java crc 學習途中的疑惑記錄

   學習途中遇到了很多想不通的地方,花了很多天才明白。

   現在記錄在學習途中對某些我認爲比較難理解的內容進行進一步的解釋,希望能加快理解的速度。

   以CRC16-CCITT(1021)爲例,提供JAVA版的 CRC bit生成與CRC 表的生成與查表的原理。

   整個程序:     

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餘式表 */ 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; //哪當前數據跟餘數進行亦或 for(byte b : bs) { //b & 0xff 將數據轉換成整型,否則會出現負數而不正確。 crc = ((crc << 8) | b & 0xff) ^ table[ (crc >> 8 ) & 0xff]; } return crc & 0xffff; } //根據高位生成表。高位爲索引,表中存儲餘數 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 ) //判斷高位是否爲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; } }  

   從上面的程序中( value = ((value << 1) + b) ^ 0x1021; )可以看出爲什麼簡記1021。

  

  表的生成原理:將低位統一認爲是0，高位的值爲索引，餘數存儲表中.

    資料上都是個這樣的公式: a ^ b ^ c =  a ^ ( b ^ c ) .

    可以理解成這樣(16位): 

    11001100 11001100  ^ 0x1021

    =  

    11001100 00000000 ^ 00000000 11001100 ^  0x1021

    這樣就可以以字節爲單位,拿高位出來跟多項式做異或求得餘數保存到表中。

    程序:createTable()以字節爲單位創建的crc16表。

    例子:   11001100 11001100  ^ 0x1021  (已經生成一張存儲着0-255的表 table)

           = 11001100 00000000 ^  0x1021  ^ 00000000 11001100 

           =  table[11001100] ^   00000000 11001100  s

  查表法的原理: 當前餘數的低位加上當前字節，異或上次的餘數。

    很繞口，我當初就是載在這了,看了幾天都不明白。

    程序:getCrc()就是查表的實現。 

   例子:    00000001 00000002 00000003 ^ 0x1021;   crc = 0;

     數據擴充16位(crc16) 00000001 00000002 00000003 00000000 00000000 ^ 0x1021;      

     第一步執行完後  00000000 ^ 00000001 ^ tsable[00000000];  得餘數crc = 00000001;

     第二步執行完後  00000001 00000000(左移後) ^ 00000002 ^ table[00000000];  得餘數crc =  00000001 00000002

     第三步執行完後  00000002 00000000 ^ 00000003 ^ table[00000001]  得餘數 crc = 00000002 00000003 ^ table[1]

     最後得餘數  24881