Bug 23677 – log1p Documentation Doesn't Match Implementation

`std.math.exponential.log1p`'s documentation says that it is 1) more accurate for small values of x and 2) that it is a conversation of the CEPHES library. 1) It is only more accurate if a) INLINE_YL2X is true (which is likely only using the hard-ware implementation on DMD), and b) you are using either reals or it is ctfe. If neither of these are true, then the function is basically calling log(1+x), so there is no improvement in accuracy (so for floats and doubles without CTFE, it is not any different). 2) The CEPHES library has an implementation of log1p [1] using doubles that uses a Taylor expansion. The version here is not using it. The only thing it has similar is the check for a value near to 1 and special casing it and even then the special casing is different. I would recommend bringing the documentation in line with the implementation by describing the accuracy of the function more accurately and removing the references to CEPHES for this one. [1] https://github.com/jeremybarnes/cephes/blob/master/cprob/unity.c

It looks like my previous comment about CEPHES is in error. What is actually happening is that the logImpl function has the CEPHES polynomials that are used for log1p (at least I know it's true for doubles, I don't see them in the CEPHES code for floats/long double, but I assume it is right). In other words, the phobos log function seems to try to be more accurate for values close to 1 in a way that is different from other programming languages (which is why log1p is typically included as a separate function). I'm still showing some funky results for log1p(1.0e-15) vs. log1p(1.0e-16) compared to when log1p did the calculation at real accuracy.

I double-checked and log1p doesn't provide the same accuracy as the CEPHES implementation for doubles.

By the time of the 2.102.2 release, the precision was properly increased for log1p.