The exponentional function can be calculated accurately for large arguments using relatively few terms of the Taylor series by using the identity
^y-:(2^n)*^(y-n*^.2) where n=<.0.5 y% ^.2 . This is the method used by Microsoft (and other) libm libraries. It has the advantage that multiplication by 2^n can be done by adding n to the exponent. Unfortunately, (y-n*^.2) involves subtracting nearly equal quantities, which leads to loss of precision. In particular, ^.2 has to be calculated to greater precision than the result. This is commonly not done carefully, and results are not reliable. I leave it to the reader to show that ^100 in J (and most languages) does not have full precision. Best wishes, John ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
