(28/48/50) Lambert W Function

[Albert Chan]

(03-23-2023 05:53 PM)John Keith Wrote:  There is one line in your program that concerns me:

if h == err then return -1 end

It seems that the program would return -1 if a is the closest machine representation of -1/e, which would be -.367879441171 on the HP calculators. Instead, we would want the program to return -.999998449288 in branch 0, or -1.00000155071 in branch -1, which are the correct 12-digit representations of W(-.367879441171).

You are right.

Guard should be if (h == 0) ... but that would never happen.
Guard is not needed. I'll remove it.

Quote:x = sqrt(2*h/r) * (x and -1 or 1)

Last term is Lua idiom for ternary operators

It says that pick -1 if x evaluated true (neither nil nor false), 1 otherwise.
Signs are the result of solving W guess quadratic equation, 2 roots for W 2 branches