K 10
svn:author
V 3
bde
K 8
svn:date
V 27
2005-11-13T00:08:23.000000Z
K 7
svn:log
V 1091
Fixed some magic numbers.

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.

END