参数模型
CRC即循环冗余校验码（Cyclic Redundancy Check）：是数据通信领域中最常用的一种查错校验码，其特征是信息字段和校验字段的长度可以任意选定。循环冗余检查（CRC）是一种数据传输检错功能，对数据进行多项式计算，并将得到的结果附在帧的后面，接收设备也执行类似的算法，以保证数据传输的正确性和完整性。
CRC算法参数模型解释：
- NAME：参数模型名称。
- WIDTH：宽度，即CRC比特数。
- POLY：生成项的简写，以16进制表示。例如：CRC-32即是0x04C11DB7，忽略了最高位的"1"，即完整的生成项是0x104C11DB7。
- INIT：这是算法开始时寄存器（crc）的初始化预置值，十六进制表示。
- REFIN：待测数据的每个字节是否按位反转，True或False。
- REFOUT：在计算后之后，异或输出之前，整个数据是否按位反转，True或False。
- XOROUT：计算结果与此参数异或后得到最终的CRC值。
常见CRC参数模型如下：
| CRC算法名称 | 多项式公式 | 宽度 | 多项式 | 初始值 | 结果异或值 | 输入反转 | 输出反转 |
|---|---|---|---|---|---|---|---|
| CRC-4/ITU | x4 + x + 1 | 4 | 03 | 00 | 00 | true | true |
| CRC-5/EPC | x5 + x3 + 1 | 5 | 09 | 09 | 00 | false | false |
| CRC-5/ITU | x5 + x4 + x2 + 1 | 5 | 15 | 00 | 00 | true | true |
| CRC-5/USB | x5 + x2 + 1 | 5 | 05 | 1F | 1F | true | true |
| CRC-6/ITU | x6 + x + 1 | 6 | 03 | 00 | 00 | true | true |
| CRC-7/MMC | x7 + x3 + 1 | 7 | 09 | 00 | 00 | false | false |
| CRC-8 | x8 + x2 + x + 1 | 8 | 07 | 00 | 00 | false | false |
| CRC-8/ITU | x8 + x2 + x + 1 | 8 | 07 | 00 | 55 | false | false |
| CRC-8/ROHC | x8 + x2 + x + 1 | 8 | 07 | FF | 00 | true | true |
| CRC-8/MAXIM | x8 + x5 + x4 + 1 | 8 | 31 | 00 | 00 | true | true |
| CRC-16/IBM | x16 + x15 + x2 + 1 | 16 | 8005 | 0000 | 0000 | true | true |
| CRC-16/MAXIM | x16 + x15 + x2 + 1 | 16 | 8005 | 0000 | FFFF | true | true |
| CRC-16/USB | x16 + x15 + x2 + 1 | 16 | 8005 | FFFF | FFFF | true | true |
| CRC-16/MODBUS | x16 + x15 + x2 + 1 | 16 | 8005 | FFFF | 0000 | true | true |
| CRC-16/CCITT | x16 + x12 + x5 + 1 | 16 | 1021 | 0000 | 0000 | true | true |
| CRC-16/CCITT-FALSE | x16 + x12 + x5 + 1 | 16 | 1021 | FFFF | 0000 | false | false |
| CRC-16/X25 | x16 + x12 + x5 + 1 | 16 | 1021 | FFFF | FFFF | true | true |
| CRC-16/XMODEM | x16 + x12 + x5 + 1 | 16 | 1021 | 0000 | 0000 | false | false |
| CRC-16/DNP | x16 + x13 + x12 + x11 + x10 + x8 + x6 + x5 + x2 + 1 | 16 | 3D65 | 0000 | FFFF | true | true |
| CRC-32 | x32 + x26 + x23 + x22 + x16 + x12 + x11 + x10 + x8 + x7 + x5 + x4 + x2 + x + 1 | 32 | 04C11DB7 | FFFFFFFF | FFFFFFFF | true | true |
| CRC-32/MPEG-2 | x32 + x26 + x23 + x22 + x16 + x12 + x11 + x10 + x8 + x7 + x5 + x4 + x2 + x + 1 | 32 | 04C11DB7 | FFFFFFFF | 00000000 | false | false |
注：CRC算法选取的多项式会影响算法本身检查错误的能力，运用时不可随意定义多项式，选择一个通用的CRC多项式即可。
算法实现
此处只给出CRC-32、CRC-32/MPEG-2两种算法的查表法代码实现，两种算法的多项式一样但参数模型有很大区别。
通过比较两种算法的实现代码可以很容易的写出其它参数模型CRC算法的查表法实现，再利用表生成算法生成对应的表即可。
CRC-32
代码如下：
public static class Crc32
{
// CRC计算表（取决于多项式和输入是否反转）
static readonly uint[] crcTable = new uint[256] {
