Computes complexnatural (basee) logarithm of a complex valuez with a branch cut along the negative real axis.

[edit]Parameters

[edit]Return value

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

[edit]Error handling and special values

Errors are reported consistent withmath_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))
• Ifz is(-0,+0), the result is(-∞,π) andFE_DIVBYZERO is raised
• Ifz is(+0,+0), the result is(-∞,+0) andFE_DIVBYZERO is raised
• Ifz is(x,+∞) (for any finite x), the result is(+∞,π/2)
• Ifz is(x,NaN) (for any finite x), the result is(NaN,NaN) andFE_INVALID may be raised
• Ifz is(-∞,y) (for any finite positive y), the result is(+∞,π)
• Ifz is(+∞,y) (for any finite positive y), the result is(+∞,+0)
• Ifz is(-∞,+∞), the result is(+∞,3π/4)
• Ifz is(+∞,+∞), the result is(+∞,π/4)
• Ifz is(±∞,NaN), the result is(+∞,NaN)
• Ifz is(NaN,y) (for any finite y), the result is(NaN,NaN) andFE_INVALID may be raised
• Ifz is(NaN,+∞), the result is(+∞,NaN)
• Ifz is(NaN,NaN), the result is(NaN,NaN)

[edit]Notes

The natural logarithm of a complex numberz with polar coordinate components(r,θ) equalsln r + i(θ+2nπ), with the principal valueln r + iθ.

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

[edit]Example

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

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)

[edit]Defect reports

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

[edit]See also

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