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bpo-39310: Add math.ulp(x) (GH-17965)

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Add math.ulp(): return the value of the least significant bit
of a float.
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Victor Stinner 2020-01-13 12:44:35 +01:00 • committed by GitHub
parent 7ba6f18de2
commit 0b2ab21956
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7 changed files with 144 additions and 37 deletions
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55
Lib/test/test_math.py
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@ -53,30 +53,6 @@ def to_ulps(x):
return n
def ulp(x):
"""Return the value of the least significant bit of a
float x, such that the first float bigger than x is x+ulp(x).
Then, given an expected result x and a tolerance of n ulps,
the result y should be such that abs(y-x) <= n * ulp(x).
The results from this function will only make sense on platforms
where native doubles are represented in IEEE 754 binary64 format.
"""
x = abs(float(x))
if math.isnan(x) or math.isinf(x):
return x
# Find next float up from x.
n = struct.unpack('<q', struct.pack('<d', x))[0]
x_next = struct.unpack('<d', struct.pack('<q', n + 1))[0]
if math.isinf(x_next):
# Corner case: x was the largest finite float. Then it's
# not an exact power of two, so we can take the difference
# between x and the previous float.
x_prev = struct.unpack('<d', struct.pack('<q', n - 1))[0]
return x - x_prev
else:
return x_next - x
# Here's a pure Python version of the math.factorial algorithm, for
# documentation and comparison purposes.
#
@ -470,9 +446,9 @@ class MathTests(unittest.TestCase):
def testCos(self):
self.assertRaises(TypeError, math.cos)
self.ftest('cos(-pi/2)', math.cos(-math.pi/2), 0, abs_tol=ulp(1))
self.ftest('cos(-pi/2)', math.cos(-math.pi/2), 0, abs_tol=math.ulp(1))
self.ftest('cos(0)', math.cos(0), 1)
self.ftest('cos(pi/2)', math.cos(math.pi/2), 0, abs_tol=ulp(1))
self.ftest('cos(pi/2)', math.cos(math.pi/2), 0, abs_tol=math.ulp(1))
self.ftest('cos(pi)', math.cos(math.pi), -1)
try:
self.assertTrue(math.isnan(math.cos(INF)))
@ -1445,7 +1421,7 @@ class MathTests(unittest.TestCase):
self.assertRaises(TypeError, math.tanh)
self.ftest('tanh(0)', math.tanh(0), 0)
self.ftest('tanh(1)+tanh(-1)', math.tanh(1)+math.tanh(-1), 0,
abs_tol=ulp(1))
abs_tol=math.ulp(1))
self.ftest('tanh(inf)', math.tanh(INF), 1)
self.ftest('tanh(-inf)', math.tanh(NINF), -1)
self.assertTrue(math.isnan(math.tanh(NAN)))
@ -2036,7 +2012,7 @@ class IsCloseTests(unittest.TestCase):
def assertEqualSign(self, x, y):
"""Similar to assertEqual(), but compare also the sign.
Function useful to check to signed zero.
Function useful to compare signed zeros.
"""
self.assertEqual(x, y)
self.assertEqual(math.copysign(1.0, x), math.copysign(1.0, y))
@ -2087,6 +2063,29 @@ class IsCloseTests(unittest.TestCase):
self.assertTrue(math.isnan(math.nextafter(1.0, NAN)))
self.assertTrue(math.isnan(math.nextafter(NAN, NAN)))
@requires_IEEE_754
def test_ulp(self):
self.assertEqual(math.ulp(1.0), sys.float_info.epsilon)
# use int ** int rather than float ** int to not rely on pow() accuracy
self.assertEqual(math.ulp(2 ** 52), 1.0)
self.assertEqual(math.ulp(2 ** 53), 2.0)
self.assertEqual(math.ulp(2 ** 64), 4096.0)
# min and max
self.assertEqual(math.ulp(0.0),
sys.float_info.min * sys.float_info.epsilon)
self.assertEqual(math.ulp(FLOAT_MAX),
FLOAT_MAX - math.nextafter(FLOAT_MAX, -INF))
# special cases
self.assertEqual(math.ulp(INF), INF)
self.assertTrue(math.isnan(math.ulp(math.nan)))
# negative number: ulp(-x) == ulp(x)
for x in (0.0, 1.0, 2 ** 52, 2 ** 64, INF):
with self.subTest(x=x):
self.assertEqual(math.ulp(-x), math.ulp(x))
def test_main():
from doctest import DocFileSuite