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Compare class method

Project: Fractions

Unit: DelphiDabbler.Lib.Fractions

Record: TFraction

Applies to: ~>0.1

class function Compare(const A, B: TFraction): TValueRelationship; static;

Description

This class method compares two TFraction instances, A and B, and returns a value indicating their relationship. The values returned are:

EqualsValue, GreaterThanValue and LessThanValue are defined in the Types unit and have integer values 0, 1 and -1 respectively.

This method can also be used to compare an integer or a floating point to a TFraction simply by passing the integer or floating point value as one of the method parameters and a TFraction value as the other parameter. The Implicit operator takes care of converting the integer and floating point parameter to a TFraction before performing the comparison.

Note

Fractions are compared by calculating and comparing the 1st and 2nd cross products of the fractions. If the 1st cross product of two fractions, A and B, is less than the 2nd cross product then fraction A is less than fraction B. If the 1st cross product is greater then the second cross product then fraction A is greater than B. If the two cross products are the same then the fractions are equal.

This means than two fractions that appear to be different may in fact compare equal, for example the 1st and 2nd cross products of 3/4 and 6/8 are both 24, so 3/4 = 6/8.

Example

var
  F0, F1, F2, F3, F4, F5: TFraction;
  D: Double;
  I: Integer;
begin
  F0 := TFraction.Create(1, 5);
  F1 := TFraction.Create(3, 4);
  F2 := TFraction.Create(6, 8);
  F3 := TFraction.Create(7, 8);
  F4 := TFraction.Create(2, 1);
  F5 := TFraction.Create(25, 7);
  D := 0.75;
  I := 2;
  Assert(TFraction.Compare(F1, F1) = EqualsValue);
  Assert(TFraction.Compare(F1, F2) = EqualsValue);
  Assert(TFraction.Compare(D, F1) = EqualsValue);
  Assert(TFraction.Compare(F4, I) = EqualsValue);
  Assert(TFraction.Compare(F0, F1) = LessThanValue);
  Assert(TFraction.Compare(F3, F5) = LessThanValue);
  Assert(TFraction.Compare(D, F3) = LessThanValue);
  Assert(TFraction.Compare(F2, I) = LessThanValue);
  Assert(TFraction.Compare(F5, F1) = GreaterThanValue);
  Assert(TFraction.Compare(F2, F0) = GreaterThanValue);
  Assert(TFraction.Compare(F3, D) = GreaterThanValue);
  Assert(TFraction.Compare(F5, I) = GreaterThanValue);
end;

See Also