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Function `std.complex.log`

Calculate the natural logarithm of x. The branch cut is along the negative axis.


						
				Complex!T log(T)(
				
  Complex!T x
				

				) pure nothrow @nogc @safe;

Parameters

Name	Description
x	A complex number

Returns

The complex natural logarithm of x

Special Values
x	log(x)
(-0, +0)	(-∞, π )
(+0, +0)	(-∞, +0)
(any, +∞)	(+∞, π /2)
(any, NAN)	(NAN, NAN)
(-∞, any)	(+∞, π )
(+∞, any)	(+∞, +0)
(-∞, +∞)	(+∞, 3π /4)
(+∞, +∞)	(+∞, π /4)
(±∞, NAN)	(+∞, NAN)
(NAN, any)	(NAN, NAN)
(NAN, +∞)	(+∞, NAN)
(NAN, NAN)	(NAN, NAN)

Example

import core.math : sqrt;
import std.math.constants : PI;
import std.math.operations : isClose;

auto a = complex(2.0, 1.0);
writeln(log(conj(a))); // conj(log(a))

auto b = 2.0 * log10(complex(0.0, 1.0));
auto c = 4.0 * log10(complex(sqrt(2.0) / 2, sqrt(2.0) / 2));
assert(isClose(b, c, 0.0, 1e-15));

writeln(log(complex(-1.0L, 0.0L))); // complex(0.0L, PI)
writeln(log(complex(-1.0L, -0.0L))); // complex(0.0L, -PI)

Authors

Lars Tandle Kyllingstad, Don Clugston

License

Boost License 1.0