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