std::polar(std::complex)
Defined in header <complex> |
||
|---|---|---|
template< class T > complex<T> polar( const T& r, const T& theta = T() ); |
Returns a complex number with magnitude r and phase angle theta.
The behavior is undefined if r is negative or NaN, or if theta is infinite.
Parameters
| r | - | magnitude |
| theta | - | phase angle |
Return value
a complex number determined by r and theta.
Notes
std::polar(r, theta) is equivalent to any of the following expressions:
-
r * std::exp(theta * 1i) -
r * (cos(theta) + sin(theta) * 1i) -
std::complex(r * cos(theta), r * sin(theta)).
Using polar instead of exp can be about 4.5x faster in vectorized loops.
Example
#include <cmath>
#include <complex>
#include <iomanip>
#include <iostream>
#include <numbers>
using namespace std::complex_literals;
int main()
{
constexpr auto π_2 {std::numbers::pi / 2.0};
constexpr auto mag {1.0};
std::cout
<< std::fixed << std::showpos << std::setprecision(1)
<< " θ: │ polar: │ exp: │ complex: │ trig:\n";
for (int n{}; n != 4; ++n) {
const auto θ {n * π_2};
std::cout
<< std::setw(4) << 90 * n << "° │ "
<< std::polar(mag, θ) << " │ "
<< mag * std::exp(θ * 1.0i) << " │ "
<< std::complex(mag * cos(θ), mag * sin(θ)) << " │ "
<< mag * (cos(θ) + 1.0i * sin(θ)) << '\n';
}
}
Output:
θ: │ polar: │ exp: │ complex: │ trig: +0° │ (+1.0,+0.0) │ (+1.0,+0.0) │ (+1.0,+0.0) │ (+1.0,+0.0) +90° │ (+0.0,+1.0) │ (+0.0,+1.0) │ (+0.0,+1.0) │ (+0.0,+1.0) +180° │ (-1.0,+0.0) │ (-1.0,+0.0) │ (-1.0,+0.0) │ (-1.0,+0.0) +270° │ (-0.0,-1.0) │ (-0.0,-1.0) │ (-0.0,-1.0) │ (-0.0,-1.0)
Defect reports
The following behavior-changing defect reports were applied retroactively to previously published C++ standards.
| DR | Applied to | Behavior as published | Correct behavior |
|---|---|---|---|
| LWG 2459 | C++98 | behavior unclear for some inputs | made undefined |
| LWG 2870 | C++98 | default value of parameter theta not dependent |
made dependent |
See also
| returns the magnitude of a complex number (function template) |
|
| returns the phase angle (function template) |
|
| complex base e exponential (function template) |
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