25efbfb212
The threshold for not being tiny was too small. Use the usual 2**-12 threshold. This change is not just an optimization, since the general code that we fell into has accuracy problems even for tiny x. Avoiding it fixes 2*1366 args with errors of more than 1 ulp, with a maximum error of 1.167 ulps. 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 code for handling the interval [2**-28, 9_was_22] has accuracy problems even for [9, 22], so this change happens to fix errors of more than 1 ulp in about 2*17000 cases. It leaves such errors in about 2*1074000 cases, with a max error of 1.242 ulps. The threshold for switching from returning exp(x)/2 to returning exp(x/2)^2/2 was a little smaller than necessary. As for coshf(), This was not quite harmless since the exp(x/2)^2/2 case is inaccurate, and fixing it avoids accuracy problems in 2*6 cases, leaving problems in 2*19997 cases. Fixed naming errors in pseudo-code in comments. |
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