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218 lines
7.1 KiB
C
218 lines
7.1 KiB
C
/* mpfr_hypot -- Euclidean distance
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Copyright 2001-2025 Free Software Foundation, Inc.
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Contributed by the Pascaline and Caramba projects, INRIA.
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This file is part of the GNU MPFR Library.
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The GNU MPFR Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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The GNU MPFR Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the GNU MPFR Library; see the file COPYING.LESSER.
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If not, see <https://www.gnu.org/licenses/>. */
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#define MPFR_NEED_LONGLONG_H
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#include "mpfr-impl.h"
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/* The computation of hypot of x and y is done by *
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* hypot(x,y)= sqrt(x^2+y^2) = z */
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int
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mpfr_hypot (mpfr_ptr z, mpfr_srcptr x, mpfr_srcptr y, mpfr_rnd_t rnd_mode)
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{
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int inexact;
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unsigned int exact; /* Warning: 0 will mean "exact" */
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mpfr_t t, te, ti; /* auxiliary variables */
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mpfr_prec_t N, Nz; /* size variables */
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mpfr_prec_t Nt; /* precision of the intermediary variable */
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mpfr_prec_t threshold;
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mpfr_exp_t Ex, sh;
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mpfr_uexp_t diff_exp;
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MPFR_SAVE_EXPO_DECL (expo);
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MPFR_ZIV_DECL (loop);
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MPFR_BLOCK_DECL (flags);
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MPFR_LOG_FUNC
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(("x[%Pd]=%.*Rg y[%Pd]=%.*Rg rnd=%d",
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mpfr_get_prec (x), mpfr_log_prec, x,
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mpfr_get_prec (y), mpfr_log_prec, y, rnd_mode),
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("z[%Pd]=%.*Rg inexact=%d",
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mpfr_get_prec (z), mpfr_log_prec, z, inexact));
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/* particular cases */
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if (MPFR_ARE_SINGULAR (x, y))
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{
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if (MPFR_IS_INF (x) || MPFR_IS_INF (y))
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{
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/* Return +inf, even when the other number is NaN. */
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MPFR_SET_INF (z);
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MPFR_SET_POS (z);
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MPFR_RET (0);
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}
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else if (MPFR_IS_NAN (x) || MPFR_IS_NAN (y))
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{
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MPFR_SET_NAN (z);
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MPFR_RET_NAN;
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}
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else if (MPFR_IS_ZERO (x))
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return mpfr_abs (z, y, rnd_mode);
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else /* y is necessarily 0 */
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return mpfr_abs (z, x, rnd_mode);
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}
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/* TODO: It may be sufficient to just compare the exponents.
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The error analysis would need to be updated. */
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if (mpfr_cmpabs (x, y) < 0)
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{
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mpfr_srcptr u;
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u = x;
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x = y;
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y = u;
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}
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/* now |x| >= |y| */
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Ex = MPFR_GET_EXP (x);
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diff_exp = (mpfr_uexp_t) Ex - MPFR_GET_EXP (y);
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N = MPFR_PREC (x); /* Precision of input variable */
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Nz = MPFR_PREC (z); /* Precision of output variable */
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threshold = (MAX (N, Nz) + (rnd_mode == MPFR_RNDN ? 1 : 0)) << 1;
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if (rnd_mode == MPFR_RNDA)
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rnd_mode = MPFR_RNDU; /* since the result is positive, RNDA = RNDU */
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/* Is |x| a suitable approximation to the precision Nz ?
