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. (merge 3.5)
This commit is contained in:
Tal Einat
commit
bc8db8fa1b
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@ -207,6 +207,38 @@ Classification functions
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and ``False`` otherwise.
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.. function:: isclose(a, b, *, rel_tol=1e-09, abs_tol=0.0)
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Return ``True`` if the values *a* and *b* are close to each other and
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``False`` otherwise.
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Whether or not two values are considered close is determined according to
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given absolute and relative tolerances.
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*rel_tol* is the relative tolerance -- it is the maximum allowed difference
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between *a* and *b*, relative to the larger absolute value of *a* or *b*.
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For example, to set a tolerance of 5%, pass ``rel_tol=0.05``. The default
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tolerance is ``1e-09``, which assures that the two values are the same
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within about 9 decimal digits. *rel_tol* must be greater than zero.
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*abs_tol* is the minimum absolute tolerance -- useful for comparisons near
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zero. *abs_tol* must be at least zero.
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If no errors occur, the result will be:
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``abs(a-b) <= max(rel_tol * max(abs(a), abs(b)), abs_tol)``.
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The IEEE 754 special values of ``NaN``, ``inf``, and ``-inf`` will be
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handled according to IEEE rules. Specifically, ``NaN`` is not considered
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close to any other value, including ``NaN``. ``inf`` and ``-inf`` are only
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considered close to themselves.
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.. versionadded:: 3.5
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.. seealso::
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:pep:`485` -- A function for testing approximate equality
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Constants
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---------
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@ -110,6 +110,38 @@ Number-theoretic and representation functions
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.. versionadded:: 3.5
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.. function:: isclose(a, b, *, rel_tol=1e-09, abs_tol=0.0)
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Return ``True`` if the values *a* and *b* are close to each other and
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``False`` otherwise.
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Whether or not two values are considered close is determined according to
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given absolute and relative tolerances.
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*rel_tol* is the relative tolerance -- it is the maximum allowed difference
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between *a* and *b*, relative to the larger absolute value of *a* or *b*.
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For example, to set a tolerance of 5%, pass ``rel_tol=0.05``. The default
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tolerance is ``1e-09``, which assures that the two values are the same
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within about 9 decimal digits. *rel_tol* must be greater than zero.
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*abs_tol* is the minimum absolute tolerance -- useful for comparisons near
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zero. *abs_tol* must be at least zero.
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If no errors occur, the result will be:
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``abs(a-b) <= max(rel_tol * max(abs(a), abs(b)), abs_tol)``.
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The IEEE 754 special values of ``NaN``, ``inf``, and ``-inf`` will be
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handled according to IEEE rules. Specifically, ``NaN`` is not considered
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close to any other value, including ``NaN``. ``inf`` and ``-inf`` are only
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considered close to themselves.
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.. versionadded:: 3.5
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.. seealso::
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:pep:`485` -- A function for testing approximate equality
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.. function:: isfinite(x)
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Return ``True`` if *x* is neither an infinity nor a NaN, and
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@ -285,6 +285,18 @@ rather than being restricted to ASCII.
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:pep:`488` -- Multi-phase extension module initialization
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PEP 485: A function for testing approximate equality
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----------------------------------------------------
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:pep:`485` adds the :func:`math.isclose` and :func:`cmath.isclose`
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functions which tell whether two values are approximately equal or
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"close" to each other. Whether or not two values are considered
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close is determined according to given absolute and relative tolerances.
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.. seealso::
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:pep:`485` -- A function for testing approximate equality
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Other Language Changes
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======================
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@ -346,6 +358,13 @@ cgi
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* :class:`~cgi.FieldStorage` now supports the context management protocol.
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(Contributed by Berker Peksag in :issue:`20289`.)
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cmath
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-----
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* :func:`cmath.isclose` function added.
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(Contributed by Chris Barker and Tal Einat in :issue:`24270`.)
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code
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----
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@ -578,6 +597,8 @@ math
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* :data:`math.inf` and :data:`math.nan` constants added. (Contributed by Mark
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Dickinson in :issue:`23185`.)
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* :func:`math.isclose` function added.
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(Contributed by Chris Barker and Tal Einat in :issue:`24270`.)
