Sorry, I let this go before finishing editting.
If converting to rationals scares you, try this based on James Farey's
"Farey fractions.
def Farey(v, lim):
'''Convert v to a rational with denom <= lim
Named after James Farey, an English surveyor.
No error checking on args -- v >= 0, lim = max denominator,
results are (numerator, denominator) in lowest terms.
Think of (1,0) as infinity.
'''
lower, upper = (0L,1L), (1L,0L)
while 1:
mediant = (lower[0] + upper[0]), (lower[1]+upper[1])
if v * mediant[1] > mediant[0]:
if lim < mediant[1]: return upper
lower = mediant
else:
if lim < mediant[1]: return lower
upper = mediant
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