Re: OT: Re: Sieve of Erastosthenes optimized to the max

Vir Campestris <vir.campestris@invalid.invalid> writes:

This post is my second response to your comments, more
specifically to one part of your comments.

On 20/07/2024 15:41, Tim Rentsch wrote:
>

Vir Campestris <vir.campestris@invalid.invalid> writes:
>

On 02/07/2024 07:20, Tim Rentsch wrote:

[...]

I had also considered looking for a mod-div value greater than 30.
>
Bonita's original code stored a bit for every prime.  We can call
that a compression ratio of 1.  I store the odd only, so the
compression ratio is 2.  By storing mod30 you increase that to
3.75.  But there's a cost on modern computers because it implies
lots of byte level access to store.
>
If on the other hand we store mod(2*3*5*7*11), which is 2310, we
get 480 candidates.  480 isn't far off 512 which is a nice size
for us to handle, and gives us an even better compression ratio of
just over 4.5.  But of course all those tables with 8 or 30
entries will be getting a bit big and painful.

I tried using a mod 240 encoding, so the units are 64-bit elements,
to see if the more natural sized access would help.  The result ran
slower than the mod 30 code.

The idea of using more primes seems like a natural extension, and
maybe it can work.  Certainly it can get greater compression, which
is a plus.  I had looked before at using a mod 210 encoding (which
is 30 * 7).  My sense is that, unless the extra compression is
essential, the added code complexity will hurt performance more
than it helps.  But I never got to the point of actually coding
it.