1. 基本类型(Primitive type)中float和double的区别
原文摘自 stackoverflow: http://stackoverflow.com/a/2386882/4710864，内容如下:
Huge difference.
As the name implies, a double has 2x the precision of float[1]. In general a double has 15 to 16 decimal digits of precision, while float only has 7.
This precision loss could lead to truncation errors much easier to float up, e.g.
float a = 1.f / 81;
float b = 0;
for (int i = 0; i < 729; ++ i)
b += a;
printf("%.7g\n", b); // prints 9.000023
// while
double a = 1.0 / 81;
double b = 0;
for (int i = 0; i < 729; ++ i)
b += a;
printf("%.15g\n", b); // prints 8.99999999999996
Also, the maximum value of float is only about 3e38, but double is about 1.7e308, so using float can hit Infinity much easier than double for something simple e.g. computing 60!.
Maybe the their test case contains these huge numbers which causes your program to fail.
Of course sometimes even double isn’t accurate enough, hence we have long double[1] (the above example gives 9.000000000000000066 on Mac), but all these floating point types suffer from round-off errors, so if precision is very important (e.g. money processing) you should use int or a fraction class.
BTW, don’t use += to sum lots of floating point numbers as the errors accumulate quickly. If you’re using Python, use “fsum”. Otherwise, try to implement the Kahan summation algorithm.
[1]: The C and C++ standards do not specify the representation of float, double and long double. It is possible that all three implemented as IEEE double-precision. Nevertheless, for most architectures (gcc, MSVC; x86, x64, ARM) float is indeed a IEEE single-precision floating point number (binary32), and double is a IEEE double-precision floating point number (binary64).
还句话说，也就是double和float都是用来表示浮点类型的，但是double的精度远远高于float类型（2倍）。如果是叠加类型的运算，float很容易出错（round-off erros）
注意上文黑体字部分，不要使用“+=”进行叠加运算，如果是Python使用“fsum”；如果是其他语言，按照Kahan summation algorithm实现算法。
