bpo-46218: Change long_pow() to sliding window algorithm #30319
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For large exponents in long_pow(), use the sliding window algorithm instead. Also boost the window size from 5 bits to 6, which should yield a modest but significant speedup for long exponents. The precomputed table remains the same size, though, because the sliding window algorithm only stores results for odd exponents. long_pow() no longer requires that the number of bits in a CPython long digit be a multiple of 5. It no longer cares at all what the digit width is.
rhettinger
reviewed
Jan 1, 2022
sweeneyde
reviewed
Jan 1, 2022
Good catch! The code is clearer the new way too.
trailing zero logic entirely into ABSORB_PENDING. These native int bit manipulations are dirt cheap in comparison to the bigint squaring needed for each exponent bit. And boost the size of exponents tested to (probabilistically) stress a greater mix of exponent bit patterns.
a million straight 1 bits, the timing difference seems insignicant. So I think it better to cut the table size in half, to cut the precomputation overhead time in half for "saner" (smaller exponent) cases.
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Note that I cut the window size back to 5 bits. Short explanation on the bpo report (nothing to do with the number of bits in a "digit"). |
Since the dynamic table of small powers needed is half the size now, the overhead of trying to use the k-ary method has been cut accordingly, which allows it to pay off at smaller exponent bit lengths.
sweeneyde
reviewed
Jan 2, 2022
arhadthedev
reviewed
Jan 2, 2022
Use shortcut initializer for the k-ary table. Co-authored-by: Oleg Iarygin <dralife@yandex.ru>
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For large exponents in long_pow(), use the sliding window algorithm instead.
Also boost the window size from 5 bits to 6, which should yield a modest but significant speedup for long exponents. The precomputed table remains the same size, though, because the sliding window algorithm only stores results for odd exponents.
long_pow() no longer requires that the number of bits in a CPython long digit be a multiple of 5. It no longer cares at all what the digit width is.
https://bugs.python.org/issue46218