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calculatePerm multiplied the k factors one at a time into a growing product, so each step was a big-by-small multiplication and the whole loop was quadratic in the result size. math.perm(615913, 286885) took about 28 s on a JVM build against about 1 s on CPython. Splitting the range in halves keeps the operands of each multiplication balanced, so BigInteger can use its faster algorithms; the same call now takes 0.3 s. Signed-off-by: Jeongseop Lim <jeongseop_lim@korea.ac.kr>
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Description
Fixes #1254
math.perm(n, k)multiplied the running product by one factor at a time, so its cost grew with the square of the result size andBigInteger.multiplynever got two large operands. CPython splits the product asP(n, k) = P(n, j) * P(n - j, k - j)withj = k / 2(mathmodule.c#L3634-L3649), so the large multiplications are between operands of similar size.AS-IS
TO-BE
Timings for
math.perm(615913, 286885)on macOS arm64:mx python-jvm(interpreted JVM)mx python-jvm(interpreted JVM)Changes
P(n, k)inPermNodeby recursive halving instead of the sequential loop.test_perm_matches_productin a newtests/test_math_perm.py.Testing
mx python-jvmon darwin-aarch64, then--tagged test_math(79 passed, same as master). The new test passes before and after the change; it checks values, not time.math.perm(n, k)equalsfactorial(n) // factorial(n - k)for everyn < 60and everyk.