Documentation.SBV.Examples.CodeGeneration.CRC_USB5

Computing the CRC symbolically, using the USB polynomial. We also generating C code for it as well. This example demonstrates the use of the crcBV function, along with how CRC's can be computed mathematically using polynomial division. While the results are the same (i.e., proven equivalent, see crcGood below), the internal CRC implementation generates much better code, compare cg1 vs cg2 below.

The USB polynomial

usb5 :: SWord16

The USB CRC polynomial: x^5 + x^2 + 1. Although this polynomial needs just 6 bits to represent (5 if higher order bit is implicitly assumed to be set), we'll simply use a 16 bit number for its representation to keep things simple for code generation purposes.

Computing CRCs

crcUSB :: SWord16 -> SWord16

Given an 11 bit message, compute the CRC of it using the USB polynomial, which is 5 bits, and then append it to the msg to get a 16-bit word. Again, the incoming 11-bits is represented as a 16-bit word, with 5 highest bits essentially ignored for input purposes.

crcUSB' :: SWord16 -> SWord16

Alternate method for computing the CRC, mathematically. We shift the number to the left by 5, and then compute the remainder from the polynomial division by the USB polynomial. The result is then appended to the end of the message.

Correctness

crcGood :: IO ThmResult

Prove that the custom crcBV function is equivalent to the mathematical definition of CRC's for 11 bit messages. We have:

>>> crcGood
Q.E.D.

Code generation

cg1 :: IO ()

Generate a C function to compute the USB CRC, using the internal CRC function.

cg2 :: IO ()

Generate a C function to compute the USB CRC, using the mathematical definition of the CRCs. While this version generates functionally equivalent C code, it's less efficient; it has about 30% more code. So, the above version is preferable for code generation purposes.