crc32.c is originally from linux/lib/{crc32.c,crc32defs.h,crc32table.h},
which is GPLv2.
This implementation is based on crc.c in JAMlib and is LGPLv2.1.
http://sourceforge.net/projects/jamlib/
Signed-off-by: Jiro SEKIBA <jir@xxxxxxxxx>
---
lib/crc32.c | 444 +++++++++++------------------------------------------------
1 files changed, 79 insertions(+), 365 deletions(-)
diff --git a/lib/crc32.c b/lib/crc32.c
index 986a1f0..32a1a16 100644
--- a/lib/crc32.c
+++ b/lib/crc32.c
@@ -1,29 +1,28 @@
/*
- * crc.c - crc32 subroutine
+ * crc32 calclulation
*
- * This code has been extracted
- * from linux/lib/{crc32.c,crc32defs.h,crc32table.h}
+ * Copyright (C) 2010 Jiro SEKIBA <jir@xxxxxxxxx>
+ *
+ * This file is based on crc.c of JAMlib.
+ * http://sourceforge.net/projects/jamlib/
*/
/*
- * Oct 15, 2000 Matt Domsch <Matt_Domsch@xxxxxxxx>
- * Nicer crc32 functions/docs submitted by linux@xxxxxxxxxxxx Thanks!
- * Code was from the public domain, copyright abandoned. Code was
- * subsequently included in the kernel, thus was re-licensed under the
- * GNU GPL v2.
- *
- * Oct 12, 2000 Matt Domsch <Matt_Domsch@xxxxxxxx>
- * Same crc32 function was used in 5 other places in the kernel.
- * I made one version, and deleted the others.
- * There are various incantations of crc32(). Some use a seed of 0 or ~0.
- * Some xor at the end with ~0. The generic crc32() function takes
- * seed as an argument, and doesn't xor at the end. Then individual
- * users can do whatever they need.
- * drivers/net/smc9194.c uses seed ~0, doesn't xor with ~0.
- * fs/jffs2 uses seed 0, doesn't xor with ~0.
- * fs/partitions/efi.c uses seed ~0, xor's with ~0.
- *
- * This source code is licensed under the GNU General Public License,
- * Version 2. See the file COPYING for more details.
+ * Crc32 - CRC32-calculation for JAM
+ * Copyright (C) 2000 Johan Billing
+ *
+ * This library is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU Lesser General Public
+ * License as published by the Free Software Foundation; either
+ * version 2.1 of the License, or (at your option) any later version.
+ *
+ * This library is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ * Lesser General Public License for more details.
+ *
+ * You should have received a copy of the GNU Lesser General Public
+ * License along with this library; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
#ifdef HAVE_CONFIG_H
@@ -38,355 +37,70 @@
#include <linux/types.h>
#endif /* HAVE_LINUX_TYPES_H */
-#include <endian.h>
-#include <byteswap.h>
-
-#ifndef likely
-#define likely(x) __builtin_expect(!!(x), 1)
-#define unlikely(x) __builtin_expect(!!(x), 0)
-#endif
-
-#ifndef __constant_swab32
-#define __constant_swab32(x) \
- ((__u32)( \
- (((__u32)(x) & (__u32)0x000000ffUL) << 24) | \
- (((__u32)(x) & (__u32)0x0000ff00UL) << 8) | \
- (((__u32)(x) & (__u32)0x00ff0000UL) >> 8) | \
- (((__u32)(x) & (__u32)0xff000000UL) >> 24) ))
-#endif
-
-#ifndef __le32_to_cpu
-#if __BYTE_ORDER == __LITTLE_ENDIAN
-#define __cpu_to_le32(x) ((__u32)(x))
-#define __le32_to_cpu(x) ((__u32)(x))
-#define __constant_cpu_to_le32(x) ((__u32)(x))
-#elif __BYTE_ORDER == __BIG_ENDIAN
-#define __le32_to_cpu(x) bswap_32(x)
-#define __cpu_to_le32(x) bswap_32(x)
-#define __constant_cpu_to_le32(x) __constant_swab32(x)
-#else
-#error "unsupported endian"
-#endif
-#endif
-
typedef __u8 u8;
typedef __u32 u32;
-/*
- * There are multiple 16-bit CRC polynomials in common use, but this is
- * *the* standard CRC-32 polynomial, first popularized by Ethernet.
