/* Implementations of operations between mpfr and mpz/mpq data
Copyright 2001, 2003-2017 Free Software Foundation, Inc.
Contributed by the AriC and Caramba projects, INRIA.
This file is part of the GNU MPFR Library.
The GNU MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 3 of the License, or (at your
option) any later version.
The GNU MPFR Library 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 Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see
http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"
/* Init and set a mpfr_t with enough precision to store a mpz.
This function should be called in the extended exponent range. */
static void
init_set_z (mpfr_ptr t, mpz_srcptr z)
{
mpfr_prec_t p;
int i;
if (mpz_size (z) <= 1)
p = GMP_NUMB_BITS;
else
MPFR_MPZ_SIZEINBASE2 (p, z);
mpfr_init2 (t, p);
i = mpfr_set_z (t, z, MPFR_RNDN);
/* Possible assertion failure in case of overflow. Such cases,
which imply that z is huge (if the function is called in
the extended exponent range), are currently not supported,
just like precisions around MPFR_PREC_MAX. */
MPFR_ASSERTN (i == 0); (void) i; /* use i to avoid a warning */
}
/* Init, set a mpfr_t with enough precision to store a mpz_t without round,
call the function, and clear the allocated mpfr_t */
static int
foo (mpfr_ptr x, mpfr_srcptr y, mpz_srcptr z, mpfr_rnd_t r,
int (*f)(mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t))
{
mpfr_t t;
int i;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_SAVE_EXPO_MARK (expo);
init_set_z (t, z); /* There should be no exceptions. */
i = (*f) (x, y, t, r);
MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags);
mpfr_clear (t);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (x, i, r);
}
static int
foo2 (mpfr_ptr x, mpz_srcptr y, mpfr_srcptr z, mpfr_rnd_t r,
int (*f)(mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t))
{
mpfr_t t;
int i;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_SAVE_EXPO_MARK (expo);
init_set_z (t, y); /* There should be no exceptions. */
i = (*f) (x, t, z, r);
MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags);
mpfr_clear (t);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (x, i, r);
}
int
mpfr_mul_z (mpfr_ptr y, mpfr_srcptr x, mpz_srcptr z, mpfr_rnd_t r)
{
return foo (y, x, z, r, mpfr_mul);
}
int
mpfr_div_z (mpfr_ptr y, mpfr_srcptr x, mpz_srcptr z, mpfr_rnd_t r)
{
return foo (y, x, z, r, mpfr_div);
}
int
mpfr_add_z (mpfr_ptr y, mpfr_srcptr x, mpz_srcptr z, mpfr_rnd_t r)
{
/* Mpz 0 is unsigned */
if (MPFR_UNLIKELY (mpz_sgn (z) == 0))
return mpfr_set (y, x, r);
else
return foo (y, x, z, r, mpfr_add);
}
int
mpfr_sub_z (mpfr_ptr y, mpfr_srcptr x, mpz_srcptr z, mpfr_rnd_t r)
{
/* Mpz 0 is unsigned */
if (MPFR_UNLIKELY (mpz_sgn (z) == 0))
return mpfr_set (y, x, r);
else
return foo (y, x, z, r, mpfr_sub);
}
int
mpfr_z_sub (mpfr_ptr y, mpz_srcptr x, mpfr_srcptr z, mpfr_rnd_t r)
{
/* Mpz 0 is unsigned */
if (MPFR_UNLIKELY (mpz_sgn (x) == 0))
return mpfr_neg (y, z, r);
else
return foo2 (y, x, z, r, mpfr_sub);
}
int
mpfr_cmp_z (mpfr_srcptr x, mpz_srcptr z)
{
mpfr_t t;
int res;
mpfr_prec_t p;
unsigned int flags;
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
return mpfr_cmp_si (x, mpz_sgn (z));
if (mpz_size (z) <= 1)
p = GMP_NUMB_BITS;
else
MPFR_MPZ_SIZEINBASE2 (p, z);
mpfr_init2 (t, p);
flags = __gmpfr_flags;
if (mpfr_set_z (t, z, MPFR_RNDN))
{
/* overflow (t is an infinity) or underflow */
mpfr_div_2ui (t, t, 2, MPFR_RNDZ); /* if underflow, set t to zero */
__gmpfr_flags = flags; /* restore the flags */
/* The real value of t (= z), which falls outside the exponent range,
has been replaced by an equivalent value for the comparison: zero
or an infinity. */
}
res = mpfr_cmp (x, t);
mpfr_clear (t);
return res;
}
/* Compute y = RND(x*n/d), where n and d are mpz integers.
