RosettaCodeData/Task/Legendre-prime-counting-fun.../C/legendre-prime-counting-fun...

91 lines
3.0 KiB
C

#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include <stdint.h>
#include <time.h>
const uint8_t masks[8] = {1, 2, 4, 8, 16, 32, 64, 128};
#define half(n) ((int64_t)((n) - 1) >> 1)
#define divide(nm, d) ((uint64_t)((double)nm / (double)d))
int64_t countPrimes(uint64_t n) {
if (n < 9) return (n < 2) ? 0 : ((int64_t)n + 1) / 2;
uint64_t rtlmt = (uint64_t)sqrt((double)n);
int64_t mxndx = (int64_t)((rtlmt - 1) / 2);
int arrlen = (int)(mxndx + 1);
uint32_t *smalls = malloc(arrlen * 4);
uint32_t *roughs = malloc(arrlen * 4);
int64_t *larges = malloc(arrlen * 8);
for (int i = 0; i < arrlen; ++i) {
smalls[i] = (uint32_t)i;
roughs[i] = (uint32_t)(i + i + 1);
larges[i] = (int64_t)((n/(uint64_t)(i + i + 1) - 1) / 2);
}
int cullbuflen = (int)((mxndx + 8) / 8);
uint8_t *cullbuf = calloc(cullbuflen, 1);
int64_t nbps = 0;
int rilmt = arrlen;
for (int64_t i = 1; ; ++i) {
int64_t sqri = (i + i) * (i + 1);
if (sqri > mxndx) break;
if (cullbuf[i >> 3] & masks[i & 7]) continue;
cullbuf[i >> 3] |= masks[i & 7];
uint64_t bp = (uint64_t)(i + i + 1);
for (int64_t c = sqri; c < (int64_t)arrlen; c += (int64_t)bp) {
cullbuf[c >> 3] |= masks[c & 7];
}
int nri = 0;
for (int ori = 0; ori < rilmt; ++ori) {
uint32_t r = roughs[ori];
int64_t rci = (int64_t)(r >> 1);
if (cullbuf[rci >> 3] & masks[rci & 7]) continue;
uint64_t d = (uint64_t)r * bp;
int64_t t = (d <= rtlmt) ? larges[(int64_t)smalls[d >> 1] - nbps] :
(int64_t)smalls[half(divide(n, d))];
larges[nri] = larges[ori] - t + nbps;
roughs[nri] = r;
nri++;
}
int64_t si = mxndx;
for (uint64_t pm = (rtlmt/bp - 1) | 1; pm >= bp; pm -= 2) {
uint32_t c = smalls[pm >> 1];
uint64_t e = (pm * bp) >> 1;
for ( ; si >= (int64_t)e; --si) smalls[si] -= c - (uint32_t)nbps;
}
rilmt = nri;
nbps++;
}
int64_t ans = larges[0] + (int64_t)((rilmt + 2*(nbps - 1)) * (rilmt - 1) / 2);
int ri, sri;
for (ri = 1; ri < rilmt; ++ri) ans -= larges[ri];
for (ri = 1; ; ++ri) {
uint64_t p = (uint64_t)roughs[ri];
uint64_t m = n / p;
int ei = (int)smalls[half((uint64_t)m/p)] - nbps;
if (ei <= ri) break;
ans -= (int64_t)((ei - ri) * (nbps + ri - 1));
for (sri = ri + 1; sri < ei + 1; ++sri) {
ans += (int64_t)smalls[half(divide(m, (uint64_t)roughs[sri]))];
}
}
free(smalls);
free(roughs);
free(larges);
free(cullbuf);
return ans + 1;
}
int main() {
uint64_t n;
int i;
clock_t start = clock();
for (i = 0, n = 1; i < 10; ++i, n *= 10) {
printf("10^%d %ld\n", i, countPrimes(n));
}
clock_t end = clock();
printf("\nTook %f seconds\n", (double) (end - start) / CLOCKS_PER_SEC);
return 0;
}