Max FFT Size? - Page 2

aketilander · 2012-04-22, 21:46

Quote:

Originally Posted by Prime95

It is trivial to add AVX FFT lengths up to 50M and SSE2 FFT lengths up to 100M, but why bother?

Well, if its trivial (that is not requiering too much work) I would, for one, humbly ask for it.

Prime95 · 2012-04-22, 22:25

Quote:

Originally Posted by aketilander

then I may try to LL (with double check) M595999993 .

In v27.6 max exponent is down to 595.8M. However, I think if you specify the FFT length to use in worktodo.txt, then the larger exponent might be accepted.

Uncwilly · 2012-04-22, 22:29

Quote:

Originally Posted by aketilander

IF (a very big IF) I can do it it would be nice to try to LL a billion digit exponent (would require almost 6 times as much work as the 596M exponent that is 91,630 GHz-Days*2).

That would take an FFT size of 182,643K.

cheesehead · 2012-04-23, 00:34

Quote:

Originally Posted by Dubslow

The FFT table can be found in mult.asm, though when I attempted to read it, ...well, I couldn't. (Also, wouldn't 4M be 4096K?)

When I look up something in the prime95 source code, I usually wind up at commonb.c, commonc.c, ecm.c or mult.asm, so I put those on my speed-dial. :-)

retina · 2012-04-23, 04:45

Quote:

Originally Posted by aketilander

Question 1: Is the limit of the FFT sizes to 32M due to hardware/software limitations? Or is it just because George have not yet written FFTs for larger sizes (due to obvious reasons)?

Here is a table I posted previously. The numbers don't precisely match that of P95 but it will give you an idea of how much more we could squeeze out of the current double FP number hardware. If you need a reference point you can see that 2^25 (32M) FFT length for DP is 436207629 (~436M) exponent in that table and P95 does 596M so the numbers there can probably be taken as a bit higher if there is ever a time that P95 needs an upgrade for larger FFTs.

axn · 2012-04-23, 13:38

Quote:

Originally Posted by aketilander

IF (a very big IF) I can do it it would be nice to try to LL a billion digit exponent (would require almost 6 times as much work as the 596M exponent that is 91,630 GHz-Days*2).

A billion digit exponent (p ~ 3.3e9) would take 40 times as much time as a 600M exponent -- not 6 times.

aketilander · 2012-04-23, 16:05

Quote:

Originally Posted by axn

A billion digit exponent (p ~ 3.3e9) would take 40 times as much time as a 600M exponent -- not 6 times.

OK I got the figures for the number of GHz-Days from Mersenne aries http://mersenne-aries.sili.net

Exponent Iterationtime GHz-Days according to Mersenne aries
M345678877 31.8 ms. 5,450
M595999993 57.0 ms. 16,440
M3321928171 don't know 91,630

If I first compare the work needed to complete M595999993 in relation to M345678877:
To be more exact if I divide 16440/5450 = 3.02
If I use the interationtime instead I get 3.09

Concerning the billion digit exponent M3321928171 I cannot do a practical test to get an estimation of the iteration time, but my guess was that I could use the number of GHz-Days needed to get a rough estimation of the time needed for a LL-test of that expo.

Thinking about it 91630 GHz-Days seems to be very little. Already the exponent is 5.6 times as large as 595999993, that is it would requrie 5.6 times as many iterations. A LL-test would use a FFT size of 183M instead of 32M, that is 5.7 times as large FFTs. 5.6*5.7 = 32

Maybe, James, the calculator on Mersenne aries is wrong?

James Heinrich · 2012-04-23, 17:21

Quote:

Originally Posted by aketilander

Maybe, James, the calculator on Mersenne aries is wrong?

Above 596M yes, it is wrong. For larger exponents I have (or rather, George's code has) no timing data on which to base the credit, and I make no effort to extrapolate FFT sizes and timings, I just return a value based on the assumption that the 32M FFT can be used indefinitely, which of course isn't correct.

aketilander · 2012-04-23, 18:15

Well, so it is surely still without reach to LL-test a billion digit exponent, but we are down to something like 35 years and that's not too bad.

davieddy · 2012-04-24, 02:05

Quote:

Originally Posted by firejuggler

As I understand it, George didn't go beyond 32M because of the non-nessecity-in-my-lifetime prospect. but i could be wrong.

Andre Previn: "You're playing the wrong notes".
Eric Morecambe: "No. I'm playing the right notes,
but not necessarily in the right order".

http://www.youtube.com/watch?v=R7GeKLE0x3s

Xyzzy · 2012-04-24, 03:31

Too many notes!

2012-04-23, 18:15	#20
aketilander "Åke Tilander" Apr 2011 Sandviken, Sweden 2·283 Posts	LL-testing a billion digit exponent Well, so it is surely still without reach to LL-test a billion digit exponent, but we are down to something like 35 years and that's not too bad.

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Force FFT-size to be used	kruoli	Software	4	2017-11-17 18:14
Pi(x) value for x at 10^16 size	edorajh	Computer Science & Computational Number Theory	6	2017-03-08 20:28
Size optimization	Sleepy	Msieve	14	2011-10-20 10:27
Exponent Size Gap	Mini-Geek	PrimeNet	8	2007-03-25 07:29
FFT-Size	andi314	Lounge	14	2007-01-22 00:21

2012-04-24, 03:31	#22
Xyzzy "Mike" Aug 2002 202A₁₆ Posts	Too many notes!