python: Greatest common divisor (gcd) for floats, preferably in numpy

2024/4/15 1:16:13

I am looking for an efficient way to determine the greatest common divisor of two floats with python. The routine should have the following layout

gcd(a, b, rtol=1e-05, atol=1e-08)
"""
Returns the greatest common divisor of a and bParameters
----------
a,b : floattwo floats for gcd
rtol, atol : float, optionalrelative and absolute toleranceReturns
-------
gcd : floatGreatest common divisor such that for x in [a,b]:np.mod(x,gcd) < rtol*x + atol .. _PEP 484:https://www.python.org/dev/peps/pep-0484/"""

Example: gcd of rational and irrational number

The gcd(1., np.pi, rtol=0, atol=1e-5) should return (roughly) 1e-5, as

In [1]: np.mod(np.pi,1e-5)
Out[1]: 2.6535897928590063e-06In [2]: np.mod(1.,1e-5)
Out[2]: 9.9999999999181978e-06

I would prefer to use a library implementation and not to write it myself. The fractions.gcd function does not seem appropriate to me here, as I do not want to work with fractions and it (obviously) does not have the tolerance parameters.

Answer

Seems like you could just modify the code of fractions.gcd to include the tolerances:

def float_gcd(a, b, rtol = 1e-05, atol = 1e-08):t = min(abs(a), abs(b))while abs(b) > rtol * t + atol:a, b = b, a % breturn a
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