cp-algo/util/complex.hpp

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• Last update: 2025-05-13 16:30:42+02:00
• Include: #include "cp-algo/util/complex.hpp"

Required by

• cp-algo/geometry/closest_pair.hpp
• cp-algo/geometry/convex_hull.hpp
• cp-algo/geometry/point.hpp
• cp-algo/linalg/frobenius.hpp
• cp-algo/math/cvector.hpp
• cp-algo/math/fft.hpp
• cp-algo/math/fft64.hpp
• cp-algo/math/multivar.hpp
• cp-algo/math/poly.hpp
• cp-algo/math/poly/impl/div.hpp
• cp-algo/math/poly/impl/euclid.hpp
• cp-algo/number_theory.hpp
• cp-algo/number_theory/two_squares.hpp

Verified with

• Sort Points by Argument (verify/geometry/arg.test.cpp)
• Closest Pair of Points (verify/geometry/closest_pair.test.cpp)
• Static Convex Hull (verify/geometry/hull.test.cpp)
• Characteristic Polynomial (verify/linalg/characteristic.test.cpp)
• Pow of Matrix (Frobenius) (verify/linalg/pow_fast.test.cpp)
• Represent A Number As Two Square Sum (verify/number_theory/two_squares.test.cpp)
• Bell Number (verify/poly/bell.test.cpp)
• Convolution mod $10^9+7$ (verify/poly/convolution107.test.cpp)
• Convolution (Mod $2^{64}$) (verify/poly/convolution64.test.cpp)
• Convolution (Large) (verify/poly/convolution_large.test.cpp)
• Convolution on the Multiplicative Monoid of $\mathbb Z/p\mathbb{Z}$ (verify/poly/convolution_mul.test.cpp)
• Division of Polynomials (verify/poly/div.test.cpp)
• Exp of Power Series (verify/poly/exp.test.cpp)
• Find Linear Recurrence (verify/poly/find_linrec.test.cpp)
• Polynomial Interpolation (verify/poly/inter.test.cpp)
• Polynomial Interpolation (Geometric Sequence) (verify/poly/inter_geo.test.cpp)
• Inv of Power Series (verify/poly/inv.test.cpp)
• Inv of Polynomials (verify/poly/inv_mod.test.cpp)
• Consecutive Terms of Linear Recursion (verify/poly/linrec_consecutive.test.cpp)
• Kth term of Linearly Recurrent Sequence (verify/poly/linrec_single.test.cpp)
• Log of Power Series (verify/poly/log.test.cpp)
• Multipoint Evaluation (verify/poly/multieval.test.cpp)
• Multipoint Evaluation (Geometric Sequence) (verify/poly/multieval_geo.test.cpp)
• Multidimensional Convolution (Truncated) (verify/poly/multivar.test.cpp)
• Conversion to Newton Basis (verify/poly/newton.test.cpp)
• Pow of Power Series (verify/poly/pow.test.cpp)
• Product of Polynomial Sequence (verify/poly/prod_sequence.test.cpp)
• Polynomial Root Finding (verify/poly/roots.test.cpp)
• Shift of Sampling Points of Polynomial (verify/poly/sampling.test.cpp)
• Sqrt of Power Series (verify/poly/sqrt.test.cpp)
• $\sum\limits_{i=0}^\infty r^i i^d$ (verify/poly/sum_exp_poly.test.cpp)
• Polynomial Taylor Shift (verify/poly/taylor.test.cpp)
• Wildcard Pattern Matching (verify/poly/wildcard.test.cpp)

