Re: mini-gmp mpz_gcdext Bézout coefficients do not match documentation
I've confirmed with my fuzzer that the committed patch resolves the issues. Thanks. On Sun, Feb 18, 2024 at 8:27 PM Niels Möller wrote: > marco.bodr...@tutanota.com writes: > > > The only reason why I prefer my solution is: when cmp<0, there is no > need to compute > > mpz_sub (t1, t0, t1); > > That's certainly a micro optimization, but let's keep things simple. > > I've pushed this fix now, I think there were only comment and ChangeLog > changes since the previous version of the patch. > > Thanks for the review, > /Niels > > -- > 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
Re: mini-gmp mpz_gcdext Bézout coefficients do not match documentation
marco.bodr...@tutanota.com writes: > The only reason why I prefer my solution is: when cmp<0, there is no need to > compute > mpz_sub (t1, t0, t1); That's certainly a micro optimization, but let's keep things simple. I've pushed this fix now, I think there were only comment and ChangeLog changes since the previous version of the patch. Thanks for the review, /Niels -- 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
Re: mini-gmp mpz_gcdext Bézout coefficients do not match documentation
Ciao Niels,
18 feb 2024, 10:10 da ni...@lysator.liu.se:
> marco.bodr...@tutanota.com writes:
>
>> 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
>
You are right, it's better with the two swaps together.
> 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);
> }
>
The only reason why I prefer my solution is: when cmp<0, there is no need to
compute
mpz_sub (t1, 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'|.
>
I agree.
Ĝis,
m
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Re: mini-gmp mpz_gcdext Bézout coefficients do not match documentation
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.cWed Dec 27 19:35:36 2023 +0100
+++ b/mini-gmp/tests/t-gcd.cSun 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",
Re: mini-gmp mpz_gcdext Bézout coefficients do not match documentation
Ciao Niels,
17 feb 2024, 21:26 da ni...@lysator.liu.se:
> marco.bodr...@tutanota.com writes:
>
>> Maybe we should also add the test:
>>
>> /* Require that s==0 iff g==abs(b) */
>> if (!mpz_sgn (s) ^ !mpz_cmpabs (g, b))
>> goto fail;
>>
>
> Good point, that's better than only checking the special case |a| ==
> |b|. (But maybe more readable with != instead of ^).
>
Yes, with != it's more readable!
> To get mini-gmp to conform, I find no simpler way than special casing s
> == 0, like
>
s==0 is not a special case, it's one of the cases with smaller |s|.
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);
}
}
Ĝis,
m
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Re: mini-gmp mpz_gcdext Bézout coefficients do not match documentation
marco.bodr...@tutanota.com writes:
> Maybe we should also add the test:
>
> /* Require that s==0 iff g==abs(b) */
> if (!mpz_sgn (s) ^ !mpz_cmpabs (g, b))
> goto fail;
Good point, that's better than only checking the special case |a| ==
|b|. (But maybe more readable with != instead of ^).
To get mini-gmp to conform, I find no simpler way than special casing s
== 0, like
if (mpz_sgn (s0) != 0)
{
/* Arrange so that |s| < |u| / 2g and |t| < |v| / 2g, if possible. */
mpz_add (s1, s0, s1);
mpz_sub (t1, t0, t1);
if (mpz_cmpabs (s0, s1) > 0 || mpz_cmpabs (t0, t1) > 0)
{
mpz_swap (s0, s1);
mpz_swap (t0, t1);
}
}
And I think this is the only condition that isn't fully symmetrical, so
perhaps not surprising if it needs a special case.
Regards,
/Niels
--
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Internet email is subject to wholesale government surveillance.