0x00000000u, 0x77073096u, 0xee0e612cu, 0x990951bau, 0x076dc419u, 0x706af48fu, 0xe963a535u, 0x9e6495a3u,
0x0edb8832u, 0x79dcb8a4u, 0xe0d5e91eu, 0x97d2d988u, 0x09b64c2bu, 0x7eb17cbdu, 0xe7b82d07u, 0x90bf1d91u,
0x1db71064u, 0x6ab020f2u, 0xf3b97148u, 0x84be41deu, 0x1adad47du, 0x6ddde4ebu, 0xf4d4b551u, 0x83d385c7u,
0x136c9856u, 0x646ba8c0u, 0xfd62f97au, 0x8a65c9ecu, 0x14015c4fu, 0x63066cd9u, 0xfa0f3d63u, 0x8d080df5u,
0x3b6e20c8u, 0x4c69105eu, 0xd56041e4u, 0xa2677172u, 0x3c03e4d1u, 0x4b04d447u, 0xd20d85fdu, 0xa50ab56bu,
0x35b5a8fau, 0x42b2986cu, 0xdbbbc9d6u, 0xacbcf940u, 0x32d86ce3u, 0x45df5c75u, 0xdcd60dcfu, 0xabd13d59u,
0x26d930acu, 0x51de003au, 0xc8d75180u, 0xbfd06116u, 0x21b4f4b5u, 0x56b3c423u, 0xcfba9599u, 0xb8bda50fu,
0x2802b89eu, 0x5f058808u, 0xc60cd9b2u, 0xb10be924u, 0x2f6f7c87u, 0x58684c11u, 0xc1611dabu, 0xb6662d3du,
0x76dc4190u, 0x01db7106u, 0x98d220bcu, 0xefd5102au, 0x71b18589u, 0x06b6b51fu, 0x9fbfe4a5u, 0xe8b8d433u,
0x7807c9a2u, 0x0f00f934u, 0x9609a88eu, 0xe10e9818u, 0x7f6a0dbbu, 0x086d3d2du, 0x91646c97u, 0xe6635c01u,
0x6b6b51f4u, 0x1c6c6162u, 0x856530d8u, 0xf262004eu, 0x6c0695edu, 0x1b01a57bu, 0x8208f4c1u, 0xf50fc457u,
0x65b0d9c6u, 0x12b7e950u, 0x8bbeb8eau, 0xfcb9887cu, 0x62dd1ddfu, 0x15da2d49u, 0x8cd37cf3u, 0xfbd44c65u,
0x4db26158u, 0x3ab551ceu, 0xa3bc0074u, 0xd4bb30e2u, 0x4adfa541u, 0x3dd895d7u, 0xa4d1c46du, 0xd3d6f4fbu,
0x4369e96au, 0x346ed9fcu, 0xad678846u, 0xda60b8d0u, 0x44042d73u, 0x33031de5u, 0xaa0a4c5fu, 0xdd0d7cc9u,
0x5005713cu, 0x270241aau, 0xbe0b1010u, 0xc90c2086u, 0x5768b525u, 0x206f85b3u, 0xb966d409u, 0xce61e49fu,
0x5edef90eu, 0x29d9c998u, 0xb0d09822u, 0xc7d7a8b4u, 0x59b33d17u, 0x2eb40d81u, 0xb7bd5c3bu, 0xc0ba6cadu,
0xedb88320u, 0x9abfb3b6u, 0x03b6e20cu, 0x74b1d29au, 0xead54739u, 0x9dd277afu, 0x04db2615u, 0x73dc1683u,
0xe3630b12u, 0x94643b84u, 0x0d6d6a3eu, 0x7a6a5aa8u, 0xe40ecf0bu, 0x9309ff9du, 0x0a00ae27u, 0x7d079eb1u,
0xf00f9344u, 0x8708a3d2u, 0x1e01f268u, 0x6906c2feu, 0xf762575du, 0x806567cbu, 0x196c3671u, 0x6e6b06e7u,
0xfed41b76u, 0x89d32be0u, 0x10da7a5au, 0x67dd4accu, 0xf9b9df6fu, 0x8ebeeff9u, 0x17b7be43u, 0x60b08ed5u,
0xd6d6a3e8u, 0xa1d1937eu, 0x38d8c2c4u, 0x4fdff252u, 0xd1bb67f1u, 0xa6bc5767u, 0x3fb506ddu, 0x48b2364bu,
0xd80d2bdau, 0xaf0a1b4cu, 0x36034af6u, 0x41047a60u, 0xdf60efc3u, 0xa867df55u, 0x316e8eefu, 0x4669be79u,
0xcb61b38cu, 0xbc66831au, 0x256fd2a0u, 0x5268e236u, 0xcc0c7795u, 0xbb0b4703u, 0x220216b9u, 0x5505262fu,
0xc5ba3bbeu, 0xb2bd0b28u, 0x2bb45a92u, 0x5cb36a04u, 0xc2d7ffa7u, 0xb5d0cf31u, 0x2cd99e8bu, 0x5bdeae1du,
0x9b64c2b0u, 0xec63f226u, 0x756aa39cu, 0x026d930au, 0x9c0906a9u, 0xeb0e363fu, 0x72076785u, 0x05005713u,
