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authorMark Dickinson <dickinsm@gmail.com>2017-01-21 13:10:52 (GMT)
committerMark Dickinson <dickinsm@gmail.com>2017-01-21 13:10:52 (GMT)
commit5e65cd39dfe73891b16d9c771892e1bc282c1eb9 (patch)
tree1e35edf9a52cf7f8f677e971be50ad0391c48dd0 /Lib/test/test_math.py
parentd1b230e48b81eb90d10f0ceb4e34c547800bd3a8 (diff)
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Issue #29282: Backed out changeset b33012ef1417
Diffstat (limited to 'Lib/test/test_math.py')
-rw-r--r--Lib/test/test_math.py234
1 files changed, 0 insertions, 234 deletions
diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index 516a004..eaa41bc 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -4,7 +4,6 @@
from test.support import run_unittest, verbose, requires_IEEE_754
from test import support
import unittest
-import itertools
import math
import os
import platform
@@ -1411,244 +1410,11 @@ class IsCloseTests(unittest.TestCase):
self.assertAllNotClose(fraction_examples, rel_tol=1e-9)
-class FMATests(unittest.TestCase):
- """ Tests for math.fma. """
-
- def test_fma_nan_results(self):
- # Selected representative values.
- values = [
- -math.inf, -1e300, -2.3, -1e-300, -0.0,
- 0.0, 1e-300, 2.3, 1e300, math.inf, math.nan
- ]
-
- # If any input is a NaN, the result should be a NaN, too.
- for a, b in itertools.product(values, repeat=2):
- self.assertIsNaN(math.fma(math.nan, a, b))
- self.assertIsNaN(math.fma(a, math.nan, b))
- self.assertIsNaN(math.fma(a, b, math.nan))
-
- def test_fma_infinities(self):
- # Cases involving infinite inputs or results.
- positives = [1e-300, 2.3, 1e300, math.inf]
- finites = [-1e300, -2.3, -1e-300, -0.0, 0.0, 1e-300, 2.3, 1e300]
- non_nans = [-math.inf, -2.3, -0.0, 0.0, 2.3, math.inf]
-
- # ValueError due to inf * 0 computation.
- for c in non_nans:
- for infinity in [math.inf, -math.inf]:
- for zero in [0.0, -0.0]:
- with self.assertRaises(ValueError):
- math.fma(infinity, zero, c)
- with self.assertRaises(ValueError):
- math.fma(zero, infinity, c)
-
- # ValueError when a*b and c both infinite of opposite signs.
- for b in positives:
- with self.assertRaises(ValueError):
- math.fma(math.inf, b, -math.inf)
- with self.assertRaises(ValueError):
- math.fma(math.inf, -b, math.inf)
- with self.assertRaises(ValueError):
- math.fma(-math.inf, -b, -math.inf)
- with self.assertRaises(ValueError):
- math.fma(-math.inf, b, math.inf)
- with self.assertRaises(ValueError):
- math.fma(b, math.inf, -math.inf)
- with self.assertRaises(ValueError):
- math.fma(-b, math.inf, math.inf)
- with self.assertRaises(ValueError):
- math.fma(-b, -math.inf, -math.inf)
- with self.assertRaises(ValueError):
- math.fma(b, -math.inf, math.inf)
-
- # Infinite result when a*b and c both infinite of the same sign.
- for b in positives:
- self.assertEqual(math.fma(math.inf, b, math.inf), math.inf)
- self.assertEqual(math.fma(math.inf, -b, -math.inf), -math.inf)
- self.assertEqual(math.fma(-math.inf, -b, math.inf), math.inf)
- self.assertEqual(math.fma(-math.inf, b, -math.inf), -math.inf)
- self.assertEqual(math.fma(b, math.inf, math.inf), math.inf)
- self.assertEqual(math.fma(-b, math.inf, -math.inf), -math.inf)
- self.assertEqual(math.fma(-b, -math.inf, math.inf), math.inf)
- self.assertEqual(math.fma(b, -math.inf, -math.inf), -math.inf)
-
- # Infinite result when a*b finite, c infinite.
- for a, b in itertools.product(finites, finites):
- self.assertEqual(math.fma(a, b, math.inf), math.inf)
- self.assertEqual(math.fma(a, b, -math.inf), -math.inf)
-
- # Infinite result when a*b infinite, c finite.
- for b, c in itertools.product(positives, finites):
- self.assertEqual(math.fma(math.inf, b, c), math.inf)
- self.assertEqual(math.fma(-math.inf, b, c), -math.inf)
- self.assertEqual(math.fma(-math.inf, -b, c), math.inf)
- self.assertEqual(math.fma(math.inf, -b, c), -math.inf)
-
- self.assertEqual(math.fma(b, math.inf, c), math.inf)
- self.assertEqual(math.fma(b, -math.inf, c), -math.inf)
- self.assertEqual(math.fma(-b, -math.inf, c), math.inf)
- self.assertEqual(math.fma(-b, math.inf, c), -math.inf)
-
- def test_fma_zero_result(self):
- nonnegative_finites = [0.0, 1e-300, 2.3, 1e300]
-
- # Zero results from exact zero inputs.