- * 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
- */
-#define CRCPOLY_LE 0xedb88320
-
-/* How many bits at a time to use. Requires a table of 4<<CRC_xx_BITS bytes. */
-/* For less performance-sensitive, use 4 */
-#ifndef CRC_LE_BITS
-# define CRC_LE_BITS 8
-#endif
-
-/*
- * Little-endian CRC computation. Used with serial bit streams sent
- * lsbit-first. Be sure to use cpu_to_le32() to append the computed CRC.
- */
-#if CRC_LE_BITS > 8 || CRC_LE_BITS < 1 || CRC_LE_BITS & CRC_LE_BITS-1
-# error CRC_LE_BITS must be a power of 2 between 1 and 8
-#endif
-
-#if CRC_LE_BITS == 8
-#define tole(x) __constant_cpu_to_le32(x)
-#else
-#define tole(x) (x)
-#endif
-
-static const u32 crc32table_le[] = {
-tole(0x00000000L), tole(0x77073096L), tole(0xee0e612cL), tole(0x990951baL),
-tole(0x076dc419L), tole(0x706af48fL), tole(0xe963a535L), tole(0x9e6495a3L),
-tole(0x0edb8832L), tole(0x79dcb8a4L), tole(0xe0d5e91eL), tole(0x97d2d988L),
-tole(0x09b64c2bL), tole(0x7eb17cbdL), tole(0xe7b82d07L), tole(0x90bf1d91L),
-tole(0x1db71064L), tole(0x6ab020f2L), tole(0xf3b97148L), tole(0x84be41deL),
-tole(0x1adad47dL), tole(0x6ddde4ebL), tole(0xf4d4b551L), tole(0x83d385c7L),
-tole(0x136c9856L), tole(0x646ba8c0L), tole(0xfd62f97aL), tole(0x8a65c9ecL),
-tole(0x14015c4fL), tole(0x63066cd9L), tole(0xfa0f3d63L), tole(0x8d080df5L),
-tole(0x3b6e20c8L), tole(0x4c69105eL), tole(0xd56041e4L), tole(0xa2677172L),
-tole(0x3c03e4d1L), tole(0x4b04d447L), tole(0xd20d85fdL), tole(0xa50ab56bL),
-tole(0x35b5a8faL), tole(0x42b2986cL), tole(0xdbbbc9d6L), tole(0xacbcf940L),
-tole(0x32d86ce3L), tole(0x45df5c75L), tole(0xdcd60dcfL), tole(0xabd13d59L),
-tole(0x26d930acL), tole(0x51de003aL), tole(0xc8d75180L), tole(0xbfd06116L),
-tole(0x21b4f4b5L), tole(0x56b3c423L), tole(0xcfba9599L), tole(0xb8bda50fL),
-tole(0x2802b89eL), tole(0x5f058808L), tole(0xc60cd9b2L), tole(0xb10be924L),
-tole(0x2f6f7c87L), tole(0x58684c11L), tole(0xc1611dabL), tole(0xb6662d3dL),
-tole(0x76dc4190L), tole(0x01db7106L), tole(0x98d220bcL), tole(0xefd5102aL),
-tole(0x71b18589L), tole(0x06b6b51fL), tole(0x9fbfe4a5L), tole(0xe8b8d433L),
-tole(0x7807c9a2L), tole(0x0f00f934L), tole(0x9609a88eL), tole(0xe10e9818L),
-tole(0x7f6a0dbbL), tole(0x086d3d2dL), tole(0x91646c97L), tole(0xe6635c01L),
-tole(0x6b6b51f4L), tole(0x1c6c6162L), tole(0x856530d8L), tole(0xf262004eL),
-tole(0x6c0695edL), tole(0x1b01a57bL), tole(0x8208f4c1L), tole(0xf50fc457L),
-tole(0x65b0d9c6L), tole(0x12b7e950L), tole(0x8bbeb8eaL), tole(0xfcb9887cL),
-tole(0x62dd1ddfL), tole(0x15da2d49L), tole(0x8cd37cf3L), tole(0xfbd44c65L),
-tole(0x4db26158L), tole(0x3ab551ceL), tole(0xa3bc0074L), tole(0xd4bb30e2L),
