File: fmpq.h

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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
    Copyright (C) 2011 Sebastian Pancratz

******************************************************************************/

#ifndef FMPQ_H
#define FMPQ_H

#ifdef FMPQ_INLINES_C
#define FMPQ_INLINE FLINT_DLL
#else
#define FMPQ_INLINE static __inline__
#endif

#undef ulong
#define ulong ulongxx /* interferes with system includes */
#include <stdio.h>
#undef ulong

#include <gmp.h>
#include <mpfr.h>
#define ulong mp_limb_t
#include "flint.h"
#include "fmpz.h"
#include "fmpz_vec.h"


#ifdef __cplusplus
 extern "C" {
#endif

typedef struct
{
    fmpz num;
    fmpz den;
}
fmpq;

typedef fmpq fmpq_t[1];

#define fmpq_numref(__x) (&(__x)->num)
#define fmpq_denref(__y) (&(__y)->den)


FMPQ_INLINE void fmpq_init(fmpq_t x)
{
    x->num = WORD(0);
    x->den = WORD(1);
}

FMPQ_INLINE void fmpq_clear(fmpq_t x)
{
    fmpz_clear(fmpq_numref(x));
    fmpz_clear(fmpq_denref(x));
}

FMPQ_INLINE fmpq * _fmpq_vec_init(slong n)
{
    fmpq * v = (fmpq *) flint_malloc(sizeof(fmpq) * n);
    slong i;

    for (i = 0; i < n; i++)
        fmpq_init(v + i);

    return v;
}

FMPQ_INLINE void _fmpq_vec_clear(fmpq * vec, slong n)
{
    _fmpz_vec_clear((fmpz *) vec, 2 * n);
}

FMPQ_INLINE void fmpq_zero(fmpq_t res)
{
    fmpz_zero(fmpq_numref(res));
    fmpz_one(fmpq_denref(res));
}

FMPQ_INLINE void fmpq_one(fmpq_t res)
{
    fmpz_one(fmpq_numref(res));
    fmpz_one(fmpq_denref(res));
}

FMPQ_INLINE int fmpq_equal(const fmpq_t x, const fmpq_t y)
{
    return fmpz_equal(fmpq_numref(x), fmpq_numref(y)) &&
           fmpz_equal(fmpq_denref(x), fmpq_denref(y));
}

FMPQ_INLINE int fmpq_sgn(const fmpq_t x)
{
    return fmpz_sgn(fmpq_numref(x));
}

FMPQ_INLINE int fmpq_is_zero(const fmpq_t x)
{
    return fmpz_is_zero(fmpq_numref(x));
}

FMPQ_INLINE int fmpq_is_one(const fmpq_t x)
{
    return fmpz_is_one(fmpq_numref(x)) && fmpz_is_one(fmpq_denref(x));
}

FMPQ_INLINE void fmpq_set(fmpq_t dest, const fmpq_t src)
{
    fmpz_set(fmpq_numref(dest), fmpq_numref(src));
    fmpz_set(fmpq_denref(dest), fmpq_denref(src));
}

FMPQ_INLINE void fmpq_swap(fmpq_t op1, fmpq_t op2)
{
    fmpz_swap(fmpq_numref(op1), fmpq_numref(op2));
    fmpz_swap(fmpq_denref(op1), fmpq_denref(op2));
}

FMPQ_INLINE void fmpq_neg(fmpq_t dest, const fmpq_t src)
{
    fmpz_neg(fmpq_numref(dest), fmpq_numref(src));
    fmpz_set(fmpq_denref(dest), fmpq_denref(src));
}

FMPQ_INLINE void fmpq_abs(fmpq_t dest, const fmpq_t src)
{
    fmpz_abs(fmpq_numref(dest), fmpq_numref(src));
    fmpz_set(fmpq_denref(dest), fmpq_denref(src));
}

FLINT_DLL int _fmpq_cmp(const fmpz_t p, const fmpz_t q, const fmpz_t r, const fmpz_t s);

FLINT_DLL int fmpq_cmp(const fmpq_t x, const fmpq_t y);

FLINT_DLL void _fmpq_canonicalise(fmpz_t num, fmpz_t den);

FLINT_DLL void fmpq_canonicalise(fmpq_t res);

FLINT_DLL int _fmpq_is_canonical(const fmpz_t num, const fmpz_t den);

FLINT_DLL int fmpq_is_canonical(const fmpq_t x);


FLINT_DLL void _fmpq_set_si(fmpz_t rnum, fmpz_t rden, slong p, ulong q);

FLINT_DLL void fmpq_set_si(fmpq_t res, slong p, ulong q);


FLINT_DLL void fmpq_set_fmpz_frac(fmpq_t res, const fmpz_t p, const fmpz_t q);


FMPQ_INLINE void fmpq_set_mpq(fmpq_t dest, const mpq_t src)
{
    fmpz_set_mpz(fmpq_numref(dest), mpq_numref(src));
    fmpz_set_mpz(fmpq_denref(dest), mpq_denref(src));
}