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Re: mini-gmp mpz_gcdext Bézout coefficients do not match documentation
Ciao, 17 feb 2024, 19:15 da : > Ciao Niels, > > 17 feb 2024, 17:53 da ni...@lysator.liu.se: > >> Niels Möller writes: >> The documented conditions say that gmp should return the same cofactors >> > > The documentation also says "If abs(a) = abs(b), then s = 0, t = sgn(b)." > Maybe we should also add the test: /* Require that s==0 iff g==abs(b) */ if (!mpz_sgn (s) ^ !mpz_cmpabs (g, b)) goto fail; Ĝis, m ___ gmp-bugs mailing list gmp-bugs@gmplib.org https://gmplib.org/mailman/listinfo/gmp-bugs
Re: mini-gmp mpz_gcdext Bézout coefficients do not match documentation
marco.bodr...@tutanota.com writes: > And if I correctly patched and tested your proposed code. with equal numbers > I get t=0, instead of s=0. Thanks for testing, I have to look into that case, then. > Shat about simply changing the test from > to >= ? > > /* Arrange so that |s| < |u| / 2g */ > mpz_add (s1, s0, s1); > - if (mpz_cmpabs (s0, s1) > 0) > + if (mpz_cmpabs (s0, s1) >= 0) I don't think that's right. My understanding is that if |s| = |s'| (notation from my mail, the variables in the code are reassigned several times, which is a bit confusing), then we ncessarily have |t| != |t'|, and we must choose candidate to get the smaller one. Regards, /Niels -- 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
Re: mini-gmp mpz_gcdext Bézout coefficients do not match documentation
Ciao Niels,
17 feb 2024, 17:53 da ni...@lysator.liu.se:
> Niels Möller writes:
> The documented conditions say that gmp should return the same cofactors
>
The documentation also says "If abs(a) = abs(b), then s = 0, t = sgn(b)."
>
> canonicalization logic at the end wasn't right. Appending a patch with a
> fix + stricter tests.
>
And if I correctly patched and tested your proposed code. with equal numbers I
get t=0, instead of s=0.
> Without the fix, we could make the wrong choice in case
>
> |s'| = |s| = |b| / 2g
>
> Since it's a bit subtle, it would be nice with a review of this code
> before I commit it.
>
Shat about simply changing the test from > to >= ?
/* Arrange so that |s| < |u| / 2g */
mpz_add (s1, s0, s1);
- if (mpz_cmpabs (s0, s1) > 0)
+ if (mpz_cmpabs (s0, s1) >= 0)
{
mpz_swap (s0, s1);
mpz_sub (t0, t0, t1);
Ĝis,
m
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Re: mini-gmp mpz_gcdext Bézout coefficients do not match documentation
Niels Möller writes:
> Guido Vranken writes:
>
>> Computing extended gcd using mpz_gcdext where a = 1, b = 2:
>>
>> libgmp: g: 1, s: 1, t: 0
>> mini-gmp: g: 1, s: -1, t: 1
>> This violates the docs: "s = sgn(a) if abs(b) = 2", e.g. s must be 1
>>
>> Computing extended gcd using mpz_gcdext where a = 6, b = 4:
>> libgmp: g: 2, s: 1, t: -1
>> mini-libgmp: g: 2, s: -1, t: 2
>
> I think mini-gmp is wrong here, I'll have to investigate. Thanks for
> reporting.
The documented conditions say that gmp should return the same cofactors
as one would get naturally with Euclid's algorithm. It appears mini-gmp
uses binary gcdext (I had forgotten that detail), and the
canonicalization logic at the end wasn't right. Appending a patch with a
fix + stricter tests.
At this place in the algorithm, we have a, b >= 0, and we have a
candidate s, t, with
-b / g <= s <= 0, 0 <= t <= a / g
(not sure at which edges we might have equality), and then we construct
another candidate s', t' as
s' = s + b / g >= 0, t' = t - a / g <= 0
And we then return s', t' if either |s'| < |s| or |t'| < |t|.
Without the fix, we could make the wrong choice in case
|s'| = |s| = |b| / 2g
Since it's a bit subtle, it would be nice with a review of this code
before I commit it.
