mirror of
https://github.com/LadybirdBrowser/ladybird.git
synced 2024-11-11 01:06:01 +03:00
343 lines
9.2 KiB
C++
343 lines
9.2 KiB
C++
/*
|
|
* Copyright (c) 2021, Cesar Torres <shortanemoia@protonmail.com>
|
|
* All rights reserved.
|
|
*
|
|
* Redistribution and use in source and binary forms, with or without
|
|
* modification, are permitted provided that the following conditions are met:
|
|
*
|
|
* 1. Redistributions of source code must retain the above copyright notice, this
|
|
* list of conditions and the following disclaimer.
|
|
*
|
|
* 2. Redistributions in binary form must reproduce the above copyright notice,
|
|
* this list of conditions and the following disclaimer in the documentation
|
|
* and/or other materials provided with the distribution.
|
|
*
|
|
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
|
|
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
|
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
|
|
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
|
|
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
|
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
|
|
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
|
|
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
|
|
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
|
|
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
|
*/
|
|
|
|
#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)
|
|
{
|
|
return (this->real() == a.real()) && (this->imag() == a.imag());
|
|
}
|
|
|
|
template<AK::Concepts::Arithmetic U>
|
|
constexpr bool operator!=(const Complex<U>& a)
|
|
{
|
|
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
|