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### 2459. `std::polar` should require a non-negative rho

Section: 26.4.8 [complex.value.ops] Status: C++17 Submitter: Marshall Clow Opened: 2014-10-22 Last modified: 2017-07-30

Priority: 0

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Discussion:

Different implementations give different answers for the following code:

>     #include <iostream>
>     #include <complex>

>     int main ()
>     {
>       std::cout << std::polar(-1.0, -1.0) << '\n';
>       return 0;
>     }

One implementation prints:

>     (nan, nan)

Another:

>     (-0.243068, 0.243068)

Which is correct? Or neither?

In this list, Howard Hinnant wrote:

> I've read this over several times. I've consulted C++11, C11, and IEC 10967-3. [snip]

> I'm finding:

> 1. The magnitude of a complex number `== abs(c) == hypot(c.real(), c.imag())` and is always non-negative (by all three of the above standards).

> 2. Therefore no complex number exists for which `abs(c) < 0`.

> 3. Therefore when the first argument to `std::polar` (which is called `rho`) is negative, no complex number can be formed which meets the post-conidtion that `abs(c) == rho`.

> One could argue that this is already covered in 26.4 [complex.numbers]/3, but I think it's worth making explicit.

[2015-02, Cologne]

Discussion on whether theta should also be constrained.
TK: infinite theta doesn't make sense, whereas infinite rho does (theta is on a compact domain, rho is on a non-compact domain).
AM: We already have a narrow contract, so I don't mind adding further requirements. Any objections to requiring that theta be finite?
Some more discussion, but general consensus. Agreement that if someone finds the restrictions problematic, they should write a proper paper to address how `std::polar` should behave. For now, we allow infinite rho (but not NaN and not negative), and require finite theta.

No objections to tentatively ready.

Proposed resolution:

This wording is relative to N4296.

1. Change 26.4.8 [complex.value.ops] around p9 as indicated

   >     template<class T> complex<T> polar(const T& rho, const T& theta = 0);

   > > -?- 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`.