Properly handle inf, nan, and built-in numeric types.

This commit also:

- Dramatically increases the number of unit tests , mostly by borrowing
  from the standard  library's unit tests for math.isclose().

- Refactors approx() into two classes, one of which handles comparing
  individual numbers (ApproxNonIterable) and another which uses the
  first to compare individual numbers or sequences of numbers.

_pytest/python.py

@@ -6,6 +6,7 @@ import inspect
 import re
 import types
 import sys
+import math
 
 import py
 import pytest
@@ -1412,37 +1413,120 @@ class approx(object):
 
     def __init__(self, expected, rel=None, abs=None):
         self.expected = expected
-        self.max_relative_error = rel
+        self.abs = abs
-        self.max_absolute_error = abs
+        self.rel = rel
 
     def __repr__(self):
-        from collections import Iterable
+        return ', '.join(repr(x) for x in self.expected)
-        utf_8 = lambda s: s.encode('utf-8') if sys.version_info[0] == 2 else s
-        plus_minus = lambda x: utf_8(u'{0} \u00b1 {1:.1e}'.format(x, self._get_margin(x)))
-
-        if isinstance(self.expected, Iterable):
-            return ', '.join([plus_minus(x) for x in self.expected])
-        else:
-            return plus_minus(self.expected)
 
     def __eq__(self, actual):
         from collections import Iterable
-        expected = self.expected
+        if not isinstance(actual, Iterable): actual = [actual]
-        almost_eq = lambda a, x: abs(x - a) < self._get_margin(x)
+        if len(actual) != len(self.expected): return False
+        return all(a == x for a, x in zip(actual, self.expected))
 
-        if isinstance(actual, Iterable) and isinstance(expected, Iterable):
+    @property
-            return all(almost_eq(a, x) for a, x in zip(actual, expected))
+    def expected(self):
+        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 almost_eq(actual, expected)
+            return [approx_non_iter(self._expected)]
 
-    def _get_margin(self, x):
+    @expected.setter
-        margin = self.max_absolute_error or 1e-12
+    def expected(self, expected):
+        self._expected = expected
         
-        if self.max_relative_error is None:
-            if self.max_absolute_error is not None:
-                return margin
 
-        return max(margin, x * (self.max_relative_error or 1e-6))
+
+class ApproxNonIterable(object):
+    """
+    Perform approximate comparisons for single numbers only.
+
+    This class contains most of the 
+    """
+
+    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 = '???'
+
+        repr = 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 repr.encode('utf-8')
+        else:
+            return repr
+
+    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
+
+    @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 absolute 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 
+        # it isn't even being used.
+        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)
+
 
 
 #

testing/python/approx.py

@@ -3,6 +3,12 @@
 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):
@@ -15,19 +21,263 @@ class MyDocTestRunner(doctest.DocTestRunner):
 
 class TestApprox:
 
-    def test_approx_doctests(self):
+    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 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)),
+        ]
+        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(
-                pytest.approx.__doc__,
+                approx.__doc__,
-                {'approx': pytest.approx},
+                {'approx': approx},
-                pytest.approx.__name__,
+                approx.__name__,
                 None, None,
         )
         runner = MyDocTestRunner()
         runner.run(test)
 
-    def test_repr_string(self):
-        # Just make sure the Unicode handling doesn't raise any exceptions.
-        print(pytest.approx(1.0))
-        print(pytest.approx([1.0, 2.0, 3.0]))
-