bpo-37128: Add math.perm(). (GH-13731)

Doc/library/math.rst

@@ -207,6 +207,19 @@ Number-theoretic and representation functions
    of *x* and are floats.
 
 
+.. function:: perm(n, k)
+
+   Return the number of ways to choose *k* items from *n* items
+   without repetition and with order.
+
+   It is mathematically equal to the expression ``n! / (n - k)!``.
+
+   Raises :exc:`TypeError` if the arguments not integers.
+   Raises :exc:`ValueError` if the arguments are negative or if *k* > *n*.
+
+   .. versionadded:: 3.8
+
+
 .. function:: prod(iterable, *, start=1)
 
    Calculate the product of all the elements in the input *iterable*.

Lib/test/test_math.py

@@ -240,6 +240,9 @@ def result_check(expected, got, ulp_tol=5, abs_tol=0.0):
     else:
         return None
 
+class IntSubclass(int):
+    pass
+
 # Class providing an __index__ method.
 class MyIndexable(object):
     def __init__(self, value):
@@ -1862,6 +1865,64 @@ class IsCloseTests(unittest.TestCase):
         self.assertAllClose(fraction_examples, rel_tol=1e-8)
         self.assertAllNotClose(fraction_examples, rel_tol=1e-9)
 
+    def testPerm(self):
+        perm = math.perm
+        factorial = math.factorial
+        # Test if factorial defintion is satisfied
+        for n in range(100):
+            for k in range(n + 1):
+                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))
+
+        # Raises TypeError if any argument is non-integer or argument count is
+        # not 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, 10)
+        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)
+
+        # Raises value error if k is greater than n
+        self.assertRaises(ValueError, perm, 1, 2)
+        self.assertRaises(ValueError, perm, 1, 2**1000)
+
+        n = 2**1000
+        self.assertEqual(perm(n, 0), 1)
+        self.assertEqual(perm(n, 1), n)
+        self.assertEqual(perm(n, 2), n * (n-1))
+        self.assertRaises((OverflowError, MemoryError), 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
@@ -1925,8 +1986,11 @@ class IsCloseTests(unittest.TestCase):
         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)
-        self.assertIs(type(comb(MyIndexable(5), MyIndexable(2))), int)
+        for k in range(3):
+            self.assertIs(type(comb(IntSubclass(5), IntSubclass(k))), int)
+            self.assertIs(type(comb(MyIndexable(5), MyIndexable(k))), int)
 
 
 def test_main():

Misc/NEWS.d/next/Library/2019-06-01-22-54-03.bpo-37128.oGXBWN.rst

+Added :func:`math.perm`.

Modules/clinic/mathmodule.c.h

@@ -638,6 +638,41 @@ exit:
     return return_value;
 }
 
+PyDoc_STRVAR(math_perm__doc__,
+"perm($module, n, k, /)\n"
+"--\n"
+"\n"
+"Number of ways to choose k items from n items without repetition and with order.\n"
+"\n"
+"It is mathematically equal to the expression n! / (n - k)!.\n"
+"\n"
+"Raises TypeError if the arguments are not integers.\n"
+"Raises ValueError if the arguments are negative or if k > n.");
+
+#define MATH_PERM_METHODDEF    \
+    {"perm", (PyCFunction)(void(*)(void))math_perm, METH_FASTCALL, math_perm__doc__},
+
+static PyObject *
+math_perm_impl(PyObject *module, PyObject *n, PyObject *k);
+
+static PyObject *
+math_perm(PyObject *module, PyObject *const *args, Py_ssize_t nargs)
+{
+    PyObject *return_value = NULL;
+    PyObject *n;
+    PyObject *k;
+
+    if (!_PyArg_CheckPositional("perm", nargs, 2, 2)) {
+        goto exit;
+    }
+    n = args[0];
+    k = args[1];
+    return_value = math_perm_impl(module, n, k);
+
+exit:
+    return return_value;
+}
+
 PyDoc_STRVAR(math_comb__doc__,
 "comb($module, n, k, /)\n"
 "--\n"
@@ -674,4 +709,4 @@ math_comb(PyObject *module, PyObject *const *args, Py_ssize_t nargs)
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=6709521e5e1d90ec input=a9049054013a1b77]*/
+/*[clinic end generated code: output=a82b0e705b6d0ec0 input=a9049054013a1b77]*/

Modules/mathmodule.c

@@ -2998,6 +2998,120 @@ math_prod_impl(PyObject *module, PyObject *iterable, PyObject *start)
 }
 