Code

#ifndef CP_ALGO_UTIL_COMPLEX_HPP
#define CP_ALGO_UTIL_COMPLEX_HPP
#include <iostream>
#include <cmath>
namespace cp_algo {
    // Custom implementation, since std::complex is UB on non-floating types
    template<typename T>
    struct complex {
        using value_type = T;
        T x, y;
        constexpr complex(): x(), y() {}
        constexpr complex(T x): x(x), y() {}
        constexpr complex(T x, T y): x(x), y(y) {}
        complex& operator *= (T t) {x *= t; y *= t; return *this;}
        complex& operator /= (T t) {x /= t; y /= t; return *this;}
        complex operator * (T t) const {return complex(*this) *= t;}
        complex operator / (T t) const {return complex(*this) /= t;}
        complex& operator += (complex t) {x += t.x; y += t.y; return *this;}
        complex& operator -= (complex t) {x -= t.x; y -= t.y; return *this;}
        complex operator * (complex t) const {return {x * t.x - y * t.y, x * t.y + y * t.x};}
        complex operator / (complex t) const {return *this * t.conj() / t.norm();}
        complex operator + (complex t) const {return complex(*this) += t;}
        complex operator - (complex t) const {return complex(*this) -= t;}
        complex& operator *= (complex t) {return *this = *this * t;}
        complex& operator /= (complex t) {return *this = *this / t;}
        complex operator - () const {return {-x, -y};}
        complex conj() const {return {x, -y};}
        T norm() const {return x * x + y * y;}
        T abs() const {return std::sqrt(norm());}
        T const real() const {return x;}
        T const imag() const {return y;}
        T& real() {return x;}
        T& imag() {return y;}
        static constexpr complex polar(T r, T theta) {return {T(r * cos(theta)), T(r * sin(theta))};}
        auto operator <=> (complex const& t) const = default;
    };
    template<typename T>
    complex<T> operator * (auto x, complex<T> y) {return y *= x;}
    template<typename T> complex<T> conj(complex<T> x) {return x.conj();}
    template<typename T> T norm(complex<T> x) {return x.norm();}
    template<typename T> T abs(complex<T> x) {return x.abs();}
    template<typename T> T& real(complex<T> &x) {return x.real();}
    template<typename T> T& imag(complex<T> &x) {return x.imag();}
    template<typename T> T const real(complex<T> const& x) {return x.real();}
    template<typename T> T const imag(complex<T> const& x) {return x.imag();}
    template<typename T>
    constexpr complex<T> polar(T r, T theta) {
        return complex<T>::polar(r, theta);
    }
    template<typename T>
    std::ostream& operator << (std::ostream &out, complex<T> x) {
        return out << x.real() << ' ' << x.imag();
    }
}
#endif // CP_ALGO_UTIL_COMPLEX_HPP

#line 1 "cp-algo/util/complex.hpp"


#include <iostream>
#include <cmath>
namespace cp_algo {
    // Custom implementation, since std::complex is UB on non-floating types
    template<typename T>
    struct complex {
        using value_type = T;
        T x, y;
        constexpr complex(): x(), y() {}
        constexpr complex(T x): x(x), y() {}
        constexpr complex(T x, T y): x(x), y(y) {}
        complex& operator *= (T t) {x *= t; y *= t; return *this;}
        complex& operator /= (T t) {x /= t; y /= t; return *this;}
        complex operator * (T t) const {return complex(*this) *= t;}
        complex operator / (T t) const {return complex(*this) /= t;}
        complex& operator += (complex t) {x += t.x; y += t.y; return *this;}
        complex& operator -= (complex t) {x -= t.x; y -= t.y; return *this;}
        complex operator * (complex t) const {return {x * t.x - y * t.y, x * t.y + y * t.x};}
        complex operator / (complex t) const {return *this * t.conj() / t.norm();}
        complex operator + (complex t) const {return complex(*this) += t;}
        complex operator - (complex t) const {return complex(*this) -= t;}
        complex& operator *= (complex t) {return *this = *this * t;}
        complex& operator /= (complex t) {return *this = *this / t;}
        complex operator - () const {return {-x, -y};}
        complex conj() const {return {x, -y};}
        T norm() const {return x * x + y * y;}
        T abs() const {return std::sqrt(norm());}
        T const real() const {return x;}
        T const imag() const {return y;}
        T& real() {return x;}
        T& imag() {return y;}
        static constexpr complex polar(T r, T theta) {return {T(r * cos(theta)), T(r * sin(theta))};}
        auto operator <=> (complex const& t) const = default;
    };
    template<typename T>
    complex<T> operator * (auto x, complex<T> y) {return y *= x;}
    template<typename T> complex<T> conj(complex<T> x) {return x.conj();}
    template<typename T> T norm(complex<T> x) {return x.norm();}
    template<typename T> T abs(complex<T> x) {return x.abs();}
    template<typename T> T& real(complex<T> &x) {return x.real();}
    template<typename T> T& imag(complex<T> &x) {return x.imag();}
    template<typename T> T const real(complex<T> const& x) {return x.real();}
    template<typename T> T const imag(complex<T> const& x) {return x.imag();}
    template<typename T>
    constexpr complex<T> polar(T r, T theta) {
        return complex<T>::polar(r, theta);
    }
    template<typename T>
    std::ostream& operator << (std::ostream &out, complex<T> x) {
        return out << x.real() << ' ' << x.imag();
    }
}

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