Java's Primitive Data Types

boolean: 1-bit. May take on the values true and false only.

byte: 1 signed byte (two's complement). Covers values from -128 to 127.

short: 2 bytes, signed (two's complement), -32,768 to 32,767

int: 4 bytes, signed (two's complement). -2,147,483,648 to 2,147,483,647.

long: 8 bytes signed (two's complement). Ranges from -9,223,372,036,854,775,808 to +9,223,372,036,854,775,807.

float: 4 bytes, IEEE 754. Covers a range from 1.40129846432481707e-45 to 3.40282346638528860e+38 (positive or negative).

double: 8 bytes IEEE 754. Covers a range from 4.94065645841246544e-324d to 1.79769313486231570e+308d (positive or negative).

char: 2 bytes, unsigned, Unicode, 0 to 65,535

Basically, floating point values are stored as a pair of mantissa and exponent. The mantissa describes the significant digits of the number (think of it as a number between 0 and 9.99). The exponent is the scale. Your number is presented as mantissa * 2^x.

We are talking about a representation in the binary system, which makes even straight numbers (in the decimal system) like 35912062 to something which may not exactly fit within the precision of the mantissa. In these cases, you get some rounding issues, especially as float has a rather limited range for the mantissa.

Executing your code with double (instead of float) gives you 3.5912062E7 as result.

If your really wanna know what java (or the floating point arithmetic) makes of your number, you should do System.out.println(new Bigdecimal(123.456)) and be surprised.

The message here is, if you really need precise arithmetics always take BigDecimal. Because there are further caveats. For example, adding a large double and a small double may result in the small double to be rounded away completely. That takes us to a funny thing:

    for (float f = 35912062f; f < 55912062f; f++) {
        System.out.println(f);
    }

will never terminate. Just try it.

The book states the MIN_VALUE and MAX_VALUE for the floating point types. This range describes available precision but it is certainly not the case that all values must fall between MIN_VALUE and MAX_VALUE as you can easily confirm by assigning zero or a negative number to a float variable.

Floating point values (float and double) can be one of the following:

• NaN (not a number)
• negative infinity
• a negative number between -MAX_VALUE and -MIN_VALUE
• negative zero
• positive zero
• a positive number between MIN_VALUE and MAX_VALUE
• positive infinity