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-impl.h"
41 #include "longlong.h"
42
43 void
44 mpn_mod_1s_2p_cps (mp_limb_t cps[5], mp_limb_t b)
45 {
46 mp_limb_t bi;
47 mp_limb_t B1modb, B2modb, B3modb;
48 int cnt;
49
50 ASSERT (b <= (~(mp_limb_t) 0) / 2);
51
52 count_leading_zeros (cnt, b);
53
54 b <<= cnt;
55 invert_limb (bi, b);
56
57 cps[0] = bi;
58 cps[1] = cnt;
59
60 B1modb = -b * ((bi >> (GMP_LIMB_BITS-cnt)) | (CNST_LIMB(1) << cnt));
61 ASSERT (B1modb <= b); /* NB: not fully reduced mod b */
62 cps[2] = B1modb >> cnt;
63
64 udiv_rnnd_preinv (B2modb, B1modb, CNST_LIMB(0), b, bi);
65 cps[3] = B2modb >> cnt;
66
67 udiv_rnnd_preinv (B3modb, B2modb, CNST_LIMB(0), b, bi);
68 cps[4] = B3modb >> cnt;
69
70 #if WANT_ASSERT
71 {
72 int i;
73 b = cps[2];
74 for (i = 3; i <= 4; i++)
75 {
76 b += cps[i];
77 ASSERT (b >= cps[i]);
78 }
79 }
80 #endif
81 }
82
83 mp_limb_t
84 mpn_mod_1s_2p (mp_srcptr ap, mp_size_t n, mp_limb_t b, const mp_limb_t cps[5])
85 {
86 mp_limb_t rh, rl, bi, ph, pl, ch, cl, r;
87 mp_limb_t B1modb, B2modb, B3modb;
88 mp_size_t i;
89 int cnt;
90
91 ASSERT (n >= 1);
92
93 B1modb = cps[2];
94 B2modb = cps[3];
95 B3modb = cps[4];
96
97 if ((n & 1) != 0)
98 {
99 if (n == 1)
100 {
101 rl = ap[n - 1];
102 bi = cps[0];
103 cnt = cps[1];
104 udiv_rnnd_preinv (r, rl >> (GMP_LIMB_BITS - cnt),
105 rl << cnt, b, bi);
106 return r >> cnt;
107 }
108
109 umul_ppmm (ph, pl, ap[n - 2], B1modb);
110 add_ssaaaa (ph, pl, ph, pl, CNST_LIMB(0), ap[n - 3]);
111 umul_ppmm (rh, rl, ap[n - 1], B2modb);
112 add_ssaaaa (rh, rl, rh, rl, ph, pl);
113 n--;
114 }
115 else
116 {
117 rh = ap[n - 1];
118 rl = ap[n - 2];
119 }
120
121 for (i = n - 4; i >= 0; i -= 2)
122 {
123 /* rr = ap[i] < B
124 + ap[i+1] * (B mod b) <= (B-1)(b-1)
125 + LO(rr) * (B^2 mod b) <= (B-1)(b-1)
126 + HI(rr) * (B^3 mod b) <= (B-1)(b-1)
127 */
128 umul_ppmm (ph, pl, ap[i + 1], B1modb);
129 add_ssaaaa (ph, pl, ph, pl, CNST_LIMB(0), ap[i + 0]);
130
131 umul_ppmm (ch, cl, rl, B2modb);
132 add_ssaaaa (ph, pl, ph, pl, ch, cl);
133
134 umul_ppmm (rh, rl, rh, B3modb);
135 add_ssaaaa (rh, rl, rh, rl, ph, pl);
136 }
137
138 umul_ppmm (rh, cl, rh, B1modb);
139 add_ssaaaa (rh, rl, rh, rl, CNST_LIMB(0), cl);
140
141 cnt = cps[1];
142 bi = cps[0];
143
144 r = (rh << cnt) | (rl >> (GMP_LIMB_BITS - cnt));
145 udiv_rnnd_preinv (r, r, rl << cnt, b, bi);
146
147 return r >> cnt;
148 }