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]
Sébastien Brisard commented on MATH722:

I've run some tests comparing the two formulas: I didn't notice any major difference. Therefore
I suggest to stick with the existing formula.
Meanwhile, the fix proposed by Juan must be implemented. It can be proved mathematically that
for any value of {{b}}, the value of {{tanh(a + i * b)}} is within one ulp of 1.0 for {{abs(a)
> 18.9}}, so the proposed threshold (20.0) is fairly safe, and consistent with other parts
of CM. Note that the same fix must be implemented for {{tan}} also.
> [math] Complex Tanh for "big" numbers
> 
>
> Key: MATH722
> URL: https://issues.apache.org/jira/browse/MATH722
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 2.2
> Environment: I'm working with Eclipse 3.6.2 on Windows XP, but the bug is Enviroment
independent
> Reporter: Juan Barandiaran
> Assignee: Sébastien Brisard
> Priority: Minor
> Labels: patch
> Fix For: 3.0
>
> Original Estimate: 0.25h
> Remaining Estimate: 0.25h
>
> Hi,
> In Complex.java the tanh is computed with the following formula:
> tanh(a + bi) = sinh(2a)/(cosh(2a)+cos(2b)) + [sin(2b)/(cosh(2a)+cos(2b))]i
> The problem that I'm finding is that as soon as "a" is a "big" number,
> both sinh(2a) and cosh(2a) are infinity and then the method tanh returns in
> the real part NaN (infinity/infinity) when it should return 1.0.
> Wouldn't it be appropiate to add something as in the FastMath library??:
> if (real>20.0){
> return createComplex(1.0, 0.0);
> }
> if (real<20.0){
> return createComplex(1.0, 0.0);
> }
> Best regards,
> JBB

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