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217 lines
6.7 KiB
C
217 lines
6.7 KiB
C
/* tballs -- test file for complex ball arithmetic.
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Copyright (C) 2018, 2020, 2021, 2022 INRIA
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This file is part of GNU MPC.
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GNU MPC is free software; you can redistribute it and/or modify it under
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the terms of the GNU Lesser General Public License as published by the
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Free Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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GNU MPC is distributed in the hope that it will be useful, but WITHOUT ANY
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WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
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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 this program. If not, see http://www.gnu.org/licenses/ .
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*/
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#include "mpc-tests.h"
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#include "mpc-impl.h"
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/* For the alternative AGM implementation, we need all the power of
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this include file. */
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static int
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mpc_mpcb_agm (mpc_ptr rop, mpc_srcptr opa, mpc_srcptr opb, mpc_rnd_t rnd)
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/* Alternative implementation of mpc_agm that uses complex balls. */
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{
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mpfr_prec_t prec;
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mpc_t b0, diff;
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mpcb_t a, b, an, bn, anp1, bnp1, res;
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mpfr_exp_t exp_an, exp_diff;
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mpcr_t rab;
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int cmp, equal, re_zero, im_zero, ok, inex;
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if (!mpc_fin_p (opa) || !mpc_fin_p (opb)
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|| mpc_zero_p (opa) || mpc_zero_p (opb)
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|| mpc_cmp (opa, opb) == 0
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|| ( mpfr_sgn (mpc_realref (opa)) == -mpfr_sgn (mpc_realref (opb))
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&& mpfr_sgn (mpc_imagref (opa)) == -mpfr_sgn (mpc_imagref (opb))
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&& mpfr_cmpabs (mpc_realref (opa), mpc_realref (opb)) == 0
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&& mpfr_cmpabs (mpc_imagref (opa), mpc_imagref (opb)) == 0)
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|| ( mpfr_zero_p (mpc_imagref (opa))
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&& mpfr_zero_p (mpc_imagref (opb))
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&& mpfr_sgn (mpc_realref (opa)) == mpfr_sgn (mpc_realref (opb)))
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|| ( mpfr_zero_p (mpc_realref (opa))
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&& mpfr_zero_p (mpc_realref (opb))
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&& mpfr_sgn (mpc_imagref (opa)) == mpfr_sgn (mpc_imagref (opb))))
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/* Special cases that are handled separately by mpc_agm; there is
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no need to rewrite them. */
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return mpc_agm (rop, opa, opb, rnd);
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/* Exclude the case of angle 0, also handled separately by mpc_agm. */
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mpc_init2 (b0, 2);
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mpc_div (b0, opb, opa, MPC_RNDZZ);
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if (mpfr_zero_p (mpc_imagref (b0)) && mpfr_sgn (mpc_realref (b0)) > 0) {
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mpc_clear (b0);
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return mpc_agm (rop, opa, opb, rnd);
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}
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mpc_clear (b0);
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cmp = mpc_cmp_abs (opa, opb);
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mpcb_init (a);
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mpcb_init (b);
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mpcb_init (an);
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mpcb_init (bn);
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mpcb_init (anp1);
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mpcb_init (bnp1);
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mpcb_init (res);
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prec = MPC_MAX (MPC_MAX (MPC_MAX_PREC (opa), MPC_MAX_PREC (opb)),
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MPC_MAX_PREC (rop) + 20);
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/* So copying opa and opb will be exact, and there is a small safety
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margin for the result. */
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do {
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mpcb_set_prec (a, prec);
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mpcb_set_prec (b, prec);
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mpcb_set_prec (an, prec);
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mpcb_set_prec (bn, prec);
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mpcb_set_prec (anp1, prec);
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mpcb_set_prec (bnp1, prec);
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mpcb_set_prec (res, prec);
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/* TODO: Think about the mpcb_set variants; mpcb_set_c, for instance,
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modifies the precision. It is probably better to add a precision
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parameter to mpcb_init and potentially round with mpcb_set_xxx. */
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mpc_set (a->c, opa, MPC_RNDNN); /* exact */
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mpcr_set_zero (a->r);
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mpc_set (b->c, opb, MPC_RNDNN);
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mpcr_set_zero (b->r);
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mpc_set_ui_ui (an->c, 1, 0, MPC_RNDNN);
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mpcr_set_zero (an->r);
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if (cmp >= 0)
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mpcb_div (bn, b, a);
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else
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mpcb_div (bn, a, b);
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/* Iterate until there is a fixed point or (often one iteration
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earlier) the arithmetic and the geometric mean coincide. */
