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/*
Copyright (C) 2011 Fredrik Johansson
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
/*
Demo FLINT program for incremental multimodular reduction and
reconstruction using the Chinese Remainder Theorem.
*/
#include <stdlib.h>
#include <stdio.h>
#include <flint/flint.h>
#include <flint/fmpz.h>
#include <flint/ulong_extras.h>
int main(int argc, char* argv[])
{
slong bit_bound;
ulong prime, res;
fmpz_t x, y, prod;
if (argc != 2)
{
flint_printf("Syntax: crt <integer>\n");
return EXIT_FAILURE;
}
fmpz_init(x);
fmpz_init(y);
fmpz_init(prod);
fmpz_set_str(x, argv[1], 10);
bit_bound = fmpz_bits(x) + 2;
fmpz_zero(y);
fmpz_one(prod);
prime = 0;
while(fmpz_bits(prod) < bit_bound)
{
prime = n_nextprime(prime, 0);
res = fmpz_fdiv_ui(x, prime);
fmpz_CRT_ui(y, y, prod, res, prime, 1);
flint_printf("residue mod %wu = %wu; reconstruction = ", prime, res);
fmpz_print(y);
flint_printf("\n");
fmpz_mul_ui(prod, prod, prime);
}
fmpz_clear(x);
fmpz_clear(y);
fmpz_clear(prod);
return 0;
}