[Solved] C++ float does not change when operand is smaller than 129 [closed]

Question

We can understand what’s going on by looking at the anatomy of a 32-bit float. The value 3.0E9 in IEEE754 format is 0x4F32D05E, with exponent value 31 (you can use this online calculator to find the value).

Now we have 23 sub-unity binary digits left for the mantissa. That means that the smallest increment, i.e. the difference between to adjacent values of the mantissa, is a number with binary scale 31 − 23 = 8. Since 128 is 2⁷, we see that it is just small enough to fall off the end of the mantissa, while 129 is large enough to be visible.

Accepted Answer

We can understand what’s going on by looking at the anatomy of a 32-bit float. The value 3.0E9 in IEEE754 format is 0x4F32D05E, with exponent value 31 (you can use this online calculator to find the value).

Now we have 23 sub-unity binary digits left for the mantissa. That means that the smallest increment, i.e. the difference between to adjacent values of the mantissa, is a number with binary scale 31 − 23 = 8. Since 128 is 2⁷, we see that it is just small enough to fall off the end of the mantissa, while 129 is large enough to be visible.