-tole(0x4adfa541L), tole(0x3dd895d7L), tole(0xa4d1c46dL), tole(0xd3d6f4fbL),
-tole(0x4369e96aL), tole(0x346ed9fcL), tole(0xad678846L), tole(0xda60b8d0L),
-tole(0x44042d73L), tole(0x33031de5L), tole(0xaa0a4c5fL), tole(0xdd0d7cc9L),
-tole(0x5005713cL), tole(0x270241aaL), tole(0xbe0b1010L), tole(0xc90c2086L),
-tole(0x5768b525L), tole(0x206f85b3L), tole(0xb966d409L), tole(0xce61e49fL),
-tole(0x5edef90eL), tole(0x29d9c998L), tole(0xb0d09822L), tole(0xc7d7a8b4L),
-tole(0x59b33d17L), tole(0x2eb40d81L), tole(0xb7bd5c3bL), tole(0xc0ba6cadL),
-tole(0xedb88320L), tole(0x9abfb3b6L), tole(0x03b6e20cL), tole(0x74b1d29aL),
-tole(0xead54739L), tole(0x9dd277afL), tole(0x04db2615L), tole(0x73dc1683L),
-tole(0xe3630b12L), tole(0x94643b84L), tole(0x0d6d6a3eL), tole(0x7a6a5aa8L),
-tole(0xe40ecf0bL), tole(0x9309ff9dL), tole(0x0a00ae27L), tole(0x7d079eb1L),
-tole(0xf00f9344L), tole(0x8708a3d2L), tole(0x1e01f268L), tole(0x6906c2feL),
-tole(0xf762575dL), tole(0x806567cbL), tole(0x196c3671L), tole(0x6e6b06e7L),
-tole(0xfed41b76L), tole(0x89d32be0L), tole(0x10da7a5aL), tole(0x67dd4accL),
-tole(0xf9b9df6fL), tole(0x8ebeeff9L), tole(0x17b7be43L), tole(0x60b08ed5L),
-tole(0xd6d6a3e8L), tole(0xa1d1937eL), tole(0x38d8c2c4L), tole(0x4fdff252L),
-tole(0xd1bb67f1L), tole(0xa6bc5767L), tole(0x3fb506ddL), tole(0x48b2364bL),
-tole(0xd80d2bdaL), tole(0xaf0a1b4cL), tole(0x36034af6L), tole(0x41047a60L),
-tole(0xdf60efc3L), tole(0xa867df55L), tole(0x316e8eefL), tole(0x4669be79L),
-tole(0xcb61b38cL), tole(0xbc66831aL), tole(0x256fd2a0L), tole(0x5268e236L),
-tole(0xcc0c7795L), tole(0xbb0b4703L), tole(0x220216b9L), tole(0x5505262fL),
-tole(0xc5ba3bbeL), tole(0xb2bd0b28L), tole(0x2bb45a92L), tole(0x5cb36a04L),
-tole(0xc2d7ffa7L), tole(0xb5d0cf31L), tole(0x2cd99e8bL), tole(0x5bdeae1dL),
-tole(0x9b64c2b0L), tole(0xec63f226L), tole(0x756aa39cL), tole(0x026d930aL),
-tole(0x9c0906a9L), tole(0xeb0e363fL), tole(0x72076785L), tole(0x05005713L),
-tole(0x95bf4a82L), tole(0xe2b87a14L), tole(0x7bb12baeL), tole(0x0cb61b38L),
-tole(0x92d28e9bL), tole(0xe5d5be0dL), tole(0x7cdcefb7L), tole(0x0bdbdf21L),
-tole(0x86d3d2d4L), tole(0xf1d4e242L), tole(0x68ddb3f8L), tole(0x1fda836eL),
-tole(0x81be16cdL), tole(0xf6b9265bL), tole(0x6fb077e1L), tole(0x18b74777L),
-tole(0x88085ae6L), tole(0xff0f6a70L), tole(0x66063bcaL), tole(0x11010b5cL),
-tole(0x8f659effL), tole(0xf862ae69L), tole(0x616bffd3L), tole(0x166ccf45L),
-tole(0xa00ae278L), tole(0xd70dd2eeL), tole(0x4e048354L), tole(0x3903b3c2L),
-tole(0xa7672661L), tole(0xd06016f7L), tole(0x4969474dL), tole(0x3e6e77dbL),
-tole(0xaed16a4aL), tole(0xd9d65adcL), tole(0x40df0b66L), tole(0x37d83bf0L),
-tole(0xa9bcae53L), tole(0xdebb9ec5L), tole(0x47b2cf7fL), tole(0x30b5ffe9L),
