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