Merge pull request #1441 from kalekundert/features

Add a convenience function for floating-point comparisons

AUTHORS

@@ -50,6 +50,7 @@ Jason R. Coombs
 Joshua Bronson
 Jurko Gospodnetić
 Katarzyna Jachim
+Kale Kundert
 Kevin Cox
 Lee Kamentsky
 Lukas Bednar

CHANGELOG.rst

@@ -11,11 +11,12 @@
   for a fixture (to solve the funcarg-shadowing-fixture problem).
   Thanks `@novas0x2a`_ for the complete PR (`#1444`_).
 
-*
+* New ``approx()`` function for easily comparing floating-point numbers in 
+  tests.
+  Thanks `@kalekundert`_ for the complete PR (`#1441`_).
 
 *
 
-
 **Changes**
 
 *
@@ -26,10 +27,11 @@
 
 .. _@milliams: https://github.com/milliams
 .. _@novas0x2a: https://github.com/novas0x2a
+.. _@kalekundert: https://github.com/kalekundert
 
 .. _#1428: https://github.com/pytest-dev/pytest/pull/1428
 .. _#1444: https://github.com/pytest-dev/pytest/pull/1444
-
+.. _#1441: https://github.com/pytest-dev/pytest/pull/1441
 
 2.9.1.dev1
 ==========

_pytest/python.py

@@ -1,10 +1,12 @@
 """ Python test discovery, setup and run of test functions. """
+
 import fnmatch
 import functools
 import inspect
 import re
 import types
 import sys
+import math
 
 import py
 import pytest
@@ -269,7 +271,8 @@ def pytest_namespace():
     return {
         'fixture': fixture,
         'yield_fixture': yield_fixture,
-        'raises' : raises,
+        'raises': raises,
+        'approx': approx,
         'collect': {
         'Module': Module, 'Class': Class, 'Instance': Instance,
         'Function': Function, 'Generator': Generator,
@@ -1211,7 +1214,8 @@ def getlocation(function, curdir):
 # builtin pytest.raises helper
 
 def raises(expected_exception, *args, **kwargs):
-    """ assert that a code block/function call raises ``expected_exception``
+    """
+    Assert that a code block/function call raises ``expected_exception``
     and raise a failure exception otherwise.
 
     This helper produces a ``ExceptionInfo()`` object (see below).
@@ -1344,6 +1348,255 @@ class RaisesContext(object):
         self.excinfo.__init__(tp)
         return issubclass(self.excinfo.type, self.expected_exception)
 
