diff --git a/AUTHORS b/AUTHORS index a6021c31143..04b87359d6c 100644 --- a/AUTHORS +++ b/AUTHORS @@ -50,6 +50,7 @@ Jason R. Coombs Joshua Bronson Jurko Gospodnetić Katarzyna Jachim +Kale Kundert Kevin Cox Lee Kamentsky Lukas Bednar diff --git a/CHANGELOG.rst b/CHANGELOG.rst index 0e7107337cb..0d61505331a 100644 --- a/CHANGELOG.rst +++ b/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 ========== diff --git a/_pytest/python.py b/_pytest/python.py index 1d1d9e158f7..2e6c8d87e48 100644 --- a/_pytest/python.py +++ b/_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 @@ def __exit__(self, *tp): 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 # diff --git a/doc/en/builtin.rst b/doc/en/builtin.rst index b18c3f8280a..d364dd56d54 100644 --- a/doc/en/builtin.rst +++ b/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: diff --git a/testing/python/approx.py b/testing/python/approx.py new file mode 100644 index 00000000000..2720c573f54 --- /dev/null +++ b/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) +