The IEEE standard doesn’t really require any particular precision for transcendental functions IIUC? The original standard doesn’t even define them. The 2008 version includes optional correctly-rounded transcendentals, but there seems to be a total of one implementation, CRlibm, which is an academic project of more than a decade (and a dead home page because of the INRIA Forge shutdown). Your run-of-the-mill libm has little to do with this.
Right, it requires correct rounding for the optional correctly-rounded functions, which ISO C, for example, does not require to correspond to your usual libm ones, or even to be provided at all (even with __STDC_IEC_559__ or __STDC_IEC_60559_BFP__). I think I saw a spec for correctly rounded functions for C somewhere, but even the latest draft[1] of C23 is content with just reserving the cr_* namespace and not mandating much for the usual functions outside it (F.10/16):
> IEC 60559 specifies correct rounding for the operations in the F.3 table of operations recommended by IEC 60559, and thereby preserves useful mathematical properties such as symmetry, monotonicity, and periodicity. The corresponding functions with (potentially) reserved `cr_`-prefixed names (7.33.8) do the same. The C functions in the table, however, are not required to be correctly rounded, but implementations should still preserve as many of these useful mathematical properties as possible.
Maybe correct rounding (and hence consistency) will be made into the standard requirements (at least for single and double precisions) in the near future?