FMPQ_INLINE void fmpq_get_mpq(mpq_t dest, const fmpq_t src)
{
    fmpz_get_mpz(mpq_numref(dest), fmpq_numref(src));
    fmpz_get_mpz(mpq_denref(dest), fmpq_denref(src));
}

FLINT_DLL int fmpq_get_mpfr(mpfr_t r, const fmpq_t x, mpfr_rnd_t rnd);

FLINT_DLL void flint_mpq_init_set_readonly(mpq_t z, const fmpq_t f);

FLINT_DLL void flint_mpq_clear_readonly(mpq_t z);

FLINT_DLL void fmpq_init_set_readonly(fmpq_t f, const mpq_t z);

FLINT_DLL void fmpq_clear_readonly(fmpq_t f);

FLINT_DLL char * _fmpq_get_str(char * str, int b, const fmpz_t num, const fmpz_t den);

FLINT_DLL char * fmpq_get_str(char * str, int b, const fmpq_t x);

FLINT_DLL void _fmpq_fprint(FILE * file, const fmpz_t num, const fmpz_t den);

FLINT_DLL void fmpq_fprint(FILE * file, const fmpq_t x);

FMPQ_INLINE void _fmpq_print(const fmpz_t num, const fmpz_t den)
{
    _fmpq_fprint(stdout, num, den);
}

FMPQ_INLINE void fmpq_print(const fmpq_t x)
{
    fmpq_fprint(stdout, x);
}

FLINT_DLL void _fmpq_randtest(fmpz_t num, fmpz_t den, flint_rand_t state, mp_bitcnt_t bits);

FLINT_DLL void fmpq_randtest(fmpq_t res, flint_rand_t state, mp_bitcnt_t bits);

FLINT_DLL void fmpq_randtest_not_zero(fmpq_t res, flint_rand_t state, mp_bitcnt_t bits);

FLINT_DLL void _fmpq_randbits(fmpz_t num, fmpz_t den, flint_rand_t state, mp_bitcnt_t bits);

FLINT_DLL void fmpq_randbits(fmpq_t res, flint_rand_t state, mp_bitcnt_t bits);

FLINT_DLL void _fmpq_add(fmpz_t rnum, fmpz_t rden, const fmpz_t op1num,
    const fmpz_t op1den, const fmpz_t op2num, const fmpz_t op2den);

FLINT_DLL void fmpq_add(fmpq_t res, const fmpq_t op1, const fmpq_t op2);

FLINT_DLL void _fmpq_add_si(fmpz_t rnum, fmpz_t rden, const fmpz_t p, 
                                                      const fmpz_t q, slong r);

FLINT_DLL void fmpq_add_si(fmpq_t res, const fmpq_t op1, slong c);

FLINT_DLL void _fmpq_add_fmpz(fmpz_t rnum, fmpz_t rden, const fmpz_t p, 
                                               const fmpz_t q, const fmpz_t r);

FLINT_DLL void fmpq_add_fmpz(fmpq_t res, const fmpq_t op1, const fmpz_t c);

FLINT_DLL void _fmpq_sub(fmpz_t rnum, fmpz_t rden, const fmpz_t op1num,
    const fmpz_t op1den, const fmpz_t op2num, const fmpz_t op2den);

FLINT_DLL void fmpq_sub(fmpq_t res, const fmpq_t op1, const fmpq_t op2);

FLINT_DLL void _fmpq_sub_si(fmpz_t rnum, fmpz_t rden, const fmpz_t p, 
                                                      const fmpz_t q, slong r);

FLINT_DLL void fmpq_sub_si(fmpq_t res, const fmpq_t op1, slong c);

FLINT_DLL void _fmpq_sub_fmpz(fmpz_t rnum, fmpz_t rden, const fmpz_t p, 
                                               const fmpz_t q, const fmpz_t r);

FLINT_DLL void fmpq_sub_fmpz(fmpq_t res, const fmpq_t op1, const fmpz_t c);

FLINT_DLL void _fmpq_mul(fmpz_t rnum, fmpz_t rden, const fmpz_t op1num,
    const fmpz_t op1den, const fmpz_t op2num, const fmpz_t op2den);

FLINT_DLL void fmpq_mul(fmpq_t res, const fmpq_t op1, const fmpq_t op2);


FLINT_DLL void fmpq_mul_fmpz(fmpq_t res, const fmpq_t op, const fmpz_t x);

FLINT_DLL void _fmpq_pow_si(fmpz_t rnum, fmpz_t rden, 
                  const fmpz_t opnum, const fmpz_t opden, slong e);

FLINT_DLL void fmpq_pow_si(fmpq_t rop, const fmpq_t op, slong e);


FLINT_DLL void _fmpq_addmul(fmpz_t rnum, fmpz_t rden, const fmpz_t op1num,
    const fmpz_t op1den, const fmpz_t op2num, const fmpz_t op2den);

FLINT_DLL void fmpq_addmul(fmpq_t res, const fmpq_t op1, const fmpq_t op2);


FLINT_DLL void _fmpq_submul(fmpz_t rnum, fmpz_t rden, const fmpz_t op1num,
    const fmpz_t op1den, const fmpz_t op2num, const fmpz_t op2den);

