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@@ -33,8 +33,8 @@ |
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else: |
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file = __file__ |
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test_dir = os.path.dirname(file) or os.curdir |
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math_testcases = os.path.join(test_dir, 'math_testcases.txt') |
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test_file = os.path.join(test_dir, 'cmath_testcases.txt') |
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math_testcases = os.path.join(test_dir, 'mathdata', 'math_testcases.txt') |
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test_file = os.path.join(test_dir, 'mathdata', 'cmath_testcases.txt') |
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def to_ulps(x): |
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@@ -2628,9 +2628,247 @@ def test_fractions(self): |
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self.assertAllNotClose(fraction_examples, rel_tol=1e-9) |
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class FMATests(unittest.TestCase): |
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""" Tests for math.fma. """ |
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def test_fma_nan_results(self): |
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# Selected representative values. |
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values = [ |
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-math.inf, -1e300, -2.3, -1e-300, -0.0, |
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0.0, 1e-300, 2.3, 1e300, math.inf, math.nan |
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] |
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# If any input is a NaN, the result should be a NaN, too. |
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for a, b in itertools.product(values, repeat=2): |
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self.assertIsNaN(math.fma(math.nan, a, b)) |
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self.assertIsNaN(math.fma(a, math.nan, b)) |
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self.assertIsNaN(math.fma(a, b, math.nan)) |
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def test_fma_infinities(self): |
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# Cases involving infinite inputs or results. |
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positives = [1e-300, 2.3, 1e300, math.inf] |
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finites = [-1e300, -2.3, -1e-300, -0.0, 0.0, 1e-300, 2.3, 1e300] |
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non_nans = [-math.inf, -2.3, -0.0, 0.0, 2.3, math.inf] |
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# ValueError due to inf * 0 computation. |
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for c in non_nans: |
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for infinity in [math.inf, -math.inf]: |
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for zero in [0.0, -0.0]: |
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with self.assertRaises(ValueError): |
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math.fma(infinity, zero, c) |
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with self.assertRaises(ValueError): |
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math.fma(zero, infinity, c) |
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# ValueError when a*b and c both infinite of opposite signs. |
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for b in positives: |
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with self.assertRaises(ValueError): |
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math.fma(math.inf, b, -math.inf) |
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with self.assertRaises(ValueError): |
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math.fma(math.inf, -b, math.inf) |
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with self.assertRaises(ValueError): |
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math.fma(-math.inf, -b, -math.inf) |
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with self.assertRaises(ValueError): |
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math.fma(-math.inf, b, math.inf) |
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with self.assertRaises(ValueError): |
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math.fma(b, math.inf, -math.inf) |
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with self.assertRaises(ValueError): |
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math.fma(-b, math.inf, math.inf) |
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with self.assertRaises(ValueError): |
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math.fma(-b, -math.inf, -math.inf) |
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with self.assertRaises(ValueError): |
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math.fma(b, -math.inf, math.inf) |
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# Infinite result when a*b and c both infinite of the same sign. |
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for b in positives: |
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self.assertEqual(math.fma(math.inf, b, math.inf), math.inf) |
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self.assertEqual(math.fma(math.inf, -b, -math.inf), -math.inf) |
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self.assertEqual(math.fma(-math.inf, -b, math.inf), math.inf) |
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self.assertEqual(math.fma(-math.inf, b, -math.inf), -math.inf) |
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self.assertEqual(math.fma(b, math.inf, math.inf), math.inf) |
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self.assertEqual(math.fma(-b, math.inf, -math.inf), -math.inf) |
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self.assertEqual(math.fma(-b, -math.inf, math.inf), math.inf) |
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self.assertEqual(math.fma(b, -math.inf, -math.inf), -math.inf) |
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# Infinite result when a*b finite, c infinite. |
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for a, b in itertools.product(finites, finites): |
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self.assertEqual(math.fma(a, b, math.inf), math.inf) |
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self.assertEqual(math.fma(a, b, -math.inf), -math.inf) |
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# Infinite result when a*b infinite, c finite. |
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for b, c in itertools.product(positives, finites): |
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self.assertEqual(math.fma(math.inf, b, c), math.inf) |
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self.assertEqual(math.fma(-math.inf, b, c), -math.inf) |
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self.assertEqual(math.fma(-math.inf, -b, c), math.inf) |
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self.assertEqual(math.fma(math.inf, -b, c), -math.inf) |
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self.assertEqual(math.fma(b, math.inf, c), math.inf) |
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self.assertEqual(math.fma(b, -math.inf, c), -math.inf) |
