[New-bugs-announce] [issue18005] faster modular exponentiation in some cases

[Pernici Mario]

New submission from Pernici Mario:

A trivial optimization can be made in ``pow(a, b, c)``
if ``b`` is even and ``c - a < a``

```
In [1]: c = (1 << 1000000) + 1 

In [2]: a = c - 1234567

In [3]: b = 2

In [4]: %timeit pow(a, b, c)
1 loops, best of 3: 3.03 s per loop

In [5]: %timeit pow(c - a if c - a < (a >> 10) else a, b, c)
1000 loops, best of 3: 287 us per loop
```

This optimization is probably done in GMP, since using gmpy.mpz
[5] is a bit slower than [4].

----------
messages: 189504
nosy: pernici
priority: normal
severity: normal
status: open
title: faster modular exponentiation in some cases
type: performance
versions: Python 2.7

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Python tracker <report at bugs.python.org>
<http://bugs.python.org/issue18005>
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