http://www.perlmonks.org?node_id=482795


in reply to Re^4: Algorithm for cancelling common factors between two lists of multiplicands
in thread Algorithm for cancelling common factors between two lists of multiplicands

Here's a benchmark for Math::Big::Factors wheels of orders 5-7:
Rate 7 6 5 7 34.1/s -- -95% -100% 6 627/s 1739% -- -94% 5 9770/s 28548% 1458% --
and for factors_wheel of numbers near 32 bits, using an order 7 wheel:
s/iter 4294967291 4294967293 4294967295 4294967291 4.45 -- -61% -71% 4294967293 1.74 156% -- -25% 4294967295 1.31 241% 33% --
Note that 4294967291 is prime, 4294967293 has 2 large factors, and 4294967295 has 5 factors, the largest of which is 2**16+1.

For 4294967291, and wheel orders 5-7:

s/iter 7 5 6 7 4.44 -- -16% -21% 5 3.71 19% -- -6% 6 3.49 27% 6% --
In all fairness, I should probably mention that I've customized my own version of Math::Big::Factors to Memoize results where possible, and to reduce the calls to Math::BigInt::new() for constants.

Note that factors_wheel creates a new wheel every time (what a shame), instead of requiring a wheel reference be passed in. Caching wheel goes a little way in correcting this, without changing the interface.

You might also consider avoiding the use of Math::BigInt where possible, as you don't need numbers that big.

Now, back to the question at hand. For numbers near 2**32, factoring a prime number seems to take 150 times longer than creating the order 7 wheel. Creating the order 6 wheel is considerably faster, and so is the factoring based on that wheel.

I'm not sure where the breakpoint is for order 7 wheels. A casual search hints that it is very large.

-QM
--
Quantum Mechanics: The dreams stuff is made of