Exponential, Logarithmic, Power functions

[tk]

Script Name: Exponential, Logarithmic, Power functions
Original Author(s): tk
Core Version: 2.6.3

function Power(Base: double; Exponent: integer): double;
function Root(Base: double; Exponent: integer): double;
function Cbrt(Base: double): double;

Code: (pascal) [Select]

const
  epsilon = 1e-6; // accuracy, number of decimal places (ie 1e-6 -> 6 decimal places accuracy)


function Power(Base: double; Exponent: integer): double;
var i: integer;
begin
  Result:=1;
  if Exponent = 0 then exit;
  for i:=1 to round(Abs(Exponent)) do Result:=Result*Base;
  if Exponent < 0 then Result:=1/Result;
end;

function Root(Base: double; Exponent: integer): double;
var r: double; neg_exp: boolean;
begin
  if Base < 0 then
    if Exponent mod 2 = 0 then exit;
  if Exponent < 0 then begin
    neg_exp:=true;
    Exponent:=-Exponent;
  end;
  Result:=1;
  repeat
    r:=Result;
    Result:=(Result*(Exponent-1)+Base/Power(Result,Exponent-1))/Exponent;
  until Abs(r-Result) < epsilon;
  if neg_exp then Result:=1/Result;
end;

function Cbrt(Base: double): double;
var r: double;
begin
  Result:=1;
  repeat
    r:=Result;
    Result:=(Result*2+Base/(Result*Result))/3;
  until Abs(r-Result) < epsilon;
end;


function Exp(X: double): double;
function Ln(X: double): double;
function Log(X: double): double;
function Power(Base: double; Exponent: double): double;
function Root(Base: double; Exponent: double): double;

Code: (pascal) [Select]

const
e = 2.71828182846; // value of e, don't touch
epsilon = 1e-6; // accuracy, number of decimal places (ie 1e-6 -> 6 decimal places accuracy)

function Exp(X: double): double;
var m, n: integer; r, fac, pow: double;
begin
m:=Round(Abs(X/10));
if m >= 2 then
X:=X/m;
Result:=1+X;
fac:=1;
pow:=X;
n:=2;
r:=1;
while r>epsilon do begin
fac:=fac*n;
pow:=pow*X;
n:=n+1;
r:=pow/fac;
Result:=Result+r;
end;
if m >= 2 then begin
pow:=Result;
for n:=2 to m do
Result:=Result*pow;
end;
end;

function Ln(X: double): double;
begin
Result:=LogN(e,X);
end;

function Log(X: double): double;
begin
Result:=LogN(10,X);
end;

function Power(Base: double; Exponent: double): double;
begin
Result:=Exp(LogN(e, Base)*Exponent);
end;

function Root(Base: double; Exponent: double): double;
begin
Result:=Exp(LogN(e, Base)/Exponent);
end;

[DarkCrusade]

For what is this script for?

[Furai]

Ready-to-use template. ;p If you was in need of any function like that you can C&P it into your script and give credits to tk. ;p

[Quantifier]

Logarithmic and Exponential functions:

You do realize there is built-in:
function LogN(base, value:Extended):Extended;
in the server?

[tk]

Since now. I tried Ln, Log, Log10, Lg, Exp names but they dont exist (I havent tried with logn). Ln, Exp exist in Pascal but they don't in the scripting core. What is more, Logn is not on any list with scriptcore functions.

[xmRipper]

Hey tk, what's your next script? Where will you use these functions? =)

[Quantifier]

Since now.

Actually since roughly year and a half ago, introduced in 2.6.2.

What is more, Logn is not on any list with scriptcore functions.

True. However, it works in scripts, and does the right thing.

[tk]

Updated
Ln, Log10, Power and Root use now built-in LogN function.

Hey tk, what's your next script? Where will you use these functions? =)

I'm not going to use it soon, I made this bacause I needed to use power with float exponent in one of my scripts.

[Mighty]

I need someone smarter than me to recreate these functions without using built-in logN, since it's not available anymore

[Savage]

Can't you guys just load an unit to SC3? http://www.freepascal.org/docs-html/rtl/math/index-5.html

[Falcon`]

It's already done, I'm kinda puzzled what's Mighty trying to accomplish.

EDIT: Ok, my bad, he wasn't aware of my changes.

[soldat-game]

Can't you guys just load an unit to SC3? http://www.freepascal.org/docs-html/rtl/math/index-5.html

haha