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Joerg Huber commented on MATH306:

Yes, it looks like a twofold check for an already solved problem. By splitting the code up
for the two cases
1. Math.abs(c) < Math.abs(d)
2. the other way around
the denominator of q is always nonzero, which would habe been a problem and may have been
the reason to apply those extra checks.
The special cases c = 0 and d = 0 lead always to q = 0, in the respective code parts.
Which is no problem, because there is no division by q.
Effective code, if the extra checks are omitted.
Thank you Phil, I encourage the code cleanup you proposed.
> Method 'divide' in class 'Complex' uses a false formula for a special case resulting
in erroneous division by zero.
> 
>
> Key: MATH306
> URL: https://issues.apache.org/jira/browse/MATH306
> Project: Commons Math
> Issue Type: Bug
> Environment: all
> Reporter: Joerg Huber
>
> The formula that 'divide' wants to implement is
> ( a + bi ) / ( c + di ) = ( ac + bd + ( bc  ad ) i ) / ( c^2 + d^2 )
> as correctly written in the description.
> When c == 0.0 this leads to the special case
> ( a + bi ) / di = ( b / d )  ( a / d ) i
> But the corresponding code is:
> if (c == 0.0) {
> return createComplex(imaginary/d, real/c);
> }
> The bug is the last division real/c, which should obviously be real/d.

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