Re: Block-level CRC checks

Brian Hurt wrote:
> Paul Schlie wrote:
>>
>> ... if that doesn't fix
>> the problem, assume a single bit error, and iteratively flip
>> single bits until the check sum matches ...
> This can actually be done much faster, if you're doing a CRC checksum 
> (aka modulo over GF(2^n)). Basically, an error flipping bit n will 
> always create the same xor between the computed CRC and the stored 
> CRC. So you can just store a table- for all n, an error in bit n will 
> create an xor of this value, sort the table in order of xor values, 
> and then you can do a binary search on the table, and get exactly what 
> bit was wrong.
>
> This is actually probably fairly safe- for an 8K page, there are only 
> 65536 possible bit positions. Assuming a 32-bit CRC, that means that 
> larger corrupts are much more likely to hit one of the other 
> 4,294,901,760 (2^32 - 2^16) CRC values- 99.998% likely, in fact.
>

Actually, I think I'm going to take this back. Thinking about it, the 
table is going to be large-ish (~512K) and it assumes a fixed 8K page 
size. I think a better solution would be a tight loop, something like:
r = 1u;
for (i = 0; i < max_bits_per_page; ++i) {
if (r == xor_difference) {
return i;
} else if ((r & 1u) == 1u) {
r = (r >> 1) ^ CRC_POLY;
} else {
r >>= 1;
}
}

Brian