Question

import numpy
import math

x = numpy.roots([2,-2,(21 - 21**2)])
print x[0], math.floor(x[0])

The output is:

15.0 14.0 

and I expect

15.0 15.0

I don’t expect any reason to have the floor equal to 14.0. Please explain!

Answer 1

I’ve used a function called fAlmostEqual before, based on numpy’s allclose function:

import math

def fAlmostEqual(a, b, rtol=1.0000000000000001e-05, atol=1e-08):
    """Checks if the given floats are almost equal. Uses the algorithm
    from numpy.allclose."""
    return math.fabs(a - b) <= (atol + rtol * math.fabs(b))

Creating a fuzzy floor function based on this:

def fuzzyFloor(v):
    """Returns the floor of the given number, unless it is equal to its
    ceiling (within floating point error)."""
    floor = math.floor(v)
    if fAlmostEqual(floor+1, v):
        return floor+1
    return floor

print fuzzyFloor(14.9999999999999)
print fuzzyFloor(15)
print fuzzyFloor(14.99)
print fuzzyFloor(14.5)

This prints:

15.0
15.0
14.0
14.0