为什么在浮点中从大到小会引入更多的误差

不知道为什么，但如果我把大到小的fp数字相加，增量误差似乎更大：

#include <iostream>
#include <math.h>
int main() {
std::cout.precision(50);
const int numLoops = 1000;
const long length = 10000;
const double rate = 0.1;
long totalLength = length * numLoops;
long long steps = (long long)(totalLength / rate);
double sum = 0.0;
double sumRemainder = 0.0;
for (long long step = 0; step < steps; step++) {
if (sumRemainder >= length) {
sumRemainder = fmod(sumRemainder, length);
}
sum += rate;
sumRemainder += rate;
}
std::cout << "                  length: " << length << std::endl;
std::cout << "               num loops: " << numLoops << std::endl;
std::cout << "                    rate: " << rate << std::endl;
std::cout << "                   steps: " << steps << std::endl << std::endl;
std::cout << "                     sum: " << sum << std::endl;
std::cout << "           sum remainder: " << sumRemainder << std::endl;
std::cout << "                   error: " << abs(totalLength - sum) << std::endl;
std::cout << "         error remainder: " << abs(length - sumRemainder) << std::endl;
std::cout << std::endl;
}

这两个和之间唯一的区别是，一个是所有步骤，而另一个是，一旦达到极限，我就简单地计算结果(因此，它会钳制到一个小值(：

sumRemainder = fmod(sumRemainder, length);

这似乎是它在求和相同数量时引入低误差的原因：1.884836819954216480255126953125e-05与0.01887054927647113800048828125

有人能用一个聪明的例子向我解释为什么会发生这种情况吗？