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118 lines
4.3 KiB
C
118 lines
4.3 KiB
C
/* mpc_fma -- Fused multiply-add of three complex numbers
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Copyright (C) 2011, 2012, 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-impl.h"
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int
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mpc_fma_naive (mpc_ptr r, mpc_srcptr a, mpc_srcptr b, mpc_srcptr c, mpc_rnd_t rnd)
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{
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mpfr_t rea_reb, rea_imb, ima_reb, ima_imb;
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mpfr_ptr sum [3];
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int inex_re, inex_im;
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mpfr_init2 (rea_reb, mpfr_get_prec (mpc_realref(a)) + mpfr_get_prec (mpc_realref(b)));
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mpfr_init2 (rea_imb, mpfr_get_prec (mpc_realref(a)) + mpfr_get_prec (mpc_imagref(b)));
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mpfr_init2 (ima_reb, mpfr_get_prec (mpc_imagref(a)) + mpfr_get_prec (mpc_realref(b)));
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mpfr_init2 (ima_imb, mpfr_get_prec (mpc_imagref(a)) + mpfr_get_prec (mpc_imagref(b)));
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mpfr_mul (rea_reb, mpc_realref(a), mpc_realref(b), MPFR_RNDZ); /* exact */
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mpfr_mul (rea_imb, mpc_realref(a), mpc_imagref(b), MPFR_RNDZ); /* exact */
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mpfr_mul (ima_reb, mpc_imagref(a), mpc_realref(b), MPFR_RNDZ); /* exact */
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mpfr_mul (ima_imb, mpc_imagref(a), mpc_imagref(b), MPFR_RNDZ); /* exact */
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mpfr_neg (ima_imb, ima_imb, MPFR_RNDZ);
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sum [0] = rea_reb;
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sum [1] = ima_imb;
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sum [2] = (mpfr_ptr) mpc_realref (c);
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inex_re = mpfr_sum (mpc_realref (r), sum, 3, MPC_RND_RE (rnd));
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sum [0] = rea_imb;
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sum [1] = ima_reb;
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sum [2] = (mpfr_ptr) mpc_imagref (c);
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inex_im = mpfr_sum (mpc_imagref (r), sum, 3, MPC_RND_IM (rnd));
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mpfr_clear (rea_reb);
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mpfr_clear (rea_imb);
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mpfr_clear (ima_reb);
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mpfr_clear (ima_imb);
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return MPC_INEX(inex_re, inex_im);
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}
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/* The algorithm is as follows:
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- in a first pass, we use the target precision + some extra bits
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- if it fails, we add the number of cancelled bits when adding
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Re(a*b) and Re(c) [similarly for the imaginary part]
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- it is fails again, we call the mpc_fma_naive function, which also
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deals with the special cases */
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int
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mpc_fma (mpc_ptr r, mpc_srcptr a, mpc_srcptr b, mpc_srcptr c, mpc_rnd_t rnd)
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{
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mpc_t ab;
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mpfr_prec_t pre, pim, wpre, wpim;
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mpfr_exp_t diffre, diffim;
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int i, inex = 0, okre = 0, okim = 0;
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if (mpc_fin_p (a) == 0 || mpc_fin_p (b) == 0 || mpc_fin_p (c) == 0)
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return mpc_fma_naive (r, a, b, c, rnd);
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pre = mpfr_get_prec (mpc_realref(r));
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pim = mpfr_get_prec (mpc_imagref(r));
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wpre = pre + mpc_ceil_log2 (pre) + 10;
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wpim = pim + mpc_ceil_log2 (pim) + 10;
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mpc_init3 (ab, wpre, wpim);
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for (i = 0; i < 2; ++i)
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{
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mpc_mul (ab, a, b, MPC_RNDZZ);
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if (mpfr_zero_p (mpc_realref(ab)) || mpfr_zero_p (mpc_imagref(ab)))
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break;
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diffre = mpfr_get_exp (mpc_realref(ab));
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diffim = mpfr_get_exp (mpc_imagref(ab));
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mpc_add (ab, ab, c, MPC_RNDZZ);
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if (mpfr_zero_p (mpc_realref(ab)) || mpfr_zero_p (mpc_imagref(ab)))
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break;
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diffre -= mpfr_get_exp (mpc_realref(ab));
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diffim -= mpfr_get_exp (mpc_imagref(ab));
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diffre = (diffre > 0 ? diffre + 1 : 1);
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diffim = (diffim > 0 ? diffim + 1 : 1);
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okre = diffre > (mpfr_exp_t) wpre ? 0 : mpfr_can_round (mpc_realref(ab),
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wpre - diffre, MPFR_RNDN, MPFR_RNDZ,
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pre + (MPC_RND_RE (rnd) == MPFR_RNDN));
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okim = diffim > (mpfr_exp_t) wpim ? 0 : mpfr_can_round (mpc_imagref(ab),
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wpim - diffim, MPFR_RNDN, MPFR_RNDZ,
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pim + (MPC_RND_IM (rnd) == MPFR_RNDN));
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if (okre && okim)
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{
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inex = mpc_set (r, ab, rnd);
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break;
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}
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if (i == 1)
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break;
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if (okre == 0 && diffre > 1)
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wpre += diffre;
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if (okim == 0 && diffim > 1)
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wpim += diffim;
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mpfr_set_prec (mpc_realref(ab), wpre);
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mpfr_set_prec (mpc_imagref(ab), wpim);
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}
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mpc_clear (ab);
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return (okre && okim) ? inex : mpc_fma_naive (r, a, b, c, rnd);
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}
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