+# builtin pytest.approx helper
+
+class approx(object):
+    """
+    Assert that two numbers (or two sets of numbers) are equal to each other
+    within some tolerance.
+
+    Due to the `intricacies of floating-point arithmetic`__, numbers that we
+    would intuitively expect to be equal are not always so::
+
+        >>> 0.1 + 0.2 == 0.3
+        False
+
+    __ https://docs.python.org/3/tutorial/floatingpoint.html
+
+    This problem is commonly encountered when writing tests, e.g. when making
+    sure that floating-point values are what you expect them to be.  One way to
+    deal with this problem is to assert that two floating-point numbers are
+    equal to within some appropriate tolerance::
+
+        >>> abs((0.1 + 0.2) - 0.3) < 1e-6
+        True
+
+    However, comparisons like this are tedious to write and difficult to
+    understand.  Furthermore, absolute comparisons like the one above are
+    usually discouraged because there's no tolerance that works well for all
+    situations.  ``1e-6`` is good for numbers around ``1``, but too small for
+    very big numbers and too big for very small ones.  It's better to express
+    the tolerance as a fraction of the expected value, but relative comparisons
+    like that are even more difficult to write correctly and concisely.
+
+    The ``approx`` class performs floating-point comparisons using a syntax
+    that's as intuitive as possible::
+
+        >>> from pytest import approx
+        >>> 0.1 + 0.2 == approx(0.3)
+        True
+
+    The same syntax also works on sequences of numbers::
+
+        >>> (0.1 + 0.2, 0.2 + 0.4) == approx((0.3, 0.6))
+        True
+
+    By default, ``approx`` considers numbers within a relative tolerance of
+    ``1e-6`` (i.e. one part in a million) of its expected value to be equal.
+    This treatment would lead to surprising results if the expected value was
+    ``0.0``, because nothing but ``0.0`` itself is relatively close to ``0.0``.
+    To handle this case less surprisingly, ``approx`` also considers numbers
+    within an absolute tolerance of ``1e-12`` of its expected value to be
+    equal.  Infinite numbers are another special case.  They are only
+    considered equal to themselves, regardless of the relative tolerance.  Both
+    the relative and absolute tolerances can be changed by passing arguments to
+    the ``approx`` constructor::
+
+        >>> 1.0001 == approx(1)
+        False
+        >>> 1.0001 == approx(1, rel=1e-3)
+        True
+        >>> 1.0001 == approx(1, abs=1e-3)
+        True
+
+    If you specify ``abs`` but not ``rel``, the comparison will not consider
+    the relative tolerance at all.  In other words, two numbers that are within
+    the default relative tolerance of ``1e-6`` will still be considered unequal
+    if they exceed the specified absolute tolerance.  If you specify both
+    ``abs`` and ``rel``, the numbers will be considered equal if either
+    tolerance is met::
+
+        >>> 1 + 1e-8 == approx(1)
+        True
+        >>> 1 + 1e-8 == approx(1, abs=1e-12)
+        False
+        >>> 1 + 1e-8 == approx(1, rel=1e-6, abs=1e-12)
+        True
+
+    If you're thinking about using ``approx``, then you might want to know how
+    it compares to other good ways of comparing floating-point numbers.  All of
+    these algorithms are based on relative and absolute tolerances and should
+    agree for the most part, but they do have meaningful differences:
+
+    - ``math.isclose(a, b, rel_tol=1e-9, abs_tol=0.0)``:  True if the relative
+      tolerance is met w.r.t. either ``a`` or ``b`` or if the absolute
+      tolerance is met.  Because the relative tolerance is calculated w.r.t.
+      both ``a`` and ``b``, this test is symmetric (i.e.  neither ``a`` nor
+      ``b`` is a "reference value").  You have to specify an absolute tolerance
+      if you want to compare to ``0.0`` because there is no tolerance by
+      default.  Only available in python>=3.5.  `More information...`__
+
+      __ https://docs.python.org/3/library/math.html#math.isclose
+
+    - ``numpy.isclose(a, b, rtol=1e-5, atol=1e-8)``: True if the difference
+      between ``a`` and ``b`` is less that the sum of the relative tolerance
+      w.r.t. ``b`` and the absolute tolerance.  Because the relative tolerance
+      is only calculated w.r.t. ``b``, this test is asymmetric and you can
+      think of ``b`` as the reference value.  Support for comparing sequences
+      is provided by ``numpy.allclose``.  `More information...`__
+
+      __ http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.isclose.html
+
+    - ``unittest.TestCase.assertAlmostEqual(a, b)``: True if ``a`` and ``b``
+      are within an absolute tolerance of ``1e-7``.  No relative tolerance is
+      considered and the absolute tolerance cannot be changed, so this function
+      is not appropriate for very large or very small numbers.  Also, it's only
+      available in subclasses of ``unittest.TestCase`` and it's ugly because it
+      doesn't follow PEP8.  `More information...`__
+
+      __ https://docs.python.org/3/library/unittest.html#unittest.TestCase.assertAlmostEqual
+
+    - ``a == pytest.approx(b, rel=1e-6, abs=1e-12)``: True if the relative
+      tolerance is met w.r.t. ``b`` or if the absolute tolerance is met.
+      Because the relative tolerance is only calculated w.r.t. ``b``, this test
+      is asymmetric and you can think of ``b`` as the reference value.  In the
+      special case that you explicitly specify an absolute tolerance but not a
