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342 lines
9.2 KiB
C++
342 lines
9.2 KiB
C++
/*
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* Copyright (c) 2021, Cesar Torres <shortanemoia@protonmail.com>
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions are met:
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*
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* 1. Redistributions of source code must retain the above copyright notice, this
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* list of conditions and the following disclaimer.
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*
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* 2. Redistributions in binary form must reproduce the above copyright notice,
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* this list of conditions and the following disclaimer in the documentation
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* and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
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* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
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* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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#pragma once
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#include <AK/Concepts.h>
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#if __has_include(<math.h>)
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# define AKCOMPLEX_CAN_USE_MATH_H
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# include <math.h>
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#endif
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#ifdef __cplusplus
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# if __cplusplus >= 201103L
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# define COMPLEX_NOEXCEPT noexcept
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# endif
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namespace AK {
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template<AK::Concepts::Arithmetic T>
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class [[gnu::packed]] Complex {
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public:
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constexpr Complex()
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: m_real(0)
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, m_imag(0)
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{
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}
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constexpr Complex(T real)
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: m_real(real)
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, m_imag((T)0)
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{
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}
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constexpr Complex(T real, T imaginary)
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: m_real(real)
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, m_imag(imaginary)
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{
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}
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constexpr T real() const COMPLEX_NOEXCEPT { return m_real; }
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constexpr T imag() const COMPLEX_NOEXCEPT { return m_imag; }
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constexpr T magnitude_squared() const COMPLEX_NOEXCEPT { return m_real * m_real + m_imag * m_imag; }
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# ifdef AKCOMPLEX_CAN_USE_MATH_H
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constexpr T magnitude() const COMPLEX_NOEXCEPT
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{
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// for numbers 32 or under bit long we don't need the extra precision of sqrt
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// although it may return values with a considerable error if real and imag are too big?
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if constexpr (sizeof(T) <= sizeof(float)) {
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return sqrtf(m_real * m_real + m_imag * m_imag);
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} else if constexpr (sizeof(T) <= sizeof(double)) {
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return sqrt(m_real * m_real + m_imag * m_imag);
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} else {
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return sqrtl(m_real * m_real + m_imag * m_imag);
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}
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}
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constexpr T phase() const COMPLEX_NOEXCEPT
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{
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return atan2(m_imag, m_real);
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}
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template<AK::Concepts::Arithmetic U, AK::Concepts::Arithmetic V>
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static constexpr Complex<T> from_polar(U magnitude, V phase)
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{
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if constexpr (sizeof(T) <= sizeof(float)) {
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return Complex<T>(magnitude * cosf(phase), magnitude * sinf(phase));
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} else if constexpr (sizeof(T) <= sizeof(double)) {
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return Complex<T>(magnitude * cos(phase), magnitude * sin(phase));
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} else {
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return Complex<T>(magnitude * cosl(phase), magnitude * sinl(phase));
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}
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}
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# endif
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template<AK::Concepts::Arithmetic U>
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constexpr Complex<T>& operator=(const Complex<U>& other)
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{
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m_real = other.real();
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m_imag = other.imag();
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return *this;
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}
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template<AK::Concepts::Arithmetic U>
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constexpr Complex<T>& operator=(const U& x)
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{
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m_real = x;
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m_imag = 0;
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return *this;
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}
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template<AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator+=(const Complex<U>& x)
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{
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m_real += x.real();
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m_imag += x.imag();
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return *this;
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}
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template<AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator+=(const U& x)
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{
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m_real += x.real();
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return *this;
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}
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template<AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator-=(const Complex<U>& x)
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{
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m_real -= x.real();
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m_imag -= x.imag();
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return *this;
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}
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template<AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator-=(const U& x)
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{
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m_real -= x.real();
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return *this;
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}
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template<AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator*=(const Complex<U>& x)
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{
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const T real = m_real;
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m_real = real * x.real() - m_imag * x.imag();
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m_imag = real * x.imag() + m_imag * x.real();
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return *this;
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}
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template<AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator*=(const U& x)
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{
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m_real *= x;
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m_imag *= x;
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return *this;
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}
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template<AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator/=(const Complex<U>& x)
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{
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const T real = m_real;
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const T divisor = x.real() * x.real() + x.imag() * x.imag();
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m_real = (real * x.real() + m_imag * x.imag()) / divisor;
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m_imag = (m_imag * x.real() - x.real() * x.imag()) / divisor;
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return *this;
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}
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template<AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator/=(const U& x)
