+- HP Forums (https://www.hpmuseum.org/forum)
+-- Forum: HP Software Libraries (/forum-10.html)
+--- Forum: HP Prime Software Library (/forum-15.html)
+--- Thread: Decimal to Fraction Function (/thread-2024.html)
Decimal to Fraction Function - Namir - 08-27-2014 06:18 PM
The following function takes the following parameters:
1) x - the fraction to be converted.
2) n - the number of continued fraction terms.
3) toler - the residual tolerance (to prevent divisions by small numbers).
The function returns the following values:
1) The approximation for x.
2) The numerator.
4) The denominator. The approximation for x = numerator / denominator.
4) The difference between x and its approximated value.
Here is the HP Prime listing:
Code:
EXPORT Dec2Frac(x,n,toler)
BEGIN
LOCAL i,numer,denom,aux,resid,y,m,x0;
x0:=x;
y:=MAKEMAT(0,n,1);
// Build continued fraction coefficients
m:=0;
FOR i FROM 1 TO n DO
m:=m+1;
y(i,1):=IP(x);
resid:=FP(x);
IF ABS(resid)<toler THEN
BREAK;
END;
x:=1/resid;
END;
// unfold the fractions
numer:=y(m,1);
denom:=1;
FOR i FROM m-1 DOWNTO 1 DO
aux:=numer;
numer:=y(i,1)*numer+denom;
denom:=aux;
END;
resid:=x0-numer/denom;
RETURN {numer/denom,numer,denom,resid};
END;Here is an example:
Code:
Dec2Frac(pi,4,0.0001)
{3.14159292035,355,113,0.00000026676}Enjoy!
Namir
PS: Many many thanks for Joe Horn who patently pointed out the many errors in the code. I feel a bit ashamed, because I should have done a much better job posting these simple programs. My former Jesuit teachers would have commented that I "did a sloppy job!". Thanks Joe!!