>From the admirably readable "The Math" page, I quote: << GIMPS double-checking goes a bit further to guard against programming errors. Prior to starting the Lucas-Lehmer test, the S0 value is left-shifted by a random amount. Each squaring just doubles how much we have shifted the S value. Note that the mod 2P-1 step merely rotates the p-th bits and above to the least significant bits, so there is no loss of information. Why do we go to this trouble? If there were a bug in the FFT code, then the shifting of the S values ensures that the FFTs in the first primality test are dealing with completely different data than the FFTs in the second primality test. It would be near impossible for a programming bug to produce the same final 64 bit residues. >>
I am wrestling to understand why this shifting works, assuming it doesn't require understanding of the FFT. Can anyone help? David _________________________________________________________________ Be one of the first to try Windows Live Mail. http://ideas.live.com/programpage.aspx?versionId=5d21c51a-b161-4314-9b0e-4911fb2b2e6d _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
