There is a request in the "C++ Standard Library Active Issues List" for a constexpr for various std::complex arithmetic and value operators. Currently the following code fails to compile:
#include <array>
#include <algorithm>
int main() {
// OK
constexpr std::complex<double> c1 { 1.0, 0.0 };
constexpr std::complex<double> c2 {};
// Failure: arithmetic operations on complex are not constexpr
constexpr auto c3 = -c1 + c2 / 100.0;
}
This proposal attempts to solve the issue.
A proof of concept implementation for is available at: constexpr complex.
This proposal is a pure library extension. It proposes changes to the
existing header <complex> such that the changes do not break existing code
and do not degrade performance. It does not require any changes in the core
language and it can be implemented in standard C++.
<complex> implementations and making them constexpr.libstdc++ uses __complex__ extension. That extension is already being used in constant expressions.
libc++ implements all the algorithms for std::complex from scratch. libc++ uses few functions from <cmath> (mostly isnan, isinf, logb and scalbn) for operations +,-,*,/,norm,conj.
Operations other than +,-,*,/,norm,conj use a lot of functions from <cmath>. It's unreasonable to mark them with constexpr right now.
abs(const complex<T>&) seems highly usable however it requires either sqrt or hypot to be constexpr. Forcing complicated math functions to be constexpr intrinsics may be a burden for compiler developers.
Adding constexpr to libc++ according to the wording in section IV of this paper resulted in a <complex> header that works well on GCC-6. __builtin_logb, __builtin_isnan and __builtin_scalbln are recognised by Clang, but they are not usable in constant expressions right now. Header with a hand-made naïve logb, isnan and scalbn became usable on CLANG-3.6 too.
namespace std {
template<class T> class complex;
template<> class complex<float>;
template<> class complex<double>;
template<> class complex<long double>;
// 26.5.6, operators:
template<class T> constexpr complex<T> operator+(const complex<T>&, const complex<T>&);
template<class T> constexpr complex<T> operator+(const complex<T>&, const T&);
template<class T> constexpr complex<T> operator+(const T&, const complex<T>&);
template<class T> constexpr complex<T> operator-(const complex<T>&, const complex<T>&);
template<class T> constexpr complex<T> operator-(const complex<T>&, const T&);
template<class T> constexpr complex<T> operator-(const T&, const complex<T>&);
template<class T> constexpr complex<T> operator*(const complex<T>&, const complex<T>&);
template<class T> constexpr complex<T> operator*(const complex<T>&, const T&);
template<class T> constexpr complex<T> operator*(const T&, const complex<T>&);
template<class T> constexpr complex<T> operator/(const complex<T>&, const complex<T>&);
template<class T> constexpr complex<T> operator/(const complex<T>&, const T&);
template<class T> constexpr complex<T> operator/(const T&, const complex<T>&);
template<class T> constexpr complex<T> operator+(const complex<T>&);
template<class T> constexpr complex<T> operator-(const complex<T>&);
template<class T> constexpr bool operator==(const complex<T>&, const complex<T>&);
template<class T> constexpr bool operator==(const complex<T>&, const T&);
template<class T> constexpr bool operator==(const T&, const complex<T>&);
template<class T> constexpr bool operator!=(const complex<T>&, const complex<T>&);
template<class T> constexpr bool operator!=(const complex<T>&, const T&);
template<class T> constexpr bool operator!=(const T&, const complex<T>&);
template<class T, class charT, class traits>
basic_istream<charT, traits>& operator>>(basic_istream<charT, traits>&, complex<T>&);
template<class T, class charT, class traits>
basic_ostream<charT, traits>& operator<<(basic_ostream<charT, traits>&, const complex<T>&);
// 26.5.7, values:
template<class T> constexpr T real(const complex<T>&);
template<class T> constexpr T imag(const complex<T>&);
template<class T> T abs(const complex<T>&);
template<class T> T arg(const complex<T>&);
template<class T> constexpr T norm(const complex<T>&);
template<class T> constexpr complex<T> conj(const complex<T>&);
template<class T> complex<T> proj(const complex<T>&);
template<class T> complex<T> polar(const T&, const T& = 0);
// 26.5.8, transcendentals:
template<class T> complex<T> acos(const complex<T>&);
template<class T> complex<T> asin(const complex<T>&);
template<class T> complex<T> atan(const complex<T>&);
template<class T> complex<T> acosh(const complex<T>&);
template<class T> complex<T> asinh(const complex<T>&);
template<class T> complex<T> atanh(const complex<T>&);
template<class T> complex<T> cos (const complex<T>&);
template<class T> complex<T> cosh (const complex<T>&);
template<class T> complex<T> exp (const complex<T>&);
template<class T> complex<T> log (const complex<T>&);
template<class T> complex<T> log10(const complex<T>&);
template<class T> complex<T> pow (const complex<T>&, const complex<T>&);
template<class T> complex<T> pow (const T&, const complex<T>&);
template<class T> complex<T> pow (const complex<T>&, const T&);
template<class T> complex<T> sin(const complex<T>&);
template<class T> complex<T> sinh(const complex<T>&);
template<class T> complex<T> sqrt(const complex<T>&);
template<class T> complex<T> tan(const complex<T>&);
template<class T> complex<T> tanh(const complex<T>&);
// 26.5.10, complex literals:
inline namespace literals {
inline namespace complex_literals {
constexpr complex<long double> operator""il(long double);
constexpr complex<long double> operator""il(unsigned long long);
constexpr complex<double> operator""i(long double);
constexpr complex<double> operator""i(unsigned long long);
constexpr complex<float> operator""if(long double);
constexpr complex<float> operator""if(unsigned long long);
}
}
}
namespace std {
template<class T>
class complex {
public:
typedef T value_type;
constexpr complex(const T& re = T(), const T& im = T());
constexpr complex(const complex&);
template<class X> constexpr complex(const complex<X>&);
constexpr T real() const;
constexpr void real(T);
constexpr T imag() const;
constexpr void imag(T);
constexpr complex<T>& operator= (const T&);
constexpr complex<T>& operator+=(const T&);
constexpr complex<T>& operator-=(const T&);
constexpr complex<T>& operator*=(const T&);
constexpr complex<T>& operator/=(const T&);
constexpr complex& operator=(const complex&);
template<class X> constexpr complex<T>& operator= (const complex<X>&);
template<class X> constexpr complex<T>& operator+=(const complex<X>&);
template<class X> constexpr complex<T>& operator-=(const complex<X>&);
template<class X> constexpr complex<T>& operator*=(const complex<X>&);
template<class X> constexpr complex<T>& operator/=(const complex<X>&);
};
}
The class complex describes an object that can store the Cartesian components, real() and imag(), of a
complex number.
