Looking at the c++ standard [1] we are missing this function: norm() = a^2 + b^2
The field norm of the complex, or the square of the absolute. An example on C++ reference states that this is faster for comparing magnitudes for ranking as it avoids the sqrt() required in abs(). z.abs() > y.abs() == z.norm() > y.norm() I suggest this is added to comply with the standard. It seems odd to me that the constructor ofPolar throws an exception. It does this when the magnitude (rho) for the complex is negative. However if the magnitude is NaN it will not throw an exception and will end up returning NaN. I think this should be changed to return NaN for negative magnitude and avoid exceptions. This is basically stating that the polar representation you used is invalid and so in the Cartesian representation it will be (nan, nan). The C++ standard on this was previously vague and was clarified in [2]: “ -?- Requires: rho shall be non-negative and non-NaN. theta shall be finite. -9- Returns: The complex value corresponding to a complex number whose magnitude is rho and whose phase angle is theta. “ The assumption is that abs(polar(rho, theta)) == rho. If this cannot be ensured then polar(rho, theta) is undefined and we return NaN. Note that if theta is finite and rho is non-negative and non-nan: x = rho * Math.cos(theta) y = rho * Math.sin(theta) In the event that sin(theta) is zero (i.e. theta is zero) then inf * 0 is NaN. In this case the complex could either be: (Inf, nan) or (inf, 0) I have tried 2 c++ implementations and both return (inf, nan). The c++ <complex> header I have found would return (inf, 0). The same header also corrects if cos(theta) is zero however in Java cos(pi/2) is not zero so this is not an issue. Note: If the result is (inf, nan) then abs((inf, nan)) should return inf to satisfy the contract abs(polar(rho, theta)) == rho. This is currently true as abs() uses Math.hypot(x, y) which will return positive infinity if either argument is infinite. So I do not think it matters. An infinite is infinite even when the other part is nan. I suggest we update ofPolar to not throw exceptions and return NAN unless theta is finite and rho is non-negative and non-nan. Alex [1] http://www.cplusplus.com/reference/complex/ <http://www.cplusplus.com/reference/complex/> [2] https://cplusplus.github.io/LWG/issue2459 <https://cplusplus.github.io/LWG/issue2459>
