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/* mpfr_hypot -- Euclidean distance
Copyright 2001, 2002 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 <stdio.h>
#include <stdlib.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"
/* The computation of hypot of x and y is done by
hypot(x,y)= sqrt(x^2+y^2) = z
*/
int
mpfr_hypot (mpfr_ptr z, mpfr_srcptr x , mpfr_srcptr y , mp_rnd_t rnd_mode)
{
int inexact;
/* Flag exact computation */
int not_exact;
mpfr_t t, te, ti; /* auxiliary variables */
mp_prec_t Nx, Ny, Nz; /* size variables */
int Nt; /* precision of the intermediary variable */
/* particular cases */
if (MPFR_IS_NAN(x) || MPFR_IS_NAN(y))
{
MPFR_SET_NAN(z);
MPFR_RET_NAN;
}
MPFR_CLEAR_NAN(z);
if (MPFR_IS_INF(x) || MPFR_IS_INF(y))
{
MPFR_SET_INF(z);
MPFR_SET_POS(z);
MPFR_RET(0);
}
MPFR_CLEAR_INF(z);
if (MPFR_IS_ZERO(x))
return mpfr_abs (z, y, rnd_mode);
if (MPFR_IS_ZERO(y))
return mpfr_abs (z, x, rnd_mode);
/* General case */
Nx = MPFR_PREC(x); /* Precision of input variable */
Ny = MPFR_PREC(y); /* Precision of input variable */
Nz = MPFR_PREC(z); /* Precision of output variable */
/* compute the working precision -- see algorithms.ps */
Nt = MAX(MAX(Nx, Ny), Nz);
Nt = Nt - 8 + _mpfr_ceil_log2 (Nt);
/* initialise the intermediary variables */
mpfr_init (t);
mpfr_init (te);
mpfr_init (ti);
mpfr_save_emin_emax ();
do
{
Nt += 10;
not_exact = 0;
/* reactualisation of the precision */
mpfr_set_prec (t, Nt);
mpfr_set_prec (te, Nt);
mpfr_set_prec (ti, Nt);
/* computations of hypot */
if (mpfr_mul (te, x, x, GMP_RNDZ)) /* x^2 */
not_exact = 1;
if (mpfr_mul (ti, y, y, GMP_RNDZ)) /* y^2 */
not_exact = 1;
if (mpfr_add (t, te, ti, GMP_RNDZ)) /* x^2+y^2 */
not_exact = 1;
if (mpfr_sqrt (t, t, GMP_RNDZ)) /* sqrt(x^2+y^2)*/
not_exact = 1;
}
while (not_exact && mpfr_can_round (t, Nt - 2, GMP_RNDZ, rnd_mode, Nz) == 0);
inexact = mpfr_set (z, t, rnd_mode);
mpfr_clear (t);
mpfr_clear (ti);
mpfr_clear (te);
if (not_exact == 0 && inexact == 0)
inexact = 0;
else if (not_exact != 0 && inexact == 0)
inexact = -1;
mpfr_restore_emin_emax ();
return mpfr_check_range (z, inexact, rnd_mode);
}
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