[CPP]cpp小笔记2 --- float 的值的精度最大为Decimal point 往左6-7位

2. float 的值的运算

c++ primier plus中有一段关于float运算的代码：

float a = 2.34E+22f;
float b = a + 1.0f;
cout << "a =" << a <<endl;
cout << "b -a =" << b - a<< endl;

结果是：

a =2.34e+22
b - a =0

这是为什么呢？

The single precision floating point type float is like this(assuming IEEE-754)

cpp在保存float type时，使用单精度#single precision#来保存float.格式是

m*2^e

where m is a number between 223 and 224,and e is an integer. 从上图来看，m的最大值是  223 #最大16777215# and e的最大值是 28

float在保存是会被rounded到最接近这个float的数值。 So the value 2.34e+22 is actually rounded to 

10391687*251, which is 23399998850475413733376. This is the value of a.

再有，float的运算结果也会被rounded到最接近的float数值。 if you add 1 to a, the result is 

23399998850475413733377, which is again rounded to the nearest floating-point number, which is still, of course, 

23399998850475413733376. So b gets the same value as a. Since both numbers are equal, a
- b == 0.