# JCL Help:MathRoutines.CRC

# JCL Help: CRC

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## Summary

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## Description

The CRC method used here is a quite "native" translation of a hardware CRC generator to software. The data array is interpreted as a bit stream with Byte 0 Bit 7 sent first. Mathematically when calculating an m-Bit CRC on a n Byte data-array, this is like calculating the "modulus" of an an 8*n + m Bit word, Byte 0 bit 7 of the array being the most significant Bit, m Zero Bits added to the end of the array. To check the CRC the Zero Bits are replaced by the CRC to be checked, thus the CRC forming the low order bits of the 8*n + m Bit word. If the CRC is correct the result of this operation is Zero, otherwise it's the "syndrome" that can be used to calculate the order of the false bit to correct it. The software comes with the CRC calculating function in two kinds. A "basic" one that works bitwise, like a hardware CRC generator would do and a fast one that uses a lookup table for complete bytes. The bitwise function can be used to calculate the table. So this kind of CRC calculating offers some specialities:

- The table based operation creates the same result as the bitwise calculation.
- The table is reproduced by calculating the CRC of a single byte, using the starting value Zero.
- The CRC check immediately creates the syndrome.Beware, that the results of different CRC software algorithms might be different even if the same Polynomial and starting value is used. The algorithm might use another order of bits in the byte stream to be checked or another order of bits in the calculated CRC-value. Moreover the input and/or output bits might be used inverted and as the CRC-result the contents of the shift register after 8*n shifts might be used instead shifting the m bits out through the generator the additional m steps as done here. E.g. as far as I know the CRC result used by "ZIP" is our CRC32 result xor $FFFFFFFF.

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