bpo-35431: Implemented math.comb (GH-11414)

2 files changed, 171 insertions, 1 deletions

diff --git a/Modules/clinic/mathmodule.c.h b/Modules/clinic/mathmodule.c.h
index e677bd896c..cba791e209 100644
--- a/Modules/clinic/mathmodule.c.h
+++ b/Modules/clinic/mathmodule.c.h
@@ -637,4 +637,53 @@ skip_optional_kwonly:
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=aeed62f403b90199 input=a9049054013a1b77]*/
+
+PyDoc_STRVAR(math_comb__doc__,
+"comb($module, /, n, k)\n"
+"--\n"
+"\n"
+"Number of ways to choose *k* items from *n* items without repetition and without order.\n"
+"\n"
+"Also called the binomial coefficient. It is mathematically equal to the expression\n"
+"n! / (k! * (n - k)!). It is equivalent to the coefficient of k-th term in\n"
+"polynomial expansion of the expression (1 + x)**n.\n"
+"\n"
+"Raises TypeError if the arguments are not integers.\n"
+"Raises ValueError if the arguments are negative or if k > n.");
+
+#define MATH_COMB_METHODDEF    \
+    {"comb", (PyCFunction)(void(*)(void))math_comb, METH_FASTCALL|METH_KEYWORDS, math_comb__doc__},
+
+static PyObject *
+math_comb_impl(PyObject *module, PyObject *n, PyObject *k);
+
+static PyObject *
+math_comb(PyObject *module, PyObject *const *args, Py_ssize_t nargs, PyObject *kwnames)
+{
+    PyObject *return_value = NULL;
+    static const char * const _keywords[] = {"n", "k", NULL};
+    static _PyArg_Parser _parser = {NULL, _keywords, "comb", 0};
+    PyObject *argsbuf[2];
+    PyObject *n;
+    PyObject *k;
+
+    args = _PyArg_UnpackKeywords(args, nargs, NULL, kwnames, &_parser, 2, 2, 0, argsbuf);
+    if (!args) {
+        goto exit;
+    }
+    if (!PyLong_Check(args[0])) {
+        _PyArg_BadArgument("comb", 1, "int", args[0]);
+        goto exit;
+    }
+    n = args[0];
+    if (!PyLong_Check(args[1])) {
+        _PyArg_BadArgument("comb", 2, "int", args[1]);
+        goto exit;
+    }
+    k = args[1];
+    return_value = math_comb_impl(module, n, k);
+
+exit:
+    return return_value;
+}
+/*[clinic end generated code: output=00aa76356759617a input=a9049054013a1b77]*/
diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index a153e984ca..007a880142 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2998,6 +2998,126 @@ math_prod_impl(PyObject *module, PyObject *iterable, PyObject *start)
 }
 
 
+/*[clinic input]
+math.comb
+
+    n: object(subclass_of='&PyLong_Type')
+    k: object(subclass_of='&PyLong_Type')
+
+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=565f340f98efb5b5]*/
+{
+    PyObject *val = NULL,
+        *temp_obj1 = NULL,
+        *temp_obj2 = NULL,
+        *dump_var = NULL;
+    int overflow, cmp;
+    long long i, terms;
+
+    cmp = PyObject_RichCompareBool(n, k, Py_LT);
+    if (cmp < 0) {
+        goto fail_comb;
+    }
+    else if (cmp > 0) {
+        PyErr_Format(PyExc_ValueError,
+                     "n must be an integer greater than or equal to k");
+        goto fail_comb;
+    }
+
+    /* b = min(b, a - b) */
+    dump_var = PyNumber_Subtract(n, k);
+    if (dump_var == NULL) {
+        goto fail_comb;
+    }
+    cmp = PyObject_RichCompareBool(k, dump_var, Py_GT);
+    if (cmp < 0) {
+        goto fail_comb;
+    }
+    else if (cmp > 0) {
+        k = dump_var;
+        dump_var = NULL;
+    }
+    else {
+        Py_DECREF(dump_var);
+        dump_var = NULL;
+    }
+
+    terms = PyLong_AsLongLongAndOverflow(k, &overflow);
+    if (terms < 0 && PyErr_Occurred()) {
+        goto fail_comb;
+    }
+    else if (overflow > 0) {
+        PyErr_Format(PyExc_OverflowError,
+                     "minimum(n - k, k) must not exceed %lld",
+                     LLONG_MAX);
+        goto fail_comb;
+    }
+    else if (overflow < 0 || terms < 0) {
+        PyErr_Format(PyExc_ValueError,
+                     "k must be a positive integer");
+        goto fail_comb;
+    }
+
+    if (terms == 0) {
+        return PyNumber_Long(_PyLong_One);
+    }
+
+    val = PyNumber_Long(n);
+    for (i = 1; i < terms; ++i) {
+        temp_obj1 = PyLong_FromSsize_t(i);
+        if (temp_obj1 == NULL) {
+            goto fail_comb;
+        }
+        temp_obj2 = PyNumber_Subtract(n, temp_obj1);
+        if (temp_obj2 == NULL) {
+            goto fail_comb;
+        }
+        dump_var = val;
+        val = PyNumber_Multiply(val, temp_obj2);
+        if (val == NULL) {
+            goto fail_comb;
+        }
+        Py_DECREF(dump_var);
+        dump_var = NULL;
+        Py_DECREF(temp_obj2);
+        temp_obj2 = PyLong_FromUnsignedLongLong((unsigned long long)(i + 1));
+        if (temp_obj2 == NULL) {
+            goto fail_comb;
+        }
+        dump_var = val;
+        val = PyNumber_FloorDivide(val, temp_obj2);
+        if (val == NULL) {
+            goto fail_comb;
+        }
+        Py_DECREF(dump_var);
+        Py_DECREF(temp_obj1);
+        Py_DECREF(temp_obj2);
+    }
+
+    return val;
+
+fail_comb:
+    Py_XDECREF(val);
+    Py_XDECREF(dump_var);
+    Py_XDECREF(temp_obj1);
+    Py_XDECREF(temp_obj2);
+
+    return NULL;
+}
+
+
 static PyMethodDef math_methods[] = {
     {"acos",            math_acos,      METH_O,         math_acos_doc},
     {"acosh",           math_acosh,     METH_O,         math_acosh_doc},
@@ -3047,6 +3167,7 @@ static PyMethodDef math_methods[] = {
     {"tanh",            math_tanh,      METH_O,         math_tanh_doc},
     MATH_TRUNC_METHODDEF
     MATH_PROD_METHODDEF
+    MATH_COMB_METHODDEF
     {NULL,              NULL}           /* sentinel */
 };