在嵌入式開發中，經常使用到CRC校驗算法，用于校驗通信數據和存儲器數據。之前只是使用，對CRC原理及各種CRC算法的區別并無研究。參考網絡上各位大神的文章和資料，從嵌入式軟件開發的角度學習了下CRC校驗算法，作個總結記錄。
參考資料：
CRC校驗手算及直觀演示

一、簡介

循環冗余校驗(Cyclic Redundancy Check, CRC)，是數據通信中最常采用的一種數據校驗方式。與其他校驗算法（如累加和校驗）相似，CRC校驗也是根據原始數據計算出特定的校驗值作為冗余碼附加在原始數據后用于數據差錯校驗。不同的是CRC使用模2運算（所謂模2運算，就是數據除2去余數）的方法，根據校驗數據計算出校驗碼。

CRC校驗可以理解為就是一個p位二進制數據序列后附加一個r位二進制校驗碼，從而構成一個總長為n = p + r位的二進制序列。CRC校驗就是使用多項式模2運算：按異或運算，即相同為0，不同為1，可以簡單理解為不考慮進位和借位的二進制加減運算，校驗數據的二進制數據流作為多項式的系數，而多項式系數作為除數，而運算后的余數作為校驗碼。

以CRC7-MMC算法(初值為0x00，多項式為X⁸ X³ + X⁰)為例，CRC校驗計算數據“0x11 0x22 0x33 0x44 0x55 0x66 0x77 0x88”過程如下所示：

// 在計算前，要在數據流前添加初值，數據流后要根據結果CRC的BIT數擴展相應比特個0。 000000000010001001000100011001101000100010101010110011001110111100010000000000100010010000000000010001100110100010001010101011001100111011110001000000000010001001000001011101000100010101010110011001110111100010000000000100010010011001100100010101010110011001110111100010000000000100010010100010110001010101011001100111011110001000000000010001001000000100001010101011001100111011110001000000000010001001000011000101011001100111011110001000000000010001001010011000110011001110111100010000000000100010010001000111001100111011110001000000000010001001000001110110011101111000100000000001000100101100101111011110001000000000010001001010000101101111000100000000001000100100001100101111000100000000001000100101000010110001000000000010001001000011001000100000000001000100101000001100000000001000100100001010000000000010001001001010010000001000100100101101000010001001001111010010001001

由上計算過程可知，數據“0x11 0x22 0x33 0x44 0x55 0x66 0x77 0x88”的CRC-MMC校驗的計算結果為：0x7D。

二、不同的CRC校驗算法

CRC校驗算法，根據校驗結果的位數，可以分為CRC-4，CRC-7，CRC-8，CRC-16，CRC-32，CRC-64等算法；根據CRC計算的多項式、初值、輸入是否反轉、輸出是否反轉、輸出異或值，又可以分為多種算法，如：CRC-16/CCITT，CRC-16/IBM。相同寬度的CRC算法，初值，多項式等信息不同，其校驗的碰撞幾率也不會不同（通俗的講，就是校驗結果的可靠性，CRC校驗算法，存在一定的幾率會出現校驗數據不同，但校驗結果相同的情況）。不同CRC校驗算法模型的碰撞幾率可以參考相關理論研究及論文。嵌入式中常用CRC校驗算法模型有：

NameWidthPolyInitRefInRefOutXorOutNote

CRC-16	16	0x8005	0x0000	True	True	0x0000
CRC-16/CCITT	16	0x1021	0x0000	True	True	0x0000
CRC-16/CCITT-FALSE	16	0x1021	0x0000	False	False	0x0000

三、CRC校驗算法代碼實現

在嵌入式應用中，實現CRC校驗算法有多種方式。在部分硬件平臺上，存在硬件CRC模塊，因此可以使用硬件CRC算法。硬件無法提供CRC計算的平臺，也可以根據CRC原理，使用軟件實現CRC算法。便于理解CRC原理，可以使用直接法實現CRC算法。而在實際應用，為提高CRC計算速度，通常使用查表法實現CRC算法。

