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.
f63f109c0b