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index 229a7c2afa8..3997acbdf84 100644
--- a/Lib/test/test_capi/test_misc.py
+++ b/Lib/test/test_capi/test_misc.py
@@ -307,7 +307,7 @@ def test_getitem_with_error(self):
CURRENT_THREAD_REGEX +
r' File .*, line 6 in <module>\n'
r'\n'
- r'Extension modules: _testcapi \(total: 1\)\n')
+ r'Extension modules: ')
else:
# Python built with NDEBUG macro defined:
# test _Py_CheckFunctionResult() instead.
diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index e3b0d4fa9ee..ddeb8ad7cd6 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -55,56 +55,6 @@ def to_ulps(x):
return n
-# Here's a pure Python version of the math.factorial algorithm, for
-# documentation and comparison purposes.
-#
-# Formula:
-#
-# factorial(n) = factorial_odd_part(n) << (n - count_set_bits(n))
-#
-# where
-#
-# factorial_odd_part(n) = product_{i >= 0} product_{0 < j <= n >> i; j odd} j
-#
-# The outer product above is an infinite product, but once i >= n.bit_length,
-# (n >> i) < 1 and the corresponding term of the product is empty. So only the
-# finitely many terms for 0 <= i < n.bit_length() contribute anything.
-#
-# We iterate downwards from i == n.bit_length() - 1 to i == 0. The inner
-# product in the formula above starts at 1 for i == n.bit_length(); for each i
-# < n.bit_length() we get the inner product for i from that for i + 1 by
-# multiplying by all j in {n >> i+1 < j <= n >> i; j odd}. In Python terms,
-# this set is range((n >> i+1) + 1 | 1, (n >> i) + 1 | 1, 2).
-
-def count_set_bits(n):
- """Number of '1' bits in binary expansion of a nonnnegative integer."""
- return 1 + count_set_bits(n & n - 1) if n else 0
-
-def partial_product(start, stop):
- """Product of integers in range(start, stop, 2), computed recursively.
- start and stop should both be odd, with start <= stop.
-
- """
- numfactors = (stop - start) >> 1
- if not numfactors:
- return 1
- elif numfactors == 1:
- return start
- else:
- mid = (start + numfactors) | 1
- return partial_product(start, mid) * partial_product(mid, stop)
-
-def py_factorial(n):
- """Factorial of nonnegative integer n, via "Binary Split Factorial Formula"
- described at http://www.luschny.de/math/factorial/binarysplitfact.html
-
- """
- inner = outer = 1
- for i in reversed(range(n.bit_length())):
- inner *= partial_product((n >> i + 1) + 1 | 1, (n >> i) + 1 | 1)
- outer *= inner
- return outer << (n - count_set_bits(n))
-
def ulp_abs_check(expected, got, ulp_tol, abs_tol):
"""Given finite floats `expected` and `got`, check that they're
approximately equal to within the given number of ulps or the
@@ -547,33 +497,6 @@ def testFabs(self):
self.ftest('fabs(0)', math.fabs(0), 0)
self.ftest('fabs(1)', math.fabs(1), 1)
- def testFactorial(self):
- self.assertEqual(math.factorial(0), 1)
- total = 1
- for i in range(1, 1000):
- total *= i
- self.assertEqual(math.factorial(i), total)
- self.assertEqual(math.factorial(i), py_factorial(i))
- self.assertRaises(ValueError, math.factorial, -1)
- self.assertRaises(ValueError, math.factorial, -10**100)
-
- def testFactorialNonIntegers(self):
- self.assertRaises(TypeError, math.factorial, 5.0)
- self.assertRaises(TypeError, math.factorial, 5.2)
- self.assertRaises(TypeError, math.factorial, -1.0)
- self.assertRaises(TypeError, math.factorial, -1e100)
- self.assertRaises(TypeError, math.factorial, decimal.Decimal('5'))
- self.assertRaises(TypeError, math.factorial, decimal.Decimal('5.2'))
- self.assertRaises(TypeError, math.factorial, "5")
-
- # Other implementations may place different upper bounds.
- @support.cpython_only
- def testFactorialHugeInputs(self):
- # Currently raises OverflowError for inputs that are too large
- # to fit into a C long.