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self.assertEqual(math.fma(-b, -math.inf, c), math.inf) |
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self.assertEqual(math.fma(-b, math.inf, c), -math.inf) |
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# gh-73468: On some platforms, libc fma() doesn't implement IEE 754-2008 |
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# properly: it doesn't use the right sign when the result is zero. |
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@unittest.skipIf( |
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sys.platform.startswith(("freebsd", "wasi", "netbsd")) |
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or (sys.platform == "android" and platform.machine() == "x86_64"), |
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f"this platform doesn't implement IEE 754-2008 properly") |
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def test_fma_zero_result(self): |
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nonnegative_finites = [0.0, 1e-300, 2.3, 1e300] |
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# Zero results from exact zero inputs. |
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for b in nonnegative_finites: |
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self.assertIsPositiveZero(math.fma(0.0, b, 0.0)) |
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self.assertIsPositiveZero(math.fma(0.0, b, -0.0)) |
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self.assertIsNegativeZero(math.fma(0.0, -b, -0.0)) |
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self.assertIsPositiveZero(math.fma(0.0, -b, 0.0)) |
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self.assertIsPositiveZero(math.fma(-0.0, -b, 0.0)) |
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self.assertIsPositiveZero(math.fma(-0.0, -b, -0.0)) |
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self.assertIsNegativeZero(math.fma(-0.0, b, -0.0)) |
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self.assertIsPositiveZero(math.fma(-0.0, b, 0.0)) |
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self.assertIsPositiveZero(math.fma(b, 0.0, 0.0)) |
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self.assertIsPositiveZero(math.fma(b, 0.0, -0.0)) |
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self.assertIsNegativeZero(math.fma(-b, 0.0, -0.0)) |
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self.assertIsPositiveZero(math.fma(-b, 0.0, 0.0)) |
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self.assertIsPositiveZero(math.fma(-b, -0.0, 0.0)) |
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self.assertIsPositiveZero(math.fma(-b, -0.0, -0.0)) |
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self.assertIsNegativeZero(math.fma(b, -0.0, -0.0)) |
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self.assertIsPositiveZero(math.fma(b, -0.0, 0.0)) |
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# Exact zero result from nonzero inputs. |
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self.assertIsPositiveZero(math.fma(2.0, 2.0, -4.0)) |
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self.assertIsPositiveZero(math.fma(2.0, -2.0, 4.0)) |
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self.assertIsPositiveZero(math.fma(-2.0, -2.0, -4.0)) |
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self.assertIsPositiveZero(math.fma(-2.0, 2.0, 4.0)) |
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# Underflow to zero. |
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tiny = 1e-300 |
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self.assertIsPositiveZero(math.fma(tiny, tiny, 0.0)) |
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self.assertIsNegativeZero(math.fma(tiny, -tiny, 0.0)) |
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self.assertIsPositiveZero(math.fma(-tiny, -tiny, 0.0)) |
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self.assertIsNegativeZero(math.fma(-tiny, tiny, 0.0)) |
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self.assertIsPositiveZero(math.fma(tiny, tiny, -0.0)) |
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self.assertIsNegativeZero(math.fma(tiny, -tiny, -0.0)) |
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self.assertIsPositiveZero(math.fma(-tiny, -tiny, -0.0)) |
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self.assertIsNegativeZero(math.fma(-tiny, tiny, -0.0)) |
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# Corner case where rounding the multiplication would |
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# give the wrong result. |
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x = float.fromhex('0x1p-500') |
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y = float.fromhex('0x1p-550') |
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z = float.fromhex('0x1p-1000') |
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self.assertIsNegativeZero(math.fma(x-y, x+y, -z)) |
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self.assertIsPositiveZero(math.fma(y-x, x+y, z)) |
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self.assertIsNegativeZero(math.fma(y-x, -(x+y), -z)) |
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self.assertIsPositiveZero(math.fma(x-y, -(x+y), z)) |
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def test_fma_overflow(self): |
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a = b = float.fromhex('0x1p512') |
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c = float.fromhex('0x1p1023') |
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# Overflow from multiplication. |
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with self.assertRaises(OverflowError): |
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math.fma(a, b, 0.0) |
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self.assertEqual(math.fma(a, b/2.0, 0.0), c) |
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# Overflow from the addition. |
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with self.assertRaises(OverflowError): |
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math.fma(a, b/2.0, c) |
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# No overflow, even though a*b overflows a float. |
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self.assertEqual(math.fma(a, b, -c), c) |
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# Extreme case: a * b is exactly at the overflow boundary, so the |
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# tiniest offset makes a difference between overflow and a finite |
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# result. |
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a = float.fromhex('0x1.ffffffc000000p+511') |
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b = float.fromhex('0x1.0000002000000p+512') |
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c = float.fromhex('0x0.0000000000001p-1022') |
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with self.assertRaises(OverflowError): |
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math.fma(a, b, 0.0) |
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with self.assertRaises(OverflowError): |
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math.fma(a, b, c) |
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self.assertEqual(math.fma(a, b, -c), |