1、直接計算法

實現算法參考網絡相關代碼，進行整理并驗證，可直接使用，存在一些細節還沒想通（如CRC4、5、6、7的計算方法），有興趣的可以一起討論下。

crc.c

#include "crc.h" #include <stdio.h>typedef enum {REF_4BIT = 4,REF_5BIT = 5,REF_6BIT = 6,REF_7BIT = 7,REF_8BIT = 8,REF_16BIT = 16,REF_24BIT = 24,REF_32BIT = 32 }REFLECTED_MODE;uint32_t ReflectedData(uint32_t data, REFLECTED_MODE mode) {data = ((data & 0xffff0000) >> 16) | ((data & 0x0000ffff) << 16);data = ((data & 0xff00ff00) >> 8) | ((data & 0x00ff00ff) << 8);data = ((data & 0xf0f0f0f0) >> 4) | ((data & 0x0f0f0f0f) << 4);data = ((data & 0xcccccccc) >> 2) | ((data & 0x33333333) << 2);data = ((data & 0xaaaaaaaa) >> 1) | ((data & 0x55555555) << 1);switch (mode){case REF_32BIT:return data;case REF_24BIT:return (data >> 8) & 0xffffff;case REF_16BIT:return (data >> 16) & 0xffff;case REF_8BIT:return (data >> 24) & 0xff;case REF_7BIT:return (data >> 25) & 0x7f;case REF_6BIT:return (data >> 26) & 0x7f;case REF_5BIT:return (data >> 27) & 0x1f;case REF_4BIT:return (data >> 28) & 0x0f;}return 0; }uint8_t CheckCrc4(uint8_t poly, uint8_t init, bool refIn, bool refOut, uint8_t xorOut,const uint8_t *buffer, uint32_t length) {uint8_t i;uint8_t crc;if (refIn == true){crc = init;poly = ReflectedData(poly, REF_4BIT);while (length--){crc ^= *buffer++;for (i = 0; i < 8; i++){if (crc & 0x01){crc >>= 1;crc ^= poly;}else{crc >>= 1;}}}return crc ^ xorOut;}else{crc = init << 4;poly <<= 4;while (length--){crc ^= *buffer++;for (i = 0; i < 8; i++){if (crc & 0x80){crc <<= 1;crc ^= poly;}else{crc <<= 1;}}}return (crc >> 4) ^ xorOut;} }uint8_t CheckCrc5(uint8_t poly, uint8_t init, bool refIn, bool refOut, uint8_t xorOut,const uint8_t *buffer, uint32_t length) {uint8_t i;uint8_t crc;if (refIn == true){crc = init;poly = ReflectedData(poly, REF_5BIT);while (length--){crc ^= *buffer++;for (i = 0; i < 8; i++){if (crc & 0x01){crc >>= 1;crc ^= poly;}else{crc >>= 1;}}}return crc ^ xorOut;}else{crc = init << 3;poly <<= 3;while (length--){crc ^= *buffer++;for (i = 0; i < 8; i++){if (crc & 0x80){crc <<= 1;crc ^= poly;}else{crc <<= 1;}}}return (crc >> 3) ^ xorOut;} }uint8_t CheckCrc6(uint8_t poly, uint8_t init, bool refIn, bool refOut, uint8_t xorOut,const uint8_t *buffer, uint32_t length) {uint8_t i;uint8_t crc;if (refIn == true){crc = init;poly = ReflectedData(poly, REF_6BIT);while (length--){crc ^= *buffer++;for (i = 0; i < 8; i++){if (crc & 0x01){crc >>= 1;crc ^= poly;}else{crc >>= 1;}}}return crc ^ xorOut;}else{crc = init << 2;poly <<= 2;while (length--){crc ^= *buffer++;for (i = 0; i < 8; i++){if (crc & 0x80){crc <<= 1;crc ^= poly;}else{crc <<= 1;}}}return (crc >> 2) ^ xorOut;} }uint8_t CheckCrc7(uint8_t poly, uint8_t init, bool refIn, bool refOut, uint8_t xorOut,const uint8_t *buffer, uint32_t length) {uint8_t i;uint8_t crc;if (refIn == true){crc = init;poly = ReflectedData(poly, REF_7BIT);while (length--){crc ^= *buffer++;for (i = 0; i < 8; i++){if (crc & 0x01){crc >>= 1;crc ^= poly;}else{crc >>= 1;}}}return crc ^ xorOut;}else{crc = init << 1;poly <<= 