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shutil
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------
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@ -1,5 +1,6 @@
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from test.support import requires_IEEE_754
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from test.test_math import parse_testfile, test_file
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import test.test_math as test_math
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import unittest
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import cmath, math
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from cmath import phase, polar, rect, pi
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@ -529,5 +530,46 @@ class CMathTests(unittest.TestCase):
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self.assertComplexIdentical(cmath.atanh(z), z)
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class IsCloseTests(test_math.IsCloseTests):
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isclose = cmath.isclose
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def test_reject_complex_tolerances(self):
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with self.assertRaises(TypeError):
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self.isclose(1j, 1j, rel_tol=1j)
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with self.assertRaises(TypeError):
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self.isclose(1j, 1j, abs_tol=1j)
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with self.assertRaises(TypeError):
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self.isclose(1j, 1j, rel_tol=1j, abs_tol=1j)
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def test_complex_values(self):
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# test complex values that are close to within 12 decimal places
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complex_examples = [(1.0+1.0j, 1.000000000001+1.0j),
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(1.0+1.0j, 1.0+1.000000000001j),
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(-1.0+1.0j, -1.000000000001+1.0j),
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(1.0-1.0j, 1.0-0.999999999999j),
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]
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self.assertAllClose(complex_examples, rel_tol=1e-12)
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self.assertAllNotClose(complex_examples, rel_tol=1e-13)
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def test_complex_near_zero(self):
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# test values near zero that are near to within three decimal places
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near_zero_examples = [(0.001j, 0),
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(0.001, 0),
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(0.001+0.001j, 0),
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(-0.001+0.001j, 0),
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(0.001-0.001j, 0),
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(-0.001-0.001j, 0),
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]
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self.assertAllClose(near_zero_examples, abs_tol=1.5e-03)
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self.assertAllNotClose(near_zero_examples, abs_tol=0.5e-03)
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self.assertIsClose(0.001-0.001j, 0.001+0.001j, abs_tol=2e-03)
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self.assertIsNotClose(0.001-0.001j, 0.001+0.001j, abs_tol=1e-03)
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if __name__ == "__main__":
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unittest.main()
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@ -1166,10 +1166,131 @@ class MathTests(unittest.TestCase):
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'\n '.join(failures))
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class IsCloseTests(unittest.TestCase):
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isclose = math.isclose # sublcasses should override this
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def assertIsClose(self, a, b, *args, **kwargs):
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self.assertTrue(self.isclose(a, b, *args, **kwargs),
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msg="%s and %s should be close!" % (a, b))
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def assertIsNotClose(self, a, b, *args, **kwargs):
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self.assertFalse(self.isclose(a, b, *args, **kwargs),
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msg="%s and %s should not be close!" % (a, b))
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def assertAllClose(self, examples, *args, **kwargs):
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for a, b in examples:
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self.assertIsClose(a, b, *args, **kwargs)
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def assertAllNotClose(self, examples, *args, **kwargs):
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for a, b in examples:
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self.assertIsNotClose(a, b, *args, **kwargs)
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def test_negative_tolerances(self):
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# ValueError should be raised if either tolerance is less than zero
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with self.assertRaises(ValueError):
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self.assertIsClose(1, 1, rel_tol=-1e-100)
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with self.assertRaises(ValueError):
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self.assertIsClose(1, 1, rel_tol=1e-100, abs_tol=-1e10)
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def test_identical(self):
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# identical values must test as close
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identical_examples = [(2.0, 2.0),
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(0.1e200, 0.1e200),
