Aaron Blosser wrote:
>>Henk Stokhorst wrote:
>>>L.S.,
>>>
>>>Just curious, what makes factoring 13.388.659 take four times as
>>>long as 13.375.793?
>>
>>It's because 13,388,659 is past the cutoff of 13,380,000 where
>>Prime95 starts factoring to the depth of 2^65 instead of 2^64.
>>Normally, increasing the depth by a factor of one only doubles
>>the time required. However, because of the nature of chip
>>architecture, it
>>takes a longer period of time than normal
>>above 2^62 and again above 2^64 to do the necessary
>>calculations (more instructions and such).
>
>Now, I may be totally off base here, but...
>
>The reason is because the integer part of the Intel CPU is 64
>bit...okay, so Prime95 does some additional steps to provide
>greater bit depth factoring...
>
>Now, if that's really the case, would it be of any advantage
>to have the FPU handle factoring? I know that some processors
>only do factoring because they have a slow FPU to begin with
>(like Cyrix and AMD K6 chips), but would a Pentium be able to
>use it's FPU to do trial-factoring to greater bit depths any
>faster than the software based solution George uses beyond 64
>bits?
Actually, George uses the FPU for trial-factoring. The problem
is that even the FPU is only 80 bits (IEEE standard). Factors
up to 2^64 can get the results in one stage (64-bits), however
you have to take extra steps to get any additional bits above
that up to 2^76 where Prime95's limit is (64-bits + 12-bits)
This means it takes one stage to get the first 64 bits of a
result and another stage to get the remaining bits....
>Better yet, do any of the wacky SIMD/MMX/3DNow instructions
>provide any possible benefits for trial factoring? I recall a
>discussion before about how those instructions wouldn't be too
>useful for LL testing because of they only handle double-word
>sized data (32 bits), but for trial-factoring...any uses?
Personally, I doubt it would benefit any, but I could be wrong...
Eric
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