log1p: ~~~~
This algorithm is part of C99, but by no means all compilers support it yet, I used a Taylor series expansion for small x: I'm aware that there are much more efficient methods, but optimizing compilers completely trash the logic of these (Intel C++ proved to be particularly bad).
I had planed to work on it (and a few related such as expm1...) something liketwo years ago and had planed to add it to the same special functions library. They really are important.
Agreed: how were you planning to implement expm1? The obvious series expansion: expm1(z) = SUM[k=1, INF] (z^k / k!) would converge in less than B steps for a B bit floating point type and |z| < 0.5 (in other words reasonable but not astounding performance), in fact it would be trivial to plug that into my existing series summation code. Alternatively there's a table based method (http://portal.acm.org/citation.cfm?doid=146847.146928) which claims to be particularly accurate. Any others? You've got my curiosity roused... John.