Re: Math functions in Ada

[dewar@merv.cs.nyu.edu (Robert Dewar)]

Jacob says

<<First of all, x**y equals exp(y * log(x)).  So, all you need are the
log (logarithm) and exp (exponential) functions.  It should be failrly
easy to write such a function as log and exp are generally provided.
Indeed, the whole thing would be:>>


AARGH! This is a *horrible* equivalence to use in any program, since the
error bounds are simply awful. In other words, even with a perfectly
accurate exp and log, the result of computing x**y can be way off (hundreds
of ULP's) 

True, as Jacob suggests, if you can use a higher precisoin intermediate
type, then this formula is OK, and indeed one of the classic illustrations
of the utility of IEEE extended precision is precisely this one (i.e. if
you have accurate extended precision long and exp, as on the x86, then
you can compute long_form x**y accurately. For a detailed analysis of 
this case, see chapter 5 of my book on Microprocessors.