std::log(std::complex)

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std::complex

Member functions
complex::complex
complex::operator=
complex::real
complex::imag
complex::operator+=complex::operator-=complex::operator*=complex::operator/=
Non-member functions
operator+operator- operator+operator-operator*operator/ operator==operator!= operator<<operator>>	real imag abs arg norm conj proj (C++11) polar operator""ioperator""ifoperator""il (C++14)(C++14)(C++14)
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exp
log
log10
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pow
sqrt
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sin cos tan	asin (C++11) acos (C++11) atan (C++11)
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sinh cosh tanh	asinh (C++11) acosh (C++11) atanh (C++11)

Defined in header <complex>
template< class T > complex<T> log( const complex<T>& z );

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

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 [i, +i] along the imaginary axis and mathematically unbounded along the real axis.

Error handling and special values

Errors are reported consistent with math_errhandling

If the implementation supports IEEE floating-point arithmetic,

• The function is continuous onto the branch cut taking into account the sign of imaginary part
• std::log(std::conj(z)) == std::conj(std::log(z))
• If z is (-0,+0), the result is (-,) and FE_DIVBYZERO is raised
• If z is (+0,+0), the result is (-,+0) and FE_DIVBYZERO is raised
• If z is (x,+) (for any finite x), the result is (+,/2)
• If z is (x,NaN) (for any finite x), the result is (NaN,NaN) and FE_INVALID may be raised
• If z is (-,y) (for any finite positive y), the result is (+,)
• If z is (+,y) (for any finite positive y), the result is (+,+0)
• If z is (-,+), the result is (+,3/4)
• If z is (+,+), the result is (+,/4)
• If z is (,NaN), the result is (+,NaN)
• If z is (NaN,y) (for any finite y), the result is (NaN,NaN) and FE_INVALID may be raised
• If z is (NaN,+), the result is (+,NaN)
• If z is (NaN,NaN), the result is (NaN,NaN)

Notes

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

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

Defect reports

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

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

Example

Run this code

#include <iostream>
#include <cmath>
#include <complex>

int main()
{
    std::complex<double> z(0, 1); // // r = 1,  = pi/2
    std::cout << "2*log" << z << " = " << 2.*std::log(z) << '\n';

    std::complex<double> z2(sqrt(2)/2, sqrt(2)/2); // r = 1,  = pi/4
    std::cout << "4*log" << z2 << " = " << 4.*std::log(z2) << '\n';

    std::complex<double> z3(-1, 0); // r = 1,  = pi
    std::cout << "log" << z3 << " = " << std::log(z3) << '\n';
    std::complex<double> z4(-1, -0.0); // the other side of the cut
    std::cout << "log" << z4 << " (the other side of the cut) = " << std::log(z4) << '\n';
}

Output:

2*log(0,1) = (0,3.14159)
4*log(0.707107,0.707107) = (0,3.14159)
log(-1,0) = (0,3.14159)
log(-1,-0) (the other side of the cut) = (0,-3.14159)

See also

log10(std::complex)	complex common logarithm with the branch cuts along the negative real axis (function template)
exp(std::complex)	complex base e exponential (function template)
log	computes natural (base e) logarithm (ln(x)) (function)
log(std::valarray)	applies the function std::log to each element of valarray (function template)