"Exact" determines whether a floating point number is equal to 0

Someone on the Forum asked, "accurately determine whether a floating point number is equal to 0. Do not use the same if (data <1e-10) method .". In fact, we understand how floating point numbers are stored in computers, and the answer to this question is clear.

In the IEEE754 standard, the single-precision floating point number (4 byte) Representation: 1bit symbol bit (S), 8bit index bit (E, expressed in order code), and 23bit decimal part (tail number M ). Double-precision floating point number (8 byte) Representation: 1bit symbol bit, 11bit index bit (expressed in order), 52bit decimal part (ending number ). So the true value of a normalized Single-precision floating point number x is x = (-1) ^ S) * (1.M) * (2 ^ (E-127); apparently, x cannot always be zero.

For the above description, when the level code E is all 0 and the tail number M is all 0, we can consider that the true value x represents the absolute 0 value in the computer, combined with the symbol bit S, there are two points: positive 0 and negative 0; that is, in addition to the maximum 1bit in 32bit, when the other 31bit is all 0, it is the absolute 0 value in the computer.
Float f = pow (float) 2, (float)-127 );;
Int * ptrToInt = (int *) (void *) & f;
If (! (* PtrToInt & (0x7fffffff )))
{
// The absolute 0 value in the computer
}

For a 32-bit floating-point number in a computer, the absolute value range of the technique is about (1e-38 )~ (1e + 38), that is, 2 ^ (-127 )~ 1.111111b * (2 ^ 128): the absolute value of a floating point number is smaller than 2 ^ (-127). There is no absolute 0 in a floating point number, so we can only take an approximate value.