bpo-35431: Add math.perm().

Doc/library/math.rst

@@ -36,6 +36,21 @@ Number-theoretic and representation functions
    :class:`~numbers.Integral` value.
 
 
+.. function:: comb(n, k)
+
+   Return the number of ways to choose *k* items from *n* items without repetition
+   and without order.
+
+   Also called the binomial coefficient. It is mathematically equal to the expression
+   ``n! / (k! (n - k)!)``. It is equivalent to the coefficient of the *k*-th term in the
+   polynomial expansion of the expression ``(1 + x) ** n``.
+
+   Raises :exc:`TypeError` if the arguments not integers.
+   Raises :exc:`ValueError` if the arguments are negative or if *k* > *n*.
+
+   .. versionadded:: 3.8
+
+
 .. function:: copysign(x, y)
 
    Return a float with the magnitude (absolute value) of *x* but the sign of
@@ -192,6 +207,18 @@ 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.
+
+   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*.
@@ -232,21 +259,6 @@ Number-theoretic and representation functions
    :meth:`x.__trunc__() <object.__trunc__>`.
 
 
-.. function:: comb(n, k)
-
-   Return the number of ways to choose *k* items from *n* items without repetition
-   and without order.
-
-   Also called the binomial coefficient. It is mathematically equal to the expression
-   ``n! / (k! (n - k)!)``. It is equivalent to the coefficient of the *k*-th term in the
-   polynomial expansion of the expression ``(1 + x) ** n``.
-
-   Raises :exc:`TypeError` if the arguments not integers.
-   Raises :exc:`ValueError` if the arguments are negative or if *k* > *n*.
-
-   .. versionadded:: 3.8
-
-
 Note that :func:`frexp` and :func:`modf` have a different call/return pattern
 than their C equivalents: they take a single argument and return a pair of
 values, rather than returning their second return value through an 'output

Lib/test/test_math.py

@@ -1862,6 +1862,61 @@ def test_fractions(self):
         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(MyIndexable(5), MyIndexable(2)), 20)
+        self.assertIs(type(perm(MyIndexable(5), MyIndexable(2))), int)
+
     def testComb(self):
         comb = math.comb
         factorial = math.factorial

Misc/NEWS.d/next/Library/2019-06-01-22-54-03.bpo-35431.oGXBWN.rst

@@ -0,0 +1 @@
+Added :func:`math.perm`.

Modules/mathmodule.c

@@ -2998,27 +2998,8 @@ math_prod_impl(PyObject *module, PyObject *iterable, PyObject *start)
 }
 
 
-/*[clinic input]
-math.comb
-
-    n: object
-    k: object
-    /
-
-Number of ways to choose k items from n items without repetition and without order.
-
-Also called the binomial coefficient. It is mathematically equal to the expression
-n! / (k! * (n - k)!). It is equivalent to the coefficient of k-th term in
-polynomial expansion of the expression (1 + x)**n.
-
-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_comb_impl(PyObject *module, PyObject *n, PyObject *k)
-/*[clinic end generated code: output=bd2cec8d854f3493 input=2f336ac9ec8242f9]*/
+perm_comb(PyObject *n, PyObject *k, int comb)
 {
     PyObject *result = NULL, *factor = NULL, *temp;
     int overflow, cmp;
@@ -3028,43 +3009,69 @@ 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,
                         "n must be a non-negative integer");
         goto error;
     }
-    /* k = min(k, n - k) */
-    temp = PyNumber_Subtract(n, k);
-    if (temp == NULL) {
-        goto error;
-    }
-    if (Py_SIZE(temp) < 0) {
-        Py_DECREF(temp);
-        PyErr_SetString(PyExc_ValueError,
-                        "k must be an integer less than or equal to n");
-        goto error;
-    }
-    cmp = PyObject_RichCompareBool(k, temp, Py_GT);
-    if (cmp > 0) {
-        Py_SETREF(k, temp);
+    if (comb) {
+        /* k = min(k, n - k) */
+        temp = PyNumber_Subtract(n, k);
+        if (temp == NULL) {
+            goto error;
+        }
+        if (Py_SIZE(temp) < 0) {
+            Py_DECREF(temp);
+            PyErr_SetString(PyExc_ValueError,
+                            "k must be an integer less than or equal to n");
+            goto error;
+        }
+        cmp = PyObject_RichCompareBool(temp, k, Py_LT);
+        if (cmp > 0) {
+            Py_SETREF(k, temp);
+        }
+        else {
+            Py_DECREF(temp);
+            if (cmp < 0) {
+                goto error;
+            }
+        }
     }
     else {
-        Py_DECREF(temp);
-        if (cmp < 0) {
+        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,
-                     "min(n - k, k) must not exceed %lld",
+                     "%s must not exceed %lld",
+                     comb ? "min(n - k, k)" : "k",
                      LLONG_MAX);
         goto error;
     }
@@ -3099,14 +3106,16 @@ math_comb_impl(PyObject *module, PyObject *n, PyObject *k)
             goto error;
         }
 
-        temp = PyLong_FromUnsignedLongLong((unsigned long long)i + 1);
-        if (temp == NULL) {
-            goto error;
-        }
-        Py_SETREF(result, PyNumber_FloorDivide(result, temp));
-        Py_DECREF(temp);
-        if (result == NULL) {
-            goto error;
+        if (comb) {
+            temp = PyLong_FromUnsignedLongLong((unsigned long long)i + 1);
+            if (temp == NULL) {
+                goto error;
+            }
+            Py_SETREF(result, PyNumber_FloorDivide(result, temp));
+            Py_DECREF(temp);
+            if (result == NULL) {
+                goto error;
+            }
         }
     }
     Py_DECREF(factor);
@@ -3125,6 +3134,55 @@ math_comb_impl(PyObject *module, PyObject *n, PyObject *k)
 }
 
 
+/*[clinic input]
+math.perm
+
+    n: object
+    k: object
+    /
+
+Number of ways to choose k items from n items without repetition.
+
+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=bad86be85158ebfd]*/
+{
+    return perm_comb(n, k, 0);
+}
+
+
+/*[clinic input]
+math.comb
+
+    n: object
+    k: object
+    /
+
+Number of ways to choose k items from n items without repetition and without order.
+
+Also called the binomial coefficient. It is mathematically equal to the expression
+n! / (k! * (n - k)!). It is equivalent to the coefficient of k-th term in
+polynomial expansion of the expression (1 + x)**n.
+
+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_comb_impl(PyObject *module, PyObject *n, PyObject *k)
+/*[clinic end generated code: output=bd2cec8d854f3493 input=2f336ac9ec8242f9]*/
+{
+    return perm_comb(n, k, 1);
+}
+
+
 static PyMethodDef math_methods[] = {
     {"acos",            math_acos,      METH_O,         math_acos_doc},
     {"acosh",           math_acosh,     METH_O,         math_acosh_doc},
@@ -3174,6 +3232,7 @@ 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 */
 };