[jira] [Commented] (NUMBERS-22) Method reciprocal() in Complex for complex numbers with parts very close to 0.0

["Eric Barnhill (JIRA)" <ji...@apache.org>]

    [ https://issues.apache.org/jira/browse/NUMBERS-22?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=16148629#comment-16148629 ] 

Eric Barnhill commented on NUMBERS-22:
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I have looked into this a bit.

There was, it turns out, no C99 standards for the reciprocal.

complex-js, whose formulas are always conformed to standards, was here no help as it has no reciprocal function.

The result comes from the lines:

            double q = imaginary / real;
            double scale = 1. / (imaginary * q + real);
            return new Complex(scale, -scale * q);

when the real value is small enough, and imag is zero, q evaluates to 0 and scale to negInf. However that last imaginary quantity, -scale*q, evaluates to NaN because in Java, zero times inf is Nan. 

Any suggestions for the cleanest way to proceed? I can always just check for this particular configuration with an if statement.

> Method reciprocal() in Complex for complex numbers with parts very close to 0.0
> -------------------------------------------------------------------------------
>
>                 Key: NUMBERS-22
>                 URL: https://issues.apache.org/jira/browse/NUMBERS-22
>             Project: Commons Numbers
>          Issue Type: Improvement
>            Reporter: Gunel Jahangirova
>            Priority: Minor
>             Fix For: 1.0
>
>
> I have been redirected here from the issue repository of Apache Commons Math, as the Complex class will likely be deprecated in favour of its equivalent in "Commons Numbers".
> In class Complex method reciprocal() returns INF only if the real and imaginary parts are exactly equal to 0.0. In the cases when real and imaginary parts are double numbers very close to 0.0, it does not hold. For example, if we run this code
> {code}
> Complex complex0 = new Complex((-2.44242319E-315));
> Complex complex1 = complex0.reciprocal();
> {code}
> the value of complex1.getReal() will be -Infinity and the value of complex1.getImaginary() will be NaN, instead of complex1 being equal to INF.
> The suggested solutions after the discussion are either checking the equality to ZERO with some tolerance or to detect if one of the real or imaginary parts is going to be infinite or NaN and then return the proper result. 



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