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/* mpfr_hypot -- Euclidean distance
Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc.
Contributed by the Arenaire and Cacao projects, INRIA.
This file is part of the GNU MPFR Library.
The GNU 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 GNU 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 GNU MPFR 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. */
#define MPFR_NEED_LONGLONG_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, exact;
mpfr_t t, te, ti; /* auxiliary variables */
mp_prec_t N, Nz; /* size variables */
mp_prec_t Nt; /* precision of the intermediary variable */
mp_prec_t threshold;
mp_exp_t Ex, sh;
mp_exp_unsigned_t diff_exp;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_ZIV_DECL (loop);
MPFR_BLOCK_DECL (flags);
/* particular cases */
if (MPFR_ARE_SINGULAR (x, y))
{
if (MPFR_IS_INF (x) || MPFR_IS_INF (y))
{
/* Return +inf, even when the other number is NaN. */
MPFR_SET_INF (z);
MPFR_SET_POS (z);
MPFR_RET (0);
}
else if (MPFR_IS_NAN (x) || MPFR_IS_NAN (y))
{
MPFR_SET_NAN (z);
MPFR_RET_NAN;
}
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 u;
u = x;
x = y;
y = u;
}
/* now |x| >= |y| */
Ex = MPFR_GET_EXP (x);
diff_exp = (mp_exp_unsigned_t) Ex - MPFR_GET_EXP (y);
N = MPFR_PREC (x); /* Precision of input variable */
Nz = MPFR_PREC (z); /* Precision of output variable */
threshold = (MAX (N, Nz) + (rnd_mode == GMP_RNDN ? 1 : 0)) << 1;
/* Is |x| a suitable approximation to the precision Nz ?
(see algorithms.tex for explanations) */
if (diff_exp > threshold)
/* result is |x| or |x|+ulp(|x|,Nz) */
{
if (MPFR_UNLIKELY (rnd_mode == GMP_RNDU))
{
/* If z > abs(x), then it was already rounded up; otherwise
z = abs(x), and we need to add one ulp due to y. */
if (mpfr_abs (z, x, rnd_mode) == 0)
mpfr_nexttoinf (z);
MPFR_RET (1);
}
else /* GMP_RNDZ, GMP_RNDD, GMP_RNDN */
{
if (MPFR_LIKELY (Nz >= N))
{
mpfr_abs (z, x, rnd_mode); /* exact */
MPFR_RET (-1);
}
else
{
MPFR_SET_EXP (z, Ex);
MPFR_SET_SIGN (z, 1);
MPFR_RNDRAW_GEN (inexact, z, MPFR_MANT (x), N, rnd_mode, 1,
goto addoneulp,
if (MPFR_UNLIKELY (++ MPFR_EXP (z) >
__gmpfr_emax))
return mpfr_overflow (z, rnd_mode, 1);
);
if (MPFR_UNLIKELY (inexact == 0))
inexact = -1;
MPFR_RET (inexact);
}
}
}
/* General case */
N = MAX (MPFR_PREC (x), MPFR_PREC (y));
/* working precision */
Nt = Nz + MPFR_INT_CEIL_LOG2 (Nz) + 4;
mpfr_init2 (t, Nt);
mpfr_init2 (te, Nt);
mpfr_init2 (ti, Nt);
MPFR_SAVE_EXPO_MARK (expo);
/* Scale x and y to avoid overflow/underflow in x^2 and overflow in y^2
(as |x| >= |y|). The scaling of y can underflow only when the target
precision is huge, otherwise the case would already have been handled
by the diff_exp > threshold code. */
sh = mpfr_get_emax () / 2 - Ex - 1;
MPFR_ZIV_INIT (loop, Nt);
for (;;)
{
mp_prec_t err;
exact = mpfr_mul_2si (te, x, sh, GMP_RNDZ);
exact |= mpfr_mul_2si (ti, y, sh, GMP_RNDZ);
exact |= mpfr_sqr (te, te, GMP_RNDZ);
/* Use fma in order to avoid underflow when diff_exp<=MPFR_EMAX_MAX-2 */
exact |= mpfr_fma (t, ti, ti, te, GMP_RNDZ);
exact |= mpfr_sqrt (t, t, GMP_RNDZ);
err = Nt < N ? 4 : 2;
if (MPFR_LIKELY (exact == 0
|| MPFR_CAN_ROUND (t, Nt-err, Nz, rnd_mode)))
break;
MPFR_ZIV_NEXT (loop, Nt);
mpfr_set_prec (t, Nt);
mpfr_set_prec (te, Nt);
mpfr_set_prec (ti, Nt);
}
MPFR_ZIV_FREE (loop);
MPFR_BLOCK (flags, inexact = mpfr_div_2si (z, t, sh, rnd_mode));
MPFR_ASSERTD (exact == 0 || inexact != 0);
mpfr_clear (t);
mpfr_clear (ti);
mpfr_clear (te);
/*
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_SAVE_EXPO_FREE (expo);
if (MPFR_OVERFLOW (flags))
mpfr_set_overflow ();
/* hypot(x,y) >= |x|, thus underflow is not possible. */
return mpfr_check_range (z, inexact, rnd_mode);
}