c++ - 使用编译时递归生成从 1 到 499 的素数

Question

我读到素数是固定的，最好在编译时生成它们而不是依赖于运行时。所以，我想到了使用 Template Metaprogramming它在内部使用编译时递归。我正在使用 Sieve of Eratosthenes生成素数的方法。这是代码:

int prime[500]; // prime[i]==0 means i is prime

template<int n> void fillMultiple(int i)
{
    prime[n*i]=1; // n is prime, mark all its multiples as non-prime
    n*i<500?fillMultiple<n>(i+1):fillMultiple<499>(i);
}

template<> void fillMultiple<499>(int i)
{
     // do nothing
     // only used as dummy function
}

template<int n> void generatePrime()
{       
    prime[n]==0?fillMultiple<n>(2):generatePrime<n+1>(); //if n is prime,mark all the multiples of n as non-prime.
    generatePrime<n+1>();
}

template<> void generatePrime<499>()
{
     // do nothing
     // only used as dummy function
}

int main()
{
    prime[0]=prime[1]=1; // 0 and 1 is non-prime
    generatePrime<2>();

    for(int i=0;i<500;i++) // print prime numbers
            if(0==prime[i]) // if prime[i]==0, then i is prime
                    cout<<i<<endl;

    return 0;
}

当我运行代码时，我得到 Runtime error

我对模板元编程不是很熟悉。请解释为什么我会遇到运行时错误？如果有任何错误，它必须在编译时显示。

Answer 1

或者:

int p[] = { 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,
            547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659,
            661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809,
            811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941,
            947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069,
            1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223,
            1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373,
            1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511,
            1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657,
            1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811,
            1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987,
            1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129,
            2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287,
            2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423,
            2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617,
            2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741,
            2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903,
            2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079,
            3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257,
            3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413,
            3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571};

I have read that prime numbers are fixed and it is better to generate them at compile time rather than depending on runtime.

是的，这是个好主意。
由于它们是固定的意味着它们只需要生成一次(不是每次)。

So, i thought of using Template Meta-programming which internally uses compile-time recursion.

没有这么好的主意。
编译器设置了最大递归级别(取决于我上次检查时(不久前)的编译器 8>16)。最好编写一个一次性程序生成您想要的值，然后使用代码生成您将在真实代码中编译的文件(或像我一样从维基百科剪切/粘贴数字)。

I am using Sieve of Eratosthenes method for generating prime numbers. Here

不幸的是，这不是模板元程序。
它在运行时工作。