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Project: Fractions
Unit: DelphiDabbler.Lib.Fractions
Record: TFraction
Applies to: ~>0.1
class operator LessThanOrEqual(const A, B: TFraction): Boolean;
This operator overload permits two TFractions to be compared using the <= (less than or equal) operator.
One fraction is considered to be less than or equal to a second if the 1st cross product of the two fractions is less than or equal to their 2nd cross product. Here are two examples:
3/4 and 7/8: The 1st cross product is 3 × 8 = 24 and the 2nd cross product is 4 × 7 = 28. Since 24 < 28, 3/4 <= 7/8.6/8 and 3/4: The 1st cross product is 6 × 4 = 24 and the 2nd cross product is 8 × 3 = 24. The cross products are equal, so 6/8 <= 3/4.A TFraction can also be compared to integer and floating point types using the <= operator. The Implicit operator takes care of converting the integer and floating point operands to TFraction before performing the comparison.
var
F1, F2, F3, F4, F5: TFraction;
D: Double;
I: Integer;
begin
F1 := TFraction.Create(1, 2);
F2 := TFraction.Create(3, 4);
F3 := TFraction.Create(6, 8);
F4 := TFraction.Create(1, 1);
F5 := TFraction.Create(15, 8);
D := 0.75;
I := 1;
Assert(F1 <= F2); // 1/2 < 3/4
Assert(F2 <= F3); // 3/4 = 6/8
Assert(F1 <= D); // 1/2 < 0.75
Assert(F2 <= D); // 3/4 = 0.75
Assert(D <= F3); // 0.76 = 6/8
Assert(D <= F5); // 0.75 < 15/8
Assert(F1 <= I); // 1/2 < 1
Assert(F4 <= I); // 1/1 = 1
Assert(I <= F4); // 1 = 1/1
Assert(I <= F5); // 1 < 15/8
end;