Question

What do you think Float.MIN_VALUE equals to?

The next code explains where my last 5 hours went to, trying solving a bug.

public static void main(String[] args) {
    compareToZero(Float.MIN_VALUE); // Out = true false false
    compareToZero(Float.MAX_VALUE); // Out = true false false

    System.out.println("Float minimum " + Float.MIN_VALUE); // Out = 1.4E-45
    System.out.println("Float maximum " + Float.MAX_VALUE); // Out = 3.4028235E38
}

private static void compareToZero(float value1) {
    System.out.print((value1 > 0) + " ");
    System.out.print((value1 < 0) + " ");
    System.out.print((value1 == 0) + "\n");
}

I didn’t imagined that minimum value of float will be a positive value… Can’t find any use for it.

Answer 1

Per the documentation for Float.MIN_VALUE:

A constant holding the smallest positive nonzero value of type float, 2-149. It is equal to the hexadecimal floating-point literal 0x0.000002P-126f and also equal to Float.intBitsToFloat(0x1).

While the name is debatable as the “true minimum value” of a float is -Float.MAX_VALUE, I suspect MIN_VALUE was chosen for consistency with the other numeric types. Using the names MIN_RANGE_VALUE and MAX_RANGE_VALUE (or similar) might have made the difference more clear.

To understand why this is the “minimum value” requires understanding a little bit about how Java (or IEEE-754) floating point values work. With this insight, after reading the documentation, it is clear that Float.MIN_VALUE is the minimum non-zero value representable by the mantissa and exponent components of a float. Or, the smallest positive value a float can represent.

The “true minimum value” is -Float.MAX_VALUE because Float.MAX_VALUE represents the maximum value that the mantissa and exponent components of a float can represent. Since the sign for a float is stored as a discrete bit, this range limit is the same for both positive and negative numbers.

This differs from how integers work in Java (and on most CPUs): they are encoded using two’s complement. (Some computer systems used a discrete sign bit, which is called “one’s complement”, which then has two integer values of zero: 0 and -0!)

Happy researching!