1;while (length--){crc ^= *buffer++;for (i = 0; i < 8; i++){if (crc & 0x80){crc <<= 1;crc ^= poly;}else{crc <<= 1;}}}return (crc >> 1) ^ xorOut;} }uint8_t CheckCrc8(uint8_t poly, uint8_t init, bool refIn, bool refOut, uint8_t xorOut,const uint8_t *buffer, uint32_t length) {uint32_t i = 0;uint8_t crc = init;while (length--){if (refIn == true){crc ^= ReflectedData(*buffer++, REF_8BIT);}else{crc ^= *buffer++;}for (i = 0; i < 8; i++){if (crc & 0x80){crc <<= 1;crc ^= poly;}else{crc <<= 1;}}}if (refOut == true){crc = ReflectedData(crc, REF_8BIT);}return crc ^ xorOut; }uint16_t CheckCrc16(uint16_t poly, uint16_t init, bool refIn, bool refOut, uint16_t xorOut,const uint8_t *buffer, uint32_t length) {uint32_t i = 0;uint16_t crc = init;while (length--){if (refIn == true){crc ^= ReflectedData(*buffer++, REF_8BIT) << 8;}else{crc ^= (*buffer++) << 8;}for (i = 0; i < 8; i++){if (crc & 0x8000){crc <<= 1;crc ^= poly;}else{crc <<= 1;}}}if (refOut == true){crc = ReflectedData(crc, REF_16BIT);}return crc ^ xorOut; }uint32_t CheckCrc24(uint32_t poly, uint32_t init, bool refIn, bool refOut, uint32_t xorOut,const uint8_t *buffer, uint32_t length) {uint32_t i = 0;uint32_t crc = init;while (length--){if (refIn == true){crc ^= ReflectedData(*buffer++, REF_8BIT) << 16;}else{crc ^= (*buffer++) << 16;}for (i = 0; i < 8; i++){if (crc & 0x800000){crc <<= 1;crc ^= poly;}else{crc <<= 1;}}}if (refOut == true){crc = ReflectedData(crc, REF_24BIT);}return (crc ^ xorOut) & 0xffffff; }uint32_t CheckCrc32(uint32_t poly, uint32_t init, bool refIn, bool refOut, uint32_t xorOut,const uint8_t *buffer, uint32_t length) {uint32_t i = 0;uint32_t crc = init;while (length--){if (refIn == true){crc ^= ReflectedData(*buffer++, REF_8BIT) << 24;}else{crc ^= (*buffer++) << 24;}for (i = 0; i < 8; i++){if (crc & 0x80000000){crc <<= 1;crc ^= poly;}else{crc <<= 1;}}}if (refOut == true){crc = ReflectedData(crc, REF_32BIT);}return crc ^ xorOut; }uint32_t CrcCheck(CRC_Type crcType, const uint8_t *buffer, uint32_t length) {switch (crcType.width){case 4:return CheckCrc4(crcType.poly, crcType.init, crcType.refIn, crcType.refOut,crcType.xorOut, buffer, length);case 5:return CheckCrc5(crcType.poly, crcType.init, crcType.refIn, crcType.refOut,crcType.xorOut, buffer, length);case 6:return CheckCrc6(crcType.poly, crcType.init, crcType.refIn, crcType.refOut,crcType.xorOut, buffer, length);case 7:return CheckCrc7(crcType.poly, crcType.init, crcType.refIn, crcType.refOut,crcType.xorOut, buffer, length);case 8:return CheckCrc8(crcType.poly, crcType.init, crcType.refIn, crcType.refOut,crcType.xorOut, buffer, length);case 16:return CheckCrc16(crcType.poly, crcType.init, crcType.refIn, crcType.refOut,crcType.xorOut, buffer, length);case 24:return CheckCrc24(crcType.poly, crcType.init, crcType.refIn, crcType.refOut,crcType.xorOut, buffer, length);case 32:return CheckCrc32(crcType.poly, crcType.init, crcType.refIn, crcType.refOut,crcType.xorOut, buffer, length);}return 0; }

