线性全余生成器的分析是错误的吗?

所以为了更好地理解MSVC++对rand的实现，我重新实现了它，并试图更好地理解它(我猜是LCG(。

我的实现(几乎完全匹配MSVC++(如下：

// vc++ impl. of random
// Xn+1 = (aXn + i) mod m
// a = 214013, i = 2531011, m = 32768
unsigned int seed = 0;
unsigned int random()
{
seed = seed * 214013L + 2531011L;
// return (seed/(1<<16)) % 32768; (equiv to below)
return seed>>16 & 0x7FFF;
}

为了找到 2 个种子新生成的种子的差异，我认为这只是(214013*h) % 2^32其中 h 是 2 个初始种子之间的差异。使用相同的逻辑，我计算了 2 个随机生成的数字之间的差异，给定初始种子作为x和下一个种子作为x+h，我在种子中取了这个不同的，除以 2^16(或向右移动 16 位(，并删除了最高有效位。

此生成的值似乎是正确的，但在某些情况下除外，例如当 x = 100 和 h = 5000 时。

以下是整个代码：

#include <iostream>
#include <cstdlib>
// vc++ impl. of random
// Xn+1 = (aXn + i) mod m
// a = 214013, i = 2531011, m = 32768
unsigned int seed = 0;
unsigned int random()
{
seed = seed * 214013L + 2531011L;
return seed>>16 & 0x7FFF;
}
int main()
{
// f(x) = (214013x + 2531011) mod 2^32 [LCG]
// g(x) = floor(f(x)/2^16) mod 2^15 [RND]
// h(x) = f(x + h) - f(x) ?= 214013*h mod 2^32
// j(x) = g(x + h) - g(x) ?= 214013*h/2^16 mod 2^15
// x: initial seed
// h: displaecment to next seed (next seed: x + h)
// a, b: first and second randomly generated values using C rand
// c, d: first and second randomly generated values using random
// newSeedA, newSeedB: seed generated from LCG after x and x + h respectively
// diffExp: experimental difference in random values
// diffCalc: calculated/theoretical difference in random vlaues
unsigned int x = 100, h = 50000;
unsigned int a, b, c, d;
unsigned int newSeedA, newSeedB;
int diffExp, diffCalc;
srand(x);
seed = x;
a = rand();
c = random();
newSeedA = seed;
srand(x + h);
seed = x + h;
b = rand();
d = random();
newSeedB = seed;
diffExp = (d - c) % 32768;
diffCalc = (214013*h)>>16 & 0x7FFF;

std::cout << "RANDOM VALUESn";
std::cout << "  VC++ rand: " << a << ", " << b << "n";
std::cout << "Custom rand: " << c << ", " << d << "n";
std::cout << "n";
std::cout << "DIFFERENCE IN SEEDn";
std::cout << "Experimental Difference: " << (newSeedB - newSeedA) << "n";
std::cout << "  Calculated Difference: " << (static_cast<unsigned int>(214013)*h) << "n";
std::cout << "n";
std::cout << "DIFFERENCE IN VALUESn";
std::cout << "Experimental Difference: " << diffExp << "n";
std::cout << "  Calculated Difference: " << diffCalc << "n";
std::cout << "n";
return 0;
}

但是，对于这些值，2 个随机生成的值之间的估计差值比实际差值小 1。我做错了什么吗？