1a787460ba
The threshold for not being tiny was too small. Use the usual 2**-12 threshold. As for sinhf, use a different method (now the same as for sinhf) to set the inexact flag for tiny nonzero x so that the larger threshold works, although this method is imperfect. As for sinhf, this change is not just an optimization, since the general code that we fell into has accuracy problems even for tiny x. On amd64, avoiding it fixes tanhf on 2*13495596 args with errors of between 1 and 1.3 ulps and thus reduces the total number of args with errors of >= 1 ulp from 37533748 to 5271278; the maximum error is unchanged at 2.2 ulps. The magic number 22 is log(DBL_MAX)/2 plus slop. This is bogus for float precision. Use 9 (log(FLT_MAX)/2 plus less slop than for double precision). Unlike for coshf and tanhf, this is just an optimization, and MAX isn't misspelled EPSILON in the commit log. I started testing with nonstandard rounding modes, and verified that the chosen thresholds work for all modes modulo problems not related to thresholds. The best thresholds are not very dependent on the mode, at least for tanhf. |
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