brad@cayman.COM (Brad Parker) (07/12/89)
I need a simple way to calculate the CRC used in Ethernet packets. This is (from what I can see) using the "AUTODON II" polynomial. I found some nice pictures in the Ethernet spec blue book, but they assume a bit stream (and seem easy to implement if you are doing VLSI, but not C code!) Anyone have a hints for a some way to do this in C? I do not need speed, just a correct algorithm. I assume there are some tricks which can be exploited for 8 or 16 (or even 32) bit computation machines. thanks -brad -- Brad Parker Cayman Systems, Inc. Cambridge, Ma. brad@cayman.com
boland@hpindda.HP.COM (Ross Boland) (07/13/89)
Try looking in "Journal of Data & Computer Communications" volume 1 Number 4, Spring 1989. They have a section dedicated to CRC calulations with examples written in C.
adnan@sgtech.UUCP (Adnan Yaqub) (07/17/89)
I asked a similar question awhile ago and was sent some `C' code. This code uses a trick which allows on to due 8 bits at a time. Based on the next character received, one can look in a table to find out what the CRC is supposed to look like (more or less). The trick is as follows: crc = (crc_32_tab[((crc) ^ (octet)) & 0xff] ^ ((crc) >> 8)); I've enclosed the code at the end of this letter. Adnan Yaqub Star Gate Technologies, 29300 Aurora Rd., Solon, OH, USA, +1 216 349 1860 ...uunet!abvax!sgtech!adnan /*% cc -O -K -dos % -o crc.exe */ /* * Crc - 32 BIT ANSI X3.66 CRC checksum files */ #include <stdio.h> #define OK 0 #define ERROR (-1) #define LINT_ARGS /**********************************************************************\ |* *| |* Demonstration program to compute the 32-bit CRC used as the frame *| |* check sequence in ADCCP (ANSI X3.66, also known as FIPS PUB 71 *| |* and FED-STD-1003, the U.S. versions of CCITT's X.25 link-level *| |* protocol). The 32-bit FCS was added via the Federal Register, *| |* 1 June 1982, p.23798. I presume but don't know for certain that *| |* this polynomial is or will be included in CCITT V.41, which *| |* defines the 16-bit CRC (often called CRC-CCITT) polynomial. FIPS *| |* PUB 78 says that the 32-bit FCS reduces otherwise undetected *| |* errors by a factor of 10^-5 over 16-bit FCS. *| |* *| \**********************************************************************/ /* Need an unsigned type capable of holding 32 bits; */ typedef unsigned long int UNS_32_BITS; /* * Copyright (C) 1986 Gary S. Brown. You may use this program, or * code or tables extracted from it, as desired without restriction. */ /* First, the polynomial itself and its table of feedback terms. The */ /* polynomial is */ /* X^32+X^26+X^23+X^22+X^16+X^12+X^11+X^10+X^8+X^7+X^5+X^4+X^2+X^1+X^0 */ /* Note that we take it "backwards" and put the highest-order term in */ /* the lowest-order bit. The X^32 term is "implied"; the LSB is the */ /* X^31 term, etc. The X^0 term (usually shown as "+1") results in */ /* the MSB being 1. */ /* Note that the usual hardware shift register implementation, which */ /* is what we're using (we're merely optimizing it by doing eight-bit */ /* chunks at a time) shifts bits into the lowest-order term. In our */ /* implementation, that means