On Tue, 2 Jan 2007, Terry Carroll wrote:
> Dick, if your goal is to have a routine to get the fraction with the least
> possible error (as opposed to learing how to use Decimal), have a look at
> this recipe from the Python Cookbook:
>
> http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/52317
BTW, to get the higher precision in Decimal:
import decimal
def farey(v, lim):
'''Named after James Farey, an English surveyor.
No error checking on args -- lim = max denominator,
results are (numerator, denominator), (1,0) is infinity
'''
if v < 0:
n,d = farey(-v, lim)
return int(-n),int(d)
z = lim-lim # get 0 of right type for denominator
lower, upper = (z,z+1), (z+1,z)
while 1:
mediant = (lower[0] + upper[0]), (lower[1]+upper[1])
if v * mediant[1] > mediant[0]:
if lim < mediant[1]: return (int(upper[0]), int(upper[1]))
lower = mediant
elif v * mediant[1] == mediant[0]:
if lim >= mediant[1]: return (int(mediant[0]), int(mediant[1]))
if lower[1] < upper[1]: return (int(lower[0]), int(lower[1]))
return (int(upper[0]), int(upper[1]))
else:
if lim < mediant[1]: return lower
upper = mediant
dec = decimal.Decimal("0.345765988765560057657654654")
me = decimal.Decimal("0.0000000001")
max_denom = 1/me
(num, denom) = farey(dec,max_denom)
error = abs(decimal.Decimal(str(float(num)/denom)) - dec) *100
print "%s = %d/%d with %s per cent error" % (dec, num, denom, error)
Which gives:
0.345765988765560057657654654 = 878844001/2541730620 with
4.3994234234534600E-11 per cent error
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