1 /* mpn_mod_1s_2p (ap, n, b, cps)
2 Divide (ap,,n) by b. Return the single-limb remainder.
3 Requires that b < B / 2.
4
5 Contributed to the GNU project by Torbjorn Granlund.
6 Based on a suggestion by Peter L. Montgomery.
7
8 THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY
9 SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
10 GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
11
12 Copyright 2008-2010 Free Software Foundation, Inc.
13
14 This file is part of the GNU MP Library.
15
16 The GNU MP Library is free software; you can redistribute it and/or modify
17 it under the terms of either:
18
19 * the GNU Lesser General Public License as published by the Free
20 Software Foundation; either version 3 of the License, or (at your
21 option) any later version.
22
23 or
24
25 * the GNU General Public License as published by the Free Software
26 Foundation; either version 2 of the License, or (at your option) any
27 later version.
28
29 or both in parallel, as here.
30
31 The GNU MP Library is distributed in the hope that it will be useful, but
32 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
33 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
34 for more details.
35
36 You should have received copies of the GNU General Public License and the
37 GNU Lesser General Public License along with the GNU MP Library. If not,
38 see https://www.gnu.org/licenses/. */
39
40 #include "gmp.h"
41 #include "gmp-impl.h"
42 #include "longlong.h"
43
44 void
mpn_mod_1s_2p_cps(mp_limb_t cps[5],mp_limb_t b)45 mpn_mod_1s_2p_cps (mp_limb_t cps[5], mp_limb_t b)
46 {
47 mp_limb_t bi;
48 mp_limb_t B1modb, B2modb, B3modb;
49 int cnt;
50
51 ASSERT (b <= (~(mp_limb_t) 0) / 2);
52
53 count_leading_zeros (cnt, b);
54
55 b <<= cnt;
56 invert_limb (bi, b);
57
58 cps[0] = bi;
59 cps[1] = cnt;
60
61 B1modb = -b * ((bi >> (GMP_LIMB_BITS-cnt)) | (CNST_LIMB(1) << cnt));
62 ASSERT (B1modb <= b); /* NB: not fully reduced mod b */
63 cps[2] = B1modb >> cnt;
64
65 udiv_rnnd_preinv (B2modb, B1modb, CNST_LIMB(0), b, bi);
66 cps[3] = B2modb >> cnt;
67
68 udiv_rnnd_preinv (B3modb, B2modb, CNST_LIMB(0), b, bi);
69 cps[4] = B3modb >> cnt;
70
71 #if WANT_ASSERT
72 {
73 int i;
74 b = cps[2];
75 for (i = 3; i <= 4; i++)
76 {
77 b += cps[i];
78 ASSERT (b >= cps[i]);
79 }
80 }
81 #endif
82 }
83
84 mp_limb_t
mpn_mod_1s_2p(mp_srcptr ap,mp_size_t n,mp_limb_t b,const mp_limb_t cps[5])85 mpn_mod_1s_2p (mp_srcptr ap, mp_size_t n, mp_limb_t b, const mp_limb_t cps[5])
86 {
87 mp_limb_t rh, rl, bi, ph, pl, ch, cl, r;
88 mp_limb_t B1modb, B2modb, B3modb;
89 mp_size_t i;
90 int cnt;
91
92 ASSERT (n >= 1);
93
94 B1modb = cps[2];
95 B2modb = cps[3];
96 B3modb = cps[4];
97
98 if ((n & 1) != 0)
99 {
100 if (n == 1)
101 {
102 rl = ap[n - 1];
103 bi = cps[0];
104 cnt = cps[1];
105 udiv_rnnd_preinv (r, rl >> (GMP_LIMB_BITS - cnt),
106 rl << cnt, b, bi);
107 return r >> cnt;
108 }
109
110 umul_ppmm (ph, pl, ap[n - 2], B1modb);
111 add_ssaaaa (ph, pl, ph, pl, CNST_LIMB(0), ap[n - 3]);
112 umul_ppmm (rh, rl, ap[n - 1], B2modb);
113 add_ssaaaa (rh, rl, rh, rl, ph, pl);
114 n--;
115 }
116 else
117 {
118 rh = ap[n - 1];
119 rl = ap[n - 2];
120 }
121
122 for (i = n - 4; i >= 0; i -= 2)
123 {
124 /* rr = ap[i] < B
125 + ap[i+1] * (B mod b) <= (B-1)(b-1)
126 + LO(rr) * (B^2 mod b) <= (B-1)(b-1)
127 + HI(rr) * (B^3 mod b) <= (B-1)(b-1)
128 */
129 umul_ppmm (ph, pl, ap[i + 1], B1modb);
130 add_ssaaaa (ph, pl, ph, pl, CNST_LIMB(0), ap[i + 0]);
131
132 umul_ppmm (ch, cl, rl, B2modb);
133 add_ssaaaa (ph, pl, ph, pl, ch, cl);
134
135 umul_ppmm (rh, rl, rh, B3modb);
136 add_ssaaaa (rh, rl, rh, rl, ph, pl);
137 }
138
139 umul_ppmm (rh, cl, rh, B1modb);
140 add_ssaaaa (rh, rl, rh, rl, CNST_LIMB(0), cl);
141
142 cnt = cps[1];
143 bi = cps[0];
144
145 r = (rh << cnt) | (rl >> (GMP_LIMB_BITS - cnt));
146 udiv_rnnd_preinv (r, r, rl << cnt, b, bi);
147
148 return r >> cnt;
149 }
150