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/* mpfr_hypot -- Euclidean distance
Copyright 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"
/* 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 */
mp_prec_t Nt; /* precision of the intermediary variable */
mp_exp_t Ex, Ey, sh;
mp_exp_unsigned_t diff_exp;
/* particular cases */
if (MPFR_ARE_SINGULAR(x,y))
{
if (MPFR_IS_NAN(x) || MPFR_IS_NAN(y))
{
MPFR_SET_NAN(z);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF(x) || MPFR_IS_INF(y))
{
MPFR_SET_INF(z);
MPFR_SET_POS(z);
MPFR_RET(0);
}
else if (MPFR_IS_ZERO(x))
return mpfr_abs (z, y, rnd_mode);
else /* y is necessarily 0 */
return mpfr_abs (z, x, rnd_mode);
}
MPFR_CLEAR_FLAGS(z);
if (mpfr_cmpabs (x, y) < 0)
{
mpfr_srcptr t;
t = x;
x = y;
y = t;
}
/* now |x| >= |y| */
Ex = MPFR_GET_EXP (x);
Ey = MPFR_GET_EXP (y);
diff_exp = (mp_exp_unsigned_t) Ex - Ey;
Nz = MPFR_PREC(z); /* Precision of output variable */
/* we have x < 2^Ex thus x^2 < 2^(2*Ex),
and ulp(x) = 2^(Ex-Nx) thus ulp(x^2) >= 2^(2*Ex-2*Nx).
y does not overlap with the result when
x^2+y^2 < (|x| + 1/2*ulp(x,Nz))^2 = x^2 + |x|*ulp(x,Nz) + 1/4*ulp(x,Nz)^2,
i.e. a sufficient condition is y^2 < |x|*ulp(x,Nz),
or 2^(2*Ey) <= 2^(2*Ex-1-Nz), i.e. 2*diff_exp > Nz.
Warning: this is true only for Nx <= Nz, otherwise the trailing bits
of x may be already very close to 1/2*ulp(x,Nz)!
*/
if (MPFR_PREC(x) <= Nz && diff_exp > Nz / 2) /* result is |x| or |x|+ulp(|x|,Nz) */
{
if (rnd_mode == GMP_RNDU)
{
/* if z > abs(x), then it was already rounded up */
if (mpfr_abs (z, x, rnd_mode) <= 0)
mpfr_add_one_ulp (z, rnd_mode);
return 1;
}
else /* GMP_RNDZ, GMP_RNDD, GMP_RNDN */
{
inexact = mpfr_abs (z, x, rnd_mode);
return (inexact) ? inexact : -1;
}
}
/* General case */
Nx = MPFR_PREC(x); /* Precision of input variable */
Ny = MPFR_PREC(y); /* Precision of input variable */
/* compute the working precision -- see algorithms.ps */
Nt = MAX(MAX(MAX(Nx, Ny), Nz), 8);
Nt = Nt - 8 + __gmpfr_ceil_log2 (Nt);
/* initialise the intermediary variables */
mpfr_init (t);
mpfr_init (te);
mpfr_init (ti);
mpfr_save_emin_emax ();
sh = MAX(0,MIN(Ex,Ey));
do
{
Nt += 10;
not_exact = 0;
/* reactualization of the precision */
mpfr_set_prec (t, Nt);
mpfr_set_prec (te, Nt);
mpfr_set_prec (ti, Nt);
/* computations of hypot */
mpfr_div_2ui (te, x, sh, GMP_RNDZ); /* exact since Nt >= Nx */
if (mpfr_mul (te, te, te, GMP_RNDZ)) /* x^2 */
not_exact = 1;
mpfr_div_2ui (ti, y, sh, GMP_RNDZ); /* exact since Nt >= Ny */
if (mpfr_mul (ti, ti, ti, 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_RNDN, GMP_RNDZ,
Nz + (rnd_mode == GMP_RNDN)));
inexact = mpfr_mul_2ui (z, t, sh, rnd_mode);
/* if not_exact=1, necessarily the last (Nt-Nz) bits of t are not all zero,
otherwise it would not have been possible to round correctly */
MPFR_ASSERTD(not_exact == 0 || inexact != 0);
mpfr_clear (t);
mpfr_clear (ti);
mpfr_clear (te);
/*
not_exact inexact
0 0 result is exact, ternary flag is 0
0 non zero t is exact, ternary flag given by inexact
1 0 impossible (see above)
1 non zero ternary flag given by inexact
*/
mpfr_restore_emin_emax ();
return mpfr_check_range (z, inexact, rnd_mode);
}
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