Regards,
/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 Sat Feb 17 17:17:21 2024 +0100
@@ -2960,12 +2960,13 @@
mpz_tdiv_q_2exp (t0, t0, 1);
}
- /* Arrange so that |s| < |u| / 2g */
+ /* Arrange so that |s| < |u| / 2g and |t| < |v| / 2g, if possible. */
mpz_add (s1, s0, s1);
- if (mpz_cmpabs (s0, s1) > 0)
+ mpz_sub (t1, t0, t1);
+ if (mpz_cmpabs (s0, s1) > 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.cWed Dec 27 19:35:36 2023 +0100
+++ b/mini-gmp/tests/t-gcd.cSat Feb 17 17:17:21 2024 +0100
@@ -79,20 +79,20 @@
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 +102,53 @@
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 +165,15 @@
}
}
+ /* 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 +192,11 @@
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 Sat Feb 17 17:17:21 2024 +0100
@@ -440,8 +440,8 @@
if (mpz_sgn
Re: mini-gmp mpz_gcdext Bézout coefficients do not match documentation
Guido Vranken writes: > Computing extended gcd using mpz_gcdext where a = 1, b = 2: > > libgmp: g: 1, s: 1, t: 0 > mini-gmp: g: 1, s: -1, t: 1 > This violates the docs: "s = sgn(a) if abs(b) = 2", e.g. s must be 1 > > Computing extended gcd using mpz_gcdext where a = 6, b = 4: > libgmp: g: 2, s: 1, t: -1 > mini-libgmp: g: 2, s: -1, t: 2 I think mini-gmp is wrong here, I'll have to investigate. Thanks for reporting. > The docs state: "abs(s) < abs(b) / (2 g) and abs(t) < abs(a) / (2 g)" > I think that should be: "abs(s) <= abs(b) / (2 g) and abs(t) <= abs(a) / (2 > g)" > (< should be <=) These strict equalities don't hold for the documented "exceptional" cases. IT seems both your examples have abs(B) = 2G, so that's the case that applies. It is a bit subtle. And even if one relaxes the inequalities as you suggest, 1 = gcd(1,1) would still be an exception (since in that case, we'd get |s|, |t| < 1/2, i.e., s = t = 0, which isn't reasonable). Can you suggest any doc change to make it clearer? Regards, /Niels -- 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
mini-gmp mpz_gcdext Bézout coefficients do not match documentation
Computing extended gcd using mpz_gcdext where a = 1, b = 2:
libgmp: g: 1, s: 1, t: 0
mini-gmp: g: 1, s: -1, t: 1
This violates the docs: "s = sgn(a) if abs(b) = 2", e.g. s must be 1
Computing extended gcd using mpz_gcdext where a = 6, b = 4:
libgmp: g: 2, s: 1, t: -1
mini-libgmp: g: 2, s: -1, t: 2
The docs state: "abs(s) < abs(b) / (2 g) and abs(t) < abs(a) / (2 g)"
I think that should be: "abs(s) <= abs(b) / (2 g) and abs(t) <= abs(a) / (2
g)"
(< should be <=)
Then, for libgmp this is true: s: 1 <= 4 / 4, t: 1 <= 6 / 4
For mini-gmp this is false for t: s: 1 <= 4 / 4, t: 2 <= 6 / 4
Reproducer:
//#include
#include "mini-gmp.c"
#include
static void test(
const unsigned long int a_ui,
const unsigned long int b_ui)
{
mpz_t a, b, g, s, t;
mpz_init(a);
mpz_init(b);
mpz_init(g);
mpz_init(s);
mpz_init(t);
mpz_set_ui(a, a_ui);
mpz_set_ui(b, b_ui);
mpz_gcdext(g, s, t, a, b);
printf("g: %s, s: %s, t: %s\n",
mpz_get_str(NULL, 10, g),
mpz_get_str(NULL, 10, s),
mpz_get_str(NULL, 10, t));
}
int main()
{
test(1, 2);
test(6, 4);
}
Tested on Linux x64 using the latest repository code.
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