CRC 实现特定的多项式。多项式与代码中使用的多项式有何关系？

Question

我有以下 CRC 函数:

#define CRC8INIT    0x00
#define CRC8POLY    0x18              //0X18 = X^8+X^5+X^4+X^0

// ----------------------------------------------------------------------------

uint8_t crc8 (uint8_t *data, uint16_t number_of_bytes_in_data)
{
    uint8_t  crc;
    uint16_t loop_count;
    uint8_t  bit_counter;
    uint8_t  b;
    uint8_t  feedback_bit;

    crc = CRC8INIT;

    for (loop_count = 0; loop_count != number_of_bytes_in_data; loop_count++) {
        b = data[loop_count];
        bit_counter = 8;

        do {
            feedback_bit = (crc ^ b) & 0x01;

            if (feedback_bit == 0x01) {
                crc = crc ^ CRC8POLY;
            }

            crc = (crc >> 1) & 0x7F;

            if (feedback_bit == 0x01) {
                crc = crc | 0x80;
            }

            b = b >> 1;
            bit_counter--;

        } while (bit_counter > 0);
    }

    return crc;
}

0x18 与多项式 X^8+X^5+X^4+X^0 有什么关系？

X^8+X^5+X^4+X^0 = 100110001

0x18 = 00011000

如果我将 CRC8POLY 定义为 0xEA(我已经看到了)，那会代表什么多项式呢？

Answer 1

How does 0x18 relate to the polynomial X^8+X^5+X^4+X^0?

由于代码是右移CRC，所以每个字节的“最高位”是bit 0而不是bit 7。poly需要从100110001反转为100011001，即0x119，右移后bit 0x119 的 0 被移出，因此可以改用 0x118。如果反馈位为 1，则代码使用第二个 if 语句 to or in (0x100) >> 1 == 0x80。作为替代方案，由于 feedback_bit 为 0 或 1，则 (0-feeback_bit) 可用作掩码 (假设对多边形的二进制补码数学)，而不是使用 if 语句。

typedef unsigned char uint8_t;
typedef unsigned short uint16_t;
#define CRC8INIT 0x00
#define CRC8POLY 0x8c   // 0x119 >> 1

uint8_t crc8 (uint8_t *data, uint16_t number_of_bytes_in_data)
{
    uint8_t  crc;
    uint16_t loop_count;
    uint8_t  bit_counter;
    uint8_t  b;
    uint8_t  feedback_bit;

    crc = CRC8INIT;

    for (loop_count = 0; loop_count != number_of_bytes_in_data; loop_count++) {
        b = data[loop_count];
        bit_counter = 8;
        do {
            feedback_bit = (crc ^ b) & 0x01;
            crc = (crc >> 1) ^ ((0-feedback_bit) & CRC8POLY);
            b = b >> 1;
            bit_counter--;
        } while (bit_counter > 0);
    }

    return crc;
}