Natural Log function ln(x)

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BigM
BigM ✭
in Robot Controller
Hi,
 

Has anyone been able to generate a function for the natual logarithm (ie: log base 'e') ???

I've looked through the RAPID reference maula and the only function that closely relates is the exponential function.

 

Is there a way to generate it?

If not, an approximation?

 

Regards,

bigM

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  • BigM
    BigM ✭
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    Well, after some investigation I have generated this so far.
     

    The natural log can be approximated by the equation

     

    Letting z = \frac{1+x}{1-x} \! and thus x = \frac{z-1}{z+1} \!, we get

    \ln z = 2 \left ( \frac{z-1}{z+1} + \frac{1}{3}{\left(\frac{z-1}{z+1}\right)}^3 + \frac{1}{5}{\left(\frac{z-1}{z+1}\right)}^5 + \cdots \right ).
    I've converted this into a RAPID function.
    In order to get the accuracy i require I've gone to the 1999th degree.

     

    Here it is...

     

      FUNC num Ln (num z)
       VAR num x;
       VAR num answer;
       !
       answer:=0;
       x:=((z-1)/(z+1));
       !
       FOR i from 1 TO 1999 STEP 2 DO
        answer:= answer + (2*(POW(x,i)/i));
       ENDFOR
       !
       RETURN (answer);
      ENDFUNC

     

    This approximation should be sufficient, are there any other suggestions?

     

    Regards,

    bigM

     

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