freebsd-dev/lib/msun
Bruce Evans 52453261e9 As usual, use a minimax polynomial that is specialized for float
precision.  The new polynomial has degree 4 instead of 10, and a maximum
error of 2**-30.04 ulps instead of 2**-33.15.  This doesn't affect the
final error significantly; the maximum error was and is about 0.5015
ulps on i386 -O1, and the number of cases with an error of > 0.5 ulps
is increased from 13851 to 14407.

Note that the error is only this close to 0.5 ulps due to excessive
extra precision caused by compiler bugs on i386.  The extra precision
could be obtained intentionally, and is useful for keeping the error
of the hyperbolic float functions below 1 ulp, since these functions
are implemented using expm1f.  My recent change for scaling by 2**k
had the unintentional side effect of retaining extra precision for
longer, so callers of expm1f see errors of more like 0.0015 ulps than
0.5015 ulps, and for the hyperbolic functions this reduces the maximum
error from nearly about 2 ulps to about 0.75 ulps.

This is about 10% faster on i386 (A64).  expm1* is still very slow,
but now the float version is actually significantly faster.  The
algorithm is very sophisticated but not very good except on machines
with fast division.
2008-02-09 12:53:15 +00:00
..
amd64 Implement rintl(), nearbyintl(), lrintl(), and llrintl(). 2008-01-14 02:12:07 +00:00
arm Use C comments since we now preprocess these files with CPP. 2007-04-29 14:05:22 +00:00
bsdsrc Fix tgamma() on some special args: 2007-05-02 15:24:49 +00:00
i387 Implement rintl(), nearbyintl(), lrintl(), and llrintl(). 2008-01-14 02:12:07 +00:00
ia64 Use C comments since we now preprocess these files with CPP. 2007-04-29 14:05:22 +00:00
ld80 Use a better method of scaling by 2**k. Instead of adding to the 2008-02-07 03:17:05 +00:00
ld128 Use a better method of scaling by 2**k. Instead of adding to the 2008-02-07 03:17:05 +00:00
man Introduce a new log(3) manpage and move the relevant functions there. 2008-01-18 21:43:00 +00:00
powerpc Use C comments since we now preprocess these files with CPP. 2007-04-29 14:05:22 +00:00
sparc64 Use C comments since we now preprocess these files with CPP. 2007-04-29 14:05:22 +00:00
src As usual, use a minimax polynomial that is specialized for float 2008-02-09 12:53:15 +00:00
Makefile Hook up exp2l() and related docs to the build. 2008-01-18 21:43:10 +00:00
Symbol.map Hook up exp2l() and related docs to the build. 2008-01-18 21:43:10 +00:00