package body Generic_Complex_Numbers is

  TWO : constant number := one+one;

-- CREATORS :

  function Create ( i : integer ) return Complex_Number is

    res : Complex_Number;

  begin
    if i = 0
     then res.re := +zero;
     elsif i = 1
         then res.re := +one;
         else res.re := Create(i);
    end if;
    res.im := +zero;
    return res;
  end Create;

  function Create ( f : number ) return Complex_Number is

    res : Complex_Number;

  begin
    res.re := +f;
    res.im := +zero;
    return res;
  end Create;

  function Create ( re,im : number ) return Complex_Number is

    res : Complex_Number;

  begin
    res.RE := +re;
    res.IM := +im;
    return res;
  end Create;

  function Conjugate ( c : Complex_Number ) return Complex_Number is

    res : Complex_Number;

  begin
    res.RE := +c.RE;
    res.IM := -c.IM;
    return res;
  end Conjugate;

-- COMPARISON and COPYING :

  function Equal ( x,y : Complex_Number ) return boolean is
  begin
    return (Equal(x.RE,y.RE) and Equal(x.IM,y.IM));
  end Equal;

  procedure Copy ( x : in Complex_Number; y : in out Complex_Number ) is
  begin
    Copy(x.RE,y.RE);
    Copy(x.IM,y.IM);
  end Copy;

  function "<" ( x,y : Complex_Number ) return boolean is

    avx : number := AbsVal(x);
    avy : number := AbsVal(y);
    res : boolean := (avx < avy);

  begin
    Clear(avx);
    Clear(avy);
    return res;
  end "<";

  function ">" ( x,y : Complex_Number ) return boolean is

    avx : number := AbsVal(x);
    avy : number := AbsVal(y);
    res : boolean := (avx > avy);

  begin
    Clear(avx);
    Clear(avy);
    return res;
  end ">";

-- SELECTORS :

  function REAL_PART ( x : Complex_Number ) return number is
  begin
    return +x.RE;
  end REAL_PART;

  function IMAG_PART ( x : Complex_Number ) return number is
  begin
    return +x.IM;
  end IMAG_PART;

  function AbsVal ( x : Complex_Number ) return number is

    res : number := AbsVal(x.RE);
    acc : number := AbsVal(x.IM);

  begin
    Add(res,acc);
    Clear(acc);
    return res;
  end AbsVal;

  function AbsVal ( x : Complex_Number ) return Complex_Number is

    abx : number := AbsVal(x);
    res : Complex_Number := Create(abx);

  begin
    Clear(abx);
    return res;
  end AbsVal;

-- ARITHMETIC OPERATIONS AS FUNCTIONS :

  function "+" ( x : Complex_Number; y : number ) return Complex_Number is
  begin
    return (x.RE+y,+x.IM);
  end "+";

  function "-" ( x : Complex_Number; y : number ) return Complex_Number is
  begin
    return (x.RE-y,+x.IM);
  end "-";

  function "*" ( x : Complex_Number; y : number ) return Complex_Number is
  begin
    return (x.RE*y,x.IM*y);
  end "*";

  function "/" ( x : Complex_Number; y : number ) return Complex_Number is
  begin
    return (x.RE/y,x.IM/y);
  end "/";

  function "+" ( x : number; y : Complex_Number ) return Complex_Number is
  begin
    return (x+y.RE,+y.IM);
  end "+";

  function "-" ( x : number; y : Complex_Number ) return Complex_Number is
  begin
    return (x-y.RE,-y.IM);
  end "-";

  function "*" ( x : number; y : Complex_Number ) return Complex_Number is
  begin
    return (x*y.RE,x*y.IM);
  end "*";

  function "/" ( x : number; y : Complex_Number ) return Complex_Number is

    res : Complex_Number;
    acc,avyim,avyre : Number;

  begin
    if Equal(y.IM,zero)
     then res.RE := x/y.RE;
          res.IM := +zero;
     elsif Equal(y.RE,zero)
         then res.RE := +zero;
              res.IM := x/y.IM; Min(res.IM);
     else avyim := AbsVal(y.IM); avyre := AbsVal(y.RE);
          if avyim < avyre
           then acc := y.IM/y.RE;
                res.RE := x*acc; Mul(acc,y.IM); Add(acc,y.RE); Div(res.RE,acc);
                res.IM := x/acc; Min(res.IM);
                Clear(acc);
           elsif avyim > avyre 
               then acc := y.RE/y.IM;
                    res.IM := x*acc; Min(res.IM); Mul(acc,y.RE); Add(acc,y.IM);
                    res.RE := x/acc;
                    Clear(acc);
           elsif Equal(y.IM,y.RE)
               then acc := TWO*y.IM;
                    res.RE := x/acc;
                    res.IM := -res.RE;
                    Clear(acc);
           else -- y.IM = -y.RE then
                    acc := TWO*y.IM;
                    res.RE := x/acc; Min(res.RE);
                    res.IM := x/acc; Min(res.IM);
                    Clear(acc);
          end if;
          Clear(avyim); Clear(avyre);
    end if;
    return res;
  end "/";

