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