(12C) Decimal to Fraction

[Dieter]

(08-08-2018 10:26 PM)Albert Chan Wrote:  Below is the patched code:

Code:

def dec2frac(f, c):
    if c < 2 or int(f) == f: return
    u, v, F = 0, 1, f
    while f:
        f = 1/f
        w = u + v * int(f)  # check before update
        if w > c: break     # guaranteed v <= c
        u, v, f = v, w, f - int(f)
    q = u + (c - u)//v * v  # biggest quotient
    if diff(F, q) >= diff(F, v): q = v
    return int(q * F + 0.5), q

I have transcoded this for the 35s. Let me add a few remarks:

First I think that q can also be calculated via q = c  –  (c–u) mod v. Can you confirm this?
Also I do not quite understand why earlier code (and Joe's as well) used the CEIL function while here it's the FLOOR (or INT) function. Thomas even calculated 1+INT() which in most cases is the same as CEIL... but not for integer arguments.

Then I wonder how exactly this Python diff() command works. Its arguments here are just the decimal input and a denominator – but not the corresponding numerator. So how does this work in detail? For instance, what is the value for diff(pi, 106) and diff(pi, 113)?

In a calculator implementation first the numerators for the two possible results (denominators v and q) are calculated and then the errors are compared. These errors are evaluated by abs(input – numerator/denominator). This may lead to inaccuracies due to digit cancellation. Think of the √2 example (577/408 vs. 816/577). Is there a better way to compare the two possible fractions?

Finally the code currently rejects integer input (which would lead to a division by zero). But can't this be trapped? For instance by leaving the while-loop if f=0? Or simply return v=1 if F is an integer?

Dieter