- self.assertRaises(OverflowError, math.factorial, 10**100)
- self.assertRaises(TypeError, math.factorial, 1e100)
-
def testFloor(self):
self.assertRaises(TypeError, math.floor)
self.assertEqual(int, type(math.floor(0.5)))
@@ -1175,68 +1098,6 @@ def test_math_dist_leak(self):
with self.assertRaises(ValueError):
math.dist([1, 2], [3, 4, 5])
- def testIsqrt(self):
- # Test a variety of inputs, large and small.
- test_values = (
- list(range(1000))
- + list(range(10**6 - 1000, 10**6 + 1000))
- + [2**e + i for e in range(60, 200) for i in range(-40, 40)]
- + [3**9999, 10**5001]
- )
-
- for value in test_values:
- with self.subTest(value=value):
- s = math.isqrt(value)
- self.assertIs(type(s), int)
- self.assertLessEqual(s*s, value)
- self.assertLess(value, (s+1)*(s+1))
-
- # Negative values
- with self.assertRaises(ValueError):
- math.isqrt(-1)
-
- # Integer-like things
- s = math.isqrt(True)
- self.assertIs(type(s), int)
- self.assertEqual(s, 1)
-
- s = math.isqrt(False)
- self.assertIs(type(s), int)
- self.assertEqual(s, 0)
-
- class IntegerLike(object):
- def __init__(self, value):
- self.value = value
-
- def __index__(self):
- return self.value
-
- s = math.isqrt(IntegerLike(1729))
- self.assertIs(type(s), int)
- self.assertEqual(s, 41)
-
- with self.assertRaises(ValueError):
- math.isqrt(IntegerLike(-3))
-
- # Non-integer-like things
- bad_values = [
- 3.5, "a string", decimal.Decimal("3.5"), 3.5j,
- 100.0, -4.0,
- ]
- for value in bad_values:
- with self.subTest(value=value):
- with self.assertRaises(TypeError):
- math.isqrt(value)
-
- @support.bigmemtest(2**32, memuse=0.85)
- def test_isqrt_huge(self, size):
- if size & 1:
- size += 1
- v = 1 << size
- w = math.isqrt(v)
- self.assertEqual(w.bit_length(), size // 2 + 1)
- self.assertEqual(w.bit_count(), 1)
-
def test_lcm(self):
lcm = math.lcm
self.assertEqual(lcm(0, 0), 0)
@@ -2392,140 +2253,6 @@ def _naive_prod(iterable, start=1):
self.assertEqual(type(prod([1, decimal.Decimal(2.0), 3, 4, 5, 6])),
decimal.Decimal)
- def testPerm(self):
- perm = math.perm
- factorial = math.factorial
- # Test if factorial definition is satisfied
- for n in range(500):
- for k in (range(n + 1) if n < 100 else range(30) if n < 200 else range(10)):
- self.assertEqual(perm(n, k),
- factorial(n) // factorial(n - k))
-
- # Test for Pascal's identity
- for n in range(1, 100):
- for k in range(1, n):
- self.assertEqual(perm(n, k), perm(n - 1, k - 1) * k + perm(n - 1, k))
-
- # Test corner cases
- for n in range(1, 100):
- self.assertEqual(perm(n, 0), 1)
- self.assertEqual(perm(n, 1), n)
- self.assertEqual(perm(n, n), factorial(n))
-
- # Test one argument form
- for n in range(20):
- self.assertEqual(perm(n), factorial(n))
- self.assertEqual(perm(n, None), factorial(n))
-
- # Raises TypeError if any argument is non-integer or argument count is
- # not 1 or 2
- self.assertRaises(TypeError, perm, 10, 1.0)
- self.assertRaises(TypeError, perm, 10, decimal.Decimal(1.0))
- self.assertRaises(TypeError, perm, 10, "1")
- self.assertRaises(TypeError, perm, 10.0, 1)
- self.assertRaises(TypeError, perm, decimal.Decimal(10.0), 1)
- self.assertRaises(TypeError, perm, "10", 1)
-
- self.assertRaises(TypeError, perm)
- self.assertRaises(TypeError, perm, 10, 1, 3)
- self.assertRaises(TypeError, perm)
-
- # Raises Value error if not k or n are negative numbers
- self.assertRaises(ValueError, perm, -1, 1)
- self.assertRaises(ValueError, perm, -2**1000, 1)
- self.assertRaises(ValueError, perm, 1, -1)
- self.assertRaises(ValueError, perm, 1, -2**1000)
-
- # Returns zero if k is greater than n
