Sieve of Atkin是一种快速的素数筛选算法,算法比较成熟和简单,http://en.wikipedia.org/wiki/Sieve_of_Atkin中的描述已经非常的细致,作者撰写此文的目的在于,对如何把伪代码转为C代码作一个引导,参考如下的示例。
#include <math.h> #include <stdio.h> /* limit ← 1000000 */ #define LIMIT (1000000) #define FALSE (0) #define TRUE (~FALSE) int main(int argc, char* argv[]) { int sieve_list[LIMIT + 1]; int n, r; int x, y; int k, i; /* is_prime(i) ← false, ∀ i ∈ [5, limit] */ for(n = 5; n <= LIMIT; n++) sieve_list[n] = FALSE; /* for (x, y) in [1, √limit] × [1, √limit]: */ for(x = 1; x <= (int)sqrt(LIMIT); x++) for(y = 1; y <= (int)sqrt(LIMIT); y++) { /* n ← 4x²+y² if (n ≤ limit) and (n mod 12 = 1 or n mod 12 = 5): is_prime(n) ← ¬is_prime(n) */ n = 4 * x * x + y * y; if(n <= LIMIT && (n % 12 == 1 || n % 12 == 5)) sieve_list[n] = ~sieve_list[n]; /* n ← 3x²+y² if (n ≤ limit) and (n mod 12 = 7): is_prime(n) ← ¬is_prime(n) */ n = 3 * x * x + y * y; if(n <= LIMIT && n % 12 == 7) sieve_list[n] = ~sieve_list[n]; /* n ← 3x²-y² if (x > y) and (n ≤ limit) and (n mod 12 = 11): is_prime(n) ← ¬is_prime(n) */ n = 3 * x * x - y * y; if(x > y && n <= LIMIT && n % 12 == 11) sieve_list[n] = ~sieve_list[n]; } /* for n in [5, √limit]: if is_prime(n): is_prime(k) ← false, k ∈ {n², 2n², 3n², ..., limit} */ for(n = 5; n <= sqrt(LIMIT); n++) if(sieve_list[n] == TRUE) { i = 1; k = i++ * n * n; while(k <= LIMIT) { sieve_list[k] = FALSE; k = i++ * n * n; } } /* print 2, 3 */ printf("2\n3\n"); /* for n in [5, limit]: if is_prime(n): print n */ for(n = 5; n <= LIMIT; n++) if(sieve_list[n] == TRUE) printf("%d\n", n); return 0; }