I'm extending j#'s built in BigInteger and BigDecimal classes to have proper operators and standard math functions like sqrt, log, exponentiation with decimal powers, trig functions, etc, in Vb.net... I already have logs and nth roots and nth powers done, and I implemented the super fast karatsuba multiplication algorithim, and a very very fast factorial algorithim....

I need a FAST Exp(x) (e^x) routine so I can define exponentiation with decimal/irrational powers.

I'm using the series deffinition of e^x

e^x = SUM TO INFINITY OF x^n/n!

It works, but I can't figure out the exact correlation between number of iterations and error... like I need to know, given an X value of relatively arbitrary magnitude (within reason), and a specified precision to a certain number of decimal points, how high of an N value I will need to go before the series converges on a correct sum to that degree of precision

please advise