marco.bodr...@tutanota.com writes: > s==0 is not a special case, it's one of the cases with smaller |s|.
Right, s == 0 is not a special case in itself, what's special is the case g = a = b, then we have too candidate cofactor pairs, s=1, t=0, s'=0, t'= 1. And we have the asymmetric preference for the first. > What about; > > /* Arrange so that |s| < |u| / 2g */ > mpz_add (s1, s0, s1); > { > int cmp = mpz_cmpabs (s0, s1); > if (cmp >= 0) > { > mpz_swap (s0, s1); > mpz_sub (t1, t0, t1); > if (cmp != 0 || mpz_cmpabs (t0, t1) > 0) > mpz_swap (t0, t1); > } > } I think swapping of s and t must go together? I've tried out this similar variant mpz_add (s1, s0, s1); mpz_sub (t1, t0, t1); cmp = mpz_cmpabs (s0, s1); if (cmp > 0 || (cmp == 0 && mpz_cmpabs (t0, t1) > 0)) { mpz_swap (s0, s1); mpz_swap (t0, t1); } Seems to work fine, and it's a rather clear way to express the "lexical" preference that we want the cofactor pair with the smallest of |s|, |s'|, but in case of a tie, we choose the pair with smallest |t|, |t'|. Updated version of the patch appended below. Regrads, /Niels diff -r 1c566525476a mini-gmp/mini-gmp.c --- a/mini-gmp/mini-gmp.c Wed Dec 27 19:35:36 2023 +0100 +++ b/mini-gmp/mini-gmp.c Sun Feb 18 10:02:56 2024 +0100 @@ -2809,6 +2809,7 @@ mpz_t tu, tv, s0, s1, t0, t1; mp_bitcnt_t uz, vz, gz; mp_bitcnt_t power; + int cmp; if (u->_mp_size == 0) { @@ -2960,12 +2961,21 @@ mpz_tdiv_q_2exp (t0, t0, 1); } - /* Arrange so that |s| < |u| / 2g */ + /* Choose small cofactors (they should satify + + |s| < |u| / 2g and |t| < |v| / 2g, + + except for documented exceptions). Always choose the smallest s, + if there are two choices for s with same absolute value, choose + the one with smallest corresponding t (this asymmetryic condition + is needed to prefer s = 0, |t| = 1 when g = |a| = |b|). */ mpz_add (s1, s0, s1); - if (mpz_cmpabs (s0, s1) > 0) + mpz_sub (t1, t0, t1); + cmp = mpz_cmpabs (s0, s1); + if (cmp > 0 || (cmp == 0 && mpz_cmpabs (t0, t1) > 0)) { mpz_swap (s0, s1); - mpz_sub (t0, t0, t1); + mpz_swap (t0, t1); } if (u->_mp_size < 0) mpz_neg (s0, s0); diff -r 1c566525476a mini-gmp/tests/t-gcd.c --- a/mini-gmp/tests/t-gcd.c Wed Dec 27 19:35:36 2023 +0100 +++ b/mini-gmp/tests/t-gcd.c Sun Feb 18 10:02:56 2024 +0100 @@ -55,6 +55,10 @@ if (mpz_sgn (g) <= 0) return 0; + /* Require that s==0 iff g==abs(b) */ + if (!mpz_sgn (s) != !mpz_cmpabs (g, b)) + goto fail; + mpz_init (ta); mpz_init (tb); mpz_init (r); @@ -79,20 +83,20 @@ if (mpz_sgn (r) != 0) goto fail; - /* Require that 2 |s| < |b/g|, or |s| == 1. */ - if (mpz_cmpabs_ui (s, 1) > 0) + /* Require that 2 |s| < |b/g|, or s == sgn(a) */ + if (mpz_cmp_si (s, mpz_sgn (a)) != 0) { mpz_mul_2exp (r, s, 1); - if (mpz_cmpabs (r, tb) > 0) + if (mpz_cmpabs (r, tb) >= 0) goto fail; } - /* Require that 2 |t| < |a/g| or |t| == 1*/ - if (mpz_cmpabs_ui (t, 1) > 0) + /* Require that 2 |t| < |a/g| or t == sgn(b) */ + if (mpz_cmp_si (t, mpz_sgn (b)) != 0) { mpz_mul_2exp (r, t, 