Object-oriented Software in Ada 95

174 Child libraries
The internal function simplify reduces the rational number to its simplest form. Thus the rational number
4/8 is reduced to 1/2.
function Simplify( The:in Rational ) return Rational is
Res: Rational := The;
D : Positive;
--Divisor to reduce with
begin
if Res.Below = 0 then --Invalid treat as 0
Res.Above := 0; Res.Below := 1;
end if;
D := 2; --Divide by 2, 3, 4 ...
while D < Res.Below loop
while Res.Below rem D = 0 and then Res.Above rem D = 0 loop
Res.Above := Res.Above / D;
Res.Below := Res.Below / D;
end loop;
D := D + 1;
end loop;
return Res;
end Simplify;
Note:
It is left to the reader to improve the efficiency of the algorithm used.
The standard operators of +, -, /, and * are overloaded to allow these standard operations to be performed
between instances of rational numbers.
function "+" (F:in Rational; S:in Rational) return Rational is
Res : Rational;
begin
Res.Below := F.Below * S.Below;
Res.Above := F.Above * S.Below + S.Above * F.Below;
return Simplify(Res);
end "+";
function "-" (F:in Rational; S:in Rational) return Rational is
Res : Rational;
begin
Res.Below := F.Below * S.Below;
Res.Above := F.Above * S.Below - S.Above * F.Below;
return Simplify(Res);
end "-";
function "*" (F:in Rational; S:in Rational) return Rational is
Res : Rational;
begin
Res.Above := F.Above * S.Above;
Res.Below := F.Below * S.Below;
return Simplify(Res);
end "*";
function "/" (F:in Rational; S:in Rational) return Rational is
Res : Rational;
begin
Res.Above := F.Above * S.Below;
Res.Below := F.Below * S.Above;
return Simplify(Res);
end "/";
Note:
Additional definitions of these standard operators would need to be provided if it was required to be
able to perform operations such as Rat_Const(1,2) + 1.
In this particular case a definition of + between a rational and an integer would also need to be
provided.
© M A Smith - May not be reproduced without permission