- self.assertEqual(perm(1, 2), 0)
- self.assertEqual(perm(1, 2**1000), 0)
-
- n = 2**1000
- self.assertEqual(perm(n, 0), 1)
- self.assertEqual(perm(n, 1), n)
- self.assertEqual(perm(n, 2), n * (n-1))
- if support.check_impl_detail(cpython=True):
- self.assertRaises(OverflowError, perm, n, n)
-
- for n, k in (True, True), (True, False), (False, False):
- self.assertEqual(perm(n, k), 1)
- self.assertIs(type(perm(n, k)), int)
- self.assertEqual(perm(IntSubclass(5), IntSubclass(2)), 20)
- self.assertEqual(perm(MyIndexable(5), MyIndexable(2)), 20)
- for k in range(3):
- self.assertIs(type(perm(IntSubclass(5), IntSubclass(k))), int)
- self.assertIs(type(perm(MyIndexable(5), MyIndexable(k))), int)
-
- def testComb(self):
- comb = math.comb
- factorial = math.factorial
- # Test if factorial definition is satisfied
- for n in range(500):
- for k in (range(n + 1) if n < 100 else range(30) if n < 200 else range(10)):
- self.assertEqual(comb(n, k), factorial(n)
- // (factorial(k) * factorial(n - k)))
-
- # Test for Pascal's identity
- for n in range(1, 100):
- for k in range(1, n):
- self.assertEqual(comb(n, k), comb(n - 1, k - 1) + comb(n - 1, k))
-
- # Test corner cases
- for n in range(100):
- self.assertEqual(comb(n, 0), 1)
- self.assertEqual(comb(n, n), 1)
-
- for n in range(1, 100):
- self.assertEqual(comb(n, 1), n)
- self.assertEqual(comb(n, n - 1), n)
-
- # Test Symmetry
- for n in range(100):
- for k in range(n // 2):
- self.assertEqual(comb(n, k), comb(n, n - k))
-
- # Raises TypeError if any argument is non-integer or argument count is
- # not 2
- self.assertRaises(TypeError, comb, 10, 1.0)
- self.assertRaises(TypeError, comb, 10, decimal.Decimal(1.0))
- self.assertRaises(TypeError, comb, 10, "1")
- self.assertRaises(TypeError, comb, 10.0, 1)
- self.assertRaises(TypeError, comb, decimal.Decimal(10.0), 1)
- self.assertRaises(TypeError, comb, "10", 1)
-
- self.assertRaises(TypeError, comb, 10)
- self.assertRaises(TypeError, comb, 10, 1, 3)
- self.assertRaises(TypeError, comb)
-
- # Raises Value error if not k or n are negative numbers
- self.assertRaises(ValueError, comb, -1, 1)
- self.assertRaises(ValueError, comb, -2**1000, 1)
- self.assertRaises(ValueError, comb, 1, -1)
- self.assertRaises(ValueError, comb, 1, -2**1000)
-
- # Returns zero if k is greater than n
- self.assertEqual(comb(1, 2), 0)
- self.assertEqual(comb(1, 2**1000), 0)
-
- n = 2**1000
- self.assertEqual(comb(n, 0), 1)
- self.assertEqual(comb(n, 1), n)
- self.assertEqual(comb(n, 2), n * (n-1) // 2)
- self.assertEqual(comb(n, n), 1)
- self.assertEqual(comb(n, n-1), n)
- self.assertEqual(comb(n, n-2), n * (n-1) // 2)
- if support.check_impl_detail(cpython=True):
- self.assertRaises(OverflowError, comb, n, n//2)
-
- for n, k in (True, True), (True, False), (False, False):
- self.assertEqual(comb(n, k), 1)
- self.assertIs(type(comb(n, k)), int)
- self.assertEqual(comb(IntSubclass(5), IntSubclass(2)), 10)
- self.assertEqual(comb(MyIndexable(5), MyIndexable(2)), 10)
- for k in range(3):
- self.assertIs(type(comb(IntSubclass(5), IntSubclass(k))), int)
- self.assertIs(type(comb(MyIndexable(5), MyIndexable(k))), int)
-
@requires_IEEE_754
def test_nextafter(self):
# around 2^52 and 2^63
diff --git a/Lib/test/test_math_integer.py b/Lib/test/test_math_integer.py
new file mode 100644
index 00000000000..09a98d93bd6
--- /dev/null
+++ b/Lib/test/test_math_integer.py
@@ -0,0 +1,403 @@
+from decimal import Decimal
+from fractions import Fraction
+import unittest
+from test import support
+
+
+class IntSubclass(int):
+ pass
+
+# Class providing an __index__ method.