  function "+" ( x : Complex_Number ) return Complex_Number is
  begin
    return (+x.RE,+x.IM);
  end "+";

  function "-" ( x : Complex_Number ) return Complex_Number is
  begin
    return (-x.RE,-x.IM);
  end "-";

  function "+" ( x,y : Complex_Number ) return Complex_Number is
  begin
    return (x.RE+y.RE,x.IM+y.IM);
  end "+";

  function "-" ( x,y : Complex_Number ) return Complex_Number is
  begin
    return (x.RE-y.RE,x.IM-y.IM);
  end "-";

  function "*" ( x,y : Complex_Number ) return Complex_Number is

    res : Complex_Number;
    acc,avyim,avyre : number;

  begin
    if Equal(y.IM,zero)
     then res.RE := x.RE*y.RE;
          res.IM := x.IM*y.RE;
     elsif Equal(y.RE,zero)
         then res.RE := x.IM*y.IM; Min(res.RE); 
              res.IM := x.RE*y.IM;
     else avyre := AbsVal(y.RE); avyim := AbsVal(y.IM);
          if avyre < avyim
           then acc := y.RE/y.IM;
                res.RE := x.RE*acc; Sub(res.RE,x.IM); Mul(res.RE,y.IM);
                res.IM := x.IM*acc; Add(res.IM,x.RE); Mul(res.IM,y.IM);
                Clear(acc);
           elsif avyre > avyim
               then acc := y.IM/y.RE;
                    res.RE := x.IM*acc; Sub(res.RE,x.RE); Min(res.RE);
                                        Mul(res.RE,y.RE);
                    res.IM := x.RE*acc; Add(res.IM,x.IM); Mul(res.IM,y.RE);
                    Clear(acc);
           elsif Equal(y.RE,y.IM)
               then res.RE := x.RE - x.IM; Mul(res.RE,y.RE);
                    res.IM := x.IM + x.RE; Mul(res.IM,y.RE);
           else -- y.RE = -y.IM then
                    res.RE := x.RE + x.IM; Mul(res.RE,y.RE);
                    res.IM := x.IM - x.RE; Mul(res.IM,y.RE); 
          end if;
          Clear(avyre); Clear(avyim);
    end if;
    return res;
  end "*";

  function "/"  ( x,y : Complex_Number ) return Complex_Number is

    res : Complex_Number;
    acc,avyre,avyim : number;

  begin
    if Equal(y.IM,zero)
     then res.RE := x.RE/y.RE;
          res.IM := x.IM/y.RE;
     elsif Equal(y.RE,zero)
         then res.RE := x.IM/y.IM;
              res.IM := x.RE/y.IM; Min(res.IM);
     else avyre := AbsVal(y.RE); avyim := AbsVal(y.IM);
          if avyre < avyim
           then acc := y.RE/y.IM;
                res.RE := x.RE*acc; Add(res.RE,x.IM);
                res.IM := x.IM*acc; Sub(res.IM,x.RE);
                Mul(acc,y.RE); Add(acc,y.IM);
                Div(res.RE,acc);
                Div(res.IM,acc);
                Clear(acc);
           elsif avyre > avyim 
               then acc := y.IM/y.RE;
                    res.RE := x.IM*acc; Add(res.RE,x.RE);
                    res.IM := x.RE*acc; Sub(res.IM,x.IM); Min(res.IM);
                    Mul(acc,y.IM); Add(acc,y.RE);
                    Div(res.RE,acc);
                    Div(res.IM,acc);
                    Clear(acc);
           elsif Equal(y.RE,y.IM)
               then acc := TWO*y.RE;
                    res.RE := x.RE + x.IM; Div(res.RE,acc);
                    res.IM := x.IM - x.RE; Div(res.IM,acc);
                    Clear(acc);
               else -- y.RE = -y.IM then
                    acc := TWO*y.RE;
                    res.RE := x.RE - x.IM; Div(res.RE,acc);
                    res.IM := x.IM + x.RE; Div(res.IM,acc);
                    Clear(acc);
          end if;
          Clear(avyre); Clear(avyim);
    end if;
    return res;
  end "/";

  function "**" ( x : Complex_Number; m : integer ) return Complex_Number is

    res : Complex_Number;

  begin
    if m = 0
     then res := Create(1);
     elsif m > 0
         then res := +x; --Copy(x,res); <- Copy CAUSED BUS ERROR!!
              for j in 2..m loop
                Mul(res,x);
              end loop;
         else res := Create(1);
              for j in 1..(-m) loop
                Div(res,x);
              end loop;
    end if;
    return res;
  end "**";