0x95bf4a82u, 0xe2b87a14u, 0x7bb12baeu, 0x0cb61b38u, 0x92d28e9bu, 0xe5d5be0du, 0x7cdcefb7u, 0x0bdbdf21u,
0x86d3d2d4u, 0xf1d4e242u, 0x68ddb3f8u, 0x1fda836eu, 0x81be16cdu, 0xf6b9265bu, 0x6fb077e1u, 0x18b74777u,
0x88085ae6u, 0xff0f6a70u, 0x66063bcau, 0x11010b5cu, 0x8f659effu, 0xf862ae69u, 0x616bffd3u, 0x166ccf45u,
0xa00ae278u, 0xd70dd2eeu, 0x4e048354u, 0x3903b3c2u, 0xa7672661u, 0xd06016f7u, 0x4969474du, 0x3e6e77dbu,
0xaed16a4au, 0xd9d65adcu, 0x40df0b66u, 0x37d83bf0u, 0xa9bcae53u, 0xdebb9ec5u, 0x47b2cf7fu, 0x30b5ffe9u,
0xbdbdf21cu, 0xcabac28au, 0x53b39330u, 0x24b4a3a6u, 0xbad03605u, 0xcdd70693u, 0x54de5729u, 0x23d967bfu,
0xb3667a2eu, 0xc4614ab8u, 0x5d681b02u, 0x2a6f2b94u, 0xb40bbe37u, 0xc30c8ea1u, 0x5a05df1bu, 0x2d02ef8du
};
public static readonly string Name = "CRC-32";
public static uint Compute(byte[] buffer)
{
if (buffer == null)
{
throw new ArgumentException("参数异常，请检查调用方");
}
return Compute(buffer, 0, buffer.Length);
}
public static uint Compute(byte[] buffer, int offset, int length)
{
if(!((buffer != null) && (offset >= 0) && (length >= 0) && (offset <= buffer.Length - length)))
{
throw new ArgumentException("参数异常，请检查调用方");
}
//寄存器初始值
uint crc32= 0xffffffffU;
while (--length >= 0)
{
//查表运算（取决于宽度和输出是否反转）
crc32 = crcTable[(crc32 ^ buffer[offset++]) & 0xFF] ^ (crc32 >> 8);
}
//结果异或
crc32 ^= 0xffffffffU;
return crc32;
}
}
测试如下：
byte[] data = new byte[] { 0x31, 0x32, 0x33, 0x34,0x35,0x36,0x37,0x38,0x39 };
uint crc32 = Crc32.Compute(data);
byte[] crc32Ary = BitConverter.GetBytes(crc32);
string crc32Str = "";
for (int i = crc32Ary.Length-1; i >=0; i--)
{
crc32Str += crc32Ary[i].ToString("X2");
}
Console.WriteLine(crc32Str);
Console.ReadLine();
测试结果：
CBF43926
CRC-32/MPEG-2
代码如下：
public static class Crc32
{
// CRC计算表（取决于多项式和输入是否反）
static readonly uint[] crcTable = new uint[256] {
0x00000000, 0x04c11db7, 0x09823b6e, 0x0d4326d9, 0x130476dc, 0x17c56b6b, 0x1a864db2, 0x1e475005,
0x2608edb8, 0x22c9f00f, 0x2f8ad6d6, 0x2b4bcb61, 0x350c9b64, 0x31cd86d3, 0x3c8ea00a, 0x384fbdbd,
0x4c11db70, 0x48d0c6c7, 0x4593e01e, 0x4152fda9, 0x5f15adac, 0x5bd4b01b, 0x569796c2, 0x52568b75,
0x6a1936c8, 0x6ed82b7f, 0x639b0da6, 0x675a1011, 0x791d4014, 0x7ddc5da3, 0x709f7b7a, 0x745e66cd,
0x9823b6e0, 0x9ce2ab57, 0x91a18d8e, 0x95609039, 0x8b27c03c, 0x8fe6dd8b, 0x82a5fb52, 0x8664e6e5,
0xbe2b5b58, 0xbaea46ef, 0xb7a96036, 0xb3687d81, 0xad2f2d84, 0xa9ee3033, 0xa4ad16ea, 0xa06c0b5d,
0xd4326d90, 0xd0f37027, 0xddb056fe, 0xd9714b49, 0xc7361b4c, 0xc3f706fb, 0xceb42022, 0xca753d95,
