Note: With this refactoring, `math/utils' no longer depends on `rackunit'.
* (flexp2 x) computes (flexpt 2.0 x) but in about 1/3 the time for integer
`x' using a lookup table. Written for exact argument reduction in `fllog2'
after discovering that (flexpt 2.0 x) was the main performance bottleneck.
* (fllog2 x) computes (/ (fllog x) (fllog 2.0)) with near perfect accuracy.
Invented an algorithm to compute it with at least 8 extra bits before
final rounding; quite pleased with the result. Needed `fllog2' to ensure
(fllogb 2.0 x) would be exact when `x' is a power of two.
* (fllogb b x) computes (/ (fllog x) (fllog b)) with better accuracy, and
also handles limit values in a way that's consistent with the mathematical
limits. When those are ambiguous, it's consistent with `flexpt', which
follows IEEE 754 and C99. Otherwise returns +nan.0. See docs for details.
* `bflogb' is currently just for testing `fllogb'.
* Refactored FPU testing and documented it. So far, the only documented way
to do it is by calling `test-floating-point', which runs a comprehensive
deterministic+randomized suite of tests and returns a list representing
failed tests. I'll document individual tests after I document flonum
expansions and result/error functions like `fl+/error'.
* Added `fllog2' and `fllogb' to the flonum tests.
in the original GitHub fork:
https://github.com/ntoronto/racket
Some things about this are known to be broken (most egregious is that the
array tests DO NOT RUN because of a problem in typed/rackunit), about half
has no coverage in the tests, and half has no documentation. Fixes and
docs are coming. This is committed now to allow others to find errors and
inconsistency in the things that appear to be working, and to give the
author a (rather incomplete) sense of closure.
