The D Programming Language

This module contains the Complex type, which is used to represent complex numbers, along with related mathematical operations and functions.

Complex will eventually replace the built-in types cfloat, cdouble, creal, ifloat, idouble, and ireal.

Lars Tandle Kyllingstad, Don Clugston
Boost License 1.0

pure nothrow @safe auto  complex(T)(T re) if (is(T : double));
pure nothrow @safe auto  complex(R, I)(R re, I im) if (is(R : double) && is(I : double));

Helper function that returns a complex number with the specified real and imaginary parts.

If neither re nor im are floating-point numbers, this function returns a Complex!double. Otherwise, the return type is deduced using std.traits.CommonType!(R, I).

auto c = complex(2.0);
static assert (is(typeof(c) == Complex!double));
assert ( == 2.0);
assert ( == 0.0);

auto w = complex(2);
static assert (is(typeof(w) == Complex!double));
assert (w == c);

auto z = complex(1, 3.14L);
static assert (is(typeof(z) == Complex!real));
assert ( == 1.0L);
assert ( == 3.14L);

struct  Complex(T) if (isFloatingPoint!T);

A complex number parametrised by a type T, which must be either float, double or real.

T  re;

The real part of the number.

T  im;

The imaginary part of the number.

const string  toString();
const void  toString(Char)(scope void delegate(const(Char)[]) sink, FormatSpec!Char formatSpec);

Converts the complex number to a string representation.

The second form of this function is usually not called directly; instead, it is used via std.format.format, as shown in the examples below. Supported format characters are 'e', 'f', 'g', 'a', and 's'.

See the std.format documentation for more information.

        auto c = complex(1.2, 3.4);

        // Vanilla toString formatting:

        assert(c.toString() == "1.2+3.4i");

        // Formatting with std.format specs: the precision and width specifiers

        // apply to both the real and imaginary parts of the complex number.

        import std.string;
        assert(format("%.2f", c)  == "1.20+3.40i");
        assert(format("%4.1f", c) == " 1.2+ 3.4i");

const string  toString(scope void delegate(const(char)[]) sink, string formatSpec = "%s");

Deprecated. This function will be removed in March 2014. Please use std.format.format instead.

Converts the complex number to a string representation.

If a sink delegate is specified, the string is passed to it and this function returns null. Otherwise, this function returns the string representation directly.

The output format is controlled via formatSpec, which should consist of a single POSIX format specifier, including the percent (%) character. Note that complex numbers are floating point numbers, so the only valid format characters are 'e', 'f', 'g', 'a', and 's', where 's' gives the default behaviour. Positional parameters are not valid in this context.

See the std.format documentation for more information.

pure nothrow @safe T  abs(T)(Complex!T z);

Calculates the absolute value (or modulus) of a complex number.

pure nothrow @safe T  arg(T)(Complex!T z);

Calculates the argument (or phase) of a complex number.

pure nothrow @safe Complex!T  conj(T)(Complex!T z);

Returns the complex conjugate of a complex number.

pure nothrow @safe Complex!(CommonType!(T, U))  fromPolar(T, U)(T modulus, U argument);

Constructs a complex number given its absolute value and argument.

pure nothrow @safe Complex!T  sin(T)(Complex!T z);
pure nothrow @safe Complex!T  cos(T)(Complex!T z);

Trigonometric functions.

pure nothrow @trusted Complex!real  expi(real y);

Calculates cos(y) + i sin(y).

 expi is included here for convenience and for easy migration of code that uses std.math.expi. Unlike std.math.expi, which uses the x87 fsincos instruction when possible, this function is no faster than calculating cos(y) and sin(y) separately.

pure nothrow @safe Complex!T  sqrt(T)(Complex!T z);

Square root.