+class MyIndexable(object):
+ def __init__(self, value):
+ self.value = value
+
+ def __index__(self):
+ return self.value
+
+# Here's a pure Python version of the math.integer.factorial algorithm, for
+# documentation and comparison purposes.
+#
+# Formula:
+#
+# factorial(n) = factorial_odd_part(n) << (n - count_set_bits(n))
+#
+# where
+#
+# factorial_odd_part(n) = product_{i >= 0} product_{0 < j <= n >> i; j odd} j
+#
+# The outer product above is an infinite product, but once i >= n.bit_length,
+# (n >> i) < 1 and the corresponding term of the product is empty. So only the
+# finitely many terms for 0 <= i < n.bit_length() contribute anything.
+#
+# We iterate downwards from i == n.bit_length() - 1 to i == 0. The inner
+# product in the formula above starts at 1 for i == n.bit_length(); for each i
+# < n.bit_length() we get the inner product for i from that for i + 1 by
+# multiplying by all j in {n >> i+1 < j <= n >> i; j odd}. In Python terms,
+# this set is range((n >> i+1) + 1 | 1, (n >> i) + 1 | 1, 2).
+
+def count_set_bits(n):
+ """Number of '1' bits in binary expansion of a nonnnegative integer."""
+ return 1 + count_set_bits(n & n - 1) if n else 0
+
+def partial_product(start, stop):
+ """Product of integers in range(start, stop, 2), computed recursively.
+ start and stop should both be odd, with start <= stop.
+
+ """
+ numfactors = (stop - start) >> 1
+ if not numfactors:
+ return 1
+ elif numfactors == 1:
+ return start
+ else:
+ mid = (start + numfactors) | 1
+ return partial_product(start, mid) * partial_product(mid, stop)
+
+def py_factorial(n):
+ """Factorial of nonnegative integer n, via "Binary Split Factorial Formula"
+ described at http://www.luschny.de/math/factorial/binarysplitfact.html
+
+ """
+ inner = outer = 1
+ for i in reversed(range(n.bit_length())):
+ inner *= partial_product((n >> i + 1) + 1 | 1, (n >> i) + 1 | 1)
+ outer *= inner
+ return outer << (n - count_set_bits(n))
+
+
+class IntMathTests(unittest.TestCase):
+ import math.integer as module
+
+ def assertIntEqual(self, actual, expected):
+ self.assertEqual(actual, expected)
+ self.assertIs(type(actual), int)
+
+ def test_factorial(self):
+ factorial = self.module.factorial
+ self.assertEqual(factorial(0), 1)
+ total = 1
+ for i in range(1, 1000):
+ total *= i
+ self.assertEqual(factorial(i), total)
+ self.assertEqual(factorial(i), py_factorial(i))
+
+ self.assertIntEqual(factorial(False), 1)
+ self.assertIntEqual(factorial(True), 1)
+ for i in range(3):
+ expected = factorial(i)
+ self.assertIntEqual(factorial(IntSubclass(i)), expected)
+ self.assertIntEqual(factorial(MyIndexable(i)), expected)
+
+ self.assertRaises(ValueError, factorial, -1)
+ self.assertRaises(ValueError, factorial, -10**1000)
+
+ def test_factorial_non_integers(self):
+ factorial = self.module.factorial
+ self.assertRaises(TypeError, factorial, 5.0)
+ self.assertRaises(TypeError, factorial, 5.2)
+ self.assertRaises(TypeError, factorial, -1.0)
+ self.assertRaises(TypeError, factorial, -1e100)
+ self.assertRaises(TypeError, factorial, Decimal('5'))
+ self.assertRaises(TypeError, factorial, Decimal('5.2'))
+ self.assertRaises(TypeError, factorial, Fraction(5, 1))
+ self.assertRaises(TypeError, factorial, "5")
+
+ # Other implementations may place different upper bounds.
+ @support.cpython_only
+ def test_factorial_huge_inputs(self):
+ factorial = self.module.factorial
+ # Currently raises OverflowError for inputs that are too large
+ # to fit into a C long.
