ladybird/AK/Complex.h

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/*
* Copyright (c) 2021, Cesar Torres <shortanemoia@protonmail.com>
*
* SPDX-License-Identifier: BSD-2-Clause
*/
#pragma once
#include <AK/Concepts.h>
#include <AK/Math.h>
#ifdef __cplusplus
# if __cplusplus >= 201103L
# define COMPLEX_NOEXCEPT noexcept
# endif
namespace AK {
template<AK::Concepts::Arithmetic T>
class [[gnu::packed]] Complex {
public:
constexpr Complex()
: m_real(0)
, m_imag(0)
{
}
constexpr Complex(T real)
: m_real(real)
, m_imag((T)0)
{
}
constexpr Complex(T real, T imaginary)
: m_real(real)
, m_imag(imaginary)
{
}
constexpr T real() const COMPLEX_NOEXCEPT { return m_real; }
constexpr T imag() const COMPLEX_NOEXCEPT { return m_imag; }
constexpr T magnitude_squared() const COMPLEX_NOEXCEPT { return m_real * m_real + m_imag * m_imag; }
constexpr T magnitude() const COMPLEX_NOEXCEPT
{
return hypot(m_real, m_imag);
}
constexpr T phase() const COMPLEX_NOEXCEPT
{
return atan2(m_imag, m_real);
}
template<AK::Concepts::Arithmetic U, AK::Concepts::Arithmetic V>
static constexpr Complex<T> from_polar(U magnitude, V phase)
{
V s, c;
sincos(phase, s, c);
return Complex<T>(magnitude * c, magnitude * s);
}
template<AK::Concepts::Arithmetic U>
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constexpr Complex<T>& operator=(Complex<U> const& other)
{
m_real = other.real();
m_imag = other.imag();
return *this;
}
template<AK::Concepts::Arithmetic U>
constexpr Complex<T>& operator=(const U& x)
{
m_real = x;
m_imag = 0;
return *this;
}
template<AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator+=(Complex<U> const& x)
{
m_real += x.real();
m_imag += x.imag();
return *this;
}
template<AK::Concepts::Arithmetic U>
constexpr Complex<T> operator+=(const U& x)
{
m_real += x.real();
return *this;
}
template<AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator-=(Complex<U> const& x)
{
m_real -= x.real();
m_imag -= x.imag();
return *this;
}
template<AK::Concepts::Arithmetic U>
constexpr Complex<T> operator-=(const U& x)
{
m_real -= x.real();
return *this;
}
template<AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator*=(Complex<U> const& x)
{
const T real = m_real;
m_real = real * x.real() - m_imag * x.imag();
m_imag = real * x.imag() + m_imag * x.real();
return *this;
}
template<AK::Concepts::Arithmetic U>
constexpr Complex<T> operator*=(const U& x)
{
m_real *= x;
m_imag *= x;
return *this;
}
template<AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator/=(Complex<U> const& x)
{
const T real = m_real;
const T divisor = x.real() * x.real() + x.imag() * x.imag();
m_real = (real * x.real() + m_imag * x.imag()) / divisor;
m_imag = (m_imag * x.real() - x.real() * x.imag()) / divisor;
return *this;
}
template<AK::Concepts::Arithmetic U>
constexpr Complex<T> operator/=(const U& x)
{
m_real /= x;
m_imag /= x;
return *this;
}
template<AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator+(Complex<U> const& a)
{
Complex<T> x = *this;
x += a;
return x;
}
template<AK::Concepts::Arithmetic U>
constexpr Complex<T> operator+(const U& a)
{
Complex<T> x = *this;
x += a;
return x;
}
template<AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator-(Complex<U> const& a)
{
Complex<T> x = *this;
x -= a;
return x;
}
template<AK::Concepts::Arithmetic U>
constexpr Complex<T> operator-(const U& a)
{
Complex<T> x = *this;
x -= a;
return x;
}
template<AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator*(Complex<U> const& a)
{
Complex<T> x = *this;
x *= a;
return x;
}
template<AK::Concepts::Arithmetic U>
constexpr Complex<T> operator*(const U& a)
{
Complex<T> x = *this;
x *= a;
return x;
}
template<AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator/(Complex<U> const& a)
{
Complex<T> x = *this;
x /= a;
return x;
}
template<AK::Concepts::Arithmetic U>
constexpr Complex<T> operator/(const U& a)
{
Complex<T> x = *this;
x /= a;
return x;
}
template<AK::Concepts::Arithmetic U>
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constexpr bool operator==(Complex<U> const& a) const
{
return (this->real() == a.real()) && (this->imag() == a.imag());
}
template<AK::Concepts::Arithmetic U>
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constexpr bool operator!=(Complex<U> const& a) const
{
return !(*this == a);
}
constexpr Complex<T> operator+()
{
return *this;
}
constexpr Complex<T> operator-()
{
return Complex<T>(-m_real, -m_imag);
}
private:
T m_real;
T m_imag;
};
// reverse associativity operators for scalars
template<AK::Concepts::Arithmetic T, AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator+(const U& b, Complex<T> const& a)
{
Complex<T> x = a;
x += b;
return x;
}
template<AK::Concepts::Arithmetic T, AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator-(const U& b, Complex<T> const& a)
{
Complex<T> x = a;
x -= b;
return x;
}
template<AK::Concepts::Arithmetic T, AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator*(const U& b, Complex<T> const& a)
{
Complex<T> x = a;
x *= b;
return x;
}
template<AK::Concepts::Arithmetic T, AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator/(const U& b, Complex<T> const& a)
{
Complex<T> x = a;
x /= b;
return x;
}
// some identities
template<AK::Concepts::Arithmetic T>
static constinit Complex<T> complex_real_unit = Complex<T>((T)1, (T)0);
template<AK::Concepts::Arithmetic T>
static constinit Complex<T> complex_imag_unit = Complex<T>((T)0, (T)1);
template<AK::Concepts::Arithmetic T, AK::Concepts::Arithmetic U>
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static constexpr bool approx_eq(Complex<T> const& a, Complex<U> const& b, double const margin = 0.000001)
{
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auto const x = const_cast<Complex<T>&>(a) - const_cast<Complex<U>&>(b);
return x.magnitude() <= margin;
}
// complex version of exp()
template<AK::Concepts::Arithmetic T>
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static constexpr Complex<T> cexp(Complex<T> const& a)
{
// FIXME: this can probably be faster and not use so many "expensive" trigonometric functions
return exp(a.real()) * Complex<T>(cos(a.imag()), sin(a.imag()));
}
}
using AK::approx_eq;
using AK::cexp;
using AK::Complex;
using AK::complex_imag_unit;
using AK::complex_real_unit;
#endif