Hardware, FFT limits and round off errors

Recently when I was assigned a new exponent; Prime95 wrote the following:

Trying 1000 iterations for exponent 15088631 using 768K FFT. If average roundoff error is above 0.24179, then a larger FFT will be used.

After 1000 iterations the average roundoff error was 0.24572, so Prime95 decided to use 896K FFT.

My question: Is the roundoff error specific to my CPU? If I had a "better" CPU could the round off error have been different? I have an Intel P4. If different CPU's would have different round off errors, what aspect of the CPU architecture makes one better (or worse) than another? Is there likely to be a difference even among different Intel P4 CPU's?

Thanks for considering my gee-whiz question!

[JHagerson]

The round-off error relates to the specific exponent and the characteristics of the Floating Point Unit (FPU) in your processor. In the past, Prime95 used "hard" transition points between the various sizes of the Fast-Fourier Transform (FFT) used to implement the Lucas-Lehmer (LL) prime checking algorithm. Now, Prime95 uses "soft" transition points; it tries the smaller FFT and checks the size of the round-off error. The smaller FFT is preferred because it would run faster. However, if the error during an LL test ever exceeds 0.4, it must be addressed and Prime95 will then back up to a checkpoint and redo work. On your machine, the error from the test of 1000 iterations of the smaller FFT had an accumulated error that was considered too big, so Prime95 is using the bigger FFT.

You can see the crossover points for the processors that do and don't support SSE2 instructions on http://www.mersenne.org/bench. (To find out if your processor supports SSE2, choose CPU from the Prime95 Options menu and look to see if SSE2 is listed on the CPU Features line in the CPU Information box.) It looks to me like your processor supports SSE2 because the cross-over for those machines is near M15.07M (look in the column headers of the upper table) and the exponent you are testing is M15.088M.

I hope that this is helpful. Welcome to the wonderful world of GIMPS!

[cheesehead]

Originally Posted by ewergela

My question: Is the roundoff error specific to my CPU?

Roundoff error could be affected by several things besides the CPU -- memory, motherboard, voltage regulators, RAM timings, overclocking ... Plus, different numbers going into the start of the test sequence will produce different roundoff errors at the end of the sequence even when all hardware is the same. Also, internal heating or circuit design might cause some component to produce an incorrect bit just once in a while.

If I had a "better" CPU could the round off error have been different?

Yes, it is possible that one CPU model could have a design that tended to produce fewer roundoff errors than another model. OTOH one CPU might be "better" than another same-model CPU that came off the assembly line right behind it.

Is there likely to be a difference even among different Intel P4 CPU's?

Manufacturers find that some CPUs run stabler than other identically-designed CPUs cut from the very same silicon wafer!

However, the influence of all the non-CPU factors I listed would often be more important than just the difference between CPUs or between CPU models or between manufacturers.

I have an Intel P4. If different CPU's would have different round off errors, what aspect of the CPU architecture makes one better (or worse) than another?

Quality of design and production: glitches on the wafers, enough spacing between circuits to minimize interference. Lots of little things.

A good Intel P4 is a good Intel P4. A good AMD XP+ is a good AMD XP+. A good Mac is a good Mac.

But a Big Mac has lots and lots of calories.

[lycorn]

Originally Posted by cheesehead

But a Big Mac has lots and lots of calories.

That fits well at the end of your 1000th post!
Here´s to cheesehead:

[cheesehead]

Thank you, lycorn!

(However, the number of posts shown at left is dynamically changed by forum software to display the current total on all of an individual's posts. So you'll see the same total number at the left of every posting ever made by that individual. My actual 1000th post was in "The Happy Me thread" in the Lounge subforum.)

[lycorn]

You´re right. I know it works that way. I just happened to read this thread before reading your post in the "Happy me", and assumed this was *the* 1000th post (why not, after all?). Anyway, the banana is still well deserved

[cheesehead]

... and I wish I had just enjoyed your banana without being picky.

Bananas go very well with cheese.

[moo]

Originally Posted by cheesehead

... and I wish I had just enjoyed your banana without being picky.

Bananas go very well with cheese.

Do they never knew that lets throw some fire to melt the chees over bananas...
CLICK HERE FOR FIRE ;)

[cheesehead]

Originally Posted by moo

Do they never knew that lets throw some fire to melt the chees over bananas...
CLICK HERE FOR FIRE ;)

moo, there's a difference between melt and dissociate into a radioactive plasma ...

It would be incinerated around the blast area.