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/* mpfr_mul -- multiply two floating-point numbers
Copyright 1999, 2000, 2001, 2002, 2003, 2004 Free Software Foundation, Inc.
This file is part of the MPFR Library.
The 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 2.1 of the License, or (at your
option) any later version.
The 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 MPFR Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */
#include "mpfr-impl.h"
int
mpfr_mul (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mp_rnd_t rnd_mode)
{
int sign_product, cc, inexact;
mp_exp_t ax, bx, cx;
mp_limb_t *tmp;
mp_limb_t b1;
mp_prec_t aq, bq, cq;
mp_size_t an, bn, cn, tn, k;
TMP_DECL(marker);
/* deal with special cases */
if (MPFR_ARE_SINGULAR(b,c))
{
if (MPFR_IS_NAN(b) || MPFR_IS_NAN(c))
{
MPFR_SET_NAN(a);
MPFR_RET_NAN;
}
sign_product = MPFR_MULT_SIGN( MPFR_SIGN(b) , MPFR_SIGN(c) );
if (MPFR_IS_INF(b))
{
if (MPFR_IS_INF(c) || MPFR_NOTZERO(c))
{
MPFR_SET_SIGN(a,sign_product);
MPFR_SET_INF(a);
MPFR_RET(0); /* exact */
}
else
{
MPFR_SET_NAN(a);
MPFR_RET_NAN;
}
}
else if (MPFR_IS_INF(c))
{
if (MPFR_NOTZERO(b))
{
MPFR_SET_SIGN(a, sign_product);
MPFR_SET_INF(a);
MPFR_RET(0); /* exact */
}
else
{
MPFR_SET_NAN(a);
MPFR_RET_NAN;
}
}
else
{
MPFR_ASSERTD(MPFR_IS_ZERO(b) || MPFR_IS_ZERO(c));
MPFR_SET_SIGN(a, sign_product);
MPFR_SET_ZERO(a);
MPFR_RET(0); /* 0 * 0 is exact */
}
}
MPFR_CLEAR_FLAGS(a);
sign_product = MPFR_MULT_SIGN( MPFR_SIGN(b) , MPFR_SIGN(c) );
bx = MPFR_GET_EXP (b);
cx = MPFR_GET_EXP (c);
/* Note: the exponent of the exact result will be e = bx + cx + ec with
ec in {-1,0,1} and the following assumes that e is representable. */
/* These ASSERT should be always true */
MPFR_ASSERTN(MPFR_EMAX_MAX <= (MPFR_EXP_MAX >> 1));
MPFR_ASSERTN(MPFR_EMIN_MIN >= -(MPFR_EXP_MAX >> 1));
/* FIXME: Usefull since we do an exponent check after ?
* It is usefull iff the precision is big, there is an overflow
* and we are doing further mults...*/
#ifdef HUGE
if (MPFR_UNLIKELY(bx + cx > __gmpfr_emax + 1))
return mpfr_set_overflow (a, rnd_mode, sign_product);
if (MPFR_UNLIKELY(bx + cx < __gmpfr_emin - 2))
return mpfr_set_underflow (a, rnd_mode == GMP_RNDN ? GMP_RNDZ : rnd_mode,
sign_product);
#endif
aq = MPFR_PREC(a);
bq = MPFR_PREC(b);
cq = MPFR_PREC(c);
/* Set the sign: can't be done before to let the multiply done */
MPFR_SET_SIGN(a, sign_product);
MPFR_ASSERTD(bq+cq > bq); /* PREC_MAX is /2 so no integer overflow */
an = (aq+BITS_PER_MP_LIMB-1)/BITS_PER_MP_LIMB; /* number of limbs of a */
bn = (bq+BITS_PER_MP_LIMB-1)/BITS_PER_MP_LIMB; /* number of limbs of b */
cn = (cq+BITS_PER_MP_LIMB-1)/BITS_PER_MP_LIMB; /* number of limbs of c */
k = bn + cn; /* effective nb of limbs used by b*c (= tn or tn+1) below */
tn = (bq + cq + BITS_PER_MP_LIMB - 1) / BITS_PER_MP_LIMB;
/* <= k, thus no int overflow */
MPFR_ASSERTD(tn <= k);
/* Check for no size_t overflow*/
MPFR_ASSERTD((size_t) k <= ((size_t) ~0) / BYTES_PER_MP_LIMB);
TMP_MARK(marker);
tmp = (mp_limb_t *) TMP_ALLOC((size_t) k * BYTES_PER_MP_LIMB);
/* multiplies two mantissa in temporary allocated space */
b1 = (MPFR_LIKELY(bn >= cn)) ?
mpn_mul (tmp, MPFR_MANT(b), bn, MPFR_MANT(c), cn)
: mpn_mul (tmp, MPFR_MANT(c), cn, MPFR_MANT(b), bn);
/* now tmp[0]..tmp[k-1] contains the product of both mantissa,
with tmp[k-1]>=2^(BITS_PER_MP_LIMB-2) */
b1 >>= BITS_PER_MP_LIMB - 1; /* msb from the product */
tmp += k - tn;
if (MPFR_UNLIKELY(b1 == 0))
mpn_lshift (tmp, tmp, tn, 1);
cc = mpfr_round_raw (MPFR_MANT(a), tmp, bq + cq,
MPFR_IS_NEG_SIGN(sign_product), aq, rnd_mode, &inexact);
if (MPFR_UNLIKELY(cc)) /* cc = 1 ==> result is a power of two */
MPFR_MANT(a)[an-1] = MPFR_LIMB_HIGHBIT;
TMP_FREE(marker);
ax = (bx + cx) + (mp_exp_t) (b1 - 1 + cc);
if (MPFR_UNLIKELY( ax > __gmpfr_emax))
return mpfr_set_overflow (a, rnd_mode, sign_product);
if (MPFR_UNLIKELY( ax < __gmpfr_emin))
{
/* In the rounding to the nearest mode, if the exponent of the exact
result (i.e. before rounding, i.e. without taking cc into account)
is < __gmpfr_emin - 1 or the exact result is a power of 2 (i.e. if
both arguments are powers of 2), then round to zero. */
if (rnd_mode == GMP_RNDN &&
((bx + cx) + (mp_exp_t) b1 < __gmpfr_emin ||
(mpfr_powerof2_raw (b) && mpfr_powerof2_raw (c))))
rnd_mode = GMP_RNDZ;
return mpfr_set_underflow (a, rnd_mode, sign_product);
}
MPFR_SET_EXP (a, ax);
return inexact;
}
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