fast accurate Kneser sexp algorithm

[sheldonison]

If the precision is manually modified via "\p 134", then "init;loop" for the base e default, it takes about 40 seconds, for 26 iterations, with results accurate to ~225 binary digits.

I tested at same setting and I got 31 seconds on my new AMD X6 1055T@2.8GHz - PC desktop (after old Intel C2D E6600) running Win 7 x64-SP1.

I tried "init(I)" but I got error: "if: incorrect type in comparison."?!?! how? I already read that you can get I^^I. wow!

Thanks. There's a dozen different "if" statements, most of which are in the initialization code, testing the value of B, the sexp base for init(B). If statements <> don't work for complex number. The if statements are required to allow a large range of bases to initialize correctly to guarantee subsequent convergence. Compare statements are required as the base approaches eta, or is less than eta, or becomes larger, to calculate the fixed point, and to setup the initial approximation for sexp(z). Its not practical to have this program work for complex bases, although someday I'd like to calculate a Kneser like mapping for a complex base with two repelling fixed points. I've also written some fixed point scripts, that calculate the superfunction and inverse superfunction for complex bases.
- Shel