Continued fraction/Arithmetic/Construct from rational number: Difference between revisions
Continued fraction/Arithmetic/Construct from rational number (view source)
Revision as of 17:11, 20 November 2023
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31428571 / 10000000 = 3 7 476190 3
314285714 / 100000000 = 3 7 7142857</pre>
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
<syntaxhighlight lang="Delphi">
function GetNextFraction(var N1,N2: integer): integer;
{Get next step in fraction series}
var R: integer;
begin
R:=FloorMod(N1, N2);
Result:= FloorDiv(N1 - R , N2);
N1 := N2;
N2 := R;
end;
procedure GetFractionList(N1,N2: integer; var IA: TIntegerDynArray);
{Get list of continuous fraction values}
var M1, M2,F : integer;
var S: integer;
begin
SetLength(IA,0);
M1 := N1;
M2 := N2;
while M2<>0 do
begin
F:=GetNextFraction(M1,M2);
SetLength(IA,Length(IA)+1);
IA[High(IA)]:=F;
end;
end;
procedure ShowConFraction(Memo: TMemo; N1,N2: integer);
{Calculate and display continues fraction for Rational number N1/N2}
var I: integer;
var S: string;
var IA: TIntegerDynArray;
begin
GetFractionList(N1,N2,IA);
S:='[';
for I:=0 to High(IA) do
begin
if I>0 then S:=S+', ';
S:=S+IntToStr(IA[I]);
end;
S:=S+']';
Memo.Lines.Add(Format('%10d / %10d --> ',[N1,N2])+S);
end;
procedure ShowContinuedFractions(Memo: TMemo);
{Show all continued fraction tests}
begin
Memo.Lines.Add('Wikipedia Example');
ShowConFraction(Memo,415,93);
Memo.Lines.Add('');
Memo.Lines.Add('Rosetta Code Examples');
ShowConFraction(Memo,1, 2);
ShowConFraction(Memo,3, 1);
ShowConFraction(Memo,23, 8);
ShowConFraction(Memo,13, 11);
ShowConFraction(Memo,22, 7);
ShowConFraction(Memo,-151, 77);
Memo.Lines.Add('');
Memo.Lines.Add('Square Root of Two');
ShowConFraction(Memo,14142, 10000);
ShowConFraction(Memo,141421, 100000);
ShowConFraction(Memo,1414214, 1000000);
ShowConFraction(Memo,14142136, 10000000);
Memo.Lines.Add('');
Memo.Lines.Add('PI');
ShowConFraction(Memo,31, 10);
ShowConFraction(Memo,314, 100);
ShowConFraction(Memo,3142, 1000);
ShowConFraction(Memo,31428, 10000);
ShowConFraction(Memo,314285, 100000);
ShowConFraction(Memo,3142857, 1000000);
ShowConFraction(Memo,31428571, 10000000);
ShowConFraction(Memo,314285714, 100000000);
end;
</syntaxhighlight>
{{out}}
<pre>
Wikipedia Example
415 / 93 --> [4, 2, 6, 7]
Rosetta Code Examples
1 / 2 --> [0, 2]
3 / 1 --> [3]
23 / 8 --> [2, 1, 7]
13 / 11 --> [1, 5, 2]
22 / 7 --> [3, 7]
-151 / 77 --> [-2, 25, 1, 2]
Square Root of Two
14142 / 10000 --> [1, 2, 2, 2, 2, 2, 1, 1, 29]
141421 / 100000 --> [1, 2, 2, 2, 2, 2, 2, 3, 1, 1, 3, 1, 7, 2]
1414214 / 1000000 --> [1, 2, 2, 2, 2, 2, 2, 2, 3, 6, 1, 2, 1, 12]
14142136 / 10000000 --> [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 1, 2, 4, 1, 1, 2]
PI
31 / 10 --> [3, 10]
314 / 100 --> [3, 7, 7]
3142 / 1000 --> [3, 7, 23, 1, 2]
31428 / 10000 --> [3, 7, 357]
314285 / 100000 --> [3, 7, 2857]
3142857 / 1000000 --> [3, 7, 142857]
31428571 / 10000000 --> [3, 7, 476190, 3]
314285714 / 100000000 --> [3, 7, 7142857]
Elapsed Time: 41.009 ms.
</pre>
=={{header|EDSAC order code}}==
Line 4,177 ⟶ 4,300:
{{in}}
<pre>
≪ { '1/2' '3' '23/8' '13/11' '22/7' '-151/77' '14142/10000' '141421/100000' '1414214/1000000' '14142136/10000000' '31/10' '314/100' '3142/1000' '31428/10000' '314285/100000' '3142857/1000000' '31428571/10000000' '314285714/100000000' } → fracs
≪ {} 1 fracs SIZE FOR j fracs j GET RC2F + NEXT ≫ ≫ EVAL
</pre>
{{out}}
Line 4,961 ⟶ 5,085:
{{libheader|Wren-rat}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="
import "./fmt" for Fmt
var toContFrac = Fn.new { |r|
| |||