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float.fromhex('0x1.fffffffffffffp+1023')) |
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# Another extreme case: here a*b is about as large as possible subject |
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# to math.fma(a, b, c) being finite. |
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a = float.fromhex('0x1.ae565943785f9p+512') |
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b = float.fromhex('0x1.3094665de9db8p+512') |
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c = float.fromhex('0x1.fffffffffffffp+1023') |
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self.assertEqual(math.fma(a, b, -c), c) |
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def test_fma_single_round(self): |
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a = float.fromhex('0x1p-50') |
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self.assertEqual(math.fma(a - 1.0, a + 1.0, 1.0), a*a) |
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def test_random(self): |
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# A collection of randomly generated inputs for which the naive FMA |
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# (with two rounds) gives a different result from a singly-rounded FMA. |
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# tuples (a, b, c, expected) |
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test_values = [ |
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('0x1.694adde428b44p-1', '0x1.371b0d64caed7p-1', |
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'0x1.f347e7b8deab8p-4', '0x1.19f10da56c8adp-1'), |
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('0x1.605401ccc6ad6p-2', '0x1.ce3a40bf56640p-2', |
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'0x1.96e3bf7bf2e20p-2', '0x1.1af6d8aa83101p-1'), |
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('0x1.e5abd653a67d4p-2', '0x1.a2e400209b3e6p-1', |
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'0x1.a90051422ce13p-1', '0x1.37d68cc8c0fbbp+0'), |
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('0x1.f94e8efd54700p-2', '0x1.123065c812cebp-1', |
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'0x1.458f86fb6ccd0p-1', '0x1.ccdcee26a3ff3p-1'), |
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('0x1.bd926f1eedc96p-1', '0x1.eee9ca68c5740p-1', |
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'0x1.960c703eb3298p-2', '0x1.3cdcfb4fdb007p+0'), |
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('0x1.27348350fbccdp-1', '0x1.3b073914a53f1p-1', |
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'0x1.e300da5c2b4cbp-1', '0x1.4c51e9a3c4e29p+0'), |
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('0x1.2774f00b3497bp-1', '0x1.7038ec336bff0p-2', |
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'0x1.2f6f2ccc3576bp-1', '0x1.99ad9f9c2688bp-1'), |
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('0x1.51d5a99300e5cp-1', '0x1.5cd74abd445a1p-1', |
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'0x1.8880ab0bbe530p-1', '0x1.3756f96b91129p+0'), |
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('0x1.73cb965b821b8p-2', '0x1.218fd3d8d5371p-1', |
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'0x1.d1ea966a1f758p-2', '0x1.5217b8fd90119p-1'), |
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('0x1.4aa98e890b046p-1', '0x1.954d85dff1041p-1', |
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'0x1.122b59317ebdfp-1', '0x1.0bf644b340cc5p+0'), |
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('0x1.e28f29e44750fp-1', '0x1.4bcc4fdcd18fep-1', |
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'0x1.fd47f81298259p-1', '0x1.9b000afbc9995p+0'), |
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('0x1.d2e850717fe78p-3', '0x1.1dd7531c303afp-1', |
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'0x1.e0869746a2fc2p-2', '0x1.316df6eb26439p-1'), |
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('0x1.cf89c75ee6fbap-2', '0x1.b23decdc66825p-1', |
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'0x1.3d1fe76ac6168p-1', '0x1.00d8ea4c12abbp+0'), |
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('0x1.3265ae6f05572p-2', '0x1.16d7ec285f7a2p-1', |
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'0x1.0b8405b3827fbp-1', '0x1.5ef33c118a001p-1'), |
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('0x1.c4d1bf55ec1a5p-1', '0x1.bc59618459e12p-2', |
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'0x1.ce5b73dc1773dp-1', '0x1.496cf6164f99bp+0'), |
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('0x1.d350026ac3946p-1', '0x1.9a234e149a68cp-2', |
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'0x1.f5467b1911fd6p-2', '0x1.b5cee3225caa5p-1'), |
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] |
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for a_hex, b_hex, c_hex, expected_hex in test_values: |
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a = float.fromhex(a_hex) |
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b = float.fromhex(b_hex) |
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c = float.fromhex(c_hex) |
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expected = float.fromhex(expected_hex) |
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self.assertEqual(math.fma(a, b, c), expected) |
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self.assertEqual(math.fma(b, a, c), expected) |
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# Custom assertions. |
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def assertIsNaN(self, value): |
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self.assertTrue( |
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math.isnan(value), |
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msg="Expected a NaN, got {!r}".format(value) |
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) |
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def assertIsPositiveZero(self, value): |
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self.assertTrue( |
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value == 0 and math.copysign(1, value) > 0, |
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msg="Expected a positive zero, got {!r}".format(value) |
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) |
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def assertIsNegativeZero(self, value): |
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self.assertTrue( |
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value == 0 and math.copysign(1, value) < 0, |
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msg="Expected a negative zero, got {!r}".format(value) |
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) |
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def load_tests(loader, tests, pattern): |
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from doctest import DocFileSuite |
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tests.addTest(DocFileSuite("ieee754.txt")) |
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tests.addTest(DocFileSuite(os.path.join("mathdata", "ieee754.txt"))) |
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return tests |
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if __name__ == '__main__': |
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