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(1.123e-300, 1.123e-300),
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(12345, 12345.0),
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(0.0, -0.0),
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(345678, 345678)]
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self.assertAllClose(identical_examples, rel_tol=0.0, abs_tol=0.0)
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def test_eight_decimal_places(self):
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# examples that are close to 1e-8, but not 1e-9
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eight_decimal_places_examples = [(1e8, 1e8 + 1),
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(-1e-8, -1.000000009e-8),
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(1.12345678, 1.12345679)]
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self.assertAllClose(eight_decimal_places_examples, rel_tol=1e-8)
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self.assertAllNotClose(eight_decimal_places_examples, rel_tol=1e-9)
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def test_near_zero(self):
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# values close to zero
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near_zero_examples = [(1e-9, 0.0),
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(-1e-9, 0.0),
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(-1e-150, 0.0)]
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# these should not be close to any rel_tol
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self.assertAllNotClose(near_zero_examples, rel_tol=0.9)
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# these should be close to abs_tol=1e-8
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self.assertAllClose(near_zero_examples, abs_tol=1e-8)
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def test_identical_infinite(self):
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# these are close regardless of tolerance -- i.e. they are equal
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self.assertIsClose(INF, INF)
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self.assertIsClose(INF, INF, abs_tol=0.0)
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self.assertIsClose(NINF, NINF)
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self.assertIsClose(NINF, NINF, abs_tol=0.0)
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def test_inf_ninf_nan(self):
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# these should never be close (following IEEE 754 rules for equality)
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not_close_examples = [(NAN, NAN),
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(NAN, 1e-100),
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(1e-100, NAN),
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(INF, NAN),
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(NAN, INF),
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(INF, NINF),
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(INF, 1.0),
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(1.0, INF),
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(INF, 1e308),
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(1e308, INF)]
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# use largest reasonable tolerance
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self.assertAllNotClose(not_close_examples, abs_tol=0.999999999999999)
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def test_zero_tolerance(self):
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# test with zero tolerance
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zero_tolerance_close_examples = [(1.0, 1.0),
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(-3.4, -3.4),
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(-1e-300, -1e-300)]
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self.assertAllClose(zero_tolerance_close_examples, rel_tol=0.0)
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zero_tolerance_not_close_examples = [(1.0, 1.000000000000001),
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(0.99999999999999, 1.0),
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(1.0e200, .999999999999999e200)]
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self.assertAllNotClose(zero_tolerance_not_close_examples, rel_tol=0.0)
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def test_assymetry(self):
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# test the assymetry example from PEP 485
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self.assertAllClose([(9, 10), (10, 9)], rel_tol=0.1)
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def test_integers(self):
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# test with integer values
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integer_examples = [(100000001, 100000000),
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(123456789, 123456788)]
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self.assertAllClose(integer_examples, rel_tol=1e-8)
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self.assertAllNotClose(integer_examples, rel_tol=1e-9)
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def test_decimals(self):
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# test with Decimal values
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from decimal import Decimal
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decimal_examples = [(Decimal('1.00000001'), Decimal('1.0')),
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(Decimal('1.00000001e-20'), Decimal('1.0e-20')),
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(Decimal('1.00000001e-100'), Decimal('1.0e-100'))]
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self.assertAllClose(decimal_examples, rel_tol=1e-8)
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self.assertAllNotClose(decimal_examples, rel_tol=1e-9)
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def test_fractions(self):
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# test with Fraction values
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from fractions import Fraction
