C++ GMP 生成随机数

Question

我正在尝试使用 GMP 库在 C++ 中生成一个巨大的随机数，但在弄清楚语法时遇到了问题。这与我发现的其他示例略有不同，因为我需要为随机数设置下限和上限。这有点像我需要做的：

mpz_class high, low;

low  = pow(2,199);
high = pow(2,210);

// code to use the high and low numbers to generate the random number

我知道这没什么好继续的，但是我再次不确定此时的语法是什么，我已经尝试了几种方法，但我发现的任何东西都无法告诉我GMP 使用高低范围生成数字。

想法？

Answer 1

来自Gmp Lib Documentation

Function: void mpz_urandomb (mpz_t rop, gmp_randstate_t state, mp_bitcnt_t n)

Generate a uniformly distributed random integer in the range 0 to 2^n−1, inclusive

因此，取 210 - 199，并将其用作 n，生成一个随机数并将结果添加到 pow(2,199)。

如果你想要比 2 的幂上限更细化的东西，这对你不起作用。您可以使用与上述相同的技术尝试 unsigned int 大小的随机函数：

— Function: unsigned long gmp_urandomm_ui (gmp_randstate_t state, unsigned long n)

Return a uniformly distributed random number in the range 0 to n-1, inclusive.

在这里，您将找到您的粒度范围并将其用于 n。然后将随机数添加到您的较低值。限制是n必须小于MAXUINT，通常是2^32 -1

Answer 2

使用@Less 提供的逻辑，我编写了以下内容来解决我的问题：

void 
makeprime ()
{
    // *********************** VARIABLE DECLARATION *********************** //
    // initilize the variables as gmp class instances
    mpz_t l, rand;
    unsigned long seed;
    // perform inits to create variable pointers with 0 value
    mpz_inits(l, rand);
    //mpz_init(rand);

    // calculate the random number floor
    mpz_ui_pow_ui(l, 2, 199);

    // initilze the state object for the random generator functions
    gmp_randstate_t rstate;
    // initialize state for a Mersenne Twister algorithm. This algorithm is fast and has good randomness properties.
    gmp_randinit_mt(rstate);

    // create the generator seed for the random engine to reference 
    gmp_randseed_ui(rstate, seed);

    /*
    Function:
    int mpz_probab_prime_p (const mpz_t n, int reps)

    Determine whether n is prime. Return 2 if n is definitely prime, return 1 if n is probably prime (without being certain), 
    or return 0 if n is definitely composite.
    */
    do {
        // return a uniformly distributed random number in the range 0 to n-1, inclusive.
        mpz_urandomb(rand, rstate, 310);

        // add the random number to the low number, which will make sure the random number is between the low and high ranges
        mpz_add(rand, rand, l);

        gmp_printf("randomly generated number: %Zd\n", rand);

    } while ( !(mpz_probab_prime_p(rand, 25)) );        

    // *********************** GARBAGE COLLECTION *********************** //
    // empty the memory location for the random generator state
    gmp_randclear(rstate);
    // clear the memory locations for the variables used to avoid leaks
    mpz_clear(l);
    mpz_clear(rand);
}

感谢@Less 的逻辑和帮助！

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