A CRC is a Cyclic Redundancy Check. It is a little piece of data typically added at the end of a packet and used to check with an high reliability that no unintended error occurred during transmission (or storage). The math to do the computation and the check of a CRC is not very complicated and can be explained to anybody who knows how to do a long division. The polynomial for the SMBus PEC CRC-8 is x**8+x**2+x**1+1 -- this is a polynomial in GF(2), but you don't really have to understand that part to be able to use CRCs in practice. It corresponds to the binary number 100000111, to be used in a particular way. The following text explains it better than I could: http://www.ross.net/crc/download/cr...
I made my own SMBus PEC CRC-8 test vectors (attached to this post). The format is one test vector per line, like:
616263 is the 3-byte message in hexadecimal ("abc" in ASCII). The resulting one byte CRC-8 in hex is 5F.
The test vectors are checked with an official Java applet from smbus.org. They include at the beginning the result for each one byte packet, which is also the table for the fast byte based implementation: CRC = table[CRC \^ byte] (because the initial value to use for CRC is zero), On the MSP430, this implementation should run in something like 9 cycles per byte when dropped in the right place. (xor CRC, Rm /* 3 cycles */; mov table[Rm], CRC; /* 6 cycles */)