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(see algorithms.tex for explanations) */
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if (diff_exp > threshold)
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/* result is |x| or |x|+ulp(|x|,Nz) */
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{
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if (MPFR_UNLIKELY (rnd_mode == MPFR_RNDU))
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{
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/* If z > abs(x), then it was already rounded up; otherwise
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z = abs(x), and we need to add one ulp due to y. */
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if (mpfr_abs (z, x, rnd_mode) == 0)
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{
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mpfr_nexttoinf (z);
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/* since mpfr_nexttoinf does not set the overflow flag,
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we have to check manually for overflow */
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if (MPFR_UNLIKELY (MPFR_IS_INF (z)))
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MPFR_SET_OVERFLOW ();
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}
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MPFR_RET (1);
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}
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else /* MPFR_RNDZ, MPFR_RNDD, MPFR_RNDN */
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{
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if (MPFR_LIKELY (Nz >= N))
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{
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mpfr_abs (z, x, rnd_mode); /* exact */
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MPFR_RET (-1);
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}
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else
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{
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MPFR_SET_EXP (z, Ex);
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MPFR_SET_SIGN (z, MPFR_SIGN_POS);
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MPFR_RNDRAW_GEN (inexact, z, MPFR_MANT (x), N, rnd_mode, 1,
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goto addoneulp,
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if (MPFR_UNLIKELY (++ MPFR_EXP (z) >
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__gmpfr_emax))
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return mpfr_overflow (z, rnd_mode, 1);
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);
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if (MPFR_UNLIKELY (inexact == 0))
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inexact = -1;
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MPFR_RET (inexact);
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}
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}
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}
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/* General case */
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N = MAX (MPFR_PREC (x), MPFR_PREC (y));
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/* working precision */
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Nt = Nz + MPFR_INT_CEIL_LOG2 (Nz) + 4;
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mpfr_init2 (t, Nt);
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mpfr_init2 (te, Nt);
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mpfr_init2 (ti, Nt);
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MPFR_SAVE_EXPO_MARK (expo);
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/* Scale x and y to avoid any overflow and underflow in x^2
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(as |x| >= |y|), and to limit underflow cases for y or y^2.
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We have: x = Mx * 2^Ex with 1/2 <= |Mx| < 1, and we choose:
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sh = floor((Emax - 1) / 2) - Ex.
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Thus (x * 2^sh)^2 = Mx^2 * 2^(2*floor((Emax-1)/2)), which has an
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exponent of at most Emax - 1. Therefore (x * 2^sh)^2 + (y * 2^sh)^2
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will have an exponent of at most Emax, even after rounding as we
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round toward zero. Using a larger sh wouldn't guarantee an absence
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of overflow. Note that the scaling of y can underflow only when the
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target precision is huge, otherwise the case would already have been
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handled by the diff_exp > threshold code; but this case is avoided
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thanks to a FMA (this problem is transferred to the FMA code). */
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sh = (mpfr_get_emax () - 1) / 2 - Ex;
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/* FIXME: ti is subject to underflow. Solution: x and y could be
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aliased with MPFR_ALIAS, and if need be, the aliases be pre-scaled
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exactly as UBF, so that x^2 + y^2 is in range. Then call mpfr_fmma
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and the square root, and scale the result. The error analysis would
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be simpler.
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Note: mpfr_fmma is currently not optimized. */
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MPFR_ZIV_INIT (loop, Nt);
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for (;;)
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{
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mpfr_prec_t err;
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exact = mpfr_mul_2si (te, x, sh, MPFR_RNDZ);
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exact |= mpfr_mul_2si (ti, y, sh, MPFR_RNDZ);
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exact |= mpfr_sqr (te, te, MPFR_RNDZ);
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/* Use fma in order to avoid underflow when diff_exp<=MPFR_EMAX_MAX-2 */
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exact |= mpfr_fma (t, ti, ti, te, MPFR_RNDZ);
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exact |= mpfr_sqrt (t, t, MPFR_RNDZ);
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err = Nt < N ? 4 : 2;
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if (MPFR_LIKELY (exact == 0
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|| MPFR_CAN_ROUND (t, Nt-err, Nz, rnd_mode)))
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break;
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MPFR_ZIV_NEXT (loop, Nt);
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mpfr_set_prec (t, Nt);
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mpfr_set_prec (te, Nt);
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mpfr_set_prec (ti, Nt);
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}
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MPFR_ZIV_FREE (loop);
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MPFR_BLOCK (flags, inexact = mpfr_div_2si (z, t, sh, rnd_mode));
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MPFR_ASSERTD (exact == 0 || inexact != 0 || rnd_mode == MPFR_RNDF);
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mpfr_clear (t);
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mpfr_clear (ti);
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mpfr_clear (te);
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/*
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exact inexact
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0 0 result is exact, ternary flag is 0
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0 non zero t is exact, ternary flag given by inexact
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1 0 impossible (see above)
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1 non zero ternary flag given by inexact
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*/
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MPFR_SAVE_EXPO_FREE (expo);
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if (MPFR_OVERFLOW (flags))
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MPFR_SET_OVERFLOW ();
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/* hypot(x,y) >= |x|, thus underflow is not possible. */
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return mpfr_check_range (z, inexact, rnd_mode);
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}
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