shifting towards the right. Why do we */ /* do it this way? Because the calculated CRC must be transmitted in */ /* order from highest-order term to lowest-order term. UARTs transmit */ /* characters in order from LSB to MSB. By storing the CRC this way, */ /* we hand it to the UART in the order low-byte to high-byte; the UART */ /* sends each low-bit to hight-bit; and the result is transmission bit */ /* by bit from highest- to lowest-order term without requiring any bit */ /* shuffling on our part. Reception works similarly. */ /* The feedback terms table consists of 256, 32-bit entries. Notes: */ /* */ /* 1. The table can be generated at runtime if desired; code to do so */ /* is shown later. It might not be obvious, but the feedback */ /* terms simply represent the results of eight shift/xor opera- */ /* tions for all combinations of data and CRC register values. */ /* */ /* 2. The CRC accumulation logic is the same for all CRC polynomials, */ /* be they sixteen or thirty-two bits wide. You simply choose the */ /* appropriate table. Alternatively, because the table can be */ /* generated at runtime, you can start by generating the table for */ /* the polynomial in question and use exactly the same "updcrc", */ /* if your application needn't simultaneously handle two CRC */ /* polynomials. (Note, however, that XMODEM is strange.) */ /* */ /* 3. For 16-bit CRCs, the table entries need be only 16 bits wide; */ /* of course, 32-bit entries work OK if the high 16 bits are zero. */ /* */ /* 4. The values must be right-shifted by eight bits by the "updcrc" */ /* logic; the shift must be unsigned (bring in zeroes). On some */ /* hardware you could probably optimize the shift in assembler by */ /* using byte-swap instructions. */ static UNS_32_BITS crc_32_tab[] = { /* CRC polynomial 0xedb88320 */ 0x00000000, 0x77073096, 0xee0e612c, 0x990951ba, 0x076dc419, 0x706af48f, 0xe963a535, 0x9e6495a3, 0x0edb8832, 0x79dcb8a4, 0xe0d5e91e, 0x97d2d988, 0x09b64c2b, 0x7eb17cbd, 0xe7b82d07, 0x90bf1d91, 0x1db71064, 0x6ab020f2, 0xf3b97148, 0x84be41de, 0x1adad47d, 0x6ddde4eb, 0xf4d4b551, 0x83d385c7, 0x136c9856, 0x646ba8c0, 0xfd62f97a, 0x8a65c9ec, 0x14015c4f, 0x63066cd9, 0xfa0f3d63, 0x8d080df5, 0x3b6e20c8, 0x4c69105e, 0xd56041e4, 0xa2677172, 0x3c03e4d1, 0x4b04d447, 0xd20d85fd, 0xa50ab56b, 0x35b5a8fa, 0x42b2986c, 0xdbbbc9d6, 0xacbcf940, 0x32d86ce3, 0x45df5c75, 0xdcd60dcf, 0xabd13d59, 0x26d930ac, 0x51de003a, 0xc8d75180, 0xbfd06116, 0x21b4f4b5, 0x56b3c423, 0xcfba9599, 0xb8bda50f, 0x2802b89e, 0x5f058808, 0xc60cd9b2, 0xb10be924, 0x2f6f7c87, 0x58684c11, 0xc1611dab, 0xb6662d3d, 0x76dc4190, 0x01db7106, 0x98d220bc, 0xefd5102a, 0x71b18589, 0x06b6b51f, 0x9fbfe4a5, 0xe8b8d433, 0x7807c9a2, 0x0f00f934, 0x9609a88e, 0xe10e9818, 0x7f6a0dbb, 0x086d3d2d, 0x91646c97, 0xe6635c01, 0x6b6b51f4, 0x1c6c6162, 0x856530d8, 0xf262004e, 0x6c0695ed, 0x1b01a57b, 0x8208f4c1, 0xf50fc457, 0x65b0d9c6, 0x12b7e950, 0x8bbeb8ea, 0xfcb9887c, 0x62dd1ddf, 0x15da2d49, 0x8cd37cf3, 0xfbd44c65, 0x4db26158, 0x3ab551ce, 0xa3bc0074, 0xd4bb30e2, 0x4adfa541, 0x3dd895d7, 0xa4d1c46d, 0xd3d6f4fb, 0x4369e96a, 0x346ed9fc, 0xad678846, 0xda60b8d0, 0x44042d73, 0x33031de5, 0xaa0a4c5f, 0xdd0d7cc9, 