Re: Sieve of Erastosthenes optimized to the max

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Sujet : Re: Sieve of Erastosthenes optimized to the max
De : tr.17687 (at) *nospam* z991.linuxsc.com (Tim Rentsch)
Groupes : comp.lang.c++
Date : 20. Jul 2024, 15:41:18
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <861q3o5do1.fsf@linuxsc.com>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
User-Agent : Gnus/5.11 (Gnus v5.11) Emacs/22.4 (gnu/linux)
Vir Campestris <vir.campestris@invalid.invalid> writes:

On 02/07/2024 07:20, Tim Rentsch wrote:
>
I got the code.  [...]
>
>
I checked.  The modulus operations (%) are easy to check for.
>
There are two for each prime number.  Not for each multiple of it, but
for the primes themselves.
>
And there's one in the "get" function that checks to see if a number
is prime.  [...]

And one divide for each modulus.

Both divide and mod can be simplified if we use a different
representation for numbers.  The idea is to separate the
number into a mod 30 part and divided by 30 part.  An
arbitrary number N can be split into an ordered pair

   N/30 , N%30

stored in, let's say, an 8 byte quantity with seven bytes
for N/30 and one byte for N%30.  Let me call these two
parts i and a for one number N, and j and b for a second
number M.  Then two form N*M we need to find

   (i*30+a) * (j*30+b)

which is

   (i*30*j*30) + (i*30*b) + (j*30*a) + a*b

Of course we want to take the product and express it in
the form (product/30, product%30), which can be done by

   30*i*j + i*b + j*a + (a*b)/30,   (a*b)%30

The two numbers a and b are both under 30, so a*b/30 and
a*b%30 can be done by lookup in a small array.

   30*i*j + i*b + j*a + divide_30[a][b],   modulo_30[a][b]

Now all operations can be done using just multiplies and
table lookups.  Dividing by 30 is just taking the first
component;  remainder 30 is just taking the second component.

One further refinement:  for numbers relatively prime to 2,
3, and 5, there are only 8 possibles, so the modulo 30
component can be reduced to just three bits.  That makes the
tables smaller, at a cost of needing a table lookup to find
and 'a' or 'b' part.

Does this all make sense?