+ self.assertRaises(OverflowError, factorial, 10**100)
+ self.assertRaises(TypeError, factorial, 1e100)
+
+ def test_gcd(self):
+ gcd = self.module.gcd
+ self.assertEqual(gcd(0, 0), 0)
+ self.assertEqual(gcd(1, 0), 1)
+ self.assertEqual(gcd(-1, 0), 1)
+ self.assertEqual(gcd(0, 1), 1)
+ self.assertEqual(gcd(0, -1), 1)
+ self.assertEqual(gcd(7, 1), 1)
+ self.assertEqual(gcd(7, -1), 1)
+ self.assertEqual(gcd(-23, 15), 1)
+ self.assertEqual(gcd(120, 84), 12)
+ self.assertEqual(gcd(84, -120), 12)
+ self.assertEqual(gcd(1216342683557601535506311712,
+ 436522681849110124616458784), 32)
+ c = 652560
+ x = 434610456570399902378880679233098819019853229470286994367836600566
+ y = 1064502245825115327754847244914921553977
+ a = x * c
+ b = y * c
+ self.assertEqual(gcd(a, b), c)
+ self.assertEqual(gcd(b, a), c)
+ self.assertEqual(gcd(-a, b), c)
+ self.assertEqual(gcd(b, -a), c)
+ self.assertEqual(gcd(a, -b), c)
+ self.assertEqual(gcd(-b, a), c)
+ self.assertEqual(gcd(-a, -b), c)
+ self.assertEqual(gcd(-b, -a), c)
+ c = 576559230871654959816130551884856912003141446781646602790216406874
+ a = x * c
+ b = y * c
+ self.assertEqual(gcd(a, b), c)
+ self.assertEqual(gcd(b, a), c)
+ self.assertEqual(gcd(-a, b), c)
+ self.assertEqual(gcd(b, -a), c)
+ self.assertEqual(gcd(a, -b), c)
+ self.assertEqual(gcd(-b, a), c)
+ self.assertEqual(gcd(-a, -b), c)
+ self.assertEqual(gcd(-b, -a), c)
+
+ self.assertRaises(TypeError, gcd, 120.0, 84)
+ self.assertRaises(TypeError, gcd, 120, 84.0)
+ self.assertIntEqual(gcd(IntSubclass(120), IntSubclass(84)), 12)
+ self.assertIntEqual(gcd(MyIndexable(120), MyIndexable(84)), 12)
+
+ def test_lcm(self):
+ lcm = self.module.lcm
+ self.assertEqual(lcm(0, 0), 0)
+ self.assertEqual(lcm(1, 0), 0)
+ self.assertEqual(lcm(-1, 0), 0)
+ self.assertEqual(lcm(0, 1), 0)
+ self.assertEqual(lcm(0, -1), 0)
+ self.assertEqual(lcm(7, 1), 7)
+ self.assertEqual(lcm(7, -1), 7)
+ self.assertEqual(lcm(-23, 15), 345)
+ self.assertEqual(lcm(120, 84), 840)
+ self.assertEqual(lcm(84, -120), 840)
+ self.assertEqual(lcm(1216342683557601535506311712,
+ 436522681849110124616458784),
+ 16592536571065866494401400422922201534178938447014944)
+
+ x = 43461045657039990237
+ y = 10645022458251153277
+ for c in (652560,
+ 57655923087165495981):
+ a = x * c
+ b = y * c
+ d = x * y * c
+ self.assertEqual(lcm(a, b), d)
+ self.assertEqual(lcm(b, a), d)
+ self.assertEqual(lcm(-a, b), d)
+ self.assertEqual(lcm(b, -a), d)
+ self.assertEqual(lcm(a, -b), d)
+ self.assertEqual(lcm(-b, a), d)
+ self.assertEqual(lcm(-a, -b), d)
+ self.assertEqual(lcm(-b, -a), d)
+
+ self.assertEqual(lcm(), 1)
+ self.assertEqual(lcm(120), 120)
+ self.assertEqual(lcm(-120), 120)
+ self.assertEqual(lcm(120, 84, 102), 14280)
+ self.assertEqual(lcm(120, 0, 84), 0)
+
+ self.assertRaises(TypeError, lcm, 120.0)
+ self.assertRaises(TypeError, lcm, 120.0, 84)
+ self.assertRaises(TypeError, lcm, 120, 84.0)
+ self.assertRaises(TypeError, lcm, 120, 0, 84.0)
+ self.assertEqual(lcm(MyIndexable(120), MyIndexable(84)), 840)
+
+ def test_isqrt(self):
+ isqrt = self.module.isqrt
+ # Test a variety of inputs, large and small.
