From nisse at lysator.liu.se  Wed Feb  8 19:57:26 2023
From: nisse at lysator.liu.se (Niels Möller)
Date: Wed, 08 Feb 2023 19:57:26 +0100
Subject: Paper with an improved bound for half-gcd matrix sizes
Message-ID: <cpf1qn0kmsp.fsf@shipon.lysator.liu.se>

Hi,

Juraj Sukop and myself just published a short paper with an improved
bound (+ one correction) to my older gcd paper which describes the
algorithm used in GMP.

See https://hal.science/hal-03976898

>From my perspective, it's a stronger and more rigorous argument, related
to this comment at
https://gmplib.org/repo/gmp/file/tip/mpn/generic/hgcd.c#l143,

  /* Furthermore, assume M ends with a quotient (1, q; 0, 1),
     then either q or q + 1 is a correct quotient, and M1 will
     start with either (1, 0; 1, 1) or (2, 1; 1, 1). This
     rules out the case that the size of M * M1 is much
     smaller than the expected M->n + M1->n. */

and it clarifies some of the subtler details.

Thanks to Paul for helping out in getting the paper published, and
suggesting publishing on HAL.

Regards,
/Niels

-- 
Niels M?ller. PGP key CB4962D070D77D7FCB8BA36271D8F1FF368C6677.
Internet email is subject to wholesale government surveillance.