Re: Use of C99 extra long double math functions after r236148

Here is a technical question.  I know that people always talk about 
ulp's in the context of how good a function implementation is.  I think 
the ulp is the number of base 2 digits at the end of the mantissa that 
we cannot rely on.

So if one were to write a naive implementation of lexp(x) that used 
Taylor's series if x is positive, and 1/lexp(-x) is x is negative - well 
one could fairly easily estimate an upper bound on the ulp, but it 
wouldn't be low (like ulp=1 or 2), but probably rather higher (ulp of 
the order of 10 or 20).

So do people really work hard to get that last drop of ulp out of their 
calculations?  Would a ulp=10 be considered unacceptable?

Also, looking through the source code for the FreeBSD implementation of 
exp, I saw that they used some rather smart rational function.  (I don't 
know how they came up with it.)

Presumably a big part of the issue is to make the functions work rather 
fast.  And a naive implementation of Taylor's series wouldn't be fast. 
But if people want lexp rather than exp, they must have already decided 
that accuracy is more important than speed.