ENH: Allow relative and/or absolute precision in assert_almost_equal

This commit makes `assert_almost_equal` accept both relative and
absolute precision when comparing numbers, through two new keyword
arguments: `rtol`, and `atol`, respectively.

Under the hood, `_libs.testing.assert_almost_equal` is now calling
`math.isclose`, instead of an adaptaion of
[numpy.testing.assert_almost_equal](https://docs.scipy.org/doc/numpy-1.17.0/reference/generated/numpy.testing.assert_almost_equal.html).

doc/source/whatsnew/v1.0.0.rst

@@ -226,8 +226,9 @@ Other enhancements
 - Added new writer for exporting Stata dta files in version 118, ``StataWriter118``.  This format supports exporting strings containing Unicode characters (:issue:`23573`)
 - :meth:`Series.map` now accepts ``collections.abc.Mapping`` subclasses as a mapper (:issue:`29733`)
 - The ``pandas.datetime`` class is now deprecated. Import from ``datetime`` instead (:issue:`30296`)
-
-
+- :meth:`util.testing.assert_almost_equal` has new keyword argument ``check_low_values``
+  for comparing numeric values by decimal places when ``check_less_precise=True``
+  (:issue:`13357`).
 
 Build Changes
 ^^^^^^^^^^^^^

pandas/_libs/testing.pyx

@@ -1,3 +1,5 @@
+import math
+
 import numpy as np
 
 from pandas.core.dtypes.missing import isna, array_equivalent
@@ -38,13 +40,6 @@ cdef bint is_dictlike(obj):
     return hasattr(obj, 'keys') and hasattr(obj, '__getitem__')
 
 
-cdef bint decimal_almost_equal(double desired, double actual, int decimal):
-    # Code from
-    # http://docs.scipy.org/doc/numpy/reference/generated
-    # /numpy.testing.assert_almost_equal.html
-    return abs(desired - actual) < (0.5 * 10.0 ** -decimal)
-
-
 cpdef assert_dict_equal(a, b, bint compare_keys=True):
     assert is_dictlike(a) and is_dictlike(b), (
         "Cannot compare dict objects, one or both is not dict-like"
@@ -63,7 +58,7 @@ cpdef assert_dict_equal(a, b, bint compare_keys=True):
 
 
 cpdef assert_almost_equal(a, b,
-                          check_less_precise=False,
+                          rtol=1e-9, atol=0.0,
                           bint check_dtype=True,
                           obj=None, lobj=None, robj=None):
     """
@@ -73,25 +68,23 @@ cpdef assert_almost_equal(a, b,
     ----------
     a : object
     b : object
-    check_less_precise : bool or int, default False
-        Specify comparison precision.
-        5 digits (False) or 3 digits (True) after decimal points are
-        compared. If an integer, then this will be the number of decimal
-        points to compare
+    rtol : float, default 1e-9
+        Relative tolerance.
+    atol : float, default 0.0
+        Absolute tolerance.
     check_dtype: bool, default True
-        check dtype if both a and b are np.ndarray
+        check dtype if both a and b are np.ndarray.
     obj : str, default None
         Specify object name being compared, internally used to show
-        appropriate assertion message
+        appropriate assertion message.
     lobj : str, default None
         Specify left object name being compared, internally used to show
-        appropriate assertion message
+        appropriate assertion message.
     robj : str, default None
         Specify right object name being compared, internally used to show
-        appropriate assertion message
+        appropriate assertion message.
     """
     cdef:
-        int decimal
         double diff = 0.0
         Py_ssize_t i, na, nb
         double fa, fb
@@ -102,8 +95,6 @@ cpdef assert_almost_equal(a, b,
     if robj is None:
         robj = b
 
-    assert isinstance(check_less_precise, (int, bool))
-
     if isinstance(a, dict) or isinstance(b, dict):
         return assert_dict_equal(a, b)
 
