00A00L, 0x95310B01L, 0x06C00C00L, 0x96510D01L, 0x97E10E01L, 0x07700F00L, 0x99011001L, 0x09901100L, 0x08201200L, 0x98B11301L, 0x0B401400L, 0x9BD11501L, 0x9A611601L, 0x0AF01700L, 0x0D801800L, 0x9D111901L, 0x9CA11A01L, 0x0C301B00L, 0x9FC11C01L, 0x0F501D00L, 0x0EE01E00L, 0x9E711F01L, 0x82012001L, 0x12902100L, 0x13202200L, 0x83B12301L, 0x10402400L, 0x80D12501L, 0x81612601L, 0x11F02700L, 0x16802800L, 0x86112901L, 0x87A12A01L, 0x17302B00L, 0x84C12C01L, 0x14502D00L, 0x15E02E00L, 0x85712F01L, 0x1B003000L, 0x8B913101L, 0x8A213201L, 0x1AB03300L, 0x89413401L, 0x19D03500L, 0x18603600L, 0x88F13701L, 0x8F813801L, 0x1F103900L, 0x1EA03A00L, 0x8E313B01L, 0x1DC03C00L, 0x8D513D01L, 0x8CE13E01L, 0x1C703F00L, 0xB4014001L, 0x24904100L, 0x25204200L, 0xB5B14301L, 0x26404400L, 0xB6D14501L, 0xB7614601L, 0x27F04700L, 0x20804800L, 0xB0114901L, 0xB1A14A01L, 0x21304B00L, 0xB2C14C01L, 0x22504D00L, 0x23E04E00L, 0xB3714F01L, 0x2D005000L, 0xBD915101L, 0xBC215201L, 0x2CB05300L, 0xBF415401L, 0x2FD05500L, 0x2E605600L, 0xBEF15701L, 0xB9815801L, 0x29105900L, 0x28A05A00L, 0xB8315B01L, 0x2BC05C00L, 0xBB515D01L, 0xBAE15E01L, 0x2A705F00L, 0x36006000L, 0xA6916101L, 0xA7216201L, 0x37B06300L, 0xA4416401L, 0x34D06500L, 0x35606600L, 0xA5F16701L, 0xA2816801L, 0x32106900L, 0x33A06A00L, 0xA3316B01L, 0x30C06C00L, 0xA0516D01L, 0xA1E16E01L, 0x31706F00L, 0xAF017001L, 0x3F907100L, 0x3E207200L, 0xAEB17301L, 0x3D407400L, 0xADD17501L, 0xAC617601L, 0x3CF07700L, 0x3B807800L, 0xAB117901L, 0xAAA17A01L, 0x3A307B00L, 0xA9C17C01L, 0x39507D00L, 0x38E07E00L, 0xA8717F01L, 0xD8018001L, 0x48908100L, 0x49208200L, 0xD9B18301L, 0x4A408400L, 0xDAD18501L, 0xDB618601L, 0x4BF08700L, 0x4C808800L, 0xDC118901L, 0xDDA18A01L, 0x4D308B00L, 0xDEC18C01L, 0x4E508D00L, 0x4FE08E00L, 0xDF718F01L, 0x41009000L, 0xD1919101L, 0xD0219201L, 0x40B09300L, 0xD3419401L, 0x43D09500L, 0x42609600L, 0xD2F19701L, 0xD5819801L, 0x45109900L, 0x44A09A00L, 0xD4319B01L, 0x47C09C00L, 0xD7519D01L, 0xD6E19E01L, 0x46709F00L, 0x5A00A000L, 0xCA91A101L, 0xCB21A201L, 0x5BB0A300L, 0xC841A401L, 0x58D0A500L, 0x5960A600L, 0xC9F1A701L, 0xCE81A801L, 0x5E10A900L, 0x5FA0AA00L, 0xCF31AB01L, 0x5CC0AC00L, 0xCC51AD01L, 0xCDE1AE01L, 0x5D70AF00L, 0xC301B001L, 0x5390B100L, 0x5220B200L, 0xC2B1B301L, 0x5140B400L, 0xC1D1B501L, 0xC061B601L, 0x50F0B700L, 0x5780B800L, 0xC711B901L, 0xC6A1BA01L, 0x5630BB00L, 0xC5C1BC01L, 0x5550BD00L, 0x54E0BE00L, 0xC471BF01L, 0x6C00C000L, 0xFC91C101L, 0xFD21C201L, 0x6DB0C300L, 0xFE41C401L, 0x6ED0C500L, 0x6F60C600L, 0xFFF1C701L, 0xF881C801L, 0x6810C900L, 0x69A0CA00L, 0xF931CB01L, 0x6AC0CC00L, 0xFA51CD01L, 0xFBE1CE01L, 0x6B70CF00L, 0xF501D001L, 0x6590D100L, 0x6420D200L, 0xF4B1D301L, 0x6740D400L, 0xF7D1D501L, 0xF661D601L, 0x66F0D700L, 0x6180D800L, 0xF111D901L, 0xF0A1DA01L, 0x6030DB00L, 0xF3C1DC01L, 0x6350DD00L, 0x62E0DE00L, 0xF271DF01L, 0xEE01E001L, 0x7E90E100L, 0x7F20E200L, 0xEFB1E301L, 0x7C40E400L, 0xECD1E501L, 0xED61E601L, 0x7DF0E700L, 0x7A80E800L, 0xEA11E901L, 0xEBA1EA01L, 0x7B30EB00L, 0xE8C1EC01L, 0x7850ED00L, 0x79E0EE00L, 0xE971EF01L, 0x7700F000L, 0xE791F101L, 0xE621F201L, 0x76B0F300L, 0xE541F401L, 0x75D0F500L, 0x7460F600L, 0xE4F1F701L, 0xE381F801L, 0x7310F900L, 0x72A0FA00L, 0xE231FB01L, 0x71C0FC00L, 0xE151FD01L, 0xE0E1FE01L, 0x7070FF00L }; /* Exploration ts B00214 : ECMA-130, 22.3.6 "CRC field" Generating polynomial: x^16 + x^12 + x^5 + 1 Also known as CRC-16-CCITT, CRC-CCITT Used in libburn for raw write modes in sector.c. There is also disabled code in read.c which would use it. ts B11222: The same algorithm is prescribed for CD-TEXT. libburn/cdtext.c uses a simple bit shifting function : crc_11021() ts B20211: Discussion why both are equivalent in respect to their result: Both map the bits of the given bytes to a polynomial over the finite field of two elements. If bytes 0 .. M are given, then bit n of byte m is mapped to the coefficient of x exponent (n + ((M - m) * 8) + 16). I.e. they translate the bits into