Floating Point Analysis in Java

Floating Point Numbers are classified into single precision and double precision. The single precision and double Precision in Java are float and double, respectively. Do you know how float and double are stored?

Float occupies 4 bytes and double occupies 8 bytes. For convenience, we will only discuss the float type here.
Float is actually the same as the size of an int type, a total of 32 bits, the first sign, 2-9 represents the index, the next 23 bits represent the fractional part. Here not much said, please refer to: http://blog.csdn.net/treeroot/archive/2004/09/05/95071.aspx

Here is only one example. If you want to learn more about the storage format of floating point number 0.1, run this program first.

Public class Test {
Public static void main (String [] args ){
Int x = 0x3d800000;
Int I = 1 <22;
Int j = 1 <4;
Float f = 0.1f;
Int y = Float. floatToIntBits (f );
Float rest = f-(float) 1)/j;
While (I> 0 ){
J <= 1;
Float deta = (float) 1)/j;
If (rest> = deta ){
Rest-= deta;
X | = I;
}
I >>= 1;
}
Pr (x );
Pr (y );
}

Static void pr (int I ){
System. out. println (Integer. toBinaryString (I ));
}

}
 
Result:
111101110011001100110011001101
111101110011001100110011001101

Program description:
Int x = 0x3d80000;
Because the floating point representation is 1. f * 2n-127 we want to represent 0.1, you can know the n-127 =-4, to n = 123
If the symbol is positive, we can see that the first 9 is 001111011, so we do not consider the next 23 decimal places, so we first assume that x = 0x3d800000;

Int I = 1 <22;
I initially sets the first 23rd bits from the right to 1, which is the 10th bits of x.

Int j = 1 <4;

I initially is 4, because the n-127 is-4, here is to calculate its reciprocal.

Float f = 0.1f;
Int y = Float. floatToIntBits (f );

Y is its 32-bit representation.

Float rest = f-(float) 1)/j;

This rest indicates the rest of 1 in 1.f, that is, 0.f.

While (I> 0 ){
J <= 1;
Float deta = (float) 1)/j;
If (rest> = deta ){
Rest-= deta;
X | = I;
}
I >>= 1;
}

This loop is used to calculate the 23th decimal part. If rest is not smaller than deta, this bit can be set to 1.

Nothing else. The input results are the same. It can be said that the floating point number 0.1 is definitely not accurate, but 0.5 can be accurately expressed. Why.