Joseph D. Darcy's Sun Weblog

Wednesday October 29, 2008

Everything Old is New Again

I was heartened to recently come across the article Java's new math, Part 1: Real numbers which detailed some of the additions I made to Java's math libraries over the years in JDK 5 and 6, including hyperbolic trigonometric functions (sinh, cosh, tanh), cube root, and base-10 log.

A few comments on the article itself, I would describe java.lang.StrictMath as java.lang.Math's fussy twin rather than evil twin. The availability of the StrictMath class allows developers who need cross-platform reproducible results from the math library to get them. Just because floating-point arithmetic is an approximation to real arithmetic doesn't mean it shouldn't be predictable! There are non-contrived circumstances where numerical programs are helped by having such strong reproducibility available. For example, to avoid unwanted communication overhead, certain parallel decomposition algorithms rely on different nodes being able to independently compute consistent numerical answers.

While the java.lang.Math class is not constrained to use the particular FDLIBM algorithms required by StrictMath, any valid Math class implementation still must meet that stated quality of implementation criteria for the methods. The criteria usually include a low worst-case relative error, as measures in ulps (units in the last place), and semi-monotonicity, whenever the mathematical function is non-decreasing, so is the floating-point approximation, likewise, whenever the mathematical function is non-increasing, so is the floating-point approximation

Simply adding more FDLIBM methods to the platform was quite easy to do; much of the effort for the math library additions went toward developing new tests, both to verify that the general quality of implementation criteria were being met as well as that verifying the particular algorithms were being used to implement the StrictMath methods. I'll discuss the techniques I used to develop those tests in a future blog entry.