c24b7984fc
The threshold for not being tiny was confusing and too small. Use the usual 2**-12 threshold and simplify the algorithm slightly so that this threshold works (now use the threshold for sinhf() instead of one for 1+expm1()). This is just a small optimization. The magic number 22 is log(DBL_EPSILON)/2 plus slop. This is bogus for float precision. Use 9 (~log(FLT_EPSILON)/2 plus less slop than for double precision). The threshold for switching from returning exp(x)/2 to returning exp(x/2)^2/2 was a little smaller than necessary. This was not quite harmless since the exp(x/2)^2/2 case is inaccurate. Fixing it happens to avoid accuracy problems for 2*6 of the 2*151 args that were handled by the exp(x)/2 case. This leaves accuracy problems for about 2*19997 args near the overflow threshold (~89); the maximum error there is 2.5029 ulps. There are also accuracy probles for args in +-[0.5*ln2, 9] -- 2*188885 args with errors of more than 1 ulp, with a maximum error of 1.384 ulps. Fixed a syntax error and naming errors in pseudo-code in comments.
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