Calculating 16-bit CRCs (CRC-16)
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I have put all my work together here so other people can use it.

CRC8 is BBC BASIC test code with BASIC, 6502, Z80 and ARM code.

'C' code

BBC BASIC

6502

Z80

6809

PDP-11

32-bit 80x86

32016

ARM

Sample calling code

Multiple passes over data can be made, for instance, as an input file is copied to an output file. The following code demonstrates how to do this, copying from an open file on in% to an open file on out%, calculating a CRC-16 as it goes. 
REM mem%=buffer
REM max%=size of buffer
S%=0                             :REM CRC starts as &0000
REPEAT
  num%=EXT#in%-PTR#in%           :REM Number of bytes to transfer
  IF num%>max% THEN num%=max%    :REM If more than size of buffer max%, use max%
  PROCgbpb(rd%,in%,mem%,num%,0)  :REM Read block of data
  PROCcrc                        :REM Update CRC
  PROCgbpb(wr%,out%,mem%,num%,0) :REM Write block of data
UNTIL PTR#in%=EXT#in%            :REM Loop until all done
The CRC is calculated with one of the following subroutines:
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Last update: 07-Jan-2013