Natural Logarithms

function Ln takes real a returns real
local real s = 1.0
local real sum = 0.0
local real g
local real e
local integer i = 10
loop
    exitwhen a < bj_E
    set a = a/bj_E
    set sum = sum + 1.
endloop
set e = (a-1.0)/10. //quite accurate for numbers < e
set g = s + e
loop
    exitwhen i <= 0 or a <= 1.0
    set i = i-1
    set sum = sum + (g-s)*(1./s + 8./(s+g) + 1./g)/6.
    set s = g
    set g = s + e
endloop
return sum
endfunction

// cubic, very good accurity for warcraft
function Ln takes real a returns real
local real sum = 0.0
loop
    exitwhen a < bj_E
    set a = a/bj_E
    set sum = sum + 1.
endloop
return sum + (a-1.)*(1. + 9./(2.+a) + 9./(1.+a*2.) + 1/a)/8.
endfunction

//Even faster! --parabollic, has a good accurity as well
function Ln takes real a returns real
local real sum = 0.0
loop
    exitwhen a < bj_E
    set a = a/bj_E
    set sum = sum + 1.
endloop
return sum + (a-1.)*(1. + 8./(1.+ a) + 1/a)/6.
endfunction

//Fourth, this one is quite a bit more accurate than the former 2, but it is a bit slower.

function Ln takes real a returns real
local real sum = 0.0
local real e = 1.284025417
loop
    exitwhen a < bj_E
    set a = a/bj_E
    set sum = sum + 1.
endloop
loop
    exitwhen a < e
    set a = a/e
    set sum = sum + .25
endloop
return sum + (a-1.)*(1. + 8./(1.+ a) + 1/a)/6. //and we apply simpson's :D
endfunction

//Added a Fifth, this one uses Taylor series instead.

function Ln takes real a returns real
local real sum = 0.0
local real e = 1.648721271
local real b
loop
    exitwhen a < bj_E
    set a = a/bj_E
    set sum = sum + 1.
endloop
if a >= e then
    set a = a/e
    set sum = sum + .5
endif
//Time to apply Taylor series of ln(1+x).
set e = 1.
set a = (a - 1.)
set b = a
loop
    exitwhen e > 5.
    set sum = sum + a/e
    set e = e + 1.
    set a = a*b*(-1.)
endloop
return sum
endfunction

function LogB takes real a, real base returns real
         return Ln(a)/Ln(base) //I would suggest that you save the nautral log of the base 
                                       //if you want to keep using it over and over.
endfunction