complex number

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Complex numbers is a mathematical concept providing solutions to equations such as [math]\displaystyle{ x^2 = -1 }[/math]. In FPC's default runtime library the unit uComplex defines a type complex and lots of operator and other functions. u in uComplex stands for the Greek letter μ, meaning “micro”, as the implementation is kept as simple as possible.

In Extended Pascal, which FPC plans to implement one day, the data type complex is defined as part of the language.

program ComplexDemo;
uses
	uComplex;
var
	x, y: complex;
begin
	// specifying real and imaginary part
	x := -5 + 2 * i;
	
	// specifying magnitude and phase angle
	// y := sqrt(2) * (cos(pi/4) + i * sin(pi/4))
	y.re :=  1;
	y.im :=  1;
	
	x := x + y;
	// there is no toString functionality:
	writeLn('x = ', x.re, ' + ', x.im, 'i');
end.

Another demo, which shows how to use functions cinit (assign value), cstr (convert value to string), csin (sinus):

program ComplexDemo2;
uses
  uComplex;
const
  L = 0;
  D = 3;
var
  c1, c2: complex;
begin
  c1 := cinit(1.0, 1.0);
  c2 := cinit(2.0, -2.0);
  WriteLn('c1      = ' + cstr(c1, L, D));
  WriteLn('c2      = ' + cstr(c2, L, D));
  WriteLn('c1+c2   = ' + cstr(c1+c2, L, D));
  WriteLn('c1-c2   = ' + cstr(c1-c2, L, D));
  WriteLn('c1*c2   = ' + cstr(c1*c2, L, D));
  WriteLn('c1/c2   = ' + cstr(c1/c2, L, D));
  WriteLn('sin(c1) = ' + cstr(csin(c1), L, D));
  ReadLn;
end.

see also

• DMath, a mathematical library also containing a complex number implementation.
• LMath, further development of LMath library, with completer support for complex numbers, where operators over them are defined.
• NumLib documentation, where typ.complex is an object.

external references

• “complex number” on Wikipedia, the free online encyclopedia
• packages/rtl-extra/src/inc/ucomplex.pp source code
• packages/numlib/src/typ.pas source code