@@ -161,8 +152,7 @@ cpdef assert_almost_equal(a, b,
 
         for i in range(len(a)):
             try:
-                assert_almost_equal(a[i], b[i],
-                                    check_less_precise=check_less_precise)
+                assert_almost_equal(a[i], b[i], rtol=rtol, atol=atol)
             except AssertionError:
                 is_unequal = True
                 diff += 1
@@ -194,24 +184,11 @@ cpdef assert_almost_equal(a, b,
             # inf comparison
             return True
 
-        if check_less_precise is True:
-            decimal = 3
-        elif check_less_precise is False:
-            decimal = 5
-        else:
-            decimal = check_less_precise
-
         fa, fb = a, b
 
-        # case for zero
-        if abs(fa) < 1e-5:
-            if not decimal_almost_equal(fa, fb, decimal):
-                assert False, (f'(very low values) expected {fb:.5f} '
-                               f'but got {fa:.5f}, with decimal {decimal}')
-        else:
-            if not decimal_almost_equal(1, fb / fa, decimal):
-                assert False, (f'expected {fb:.5f} but got {fa:.5f}, '
-                               f'with decimal {decimal}')
+        if not math.isclose(fa, fb, rel_tol=rtol, abs_tol=atol):
+            assert False, (f"expected {fb:.5f} but got {fa:.5f}, "
+                           f"with rtol={rtol}, atol={atol}")
         return True
 
     raise AssertionError(f"{a} != {b}")

pandas/tests/util/test_assert_almost_equal.py

@@ -80,11 +80,62 @@ def test_assert_almost_equal_numbers(a, b):
     _assert_almost_equal_both(a, b)
 
 
-@pytest.mark.parametrize("a,b", [(1.1, 1), (1.1, True), (1, 2), (1.0001, np.int16(1))])
+@pytest.mark.parametrize(
+    "a,b",
+    [
+        (1.1, 1),
+        (1.1, True),
+        (1, 2),
+        (1.0001, np.int16(1)),
+        # The following two examples are not "almost equal" due to tol.
+        (0.1, 0.1001),
+        (0.0011, 0.0012),
+    ],
+)
 def test_assert_not_almost_equal_numbers(a, b):
     _assert_not_almost_equal_both(a, b)
 
 
+@pytest.mark.parametrize(
+    "a,b",
+    [
+        (1.1, 1.1),
+        (1.1, 1.100001),
+        (1.1, 1.1001),
+        (0.000001, 0.000005),
+        (1000.0, 1000.0005),
+        # Testing this example, as per #13357
+        (0.000011, 0.000012),
+    ],
+)
+def test_assert_almost_equal_numbers_atol(a, b):
+    # Equivalent to the deprecated check_less_precise=True
+    _assert_almost_equal_both(a, b, atol=1e-3)
+
+
+@pytest.mark.parametrize("a,b", [(1.1, 1.11), (0.1, 0.101), (0.000011, 0.001012)])
+def test_assert_not_almost_equal_numbers_atol(a, b):
+    _assert_not_almost_equal_both(a, b, atol=1e-3)
+
+
+@pytest.mark.parametrize(
+    "a,b",
+    [
+        (1.1, 1.1),
+        (1.1, 1.100001),
+        (1.1, 1.1001),
+        (0.000001, 0.000005),
+        (1000.0, 1000.0005),
+        (0.000011, 0.000012),
+        # These 2 examples pass because we're using relative tolerance
+        (1.1, 1.11),
+        (0.1, 0.101),
+    ],
+)
+def test_assert_almost_equal_numbers_rtol(a, b):
+    _assert_almost_equal_both(a, b, rtol=.05)
+
+
 @pytest.mark.parametrize("a,b", [(0, 0), (0, 0.0), (0, np.float64(0)), (0.000001, 0)])
 def test_assert_almost_equal_numbers_with_zeros(a, b):
     _assert_almost_equal_both(a, b)
@@ -237,7 +288,7 @@ def test_assert_almost_equal_object():
 
 
 def test_assert_almost_equal_value_mismatch():
-    msg = "expected 2\\.00000 but got 1\\.00000, with decimal 5"
+    msg = "expected 2\\.00000 but got 1\\.00000, with rtol=1e-09, atol=1e-05"
 
     with pytest.raises(AssertionError, match=msg):
         tm.assert_almost_equal(1, 2)