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# could use some more examples here!
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fraction_examples = [(Fraction(1, 100000000) + 1, Fraction(1))]
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self.assertAllClose(fraction_examples, rel_tol=1e-8)
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self.assertAllNotClose(fraction_examples, rel_tol=1e-9)
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def test_main():
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from doctest import DocFileSuite
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suite = unittest.TestSuite()
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suite.addTest(unittest.makeSuite(MathTests))
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suite.addTest(unittest.makeSuite(IsCloseTests))
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suite.addTest(DocFileSuite("ieee754.txt"))
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run_unittest(suite)
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|
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@ -288,6 +288,9 @@ Library
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- Issue #24298: Fix inspect.signature() to correctly unwrap wrappers
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around bound methods.
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- Issue #24270: Add math.isclose() and cmath.isclose() functions as per PEP 485.
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Contributed by Chris Barker and Tal Einat.
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IDLE
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----
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|
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@ -806,4 +806,55 @@ cmath_isinf(PyModuleDef *module, PyObject *arg)
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exit:
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return return_value;
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}
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/*[clinic end generated code: output=274f59792cf4f418 input=a9049054013a1b77]*/
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PyDoc_STRVAR(cmath_isclose__doc__,
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"isclose($module, /, a, b, *, rel_tol=1e-09, abs_tol=0.0)\n"
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"--\n"
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"\n"
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"Determine whether two complex numbers are close in value.\n"
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"\n"
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" rel_tol\n"
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" maximum difference for being considered \"close\", relative to the\n"
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" magnitude of the input values\n"
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" abs_tol\n"
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" maximum difference for being considered \"close\", regardless of the\n"
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" magnitude of the input values\n"
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"\n"
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"Return True if a is close in value to b, and False otherwise.\n"
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"\n"
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"For the values to be considered close, the difference between them must be\n"
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"smaller than at least one of the tolerances.\n"
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"\n"
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"-inf, inf and NaN behave similarly to the IEEE 754 Standard. That is, NaN is\n"
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"not close to anything, even itself. inf and -inf are only close to themselves.");
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|
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#define CMATH_ISCLOSE_METHODDEF \
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{"isclose", (PyCFunction)cmath_isclose, METH_VARARGS|METH_KEYWORDS, cmath_isclose__doc__},
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|
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static int
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cmath_isclose_impl(PyModuleDef *module, Py_complex a, Py_complex b,
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double rel_tol, double abs_tol);
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static PyObject *
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cmath_isclose(PyModuleDef *module, PyObject *args, PyObject *kwargs)
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{
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PyObject *return_value = NULL;
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static char *_keywords[] = {"a", "b", "rel_tol", "abs_tol", NULL};
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Py_complex a;
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Py_complex b;
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double rel_tol = 1e-09;
|
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double abs_tol = 0.0;
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int _return_value;
|
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|
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if (!PyArg_ParseTupleAndKeywords(args, kwargs, "DD|$dd:isclose", _keywords,
|
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&a, &b, &rel_tol, &abs_tol))
|
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goto exit;
|
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_return_value = cmath_isclose_impl(module, a, b, rel_tol, abs_tol);
|
||||
if ((_return_value == -1) && PyErr_Occurred())
|
||||
goto exit;
|
||||
return_value = PyBool_FromLong((long)_return_value);
|
||||
|
||||
exit:
|
||||
return return_value;
|
||||
}
|
||||
/*[clinic end generated code: output=229e9c48c9d27362 input=a9049054013a1b77]*/
|
||||
|
|
|
|||
|
|
@ -1114,6 +1114,73 @@ cmath_isinf_impl(PyModuleDef *module, Py_complex z)
|
|||
