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/* blow.c -- Interval blow.
Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2010,
Spaces project, Inria Lorraine
and Salsa project, INRIA Rocquencourt,
and Arenaire project, Inria Rhone-Alpes, France
and Lab. ANO, USTL (Univ. of Lille), France
This file is part of the MPFI Library.
The MPFI 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 MPFI 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 MPFI Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
MA 02110-1301, USA. */
#include "mpfi-impl.h"
/* keeps the same center and multiplies the radius by (1+fact), the result may
be grossly overestimated */
int
mpfi_blow (mpfi_ptr y, mpfi_srcptr x, double fact)
/* if c = mid (x) and r = rad (x), y = [c - (1+fact)*r , c + (1+fact)*r] */
{
mpfr_prec_t prec;
mpfr_t radius, factor;
mpfr_t centre;
int inex_diam, inex_div, inex_conv, inex_factor, inex_rad;
int inex_centre, inex_left, inex_right;
int inexact = 0;
if (MPFI_NAN_P (x)) {
mpfr_set_nan (&(y->left));
mpfr_set_nan (&(y->right));
MPFR_RET_NAN;
}
prec = mpfi_get_prec (x);
mpfr_init2 (radius, prec);
mpfr_init2 (factor, prec);
mpfr_init2 (centre, prec);
inex_diam = mpfi_diam_abs (radius, x);
if (mpfr_zero_p (radius)) {
/* x is a singleton */
return mpfi_set (y, x);
}
inex_div = mpfr_div_2exp (radius, radius, 1, MPFI_RNDU); /* either underflow
or exact*/
/* factor must be greater than 1 + |fact|, so it is not possible to perform
this addition directly in C with the double precision since the usual
rouding mode is rounding to nearest. */
inex_conv = mpfr_set_d (factor, fact < 0.0 ? -fact : fact, MPFI_RNDU);
inex_factor = mpfr_add_ui (factor, factor, 1, MPFI_RNDU);
inex_rad = mpfr_mul (radius, radius, factor, MPFI_RNDU);
inex_centre = mpfi_mid (centre, x);
inex_left = mpfr_sub (&(y->left), centre, radius, MPFI_RNDD);
inex_right = mpfr_add (&(y->right), centre, radius, MPFI_RNDU);
mpfr_clear (radius);
mpfr_clear (factor);
mpfr_clear (centre);
if ( MPFI_NAN_P (y) )
MPFR_RET_NAN;
/* do not allow -0 as lower bound */
if (mpfr_zero_p (&(y->left)) && mpfr_signbit (&(y->left))) {
mpfr_neg (&(y->left), &(y->left), MPFI_RNDU);
}
/* do not allow +0 as upper bound */
if (mpfr_zero_p (&(y->right)) && !mpfr_signbit (&(y->right))) {
mpfr_neg (&(y->right), &(y->right), MPFI_RNDD);
}
if (inex_diam || inex_div || inex_conv || inex_factor || inex_rad
|| inex_centre || inex_left)
inexact += 1;
if (inex_diam || inex_div || inex_conv || inex_factor || inex_rad
|| inex_centre || inex_right)
inexact += 2;
return inexact;
}
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