frac/frac.py

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# frac.py (C) 2015-present SheetJS -- http://sheetjs.com
# vim: set fileencoding=utf-8 :
"""
Rational approximations to numbers
This module can generate fraction representations using:
- Mediant method (akin to fractions.Fraction#limit_denominator)
- Aberth method (as used by spreadsheet software)
All functions take 3 arguments:
- x: the number to be approximated
- D: the max denominator
- mixed: if True, generate a mixed representation
The return value is a list of 3 elements: [quotient, numerator, denominator]
"""
def med(x, D, mixed=False):
"""Generate fraction representation using Mediant method"""
n1, d1 = int(x), 1
n2, d2 = n1+1, 1
m = 0.
if x != n1:
while d1 <= D and d2 <= D:
m = float(n1 + n2) / (d1 + d2)
if x == m:
if d1 + d2 <= D:
n1, d1 = n1 + n2, d1 + d2
d2 = D + 1
elif d1 > d2:
d2 = D+1
else:
d1 = D+1
break
elif x < m:
n2, d2 = n1+n2, d1+d2
else:
n1, d1 = n1+n2, d1+d2
if d1 > D:
n1, d1 = n2, d2
if not mixed:
return [0, n1, d1]
q = divmod(n1, d1)
return [q[0], q[1], d1]
def cont(x, D, mixed=False):
"""Generate fraction representation using Aberth method"""
B = abs(x)
I = int
P_2, P_1, P, Q_2, Q_1, Q = 0, 1, 0, 1, 0, 0
while Q_1 < D:
A = I(B)
P = A * P_1 + P_2
Q = A * Q_1 + Q_2
if (B - A) < 0.00000005:
break
B = 1. / (B-A)
P_2, P_1 = P_1, P
Q_2, Q_1 = Q_1, Q
if Q > D:
if Q_1 <= D:
P, Q = P_1, Q_1
else:
P, Q = P_2, Q_2
sgn = -1 if x < 0 else 1
if not mixed:
return [0, sgn * P, Q]
q = divmod(sgn * P, Q)
return [q[0], q[1], Q]