学习途中遇到了很多想不通的地方,花了很多天才明白。
现在记录在学习途中对某些我认为比较难理解的内容进行进一步的解释,希望能加快理解的速度。
以CRC16-CCITT(1021)为例,提供JAVA版的 CRC bit生成与CRC 表的生成与查表的原理。
整个程序:
package crc; import sun.misc.CRC16; /** * @Title MyCrc16.java * @Package crc * @author * @date 2011-2-18 下午03:35:14 * @version V1.0 * @Description TODO */ public class MyCrc16 { private static int poly = 0x1021; private static int table[] = { /* CRC1021余式表 */ 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 }; public static void main(String str[]) { createTable(); byte bs[] = new byte[]{(byte) 0x01,(byte)0x02,(byte)0x03,(byte)0x00,(byte)0x00}; System.out.println(); System.out.println(getCrc(bs)); CRC16 crc = new CRC16(); crc.update(bs[0]); crc.update(bs[1]); crc.update(bs[2]); crc.update(bs[3]); crc.update(bs[4]); System.out.println(crc.value); } //查表法 public static int getCrc(byte[] bs) { int crc =0; //哪当前数据跟余数进行亦或 for(byte b : bs) { //b & 0xff 将数据转换成整型,否则会出现负数而不正确。 crc = ((crc << 8) | b & 0xff) ^ table[ (crc >> 8 ) & 0xff]; } return crc & 0xffff; } //根据高位生成表。高位为索引,表中存储余数 public static void createTable() { int crc = 0; for(int i=0;i<256;i++) { crc = i << 8; for(int j=0;j<8;j++) { if( (crc & 0x8000) != 0 ) //判断高位是否为1. crc = (crc << 1) ^ poly; else crc <<=1; } System.out.print(Integer.toHexString(crc & 0xffff) + ","); if( (i + 1) % 8 == 0) System.out.println(); } } }
crc16:
package sum.misc; /** * The CRC-16 class calculates a 16 bit cyclic redundancy check of a set * of bytes. This error detecting code is used to determine if bit rot * has occured in a byte stream. */ public class CRC16 { /** value contains the currently computed CRC, set it to 0 initally */ public int value; public CRC16() { value = 0; } /** update CRC with byte b */ public void update(byte aByte) { int a, b; a = (int) aByte; for (int count = 7; count >=0; count--) { a = a << 1; b = (a >>> 8) & 1; if ((value & 0x8000) != 0) { value = ((value << 1) + b) ^ 0x1021; } else { value = (value << 1) + b; } } value = value & 0xffff; return; } /** reset CRC value to 0 */ public void reset() { value = 0; } }
从上面的程序中( value = ((value << 1) + b) ^ 0x1021; )可以看出为什么简记1021。
表的生成原理:将低位统一认为是0，高位的值为索引，余数存储表中.
资料上都是个这样的公式: a ^ b ^ c = a ^ ( b ^ c ) .
可以理解成这样(16位):
11001100 11001100 ^ 0x1021
=
11001100 00000000 ^ 00000000 11001100 ^ 0x1021
这样就可以以字节为单位,拿高位出来跟多项式做异或求得余数保存到表中。
程序:createTable()以字节为单位创建的crc16表。
例子: 11001100 11001100 ^ 0x1021 (已经生成一张存储着0-255的表 table)
= 11001100 00000000 ^ 0x1021 ^ 00000000 11001100
= table[11001100] ^ 00000000 11001100 s
查表法的原理: 当前余数的低位加上当前字节，异或上次的余数。
很绕口，我当初就是载在这了,看了几天都不明白。
程序:getCrc()就是查表的实现。
例子: 00000001 00000002 00000003 ^ 0x1021; crc = 0;
数据扩充16位(crc16) 00000001 00000002 00000003 00000000 00000000 ^ 0x1021;
第一步执行完后 00000000 ^ 00000001 ^ tsable[00000000]; 得余数crc = 00000001;
第二步执行完后 00000001 00000000(左移后) ^ 00000002 ^ table[00000000]; 得余数crc = 00000001 00000002
第三步执行完后 00000002 00000000 ^ 00000003 ^ table[00000001] 得余数 crc = 00000002 00000003 ^ table[1]
最后得余数 24881
