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/* mpfr_fmma, mpfr_fmms -- Compute a*b +/- c*d
Copyright 2014-2016 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. */
#include "mpfr-impl.h"
static int
mpfr_fmma_slow (mpfr_ptr z, mpfr_srcptr a, mpfr_srcptr b, mpfr_srcptr c,
mpfr_srcptr d, mpfr_rnd_t rnd)
{
mpfr_t ab, cd;
int inex;
mpfr_init2 (ab, MPFR_PREC(a) + MPFR_PREC(b));
mpfr_init2 (cd, MPFR_PREC(c) + MPFR_PREC(d));
/* FIXME: The following multiplications may overflow or underflow
(even more often with the fact that the exponent range is not
extended), in which case the result is not exact. This should
be solved with future unbounded floats. */
mpfr_mul (ab, a, b, MPFR_RNDZ); /* exact */
mpfr_mul (cd, c, d, MPFR_RNDZ); /* exact */
inex = mpfr_add (z, ab, cd, rnd);
mpfr_clear (ab);
mpfr_clear (cd);
return inex;
}
/* z <- a*b + c*d */
static int
mpfr_fmma_fast (mpfr_ptr z, mpfr_srcptr a, mpfr_srcptr b, mpfr_srcptr c,
mpfr_srcptr d, mpfr_rnd_t rnd)
{
/* Assumes that a, b, c, d are finite and non-zero; so any multiplication
of two of them yielding an infinity is an overflow, and a
multiplication yielding 0 is an underflow.
Assumes further that z is distinct from a, b, c, d. */
int inex;
mpfr_t u, v;
mp_size_t an, bn, cn, dn;
mpfr_limb_ptr up, vp;
MPFR_TMP_DECL(marker);
MPFR_SAVE_EXPO_DECL (expo);
MPFR_TMP_MARK(marker);
MPFR_SAVE_EXPO_MARK (expo);
/* u=a*b, v=c*d exactly */
an = MPFR_LIMB_SIZE(a);
bn = MPFR_LIMB_SIZE(b);
cn = MPFR_LIMB_SIZE(c);
dn = MPFR_LIMB_SIZE(d);
MPFR_TMP_INIT (up, u, (an + bn) * GMP_NUMB_BITS, an + bn);
MPFR_TMP_INIT (vp, v, (cn + dn) * GMP_NUMB_BITS, cn + dn);
/* u <- a*b */
if (an >= bn)
mpn_mul (up, MPFR_MANT(a), an, MPFR_MANT(b), bn);
else
mpn_mul (up, MPFR_MANT(b), bn, MPFR_MANT(a), an);
if ((up[an + bn - 1] & MPFR_LIMB_HIGHBIT) == 0)
{
mpn_lshift (up, up, an + bn, 1);
/* EXP(a) and EXP(b) are in [1-2^(n-2), 2^(n-2)-1] where
mpfr_exp_t has is n-bit wide, thus EXP(a)+EXP(b) is in
[2-2^(n-1), 2^(n-1)-2]. We use the fact here that 2*MPFR_EMIN_MIN-1
is a valid exponent (see mpfr-impl.h). However we don't use
MPFR_SET_EXP() which only allows the restricted exponent range
[1-2^(n-2), 2^(n-2)-1]. */
MPFR_EXP(u) = MPFR_EXP(a) + MPFR_EXP(b) - 1;
}
else
MPFR_EXP(u) = MPFR_EXP(a) + MPFR_EXP(b);
/* v <- c*d */
if (cn >= dn)
mpn_mul (vp, MPFR_MANT(c), cn, MPFR_MANT(d), dn);
else
mpn_mul (vp, MPFR_MANT(d), dn, MPFR_MANT(c), cn);
if ((vp[cn + dn - 1] & MPFR_LIMB_HIGHBIT) == 0)
{
mpn_lshift (vp, vp, cn + dn, 1);
MPFR_EXP(v) = MPFR_EXP(c) + MPFR_EXP(d) - 1;
}
else
MPFR_EXP(v) = MPFR_EXP(c) + MPFR_EXP(d);
MPFR_PREC(u) = (an + bn) * GMP_NUMB_BITS;
MPFR_PREC(v) = (cn + dn) * GMP_NUMB_BITS;
MPFR_SIGN(u) = MPFR_MULT_SIGN(MPFR_SIGN(a), MPFR_SIGN(b));
MPFR_SIGN(v) = MPFR_MULT_SIGN(MPFR_SIGN(c), MPFR_SIGN(d));
/* tentatively compute z as u+v; here we need z to be distinct
from a, b, c, d to avoid losing the input values in case we
need to call mpfr_fmma_slow */
/* FIXME: The above comment is no longer valid. Anyway, with
unbounded floats (based on an exact multiplication like above),
it will no longer be necessary to distinguish fast and slow. */
inex = mpfr_add (z, u, v, rnd);
MPFR_TMP_FREE(marker);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (z, inex, rnd);
}
/* z <- a*b + c*d */
int
mpfr_fmma (mpfr_ptr z, mpfr_srcptr a, mpfr_srcptr b, mpfr_srcptr c,
mpfr_srcptr d, mpfr_rnd_t rnd)
{
mpfr_limb_ptr zp = MPFR_MANT(z);
return (mpfr_regular_p (a) && mpfr_regular_p (b) && mpfr_regular_p (c) &&
mpfr_regular_p (d) && zp != MPFR_MANT(a) && zp != MPFR_MANT(b) &&
zp != MPFR_MANT(c) && zp != MPFR_MANT(d))
? mpfr_fmma_fast (z, a, b, c, d, rnd)
: mpfr_fmma_slow (z, a, b, c, d, rnd);
}
/* z <- a*b - c*d */
int
mpfr_fmms (mpfr_ptr z, mpfr_srcptr a, mpfr_srcptr b, mpfr_srcptr c,
mpfr_srcptr d, mpfr_rnd_t rnd)
{
mpfr_t minus_c;
MPFR_ALIAS (minus_c, c, -MPFR_SIGN(c), MPFR_EXP(c));
return mpfr_fmma (z, a, b, minus_c, d, rnd);
}
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