+      relative tolerance, only the absolute tolerance is considered.
+    """
+
+    def __init__(self, expected, rel=None, abs=None):
+        self.expected = expected
+        self.abs = abs
+        self.rel = rel
+
+    def __repr__(self):
+        return ', '.join(repr(x) for x in self.expected)
+
+    def __eq__(self, actual):
+        from collections import Iterable
+        if not isinstance(actual, Iterable):
+            actual = [actual]
+        if len(actual) != len(self.expected):
+            return False
+        return all(a == x for a, x in zip(actual, self.expected))
+
+    def __ne__(self, actual):
+        return not (actual == self)
+
+    @property
+    def expected(self):
+        # Regardless of whether the user-specified expected value is a number
+        # or a sequence of numbers, return a list of ApproxNotIterable objects
+        # that can be compared against.
+        from collections import Iterable
+        approx_non_iter = lambda x: ApproxNonIterable(x, self.rel, self.abs)
+        if isinstance(self._expected, Iterable):
+            return [approx_non_iter(x) for x in self._expected]
+        else:
+            return [approx_non_iter(self._expected)]
+
+    @expected.setter
+    def expected(self, expected):
+        self._expected = expected
+
+
+class ApproxNonIterable(object):
+    """
+    Perform approximate comparisons for single numbers only.
+
+    In other words, the ``expected`` attribute for objects of this class must
+    be some sort of number.  This is in contrast to the ``approx`` class, where
+    the ``expected`` attribute can either be a number of a sequence of numbers.
+    This class is responsible for making comparisons, while ``approx`` is
+    responsible for abstracting the difference between numbers and sequences of
+    numbers.  Although this class can stand on its own, it's only meant to be
+    used within ``approx``.
+    """
+
+    def __init__(self, expected, rel=None, abs=None):
+        self.expected = expected
+        self.abs = abs
+        self.rel = rel
+
+    def __repr__(self):
+        # Infinities aren't compared using tolerances, so don't show a
+        # tolerance.
+        if math.isinf(self.expected):
+            return str(self.expected)
+
+        # If a sensible tolerance can't be calculated, self.tolerance will
+        # raise a ValueError.  In this case, display '???'.
+        try:
+            vetted_tolerance = '{:.1e}'.format(self.tolerance)
+        except ValueError:
+            vetted_tolerance = '???'
+
+        plus_minus = u'{0} \u00b1 {1}'.format(self.expected, vetted_tolerance)
+
+        # In python2, __repr__() must return a string (i.e. not a unicode
+        # object).  In python3, __repr__() must return a unicode object
+        # (although now strings are unicode objects and bytes are what
+        # strings were).
+        if sys.version_info[0] == 2:
+            return plus_minus.encode('utf-8')
+        else:
+            return plus_minus
+
+    def __eq__(self, actual):
+        # Short-circuit exact equality.
+        if actual == self.expected:
+            return True
+
+        # Infinity shouldn't be approximately equal to anything but itself, but
+        # if there's a relative tolerance, it will be infinite and infinity
+        # will seem approximately equal to everything.  The equal-to-itself
+        # case would have been short circuited above, so here we can just
+        # return false if the expected value is infinite.  The abs() call is
+        # for compatibility with complex numbers.
+        if math.isinf(abs(self.expected)):
+            return False
+
+        # Return true if the two numbers are within the tolerance.
+        return abs(self.expected - actual) <= self.tolerance
+
+    def __ne__(self, actual):
+        return not (actual == self)
+
+    @property
+    def tolerance(self):
+        set_default = lambda x, default: x if x is not None else default
+
+        # Figure out what the absolute tolerance should be.  ``self.abs`` is
+        # either None or a value specified by the user.
+        absolute_tolerance = set_default(self.abs, 1e-12)
+
+        if absolute_tolerance < 0:
+            raise ValueError("absolute tolerance can't be negative: {}".format(absolute_tolerance))
+        if math.isnan(absolute_tolerance):
+            raise ValueError("absolute tolerance can't be NaN.")
+
+        # If the user specified an absolute tolerance but not a relative one,
+        # just return the absolute tolerance.
+        if self.rel is None:
+            if self.abs is not None:
+                return absolute_tolerance
+
+        # Figure out what the relative tolerance should be.  ``self.rel`` is
+        # either None or a value specified by the user.  This is done after
+        # we've made sure the user didn't ask for an absolute tolerance only,
+        # because we don't want to raise errors about the relative tolerance if
+        # we aren't even going to use it.
+        relative_tolerance = set_default(self.rel, 1e-6) * abs(self.expected)
+
+        if relative_tolerance < 0:
+            raise ValueError("relative tolerance can't be negative: {}".format(absolute_tolerance))
+        if math.isnan(relative_tolerance):
+            raise ValueError("relative tolerance can't be NaN.")
+
+        # Return the larger of the relative and absolute tolerances.
+        return max(relative_tolerance, absolute_tolerance)
+
+
 #
 #  the basic pytest Function item
 #