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{
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m_real /= x;
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m_imag /= x;
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return *this;
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}
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template<AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator+(const Complex<U>& a)
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{
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Complex<T> x = *this;
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x += a;
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return x;
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}
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template<AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator+(const U& a)
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{
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Complex<T> x = *this;
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x += a;
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return x;
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}
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template<AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator-(const Complex<U>& a)
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{
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Complex<T> x = *this;
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x -= a;
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return x;
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}
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template<AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator-(const U& a)
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{
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Complex<T> x = *this;
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x -= a;
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return x;
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}
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template<AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator*(const Complex<U>& a)
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{
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Complex<T> x = *this;
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x *= a;
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return x;
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}
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template<AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator*(const U& a)
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{
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Complex<T> x = *this;
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x *= a;
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return x;
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}
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template<AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator/(const Complex<U>& a)
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{
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Complex<T> x = *this;
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x /= a;
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return x;
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}
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template<AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator/(const U& a)
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{
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Complex<T> x = *this;
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x /= a;
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return x;
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}
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template<AK::Concepts::Arithmetic U>
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constexpr bool operator==(const Complex<U>& a)
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{
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return (this->real() == a.real()) && (this->imag() == a.imag());
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}
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template<AK::Concepts::Arithmetic U>
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constexpr bool operator!=(const Complex<U>& a)
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{
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return !(*this == a);
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}
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constexpr Complex<T> operator+()
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{
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return *this;
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}
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constexpr Complex<T> operator-()
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{
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return Complex<T>(-m_real, -m_imag);
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}
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private:
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T m_real;
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T m_imag;
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};
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// reverse associativity operators for scalars
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template<AK::Concepts::Arithmetic T, AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator+(const U& b, const Complex<T>& a)
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{
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Complex<T> x = a;
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x += b;
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return x;
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}
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template<AK::Concepts::Arithmetic T, AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator-(const U& b, const Complex<T>& a)
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{
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Complex<T> x = a;
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x -= b;
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return x;
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}
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template<AK::Concepts::Arithmetic T, AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator*(const U& b, const Complex<T>& a)
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{
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Complex<T> x = a;
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x *= b;
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return x;
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}
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template<AK::Concepts::Arithmetic T, AK::Concepts::Arithmetic U>
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constexpr Complex<T> operator/(const U& b, const Complex<T>& a)
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{
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Complex<T> x = a;
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x /= b;
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return x;
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}
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// some identities
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template<AK::Concepts::Arithmetic T>
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static constinit Complex<T> complex_real_unit = Complex<T>((T)1, (T)0);
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template<AK::Concepts::Arithmetic T>
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static constinit Complex<T> complex_imag_unit = Complex<T>((T)0, (T)1);
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# ifdef AKCOMPLEX_CAN_USE_MATH_H
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template<AK::Concepts::Arithmetic T, AK::Concepts::Arithmetic U>
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static constexpr bool approx_eq(const Complex<T>& a, const Complex<U>& b, const double margin = 0.000001)
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{
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const auto x = const_cast<Complex<T>&>(a) - const_cast<Complex<U>&>(b);
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return x.magnitude() <= margin;
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}
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//complex version of exp()
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template<AK::Concepts::Arithmetic T>
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static constexpr Complex<T> cexp(const Complex<T>& a)
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{
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//FIXME: this can probably be faster and not use so many expensive trigonometric functions
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if constexpr (sizeof(T) <= sizeof(float)) {
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return expf(a.real()) * Complex<T>(cosf(a.imag()), sinf(a.imag()));
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} else if constexpr (sizeof(T) <= sizeof(double)) {
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return exp(a.real()) * Complex<T>(cos(a.imag()), sin(a.imag()));
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} else {
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return expl(a.real()) * Complex<T>(cosl(a.imag()), sinl(a.imag()));
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}
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}
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}
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# endif
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using AK::Complex;
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using AK::complex_imag_unit;
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using AK::complex_real_unit;
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# ifdef AKCOMPLEX_CAN_USE_MATH_H
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using AK::approx_eq;
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using AK::cexp;
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# endif
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#endif
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