361 lines
10 KiB
C
361 lines
10 KiB
C
|
/*=============================================================================
|
||
|
|
|
||
|
|
This file is part of FLINT.
|
||
|
|
|
||
|
|
FLINT is free software; you can redistribute it and/or modify
|
||
|
|
it under the terms of the GNU General Public License as published by
|
||
|
|
the Free Software Foundation; either version 2 of the License, or
|
||
|
|
(at your option) any later version.
|
||
|
|
|
||
|
|
FLINT is distributed in the hope that it will be useful,
|
||
|
|
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||
|
|
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||
|
|
GNU General Public License for more details.
|
||
|
|
|
||
|
|
You should have received a copy of the GNU General Public License
|
||
|
|
along with FLINT; if not, write to the Free Software
|
||
|
|
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||
|
|
|
||
|
|
=============================================================================*/
|
||
|
|
/******************************************************************************
|
||
|
|
|
||
|
|
Copyright (C) 2011, 2012 Sebastian Pancratz
|
||
|
|
|
||
|
|
******************************************************************************/
|
||
|
|
|
||
|
|
#include "ulong_extras.h"
|
||
|
|
#include "padic.h"
|
||
|
|
|
||
|
|
/*
|
||
|
|
Set-up. Currently we only test the logarithm for positive values of N.
|
||
|
|
This is important as for negative N, exp(0) is 1, which is 0 mod p^N,
|
||
|
|
and then log(0) does not converge.
|
||
|
|
*/
|
||
|
|
static slong __rand_prec(flint_rand_t state, slong i)
|
||
|
|
{
|
||
|
|
slong N;
|
||
|
|
|
||
|
|
N = n_randint(state, PADIC_TEST_PREC_MAX) + 1;
|
||
|
|
|
||
|
|
return N;
|
||
|
|
}
|
||
|
|
|
||
|
|
int
|
||
|
|
main(void)
|
||
|
|
{
|
||
|
|
int i, result;
|
||
|
|
FLINT_TEST_INIT(state);
|
||
|
|
|
||
|
|
flint_printf("log_balanced... ");
|
||
|
|
fflush(stdout);
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
/** p == 2 *******************************************************************/
|
||
|
|
|
||
|
|
/* Check aliasing: a = log(a) */
|
||
|
|
for (i = 0; i < 1000; i++)
|
||
|
|
{
|
||
|
|
fmpz_t p = {WORD(2)};
|
||
|
|
slong N;
|
||
|
|
padic_ctx_t ctx;
|
||
|
|
|
||
|
|
padic_t a, b;
|
||
|
|
int ans1, ans2;
|
||
|
|
|
||
|
|
N = __rand_prec(state, i);
|
||
|
|
padic_ctx_init(ctx, p, FLINT_MAX(0, N-10), FLINT_MAX(0, N+10), PADIC_SERIES);
|
||
|
|
|
||
|
|
padic_init2(a, N);
|
||
|
|
padic_init2(b, N);
|
||
|
|
|
||
|
|
padic_randtest(a, state, ctx);
|
||
|
|
|
||
|
|
padic_one(b);
|
||
|
|
padic_add(a, a, b, ctx);
|
||
|
|
|
||
|
|
ans1 = padic_log_balanced(b, a, ctx);
|
||
|
|
ans2 = padic_log_balanced(a, a, ctx);
|
||
|
|
|
||
|
|
result = (ans1 == ans2) && (!ans1 || padic_equal(a, b));
|
||
|
|
if (!result)
|
||
|
|
{
|
||
|
|
flint_printf("FAIL (aliasing):\n\n");
|
||
|
|
