math/big: avoid DIVQ

[griesemer]

Suggested by Torbjörn Granlund (personal communication):

"
Division:

The DIVQ instruction is terrible. Don't ever use it. You might
want to take a look at "Improved Division by Invariant Integers" by
me and a collegue of mine. Your loop will become about 10 times
faster. You need to apply this also to generic division (not just the
one-divisor-word case.
"

(paper reference: https://gmplib.org/~tege/division-paper.pdf)

[rsc]

The Go compiler already does this. If you want to know the sequence, write
a program with a constant divide and use go tool 6g -S.

[ianlancetaylor]

I think the suggestion here is to do it when dividing in a loop by an invariant value that is only known at run time.

[griesemer]

Ok, good to know. Note that Torbjörn's paper suggests that even for a non-constant divisor, division via mutiplication by inverse is faster:

"Somewhat surprisingly, a well-tuned Newton reciprocal followed by multiplication and adjustments wins over the hardware division instructions even for a single non-invariant division on modern 64-bit PC processors."

[andig]

This has been implemented in https://golang.org/cl/250417