An integer 0 is assumed to have a positive sign.
This function is used by mpfr_mul_q and mpfr_div_q.
Note: the status of the rational 0/(-1) is not clear (if there is
a signed infinity, there should be a signed zero). But infinities
are not currently supported/documented in GMP, and if the rational
is canonicalized as it should be, the case 0/(-1) cannot occur. */
static int
mpfr_muldiv_z (mpfr_ptr y, mpfr_srcptr x, mpz_srcptr n, mpz_srcptr d,
mpfr_rnd_t rnd_mode)
{
if (MPFR_UNLIKELY (mpz_sgn (n) == 0))
{
if (MPFR_UNLIKELY (mpz_sgn (d) == 0))
MPFR_SET_NAN (y);
else
{
mpfr_mul_ui (y, x, 0, MPFR_RNDN); /* exact: +0, -0 or NaN */
if (MPFR_UNLIKELY (mpz_sgn (d) < 0))
MPFR_CHANGE_SIGN (y);
}
return 0;
}
else if (MPFR_UNLIKELY (mpz_sgn (d) == 0))
{
mpfr_div_ui (y, x, 0, MPFR_RNDN); /* exact: +Inf, -Inf or NaN */
if (MPFR_UNLIKELY (mpz_sgn (n) < 0))
MPFR_CHANGE_SIGN (y);
return 0;
}
else
{
mpfr_prec_t p;
mpfr_t tmp;
int inexact;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_SAVE_EXPO_MARK (expo);
/* With the current MPFR code, using mpfr_mul_z and mpfr_div_z
for the general case should be faster than doing everything
in mpn, mpz and/or mpq. MPFR_SAVE_EXPO_MARK could be avoided
here, but it would be more difficult to handle corner cases. */
MPFR_MPZ_SIZEINBASE2 (p, n);
mpfr_init2 (tmp, MPFR_PREC (x) + p);
inexact = mpfr_mul_z (tmp, x, n, MPFR_RNDN);
/* Since |n| >= 1, an underflow is not possible. And the precision of
tmp has been chosen so that inexact != 0 iff there's an overflow. */
if (MPFR_UNLIKELY (inexact != 0))
{
mpfr_t x0;
mpfr_exp_t ex;
MPFR_BLOCK_DECL (flags);
/* intermediate overflow case */
MPFR_ASSERTD (mpfr_inf_p (tmp));
ex = MPFR_GET_EXP (x); /* x is a pure FP number */
MPFR_ALIAS (x0, x, MPFR_SIGN(x), 0); /* x0 = x / 2^ex */
MPFR_BLOCK (flags,
inexact = mpfr_mul_z (tmp, x0, n, MPFR_RNDN);
MPFR_ASSERTD (inexact == 0);
inexact = mpfr_div_z (y, tmp, d, rnd_mode);
/* Just in case the division underflows
(highly unlikely, not supported)... */
MPFR_ASSERTN (!MPFR_BLOCK_EXCEP));
MPFR_EXP (y) += ex;
/* Detect highly unlikely, not supported corner cases... */
MPFR_ASSERTN (MPFR_EXP (y) >= __gmpfr_emin && MPFR_IS_PURE_FP (y));
/* The potential overflow will be detected by mpfr_check_range. */
}
else
inexact = mpfr_div_z (y, tmp, d, rnd_mode);
mpfr_clear (tmp);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (y, inexact, rnd_mode);
}
}
int
mpfr_mul_q (mpfr_ptr y, mpfr_srcptr x, mpq_srcptr z, mpfr_rnd_t rnd_mode)
{
return mpfr_muldiv_z (y, x, mpq_numref (z), mpq_denref (z), rnd_mode);
}
int
mpfr_div_q (mpfr_ptr y, mpfr_srcptr x, mpq_srcptr z, mpfr_rnd_t rnd_mode)
{
return mpfr_muldiv_z (y, x, mpq_denref (z), mpq_numref (z), rnd_mode);
}
int
