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Project: Fractions
Unit: DelphiDabbler.Lib.Fractions
Record: TFraction
Applies to: ~>0.1
function TruncateToMultiple(const F: TFraction): TFraction;
This method truncates the fraction to the nearest whole number multiple of the given fraction F in the direction of zero. It returns the result.
For example, if you truncate 11/16 to a whole number multiple of 1/8 the result is 5/8.
This example displays a sequence of ranges of fraction that converge towards π
var
FRangeLo, FRangeHi, FMult, FPi: TFraction;
N: Integer;
begin
Memo1.Clear;
FPi := PI; // Pi is automatically converted to fraction
for N := 1 to 20 do
begin
FMult := TFraction.Create(1, N);
FRangeLo := FPi.TruncateToMultiple(FMult);
FRangeHi := FRangeLo + FMult; // this value will be > Pi
// Added FMult to FRangeHi simplifies answer, so we un-simplify it
FRangeHi := FRangeHi.Convert(FRangeLo.Denominator div FRangeHi.Denominator);
WriteLn(
Format(
'Pi in falls in range [%d/%d..%d/%d]',
[
FRangeLo.Numerator, FRangeLo.Denominator,
FRangeHi.Numerator, FRangeHi.Denominator
]
)
);
end;
end;