- for b in nonnegative_finites:
- self.assertIsPositiveZero(math.fma(0.0, b, 0.0))
- self.assertIsPositiveZero(math.fma(0.0, b, -0.0))
- self.assertIsNegativeZero(math.fma(0.0, -b, -0.0))
- self.assertIsPositiveZero(math.fma(0.0, -b, 0.0))
- self.assertIsPositiveZero(math.fma(-0.0, -b, 0.0))
- self.assertIsPositiveZero(math.fma(-0.0, -b, -0.0))
- self.assertIsNegativeZero(math.fma(-0.0, b, -0.0))
- self.assertIsPositiveZero(math.fma(-0.0, b, 0.0))
-
- self.assertIsPositiveZero(math.fma(b, 0.0, 0.0))
- self.assertIsPositiveZero(math.fma(b, 0.0, -0.0))
- self.assertIsNegativeZero(math.fma(-b, 0.0, -0.0))
- self.assertIsPositiveZero(math.fma(-b, 0.0, 0.0))
- self.assertIsPositiveZero(math.fma(-b, -0.0, 0.0))
- self.assertIsPositiveZero(math.fma(-b, -0.0, -0.0))
- self.assertIsNegativeZero(math.fma(b, -0.0, -0.0))
- self.assertIsPositiveZero(math.fma(b, -0.0, 0.0))
-
- # Exact zero result from nonzero inputs.
- self.assertIsPositiveZero(math.fma(2.0, 2.0, -4.0))
- self.assertIsPositiveZero(math.fma(2.0, -2.0, 4.0))
- self.assertIsPositiveZero(math.fma(-2.0, -2.0, -4.0))
- self.assertIsPositiveZero(math.fma(-2.0, 2.0, 4.0))
-
- # Underflow to zero.
- tiny = 1e-300
- self.assertIsPositiveZero(math.fma(tiny, tiny, 0.0))
- self.assertIsNegativeZero(math.fma(tiny, -tiny, 0.0))
- self.assertIsPositiveZero(math.fma(-tiny, -tiny, 0.0))
- self.assertIsNegativeZero(math.fma(-tiny, tiny, 0.0))
- self.assertIsPositiveZero(math.fma(tiny, tiny, -0.0))
- self.assertIsNegativeZero(math.fma(tiny, -tiny, -0.0))
- self.assertIsPositiveZero(math.fma(-tiny, -tiny, -0.0))
- self.assertIsNegativeZero(math.fma(-tiny, tiny, -0.0))
-
- # Corner case where rounding the multiplication would
- # give the wrong result.
- x = float.fromhex('0x1p-500')
- y = float.fromhex('0x1p-550')
- z = float.fromhex('0x1p-1000')
- self.assertIsNegativeZero(math.fma(x-y, x+y, -z))
- self.assertIsPositiveZero(math.fma(y-x, x+y, z))
- self.assertIsNegativeZero(math.fma(y-x, -(x+y), -z))
- self.assertIsPositiveZero(math.fma(x-y, -(x+y), z))
-
- def test_fma_overflow(self):
- a = b = float.fromhex('0x1p512')
- c = float.fromhex('0x1p1023')
- # Overflow from multiplication.
- with self.assertRaises(OverflowError):
- math.fma(a, b, 0.0)
- self.assertEqual(math.fma(a, b/2.0, 0.0), c)
- # Overflow from the addition.
- with self.assertRaises(OverflowError):
- math.fma(a, b/2.0, c)
- # No overflow, even though a*b overflows a float.
- self.assertEqual(math.fma(a, b, -c), c)
-
- # Extreme case: a * b is exactly at the overflow boundary, so the
- # tiniest offset makes a difference between overflow and a finite
- # result.
- a = float.fromhex('0x1.ffffffc000000p+511')
- b = float.fromhex('0x1.0000002000000p+512')
- c = float.fromhex('0x0.0000000000001p-1022')
- with self.assertRaises(OverflowError):
- math.fma(a, b, 0.0)
- with self.assertRaises(OverflowError):
- math.fma(a, b, c)
- self.assertEqual(math.fma(a, b, -c),
- float.fromhex('0x1.fffffffffffffp+1023'))
-
- # Another extreme case: here a*b is about as large as possible subject
- # to math.fma(a, b, c) being finite.