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do {
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mpcb_add (anp1, an, bn);
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mpcb_div_2ui (anp1, anp1, 1);
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mpcb_mul (bnp1, an, bn);
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mpcb_sqrt (bnp1, bnp1);
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/* Be aware of the branch cut! The current function does
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what is needed here. */
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equal = mpc_cmp (an->c, bn->c) == 0
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|| ( mpc_cmp (an->c, anp1->c) == 0
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&& mpc_cmp (bn->c, bnp1->c) == 0);
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mpcb_set (an, anp1);
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mpcb_set (bn, bnp1);
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} while (!equal);
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/* Check whether we can conclude, see the error analysis in
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algorithms.tex. */
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if (mpcr_inf_p (anp1->r))
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ok = 0;
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else {
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mpc_init2 (diff, prec);
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mpc_sub (diff, an->c, bn->c, MPC_RNDZZ);
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/* FIXME: We would need to round away, but this is not yet
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implemented. */
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re_zero = mpfr_zero_p (mpc_realref (diff));
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if (!re_zero)
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MPFR_ADD_ONE_ULP (mpc_realref (diff));
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im_zero = mpfr_zero_p (mpc_imagref (diff));
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if (!im_zero)
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MPFR_ADD_ONE_ULP (mpc_imagref (diff));
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mpcb_set (res, anp1);
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if (re_zero && im_zero)
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mpcr_set_zero (rab);
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else {
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exp_an = MPC_MIN (mpfr_get_exp (mpc_realref (an->c)),
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mpfr_get_exp (mpc_imagref (an->c))) - 1;
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if (re_zero)
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exp_diff = mpfr_get_exp (mpc_imagref (diff)) + 1;
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else if (im_zero)
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exp_diff = mpfr_get_exp (mpc_realref (diff)) + 1;
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else
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exp_diff = MPC_MAX (mpfr_get_exp (mpc_realref (diff)),
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mpfr_get_exp (mpc_imagref (diff)) + 1);
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mpcr_set_one (rab);
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(rab->exp) += (exp_diff - exp_an);
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/* TODO: Should be done by an mpcr function. */
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}
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mpcr_add (rab, rab, an->r);
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(rab->exp)++;
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mpcr_add (res->r, rab, bn->r);
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/* r = 2 * (rab + an->r) + bn->r */
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if (cmp >= 0)
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mpcb_mul (res, res, a);
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else
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mpcb_mul (res, res, b);
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ok = mpcb_can_round (res, MPC_PREC_RE (rop), MPC_PREC_IM (rop),
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rnd);
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mpc_clear (diff);
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}
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if (!ok)
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prec += prec + mpcr_get_exp (res->r);
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} while (!ok);
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inex = mpcb_round (rop, res, rnd);
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mpcb_clear (a);
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mpcb_clear (b);
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mpcb_clear (an);
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mpcb_clear (bn);
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mpcb_clear (anp1);
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mpcb_clear (bnp1);
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mpcb_clear (res);
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return inex;
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}
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static int
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test_agm (void)
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{
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mpfr_prec_t prec;
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mpc_t a, b, agm1, agm2;
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mpc_rnd_t rnd = MPC_RNDDU;
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int inex, inexb, ok;
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prec = 1000;
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mpc_init2 (a, prec);
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mpc_init2 (b, prec);
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mpc_set_si_si (a, 100, 0, MPC_RNDNN);
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mpc_set_si_si (b, 0, 100, MPC_RNDNN);
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mpc_init2 (agm1, prec);
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mpc_init2 (agm2, prec);
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inex = mpc_agm (agm1, a, b, rnd);
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inexb = mpc_mpcb_agm (agm2, a, b, rnd);
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ok = (inex == inexb) && (mpc_cmp (agm1, agm2) == 0);
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mpc_clear (a);
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mpc_clear (b);
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mpc_clear (agm1);
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mpc_clear (agm2);
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return !ok;
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}
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int
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main (void)
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{
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return test_agm ();
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}
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