flint_printf("a = "), padic_print(a, ctx), flint_printf("\n");
|
||
|
|
flint_printf("b = "), padic_print(b, ctx), flint_printf("\n");
|
||
|
|
abort();
|
||
|
|
}
|
||
|
|
|
||
|
|
padic_clear(a);
|
||
|
|
padic_clear(b);
|
||
|
|
|
||
|
|
padic_ctx_clear(ctx);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Check: log(a) + log(b) == log(a * b) */
|
||
|
|
for (i = 0; i < 10000; i++)
|
||
|
|
{
|
||
|
|
fmpz_t p = {WORD(2)};
|
||
|
|
slong N;
|
||
|
|
padic_ctx_t ctx;
|
||
|
|
|
||
|
|
padic_t a, b, c, d, e, f, g;
|
||
|
|
int ans1, ans2, ans3;
|
||
|
|
|
||
|
|
N = __rand_prec(state, i);
|
||
|
|
padic_ctx_init(ctx, p, FLINT_MAX(0, N-10), FLINT_MAX(0, N+10), PADIC_SERIES);
|
||
|
|
|
||
|
|
padic_init2(a, N);
|
||
|
|
padic_init2(b, N);
|
||
|
|
padic_init2(c, N);
|
||
|
|
padic_init2(d, N);
|
||
|
|
padic_init2(e, N);
|
||
|
|
padic_init2(f, N);
|
||
|
|
padic_init2(g, N);
|
||
|
|
|
||
|
|
padic_randtest(a, state, ctx);
|
||
|
|
padic_randtest(b, state, ctx);
|
||
|
|
|
||
|
|
padic_one(c);
|
||
|
|
padic_add(a, a, c, ctx);
|
||
|
|
padic_add(b, b, c, ctx);
|
||
|
|
|
||
|
|
padic_mul(c, a, b, ctx);
|
||
|
|
|
||
|
|
ans1 = padic_log_balanced(d, a, ctx);
|
||
|
|
ans2 = padic_log_balanced(e, b, ctx);
|
||
|
|
padic_add(f, d, e, ctx);
|
||
|
|
|
||
|
|
ans3 = padic_log_balanced(g, c, ctx);
|
||
|
|
|
||
|
|
result = (!ans1 || !ans2 || (ans3 && padic_equal(f, g)));
|
||
|
|
if (!result)
|
||
|
|
{
|
||
|
|
flint_printf("FAIL (functional equation):\n\n");
|
||
|
|
flint_printf("a = "), padic_print(a, ctx), flint_printf("\n");
|
||
|
|
flint_printf("b = "), padic_print(b, ctx), flint_printf("\n");
|
||
|
|
flint_printf("c = a * b = "), padic_print(c, ctx), flint_printf("\n");
|
||
|
|
flint_printf("d = log(a) = "), padic_print(d, ctx), flint_printf("\n");
|
||
|
|
flint_printf("e = log(b) = "), padic_print(e, ctx), flint_printf("\n");
|
||
|
|
flint_printf("f = log(a) + log(b) = "), padic_print(f, ctx), flint_printf("\n");
|
||
|
|
flint_printf("g = log(a * b) = "), padic_print(g, ctx), flint_printf("\n");
|
||
|
|
abort();
|
||
|
|
}
|
||
|
|
|
||
|
|
padic_clear(a);
|
||
|
|
padic_clear(b);
|
||
|
|
padic_clear(c);
|
||
|
|
padic_clear(d);
|
||
|
|
padic_clear(e);
|
||
|
|
padic_clear(f);
|
||
|
|
padic_clear(g);
|
||
|
|
|
||
|
|
padic_ctx_clear(ctx);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Check: log(exp(x)) == x */
|
||
|
|
for (i = 0; i < 10000; i++)
|
||
|
|
{
|
||
|
|
fmpz_t p = {WORD(2)};
|
||
|
|
slong N;
|
||
|
|
padic_ctx_t ctx;
|
||
|
|
|
||
|
|
padic_t a, b, c;
|
||
|
|
int ans1, ans2;
|
||
|
|
|
||
|
|
N = __rand_prec(state, i);
|
||
|
|
padic_ctx_init(ctx, p, FLINT_MAX(0, N-10), FLINT_MAX(0, N+10), PADIC_SERIES);
|
||
|
|
|
||
|
|
padic_init2(a, N);
|
||
|
|
padic_init2(b, N);
|
||
|
|
padic_init2(c, N);
|
||
|
|
|
||
|
|
padic_randtest(a, state, ctx);
|
||
|
|
|
||
|
|
ans1 = padic_exp(b, a, ctx);
|
||
|
|
if (ans1)
|
||
|
