bpo-39310: Add math.ulp(x) (GH-17965)
Add math.ulp(): return the value of the least significant bit
of a float.
diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index b64fd41..6d10227 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -53,30 +53,6 @@
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 @@
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 @@
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 @@
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 @@
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