0xf23a8028, 0xf6fb9d9f, 0xfbb8bb46, 0xff79a6f1, 0xe13ef6f4, 0xe5ffeb43, 0xe8bccd9a, 0xec7dd02d,
0x34867077, 0x30476dc0, 0x3d044b19, 0x39c556ae, 0x278206ab, 0x23431b1c, 0x2e003dc5, 0x2ac12072,
0x128e9dcf, 0x164f8078, 0x1b0ca6a1, 0x1fcdbb16, 0x018aeb13, 0x054bf6a4, 0x0808d07d, 0x0cc9cdca,
0x7897ab07, 0x7c56b6b0, 0x71159069, 0x75d48dde, 0x6b93dddb, 0x6f52c06c, 0x6211e6b5, 0x66d0fb02,
0x5e9f46bf, 0x5a5e5b08, 0x571d7dd1, 0x53dc6066, 0x4d9b3063, 0x495a2dd4, 0x44190b0d, 0x40d816ba,
0xaca5c697, 0xa864db20, 0xa527fdf9, 0xa1e6e04e, 0xbfa1b04b, 0xbb60adfc, 0xb6238b25, 0xb2e29692,
0x8aad2b2f, 0x8e6c3698, 0x832f1041, 0x87ee0df6, 0x99a95df3, 0x9d684044, 0x902b669d, 0x94ea7b2a,
0xe0b41de7, 0xe4750050, 0xe9362689, 0xedf73b3e, 0xf3b06b3b, 0xf771768c, 0xfa325055, 0xfef34de2,
0xc6bcf05f, 0xc27dede8, 0xcf3ecb31, 0xcbffd686, 0xd5b88683, 0xd1799b34, 0xdc3abded, 0xd8fba05a,
0x690ce0ee, 0x6dcdfd59, 0x608edb80, 0x644fc637, 0x7a089632, 0x7ec98b85, 0x738aad5c, 0x774bb0eb,
0x4f040d56, 0x4bc510e1, 0x46863638, 0x42472b8f, 0x5c007b8a, 0x58c1663d, 0x558240e4, 0x51435d53,
0x251d3b9e, 0x21dc2629, 0x2c9f00f0, 0x285e1d47, 0x36194d42, 0x32d850f5, 0x3f9b762c, 0x3b5a6b9b,
0x0315d626, 0x07d4cb91, 0x0a97ed48, 0x0e56f0ff, 0x1011a0fa, 0x14d0bd4d, 0x19939b94, 0x1d528623,
0xf12f560e, 0xf5ee4bb9, 0xf8ad6d60, 0xfc6c70d7, 0xe22b20d2, 0xe6ea3d65, 0xeba91bbc, 0xef68060b,
0xd727bbb6, 0xd3e6a601, 0xdea580d8, 0xda649d6f, 0xc423cd6a, 0xc0e2d0dd, 0xcda1f604, 0xc960ebb3,
0xbd3e8d7e, 0xb9ff90c9, 0xb4bcb610, 0xb07daba7, 0xae3afba2, 0xaafbe615, 0xa7b8c0cc, 0xa379dd7b,
0x9b3660c6, 0x9ff77d71, 0x92b45ba8, 0x9675461f, 0x8832161a, 0x8cf30bad, 0x81b02d74, 0x857130c3,
0x5d8a9099, 0x594b8d2e, 0x5408abf7, 0x50c9b640, 0x4e8ee645, 0x4a4ffbf2, 0x470cdd2b, 0x43cdc09c,
0x7b827d21, 0x7f436096, 0x7200464f, 0x76c15bf8, 0x68860bfd, 0x6c47164a, 0x61043093, 0x65c52d24,
0x119b4be9, 0x155a565e, 0x18197087, 0x1cd86d30, 0x029f3d35, 0x065e2082, 0x0b1d065b, 0x0fdc1bec,
0x3793a651, 0x3352bbe6, 0x3e119d3f, 0x3ad08088, 0x2497d08d, 0x2056cd3a, 0x2d15ebe3, 0x29d4f654,
0xc5a92679, 0xc1683bce, 0xcc2b1d17, 0xc8ea00a0, 0xd6ad50a5, 0xd26c4d12, 0xdf2f6bcb, 0xdbee767c,
0xe3a1cbc1, 0xe760d676, 0xea23f0af, 0xeee2ed18, 0xf0a5bd1d, 0xf464a0aa, 0xf9278673, 0xfde69bc4,
0x89b8fd09, 0x8d79e0be, 0x803ac667, 0x84fbdbd0, 0x9abc8bd5, 0x9e7d9662, 0x933eb0bb, 0x97ffad0c,
0xafb010b1, 0xab710d06, 0xa6322bdf, 0xa2f33668, 0xbcb4666d, 0xb8757bda, 0xb5365d03, 0xb1f740b4
};
public static readonly string Name = "CRC-32/MPEG-2";
public static uint Compute(byte[] buffer)
{
if (buffer == null)
{
throw new ArgumentException("参数异常，请检查调用方");
}