doc/en/builtin.rst

@@ -35,6 +35,11 @@ Examples at :ref:`assertraises`.
 
 .. autofunction:: deprecated_call
 
+Comparing floating point numbers
+--------------------------------
+
+.. autoclass:: approx
+
 Raising a specific test outcome
 --------------------------------------
 
@@ -48,7 +53,7 @@ you can rather use declarative marks, see :ref:`skipping`.
 .. autofunction:: _pytest.skipping.xfail
 .. autofunction:: _pytest.runner.exit
 
-fixtures and requests
+Fixtures and requests
 -----------------------------------------------------
 
 To mark a fixture function:

testing/python/approx.py

@@ -0,0 +1,286 @@
+# encoding: utf-8
+
+import pytest
+import doctest
+
+from pytest import approx
+from operator import eq, ne
+from decimal import Decimal
+from fractions import Fraction
+inf, nan = float('inf'), float('nan')
+
+class MyDocTestRunner(doctest.DocTestRunner):
+
+    def __init__(self):
+        doctest.DocTestRunner.__init__(self)
+
+    def report_failure(self, out, test, example, got):
+        raise AssertionError("'{}' evaluates to '{}', not '{}'".format(
+            example.source.strip(), got.strip(), example.want.strip()))
+
+
+class TestApprox:
+
+    def test_repr_string(self):
+        # Just make sure the Unicode handling doesn't raise any exceptions.
+        print(approx(1.0))
+        print(approx([1.0, 2.0, 3.0]))
+        print(approx(inf))
+        print(approx(1.0, rel=nan))
+        print(approx(1.0, rel=inf))
+
+    def test_operator_overloading(self):
+        assert 1 == approx(1, rel=1e-6, abs=1e-12)
+        assert not (1 != approx(1, rel=1e-6, abs=1e-12))
+        assert 10 != approx(1, rel=1e-6, abs=1e-12)
+        assert not (10 == approx(1, rel=1e-6, abs=1e-12))
+
+    def test_exactly_equal(self):
+        examples = [
+                (2.0, 2.0),
+                (0.1e200, 0.1e200),
+                (1.123e-300, 1.123e-300),
+                (12345, 12345.0),
+                (0.0, -0.0),
+                (345678, 345678),
+                (Decimal('1.0001'), Decimal('1.0001')),
+                (Fraction(1, 3), Fraction(-1, -3)),
+        ]
+        for a, x in examples:
+            assert a == approx(x)
+
+    def test_opposite_sign(self):
+        examples = [
+                (eq, 1e-100, -1e-100),
+                (ne, 1e100, -1e100),
+        ]
+        for op, a, x in examples:
+            assert op(a, approx(x))
+
+    def test_zero_tolerance(self):
+        within_1e10 = [
+                (1.1e-100, 1e-100),
+                (-1.1e-100, -1e-100),
+        ]
+        for a, x in within_1e10:
+            assert x == approx(x, rel=0.0, abs=0.0)
+            assert a != approx(x, rel=0.0, abs=0.0)
+            assert a == approx(x, rel=0.0, abs=5e-101)
+            assert a != approx(x, rel=0.0, abs=5e-102)
+            assert a == approx(x, rel=5e-1, abs=0.0)
+            assert a != approx(x, rel=5e-2, abs=0.0)
+
+    def test_negative_tolerance(self):
+        # Negative tolerances are not allowed.
+        illegal_kwargs = [
+                dict(rel=-1e100),
+                dict(abs=-1e100),
+                dict(rel=1e100, abs=-1e100),
+                dict(rel=-1e100, abs=1e100),
+                dict(rel=-1e100, abs=-1e100),
+        ]
+        for kwargs in illegal_kwargs:
+            with pytest.raises(ValueError):
+                1.1 == approx(1, **kwargs)
+
+    def test_inf_tolerance(self):
+        # Everything should be equal if the tolerance is infinite.
+        large_diffs = [
+                (1, 1000),
+                (1e-50, 1e50),
