Java – about the precision of float type

I can't understand why

float f = Integer.MAX_VALUE;
System.out.println(Integer.MAX_VALUE);
System.out.println((int)f);

Produce the same line,

And why

Float f2 = (float) Integer.MAX_VALUE;
System.out.println(Integer.MAX_VALUE);
System.out.println(f2.intValue());

I mean, the mantissa length of a floating point number is 2 ^ 23-1 How does it try to keep the max of an integer_ Value, i.e. 2 ^ 31 – 1?

Solution

It doesn't actually The value of F is 2147483648

However, narrowing primitive conversion clamps this value from float to int It reaches this part:

You can easily see this by making the number bigger:

float f = Integer.MAX_VALUE;
f = f * 1000;
System.out.println(Integer.MAX_VALUE); // 2147483647
System.out.println((int)f); // 2147483647

Or by casting instead, it is obviously not necessary to clamp at the same point:

float f = Integer.MAX_VALUE;
System.out.println(Integer.MAX_VALUE); // 2147483647
System.out.println((long)f); // 2147483648