FLINT_DLL void fmpq_submul(fmpq_t res, const fmpq_t op1, const fmpq_t op2);


FLINT_DLL void fmpq_inv(fmpq_t dest, const fmpq_t src);

FLINT_DLL void fmpq_div(fmpq_t res, const fmpq_t op1, const fmpq_t op2);

FLINT_DLL void fmpq_div_fmpz(fmpq_t res, const fmpq_t op, const fmpz_t x);


FLINT_DLL void fmpq_mul_2exp(fmpq_t res, const fmpq_t x, mp_bitcnt_t exp);

FLINT_DLL void fmpq_div_2exp(fmpq_t res, const fmpq_t x, mp_bitcnt_t exp);


FLINT_DLL int _fmpq_mod_fmpz(fmpz_t res, const fmpz_t num, const fmpz_t den, const fmpz_t mod);

FLINT_DLL int fmpq_mod_fmpz(fmpz_t res, const fmpq_t x, const fmpz_t mod);

FMPQ_INLINE void
_fmpq_gcd(fmpz_t rnum, fmpz_t rden, const fmpz_t p, const fmpz_t q,
            const fmpz_t r, const fmpz_t s)
{
   fmpz_t a, b;
   fmpz_init(a); fmpz_init(b);
   fmpz_mul(a, p, s);
   fmpz_mul(b, q, r);
   fmpz_gcd(rnum, a, b);
   fmpz_mul(rden, q, s);
   _fmpq_canonicalise(rnum, rden);
   fmpz_clear(a); fmpz_clear(b);
}

FMPQ_INLINE void 
fmpq_gcd(fmpq_t res, const fmpq_t op1, const fmpq_t op2)
{
    _fmpq_gcd(fmpq_numref(res), fmpq_denref(res), fmpq_numref(op1), 
              fmpq_denref(op1), fmpq_numref(op2), fmpq_denref(op2));
}

FLINT_DLL int _fmpq_reconstruct_fmpz(fmpz_t num, fmpz_t den, const fmpz_t a, const fmpz_t m);

FLINT_DLL int fmpq_reconstruct_fmpz(fmpq_t res, const fmpz_t a, const fmpz_t m);

FLINT_DLL int _fmpq_reconstruct_fmpz_2(fmpz_t n, fmpz_t d,
    const fmpz_t a, const fmpz_t m, const fmpz_t N, const fmpz_t D);

FLINT_DLL int fmpq_reconstruct_fmpz_2(fmpq_t res, const fmpz_t a, const fmpz_t m,
                                        const fmpz_t N, const fmpz_t D);

FLINT_DLL mp_bitcnt_t fmpq_height_bits(const fmpq_t x);

FLINT_DLL void fmpq_height(fmpz_t height, const fmpq_t x);

FLINT_DLL void _fmpq_next_calkin_wilf(fmpz_t rnum, fmpz_t rden,
    const fmpz_t num, const fmpz_t den);

FLINT_DLL void fmpq_next_calkin_wilf(fmpq_t res, const fmpq_t x);

FLINT_DLL void _fmpq_next_signed_calkin_wilf(fmpz_t rnum, fmpz_t rden,
    const fmpz_t num, const fmpz_t den);

FLINT_DLL void fmpq_next_signed_calkin_wilf(fmpq_t res, const fmpq_t x);

FLINT_DLL void _fmpq_next_minimal(fmpz_t rnum, fmpz_t rden,
    const fmpz_t num, const fmpz_t den);

FLINT_DLL void fmpq_next_minimal(fmpq_t res, const fmpq_t x);

FLINT_DLL void _fmpq_next_signed_minimal(fmpz_t rnum, fmpz_t rden,
    const fmpz_t num, const fmpz_t den);

FLINT_DLL void fmpq_next_signed_minimal(fmpq_t res, const fmpq_t x);

FLINT_DLL slong fmpq_get_cfrac(fmpz * c, fmpq_t rem, const fmpq_t x, slong n);

FLINT_DLL void fmpq_set_cfrac(fmpq_t x, const fmpz * c, slong n);

FLINT_DLL slong fmpq_cfrac_bound(const fmpq_t x);

FLINT_DLL void fmpq_dedekind_sum_naive(fmpq_t s, const fmpz_t h, const fmpz_t k);

FLINT_DLL void fmpq_dedekind_sum_coprime_large(fmpq_t s, const fmpz_t h, const fmpz_t k);

FLINT_DLL double fmpq_dedekind_sum_coprime_d(double h, double k);

FLINT_DLL void fmpq_dedekind_sum_coprime(fmpq_t s, const fmpz_t h, const fmpz_t k);

FLINT_DLL void fmpq_dedekind_sum(fmpq_t s, const fmpz_t h, const fmpz_t k);

FLINT_DLL void _fmpq_harmonic_ui(fmpz_t num, fmpz_t den, ulong n);

FLINT_DLL void fmpq_harmonic_ui(fmpq_t x, ulong n);

#ifdef __cplusplus
}
#endif

#endif