math/big: replace the division with multiplicative inverse

[SparrowLii]

Division is much slower than multiplication, as we know. The algorithm for dividing 128 digits by 64 digits in math/bits.go/Div64, which has a certain impact on the efficiency of nats division, requires two divisions. And the method of using multiplication by 2/1 (128bits divide 64bits )multiplicative inverse and replacing division with it can increase the speed of divWVW algorithm by three times, and at the same time increase the speed of nats division.

I have submitted a code change using 2/1 type multiplicative inverse and the corresponding benchmark data in gerrit. If possible, using a 3/2(192bits divide 128bits) type multiplicative inverse and changing the structure of nats division code will get a more obvious improvement.

[gopherbot]

Change https://golang.org/cl/250417 mentions this issue: math/big: treble the speed of divWVW and optimize the div of nats by replacing the division with multiplicative inverse

[randall77]

This issue doesn't need to be a proposal. It's just an optimization - go for it.
That said, it looks like your CL is adding API to math/bits (GetInvert and DivByInv). That change would require a proposal.
Is there any way to do your change without adding API?

[SparrowLii]

This issue doesn't need to be a proposal. It's just an optimization - go for it.
That said, it looks like your CL is adding API to math/bits (GetInvert and DivByInv). That change would require a proposal.
Is there any way to do your change without adding API?

Yes there is. I added the API because I am not sure if I should completely replace the original division method. If we want to think of it as an optimization, we can use a more sophisticated method without adding an API. I will make the corresponding changes in my CL.

[SparrowLii]

@randall77 Im sry that I don't know how to remove the proposal tag. I replaced the original division function, deleted the modification to the bits package and changed getInvert to internal interface so that there's no new API in bits package.