CRC8 algorithm clarifications

Question

I have stumbled upon this implementation of 8 bit CRC: https://stackoverflow.com/a/15171925/243827

Can someone shed some light on how that table was obtained ? I have uncommented the crc8_slow function and tried feeding it with

  byte crc;
  byte data[1] = {0x01};
  crc = crc8_slow(0, data, sizeof(data)/sizeof(byte));
  printf("0x%.2X", crc);

for POLY defined to 4d, d4, a6 or b2. I can't seem to reproduce the value from that table. Also, how do I need to modify that code for a non 0xff initial value of the shift register ?

EDIT1:

#define POLY              0xB2

byte crc;
byte data[1] = {0x80};
crc = crc8_slow(0, data, sizeof(data)/sizeof(byte));
printf("0x%.2X", crc);

byte crc8_slow(byte crc, byte *data, size_t len)
{
    byte *end;

    if (len == 0)
        return crc;

//    crc ^= 0xff;
    end = data + len;

    do {
        crc ^= *data++;
        crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
        crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
        crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
        crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
        crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
        crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
        crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
        crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
    } while (data < end);

//    return crc ^ 0xff;
    return crc;
}

Yields 0x01 when ran. I am on an Atmega 8 bits should it matter.

Answer 1

Poly is 0x14D reversed, then shifted right 1 bit to get 0xB2. The crc is bit reflected, which uses right shifts instead of left shifts.

101001101      0x14d
101100101      0x14d bit reversed = 0x165
 10110010      0x14d bit reversed >> 1 = 0xB2

If you look at crc8_table[0x80], you'll see a 0xB2. Each row is 12 bytes long, and since index 0x80 is decimal 128, look at the 10th row starting with 0x1d, and look at byte 8 (first byte of that row is 120), to see the 0xB2.

I tested this code and it prints a 0xB2:

#include <stdio.h>
typedef unsigned char byte;
#define POLY              0xB2

// prototype
byte crc8_slow(byte crc, byte *data, size_t len);

int main(){
    byte crc;
    byte data[1] = {0x80};
    crc = crc8_slow(0, data, sizeof(data)/sizeof(byte));
    printf("0x%.2X", crc);
    return 0;
}

byte crc8_slow(byte crc, byte *data, size_t len)
{
    byte *end;
    if (len == 0)
        return crc;
//  crc ^= 0xff;
    end = data + len;
    do {
        crc ^= *data++;
        crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
        crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
        crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
        crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
        crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
        crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
        crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
        crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
    } while (data < end);
//  return crc ^ 0xff;
    return crc;
}