|
ans2 = padic_log_balanced(c, b, ctx);
|
||
|
|
|
||
|
|
result = !ans1 || (ans1 == ans2 && padic_equal(a, c));
|
||
|
|
if (!result)
|
||
|
|
{
|
||
|
|
flint_printf("FAIL (log(exp(x)) == x):\n\n");
|
||
|
|
flint_printf("a = "), padic_print(a, ctx), flint_printf("\n");
|
||
|
|
flint_printf("b = "), padic_print(b, ctx), flint_printf("\n");
|
||
|
|
flint_printf("c = "), padic_print(c, ctx), flint_printf("\n");
|
||
|
|
flint_printf("ans1 = %d\n", ans1);
|
||
|
|
flint_printf("ans2 = %d\n", ans2);
|
||
|
|
abort();
|
||
|
|
}
|
||
|
|
|
||
|
|
padic_clear(a);
|
||
|
|
padic_clear(b);
|
||
|
|
padic_clear(c);
|
||
|
|
|
||
|
|
padic_ctx_clear(ctx);
|
||
|
|
}
|
||
|
|
|
||
|
|
/** p > 2 ********************************************************************/
|
||
|
|
|
||
|
|
/* Check aliasing: a = log(a) */
|
||
|
|
for (i = 0; i < 1000; i++)
|
||
|
|
{
|
||
|
|
fmpz_t p;
|
||
|
|
slong N;
|
||
|
|
padic_ctx_t ctx;
|
||
|
|
|
||
|
|
padic_t a, b;
|
||
|
|
int ans1, ans2;
|
||
|
|
|
||
|
|
fmpz_init_set_ui(p, n_randtest_prime(state, 0));
|
||
|
|
N = __rand_prec(state, i);
|
||
|
|
padic_ctx_init(ctx, p, FLINT_MAX(0, N-10), FLINT_MAX(0, N+10), PADIC_SERIES);
|
||
|
|
|
||
|
|
padic_init2(a, N);
|
||
|
|
padic_init2(b, N);
|
||
|
|
|
||
|
|
padic_randtest(a, state, ctx);
|
||
|
|
|
||
|
|
padic_one(b);
|
||
|
|
padic_add(a, a, b, ctx);
|
||
|
|
|
||
|
|
ans1 = padic_log_balanced(b, a, ctx);
|
||
|
|
ans2 = padic_log_balanced(a, a, ctx);
|
||
|
|
|
||
|
|
result = (ans1 == ans2) && (!ans1 || padic_equal(a, b));
|
||
|
|
if (!result)
|
||
|
|
{
|
||
|
|
flint_printf("FAIL (aliasing):\n\n");
|
||
|
|
flint_printf("a = "), padic_print(a, ctx), flint_printf("\n");
|
||
|
|
flint_printf("b = "), padic_print(b, ctx), flint_printf("\n");
|
||
|
|
abort();
|
||
|
|
}
|
||
|
|
|
||
|
|
padic_clear(a);
|
||
|
|
padic_clear(b);
|
||
|
|
|
||
|
|
fmpz_clear(p);
|
||
|
|
padic_ctx_clear(ctx);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Check: log(a) + log(b) == log(a * b) */
|
||
|
|
for (i = 0; i < 10000; i++)
|
||
|
|
{
|
||
|
|
fmpz_t p;
|
||
|
|
slong N;
|
||
|
|
padic_ctx_t ctx;
|
||
|
|
|
||
|
|
padic_t a, b, c, d, e, f, g;
|
||
|
|
int ans1, ans2, ans3;
|
||
|
|
|
||
|
|
fmpz_init_set_ui(p, n_randtest_prime(state, 0));
|
||
|
|
/* fmpz_init_set_ui(p, n_randprime(state, 5, 1));*/
|
||
|
|
N = __rand_prec(state, i);
|
||
|
|
padic_ctx_init(ctx, p, FLINT_MAX(0, N-10), FLINT_MAX(0, N+10), PADIC_SERIES);
|
||
|
|
|
||
|
|
padic_init2(a, N);
|
||
|
|
padic_init2(b, N);
|
||
|
|
padic_init2(c, N);
|
||
|
|
padic_init2(d, N);
|
||
|
|
padic_init2(e, N);
|
||
|
|
padic_init2(f, N);
|
||
|
|
padic_init2(g, N);
|
||
|
|
|
||
|
|
padic_randtest(a, state, ctx);
|
||
|
|
padic_randtest(b, state, ctx);
|
||
|
|
|
||
|
|
padic_one(c);
|
||
|
|
padic_add(a, a, c, ctx);
|
||
|
|
|
||
|
|
padic_one(c);
|
||
|
|
padic_add(b, b, c, ctx);
|
||
|
|
|
||
|
|
