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/* Functions to work with unbounded floats (limited low-level interface).
Copyright 2016-2017 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"
/* Note: In MPFR math functions, even if UBF code is not called first,
we may still need to handle special values NaN and infinities here.
Indeed, for MAXR * MAXR + (-inf), even though this is a special case,
the computation will also generate an overflow due to MAXR * MAXR,
so that UBF code will be called anyway (except if special cases are
detected and handled separately, but for polynomial, this should not
be needed). */
/* This function does not change the flags. */
static void
mpfr_init_get_zexp (mpz_ptr ez, mpfr_srcptr x)
{
mpz_init (ez);
if (MPFR_IS_UBF (x))
mpz_set (ez, MPFR_ZEXP (x));
else
{
mp_limb_t e_limb[MPFR_EXP_LIMB_SIZE];
mpfr_t e;
int inex;
MPFR_SAVE_EXPO_DECL (expo);
/* TODO: Once this has been tested, optimize based on whether
_MPFR_EXP_FORMAT <= 3. */
MPFR_TMP_INIT1 (e_limb, e, sizeof (mpfr_exp_t) * CHAR_BIT);
MPFR_SAVE_EXPO_MARK (expo);
MPFR_DBGRES (inex = mpfr_set_exp_t (e, MPFR_GET_EXP (x), MPFR_RNDN));
MPFR_ASSERTD (inex == 0);
MPFR_DBGRES (inex = mpfr_get_z (ez, e, MPFR_RNDN));
MPFR_ASSERTD (inex == 0);
MPFR_SAVE_EXPO_FREE (expo);
}
}
/* Exact product. The number a is assumed to have enough allocated memory,
where the trailing bits are regarded as being part of the input numbers
(no reallocation is attempted and no check is performed as MPFR_TMP_INIT
could have been used). The arguments b and c may actually be UBF numbers
(mpfr_srcptr can be seen a bit like void *, but is stronger).
This function does not change the flags, except in case of NaN. */
void
mpfr_ubf_mul_exact (mpfr_ubf_ptr a, mpfr_srcptr b, mpfr_srcptr c)
{
MPFR_LOG_FUNC
(("b[%Pu]=%.*Rg c[%Pu]=%.*Rg",
mpfr_get_prec (b), mpfr_log_prec, b,
mpfr_get_prec (c), mpfr_log_prec, c),
("a[%Pu]=%.*Rg",
mpfr_get_prec (a), mpfr_log_prec, a));
MPFR_ASSERTD ((mpfr_ptr) a != b);
MPFR_ASSERTD ((mpfr_ptr) a != c);
MPFR_SIGN (a) = MPFR_MULT_SIGN (MPFR_SIGN (b), MPFR_SIGN (c));
if (MPFR_ARE_SINGULAR (b, c))
{
if (MPFR_IS_NAN (b) || MPFR_IS_NAN (c))
MPFR_SET_NAN (a);
else if (MPFR_IS_INF (b))
{
if (MPFR_NOTZERO (c))
MPFR_SET_INF (a);
else
MPFR_SET_NAN (a);
}
else if (MPFR_IS_INF (c))
{
if (!MPFR_IS_ZERO (b))
MPFR_SET_INF (a);
else
MPFR_SET_NAN (a);
}
else
{
MPFR_ASSERTD (MPFR_IS_ZERO(b) || MPFR_IS_ZERO(c));
MPFR_SET_ZERO (a);
}
}
else
{
mpfr_exp_t e;
mp_size_t bn, cn;
mpfr_limb_ptr ap;
mp_limb_t u, v;
int m;
/* Note about the code below: For the choice of the precision of
* the result a, one could choose PREC(b) + PREC(c), instead of
* taking whole limbs into account, but in most cases where one
* would gain one limb, one would need to copy the significand
* instead of a no-op (see the mul.c code).
* But in the case MPFR_LIMB_MSB (u) == 0, if the result fits in
* an-1 limbs, one could actually do
* mpn_rshift (ap, ap, k, GMP_NUMB_BITS - 1)
* instead of
* mpn_lshift (ap, ap, k, 1)
* to gain one limb (and reduce the precision), replacing a shift
* by another one. Would this be interesting?
