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cpython

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    Miss Islington (bot) authored
    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: default avatarGregory P. Smith [Google LLC] <greg@krypto.org>
    (cherry picked from commit b1261968)
    
    Co-authored-by: default avatarMark Dickinson <dickinsm@gmail.com>
    8a776d1d
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