0x5005713c, 0x270241aa, 0xbe0b1010, 0xc90c2086, 0x5768b525, 0x206f85b3, 0xb966d409, 0xce61e49f, 0x5edef90e, 0x29d9c998, 0xb0d09822, 0xc7d7a8b4, 0x59b33d17, 0x2eb40d81, 0xb7bd5c3b, 0xc0ba6cad, 0xedb88320, 0x9abfb3b6, 0x03b6e20c, 0x74b1d29a, 0xead54739, 0x9dd277af, 0x04db2615, 0x73dc1683, 0xe3630b12, 0x94643b84, 0x0d6d6a3e, 0x7a6a5aa8, 0xe40ecf0b, 0x9309ff9d, 0x0a00ae27, 0x7d079eb1, 0xf00f9344, 0x8708a3d2, 0x1e01f268, 0x6906c2fe, 0xf762575d, 0x806567cb, 0x196c3671, 0x6e6b06e7, 0xfed41b76, 0x89d32be0, 0x10da7a5a, 0x67dd4acc, 0xf9b9df6f, 0x8ebeeff9, 0x17b7be43, 0x60b08ed5, 0xd6d6a3e8, 0xa1d1937e, 0x38d8c2c4, 0x4fdff252, 0xd1bb67f1, 0xa6bc5767, 0x3fb506dd, 0x48b2364b, 0xd80d2bda, 0xaf0a1b4c, 0x36034af6, 0x41047a60, 0xdf60efc3, 0xa867df55, 0x316e8eef, 0x4669be79, 0xcb61b38c, 0xbc66831a, 0x256fd2a0, 0x5268e236, 0xcc0c7795, 0xbb0b4703, 0x220216b9, 0x5505262f, 0xc5ba3bbe, 0xb2bd0b28, 0x2bb45a92, 0x5cb36a04, 0xc2d7ffa7, 0xb5d0cf31, 0x2cd99e8b, 0x5bdeae1d, 0x9b64c2b0, 0xec63f226, 0x756aa39c, 0x026d930a, 0x9c0906a9, 0xeb0e363f, 0x72076785, 0x05005713, 0x95bf4a82, 0xe2b87a14, 0x7bb12bae, 0x0cb61b38, 0x92d28e9b, 0xe5d5be0d, 0x7cdcefb7, 0x0bdbdf21, 0x86d3d2d4, 0xf1d4e242, 0x68ddb3f8, 0x1fda836e, 0x81be16cd, 0xf6b9265b, 0x6fb077e1, 0x18b74777, 0x88085ae6, 0xff0f6a70, 0x66063bca, 0x11010b5c, 0x8f659eff, 0xf862ae69, 0x616bffd3, 0x166ccf45, 0xa00ae278, 0xd70dd2ee, 0x4e048354, 0x3903b3c2, 0xa7672661, 0xd06016f7, 0x4969474d, 0x3e6e77db, 0xaed16a4a, 0xd9d65adc, 0x40df0b66, 0x37d83bf0, 0xa9bcae53, 0xdebb9ec5, 0x47b2cf7f, 0x30b5ffe9, 0xbdbdf21c, 0xcabac28a, 0x53b39330, 0x24b4a3a6, 0xbad03605, 0xcdd70693, 0x54de5729, 0x23d967bf, 0xb3667a2e, 0xc4614ab8, 0x5d681b02, 0x2a6f2b94, 0xb40bbe37, 0xc30c8ea1, 0x5a05df1b, 0x2d02ef8d }; #define UPDC32(octet, crc) (crc_32_tab[((crc) ^ (octet)) & 0xff] ^ ((crc) >> 8)) main(argc, argp) char **argp; { register errors = 0; while( --argc > 0) errors |= crc32file( *++argp); exit(errors != 0); } crc32file(name) char *name; { register FILE *fin; register unsigned long oldcrc32; register unsigned long crc32; register unsigned long oldcrc; register c; register long charcnt; oldcrc32 = 0xFFFFFFFF; charcnt = 0; #ifdef M_I86SM if ((fin=fopen(name, "rb"))==NULL) #else if ((fin=fopen(name, "r"))==NULL) #endif { perror(name); return ERROR; } while ((c=getc(fin))!=EOF) { ++charcnt; oldcrc32 = UPDC32(c, oldcrc32); } if (ferror(fin)) { perror(name); charcnt = -1; } fclose(fin); crc32 = oldcrc32; oldcrc = oldcrc32 = ~oldcrc32; /* crc32 = UPDC32((oldcrc32 & 0377), crc32); oldcrc32 >>=8; crc32 = UPDC32((oldcrc32 & 0377), crc32); oldcrc32 >>=8; crc32 = UPDC32((oldcrc32 & 0377), crc32); oldcrc32 >>=8; crc32 = UPDC32((oldcrc32 & 0377), crc32); oldcrc32 >>=8; printf("%08lX ", crc32); */ printf("%08lX %7ld %s\n", oldcrc, charcnt, name); return OK; } -- Adnan Yaqub Star Gate Technologies, 29300 Aurora Rd., Solon, OH, USA, +1 216 349 1860 ...uunet!abvax!sgtech!adnan
Mills@UDEL.EDU (07/19/89)
Ross, About every couple of years since the early seventies somebody rediscovers how to shortcut the Galois field and exchange bytes for microseconds. The primal reference is Peterson and Weldon (Vol. 2) "Error Correcting Codes." Happy factoring. Dave