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/*
* Copyright (c) 2021, Cesar Torres <shortanemoia@protonmail.com>
*
* SPDX-License-Identifier: BSD-2-Clause
*/
#pragma once
#include <AK/Concepts.h>
#if __has_include(<math.h>)
# define AKCOMPLEX_CAN_USE_MATH_H
# include <math.h>
#endif
#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; }
# ifdef AKCOMPLEX_CAN_USE_MATH_H
constexpr T magnitude() const COMPLEX_NOEXCEPT
{
// for numbers 32 or under bit long we don't need the extra precision of sqrt
// although it may return values with a considerable error if real and imag are too big?
if constexpr (sizeof(T) <= sizeof(float)) {
return sqrtf(m_real * m_real + m_imag * m_imag);
} else if constexpr (sizeof(T) <= sizeof(double)) {
return sqrt(m_real * m_real + m_imag * m_imag);
} else {
return sqrtl(m_real * m_real + m_imag * 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)
{
if constexpr (sizeof(T) <= sizeof(float)) {
return Complex<T>(magnitude * cosf(phase), magnitude * sinf(phase));
} else if constexpr (sizeof(T) <= sizeof(double)) {
return Complex<T>(magnitude * cos(phase), magnitude * sin(phase));
} else {
return Complex<T>(magnitude * cosl(phase), magnitude * sinl(phase));
}
}
# endif
template<AK::Concepts::Arithmetic U>
constexpr Complex<T>& operator=(const Complex<U>& 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>
constexpr Complex<T> operator+=(const Complex<U>& 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>
constexpr Complex<T> operator-=(const Complex<U>& 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>
constexpr Complex<T> operator*=(const Complex<U>& 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>
constexpr Complex<T> operator/=(const Complex<U>& 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>
constexpr Complex<T> operator+(const Complex<U>& 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>
constexpr Complex<T> operator-(const Complex<U>& 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>
constexpr Complex<T> operator*(const Complex<U>& 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>
constexpr Complex<T> operator/(const Complex<U>& 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>
constexpr bool operator==(const Complex<U>& a) const
{
return (this->real() == a.real()) && (this->imag() == a.imag());
}
template<AK::Concepts::Arithmetic U>
constexpr bool operator!=(const Complex<U>& 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>
constexpr Complex<T> operator+(const U& b, const Complex<T>& a)
{
Complex<T> x = a;
x += b;
return x;
}
template<AK::Concepts::Arithmetic T, AK::Concepts::Arithmetic U>
constexpr Complex<T> operator-(const U& b, const Complex<T>& a)
{
Complex<T> x = a;
x -= b;
return x;
}
template<AK::Concepts::Arithmetic T, AK::Concepts::Arithmetic U>
constexpr Complex<T> operator*(const U& b, const Complex<T>& a)
{
Complex<T> x = a;
x *= b;
return x;
}
template<AK::Concepts::Arithmetic T, AK::Concepts::Arithmetic U>
constexpr Complex<T> operator/(const U& b, const Complex<T>& 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);
# ifdef AKCOMPLEX_CAN_USE_MATH_H
template<AK::Concepts::Arithmetic T, AK::Concepts::Arithmetic U>
static constexpr bool approx_eq(const Complex<T>& a, const Complex<U>& b, const double margin = 0.000001)
{
const auto x = const_cast<Complex<T>&>(a) - const_cast<Complex<U>&>(b);
return x.magnitude() <= margin;
}
// complex version of exp()
template<AK::Concepts::Arithmetic T>
static constexpr Complex<T> cexp(const Complex<T>& a)
{
// FIXME: this can probably be faster and not use so many expensive trigonometric functions
if constexpr (sizeof(T) <= sizeof(float)) {
return expf(a.real()) * Complex<T>(cosf(a.imag()), sinf(a.imag()));
} else if constexpr (sizeof(T) <= sizeof(double)) {
return exp(a.real()) * Complex<T>(cos(a.imag()), sin(a.imag()));
} else {
return expl(a.real()) * Complex<T>(cosl(a.imag()), sinl(a.imag()));
}
}
}
# endif
using AK::Complex;
using AK::complex_imag_unit;
using AK::complex_real_unit;
# ifdef AKCOMPLEX_CAN_USE_MATH_H
using AK::approx_eq;
using AK::cexp;
# endif
#endif
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