Date Sujet#  Auteur
30 Jun 24 * Re: Sieve of Erastosthenes optimized to the max54Vir Campestris
2 Jul 24 `* Re: Sieve of Erastosthenes optimized to the max53Tim Rentsch
2 Jul 24  +- Re: Sieve of Erastosthenes optimized to the max1Vir Campestris
3 Jul 24  `* Re: Sieve of Erastosthenes optimized to the max51Vir Campestris
15 Jul 24   +- Re: Sieve of Erastosthenes optimized to the max1Tim Rentsch
20 Jul 24   +* Re: Sieve of Erastosthenes optimized to the max48Tim Rentsch
25 Jul 24   i`* OT: Re: Sieve of Erastosthenes optimized to the max47Vir Campestris
10 Aug 24   i +* Re: OT: Re: Sieve of Erastosthenes optimized to the max44Tim Rentsch
12 Aug 24   i i+* Re: OT: Re: Sieve of Erastosthenes optimized to the max2Vir Campestris
16 Aug 24   i ii`- Re: OT: Re: Sieve of Erastosthenes optimized to the max1Tim Rentsch
15 Aug 24   i i`* Re: OT: Re: Sieve of Erastosthenes optimized to the max41Vir Campestris
16 Aug 24   i i `* Re: OT: Re: Sieve of Erastosthenes optimized to the max40Tim Rentsch
16 Aug 24   i i  +* Re: OT: Re: Sieve of Erastosthenes optimized to the max38Bonita Montero
16 Aug 24   i i  i+- Re: OT: Re: Sieve of Erastosthenes optimized to the max1Bonita Montero
19 Aug 24   i i  i+* Re: OT: Re: Sieve of Erastosthenes optimized to the max19Vir Campestris
20 Aug 24   i i  ii`* Re: OT: Re: Sieve of Erastosthenes optimized to the max18Bonita Montero
20 Aug 24   i i  ii `* Re: OT: Re: Sieve of Erastosthenes optimized to the max17Bonita Montero
20 Aug 24   i i  ii  +- Re: OT: Re: Sieve of Erastosthenes optimized to the max1Bonita Montero
20 Aug 24   i i  ii  `* Re: OT: Re: Sieve of Erastosthenes optimized to the max15Vir Campestris
20 Aug 24   i i  ii   +- Re: OT: Re: Sieve of Erastosthenes optimized to the max1Bonita Montero
26 Aug 24   i i  ii   `* Re: OT: Re: Sieve of Erastosthenes optimized to the max13Tim Rentsch
27 Aug 24   i i  ii    `* Re: OT: Re: Sieve of Erastosthenes optimized to the max12Bonita Montero
1 Sep 24   i i  ii     `* Re: OT: Re: Sieve of Erastosthenes optimized to the max11Vir Campestris
2 Sep 24   i i  ii      `* Re: OT: Re: Sieve of Erastosthenes optimized to the max10Tim Rentsch
2 Sep 24   i i  ii       +- Re: OT: Re: Sieve of Erastosthenes optimized to the max1Bonita Montero
3 Sep 24   i i  ii       `* Re: OT: Re: Sieve of Erastosthenes optimized to the max8Vir Campestris
28 Sep 24   i i  ii        `* Re: OT: Re: Sieve of Erastosthenes optimized to the max7Tim Rentsch
28 Sep 24   i i  ii         `* Re: OT: Re: Sieve of Erastosthenes optimized to the max6Keith Thompson
2 Oct 24   i i  ii          `* Re: OT: Re: Sieve of Erastosthenes optimized to the max5Vir Campestris
2 Oct 24   i i  ii           +- Re: OT: Re: Sieve of Erastosthenes optimized to the max1Bonita Montero
7 Oct 24   i i  ii           `* Re: OT: Re: Sieve of Erastosthenes optimized to the max3Tim Rentsch
20 Oct 24   i i  ii            `* Re: OT: Re: Sieve of Erastosthenes optimized to the max2Vir Campestris
4 Nov 24   i i  ii             `- Re: OT: Re: Sieve of Erastosthenes optimized to the max1Tim Rentsch
19 Aug 24   i i  i+* Re: OT: Re: Sieve of Erastosthenes optimized to the max12Vir Campestris
20 Aug 24   i i  ii+* Re: OT: Re: Sieve of Erastosthenes optimized to the max4red floyd
20 Aug 24   i i  iii+* Re: OT: Re: Sieve of Erastosthenes optimized to the max2Vir Campestris
26 Aug 24   i i  iiii`- Re: OT: Re: Sieve of Erastosthenes optimized to the max1Tim Rentsch
26 Aug 24   i i  iii`- Re: OT: Re: Sieve of Erastosthenes optimized to the max1Tim Rentsch
20 Aug 24   i i  ii+* Re: OT: Re: Sieve of Erastosthenes optimized to the max3Bonita Montero
20 Aug 24   i i  iii+- Re: OT: Re: Sieve of Erastosthenes optimized to the max1Bonita Montero
20 Aug 24   i i  iii`- Re: OT: Re: Sieve of Erastosthenes optimized to the max1Bonita Montero
20 Aug 24   i i  ii`* Re: OT: Re: Sieve of Erastosthenes optimized to the max4Bonita Montero
22 Aug 24   i i  ii `* Re: OT: Re: Sieve of Erastosthenes optimized to the max3Vir Campestris
22 Aug 24   i i  ii  `* Re: OT: Re: Sieve of Erastosthenes optimized to the max2Bonita Montero
22 Aug 24   i i  ii   `- Re: OT: Re: Sieve of Erastosthenes optimized to the max1Vir Campestris
22 Aug 24   i i  i`* Re: OT: Re: Sieve of Erastosthenes optimized to the max5Vir Campestris
23 Aug 24   i i  i +* Re: OT: Re: Sieve of Erastosthenes optimized to the max3red floyd
26 Aug 24   i i  i i+- Re: OT: Re: Sieve of Erastosthenes optimized to the max1Tim Rentsch
28 Sep 24   i i  i i`- Re: OT: Re: Sieve of Erastosthenes optimized to the max1Andrey Tarasevich
26 Aug 24   i i  i `- Re: OT: Re: Sieve of Erastosthenes optimized to the max1Tim Rentsch
19 Aug 24   i i  `- Re: OT: Re: Sieve of Erastosthenes optimized to the max1Tim Rentsch
11 Aug 24   i +- Re: OT: Re: Sieve of Erastosthenes optimized to the max1Tim Rentsch
11 Aug 24   i `- Re: OT: Re: Sieve of Erastosthenes optimized to the max1Tim Rentsch
23 Jul 24   `- Re: Sieve of Erastosthenes optimized to the max1Tim Rentsch

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