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/* mpfr_mul -- multiply two floating-point numbers
Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2005
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, inexact;
mp_exp_t ax, ax2;
mp_limb_t *tmp;
mp_limb_t b1;
mp_prec_t bq, cq;
mp_size_t 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 = MPFR_MULT_SIGN (MPFR_SIGN (b), MPFR_SIGN (c));
if (MPFR_IS_INF (b))
{
if (!MPFR_IS_ZERO (c))
{
MPFR_SET_SIGN (a, sign);
MPFR_SET_INF (a);
MPFR_RET (0);
}
else
{
MPFR_SET_NAN (a);
MPFR_RET_NAN;
}
}
else if (MPFR_IS_INF (c))
{
if (!MPFR_IS_ZERO (b))
{
MPFR_SET_SIGN (a, sign);
MPFR_SET_INF (a);
MPFR_RET(0);
}
else
{
MPFR_SET_NAN (a);
MPFR_RET_NAN;
}
}
else
{
MPFR_ASSERTD (MPFR_IS_ZERO(b) || MPFR_IS_ZERO(c));
MPFR_SET_SIGN (a, sign);
MPFR_SET_ZERO (a);
MPFR_RET (0);
}
}
MPFR_CLEAR_FLAGS (a);
sign = MPFR_MULT_SIGN (MPFR_SIGN (b), MPFR_SIGN (c));
ax = MPFR_GET_EXP (b) + 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. */
/* FIXME: Useful since we do an exponent check after ?
* It is useful iff the precision is big, there is an overflow
* and we are doing further mults...*/
#ifdef HUGE
if (MPFR_UNLIKELY (ax > __gmpfr_emax + 1))
return mpfr_overflow (a, rnd_mode, sign);
if (MPFR_UNLIKELY (ax < __gmpfr_emin - 2))
return mpfr_underflow (a, rnd_mode == GMP_RNDN ? GMP_RNDZ : rnd_mode,
sign);
#endif
bq = MPFR_PREC (b);
cq = MPFR_PREC (c);
MPFR_ASSERTD (bq+cq > bq); /* PREC_MAX is /2 so no integer overflow */
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;
MPFR_ASSERTD (tn <= k); /* tn <= k, thus no int overflow */
/* 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 */
/* if the mantissas of b and c are uniformly distributed in ]1/2, 1],
then their product is in ]1/4, 1/2] with probability 2*ln(2)-1 ~ 0.386
and in [1/2, 1] with probability 2-2*ln(2) ~ 0.614 */
tmp += k - tn;
if (MPFR_UNLIKELY (b1 == 0))
mpn_lshift (tmp, tmp, tn, 1); /* tn <= k, so no stack corruption */
ax2 = ax + (mp_exp_t) (b1 - 1);
MPFR_RNDRAW (inexact, a, tmp, bq+cq, rnd_mode, sign, ax2++);
TMP_FREE (marker);
MPFR_EXP (a) = ax2; /* Can't use MPFR_SET_EXP: Exponent may be out of range */
MPFR_SET_SIGN (a, sign);
if (MPFR_UNLIKELY (ax2 > __gmpfr_emax))
return mpfr_overflow (a, rnd_mode, sign);
if (MPFR_UNLIKELY (ax2 < __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
&& (ax + (mp_exp_t) b1 < __gmpfr_emin
|| (mpfr_powerof2_raw (b) && mpfr_powerof2_raw (c))))
rnd_mode = GMP_RNDZ;
return mpfr_underflow (a, rnd_mode, sign);
}
return inexact;
}
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