mpfr_add_q (mpfr_ptr y, mpfr_srcptr x, mpq_srcptr z, mpfr_rnd_t rnd_mode)
{
mpfr_t t,q;
mpfr_prec_t p;
mpfr_exp_t err;
int res;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_ZIV_DECL (loop);
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
{
if (MPFR_IS_NAN (x))
{
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF (x))
{
if (MPFR_UNLIKELY (mpz_sgn (mpq_denref (z)) == 0 &&
MPFR_MULT_SIGN (mpz_sgn (mpq_numref (z)),
MPFR_SIGN (x)) <= 0))
{
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
MPFR_SET_INF (y);
MPFR_SET_SAME_SIGN (y, x);
MPFR_RET (0);
}
else
{
MPFR_ASSERTD (MPFR_IS_ZERO (x));
if (MPFR_UNLIKELY (mpq_sgn (z) == 0))
return mpfr_set (y, x, rnd_mode); /* signed 0 - Unsigned 0 */
else
return mpfr_set_q (y, z, rnd_mode);
}
}
MPFR_SAVE_EXPO_MARK (expo);
p = MPFR_PREC (y) + 10;
mpfr_init2 (t, p);
mpfr_init2 (q, p);
MPFR_ZIV_INIT (loop, p);
for (;;)
{
MPFR_BLOCK_DECL (flags);
res = mpfr_set_q (q, z, MPFR_RNDN); /* Error <= 1/2 ulp(q) */
/* If z if @INF@ (1/0), res = 0, so it quits immediately */
if (MPFR_UNLIKELY (res == 0))
/* Result is exact so we can add it directly! */
{
res = mpfr_add (y, x, q, rnd_mode);
break;
}
MPFR_BLOCK (flags, mpfr_add (t, x, q, MPFR_RNDN));
/* Error on t is <= 1/2 ulp(t), except in case of overflow/underflow,
but such an exception is very unlikely as it would be possible
only if q has a huge numerator or denominator. Not supported! */
MPFR_ASSERTN (! (MPFR_OVERFLOW (flags) || MPFR_UNDERFLOW (flags)));
/* Error / ulp(t) <= 1/2 + 1/2 * 2^(EXP(q)-EXP(t))
If EXP(q)-EXP(t)>0, <= 2^(EXP(q)-EXP(t)-1)*(1+2^-(EXP(q)-EXP(t)))
<= 2^(EXP(q)-EXP(t))
If EXP(q)-EXP(t)<0, <= 2^0 */
/* We can get 0, but we can't round since q is inexact */
if (MPFR_LIKELY (!MPFR_IS_ZERO (t)))
{
err = (mpfr_exp_t) p - 1 - MAX (MPFR_GET_EXP(q)-MPFR_GET_EXP(t), 0);
if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, MPFR_PREC (y), rnd_mode)))
{
res = mpfr_set (y, t, rnd_mode);
break;
}
}
MPFR_ZIV_NEXT (loop, p);
mpfr_set_prec (t, p);
mpfr_set_prec (q, p);
}
MPFR_ZIV_FREE (loop);
mpfr_clear (t);
mpfr_clear (q);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (y, res, rnd_mode);
}
int
mpfr_sub_q (mpfr_ptr y, mpfr_srcptr x, mpq_srcptr z,mpfr_rnd_t rnd_mode)
{
mpfr_t t,q;
mpfr_prec_t p;
int res;
mpfr_exp_t err;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_ZIV_DECL (loop);
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
{
if (MPFR_IS_NAN (x))
{
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF (x))
{
if (MPFR_UNLIKELY (mpz_sgn (mpq_denref (z)) == 0 &&
MPFR_MULT_SIGN (mpz_sgn (mpq_numref (z)),
MPFR_SIGN (x)) >= 0))
{
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
MPFR_SET_INF (y);
MPFR_SET_SAME_SIGN (y, x);
MPFR_RET (0);
}
else
{