 
+/*[clinic input]
+math.perm
+
+    n: object
+    k: object
+    /
+
+Number of ways to choose k items from n items without repetition and with order.
+
+It is mathematically equal to the expression n! / (n - k)!.
+
+Raises TypeError if the arguments are not integers.
+Raises ValueError if the arguments are negative or if k > n.
+[clinic start generated code]*/
+
+static PyObject *
+math_perm_impl(PyObject *module, PyObject *n, PyObject *k)
+/*[clinic end generated code: output=e021a25469653e23 input=f71ee4f6ff26be24]*/
+{
+    PyObject *result = NULL, *factor = NULL;
+    int overflow, cmp;
+    long long i, factors;
+
+    n = PyNumber_Index(n);
+    if (n == NULL) {
+        return NULL;
+    }
+    if (!PyLong_CheckExact(n)) {
+        Py_SETREF(n, _PyLong_Copy((PyLongObject *)n));
+        if (n == NULL) {
+            return NULL;
+        }
+    }
+    k = PyNumber_Index(k);
+    if (k == NULL) {
+        Py_DECREF(n);
+        return NULL;
+    }
+    if (!PyLong_CheckExact(k)) {
+        Py_SETREF(k, _PyLong_Copy((PyLongObject *)k));
+        if (k == NULL) {
+            Py_DECREF(n);
+            return NULL;
+        }
+    }
+
+    if (Py_SIZE(n) < 0) {
+        PyErr_SetString(PyExc_ValueError,
+                        "n must be a non-negative integer");
+        goto error;
+    }
+    cmp = PyObject_RichCompareBool(n, k, Py_LT);
+    if (cmp != 0) {
+        if (cmp > 0) {
+            PyErr_SetString(PyExc_ValueError,
+                            "k must be an integer less than or equal to n");
+        }
+        goto error;
+    }
+
+    factors = PyLong_AsLongLongAndOverflow(k, &overflow);
+    if (overflow > 0) {
+        PyErr_Format(PyExc_OverflowError,
+                     "k must not exceed %lld",
+                     LLONG_MAX);
+        goto error;
+    }
+    else if (overflow < 0 || factors < 0) {
+        if (!PyErr_Occurred()) {
+            PyErr_SetString(PyExc_ValueError,
+                            "k must be a non-negative integer");
+        }
+        goto error;
+    }
+
+    if (factors == 0) {
+        result = PyLong_FromLong(1);
+        goto done;
+    }
+
+    result = n;
+    Py_INCREF(result);
+    if (factors == 1) {
+        goto done;
+    }
+
+    factor = n;
+    Py_INCREF(factor);
+    for (i = 1; i < factors; ++i) {
+        Py_SETREF(factor, PyNumber_Subtract(factor, _PyLong_One));
+        if (factor == NULL) {
+            goto error;
+        }
+        Py_SETREF(result, PyNumber_Multiply(result, factor));
+        if (result == NULL) {
+            goto error;
+        }
+    }
+    Py_DECREF(factor);
+
+done:
+    Py_DECREF(n);
+    Py_DECREF(k);
+    return result;
+
+error:
+    Py_XDECREF(factor);
+    Py_XDECREF(result);
+    Py_DECREF(n);
+    Py_DECREF(k);
+    return NULL;
+}
+
+
 /*[clinic input]
 math.comb
 
@@ -3028,11 +3142,24 @@ math_comb_impl(PyObject *module, PyObject *n, PyObject *k)
     if (n == NULL) {
         return NULL;
     }
+    if (!PyLong_CheckExact(n)) {
+        Py_SETREF(n, _PyLong_Copy((PyLongObject *)n));
+        if (n == NULL) {
+            return NULL;
+        }
+    }
     k = PyNumber_Index(k);
     if (k == NULL) {
         Py_DECREF(n);
         return NULL;
     }
+    if (!PyLong_CheckExact(k)) {
+        Py_SETREF(k, _PyLong_Copy((PyLongObject *)k));
+        if (k == NULL) {
+            Py_DECREF(n);
+            return NULL;
+        }
+    }
 
     if (Py_SIZE(n) < 0) {
         PyErr_SetString(PyExc_ValueError,
@@ -3050,7 +3177,7 @@ math_comb_impl(PyObject *module, PyObject *n, PyObject *k)
                         "k must be an integer less than or equal to n");
         goto error;
     }
-    cmp = PyObject_RichCompareBool(k, temp, Py_GT);
+    cmp = PyObject_RichCompareBool(temp, k, Py_LT);
     if (cmp > 0) {
         Py_SETREF(k, temp);
     }
@@ -3174,6 +3301,7 @@ static PyMethodDef math_methods[] = {
     {"tanh",            math_tanh,      METH_O,         math_tanh_doc},
     MATH_TRUNC_METHODDEF
     MATH_PROD_METHODDEF
+    MATH_PERM_METHODDEF
     MATH_COMB_METHODDEF
     {NULL,              NULL}           /* sentinel */
 };