+ test_values = (
+ list(range(1000))
+ + list(range(10**6 - 1000, 10**6 + 1000))
+ + [2**e + i for e in range(60, 200) for i in range(-40, 40)]
+ + [3**9999, 10**5001]
+ )
+
+ for value in test_values:
+ with self.subTest(value=value):
+ s = isqrt(value)
+ self.assertIs(type(s), int)
+ self.assertLessEqual(s*s, value)
+ self.assertLess(value, (s+1)*(s+1))
+
+ # Negative values
+ with self.assertRaises(ValueError):
+ isqrt(-1)
+
+ # Integer-like things
+ self.assertIntEqual(isqrt(True), 1)
+ self.assertIntEqual(isqrt(False), 0)
+ self.assertIntEqual(isqrt(MyIndexable(1729)), 41)
+
+ with self.assertRaises(ValueError):
+ isqrt(MyIndexable(-3))
+
+ # Non-integer-like things
+ bad_values = [
+ 3.5, "a string", Decimal("3.5"), 3.5j,
+ 100.0, -4.0,
+ ]
+ for value in bad_values:
+ with self.subTest(value=value):
+ with self.assertRaises(TypeError):
+ isqrt(value)
+
+ @support.bigmemtest(2**32, memuse=0.85)
+ def test_isqrt_huge(self, size):
+ isqrt = self.module.isqrt
+ if size & 1:
+ size += 1
+ v = 1 << size
+ w = isqrt(v)
+ self.assertEqual(w.bit_length(), size // 2 + 1)
+ self.assertEqual(w.bit_count(), 1)
+
+ def test_perm(self):
+ perm = self.module.perm
+ factorial = self.module.factorial
+ # Test if factorial definition is satisfied
+ for n in range(500):
+ for k in (range(n + 1) if n < 100 else range(30) if n < 200 else range(10)):
+ self.assertEqual(perm(n, k),
+ factorial(n) // factorial(n - k))
+
+ # Test for Pascal's identity
+ for n in range(1, 100):
+ for k in range(1, n):
+ self.assertEqual(perm(n, k), perm(n - 1, k - 1) * k + perm(n - 1, k))
+
+ # Test corner cases
+ for n in range(1, 100):
+ self.assertEqual(perm(n, 0), 1)
+ self.assertEqual(perm(n, 1), n)
+ self.assertEqual(perm(n, n), factorial(n))
+
+ # Test one argument form
+ for n in range(20):
+ self.assertEqual(perm(n), factorial(n))
+ self.assertEqual(perm(n, None), factorial(n))
+
+ # Raises TypeError if any argument is non-integer or argument count is
+ # not 1 or 2
+ self.assertRaises(TypeError, perm, 10, 1.0)
+ self.assertRaises(TypeError, perm, 10, Decimal(1.0))
+ self.assertRaises(TypeError, perm, 10, Fraction(1, 1))
+ self.assertRaises(TypeError, perm, 10, "1")
+ self.assertRaises(TypeError, perm, 10.0, 1)
+ self.assertRaises(TypeError, perm, Decimal(10.0), 1)
+ self.assertRaises(TypeError, perm, Fraction(10, 1), 1)
+ self.assertRaises(TypeError, perm, "10", 1)
+
+ self.assertRaises(TypeError, perm)
+ self.assertRaises(TypeError, perm, 10, 1, 3)
+ self.assertRaises(TypeError, perm)
+
+ # Raises Value error if not k or n are negative numbers
+ self.assertRaises(ValueError, perm, -1, 1)
+ self.assertRaises(ValueError, perm, -2**1000, 1)
+ self.assertRaises(ValueError, perm, 1, -1)
+ self.assertRaises(ValueError, perm, 1, -2**1000)
+
+ # Returns zero if k is greater than n
+ self.assertEqual(perm(1, 2), 0)
+ self.assertEqual(perm(1, 2**1000), 0)
+
+ n = 2**1000
+ self.assertEqual(perm(n, 0), 1)
+ self.assertEqual(perm(n, 1), n)
+ self.assertEqual(perm(n, 2), n * (n-1))
+ if support.check_impl_detail(cpython=True):
+ self.assertRaises(OverflowError, perm, n, n)
+
+ for n, k in (True, True), (True, False), (False, False):
