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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) 2011 Fredrik Johansson
******************************************************************************/
#include "fmpq.h"
void
_fmpq_add(fmpz_t rnum, fmpz_t rden, const fmpz_t p, const fmpz_t q,
const fmpz_t r, const fmpz_t s)
{
fmpz_t g, a, b, t, u;
/* Same denominator */
if (fmpz_equal(q, s))
{
fmpz_add(rnum, p, r);
/* Both are integers */
if (fmpz_is_one(q))
{
fmpz_set(rden, q);
}
else
{
fmpz_init(g);
fmpz_gcd(g, rnum, q);
if (fmpz_is_one(g))
{
fmpz_set(rden, q);
}
else
{
fmpz_divexact(rnum, rnum, g);
fmpz_divexact(rden, q, g);
}
fmpz_clear(g);
}
return;
}
/* p/q is an integer */
if (fmpz_is_one(q))
{
fmpz_init(t);
fmpz_mul(t, p, s);
fmpz_add(rnum, t, r);
fmpz_set(rden, s);
fmpz_clear(t);
return;
}
/* r/s is an integer */
if (fmpz_is_one(s))
{
fmpz_init(t);
fmpz_mul(t, r, q);
fmpz_add(rnum, t, p);
fmpz_set(rden, q);
fmpz_clear(t);
return;
}
/*
We want to compute p/q + r/s where the inputs are already
in canonical form.
If q and s are coprime, then (p*s + q*r, q*s) is in canonical form.
Otherwise, let g = gcd(q, s) with q = g*a, s = g*b. Then the sum
is given by ((p*b + r*a) / (a*b)) / g.
As above, (p*b + r*a) / (a*b) is in canonical form, and g has
no common factor with a*b. Thus we only need to reduce (p*b + r*a, g).
If the gcd is 1, the reduced denominator is g*a*b = q*b.
*/
fmpz_init(g);
fmpz_gcd(g, q, s);
if (fmpz_is_one(g))
{
fmpz_init(t);
fmpz_init(u);
fmpz_mul(t, p, s);
fmpz_mul(u, q, r);
fmpz_add(rnum, t, u);
fmpz_mul(rden, q, s);
fmpz_clear(t);
fmpz_clear(u);
}
else
{
fmpz_init(a);
fmpz_init(b);
fmpz_init(t);
fmpz_init(u);
fmpz_divexact(a, q, g);
fmpz_divexact(b, s, g);
fmpz_mul(t, p, b);
fmpz_mul(u, r, a);
fmpz_add(rnum, t, u);
fmpz_gcd(t, rnum, g);
if (fmpz_is_one(t))
{
fmpz_mul(rden, q, b);
}
else
{
fmpz_divexact(rnum, rnum, t);
fmpz_divexact(g, q, t);
fmpz_mul(rden, g, b);
}
fmpz_clear(a);
fmpz_clear(b);
fmpz_clear(t);
fmpz_clear(u);
}
fmpz_clear(g);
}
void fmpq_add(fmpq_t res, const fmpq_t op1, const fmpq_t op2)
{
_fmpq_add(fmpq_numref(res), fmpq_denref(res),
fmpq_numref(op1), fmpq_denref(op1),
fmpq_numref(op2), fmpq_denref(op2));
}
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