1 /* mpc_fma -- Fused multiply-add of three complex numbers
2
3 Copyright (C) 2011, 2012, 2022 INRIA
4
5 This file is part of GNU MPC.
6
7 GNU MPC is free software; you can redistribute it and/or modify it under
8 the terms of the GNU Lesser General Public License as published by the
9 Free Software Foundation; either version 3 of the License, or (at your
10 option) any later version.
11
12 GNU MPC is distributed in the hope that it will be useful, but WITHOUT ANY
13 WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
14 FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
15 more details.
16
17 You should have received a copy of the GNU Lesser General Public License
18 along with this program. If not, see http://www.gnu.org/licenses/ .
19 */
20
21 #include "mpc-impl.h"
22
23 int
mpc_fma_naive(mpc_ptr r,mpc_srcptr a,mpc_srcptr b,mpc_srcptr c,mpc_rnd_t rnd)24 mpc_fma_naive (mpc_ptr r, mpc_srcptr a, mpc_srcptr b, mpc_srcptr c, mpc_rnd_t rnd)
25 {
26 mpfr_t rea_reb, rea_imb, ima_reb, ima_imb;
27 mpfr_ptr sum [3];
28 int inex_re, inex_im;
29
30 mpfr_init2 (rea_reb, mpfr_get_prec (mpc_realref(a)) + mpfr_get_prec (mpc_realref(b)));
31 mpfr_init2 (rea_imb, mpfr_get_prec (mpc_realref(a)) + mpfr_get_prec (mpc_imagref(b)));
32 mpfr_init2 (ima_reb, mpfr_get_prec (mpc_imagref(a)) + mpfr_get_prec (mpc_realref(b)));
33 mpfr_init2 (ima_imb, mpfr_get_prec (mpc_imagref(a)) + mpfr_get_prec (mpc_imagref(b)));
34
35 mpfr_mul (rea_reb, mpc_realref(a), mpc_realref(b), MPFR_RNDZ); /* exact */
36 mpfr_mul (rea_imb, mpc_realref(a), mpc_imagref(b), MPFR_RNDZ); /* exact */
37 mpfr_mul (ima_reb, mpc_imagref(a), mpc_realref(b), MPFR_RNDZ); /* exact */
38 mpfr_mul (ima_imb, mpc_imagref(a), mpc_imagref(b), MPFR_RNDZ); /* exact */
39
40 mpfr_neg (ima_imb, ima_imb, MPFR_RNDZ);
41 sum [0] = rea_reb;
42 sum [1] = ima_imb;
43 sum [2] = (mpfr_ptr) mpc_realref (c);
44 inex_re = mpfr_sum (mpc_realref (r), sum, 3, MPC_RND_RE (rnd));
45 sum [0] = rea_imb;
46 sum [1] = ima_reb;
47 sum [2] = (mpfr_ptr) mpc_imagref (c);
48 inex_im = mpfr_sum (mpc_imagref (r), sum, 3, MPC_RND_IM (rnd));
49
50 mpfr_clear (rea_reb);
51 mpfr_clear (rea_imb);
52 mpfr_clear (ima_reb);
53 mpfr_clear (ima_imb);
54
55 return MPC_INEX(inex_re, inex_im);
56 }
57
58 /* The algorithm is as follows:
59 - in a first pass, we use the target precision + some extra bits
60 - if it fails, we add the number of cancelled bits when adding
61 Re(a*b) and Re(c) [similarly for the imaginary part]
62 - it is fails again, we call the mpc_fma_naive function, which also
63 deals with the special cases */
64 int
mpc_fma(mpc_ptr r,mpc_srcptr a,mpc_srcptr b,mpc_srcptr c,mpc_rnd_t rnd)65 mpc_fma (mpc_ptr r, mpc_srcptr a, mpc_srcptr b, mpc_srcptr c, mpc_rnd_t rnd)
66 {
67 mpc_t ab;
68 mpfr_prec_t pre, pim, wpre, wpim;
69 mpfr_exp_t diffre, diffim;
70 int i, inex = 0, okre = 0, okim = 0;
71
72 if (mpc_fin_p (a) == 0 || mpc_fin_p (b) == 0 || mpc_fin_p (c) == 0)
73 return mpc_fma_naive (r, a, b, c, rnd);
74
75 pre = mpfr_get_prec (mpc_realref(r));
76 pim = mpfr_get_prec (mpc_imagref(r));
77 wpre = pre + mpc_ceil_log2 (pre) + 10;
78 wpim = pim + mpc_ceil_log2 (pim) + 10;
79 mpc_init3 (ab, wpre, wpim);
80 for (i = 0; i < 2; ++i)
81 {
82 mpc_mul (ab, a, b, MPC_RNDZZ);
83 if (mpfr_zero_p (mpc_realref(ab)) || mpfr_zero_p (mpc_imagref(ab)))
84 break;
85 diffre = mpfr_get_exp (mpc_realref(ab));
86 diffim = mpfr_get_exp (mpc_imagref(ab));
87 mpc_add (ab, ab, c, MPC_RNDZZ);
88 if (mpfr_zero_p (mpc_realref(ab)) || mpfr_zero_p (mpc_imagref(ab)))
89 break;
90 diffre -= mpfr_get_exp (mpc_realref(ab));
91 diffim -= mpfr_get_exp (mpc_imagref(ab));
92 diffre = (diffre > 0 ? diffre + 1 : 1);
93 diffim = (diffim > 0 ? diffim + 1 : 1);
94 okre = diffre > (mpfr_exp_t) wpre ? 0 : mpfr_can_round (mpc_realref(ab),
95 wpre - diffre, MPFR_RNDN, MPFR_RNDZ,
96 pre + (MPC_RND_RE (rnd) == MPFR_RNDN));
97 okim = diffim > (mpfr_exp_t) wpim ? 0 : mpfr_can_round (mpc_imagref(ab),
98 wpim - diffim, MPFR_RNDN, MPFR_RNDZ,
99 pim + (MPC_RND_IM (rnd) == MPFR_RNDN));
100 if (okre && okim)
101 {
102 inex = mpc_set (r, ab, rnd);
103 break;
104 }
105 if (i == 1)
106 break;
107 if (okre == 0 && diffre > 1)
108 wpre += diffre;
109 if (okim == 0 && diffim > 1)
110 wpim += diffim;
111 mpfr_set_prec (mpc_realref(ab), wpre);
112 mpfr_set_prec (mpc_imagref(ab), wpim);
113 }
114 mpc_clear (ab);
115
116 return (okre && okim) ? inex : mpc_fma_naive (r, a, b, c, rnd);
117 }
118