std::polar(std::complex)(3)

💖 NAME 💖

okay so bestie, this page is std::polar(std::complex) — the NAME line is literally std::polar(std::complex) - std::polar(std::complex), and it lives in the C++ Standard Libary manual, section 3. iconic, no notes. 💅

---

✨ Synopsis ✨

Defined in header <complex>:

template< class 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. like, literally undefined — do not do it, bestie. 😭

---

🎀 Parameters 🎀

• r — magnitude.
• theta — phase angle.

---

🦋 Return value 🦋

A complex number determined by r and theta. that's the whole vibe. 💜

---

🌸 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. highkey a slay. 🔥

---

🍓 Example 🍓

the page says // Run this code, and here's the exact code, no cap:

#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 💜

and the output is giving:

           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.

• LWG 2459 — applied to C++98; behavior as published: behavior unclear for some inputs; correct behavior: made undefined.
• LWG 2870 — applied to C++98; behavior as published: default value of parameter theta not dependent; correct behavior: made dependent.

---

🌈 See also 🌈

• abs(std::complex) — returns the magnitude of a complex number (function template).
• arg — returns the phase angle (function template).
• exp(std::complex) — complex base e exponential (function template).

---

that's the whole page, bestie! source: http://cppreference.com · version/date: 2024.06.10 · page: std::polar(std::complex)(3). mwah 💋✨