std::log(std::complex)

Header: <complex>

Computes complex natural (base e) logarithm of a complex value z with a branch cut along the negative real axis.

# Declarations

template< class T >
std::complex<T> log( const std::complex<T>& z );

# Parameters

z: complex value

# Return value

If no errors occur, the complex natural logarithm of z is returned, in the range of a strip in the interval [−iπ, +iπ] along the imaginary axis and mathematically unbounded along the real axis.

# Notes

The natural logarithm of a complex number z with polar coordinate components (r,θ) equals ln r + i(θ+2nπ), with the principal value ln r + iθ.

The semantics of this function are intended to be consistent with the C function clog.

# Example

#include <cmath>
#include <complex>
#include <iostream>
 
int main()
{
    std::complex<double> z {0.0, 1.0}; // r = 1, θ = pi / 2
    std::cout << "2 * log" << z << " = " << 2.0 * std::log(z) << '\n';
 
    std::complex<double> z2 {sqrt(2.0) / 2, sqrt(2.0) / 2}; // r = 1, θ = pi / 4
    std::cout << "4 * log" << z2 << " = " << 4.0 * std::log(z2) << '\n';
 
    std::complex<double> z3 {-1.0, 0.0}; // r = 1, θ = pi
    std::cout << "log" << z3 << " = " << std::log(z3) << '\n';
    std::complex<double> z4 {-1.0, -0.0}; // the other side of the cut
    std::cout << "log" << z4 << " (the other side of the cut) = " << std::log(z4) << '\n';
}

# Defect reports

DR	Applied to	Behavior as published	Correct behavior
LWG 2597	C++98	specification mishandles signed zero imaginary parts	erroneous requirement removed