Instead of using eta=-delta, use zeta=-(delta+1/2) to represent
delta. This variant only needs at most 590 iterations for 256-bit
inputs rather than 724 (by convex hull bounds analysis).
The magnitude of the f and g variables generally goes down as the algorithm
progresses. Make use of this by keeping tracking how many limbs are used, and
when the number becomes small enough, make use of this to reduce the complexity
of arithmetic on them.
Refactored by: Pieter Wuille <pieter@wuille.net>
Both the field and scalar modulus can be written in signed{30,62} notation
with one or more zero limbs. Make use of this in the update_de function to
avoid a few wide multiplications when that is the case.
This doesn't appear to be a win in the 32-bit implementation, so only
do it for the 64-bit one.
This commit adds functions to verify and compare numbers in signed{30,62} notation,
and uses that to do more extensive bounds checking on various variables in the modinv
code.
This adds a long comment explaining the algorithm and implementation choices by building
it up step by step in Python.
Comments in the code are also reworked/added, with references to the long explanation.