+ self.assertIntEqual(perm(n, k), 1)
+ self.assertEqual(perm(IntSubclass(5), IntSubclass(2)), 20)
+ self.assertEqual(perm(MyIndexable(5), MyIndexable(2)), 20)
+ for k in range(3):
+ self.assertIs(type(perm(IntSubclass(5), IntSubclass(k))), int)
+ self.assertIs(type(perm(MyIndexable(5), MyIndexable(k))), int)
+
+ def test_comb(self):
+ comb = self.module.comb
+ factorial = self.module.factorial
+ # Test if factorial definition is satisfied
+ for n in range(500):
+ for k in (range(n + 1) if n < 100 else range(30) if n < 200 else range(10)):
+ self.assertEqual(comb(n, k), factorial(n)
+ // (factorial(k) * factorial(n - k)))
+
+ # Test for Pascal's identity
+ for n in range(1, 100):
+ for k in range(1, n):
+ self.assertEqual(comb(n, k), comb(n - 1, k - 1) + comb(n - 1, k))
+
+ # Test corner cases
+ for n in range(100):
+ self.assertEqual(comb(n, 0), 1)
+ self.assertEqual(comb(n, n), 1)
+
+ for n in range(1, 100):
+ self.assertEqual(comb(n, 1), n)
+ self.assertEqual(comb(n, n - 1), n)
+
+ # Test Symmetry
+ for n in range(100):
+ for k in range(n // 2):
+ self.assertEqual(comb(n, k), comb(n, n - k))
+
+ # Raises TypeError if any argument is non-integer or argument count is
+ # not 2
+ self.assertRaises(TypeError, comb, 10, 1.0)
+ self.assertRaises(TypeError, comb, 10, Decimal(1.0))
+ self.assertRaises(TypeError, comb, 10, "1")
+ self.assertRaises(TypeError, comb, 10.0, 1)
+ self.assertRaises(TypeError, comb, Decimal(10.0), 1)
+ self.assertRaises(TypeError, comb, "10", 1)
+
+ self.assertRaises(TypeError, comb, 10)
+ self.assertRaises(TypeError, comb, 10, 1, 3)
+ self.assertRaises(TypeError, comb)
+
+ # Raises Value error if not k or n are negative numbers
+ self.assertRaises(ValueError, comb, -1, 1)
+ self.assertRaises(ValueError, comb, -2**1000, 1)
+ self.assertRaises(ValueError, comb, 1, -1)
+ self.assertRaises(ValueError, comb, 1, -2**1000)
+
+ # Returns zero if k is greater than n
+ self.assertEqual(comb(1, 2), 0)
+ self.assertEqual(comb(1, 2**1000), 0)
+
+ n = 2**1000
+ self.assertEqual(comb(n, 0), 1)
+ self.assertEqual(comb(n, 1), n)
+ self.assertEqual(comb(n, 2), n * (n-1) // 2)
+ self.assertEqual(comb(n, n), 1)
+ self.assertEqual(comb(n, n-1), n)
+ self.assertEqual(comb(n, n-2), n * (n-1) // 2)
+ if support.check_impl_detail(cpython=True):
+ self.assertRaises(OverflowError, comb, n, n//2)
+
+ for n, k in (True, True), (True, False), (False, False):
+ self.assertIntEqual(comb(n, k), 1)
+ self.assertEqual(comb(IntSubclass(5), IntSubclass(2)), 10)
+ self.assertEqual(comb(MyIndexable(5), MyIndexable(2)), 10)
+ for k in range(3):
+ self.assertIs(type(comb(IntSubclass(5), IntSubclass(k))), int)
+ self.assertIs(type(comb(MyIndexable(5), MyIndexable(k))), int)
+
+
+class MathTests(IntMathTests):
+ import math as module
+
+
+class MiscTests(unittest.TestCase):
+
+ def test_module_name(self):
+ import math.integer
+ self.assertEqual(math.integer.__name__, 'math.integer')
+ for name in dir(math.integer):
+ if not name.startswith('_'):
+ obj = getattr(math.integer, name)
+ self.assertEqual(obj.__module__, 'math.integer')
+
+
+if __name__ == '__main__':
+ unittest.main()
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