-- ARITHMETIC OPERATIONS AS PROCEDURES :

  procedure Add ( x : in out Complex_Number; y : in number ) is
  begin
    Add(x.RE,y);
  end Add;

  procedure Sub ( x : in out Complex_Number; y : in number ) is
  begin
    Sub(x.RE,y);
  end Sub;

  procedure Mul ( x : in out Complex_Number; y : in number ) is
  begin
    Mul(x.RE,y);
    Mul(x.IM,y);
  end Mul;

  procedure Div ( x : in out Complex_Number; y : in number ) is
  begin
    Div(x.RE,y);
    Div(x.IM,y);
  end Div;

  procedure Add ( x : in out Complex_Number; y : in Complex_Number ) is
  begin
    Add(x.RE,y.RE);
    Add(x.IM,y.IM);
  end Add;

  procedure Sub ( x : in out Complex_Number; y : in Complex_Number ) is
  begin
    Sub(x.RE,y.RE);
    Sub(x.IM,y.IM);
  end Sub;

  procedure Min ( x : in out Complex_Number ) is
  begin
    Min(x.RE);
    Min(x.IM);
  end Min;

  procedure Mul ( x : in out Complex_Number; y : in Complex_Number ) is

    res : Complex_Number;
    acc,avyim,avyre : number;

  begin
    if Equal(y.IM,zero)
     then Mul(x.RE,y.RE);
          Mul(x.IM,y.RE);
     elsif Equal(y.RE,zero)
         then res.RE := x.IM*y.IM; Min(res.RE);
              res.IM := x.RE*y.IM;
              Clear(x); x := res;
     else avyre := AbsVal(y.RE); avyim := AbsVal(y.IM);
          if avyre < avyim
           then acc := y.RE/y.IM;
                res.RE := x.RE*acc; Sub(res.RE,x.IM); Mul(res.RE,y.IM);
                res.IM := x.IM*acc; Add(res.IM,x.RE); Mul(res.IM,y.IM);
                Clear(acc);
           elsif avyre > avyim
               then acc := y.IM/y.RE;
                    res.RE := x.IM*acc; Sub(res.RE,x.RE); Min(res.RE);
                                        Mul(res.RE,y.RE);
                    res.IM := x.RE*acc; Add(res.IM,x.IM); Mul(res.IM,y.RE);
                    Clear(acc);
           elsif Equal(y.RE,y.IM)
               then res.RE := x.RE - x.IM; Mul(res.RE,y.RE);
                    res.IM := x.IM + x.RE; Mul(res.IM,y.RE);
           else -- y.RE = -y.IM then
                    res.RE := x.RE + x.IM; Mul(res.RE,y.RE);
                    res.IM := x.IM - x.RE; Mul(res.IM,y.RE);
          end if;
          Clear(avyre); Clear(avyim);
          Clear(x); x := res;
    end if;
  end Mul;

  procedure Div ( x : in out Complex_Number; y : in Complex_Number ) is

    res : Complex_Number;
    acc,avyre,avyim : number;

  begin
    if Equal(y.IM,zero)
     then Div(x.RE,y.RE);
          Div(x.IM,y.RE);
     elsif Equal(y.IM,zero)
         then res.RE := x.IM/y.IM;
              res.IM := x.RE/y.IM; Min(res.IM);
              Clear(x); x := res;
     else avyre := AbsVal(y.RE); avyim := AbsVal(y.IM);
          if avyre < avyim
           then acc := y.RE/y.IM;
                res.RE := x.RE*acc; Add(res.RE,x.IM);
                res.IM := x.IM*acc; Sub(res.IM,x.RE);
                Mul(acc,y.RE); Add(acc,y.IM);
                Div(res.RE,acc);
                Div(res.IM,acc);
                Clear(acc);
           elsif avyre > avyim
               then acc := y.IM/y.RE;
                    res.RE := x.IM*acc; Add(res.RE,x.RE);
                    res.IM := x.RE*acc; Sub(res.IM,x.IM); Min(res.IM);
                    Mul(acc,y.IM); Add(acc,y.RE);
                    Div(res.RE,acc);
                    Div(res.IM,acc);
                    Clear(acc);
           elsif Equal(y.RE,y.IM)
               then acc := TWO*y.RE;
                    res.RE := x.RE + x.IM; Div(res.RE,acc);
                    res.IM := x.IM - x.RE; Div(res.IM,acc);
                    Clear(acc);
               else -- y.RE = -y.IM then
                    acc := TWO*y.RE;
                    res.RE := x.RE - x.IM; Div(res.RE,acc);
                    res.IM := x.IM + x.RE; Div(res.IM,acc);
                    Clear(acc);
          end if;
          Clear(avyre); Clear(avyim);
          Clear(x); x := res;
    end if;
  end Div;

-- DESTRUCTOR :

  procedure Clear ( x : in out Complex_Number ) is
  begin
    Clear(x.RE);
    Clear(x.IM);
  end Clear;

end Generic_Complex_Numbers;