namespace std {
template<> class complex<float> {
public:
typedef float value_type;
constexpr complex(float re = 0.0f, float im = 0.0f);
constexpr explicit complex(const complex<double>&);
constexpr explicit complex(const complex<long double>&);
constexpr float real() const;
constexpr void real(float);
constexpr float imag() const;
constexpr void imag(float);
constexpr complex<float>& operator= (float);
constexpr complex<float>& operator+=(float);
constexpr complex<float>& operator-=(float);
constexpr complex<float>& operator*=(float);
constexpr complex<float>& operator/=(float);
constexpr complex<float>& operator=(const complex<float>&);
template<class X> constexpr complex<float>& operator= (const complex<X>&);
template<class X> constexpr complex<float>& operator+=(const complex<X>&);
template<class X> constexpr complex<float>& operator-=(const complex<X>&);
template<class X> constexpr complex<float>& operator*=(const complex<X>&);
template<class X> constexpr complex<float>& operator/=(const complex<X>&);
};
template<> class complex<double> {
public:
typedef double value_type;
constexpr complex(double re = 0.0, double im = 0.0);
constexpr complex(const complex<float>&);
constexpr explicit complex(const complex<long double>&);
constexpr double real() const;
constexpr void real(double);
constexpr double imag() const;
constexpr void imag(double);
constexpr complex<double>& operator= (double);
constexpr complex<double>& operator+=(double);
constexpr complex<double>& operator-=(double);
constexpr complex<double>& operator*=(double);
constexpr complex<double>& operator/=(double);
constexpr complex<double>& operator=(const complex<double>&);
template<class X> constexpr complex<double>& operator= (const complex<X>&);
template<class X> constexpr complex<double>& operator+=(const complex<X>&);
template<class X> constexpr complex<double>& operator-=(const complex<X>&);
template<class X> constexpr complex<double>& operator*=(const complex<X>&);
template<class X> constexpr complex<double>& operator/=(const complex<X>&);
};
template<> class complex<long double> {
public:
typedef long double value_type;
constexpr complex(long double re = 0.0, long double im = 0.0);
constexpr complex(const complex<float>&);
constexpr explicit complex(const complex<double>&);
constexpr long double real() const;
constexpr void real(long double);
constexpr long double imag() const;
constexpr void imag(long double);
constexpr complex<long double>& operator= (long double);
constexpr complex<long double>& operator+=(long double);
constexpr complex<long double>& operator-=(long double);
constexpr complex<long double>& operator*=(long double);
constexpr complex<long double>& operator/=(long double);
constexpr complex<long double>& operator=(const complex<long double>&);
template<class X> constexpr complex<long double>& operator= (const complex<X>&);
template<class X> constexpr complex<long double>& operator+=(const complex<X>&);
template<class X> constexpr complex<long double>& operator-=(const complex<X>&);
template<class X> constexpr complex<long double>& operator*=(const complex<X>&);
template<class X> constexpr complex<long double>& operator/=(const complex<X>&);
};
}
Note for the editor: All the functions marked with constexpr in previous paragraphs of this document must be accordingly marked with constexpr
in detailed descriptions.
For brevity only modifications to "complex member functions" [complex.members] are shown in this paper.
template<class T> constexpr complex(const T& re = T(), const T& im = T());
Effects: Constructs an object of class complex.
Postcondition: real() == re && imag() == im.
constexpr T real() const;
Returns: The value of the real component.
constexpr void real(T val);
Effects: Assigns val to the real component.
constexpr T imag() const;
Returns: The value of the imaginary component.
constexpr void imag(T val);
Effects: Assigns val to the imaginary component.
For the purposes of SG10, we recommend the feature-testing macro name __cpp_lib_constexpr_complex.
Revision 0:
[N4594] Working Draft, Standard for Programming Language C++. Available online at www.open-std.org/jtc1/sc22/wg21/docs/papers/2016/n4594.pdf.
[Antony Polukhin] Proof of concept implementation. Available online at https://github.com/apolukhin/apolukhin.github.io/tree/master/papers/constexpr_complex/.
[LWG2693] constexpr for various std::complex arithmetic and value operators. Available online at http://www.open-std.org/jtc1/sc22/wg21/docs/lwg-active.html#2693.
Walter E. Brown pointed me at the LWG 2693 issue, provided numerous comments, corrections, and suggestions for this proposal.