问题描述
如何创建一个函数,该函数在每次调用时都会生成一个随机整数?此数字必须是尽可能随机的(根据均匀分布).仅允许使用一个静态变量和最多3个基本步骤,其中每个步骤仅由 arity 1或2.
How to create a function, which on every call generates a random integer number? This number must be most random as possible (according to uniform distribution). It is only allowed to use one static variable and at most 3 elementary steps, where each step consists of only one basic arithmetic operation of arity 1 or 2.
示例:
int myrandom(void){
static int x;
x = some_step1;
x = some_step2;
x = some_step3;
return x;
}
基本算术运算是+,-,%和,而不是xor,或左移,右移,乘法和除法.当然,不允许使用rand(),random()或类似内容.
Basic arithmetic operations are +,-,%,and, not, xor, or, left shift, right shift, multiplication and division. Of course, no rand(), random() or similar stuff is allowed.
推荐答案
线性同余生成器是最古老,最简单的方法之一:
Linear congruential generators are one of the oldest and simplest methods:
int seed = 123456789;
int rand()
{
seed = (a * seed + c) % m;
return seed;
}
仅需几条具有基本算术运算的指令即可.
Only a few instruction with basic arithmetic operations, that's all you need.
请注意,只有以特定方式选择 a , c 和 m 时,该算法才能正常工作!
Mind that this algorithm works fine only if a, c and m are chosen in a particular way!
为了保证该序列的最长可能周期, c 和 m 应为互质数, a −1应可被所有质数整除 m 的因子,如果 m 被4整除,则因子为4.
To guarantee the longest possible period of this sequence, c and m should be coprime, a − 1 should be divisible by all prime factors of m, and also for 4 if m is divisible by 4.
一些参数示例在Wikipedia上显示:例如,某些编译器的ANSI C建议 m =2³¹, a = 1103515245和 c = 12345.
Some examples of parameters are shown on Wikipedia: for example ANSI C for some compilers proposes m = 2 ³¹, a = 1103515245 and c = 12345.
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