Enhancements to java.math

JDK 5.0

The BigDecimal class has added support for fixed-precision floating-point computation. Refer to JSR 13.
The Math and StrictMath libraries include hyperbolic transcendental functions (sinh, cosh, tanh), cube root, base 10 logarithm, etc.
Hexadecimal floating-point support - To allow precise and predictable specification of particular floating-point values, hexadecimal notation can be used for floating-point literals and for string to floating-point conversion methods in Float and Double.

Performance enhancements for prime generation in BigInteger
New static method probablePrime has been added to class BigInteger for generating prime numbers. Previously, the sole means of generating a prime BigInteger required the caller to provide a 'certainty' (the log of the probability of compositeness that the caller was willing to tolerate). However, providing an unreasonable value for the certainty could lead to poor performance (if the certainty was too high) or serious bugs (if it was too low). The new prime-generation method provides an efficient algorithm for generating primes using an automatically determined, appropriate value for the certainty based on a draft ANSI specification (X9-80).

Performance enhancements in BigInteger
Class java.math.BigInteger has been reimplemented in pure Java programming-language code. Previously, BigInteger's implementation was based on an underlying C library. On a high-quality VM, the new implementation performs all operations faster than the old implementation. The speed-up can be as much as 5x or more, depending on the operation being performed and the length of the operands.
More robust BigDecimal(String) constructor
The BigDecimal(String) constructor has been enhanced to allow signed strings (for example, "+2.71828") and exponential notation (for example, "1.23E-23") as input.