+                (-1.0, -1e300),
+                (0.0, 10),
+        ]
+        for a, x in large_diffs:
+            assert a != approx(x, rel=0.0, abs=0.0)
+            assert a == approx(x, rel=inf, abs=0.0)
+            assert a == approx(x, rel=0.0, abs=inf)
+            assert a == approx(x, rel=inf, abs=inf)
+
+    def test_inf_tolerance_expecting_zero(self):
+        # If the relative tolerance is zero but the expected value is infinite,
+        # the actual tolerance is a NaN, which should be an error.
+        illegal_kwargs = [
+                dict(rel=inf, abs=0.0),
+                dict(rel=inf, abs=inf),
+        ]
+        for kwargs in illegal_kwargs:
+            with pytest.raises(ValueError):
+                1 == approx(0, **kwargs)
+
+    def test_nan_tolerance(self):
+        illegal_kwargs = [
+                dict(rel=nan),
+                dict(abs=nan),
+                dict(rel=nan, abs=nan),
+        ]
+        for kwargs in illegal_kwargs:
+            with pytest.raises(ValueError):
+                1.1 == approx(1, **kwargs)
+
+    def test_reasonable_defaults(self):
+        # Whatever the defaults are, they should work for numbers close to 1
+        # than have a small amount of floating-point error.
+        assert 0.1 + 0.2 == approx(0.3)
+
+    def test_default_tolerances(self):
+        # This tests the defaults as they are currently set.  If you change the
+        # defaults, this test will fail but you should feel free to change it.
+        # None of the other tests (except the doctests) should be affected by
+        # the choice of defaults.
+        examples = [
+                # Relative tolerance used.
+                (eq, 1e100 + 1e94, 1e100),
+                (ne, 1e100 + 2e94, 1e100),
+                (eq, 1e0 + 1e-6, 1e0),
+                (ne, 1e0 + 2e-6, 1e0),
+                # Absolute tolerance used.
+                (eq, 1e-100, + 1e-106),
+                (eq, 1e-100, + 2e-106),
+                (eq, 1e-100, 0),
+        ]
+        for op, a, x in examples:
+            assert op(a, approx(x))
+
+    def test_custom_tolerances(self):
+        assert 1e8 + 1e0 == approx(1e8, rel=5e-8, abs=5e0)
+        assert 1e8 + 1e0 == approx(1e8, rel=5e-9, abs=5e0)
+        assert 1e8 + 1e0 == approx(1e8, rel=5e-8, abs=5e-1)
+        assert 1e8 + 1e0 != approx(1e8, rel=5e-9, abs=5e-1)
+
+        assert 1e0 + 1e-8 == approx(1e0, rel=5e-8, abs=5e-8)
+        assert 1e0 + 1e-8 == approx(1e0, rel=5e-9, abs=5e-8)
+        assert 1e0 + 1e-8 == approx(1e0, rel=5e-8, abs=5e-9)
+        assert 1e0 + 1e-8 != approx(1e0, rel=5e-9, abs=5e-9)
+
+        assert 1e-8 + 1e-16 == approx(1e-8, rel=5e-8, abs=5e-16)
+        assert 1e-8 + 1e-16 == approx(1e-8, rel=5e-9, abs=5e-16)
+        assert 1e-8 + 1e-16 == approx(1e-8, rel=5e-8, abs=5e-17)
+        assert 1e-8 + 1e-16 != approx(1e-8, rel=5e-9, abs=5e-17)
+
+    def test_relative_tolerance(self):
+        within_1e8_rel = [
+                (1e8 + 1e0, 1e8),
+                (1e0 + 1e-8, 1e0),
+                (1e-8 + 1e-16, 1e-8),
+        ]
+        for a, x in within_1e8_rel:
+            assert a == approx(x, rel=5e-8, abs=0.0)
+            assert a != approx(x, rel=5e-9, abs=0.0)
+
+    def test_absolute_tolerance(self):
+        within_1e8_abs = [
+                (1e8 + 9e-9, 1e8),
+                (1e0 + 9e-9, 1e0),
+                (1e-8 + 9e-9, 1e-8),
+        ]
+        for a, x in within_1e8_abs:
+            assert a == approx(x, rel=0, abs=5e-8)
+            assert a != approx(x, rel=0, abs=5e-9)
+
