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Date: Fri, 27 Jan 2012 03:55:41 +0000 (UTC)
From: =?utf-8?Q?S=C3=A9bastien_Brisard_=28Commented=29_=28JIRA=29?=
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Subject: [jira] [Commented] (MATH-722) [math] Complex Tanh for "big" numbers
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    [ https://issues.apache.org/jira/browse/MATH-722?page=3Dcom.atlassian.j=
ira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=3D131944=
19#comment-13194419 ]=20

S=C3=A9bastien Brisard commented on MATH-722:
----------------------------------------

I've run some tests comparing the two formulas: I didn't notice any major d=
ifference. Therefore I suggest to stick with the existing formula.
Meanwhile, the fix proposed by Juan must be implemented. It can be proved m=
athematically 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.
               =20
> [math] Complex Tanh for "big" numbers
> -------------------------------------
>
>                 Key: MATH-722
>                 URL: https://issues.apache.org/jira/browse/MATH-722
>             Project: Commons Math
>          Issue Type: Bug
>    Affects Versions: 2.2
>         Environment: I'm working with Eclipse 3.6.2 on Windows XP, but th=
e bug is Enviroment independent
>            Reporter: Juan Barandiaran
>            Assignee: S=C3=A9bastien 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) =3D 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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