- a = float.fromhex('0x1.ae565943785f9p+512')
- b = float.fromhex('0x1.3094665de9db8p+512')
- c = float.fromhex('0x1.fffffffffffffp+1023')
- self.assertEqual(math.fma(a, b, -c), c)
-
- def test_fma_single_round(self):
- a = float.fromhex('0x1p-50')
- self.assertEqual(math.fma(a - 1.0, a + 1.0, 1.0), a*a)
-
- def test_random(self):
- # A collection of randomly generated inputs for which the naive FMA
- # (with two rounds) gives a different result from a singly-rounded FMA.
-
- # tuples (a, b, c, expected)
- test_values = [
- ('0x1.694adde428b44p-1', '0x1.371b0d64caed7p-1',
- '0x1.f347e7b8deab8p-4', '0x1.19f10da56c8adp-1'),
- ('0x1.605401ccc6ad6p-2', '0x1.ce3a40bf56640p-2',
- '0x1.96e3bf7bf2e20p-2', '0x1.1af6d8aa83101p-1'),
- ('0x1.e5abd653a67d4p-2', '0x1.a2e400209b3e6p-1',
- '0x1.a90051422ce13p-1', '0x1.37d68cc8c0fbbp+0'),
- ('0x1.f94e8efd54700p-2', '0x1.123065c812cebp-1',
- '0x1.458f86fb6ccd0p-1', '0x1.ccdcee26a3ff3p-1'),
- ('0x1.bd926f1eedc96p-1', '0x1.eee9ca68c5740p-1',
- '0x1.960c703eb3298p-2', '0x1.3cdcfb4fdb007p+0'),
- ('0x1.27348350fbccdp-1', '0x1.3b073914a53f1p-1',
- '0x1.e300da5c2b4cbp-1', '0x1.4c51e9a3c4e29p+0'),
- ('0x1.2774f00b3497bp-1', '0x1.7038ec336bff0p-2',
- '0x1.2f6f2ccc3576bp-1', '0x1.99ad9f9c2688bp-1'),
- ('0x1.51d5a99300e5cp-1', '0x1.5cd74abd445a1p-1',
- '0x1.8880ab0bbe530p-1', '0x1.3756f96b91129p+0'),
- ('0x1.73cb965b821b8p-2', '0x1.218fd3d8d5371p-1',
- '0x1.d1ea966a1f758p-2', '0x1.5217b8fd90119p-1'),
- ('0x1.4aa98e890b046p-1', '0x1.954d85dff1041p-1',
- '0x1.122b59317ebdfp-1', '0x1.0bf644b340cc5p+0'),
- ('0x1.e28f29e44750fp-1', '0x1.4bcc4fdcd18fep-1',
- '0x1.fd47f81298259p-1', '0x1.9b000afbc9995p+0'),
- ('0x1.d2e850717fe78p-3', '0x1.1dd7531c303afp-1',
- '0x1.e0869746a2fc2p-2', '0x1.316df6eb26439p-1'),
- ('0x1.cf89c75ee6fbap-2', '0x1.b23decdc66825p-1',
- '0x1.3d1fe76ac6168p-1', '0x1.00d8ea4c12abbp+0'),
- ('0x1.3265ae6f05572p-2', '0x1.16d7ec285f7a2p-1',
- '0x1.0b8405b3827fbp-1', '0x1.5ef33c118a001p-1'),
- ('0x1.c4d1bf55ec1a5p-1', '0x1.bc59618459e12p-2',
- '0x1.ce5b73dc1773dp-1', '0x1.496cf6164f99bp+0'),
- ('0x1.d350026ac3946p-1', '0x1.9a234e149a68cp-2',
- '0x1.f5467b1911fd6p-2', '0x1.b5cee3225caa5p-1'),
- ]
- for a_hex, b_hex, c_hex, expected_hex in test_values:
- a = float.fromhex(a_hex)
- b = float.fromhex(b_hex)
- c = float.fromhex(c_hex)
- expected = float.fromhex(expected_hex)
- self.assertEqual(math.fma(a, b, c), expected)
- self.assertEqual(math.fma(b, a, c), expected)
-
- # Custom assertions.
- def assertIsNaN(self, value):
- self.assertTrue(
- math.isnan(value),
- msg="Expected a NaN, got {!r}".format(value)
- )
-
- def assertIsPositiveZero(self, value):
- self.assertTrue(
- value == 0 and math.copysign(1, value) > 0,
- msg="Expected a positive zero, got {!r}".format(value)
- )
-
- def assertIsNegativeZero(self, value):
- self.assertTrue(
- value == 0 and math.copysign(1, value) < 0,
- msg="Expected a negative zero, got {!r}".format(value)
- )
-
-
def test_main():
from doctest import DocFileSuite
suite = unittest.TestSuite()
suite.addTest(unittest.makeSuite(MathTests))
suite.addTest(unittest.makeSuite(IsCloseTests))
- suite.addTest(unittest.makeSuite(FMATests))
suite.addTest(DocFileSuite("ieee754.txt"))
run_unittest(suite)