(12C) Decimal to Fraction

[Thomas Klemm]

Maybe I missed something but is there a reason for not using Farey sequences?

Python

Code:

def farey(q, n):
    a = 0
    b = c = d = 1
    while True:
        e, f = a+c, b+d
        k = f * q
        if e == k:
            return e, f
        if e < k:
            a, b = e, f
        else:
            c, d = e, f
        if b+d > n:
            return e, f

HP-11C

Code:

LBL A
STO 1       ; n q
R↓          ; q
STO 0       ; q
CLx         ; 0
STO 2       ; a = 0
1           ; 1
STO 3       ; b = 1
STO 4       ; c = 1
STO 5       ; d = 1
RCL 3       ; 1 1
+           ; 2
LBL 0       ; while
STO 7       ; f = b+d
RCL 0       ; q f
*           ; k
RCL 2       ; a k
RCL 4       ; c a k
+           ; a+c k
STO 6       ; e=a+c k
x=y         ; e = k ?
GTO 3       ; done
x≤y?        ; e < k ?
GTO 1
RCL 6       ; e
STO 4       ; c = e
RCL 7       ; f
STO 5       ; d = f
GTO 2
LBL 1
RCL 6       ; e
STO 2       ; a = e
RCL 7       ; f
STO 3       ; b = f
LBL 2
RCL 1       ; n
RCL 3       ; b n
RCL 5       ; d b n
+           ; b+d n
x≤y         ; b+d ≤ n ?
GTO 0       ; while
LBL 3       ; done
RCL 6       ; e
RCL 7       ; f
RTN

This should also be easier to convert for the HP-12C since no subroutines are used.

However the decimal number \(q\) to transform must be \(0 < q < 1\).

Example

0.10322 ENTER EEX 8 [A]
Y: 5,161
X: 50,000


Cheers
Thomas