Java Notes

Floating-point

Floating-point numbers are like real numbers in mathematics, for example, 3.14159, -0.000001. Java has two kinds of floating-point numbers: float and double, both stored in IEEE-754 format. The default type when you write a floating-point literal is double.

Java floating-point types

type	Size		Range	Precision
name	bytes	bits	approximate	in decimal digits
float	4	32	+/- 3.4 * 1038	6-7
double	8	64	+/- 1.8 * 10308	15

Limited precision

Because there are only a limited number of bits in each floating-point type, some numbers are inexact, just as the decimal system can not represent some numbers exactly, for example 1/3. The most troublesome of these is that 1/10 can not be represented exactly in binary.

Floating-point literals

There are two types of notation for floating-point numbers. Any of these numbers can be followed by "F" (or "f") to make it a float instead of the default double.

• Standard (American) notation which is a series of digits for the integer part followed by a decimal point followed by a series of digits for the fraction part. Eg, 3.14159 is a double. A sign (+ or -) may precede the number.
• Scientific notation which is a standard floating-point literal followed by the letter "E" (or "e") followed by an optionally signed exponent of 10 which is used as a multiplier (ie, how to shift the decimal point). Generally scientific notation is used only for very large or small numbers.

  Scientific	Standard
  1.2345e5	123450.0
  1.2345e+5	123450.0
  1.2345e-5	0.000012345

Infinity and NaN

No exceptions are generated by floating-point operations. Instead of an interruption in execution, the result of an operation may be positive infinity, negative infinity, or NaN (not a number). Division by zero or overflow produce infinity. Subtracting two infinities produces a NaN. Use methods in the wrapper classes (Float or Double) to test for these values.

References

• What Every Computer Scientist Should Know About Floating-Point Arithmetic (http://www.physics.ohio-state.edu/~dws/grouplinks/floating_point_math.pdf) has a very detailed, and mathematical, analysis of floating-point.