ni...@lysator.liu.se (Niels Möller) writes:
Torbjorn Granlund <t...@gmplib.org> writes:
> The quotient might need one more bit using this alternative convention.
> Right? We have no great place to return it.
I'd suggest the convention that
Q = -N D^{-1} (mod B^{nn - dn})
R B^{qn} = N + Q D
Then Q is qn = nn - dn limbs, no extra bit, and
0 <= R < B^dn + D
This is the same as for the current redc functions. But I'm leaning
towards putting the returned R at the high end rather than the low, and
with the loop organization you suggest it should then work fine to put Q
at the low end.
Could you perhaps write a new proposed sbpi1_bdiv_qr with the result
normalisation you suggest, using my proposed sbpi1_bdiv_r style? That
would allow for a single outer loop, unlike the current sbpi1_bdiv_qr.
Maybe we don't even need bdiv_r then, if
bdiv_qr (up, up, un, dp, dn)
is cheap enough (storing the q limbs at the low end of U).
That would be nice. But cutting even a few constant cycles off redc is
worth it, so "cheap enough" should be taken in a very strict sense...
Ah, and notation. I suggest we write U for the numerator, rather than N,
like we have been doing in some other division work. To avoid confusion
with n used as a limb count (worse when talking than when writing).
OK, I started with the header of sbpi1_bdiv_qr and got these variable
names. (There is a disadvantage with up since up can be confused with
the english word up in comments; up can thereby mess thing up. :-)
--
Torbjörn
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