a polynomial with the highest bit becomming the coefficient of the highest power of x. Then this polynomial is multiplied by (x exp 16). The set of all such polynomials forms a commutative ring. Its addition corresponds to bitwise exclusive or. Addition and subtraction are identical. Multiplication with polynomials of only one single non-zero coefficient corresponds to leftward bit shifting by the exponent of that coefficient. The same rules apply as with elementary school arithmetics on integer numbers, but with surprising results due to the finite nature of the coefficient number space. Note that multiplication is _not_ an iteration of addition here. Function crc_11021() performs a division with residue by the euclidian algorithm. I.e. it splits polynomial d into quotient q(d) and residue r(d) in respect to the polynomial p = x exp 16 + x exp 12 + x exp 5 + x exp 0 d = p * q(d) + r(d) where r(d) is of a polynomial rank lower than p, i.e. only x exp 15 or lower have non-zero coefficients. The checksum crc(D) is derived by reverse mapping (r(d) * (x exp 16)). I.e. by mapping the coefficient of (x exp n) to bit n of the 16 bit word crc(D). The function result is the bit-wise complement of crc(D). Function crc_ccitt uses a table ccitt_table of r(d) values for the polynomials d which represent the single byte values 0x00 to 0xff. It computes r(d) by computing the residues of an iteratively expanded polynomial. The expansion of the processed byte string A by the next byte B from the input byte string happens by shifting the string 8 bits to the left, and by oring B onto bits 0 to 7. In the space of polynomials, the already processed polynomial "a" (image of byte string A) gets expanded by polynomial b (the image of byte B) like this a * X + b where X is (x exp 8), i.e. the single coefficient polynomial of rank 8. The following argumentation uses algebra with commutative, associative and distributive laws. Valid especially with polynomials is this rule: (1): r(a + b) = r(a) + r(b) because r(a) and r(b) are of rank lower than rank(p) and rank(a + b) <= max(rank(a), rank(b)) Further valid are: (2): r(a) = r(r(a)) (3): r(p * a) = 0 The residue of this expanded polynomials can be expressed by means of the residue r(a) which is known from the previous iteration step, and the residue r(b) which may be looked up in ccitt_table. r(a * X + b) = r(p * q(a) * X + r(a) * X + p * q(b) + r(b)) Applying rule (1): = r(p * q(a) * X) + r(r(a) * X) + r(p * q(b)) + r(r(b)) Rule (3) and rule (2): = r(r(a) * X) + r(b) Be h(a) and l(a) chosen so that: r(a) = h(a) * X + l(a), and l(a) has zero coefficients above (x exp 7), and h(a) * X has zero coefficients below (x exp 8). (They correspond to the high and low byte of the 16 bit word crc(A).) Now we have: = r(h(a) * X * X) + r(l(a) * X) + r(b) Since the rank of l(a) is lower than 8, rank of l(a) * X is lower than 16. Thus it cannot be divisible by p which has rank 16. So: r(l(a) * X) = l(a) * X This yields = l(a) * X + r(h(a) * X * X + b) h(a) * X * X is the polynomial representation of the high byte of 16 bit word crc(A). So in the world of bit patterns we have: crc(byte string A expanded by byte B) = (low_byte(crc(A)) << 8) ^ crc(high_byte(crc(A)) ^ B) And this is what function crc_ccitt() does, modulo swapping the exor operants and some C obfuscation. */ unsigned short crc_ccitt(unsigned char *q, int len) { unsigned short crc = 0; while (len-- > 0) crc = ccitt_table[(crc >> 8 ^ *q++) & 0xff] ^ (crc << 8); return ~crc; } /* Exploration ts B00214 : ECMA-130, 14.3 "EDC field" "The EDC codeword must be divisible by the check polynomial: P(x) = (x^16 + x^15 + x^2 + 1) . (x^16 + x^2 + x + 1) " Used for raw writing in sector.c */ unsigned int crc_32(unsigned char *data, int len) { unsigned int crc = 0; while (len-- > 0) crc = crc32_table[(crc ^ *data++) & 0xffL] ^ (crc >> 8); return crc; }