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Computing natural log, ln(x)

MEL, SQL, Oracle

Last Post by Anonymous 1 second ago

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jfitzmd

(@jfitzmd)

Posts: 419

Reputable Member

Topic starter

A question was recently asked about computing log as there is no intrinsic function in MEL. I suggested using a Taylor series. The following is based on a derivation of the Taylor series, hyperbolic tangent function (don't ask). The form to drive this code consists of a variable field, a result field, and a button to calculate the Ln. I made it a little more complicated as I made the input number <=10 by series of divisions by 10 then calculated the result as ln(z)=ln(zdiv10 value)+(num of div10)*ln(10). This allows the value to rapidly converge. The VFE is as follows:

/*Compute Natural Log*/

{ fn Calc_Ln(strZ)

{

//note where z is input number, n10 is number of divisions by 10

//ln(z)=ln(zdiv10)+n10*ln(10)

sumZ=0

strLnZ=""

presumZ=0

strSumZ=""

z=val(strZ)

n=1

n10=0

zdiv10=z

//divide by powers of 10 such than z/10^n<10

while zdiv10>10 do

zdiv10=zdiv10/10

n10=n10+1

endwhile

z=zdiv10

//calculate ln(z) where z now<=10

presumZ=2*((z-1)/(z+1))

sumZ=presumZ+(2/3)*((z-1)/(z+1))^3

while ((sumZ-presumZ)/sumZ)>.000001 do

presumZ=sumZ

n=n+1

sumZ=sumZ+(2/(2*n+1))*((z-1)/(z+1))^(2*n+1)

endwhile

//ln(z)=ln(zdiv10)+n10*ln(10)

sumZ=sumZ+n10*2.30258509

strAns="iterations: "+str(n)+" num div 10: "+str(N10)+" lnz "+str(round(SumZ,6))

document.Ln=strAns

}
}

Computing natural log of 400, 11 interations through the series, result accurate to 6 places, 5.991464. To any mathematicians out there, I apologize in advance if I have butchered the approach, but this seems to be fast and accurate.

Posted : March 3, 2017 9:26 am

cprice7

(@cprice7)

Posts: 71

Estimable Member

I know this is an old post, but you are truly the gift the keeps on giving. I haven't tried this yet, but I think you just saved my life!

Posted : March 30, 2023 1:27 am

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