Lambert W Function (hp-42s)

[Albert Chan]

Hi Werner

Nice idea putting constant 0.3 up front !

Tracking LASTX is hard, it might be a good idea to use it up ASAP, like this:
(I am leaving out the LBL01 ... GTO 01 loops)

Code:

01▸LBL "eW"
02 0.3 @        L       X       Y       Z           T
03 -1
04 E^X @                r       .3      x
05 RCL+ ST Z @  r       r+x     .3      x
06 STO× ST Y @                  .3(r+x)
08 LASTX @              r       r+x     .3(r+x)     x
09 STO+ ST Z @         
09 STO+ ST X @          2r      r+x     .3(r+x)+r   x
10 ×
11 SQRT
12 +
13 X<>Y
14 +/-
15 X<>Y @               y       -x      x       x

Here is a version that does not use LASTX to build guess, (same steps and bytes count)
Rewrite guess(x) = √(2r(x+r)) + 1.3(x+r) - x

This is not as accurate when |x| is huge, but for guess, it does not matter.
The up side is that code is easier to follow.

Code:

01▸LBL "eW"
02 1.3
03 -1
04 E^X
05 ENTER
07 RCL+ ST T @      #   r+x     r      1.3      x
08 STO× ST Z @
09 STO+ ST X @      #   2(r+x)  r   1.3(r+x)    x
09 ×
10 SQRT       
11 +                #   y+x     x       x       x
12 X<>Y
13 +/-              #   -x      y+x     x       x
14 STO ST Z
15 +                #    y      -x      x       x