1); - if (mpz_cmpabs (r, ta) > 0) - return 0; + if (mpz_cmpabs (r, ta) >= 0) + goto fail; } mpz_clear (ta); @@ -102,17 +106,53 @@ return 1; } +static void test_one(const mpz_t a, const mpz_t b) +{ + mpz_t g, s, t; + + mpz_init (g); + mpz_init (s); + mpz_init (t); + + mpz_gcdext (g, s, t, a, b); + if (!gcdext_valid_p (a, b, g, s, t)) + { + fprintf (stderr, "mpz_gcdext failed:\n"); + dump ("a", a); + dump ("b", b); + dump ("g", g); + dump ("s", s); + dump ("t", t); + abort (); + } + + mpz_gcd (s, a, b); + if (mpz_cmp (g, s)) + { + fprintf (stderr, "mpz_gcd failed:\n"); + dump ("a", a); + dump ("b", b); + dump ("r", g); + dump ("ref", s); + abort (); + } + + mpz_clear (g); + mpz_clear (s); + mpz_clear (t); +} + void testmain (int argc, char **argv) { unsigned i; - mpz_t a, b, g, s, t; + mpz_t a, b, g, s; + int ai, bi; mpz_init (a); mpz_init (b); mpz_init (g); mpz_init (s); - mpz_init (t); for (i = 0; i < COUNT; i++) { @@ -129,6 +169,15 @@ } } + /* Exhaustive test of small inputs */ + for (ai = -30; ai <= 30; ai++) + for (bi = -30; bi <= 30; bi++) + { + mpz_set_si (a, ai); + mpz_set_si (b, bi); + test_one (a, b); + } + for (i = 0; i < COUNT; i++) { unsigned flags; @@ -147,32 +196,11 @@ if (flags & 2) mpz_neg (b, b); - mpz_gcdext (g, s, t, a, b); - if (!gcdext_valid_p (a, b, g, s, t)) - { - fprintf (stderr, "mpz_gcdext failed:\n"); - dump ("a", a); - dump ("b", b); - dump ("g", g); - dump ("s", s); - dump ("t", t); - abort (); - } + test_one (a, b); + } - mpz_gcd (s, a, b); - if (mpz_cmp (g, s)) - { - fprintf (stderr, "mpz_gcd failed:\n"); - dump ("a", a); - dump ("b", b); - dump ("r", g); - dump ("ref", s); - abort (); - } - } mpz_clear (a); mpz_clear (b); mpz_clear (g); mpz_clear (s); - mpz_clear (t); } diff -r 1c566525476a tests/mpz/t-gcd.c --- a/tests/mpz/t-gcd.c Wed Dec 27 19:35:36 2023 +0100 +++ b/tests/mpz/t-gcd.c Sun Feb 18 10:02:56 2024 +0100 @@ -432,6 +432,10 @@ if (mpz_sgn (g) <= 0) return 0; + /* Require that s==0 iff g==abs(b) */ + if (!mpz_sgn (s) != !mpz_cmpabs (g, b)) + return 0; + mpz_tdiv_qr (temp1, temp3, a, g); if (mpz_sgn (temp3) != 0) return 0; @@ -440,8 +444,8 @@ if (mpz_sgn (temp3) != 0) return 0; - /* Require that 2 |s| < |b/g|, or |s| == 1. */ - if (mpz_cmpabs_ui (s, 1) > 0) + /* Require that 2 |s| < |b/g|, or s == sgn(a) */ + if (mpz_cmp_si (s, mpz_sgn (a)) != 0) { mpz_mul_2exp (temp3, s, 1); if (mpz_cmpabs (temp3, temp2) >= 0) @@ -456,8 +460,8 @@ if (mpz_sgn (temp3) != 0) return 0; - /* Require that 2 |t| < |a/g| or |t| == 1*/ - if (mpz_cmpabs_ui (temp2, 1) > 0) + /* Require that 2 |t| < |a/g| or t == sgn(b) */ + if (mpz_cmp_si (temp2, mpz_sgn (b)) != 0) { mpz_mul_2exp (temp2, temp2, 1); if (mpz_cmpabs (temp2, temp1) >= 0) -- Niels Möller. PGP key CB4962D070D77D7FCB8BA36271D8F1FF368C6677. Internet email is subject to wholesale government surveillance. _______________________________________________ gmp-bugs mailing list gmp-bugs@gmplib.org https://gmplib.org/mailman/listinfo/gmp-bugs