std::log(std::complex) - cppreference.com (original) (raw)

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

Contents

• 1 Parameters
• 2 Return value
• 3 Error handling and special values
• 4 Notes
• 5 Example
• 6 Defect reports
• 7 See also

[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 #include #include   int main() { std::complex z {0.0, 1.0}; // r = 1, θ = pi / 2 std::cout << "2 * log" << z << " = " << 2.0 * std::log(z) << '\n';   std::complex 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 z3 {-1.0, 0.0}; // r = 1, θ = pi std::cout << "log" << z3 << " = " << std::log(z3) << '\n'; std::complex 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'; }

Possible 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)

[edit] Defect reports

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

[edit] See also