Computing exponentials and Trig functions

[mr.janus at mac.com]

Hello,

I'm trying to write a program in C using GMP as matlab is unable to handle the precision i need for solving my coupled equations accurately. However, one of the many problems i'm having is how to speed up the calculation of trig functions.

I often have to solve complex exponentials but the way i have coded it is painfully slow. I split the exponential into the real and imaginary parts and solve separately. I then solve using sin, cos, sinh, and cosh identities.

However the slowdown problem arises from my calculation of the trigonometric functions, which i do by Taylor expansion. Obviously, as I push the precision the Taylor expansion takes longer and longer to converge to the required precision. How does everyone else do this?

Many thanks

Huw