CRC-16-CCITT

 

 

 

CRC-16-CCITT의 다항식(Polynomial)은 아래와 같다. XMODEM, YMODEM 등에 쓰이는 방식이다.

 

 

 

이 다항식의 16진수 표현

표준 노멀 는 0x1021이며, 리버스 폴리는 0x8408이다. RefIn = false, RefOut = false 조건으로 대부분의 SW 구현에서 노멀 폴리인 0x1021을 사용한다.

 

 

 

 

 

 

CRC-16-CCITT 함수

 

uint16_t crc16_ccitt(const uint8_t* data, size_t length) {
	uint16_t crc = 0x0000;

	while (length--) {
		crc ^= (*data++) << 8;

		for (int i = 0; i < 8; ++i) {
			if (crc & 0x8000)
				crc = (crc << 1) ^ 0x1021;
			else
				crc <<= 1;
		}
	}
	return crc;
}

 

CRC-16-CCITT (XMODEM) 표준의 초기값인 SEED는 0x0000이고 Final XOR도 0x0000이다.

 

 

 

 

 

 

문자열 "123456789"의 CRC-16-CCITT 결과는 0x31C3이다.

 

int main() {
	uint8_t test_data[] = "123456789";

	uint16_t result = crc16_ccitt(test_data, 9);

	printf("CRC-16-CCITT: 0x%04X\n", result);

	return 0;
}

 

 

 

 

 

 

 

 

 

 

 

좀 더 빠르게 CRC-16-CCITT 계산하는 방법

 

룩업 테이블을 사용하는 방식이다.

static const uint16_t crc16_table[256] = {
    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
};

unsigned short Cal_CRC16(unsigned short crc_accum, unsigned char* data_blk_ptr, unsigned short data_blk_size)
{
    unsigned short i, j;

    for (j = 0; j < data_blk_size; j++)
    {
        i = ((unsigned short)(crc_accum >> 8) ^ data_blk_ptr[j]) & 0xFF;
        crc_accum = (crc_accum << 8) ^ crc16_table[i];
    }

    return crc_accum;
}

 

 

 

 

0x01020304의 CRC-16-CCITT 결과는 0x0D03이다.

int main(void)
{
    uint8_t data[] = { 0x01, 0x02, 0x03, 0x04 };

    printf("0x%04X\n", Cal_CRC16(0, data, sizeof(data)));
    return 0;
}