Java resources to do number crunching?

What are the best resources on learning 'number crunching' using Java ? I am referring to things like correct methods of decimal number processing , best practices , API , notable idioms for performance and common pitfalls ( and their solutions ) while coding for number pr开发者_JAVA百科ocessing using Java.

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This question seems a bit open ended and open to interpretation. As such, I will just give two short things.

1) Decimal precision - never assume that two floating point (or double) numbers are equal, even if you went through the exact same steps to calculate them both. Due to a number of issues with rounding in various situations, you often cannot be certain that a decimal number is exactly what you expect. If you do double myNumber = calculateMyNumber() and then do a bunch of things and then come back to it and check if(myNumber == calculateMyNumber(), that evaluation could be false even if you have not changed the calculations done in calculateMyNumber()

2) There are limitations in the size and precision of numbers that you can keep track of. If you have int myNumber = 2000000000 and if(myNumber*2 < myNumber), that will actually evaluate to true, as myNumber*2 will result in a number less than myNumber, because the memory allocated for the number isn't big enough to hold a number that large and it will overflow, becoming smaller than it was before. Look into classes that encapsulate large numbers, such as BigInteger and BigDecimal.

You will figure stuff like this out as a side effect if you study the computer representations of numbers, or binary representations of numbers.

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First, you should learn about floating point math. This is not specific to java, but it will allow you to make informed decisions later about, for example, when it's OK to use Java primitives such as float and double. Relevant topics include (copied from a course that I took on scientific computing):

1. Sources of error: roundoff, truncation error, incomplete convergence, statistical error, program bug.
2. Computer floating point arithmetic and the IEEE standard.
3. Error amplification through cancellation.
4. Conditioning, condition number, and error amplification.

This leads you to decisions about whether to use Java's BigDecimal, BigInteger, etc. There are lots of questions and answers about this already.

Next, you're going to hit performance, including both CPU and memory. You probably will find various rules of thumb, such as "autoboxing a lot is a serious performance problem." But as always, the best thing to do is profile your own application. For example, let's say somebody insists that some optimization is important, even though it affects legibility. If that optimization doesn't matter for your application, then don't do it!

Finally, where possible, it often pays to use a library for numerical stuff. Your first attempt probably will be slower and more buggy than existing libraries. For example, for goodness sake, don't implement your own linear programming routine.