return Compute(buffer, 0, buffer.Length);
}
public static uint Compute(byte[] buffer, int offset, int length)
{
if (!((buffer != null) && (offset >= 0) && (length >= 0) && (offset <= buffer.Length - length)))
{
throw new ArgumentException("参数异常，请检查调用方");
}
//寄存器初始值
uint crc32= 0xffffffffU;
//输出反转处理：32是crc校验的宽度
int ToRight = 32 - 8;
ToRight = ToRight < 0 ? 0 : ToRight;
while (--length >= 0)
{
//查表运算（取决于宽度和输出是否反转）
crc32 = crcTable[((crc32 >> ToRight) ^ buffer[offset++]) & 0xFF] ^ (crc32 << 8);
}
//结果异或处理
crc32 ^= 0x00000000U;
return crc32;
}
}
测试如下：
byte[] data = new byte[] { 0x31, 0x32, 0x33, 0x34,0x35,0x36,0x37,0x38,0x39 };
uint crc32 = Crc32.Compute(data);
byte[] crc32Ary = BitConverter.GetBytes(crc32);
string crc32Str = "";
for (int i = crc32Ary.Length-1; i >=0; i--)
{
crc32Str += crc32Ary[i].ToString("X2");
}
Console.WriteLine(crc32Str);
Console.ReadLine();
测试结果：
0376E6E7
表生成算法
static UInt64[] PrecomputationTable = new UInt64[256];
static void CreateCrcTable(string Name,Int32 width, UInt64 polynomial, UInt64 initial, Boolean isInputReflected, Boolean isOutputReflected, UInt64 outputXor)
{
if (width < 8 || width > 64) { throw new ArgumentOutOfRangeException("width", "必须是8的倍数，并且介于8和64之间。"); }
for (var i = 0; i < PrecomputationTable.Length; i++) {
var r = (UInt64) i;
if (isInputReflected) {
r = ReverseBits(r, width);
} else if (width > 8) {
r <<= width - 8;
}
var lastBit = 1ul << (width - 1);
for (var j = 0; j < 8; j++) {
if ((r & lastBit) != 0) {
r = (r << 1) ^ polynomial;
} else {
r <<= 1;
}
}
if (isInputReflected) {
r = ReverseBits(r, width);
}
PrecomputationTable[i] = r;
}
//打印表
StringBuilder sbr = new StringBuilder();
sbr.Append(Name);
sbr.AppendLine("的表如下：");
for (int i = 0; i < PrecomputationTable.Length; i++)
{
if (i % 5 == 0) sbr.AppendLine();
sbr.Append("0x");
sbr.Append(string.Format("{0:x}", PrecomputationTable[i]).PadLeft(16,'0').Substring(16-width/4,width/4));
sbr.Append(",");
}
string tab = sbr.ToString();
Console.WriteLine(tab);
Console.ReadLine();
}
static UInt64 ReverseBits(UInt64 value, Int32 valueLength)
{
UInt64 output = 0;
for (var i = valueLength - 1; i >= 0; i--)
{
output |= (value & 1) << i;
value >>= 1;
}
return output;
}
测试如下：
//CreateCrcTable("CRC-32", 32, 0x04C11DB7, 0xFFFFFFFF, true, true, 0xFFFFFFFF);
//CreateCrcTable("CRC-32/MPEG-2", 32, 0x04C11DB7, 0xFFFFFFFF, false, false, 0x00000000);
//CreateCrcTable("CRC-16/XMODEM", 16, 0x1021, 0x0, false, false, 0x0);
CreateCrcTable("CRC-16/USB", 16, 0x8005, 0xffff, true, true, 0xffff);
参考资料
CRC（循环冗余校验）在线计算——ip33.com
Crc32Helper——.NET源码
crc——github