Round a decimal value to fraction using Farey series

[patrice]

Here is an update.
The program is made for Home but should work in CAS
It list all successives fractions in terminal as they get better
Exemple: FareyMax(π;10000)

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;
PRINT();
VlE:= ABS(Vl);
DbN:= IP(VlE); DbD:=1; FnN:=DbN+1; FnD:=1;
RsN:= ROUND(VlE,0); RsD:= 1; RsE:= ABS(VlE-(RsN/RsD));
PRINT(SIGN(Vl)*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)); PRINT(SIGN(Vl)*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+"'";
// RETURN EXPR("QUOTE("+SIGN(Vl)*RsN+"/"+RsD+")");
END;