XProfan

Window Title "Mittels Newton-Raphson in the accuracy improved Lambert-W-Funktion"
Cls:Set("decimals",17)
print $profver:waitinput 7000

proc Wu :parameters y!

    declare Wu!

    if y!>1

        Wu!=ln(y!)-ln(ln(y!)) + 0.5*ln(ln(y!))/ln(y!)

    else

        Wu!=1

    endif

    return Wu!

endproc

proc where :parameters x!

    declare where!
    where!=ln(x!)-ln(ln(x!))+ exp(1)/(exp(1)-1)*ln(ln(x!))/ln(x!)
    return where!

endproc

Declare xn!,x!,y!,epsilon!,i&,max&
y!=1.295' steady first on the master-branch

Repeat

    if  y! > if($profver="11.2a-NT",10^305 , 10^53)

        sound 500,200:sound 300,200
        waitinput 20000:end

    endif

    y!=y!*1.1
    max&=4000'Verbesserungs-runs
    epsilon!=5/10^16:case y!>227.93:epsilon!=5.687/10^14
    xn!=Wu(y!)'Startwert (To small) for Newton-Raphson
    i&=0

    Repeat

        inc i&
        x!=xn!

        if ((x!+1)*exp(x!)) = 0

            xn!=(Wu(y!)+where(y!))/2'then even ex here from Näherungsformel... ex x~18.56
            break

        else

            xn! = x!-(x!*exp(x!)-y!)/((x!+1)*exp(x!))

        endif

    until (abs(xn!-x!)<=epsilon!) or (i&>max&)

    if i&>max&

        print " x-Search for y=";stature$("%g",y!);" nach",i&,"Durchläufen aborted!"
        print tab(2);i&,
        print tab(10);"Y=";stature$("%g",y!),
        print tab(23);"x=";stature$("%g",xn!),
        print tab(50);"err=";stature$("%g",abs(x!-xn!))
        '   print tab(50);"Y2=";format$("%g",xn!*exp(xn!))
        sound 2000,200:waitinput

    else

        print i&,
        print tab(5);"Y=";stature$("%g",y!),
        print tab(29);"x=";stature$("%g",xn!),
        print tab(52);"err=";stature$("%g",abs(x!-xn!))
        '   print tab(50);"Y2=";format$("%g",xn!*exp(xn!))

    endif

    if %csrlin>22:waitinput :locate 1,1:endif' cls:endif

    Until %key=27

    END