is the next mersenne prime Ever going to be found? Any probability time frame?
On Feb 3, 2008 9:00 PM, <[EMAIL PROTECTED]> wrote: > Send Prime mailing list submissions to > [email protected] > > To subscribe or unsubscribe via the World Wide Web, visit > http://hogranch.com/mailman/listinfo/prime > or, via email, send a message with subject or body 'help' to > [EMAIL PROTECTED] > > You can reach the person managing the list at > [EMAIL PROTECTED] > > When replying, please edit your Subject line so it is more specific > than "Re: Contents of Prime digest..." > > > Today's Topics: > > 1. twiddle factor computation error: cos(PI / (2^n)) (Paul Charlton) > 2. Re: twiddle factor computation error: cos(PI / (2^n)) > (Steinar H. Gunderson) > > > ---------------------------------------------------------------------- > > Message: 1 > Date: Sun, 3 Feb 2008 09:33:55 -0800 > From: "Paul Charlton" <[EMAIL PROTECTED]> > Subject: [Prime] twiddle factor computation error: cos(PI / (2^n)) > To: "'The Great Internet Mersenne Prime Search list'" > <[email protected]> > Message-ID: <[EMAIL PROTECTED]> > Content-Type: text/plain; charset="US-ASCII" > > Can anyone point to cogent analysis of the representational error in > twiddle > factors due to cos(PI / 2^N) ? > > > > ie: representational error = cos(PI/2^N) - CPU_representation( cos(PI/2^N) > ) > > > > For example, when represented as single-precision FP, cos(PI / 2^N) only > has > 5 or 6 significant bits when N=20, and drops to 3 significant bits when > N=22. Clearly the problem is less acute with double-precision, since at > N=20, there will still be 37 significant bits in "cos" > > > > It seems that the representational error would create a phase error in the > transform, and make accurate convolution increasingly difficult in > proportion to N. > > > > looking forward to your insights, > > > > Paul > > > > > > > > ------------------------------ > > Message: 2 > Date: Sun, 3 Feb 2008 18:57:32 +0100 > From: "Steinar H. Gunderson" <[EMAIL PROTECTED]> > Subject: Re: [Prime] twiddle factor computation error: cos(PI / > (2^n)) > To: [email protected] > Message-ID: <[EMAIL PROTECTED]> > Content-Type: text/plain; charset=utf-8 > > On Sun, Feb 03, 2008 at 09:33:55AM -0800, Paul Charlton wrote: > > Can anyone point to cogent analysis of the representational error in > twiddle > > factors due to cos(PI / 2^N) ? > > The only paper I've seen regarding twiddle factor accuracy's influence on > the > FFT is > > James C. Schatzman. Accuracy of the discrete Fourier transform and the > fast Fourier transform. SIAM Journal on Scientific Computing, > 17(5):1150?1166, 1996. > > IIRC it's a bit hard to find online, though, and it was mostly > experimental. > > /* Steinar */ > -- > Homepage: http://www.sesse.net/ > > > ------------------------------ > > _______________________________________________ > Prime mailing list > [email protected] > http://hogranch.com/mailman/listinfo/prime > > > End of Prime Digest, Vol 43, Issue 1 > ************************************ > _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