padic_mul(c, a, b, ctx);
|
||
|
|
|
||
|
|
ans1 = padic_log_balanced(d, a, ctx);
|
||
|
|
ans2 = padic_log_balanced(e, b, ctx);
|
||
|
|
padic_add(f, d, e, ctx);
|
||
|
|
|
||
|
|
ans3 = padic_log_balanced(g, c, ctx);
|
||
|
|
|
||
|
|
result = (!ans1 || !ans2 || (ans3 && padic_equal(f, g)));
|
||
|
|
if (!result)
|
||
|
|
{
|
||
|
|
flint_printf("FAIL (functional equation):\n\n");
|
||
|
|
flint_printf("a = "), padic_print(a, ctx), flint_printf("\n");
|
||
|
|
flint_printf("b = "), padic_print(b, ctx), flint_printf("\n");
|
||
|
|
flint_printf("c = a * b = "), padic_print(c, ctx), flint_printf("\n");
|
||
|
|
flint_printf("d = log(a) = "), padic_print(d, ctx), flint_printf("\n");
|
||
|
|
flint_printf("e = log(b) = "), padic_print(e, ctx), flint_printf("\n");
|
||
|
|
flint_printf("f = log(a) + log(b) = "), padic_print(f, ctx), flint_printf("\n");
|
||
|
|
flint_printf("g = log(a * b) = "), padic_print(g, ctx), flint_printf("\n");
|
||
|
|
flint_printf("ans1 = %d\n", ans1);
|
||
|
|
flint_printf("ans2 = %d\n", ans2);
|
||
|
|
flint_printf("ans3 = %d\n", ans3);
|
||
|
|
abort();
|
||
|
|
}
|
||
|
|
|
||
|
|
padic_clear(a);
|
||
|
|
padic_clear(b);
|
||
|
|
padic_clear(c);
|
||
|
|
padic_clear(d);
|
||
|
|
padic_clear(e);
|
||
|
|
padic_clear(f);
|
||
|
|
padic_clear(g);
|
||
|
|
|
||
|
|
fmpz_clear(p);
|
||
|
|
padic_ctx_clear(ctx);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Check: log(exp(x)) == x */
|
||
|
|
for (i = 0; i < 10000; i++)
|
||
|
|
{
|
||
|
|
fmpz_t p;
|
||
|
|
slong N;
|
||
|
|
padic_ctx_t ctx;
|
||
|
|
|
||
|
|
padic_t a, b, c;
|
||
|
|
int ans1, ans2;
|
||
|
|
|
||
|
|
/* fmpz_init_set_ui(p, n_randtest_prime(state, 0)); */
|
||
|
|
fmpz_init_set_ui(p, n_randprime(state, 5, 1));
|
||
|
|
N = __rand_prec(state, i);
|
||
|
|
padic_ctx_init(ctx, p, FLINT_MAX(0, N-10), FLINT_MAX(0, N+10), PADIC_SERIES);
|
||
|
|
|
||
|
|
padic_init2(a, N);
|
||
|
|
padic_init2(b, N);
|
||
|
|
padic_init2(c, N);
|
||
|
|
|
||
|
|
padic_randtest(a, state, ctx);
|
||
|
|
|
||
|
|
ans1 = padic_exp(b, a, ctx);
|
||
|
|
if (ans1)
|
||
|
|
ans2 = padic_log_balanced(c, b, ctx);
|
||
|
|
|
||
|
|
result = !ans1 || (ans1 == ans2 && padic_equal(a, c));
|
||
|
|
if (!result)
|
||
|
|
{
|
||
|
|
flint_printf("FAIL (log(exp(x)) == x):\n\n");
|
||
|
|
flint_printf("a = "), padic_print(a, ctx), flint_printf("\n");
|
||
|
|
flint_printf("b = "), padic_print(b, ctx), flint_printf("\n");
|
||
|
|
flint_printf("c = "), padic_print(c, ctx), flint_printf("\n");
|
||
|
|
flint_printf("ans1 = %d\n", ans1);
|
||
|
|
flint_printf("ans2 = %d\n", ans2);
|
||
|
|
abort();
|
||
|
|
}
|
||
|
|
|
||
|
|
padic_clear(a);
|
||
|
|
padic_clear(b);
|
||
|
|
padic_clear(c);
|
||
|
|
|
||
|
|
fmpz_clear(p);
|
||
|
|
padic_ctx_clear(ctx);
|
||
|
|
}
|
||
|
|
|
||
|
|
FLINT_TEST_CLEANUP(state);
|
||
|
|
|
||
|
|
flint_printf("PASS\n");
|
||
|
|
return EXIT_SUCCESS;
|
||
|
|
}
|
||
|
|
|