Issue #19543: Implementation of isclose as per PEP 485

For details, see:
PEP 0485 -- A Function for testing approximate equality

Functions added: math.isclose() and cmath.isclose().

Original code by Chris Barker. Patch by Tal Einat.

Lib/test/test_cmath.py

@@ -1,5 +1,6 @@
 from test.support import requires_IEEE_754
 from test.test_math import parse_testfile, test_file
+import test.test_math as test_math
 import unittest
 import cmath, math
 from cmath import phase, polar, rect, pi
@@ -529,5 +530,46 @@ class CMathTests(unittest.TestCase):
             self.assertComplexIdentical(cmath.atanh(z), z)
 
 
+class IsCloseTests(test_math.IsCloseTests):
+    isclose = cmath.isclose
+
+    def test_reject_complex_tolerances(self):
+        with self.assertRaises(TypeError):
+            self.isclose(1j, 1j, rel_tol=1j)
+
+        with self.assertRaises(TypeError):
+            self.isclose(1j, 1j, abs_tol=1j)
+
+        with self.assertRaises(TypeError):
+            self.isclose(1j, 1j, rel_tol=1j, abs_tol=1j)
+
+    def test_complex_values(self):
+        # test complex values that are close to within 12 decimal places
+        complex_examples = [(1.0+1.0j, 1.000000000001+1.0j),
+                            (1.0+1.0j, 1.0+1.000000000001j),
+                            (-1.0+1.0j, -1.000000000001+1.0j),
+                            (1.0-1.0j, 1.0-0.999999999999j),
+                            ]
+
+        self.assertAllClose(complex_examples, rel_tol=1e-12)
+        self.assertAllNotClose(complex_examples, rel_tol=1e-13)
+
+    def test_complex_near_zero(self):
+        # test values near zero that are near to within three decimal places
+        near_zero_examples = [(0.001j, 0),
+                              (0.001, 0),
+                              (0.001+0.001j, 0),
+                              (-0.001+0.001j, 0),
+                              (0.001-0.001j, 0),
+                              (-0.001-0.001j, 0),
+                              ]
+
+        self.assertAllClose(near_zero_examples, abs_tol=1.5e-03)
+        self.assertAllNotClose(near_zero_examples, abs_tol=0.5e-03)
+
+        self.assertIsClose(0.001-0.001j, 0.001+0.001j, abs_tol=2e-03)
+        self.assertIsNotClose(0.001-0.001j, 0.001+0.001j, abs_tol=1e-03)
+
+
 if __name__ == "__main__":
     unittest.main()

Lib/test/test_math.py

@@ -1166,10 +1166,131 @@ class MathTests(unittest.TestCase):
                       '\n  '.join(failures))
 
