std::polar(std::complex)
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Defined in header
<complex>
template< class T >
std::complex <T> polar( const T& r, const T& theta = T() );
std::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.
[edit] Parameters
r
-
magnitude
theta
-
phase angle
[edit] Return value
A complex number determined by r and theta.
[edit] 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.
[edit] Example
Run this code
#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)
[edit] 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 |