From: Melzzzzz@nospicedham.zzzzz.com
On 2018-04-24, wolfgang kern wrote:
>
> I try to shorten my current 512 bit 1/primes LUT because reciprocals of
> primes (all except 2) are periodic (yes, also 1/5 is periodic in binary).
>
> So the LUT may just hold the bit-patterns of the periods with their size
> in bits or bytes and leading zero-bit count for byte aligned storage plus
> some space saving and a 2^-n scaling info.
> This patterns can be repeated to any desired precision then ie:
> ________________________________________________________
> Prime|bits|pattern |stored as |leading Z-bits(comment)
>
> 3 2 01 0x55(555555) -
> 5 4 0011 0x03(030303) -
> 7 3 001 0x249249 -(doubled for byte allign)
> 11 10 0001011101 0x1745D1745D -(ditto)
> 13 12 000100111101 0x13B13B -(ditto)
> 17 8 00001111 0x0f(0f0f0f) -
> 19 18 000011010111100101 0xD79435E5 4
> 23 11 00001011001 0xB21642C859 4
> 29 28 00001000110111001011 0x8D3DCB 4
> 31 5 00001 0x8421 4
> ...
> 53 52 see hex 0x4D4873ECADE3 4
> ...
> 73 9 000000111 0x381C0E07 4
> ... and so on
> _____________
>
> values for higher primes will really need 512 bits or more, but the whole
> LUT will become quite shorter and so allow addon of higher primes.
>
> Even this idea need some overhead with linked lists, multiple unaligned
> loads and shifts, it may gain size and speed compared to my previous
> 512 bit LUT.
>
> I can already hear: "why not use NR 1/x with AVX512 ?". Because only
> my newest PC has AVX512 and ~160 client machines haven't got it yet.
> And how fast and precise can the NR-methode become in comparision to
> a LUT ? ;)
Why not avx2? reciprocal calculation is 4 tacts on my machine.
Program was shown on comp.arch some time ago.
> __
> wolfgang
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