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

Am 16.08.2024 um 19:35 schrieb Bonita Montero:

But basically I don't think it is a good idea to skip numbers exept
multiples of two. With the three you save a sixth of memory, with
the five you save a 15-th and at the end you get about 20% less
storage (1 / (2 * 3) + 1 / (2 * 3 * 5) + 1 / (2 * 3 * 5 * 7) ...)
for a lot of computation. That's the point where I dropped this
idea and I think this extra computation is higher than the time
for the saved memory loads.
 

This calculates the percentage of the memory-access-savings:
#include <iostream>
#include <span>
#include <algorithm>
using namespace std;
int main()
{
static unsigned const rawPrimes[] =
{
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151,
157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233,
239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317,
331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419,
421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503,
509, 521, 523, 541
};
span primes( rawPrimes );
double sum = 0.0;
auto
rEnd = primes.rend(),
cur = rEnd - 2;
do
{
double add = 1.0;
for_each( cur, rEnd, [&]( int p )
{ add /= p; } );
sum += add;
} while( --cur != primes.rbegin() );
cout << 100 * sum << "%" << endl;
}