Round a decimal value to fraction using Farey series

[patrice]

Round Vl to best fraction with denominator smaller than DMax

Code:

EXPORT FareyMax(Vl, DMax)
// Round a Vl to the best fraction with denominator < DMax
BEGIN
LOCAL VlE, Tmp;
LOCAL DbN,DbD, FnN,FnD, RsN,RsD,RsE;
VlE:= ABS(Vl);
DbN:= IP(VlE); DbD:=1; FnN:=DbN+1; FnD:=1;
RsN:= ROUND(VlE,0); RsD:= 1; RsE:= ABS(VlE-(RsN/RsD));
WHILE DbD+FnD <= DMax DO
  Tmp:= (DbN+FnN)/(DbD+FnD);
  IF RsE > ABS(VlE-Tmp) THEN RsN:= (DbN+FnN); RsD:= (DbD+FnD); RsE:= ABS(VlE-(RsN/RsD)); END;
  IF Tmp < VlE THEN DbN:= (DbN+FnN); DbD:= (DbD+FnD); ELSE FnN:= (DbN+FnN); FnD:= (DbD+FnD); END;
END;
RETURN "'"+SIGN(Vl)*RsN+"/"+RsD+"'";
END;

Round Vl to best fraction with Vl-Error < Fraction < Vl+Error

Code:

EXPORT FareyDelta(Vl, Error)
// round Vl to the smallest fraction with |Vl - fraction| < Error
BEGIN
LOCAL VlE, Tmp;
LOCAL DbN,DbD, FnN,FnD, RsN,RsD,RsE;
VlE:= ABS(Vl);
DbN:= IP(VlE); DbD:=1; FnN:=DbN+1; FnD:=1;
RsN:= ROUND(VlE,0); RsD:= 1; RsE:= ABS(VlE-(RsN/RsD));
WHILE RsE > Error DO
  Tmp:= (DbN+FnN)/(DbD+FnD);
  IF RsE > ABS(VlE-Tmp) THEN RsN:= (DbN+FnN); RsD:= (DbD+FnD); RsE:= ABS(VlE-(RsN/RsD)); END;
  IF Tmp < VlE THEN DbN:= (DbN+FnN); DbD:= (DbD+FnD); ELSE FnN:= (DbN+FnN); FnD:= (DbD+FnD); END;
END;
RETURN "'"+SIGN(Vl)*RsN+"/"+RsD+"'";
END;