-tole(0xbdbdf21cL), tole(0xcabac28aL), tole(0x53b39330L), tole(0x24b4a3a6L),
-tole(0xbad03605L), tole(0xcdd70693L), tole(0x54de5729L), tole(0x23d967bfL),
-tole(0xb3667a2eL), tole(0xc4614ab8L), tole(0x5d681b02L), tole(0x2a6f2b94L),
-tole(0xb40bbe37L), tole(0xc30c8ea1L), tole(0x5a05df1bL), tole(0x2d02ef8dL)
+u32 crc32tab[] = { /* 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
};
-/**
- * crc32_le() - Calculate bitwise little-endian Ethernet AUTODIN II CRC32
- * @crc: seed value for computation. ~0 for Ethernet, sometimes 0 for
- * other uses, or the previous crc32 value if computing incrementally.
- * @p: pointer to buffer over which CRC is run
- * @len: length of buffer @p
- */
-u32 __attribute_pure__ crc32_le(u32 crc, unsigned char const *p, size_t len);
-
-#if CRC_LE_BITS == 1
-/*
- * In fact, the table-based code will work in this case, but it can be
- * simplified by inlining the table in ?: form.
- */
-
-u32 __attribute_pure__ crc32_le(u32 crc, unsigned char const *p, size_t len)
-{
- int i;
- while (len--) {
- crc ^= *p++;
- for (i = 0; i < 8; i++)
- crc = (crc >> 1) ^ ((crc & 1) ? CRCPOLY_LE : 0);
- }
- return crc;
-}
-#else /* Table-based approach */
-
-u32 __attribute_pure__ crc32_le(u32 crc, unsigned char const *p, size_t len)
+u32 crc32_le(u32 Crc_I, unsigned char *Buffer_PC, size_t Length_I)
{
-# if CRC_LE_BITS == 8
- const u32 *b =(u32 *)p;
- const u32 *tab = crc32table_le;
-
-#if __BYTE_ORDER == __LITTLE_ENDIAN
-#define DO_CRC(x) crc = tab[ (crc ^ (x)) & 255 ] ^ (crc>>8)
-#elif __BYTE_ORDER == __BIG_ENDIAN
-#define DO_CRC(x) crc = tab[ ((crc >> 24) ^ (x)) & 255] ^ (crc<<8)
-#else
-#error "unsupported endian"
-#endif
-
- crc = __cpu_to_le32(crc);
- /* Align it */
- if(unlikely(((long)b)&3 && len)){
- do {
- u8 *p = (u8 *)b;
- DO_CRC(*p++);
- b = (void *)p;
- } while ((--len) && ((long)b)&3 );
- }
- if(likely(len >= 4)){
- /* load data 32 bits wide, xor data 32 bits wide. */
- size_t save_len = len & 3;
- len = len >> 2;
- --b; /* use pre increment below(*++b) for speed */
- do {
- crc ^= *++b;
- DO_CRC(0);
- DO_CRC(0);
- DO_CRC(0);
- DO_CRC(0);
- } while (--len);
- b++; /* point to next byte(s) */
- len = save_len;
- }
- /* And the last few bytes */
- if(len){
- do {
- u8 *p = (u8 *)b;
- DO_CRC(*p++);
- b = (void *)p;
- } while (--len);
- }
+ size_t c;
- return __le32_to_cpu(crc);
-#undef ENDIAN_SHIFT
-#undef DO_CRC
+ for (c = 0; c < Length_I; c++)
+ Crc_I = (Crc_I>>8) ^ crc32tab[(u8)Crc_I ^ Buffer_PC[c]];
-# elif CRC_LE_BITS == 4
- while (len--) {
- crc ^= *p++;
- crc = (crc >> 4) ^ crc32table_le[crc & 15];
- crc = (crc >> 4) ^ crc32table_le[crc & 15];
- }
- return crc;