*/
bn = MPFR_LIMB_SIZE (b);
cn = MPFR_LIMB_SIZE (c);
ap = MPFR_MANT (a);
if (bn == 1 && cn == 1)
{
umul_ppmm (ap[1], ap[0], MPFR_MANT(b)[0], MPFR_MANT(c)[0]);
if (ap[1] & MPFR_LIMB_HIGHBIT)
m = 0;
else
{
ap[1] = (ap[1] << 1) | (ap[0] >> (GMP_NUMB_BITS - 1));
ap[0] = ap[0] << 1;
m = 1;
}
}
else
{
u = (bn >= cn) ?
mpn_mul (ap, MPFR_MANT (b), bn, MPFR_MANT (c), cn) :
mpn_mul (ap, MPFR_MANT (c), cn, MPFR_MANT (b), bn);
if (MPFR_LIMB_MSB (u) == 0)
{
m = 1;
MPFR_DBGRES (v = mpn_lshift (ap, ap, bn + cn, 1));
MPFR_ASSERTD (v == 0);
}
else
m = 0;
}
if (! MPFR_IS_UBF (b) && ! MPFR_IS_UBF (c) &&
(e = MPFR_GET_EXP (b) + MPFR_GET_EXP (c) - m,
MPFR_EXP_IN_RANGE (e)))
{
MPFR_SET_EXP (a, e);
}
else
{
mpz_t be, ce;
mpz_init (MPFR_ZEXP (a));
/* This may involve copies of mpz_t, but exponents should not be
very large integers anyway. */
mpfr_init_get_zexp (be, b);
mpfr_init_get_zexp (ce, c);
mpz_add (MPFR_ZEXP (a), be, ce);
mpz_clear (be);
mpz_clear (ce);
mpz_sub_ui (MPFR_ZEXP (a), MPFR_ZEXP (a), m);
MPFR_SET_UBF (a);
}
}
}
int
mpfr_ubf_exp_less_p (mpfr_srcptr x, mpfr_srcptr y)
{
mpz_t xe, ye;
int c;
mpfr_init_get_zexp (xe, x);
mpfr_init_get_zexp (ye, y);
c = mpz_cmp (xe, ye) < 0;
mpz_clear (xe);
mpz_clear (ye);
return c;
}
/* Convert an mpz_t to an mpfr_exp_t, restricted to
the interval [MPFR_EXP_MIN,MPFR_EXP_MAX]. */
mpfr_exp_t
mpfr_ubf_zexp2exp (mpz_ptr ez)
{
mp_size_t n;
mpfr_eexp_t e;
mpfr_t d;
int inex;
MPFR_SAVE_EXPO_DECL (expo);
n = ABSIZ (ez); /* limb size of ez */
if (n == 0)
return 0;
MPFR_SAVE_EXPO_MARK (expo);
mpfr_init2 (d, n * GMP_NUMB_BITS);
MPFR_DBGRES (inex = mpfr_set_z (d, ez, MPFR_RNDN));
MPFR_ASSERTD (inex == 0);
e = mpfr_get_exp_t (d, MPFR_RNDZ);
mpfr_clear (d);
MPFR_SAVE_EXPO_FREE (expo);
if (MPFR_UNLIKELY (e < MPFR_EXP_MIN))
return MPFR_EXP_MIN;
if (MPFR_UNLIKELY (e > MPFR_EXP_MAX))
return MPFR_EXP_MAX;
return e;
}
/* Return the difference of the exponents of x and y, restricted to
the interval [MPFR_EXP_MIN,MPFR_EXP_MAX]. */
mpfr_exp_t
mpfr_ubf_diff_exp (mpfr_srcptr x, mpfr_srcptr y)
{
mpz_t xe, ye;
mpfr_exp_t e;
mpfr_init_get_zexp (xe, x);
mpfr_init_get_zexp (ye, y);
mpz_sub (xe, xe, ye);
mpz_clear (ye);
e = mpfr_ubf_zexp2exp (xe);
mpz_clear (xe);
return e;
}
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