 
+class IsCloseTests(unittest.TestCase):
+    isclose = math.isclose # sublcasses should override this
+
+    def assertIsClose(self, a, b, *args, **kwargs):
+        self.assertTrue(self.isclose(a, b, *args, **kwargs),
+                        msg="%s and %s should be close!" % (a, b))
+
+    def assertIsNotClose(self, a, b, *args, **kwargs):
+        self.assertFalse(self.isclose(a, b, *args, **kwargs),
+                         msg="%s and %s should not be close!" % (a, b))
+
+    def assertAllClose(self, examples, *args, **kwargs):
+        for a, b in examples:
+            self.assertIsClose(a, b, *args, **kwargs)
+
+    def assertAllNotClose(self, examples, *args, **kwargs):
+        for a, b in examples:
+            self.assertIsNotClose(a, b, *args, **kwargs)
+
+    def test_negative_tolerances(self):
+        # ValueError should be raised if either tolerance is less than zero
+        with self.assertRaises(ValueError):
+            self.assertIsClose(1, 1, rel_tol=-1e-100)
+        with self.assertRaises(ValueError):
+            self.assertIsClose(1, 1, rel_tol=1e-100, abs_tol=-1e10)
+
+    def test_identical(self):
+        # identical values must test as close
+        identical_examples = [(2.0, 2.0),
+                              (0.1e200, 0.1e200),
+                              (1.123e-300, 1.123e-300),
+                              (12345, 12345.0),
+                              (0.0, -0.0),
+                              (345678, 345678)]
+        self.assertAllClose(identical_examples, rel_tol=0.0, abs_tol=0.0)
+
+    def test_eight_decimal_places(self):
+        # examples that are close to 1e-8, but not 1e-9
+        eight_decimal_places_examples = [(1e8, 1e8 + 1),
+                                         (-1e-8, -1.000000009e-8),
+                                         (1.12345678, 1.12345679)]
+        self.assertAllClose(eight_decimal_places_examples, rel_tol=1e-8)
+        self.assertAllNotClose(eight_decimal_places_examples, rel_tol=1e-9)
+
+    def test_near_zero(self):
+        # values close to zero
+        near_zero_examples = [(1e-9, 0.0),
+                              (-1e-9, 0.0),
+                              (-1e-150, 0.0)]
+        # these should not be close to any rel_tol
+        self.assertAllNotClose(near_zero_examples, rel_tol=0.9)
+        # these should be close to abs_tol=1e-8
+        self.assertAllClose(near_zero_examples, abs_tol=1e-8)
+
+    def test_identical_infinite(self):
+        # these are close regardless of tolerance -- i.e. they are equal
+        self.assertIsClose(INF, INF)
+        self.assertIsClose(INF, INF, abs_tol=0.0)
+        self.assertIsClose(NINF, NINF)
+        self.assertIsClose(NINF, NINF, abs_tol=0.0)
+
+    def test_inf_ninf_nan(self):
+        # these should never be close (following IEEE 754 rules for equality)
+        not_close_examples = [(NAN, NAN),
+                              (NAN, 1e-100),
+                              (1e-100, NAN),
+                              (INF, NAN),
+                              (NAN, INF),
+                              (INF, NINF),
+                              (INF, 1.0),
+                              (1.0, INF),
+                              (INF, 1e308),
+                              (1e308, INF)]
+        # use largest reasonable tolerance
+        self.assertAllNotClose(not_close_examples, abs_tol=0.999999999999999)
+
+    def test_zero_tolerance(self):
+        # test with zero tolerance
+        zero_tolerance_close_examples = [(1.0, 1.0),
+                                         (-3.4, -3.4),
+                                         (-1e-300, -1e-300)]
+        self.assertAllClose(zero_tolerance_close_examples, rel_tol=0.0)
+
+        zero_tolerance_not_close_examples = [(1.0, 1.000000000000001),
+                                             (0.99999999999999, 1.0),
+                                             (1.0e200, .999999999999999e200)]
+        self.assertAllNotClose(zero_tolerance_not_close_examples, rel_tol=0.0)
+
+    def test_assymetry(self):
+        # test the assymetry example from PEP 485
+        self.assertAllClose([(9, 10), (10, 9)], rel_tol=0.1)
+
+    def test_integers(self):
+        # test with integer values
+        integer_examples = [(100000001, 100000000),
+                            (123456789, 123456788)]
+
+        self.assertAllClose(integer_examples, rel_tol=1e-8)
+        self.assertAllNotClose(integer_examples, rel_tol=1e-9)
+
+    def test_decimals(self):
+        # test with Decimal values
+        from decimal import Decimal
+
+        decimal_examples = [(Decimal('1.00000001'), Decimal('1.0')),
+                            (Decimal('1.00000001e-20'), Decimal('1.0e-20')),
+                            (Decimal('1.00000001e-100'), Decimal('1.0e-100'))]
+        self.assertAllClose(decimal_examples, rel_tol=1e-8)
+        self.assertAllNotClose(decimal_examples, rel_tol=1e-9)
+
+    def test_fractions(self):
+        # test with Fraction values
+        from fractions import Fraction
+
+        # could use some more examples here!
+        fraction_examples = [(Fraction(1, 100000000) + 1, Fraction(1))]
+        self.assertAllClose(fraction_examples, rel_tol=1e-8)
+        self.assertAllNotClose(fraction_examples, rel_tol=1e-9)
+
+
 def test_main():
     from doctest import DocFileSuite
     suite = unittest.TestSuite()
     suite.addTest(unittest.makeSuite(MathTests))
+    suite.addTest(unittest.makeSuite(IsCloseTests))
     suite.addTest(DocFileSuite("ieee754.txt"))
     run_unittest(suite)