Java Summary: Math and java.util.Random Classes

Some basic math functions can be found in the Math class. The StrictMath class (not described here) may produce less accurate results and be slower, but will produce absolutely identical results, bit for bit, on all machines. Don't use StrictMath unless you need this very specific kind of portability.

If you need numbers that exceed the range of long, use java.math.BigInteger. If you need to do exact decimal arithmetic, use java.math.BigDecimal, which gives complete control over precision and rounding, eg for financial calculations. Assume following declarations

float f;
double d, d1, d2;
double ar;  // angle in radians.
x is any of int, long, float, or double.

Math Constants
Two common constants are defined in the Math class.
double	Math.E()	Value of e, 2.718282..., base of the natural logarithms.
double	Math.PI()	Value of pi, 3.14159265 ....
Math Methods
Trigonometric Methods
All trigonometric method parameters are measured in radians, the normal mathematical system of angles, and not in degrees, the normal human angular measurement system. Use the toRadians or toDegrees methods to convert between these systems, or use the knowledge that there are 2*PI radians in 360 degrees. In addition to those below, the arc functions are also available.
double	Math.sin(ar)	Returns the sine of ar.
double	Math.cos(ar)	Returns the cosine of ar.
double	Math.tan(ar)	Returns the tangent of ar.
double	Math.toRadians(d)	Returns d (angle in degrees) converted to radians.
double	Math.toDegrees(ar)	Returns ar (angle in radians) converted to degrees.
Exponential Methods
The two basic functions for logarithms and power are available. These both use the base e (Math.E) as is the usual case in mathematics.
double	Math.exp(d)	Returns e (2.71...) to the power d.
double	Math.pow(d1, d2)	Returns d1^d2.
double	Math.log(d)	Returns the logarithm of d to base e.
Misc Methods
double	Math.sqrt(d)	Returns the square root of d.
t	Math.abs(x)	Returns absolute value of x with same type as the parameter: int, long, float, or double.
t	Math.max(x, y)	Returns maximum of x and y with same type as the parameter: int, long, float, or double.
t	Math.min(x, y)	Returns minimum of x and y with same type as the parameter: int, long, float, or double.
Integer Related Methods
The following methods translate floating point values to integer values, altho these values may still be stored in a double.
double	Math.floor(d)	Returns the closest integer-valued double which is equal to or less than d.
double	Math.ceil(d)	Returns the closest integer-valued double which is equal to or greater than d.
double	Math.rint(d)	Returns the closest integer-valued double to d.
long	Math.round(d)	Returns the long which is closest in value to the double d.
int	Math.round(f)	Returns the int which is closest in value to the float f.
Random Numbers
For significantly more control over random number generation use the java.util.Random class (see below).
double	Math.random()	Returns a number x in the range, 0.0 <= x < 1.0.
java.util.Random Class
The java.util.Random class provides more flexible ways to generate uniformly distributed random numbers, providing easy generation of types other than double, as well as providing a Gaussian distribution.
Random Constructors
It's necessary to construct a Random object.
Random	new Random();	Uses time in milliseconds as the seed.
Random	new Random(long seed);	Uses the provided seed for testing purposes.
Random Methods
All methods return a uniform distribution of values, except `nextGaussian()`. Assume r is a Random* object.*.
int	r.nextInt(int n)	Returns random int >= 0 and < n.
int	r.nextInt()	Returns random int (full range).
long	r.nextLong()	Returns random long (full range).
float	r.nextFloat()	Returns random float >=0.0 and < 1.0.
double	r.nextDouble()	Returns random double >=0.0 and < 1.0.
boolean	r.nextBoolean()	Returns random boolean (true or false).
double	r.nextGaussian()	Returns random double with mean 0.0 and standard deviation 1.0.

Other math libraries

I don't keep track of math libraries, but I'll add links below as I run across them. I have no idea if these are good or bad.

jakarta.apache.org/commons/math/ - Apache Jakarta Math library.
www.ia.hiof.no/~kyvh/SciLib/docs/scilib.html - SciLib