MPFR_ASSERTD (MPFR_IS_ZERO (x));
if (MPFR_UNLIKELY (mpq_sgn (z) == 0))
return mpfr_set (y, x, rnd_mode); /* signed 0 - Unsigned 0 */
else
{
res = mpfr_set_q (y, z, MPFR_INVERT_RND (rnd_mode));
MPFR_CHANGE_SIGN (y);
return -res;
}
}
}
MPFR_SAVE_EXPO_MARK (expo);
p = MPFR_PREC (y) + 10;
mpfr_init2 (t, p);
mpfr_init2 (q, p);
MPFR_ZIV_INIT (loop, p);
for(;;)
{
MPFR_BLOCK_DECL (flags);
res = mpfr_set_q(q, z, MPFR_RNDN); /* Error <= 1/2 ulp(q) */
/* If z if @INF@ (1/0), res = 0, so it quits immediately */
if (MPFR_UNLIKELY (res == 0))
/* Result is exact so we can add it directly!*/
{
res = mpfr_sub (y, x, q, rnd_mode);
break;
}
MPFR_BLOCK (flags, mpfr_sub (t, x, q, MPFR_RNDN));
/* Error on t is <= 1/2 ulp(t), except in case of overflow/underflow,
but such an exception is very unlikely as it would be possible
only if q has a huge numerator or denominator. Not supported! */
MPFR_ASSERTN (! (MPFR_OVERFLOW (flags) || MPFR_UNDERFLOW (flags)));
/* Error / ulp(t) <= 1/2 + 1/2 * 2^(EXP(q)-EXP(t))
If EXP(q)-EXP(t)>0, <= 2^(EXP(q)-EXP(t)-1)*(1+2^-(EXP(q)-EXP(t)))
<= 2^(EXP(q)-EXP(t))
If EXP(q)-EXP(t)<0, <= 2^0 */
/* We can get 0, but we can't round since q is inexact */
if (MPFR_LIKELY (!MPFR_IS_ZERO (t)))
{
err = (mpfr_exp_t) p - 1 - MAX (MPFR_GET_EXP(q)-MPFR_GET_EXP(t), 0);
res = MPFR_CAN_ROUND (t, err, MPFR_PREC (y), rnd_mode);
if (MPFR_LIKELY (res != 0)) /* We can round! */
{
res = mpfr_set (y, t, rnd_mode);
break;
}
}
MPFR_ZIV_NEXT (loop, p);
mpfr_set_prec (t, p);
mpfr_set_prec (q, p);
}
MPFR_ZIV_FREE (loop);
mpfr_clear (t);
mpfr_clear (q);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (y, res, rnd_mode);
}
int
mpfr_cmp_q (mpfr_srcptr x, mpq_srcptr q)
{
mpfr_t t;
int res;
mpfr_prec_t p;
MPFR_SAVE_EXPO_DECL (expo);
if (MPFR_UNLIKELY (mpq_denref (q) == 0))
{
/* q is an infinity or NaN */
mpfr_init2 (t, 2);
mpfr_set_q (t, q, MPFR_RNDN);
res = mpfr_cmp (x, t);
mpfr_clear (t);
return res;
}
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
return mpfr_cmp_si (x, mpq_sgn (q));
MPFR_SAVE_EXPO_MARK (expo);
/* x < a/b ? <=> x*b < a */
MPFR_MPZ_SIZEINBASE2 (p, mpq_denref (q));
mpfr_init2 (t, MPFR_PREC(x) + p);
res = mpfr_mul_z (t, x, mpq_denref (q), MPFR_RNDN);
MPFR_ASSERTD (res == 0);
res = mpfr_cmp_z (t, mpq_numref (q));
mpfr_clear (t);
MPFR_SAVE_EXPO_FREE (expo);
return res;
}
int
mpfr_cmp_f (mpfr_srcptr x, mpf_srcptr z)
{
mpfr_t t;
int res;
MPFR_SAVE_EXPO_DECL (expo);
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
return mpfr_cmp_si (x, mpf_sgn (z));
MPFR_SAVE_EXPO_MARK (expo);
mpfr_init2 (t, MPFR_PREC_MIN + ABS(SIZ(z)) * GMP_NUMB_BITS );
res = mpfr_set_f (t, z, MPFR_RNDN);
MPFR_ASSERTD (res == 0);
res = mpfr_cmp (x, t);
mpfr_clear (t);
MPFR_SAVE_EXPO_FREE (expo);
return res;
}