Difference between revisions of "cpp/numeric/complex"

Latest revision as of 07:50, 5 August 2024

Specializations of std::complex for cv-unqualified standard(until C++23) floating-point types are TriviallyCopyable(since C++23) LiteralTypes for representing and manipulating complex number.

[edit] Template parameters

[edit] Member types

[edit] Member functions

[edit] Non-member functions

[edit] Helper types

[edit] Array-oriented access

For any object z of type std::complex<T>, reinterpret_cast<T(&)[2]>(z)[0] is the real part of z and reinterpret_cast<T(&)[2]>(z)[1] is the imaginary part of z.

For any pointer to an element of an array of std::complex<T> named p and any valid array index i, reinterpret_cast<T*>(p)[2 * i] is the real part of the complex number p[i], and reinterpret_cast<T*>(p)[2 * i + 1] is the imaginary part of the complex number p[i].

The intent of this requirement is to preserve binary compatibility between the C++ library complex number types and the C language complex number types (and arrays thereof), which have an identical object representation requirement.

[edit] Implementation notes

In order to satisfy the requirements of array-oriented access, an implementation is constrained to store the real and imaginary parts of a std::complex specialization in separate and adjacent memory locations. Possible declarations for its non-static data members include:

• an array of type value_type[2], with the first element holding the real part and the second element holding the imaginary part (e.g. Microsoft Visual Studio);
• a single member of type value_type _Complex (encapsulating the corresponding C language complex number type) (e.g. GNU libstdc++);
• two members of type value_type, with the same member access, holding the real and the imaginary parts respectively (e.g. LLVM libc++).

An implementation cannot declare additional non-static data members that would occupy storage disjoint from the real and imaginary parts, and must ensure that the class template specialization does not contain any padding bit. The implementation must also ensure that optimizations to array access account for the possibility that a pointer to value_type may be aliasing a std::complex specialization or array thereof.

[edit] Literals

[edit] Notes

[edit] Example

#include <cmath>
#include <complex>
#include <iomanip>
#include <iostream>
#include <ranges>
 
int main()
{
    using namespace std::complex_literals;
    std::cout << std::fixed << std::setprecision(1);
 
    std::complex<double> z1 = 1i * 1i; // imaginary unit squared
    std::cout << "i * i = " << z1 << '\n';
 
    std::complex<double> z2 = std::pow(1i, 2); // imaginary unit squared
    std::cout << "pow(i, 2) = " << z2 << '\n';
 
    const double PI = std::acos(-1); // or std::numbers::pi in C++20
    std::complex<double> z3 = std::exp(1i * PI); // Euler's formula
    std::cout << "exp(i * pi) = " << z3 << '\n';
 
    std::complex<double> z4 = 1.0 + 2i, z5 = 1.0 - 2i; // conjugates
    std::cout << "(1 + 2i) * (1 - 2i) = " << z4 * z5 << '\n';
 
    const auto zz = {0.0 + 1i, 2.0 + 3i, 4.0 + 5i};
#if __cpp_lib_tuple_like >= 202311L
    for (double re : zz | std::views::keys)
        std::cout << re << ' ';
    std::cout << '\n';
    for (double im : zz | std::views::values)
        std::cout << im << ' ';
    std::cout << '\n';
#else
    for (double re : zz | std::views::transform([](auto z){ return z.real(); }))
        std::cout << re << ' ';
    std::cout << '\n';
    for (double im : zz | std::views::transform([](auto z){ return z.imag(); }))
        std::cout << im << ' ';
    std::cout << '\n';
#endif
}

i * i = (-1.0,0.0)
pow(i, 2) = (-1.0,0.0)
exp(i * pi) = (-1.0,0.0)
(1 + 2i) * (1 - 2i) = (5.0,0.0)
0.0 2.0 4.0
1.0 3.0 5.0

[edit] Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

[edit] See also