[oxxoxoxooo]

Hi fish,

thanks for very interesting article, again!

Do you think the very fast division on M1 has any implications for 128/64 narrowing division as well? Do you know of a faster way than the method by Moller and Granlund? Do you plan on to include 128/64 division in libdivide?

And I asked this question before but the parent post got flagged so I'm trying once more: at the very bottom of the Labor of Division (Episode V) post [1], is it really possible for the second `qhat` (i.e. `q0`) to be off by 2? Do you have any examples of that?

[1] https://ridiculousfish.com/blog/posts/labor-of-division-epis...

[ridiculous_fish]

I haven't yet read the Moller and Granlund paper, but its narrowing division using precomputed reciprocal would be a natural fit for libdivide. (libdivide does have a narrowing divide, but it is Algorithm D based).

Regarding the second question, it is possible to be off by 2. Consider (base 10) 500 ÷ 59. The estimated quotient qhat is 50 ÷ 5 = 10, but the true digit is 8. So if our partial remainder is 50, we'll be off by 2 in the second digit.

[stephencanon]

> is it really possible for the second `qhat` (i.e. `q0`) to be off by 2?

Yes. I don't have an example in front of me, though. I think there may be one in Knuth vol 2. I'll take a look after toddler bedtime is over =)