Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: Vir Campestris <vir.campestris@invalid.invalid>
Newsgroups: comp.lang.c++
Subject: Re: OT: Re: Sieve of Erastosthenes optimized to the max
Date: Sun, 1 Sep 2024 21:23:04 +0100
Organization: A noiseless patient Spider
Lines: 45
Message-ID: <vb2if8$1jqts$2@dont-email.me>
References: <ul41d4$2koct$1@raubtier-asyl.eternal-september.org>
 <v39o3l$1lvju$1@dont-email.me> <86o78mpnlf.fsf@linuxsc.com>
 <v3fv2u$2ursd$1@dont-email.me> <86ttibod7n.fsf@linuxsc.com>
 <86h6eaoi2r.fsf@linuxsc.com> <v4sool$1grge$1@dont-email.me>
 <867celixcw.fsf@linuxsc.com> <v5sg9s$mat4$1@dont-email.me>
 <86zfr0b9hw.fsf@linuxsc.com> <v638ud$25623$1@dont-email.me>
 <861q3o5do1.fsf@linuxsc.com> <v7tdts$29195$1@dont-email.me>
 <868qx45v5g.fsf@linuxsc.com> <v9lbns$11alj$1@dont-email.me>
 <86r0aojx1m.fsf@linuxsc.com>
 <v9o2kf$1gqv1$1@raubtier-asyl.eternal-september.org>
 <va09jq$30cvv$1@dont-email.me>
 <va2ca2$3e60e$1@raubtier-asyl.eternal-september.org>
 <va2cfr$3e9l1$1@raubtier-asyl.eternal-september.org>
 <va2hq5$3f1gl$1@dont-email.me> <86v7zn3xwk.fsf@linuxsc.com>
 <vajji3$2rbid$1@raubtier-asyl.eternal-september.org>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Sun, 01 Sep 2024 22:23:05 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="8abda7a42fb8d7e82c244a4b19407a73";
	logging-data="1698748"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+ViejLjLdD3OKdN4P09XO3SVVKdoOSlI8="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:1X6WuSqdaFSVXLGRvILsXy1pC7o=
Content-Language: en-GB
In-Reply-To: <vajji3$2rbid$1@raubtier-asyl.eternal-september.org>
Bytes: 3366

On 27/08/2024 05:09, Bonita Montero wrote:
> Am 26.08.2024 um 21:08 schrieb Tim Rentsch:
> 
>> One motivation for choosing a mod30 representation is being able to
>> compute more primes -- almost twice as many.  Any machine with 64GB
>> of memory should be able to compute primes up to 1.5 trillion.
> 
> You don't need to hold all primes in memory. Just calculate the primes
> up to the square root and then you can calculate every segment up to
> the maximum from that.

So you compute all the primes up to the square root of a larger number.

I was cleaning up my odds-only code with a view to posting it, when I 
had an idea.

Take 101 (because I can write things more easily).

I want to mark

10201,10302,10403,10504,10605,10706...

With odds only that becomes
10201,10403,10605,10807,11009,11211...

and as the loop increment is a constant it is nice and fast. With mod30 
it isn't a constant, and it hurts to work out the increment.

Except...

If I mark 10201,13231,16261,19291,22321
with an increment of 30*p,

then go back to 10201, add 2p, then increment that by 30
10201	13231	16261
and do that for the other 6 of the 8, my inner loop has a constant 
increment, and my code is compatible with the mod30 store.

That might be quicker. I also have some thoughts over storing the prime 
as two parts. It's 30m+r, where m is modulus and r remainder. r maps 
one-for-one into the byte mask, and m is the index.

I'm going to waste lots more time on this I can see!

Andy