crc.h

#ifndef __CRC_H__ #define __CRC_H__#include <stdint.h> #include <stdbool.h>typedef struct {uint8_t width;uint32_t poly;uint32_t init;bool refIn;bool refOut;uint32_t xorOut; }CRC_Type;uint32_t CrcCheck(CRC_Type crcType, const uint8_t *buffer, uint32_t length);#endif

main.c

#include <stdio.h> #include <stdint.h> #include <stdbool.h> #include "crc.h"#define LENGTH 8 const uint8_t data[3][LENGTH] = {{ 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08 },{ 0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80 },{ 0xfe, 0xfd, 0xfb, 0xf7, 0xef, 0xdf, 0xbf, 0x7f } };typedef struct {CRC_Type crcType;uint32_t result[3]; }CRC_Test;CRC_Test crc4_ITU = { { 4, 0x03, 0x00, true, true, 0x00 }, { 0x0f, 0x0a, 0x0e } }; CRC_Test crc5_EPC = { { 5, 0x09, 0x09, false, false, 0x00 }, { 0x00, 0x0c, 0x17 } }; CRC_Test crc5_ITU = { { 5, 0x15, 0x00, true, true, 0x00 }, { 0x16, 0x0a, 0x17 } }; CRC_Test crc5_USB = { { 5, 0x05, 0x1f, true, true, 0x1f }, { 0x10, 0x09, 0x17 } }; CRC_Test crc6_ITU = { { 6, 0x03, 0x00, true, true, 0x00 }, { 0x1d, 0x30, 0x00 } }; CRC_Test crc7_MMC = { { 7, 0x09, 0x00, false, false, 0x00 }, { 0x57, 0x30, 0x5b } }; CRC_Test crc8 = { { 8, 0x07, 0x00, false, false, 0x00 }, { 0x3e, 0xe1, 0x36 } }; CRC_Test crc8_ITU = { { 8, 0x07, 0x00, false, false, 0x55 }, { 0x6b, 0xb4, 0x63 } }; CRC_Test crc8_ROHC = { { 8, 0x07, 0xff, true, true, 0x00 }, { 0x6b, 0x78, 0x93 } }; CRC_Test crc8_MAXIM = { { 8, 0x31, 0x00, true, true, 0x00 }, { 0x83, 0x60, 0xa9 } }; CRC_Test crc16_IBM = { { 16, 0x8005, 0x0000, true, true, 0x0000 }, { 0xc4f0, 0x2337, 0xa776 } }; CRC_Test crc16_MAXIM = { { 16, 0x8005, 0x0000, true, true, 0xffff }, { 0x3b0f, 0xdcc8, 0x5889 } }; CRC_Test crc16_USB = { { 16, 0x8005, 0xffff, true, true, 0xffff }, { 0x304f, 0xd788, 0x53c9 } }; CRC_Test crc16_MODBUS = { { 16, 0x8005, 0xffff, true, true, 0x0000 }, { 0xcfb0, 0x2877, 0xac36 } }; CRC_Test crc16_CCITT = { { 16, 0x1021, 0x0000, true, true, 0x0000 }, { 0xeea7, 0xfe7c, 0x7919 } }; CRC_Test crc16_CCITT_FALSE = { { 16, 0x1021, 0xffff, false, false, 0x0000 }, { 0x4792, 0x13a7, 0xb546 } }; CRC_Test crc16_X25 = { { 16, 0x1021, 0xffff, true, true, 0xffff }, { 0x6dd5, 0x7d0f, 0xfa6a } }; CRC_Test crc16_XMODEM = { { 16, 0x1021, 0x0000, false, false, 0x0000 }, { 0x76ac, 0x2299, 0x8478 } }; CRC_Test crc16_DNP = { { 16, 0x3D65, 0x0000, true, true, 0xffff }, { 0x7bda, 0x0535, 0x08c4 } }; CRC_Test crc24 = { { 24, 0x864cfb, 0x000000, false, false, 0x000000 }, { 0x4c9612, 0x352d9f, 0x1c3c32 } }; CRC_Test crc32 = { { 32, 0x04c11db7, 0xffffffff, true, true, 0xffffffff }, { 0x3fca88c5, 0xe0631a53, 0xa4051a26 } }; CRC_Test crc32_MPEG2 = { { 32, 0x4c11db7, 0xffffffff, false, false, 0x00000000 }, { 0x14dbbdd8, 0x6509b4b6, 0xcb09d294 } };void CrcTest(CRC_Test crcTest) {uint32_t i;for (i = 0; i < 3; i++){printf("%08x\t%08x\r\n", CrcCheck(crcTest.crcType, data[i], LENGTH), crcTest.result[i]);}printf("\r\n"); }int main(void) {CrcTest(crc4_ITU);CrcTest(crc5_EPC);CrcTest(crc5_ITU);CrcTest(crc5_USB);CrcTest(crc6_ITU);CrcTest(crc7_MMC);CrcTest(crc8);CrcTest(crc8_ITU);CrcTest(crc8_ROHC);CrcTest(crc8_MAXIM);CrcTest(crc16_IBM);CrcTest(crc16_MAXIM);CrcTest(crc16_USB);CrcTest(crc16_MODBUS);CrcTest(crc16_CCITT);CrcTest(crc16_CCITT_FALSE);CrcTest(crc16_X25);CrcTest(crc16_XMODEM);CrcTest(crc16_DNP);CrcTest(crc24);CrcTest(crc32);CrcTest(crc32_MPEG2);return 0; }

四、注意

• 不同的CRC算法，對00H或FFH數據流的計算結果不一樣，部分算法存在校驗結果也為00H或FFH的情況（也就意味著存儲空間處于初始化狀態時：全0或全1，CRC校驗反而是正確的），在應用中需要注意避免。
• 對數據流的CRC校驗進行檢查時，可以將原數據流和CRC校驗結果一起再做CRC校驗，若CRC校驗正確則計算結果為0。利用這個特性可簡化CRC驗證的軟件實現（對CRC校驗結果又進行異或非0的CRC算法不適用）。

總結

以上是生活随笔為你收集整理的CRC校验算法及实现的全部內容，希望文章能夠幫你解決所遇到的問題。

如果覺得生活随笔網站內容還不錯，歡迎將生活随笔推薦給好友。