Py_IS_INFINITY(z.imag));
|
||||
}
|
||||
|
||||
/*[clinic input]
|
||||
cmath.isclose -> bool
|
||||
|
||||
a: Py_complex
|
||||
b: Py_complex
|
||||
*
|
||||
rel_tol: double = 1e-09
|
||||
maximum difference for being considered "close", relative to the
|
||||
magnitude of the input values
|
||||
abs_tol: double = 0.0
|
||||
maximum difference for being considered "close", regardless of the
|
||||
magnitude of the input values
|
||||
|
||||
Determine whether two complex numbers are close in value.
|
||||
|
||||
Return True if a is close in value to b, and False otherwise.
|
||||
|
||||
For the values to be considered close, the difference between them must be
|
||||
smaller than at least one of the tolerances.
|
||||
|
||||
-inf, inf and NaN behave similarly to the IEEE 754 Standard. That is, NaN is
|
||||
not close to anything, even itself. inf and -inf are only close to themselves.
|
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[clinic start generated code]*/
|
||||
|
||||
static int
|
||||
cmath_isclose_impl(PyModuleDef *module, Py_complex a, Py_complex b,
|
||||
double rel_tol, double abs_tol)
|
||||
/*[clinic end generated code: output=da0c535fb54e2310 input=df9636d7de1d4ac3]*/
|
||||
{
|
||||
double diff;
|
||||
|
||||
/* sanity check on the inputs */
|
||||
if (rel_tol < 0.0 || abs_tol < 0.0 ) {
|
||||
PyErr_SetString(PyExc_ValueError,
|
||||
"tolerances must be non-negative");
|
||||
return -1;
|
||||
}
|
||||
|
||||
if ( (a.real == b.real) && (a.imag == b.imag) ) {
|
||||
/* short circuit exact equality -- needed to catch two infinities of
|
||||
the same sign. And perhaps speeds things up a bit sometimes.
|
||||
*/
|
||||
return 1;
|
||||
}
|
||||
|
||||
/* This catches the case of two infinities of opposite sign, or
|
||||
one infinity and one finite number. Two infinities of opposite
|
||||
sign would otherwise have an infinite relative tolerance.
|
||||
Two infinities of the same sign are caught by the equality check
|
||||
above.
|
||||
*/
|
||||
|
||||
if (Py_IS_INFINITY(a.real) || Py_IS_INFINITY(a.imag) ||
|
||||
Py_IS_INFINITY(b.real) || Py_IS_INFINITY(b.imag)) {
|
||||
return 0;
|
||||
}
|
||||
|
||||
/* now do the regular computation
|
||||
this is essentially the "weak" test from the Boost library
|
||||
*/
|
||||
|
||||
diff = _Py_c_abs(_Py_c_diff(a, b));
|
||||
|
||||
return (((diff <= rel_tol * _Py_c_abs(b)) ||
|
||||
(diff <= rel_tol * _Py_c_abs(a))) ||
|
||||
(diff <= abs_tol));
|
||||
}
|
||||
|
||||
PyDoc_STRVAR(module_doc,
|
||||
"This module is always available. It provides access to mathematical\n"
|
||||
|
|
@ -1129,6 +1196,7 @@ static PyMethodDef cmath_methods[] = {
|
|||
CMATH_COS_METHODDEF
|
||||
CMATH_COSH_METHODDEF
|
||||
CMATH_EXP_METHODDEF
|
||||
CMATH_ISCLOSE_METHODDEF
|
||||
CMATH_ISFINITE_METHODDEF
|
||||
CMATH_ISINF_METHODDEF
|
||||
CMATH_ISNAN_METHODDEF
|
||||
|
|
|
|||
|
|
@ -1990,6 +1990,83 @@ PyDoc_STRVAR(math_isinf_doc,
|
|||
"isinf(x) -> bool\n\n\
|
||||
Return True if x is a positive or negative infinity, and False otherwise.");
|
||||
|
||||
static PyObject *
|
||||
math_isclose(PyObject *self, PyObject *args, PyObject *kwargs)
|
||||
{
|
||||
double a, b;
|
||||
double rel_tol = 1e-9;
|
||||
double abs_tol = 0.0;
|
||||
double diff = 0.0;
|
||||
long result = 0;
|
||||
|
||||
static char *keywords[] = {"a", "b", "rel_tol", "abs_tol", NULL};
|
||||
|
||||
|
||||
if (!PyArg_ParseTupleAndKeywords(args, kwargs, "dd|$dd:isclose",
|
||||
keywords,
|
||||
&a, &b, &rel_tol, &abs_tol
|
||||
))
|
||||
return NULL;
|
||||
|
||||
/* sanity check on the inputs */
|
||||
if (rel_tol < 0.0 || abs_tol < 0.0 ) {
|
||||
PyErr_SetString(PyExc_ValueError,
|
||||
"tolerances must be non-negative");
|
||||
return NULL;
|
||||
}
|
||||
|
||||
if ( a == b ) {
|
||||
/* short circuit exact equality -- needed to catch two infinities of
|
||||
the same sign. And perhaps speeds things up a bit sometimes.
|
||||
*/
|
||||
Py_RETURN_TRUE;
|
||||
}
|
||||
|
||||
/* This catches the case of two infinities of opposite sign, or
|
||||
one infinity and one finite number. Two infinities of opposite
|
||||
sign would otherwise have an infinite relative tolerance.
|
||||
Two infinities of the same sign are caught by the equality check
|
||||
above.
|
||||
*/
|
||||
|
||||
if (Py_IS_INFINITY(a) || Py_IS_INFINITY(b)) {
|
||||
Py_RETURN_FALSE;
|
||||
}
|
||||
|
||||
/* now do the regular computation
|
||||
this is essentially the "weak" test from the Boost library
|
||||
*/
|
||||
|
||||
diff = fabs(b - a);
|
||||
|
||||
result = (((diff <= fabs(rel_tol * b)) ||
|
||||
(diff <= fabs(rel_tol * a))) ||
|
||||
(diff <= abs_tol));
|
||||
|
||||
return PyBool_FromLong(result);
|
||||
}
|
||||
|
||||
PyDoc_STRVAR(math_isclose_doc,
|
||||
"is_close(a, b, *, rel_tol=1e-09, abs_tol=0.0) -> bool\n"
|
||||
"\n"
|
||||
"Determine whether two floating point numbers are close in value.\n"
|
||||
"\n"
|
||||
" rel_tol\n"
|
||||
" maximum difference for being considered \"close\", relative to the\n"
|
||||
" magnitude of the input values\n"
|
||||
" abs_tol\n"
|
||||
" maximum difference for being considered \"close\", regardless of the\n"
|
||||
" magnitude of the input values\n"
|
||||
"\n"
|
||||
"Return True if a is close in value to b, and False otherwise.\n"
|
||||
"\n"
|
||||
"For the values to be considered close, the difference between them\n"
|
||||
"must be smaller than at least one of the tolerances.\n"
|
||||
"\n"
|
||||
"-inf, inf and NaN behave similarly to the IEEE 754 Standard. That\n"
|
||||
"is, NaN is not close to anything, even itself. inf and -inf are\n"
|
||||
"only close to themselves.");
|
||||
|
||||
static PyMethodDef math_methods[] = {
|
||||
{"acos", math_acos, METH_O, math_acos_doc},
|
||||
{"acosh", math_acosh, METH_O, math_acosh_doc},
|
||||
|
|
@ -2016,6 +2093,8 @@ static PyMethodDef math_methods[] = {
|
|||
{"gamma", math_gamma, METH_O, math_gamma_doc},
|
||||
{"gcd", math_gcd, METH_VARARGS, math_gcd_doc},
|
||||
{"hypot", math_hypot, METH_VARARGS, math_hypot_doc},
|
||||
{"isclose", (PyCFunction) math_isclose, METH_VARARGS | METH_KEYWORDS,
|
||||
math_isclose_doc},
|
||||
{"isfinite", math_isfinite, METH_O, math_isfinite_doc},
|
||||
{"isinf", math_isinf, METH_O, math_isinf_doc},
|
||||
{"isnan", math_isnan, METH_O, math_isnan_doc},
|
||||
|
|
|
|||
Loading…
Reference in New Issue