std::log(std::complex)

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

[edit] Parameters

[edit] 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.

[edit] 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 (-∞,π) 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 (+∞,π/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 (+∞,π)
• If z is (+∞,y) (for any finite positive y), the result is (+∞,+0)
• If z is (-∞,+∞), the result is (+∞,3π/4)
• If z is (+∞,+∞), the result is (+∞,π/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)

[edit] 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.

[edit] 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';
}

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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