bdiv vs redc

[Niels Möller]

Torbjorn Granlund <tg at 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.

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).

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).

Regards,
/Niels

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