+    def test_expecting_zero(self):
+        examples = [
+                (ne, 1e-6, 0.0),
+                (ne, -1e-6, 0.0),
+                (eq, 1e-12, 0.0),
+                (eq, -1e-12, 0.0),
+                (ne, 2e-12, 0.0),
+                (ne, -2e-12, 0.0),
+                (ne, inf, 0.0),
+                (ne, nan, 0.0),
+         ]
+        for op, a, x in examples:
+            assert op(a, approx(x, rel=0.0, abs=1e-12))
+            assert op(a, approx(x, rel=1e-6, abs=1e-12))
+
+    def test_expecting_inf(self):
+        examples = [
+                (eq, inf, inf),
+                (eq, -inf, -inf),
+                (ne, inf, -inf),
+                (ne, 0.0, inf),
+                (ne, nan, inf),
+        ]
+        for op, a, x in examples:
+            assert op(a, approx(x))
+
+    def test_expecting_nan(self):
+        examples = [
+                (nan, nan),
+                (-nan, -nan),
+                (nan, -nan),
+                (0.0, nan),
+                (inf, nan),
+        ]
+        for a, x in examples:
+            # If there is a relative tolerance and the expected value is NaN,
+            # the actual tolerance is a NaN, which should be an error.
+            with pytest.raises(ValueError):
+                a != approx(x, rel=inf)
+
+            # You can make comparisons against NaN by not specifying a relative
+            # tolerance, so only an absolute tolerance is calculated.
+            assert a != approx(x, abs=inf)
+
+    def test_expecting_sequence(self):
+        within_1e8 = [
+                (1e8 + 1e0, 1e8),
+                (1e0 + 1e-8, 1e0),
+                (1e-8 + 1e-16, 1e-8),
+        ]
+        actual, expected = zip(*within_1e8)
+        assert actual == approx(expected, rel=5e-8, abs=0.0)
+
+    def test_expecting_sequence_wrong_len(self):
+        assert [1, 2] != approx([1])
+        assert [1, 2] != approx([1,2,3])
+
+    def test_complex(self):
+        within_1e6 = [
+                ( 1.000001 + 1.0j, 1.0 + 1.0j),
+                (1.0 + 1.000001j, 1.0 + 1.0j),
+                (-1.000001 + 1.0j, -1.0 + 1.0j),
+                (1.0 - 1.000001j, 1.0 - 1.0j),
+        ]
+        for a, x in within_1e6:
+            assert a == approx(x, rel=5e-6, abs=0)
+            assert a != approx(x, rel=5e-7, abs=0)
+
+    def test_int(self):
+        within_1e6 = [
+                (1000001, 1000000),
+                (-1000001, -1000000),
+        ]
+        for a, x in within_1e6:
+            assert a == approx(x, rel=5e-6, abs=0)
+            assert a != approx(x, rel=5e-7, abs=0)
+
+    def test_decimal(self):
+        within_1e6 = [
+                (Decimal('1.000001'), Decimal('1.0')),
+                (Decimal('-1.000001'), Decimal('-1.0')),
+        ]
+        for a, x in within_1e6:
+            assert a == approx(x, rel=Decimal('5e-6'), abs=0)
+            assert a != approx(x, rel=Decimal('5e-7'), abs=0)
+
+    def test_fraction(self):
+        within_1e6 = [
+                (1 + Fraction(1, 1000000), Fraction(1)),
+                (-1 - Fraction(-1, 1000000), Fraction(-1)),
+        ]
+        for a, x in within_1e6:
+            assert a == approx(x, rel=5e-6, abs=0)
+            assert a != approx(x, rel=5e-7, abs=0)
+
+    def test_doctests(self):
+        parser = doctest.DocTestParser()
+        test = parser.get_doctest(
+                approx.__doc__,
+                {'approx': approx},
+                approx.__name__,
+                None, None,
+        )
+        runner = MyDocTestRunner()
+        runner.run(test)
+