-# elif CRC_LE_BITS == 2
- while (len--) {
- crc ^= *p++;
- crc = (crc >> 2) ^ crc32table_le[crc & 3];
- crc = (crc >> 2) ^ crc32table_le[crc & 3];
- crc = (crc >> 2) ^ crc32table_le[crc & 3];
- crc = (crc >> 2) ^ crc32table_le[crc & 3];
- }
- return crc;
-# endif
+ return Crc_I;
}
-#endif
-
-/*
- * A brief CRC tutorial.
- *
- * A CRC is a long-division remainder. You add the CRC to the message,
- * and the whole thing (message+CRC) is a multiple of the given
- * CRC polynomial. To check the CRC, you can either check that the
- * CRC matches the recomputed value, *or* you can check that the
- * remainder computed on the message+CRC is 0. This latter approach
- * is used by a lot of hardware implementations, and is why so many
- * protocols put the end-of-frame flag after the CRC.
- *
- * It's actually the same long division you learned in school, except that
- * - We're working in binary, so the digits are only 0 and 1, and
- * - When dividing polynomials, there are no carries. Rather than add and
- * subtract, we just xor. Thus, we tend to get a bit sloppy about
- * the difference between adding and subtracting.
- *
- * A 32-bit CRC polynomial is actually 33 bits long. But since it's
- * 33 bits long, bit 32 is always going to be set, so usually the CRC
- * is written in hex with the most significant bit omitted. (If you're
- * familiar with the IEEE 754 floating-point format, it's the same idea.)
- *
- * Note that a CRC is computed over a string of *bits*, so you have
- * to decide on the endianness of the bits within each byte. To get
- * the best error-detecting properties, this should correspond to the
- * order they're actually sent. For example, standard RS-232 serial is
- * little-endian; the most significant bit (sometimes used for parity)
- * is sent last. And when appending a CRC word to a message, you should
- * do it in the right order, matching the endianness.
- *
- * Just like with ordinary division, the remainder is always smaller than
- * the divisor (the CRC polynomial) you're dividing by. Each step of the
- * division, you take one more digit (bit) of the dividend and append it
- * to the current remainder. Then you figure out the appropriate multiple
- * of the divisor to subtract to being the remainder back into range.
- * In binary, it's easy - it has to be either 0 or 1, and to make the
- * XOR cancel, it's just a copy of bit 32 of the remainder.
- *
- * When computing a CRC, we don't care about the quotient, so we can
- * throw the quotient bit away, but subtract the appropriate multiple of
- * the polynomial from the remainder and we're back to where we started,
- * ready to process the next bit.
