Generic "approximately equal" function for any object type, with customisable error tolerance.

When called with float arguments, approx_equal(x, y[, tol[, rel]) compares x and y numerically, and returns True if y is within either absolute error tol or relative error rel of x, otherwise return False. The function defaults to sensible default values for tol and rel.

For any other pair of objects, approx_equal() looks for a method __approx_equal__ and, if found, calls it with arbitrary optional arguments. This allows types to define their own concept of "close enough".

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 | ```
def _float_approx_equal(x, y, tol=1e-18, rel=1e-7):
if tol is rel is None:
raise TypeError('cannot specify both absolute and relative errors are None')
tests = []
if tol is not None: tests.append(tol)
if rel is not None: tests.append(rel*abs(x))
assert tests
return abs(x - y) <= max(tests)
def approx_equal(x, y, *args, **kwargs):
"""approx_equal(float1, float2[, tol=1e-18, rel=1e-7]) -> True|False
approx_equal(obj1, obj2[, *args, **kwargs]) -> True|False
Return True if x and y are approximately equal, otherwise False.
If x and y are floats, return True if y is within either absolute error
tol or relative error rel of x. You can disable either the absolute or
relative check by passing None as tol or rel (but not both).
For any other objects, x and y are checked in that order for a method
__approx_equal__, and the result of that is returned as a bool. Any
optional arguments are passed to the __approx_equal__ method.
__approx_equal__ can return NotImplemented to signal that it doesn't know
how to perform that specific comparison, in which case the other object is
checked instead. If neither object have the method, or both defer by
returning NotImplemented, approx_equal falls back on the same numeric
comparison used for floats.
>>> almost_equal(1.2345678, 1.2345677)
True
>>> almost_equal(1.234, 1.235)
False
"""
if not (type(x) is type(y) is float):
# Skip checking for __approx_equal__ in the common case of two floats.
methodname = '__approx_equal__'
# Allow the objects to specify what they consider "approximately equal",
# giving precedence to x. If either object has the appropriate method, we
# pass on any optional arguments untouched.
for a,b in ((x, y), (y, x)):
try:
method = getattr(a, methodname)
except AttributeError:
continue
else:
result = method(b, *args, **kwargs)
if result is NotImplemented:
continue
return bool(result)
# If we get here without returning, then neither x nor y knows how to do an
# approximate equal comparison (or are both floats). Fall back to a numeric
# comparison.
return _float_approx_equal(x, y, *args, **kwargs)
``` |

It is very common to need to test whether two floats are nearly equal, or equal to within some rounding error. This function provides a flexible way to make such tests, using either an absolute tolerance or a relative error.

Other types may also define their own version of "close enough":

```
>>> class MyStr(str):
... def __approx_equal__(self, other, delta=2):
... count = abs(len(self) - len(other))
... for c,k in zip(self, other):
... count += c != k
... return count <= delta
...
>>> s = MyStr('abcdef')
>>> approx_equal('aXYZef', s)
False
>>> approx_equal('aXYZef', s, delta=3)
True
```

Nice function, Steven. I've been doing numerical computing with python for about 12 years and I always write something like this when I need it. Your implementation is better -- so now it's going in my utility module. Thanks!