(28/48/50) Lambert W Function

[John Keith]

(03-20-2023 10:51 PM)Albert Chan Wrote:  For accurate denominator, we need "doubled" precision for 1/e
For 12 digits, 1/e ≈ 0.367879441171 + 0.442321595524E-12

To reduce iterations, we also need good starting estimate.
Lua e^W code (0, -1 branch): https://www.hpmuseum.org/forum/thread-19...#pid167919

That's pretty much what I feared. I imagine that the best compromise would be to use extended precision reals, but SysRPL is beyond my skill set.

The estimation code I used for branch 0 is amazingly accurate over the entire numerical range representable by Saturn-based HP's. Also, the recurrence that I used converges faster than Newton's method while not being much larger in code size. Newton's method may be somewhat more accurate near the branch point but it wouldn't be much of an improvement without double-precision numbers.

Of more interest to me is computing W(z) for branches other than 0 and -1. I have not been able to find any methods for doing so. Any insight in this area would be greatly appreciated.