- *
- * A big-endian CRC written this way would be coded like:
- * for (i = 0; i < input_bits; i++) {
- * multiple = remainder & 0x80000000 ? CRCPOLY : 0;
- * remainder = (remainder << 1 | next_input_bit()) ^ multiple;
- * }
- * Notice how, to get at bit 32 of the shifted remainder, we look
- * at bit 31 of the remainder *before* shifting it.
- *
- * But also notice how the next_input_bit() bits we're shifting into
- * the remainder don't actually affect any decision-making until
- * 32 bits later. Thus, the first 32 cycles of this are pretty boring.
- * Also, to add the CRC to a message, we need a 32-bit-long hole for it at
- * the end, so we have to add 32 extra cycles shifting in zeros at the
- * end of every message,
- *
- * So the standard trick is to rearrage merging in the next_input_bit()
- * until the moment it's needed. Then the first 32 cycles can be precomputed,
- * and merging in the final 32 zero bits to make room for the CRC can be
- * skipped entirely.
- * This changes the code to:
- * for (i = 0; i < input_bits; i++) {
- * remainder ^= next_input_bit() << 31;
- * multiple = (remainder & 0x80000000) ? CRCPOLY : 0;
- * remainder = (remainder << 1) ^ multiple;
- * }
- * With this optimization, the little-endian code is simpler:
- * for (i = 0; i < input_bits; i++) {
- * remainder ^= next_input_bit();
- * multiple = (remainder & 1) ? CRCPOLY : 0;
- * remainder = (remainder >> 1) ^ multiple;
- * }
- *
- * Note that the other details of endianness have been hidden in CRCPOLY
- * (which must be bit-reversed) and next_input_bit().
- *
- * However, as long as next_input_bit is returning the bits in a sensible
- * order, we can actually do the merging 8 or more bits at a time rather
- * than one bit at a time:
- * for (i = 0; i < input_bytes; i++) {
- * remainder ^= next_input_byte() << 24;
- * for (j = 0; j < 8; j++) {
- * multiple = (remainder & 0x80000000) ? CRCPOLY : 0;
- * remainder = (remainder << 1) ^ multiple;
- * }
- * }
- * Or in little-endian:
- * for (i = 0; i < input_bytes; i++) {
- * remainder ^= next_input_byte();
- * for (j = 0; j < 8; j++) {
- * multiple = (remainder & 1) ? CRCPOLY : 0;
- * remainder = (remainder << 1) ^ multiple;
- * }
- * }
- * If the input is a multiple of 32 bits, you can even XOR in a 32-bit
- * word at a time and increase the inner loop count to 32.
- *
- * You can also mix and match the two loop styles, for example doing the
- * bulk of a message byte-at-a-time and adding bit-at-a-time processing
- * for any fractional bytes at the end.
- *
- * The only remaining optimization is to the byte-at-a-time table method.
- * Here, rather than just shifting one bit of the remainder to decide
- * in the correct multiple to subtract, we can shift a byte at a time.
- * This produces a 40-bit (rather than a 33-bit) intermediate remainder,
- * but again the multiple of the polynomial to subtract depends only on
- * the high bits, the high 8 bits in this case.
- *
- * The multile we need in that case is the low 32 bits of a 40-bit
- * value whose high 8 bits are given, and which is a multiple of the
- * generator polynomial. This is simply the CRC-32 of the given
- * one-byte message.
- *
- * Two more details: normally, appending zero bits to a message which
- * is already a multiple of a polynomial produces a larger multiple of that
- * polynomial. To enable a CRC to detect this condition, it's common to
- * invert the CRC before appending it. This makes the remainder of the
- * message+crc come out not as zero, but some fixed non-zero value.
- *
- * The same problem applies to zero bits prepended to the message, and
- * a similar solution is used. Instead of starting with a remainder of
- * 0, an initial remainder of all ones is used. As long as you start
- * the same way on decoding, it doesn't make a difference.
- */
--
1.7.0.4
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