[3.9] gh-95778: CVE-2020-10735: Prevent DoS by very large int() (#96502)

* Correctly pre-check for int-to-str conversion (#96537)

Converting a large enough `int` to a decimal string raises `ValueError` as expected. However, the raise comes _after_ the quadratic-time base-conversion algorithm has run to completion. For effective DOS prevention, we need some kind of check before entering the quadratic-time loop. Oops! =)

The quick fix: essentially we catch _most_ values that exceed the threshold up front. Those that slip through will still be on the small side (read: sufficiently fast), and will get caught by the existing check so that the limit remains exact.

The justification for the current check. The C code check is:
```c
max_str_digits / (3 * PyLong_SHIFT) <= (size_a - 11) / 10
```

In GitHub markdown math-speak, writing $M$ for `max_str_digits`, $L$ for `PyLong_SHIFT` and $s$ for `size_a`, that check is:
$$\left\lfloor\frac{M}{3L}\right\rfloor \le \left\lfloor\frac{s - 11}{10}\right\rfloor$$

From this it follows that
$$\frac{M}{3L} < \frac{s-1}{10}$$
hence that
$$\frac{L(s-1)}{M} > \frac{10}{3} > \log_2(10).$$
So
$$2^{L(s-1)} > 10^M.$$
But our input integer $a$ satisfies $|a| \ge 2^{L(s-1)}$, so $|a|$ is larger than $10^M$. This shows that we don't accidentally capture anything _below_ the intended limit in the check.

<!-- gh-issue-number: gh-95778 -->
* Issue: gh-95778
<!-- /gh-issue-number -->

Co-authored-by: Gregory P. Smith [Google LLC] <greg@krypto.org>
Co-authored-by: Christian Heimes <christian@python.org>
Co-authored-by: Mark Dickinson <dickinsm@gmail.com>

Python/clinic/sysmodule.c.h

@@ -667,6 +667,64 @@ exit:
 
 #endif /* defined(USE_MALLOPT) */
 
+PyDoc_STRVAR(sys_get_int_max_str_digits__doc__,
+"get_int_max_str_digits($module, /)\n"
+"--\n"
+"\n"
+"Set the maximum string digits limit for non-binary int<->str conversions.");
+
+#define SYS_GET_INT_MAX_STR_DIGITS_METHODDEF    \
+    {"get_int_max_str_digits", (PyCFunction)sys_get_int_max_str_digits, METH_NOARGS, sys_get_int_max_str_digits__doc__},
+
+static PyObject *
+sys_get_int_max_str_digits_impl(PyObject *module);
+
+static PyObject *
+sys_get_int_max_str_digits(PyObject *module, PyObject *Py_UNUSED(ignored))
+{
+    return sys_get_int_max_str_digits_impl(module);
+}
+
+PyDoc_STRVAR(sys_set_int_max_str_digits__doc__,
+"set_int_max_str_digits($module, /, maxdigits)\n"
+"--\n"
+"\n"
+"Set the maximum string digits limit for non-binary int<->str conversions.");
+
+#define SYS_SET_INT_MAX_STR_DIGITS_METHODDEF    \
+    {"set_int_max_str_digits", (PyCFunction)(void(*)(void))sys_set_int_max_str_digits, METH_FASTCALL|METH_KEYWORDS, sys_set_int_max_str_digits__doc__},
+
+static PyObject *
+sys_set_int_max_str_digits_impl(PyObject *module, int maxdigits);
+
+static PyObject *
+sys_set_int_max_str_digits(PyObject *module, PyObject *const *args, Py_ssize_t nargs, PyObject *kwnames)
+{
+    PyObject *return_value = NULL;
+    static const char * const _keywords[] = {"maxdigits", NULL};
+    static _PyArg_Parser _parser = {NULL, _keywords, "set_int_max_str_digits", 0};
+    PyObject *argsbuf[1];
+    int maxdigits;
+
+    args = _PyArg_UnpackKeywords(args, nargs, NULL, kwnames, &_parser, 1, 1, 0, argsbuf);
+    if (!args) {
+        goto exit;
+    }
+    if (PyFloat_Check(args[0])) {
+        PyErr_SetString(PyExc_TypeError,
+                        "integer argument expected, got float" );
+        goto exit;
+    }
+    maxdigits = _PyLong_AsInt(args[0]);
+    if (maxdigits == -1 && PyErr_Occurred()) {
+        goto exit;
+    }
+    return_value = sys_set_int_max_str_digits_impl(module, maxdigits);
+
+exit:
+    return return_value;
+}
+
 PyDoc_STRVAR(sys_getrefcount__doc__,
 "getrefcount($module, object, /)\n"
 "--\n"
@@ -970,4 +1028,4 @@ sys_getandroidapilevel(PyObject *module, PyObject *Py_UNUSED(ignored))
 #ifndef SYS_GETANDROIDAPILEVEL_METHODDEF
     #define SYS_GETANDROIDAPILEVEL_METHODDEF
 #endif /* !defined(SYS_GETANDROIDAPILEVEL_METHODDEF) */
-/*[clinic end generated code: output=39eb34a01fb9a919 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=401254a595859ac6 input=a9049054013a1b77]*/