gh-102221: Optimize math.integer.lcm() for multiple arguments (non-recursive)

[serhiy-storchaka]

This version uses manually supported stack instead of the C stack. It has less C stack consumption for very large number of arguments. But for not such large number of arguments (thousands or millions) it may actually have larger C stack consumption.

• Issue: Optimize math.lcm(*xs) #102221

[skirpichev]

very large number of arguments

How common it is? Where the cutoff when this version will payoff us it's complexity over #135554?

[serhiy-storchaka]

I did not measure it. But estimation for #135554 on abstract machine is 6 words/level (return address, two parameters and three local variables), so this is 6 and 11 on 32- and 64-bit platforms. Or 64 and 2048 arguments correspondingly. It may be less if recursion needs more than just a return address or larger if the compiler is extra clever in reusing stack variable.

The maximal stack consumption of this version is 8*64=512 bytes for the stack variable, plus up to 64 byte for other variables/parameters (but registers can be used for many of them). In #135554 it can be about 3KB in worst case.

[github-actions]

This PR is stale because it has been open for 30 days with no activity.