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/*=============================================================================
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) 2010,2011 Fredrik Johansson
******************************************************************************/
#include <stdio.h>
#include <stdlib.h>
#include <limits.h>
#include <gmp.h>
#include "flint.h"
#include "arith.h"
#include "fmpz.h"
#include "fmpq.h"
#include "ulong_extras.h"
#include "profiler.h"
void numerical_test(fmpq_t res, slong n, double ans)
{
const double tol = 1e-13;
double err;
mpq_t tmp;
mpq_init(tmp);
arith_harmonic_number(res, n);
fmpq_get_mpq(tmp, res);
err = mpq_get_d(tmp) - ans;
err = FLINT_ABS(err);
if (err > tol)
{
flint_printf("FAIL: %wd %.16f %.16f\n", n, mpq_get_d(tmp), ans);
abort();
}
mpq_clear(tmp);
}
void
mpq_harmonic_balanced(mpq_t res, slong a, slong b)
{
slong k;
mpq_t t;
mpq_init(t);
if (b - a < 50)
{
flint_mpq_set_ui(res, 0, UWORD(1));
for (k = a; k <= b; k++)
{
flint_mpq_set_ui(t, UWORD(1), k);
mpq_add(res, res, t);
}
}
else
{
mpq_harmonic_balanced(res, a, (a+b)/2);
mpq_harmonic_balanced(t, (a+b)/2+1, b);
mpq_add(res, res, t);
}
mpq_clear(t);
}
int main(void)
{
slong i;
mpq_t x, y;
fmpq_t t;
FLINT_TEST_INIT(state);
flint_printf("harmonic_number....");
fflush(stdout);
fmpq_init(t);
mpq_init(x);
mpq_init(y);
for (i = -2; i < 1000; i++)
{
mpq_harmonic_balanced(x, 1, i);
arith_harmonic_number(t, i);
fmpq_get_mpq(y, t);
if (!mpq_equal(x, y))
{
flint_printf("FAIL: %wd\n", i);
abort();
}
}
numerical_test(t, 1000, 7.4854708605503449127);
numerical_test(t, 1001, 7.4864698615493459117);
numerical_test(t, 1002, 7.4874678655413618797);
numerical_test(t, 1003, 7.4884648745144426375);
numerical_test(t, 10000, 9.7876060360443822642);
numerical_test(t, 10001, 9.7877060260453821642);
numerical_test(t, 10002, 9.7878060060493813643);
numerical_test(t, 10003, 9.7879059760583786652);
numerical_test(t, 10004, 9.7880059360743722677);
numerical_test(t, 20000, 10.480728217229327573);
numerical_test(t, 30000, 10.886184992119899362);
numerical_test(t, 40000, 11.173862897945522882);
numerical_test(t, 50000, 11.397003949278482638);
numerical_test(t, 60000, 11.579323839415955783);
numerical_test(t, 70000, 11.733473328773164956);
numerical_test(t, 80000, 11.867003828544530692);
numerical_test(t, 90000, 11.984786169759202469);
numerical_test(t, 100000, 12.090146129863427947);
numerical_test(t, 100001, 12.090156129763428947);
numerical_test(t, 100002, 12.090166129563432947);
numerical_test(t, 100003, 12.090176129263441947);
numerical_test(t, 100004, 12.090186128863457946);
numerical_test(t, 300000, 13.188755085205611713);
numerical_test(t, 500000, 13.699580042305528322);
numerical_test(t, 700000, 14.036051993212618803);
numerical_test(t, 900000, 14.287366262763433338);
mpq_clear(x);
mpq_clear(y);
fmpq_clear(t);
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
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