1 /* mpn_mod_1s_4p (ap, n, b, cps)
2 Divide (ap,,n) by b. Return the single-limb remainder.
3 Requires that b < B / 4.
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_4p_cps (mp_limb_t cps[7], mp_limb_t b)
45 {
46 mp_limb_t bi;
47 mp_limb_t B1modb, B2modb, B3modb, B4modb, B5modb;
48 int cnt;
49
50 ASSERT (b <= (~(mp_limb_t) 0) / 4);
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 udiv_rnnd_preinv (B4modb, B3modb, CNST_LIMB(0), b, bi);
71 cps[5] = B4modb >> cnt;
72
73 udiv_rnnd_preinv (B5modb, B4modb, CNST_LIMB(0), b, bi);
74 cps[6] = B5modb >> cnt;
75
76 #if WANT_ASSERT
77 {
78 int i;
79 b = cps[2];
80 for (i = 3; i <= 6; i++)
81 {
82 b += cps[i];
83 ASSERT (b >= cps[i]);
84 }
85 }
86 #endif
87 }
88
89 mp_limb_t
90 mpn_mod_1s_4p (mp_srcptr ap, mp_size_t n, mp_limb_t b, const mp_limb_t cps[7])
91 {
92 mp_limb_t rh, rl, bi, ph, pl, ch, cl, r;
93 mp_limb_t B1modb, B2modb, B3modb, B4modb, B5modb;
94 mp_size_t i;
95 int cnt;
96
97 ASSERT (n >= 1);
98
99 B1modb = cps[2];
100 B2modb = cps[3];
101 B3modb = cps[4];
102 B4modb = cps[5];
103 B5modb = cps[6];
104
105 switch (n & 3)
106 {
107 case 0:
108 umul_ppmm (ph, pl, ap[n - 3], B1modb);
109 add_ssaaaa (ph, pl, ph, pl, CNST_LIMB(0), ap[n - 4]);
110 umul_ppmm (ch, cl, ap[n - 2], B2modb);
111 add_ssaaaa (ph, pl, ph, pl, ch, cl);
112 umul_ppmm (rh, rl, ap[n - 1], B3modb);
113 add_ssaaaa (rh, rl, rh, rl, ph, pl);
114 n -= 4;
115 break;
116 case 1:
117 rh = 0;
118 rl = ap[n - 1];
119 n -= 1;
120 break;
121 case 2:
122 rh = ap[n - 1];
123 rl = ap[n - 2];
124 n -= 2;
125 break;
126 case 3:
127 umul_ppmm (ph, pl, ap[n - 2], B1modb);
128 add_ssaaaa (ph, pl, ph, pl, CNST_LIMB(0), ap[n - 3]);
129 umul_ppmm (rh, rl, ap[n - 1], B2modb);
130 add_ssaaaa (rh, rl, rh, rl, ph, pl);
131 n -= 3;
132 break;
133 }
134
135 for (i = n - 4; i >= 0; i -= 4)
136 {
137 /* rr = ap[i] < B
138 + ap[i+1] * (B mod b) <= (B-1)(b-1)
139 + ap[i+2] * (B^2 mod b) <= (B-1)(b-1)
140 + ap[i+3] * (B^3 mod b) <= (B-1)(b-1)
141 + LO(rr) * (B^4 mod b) <= (B-1)(b-1)
142 + HI(rr) * (B^5 mod b) <= (B-1)(b-1)
143 */
144 umul_ppmm (ph, pl, ap[i + 1], B1modb);
145 add_ssaaaa (ph, pl, ph, pl, CNST_LIMB(0), ap[i + 0]);
146
147 umul_ppmm (ch, cl, ap[i + 2], B2modb);
148 add_ssaaaa (ph, pl, ph, pl, ch, cl);
149
150 umul_ppmm (ch, cl, ap[i + 3], B3modb);
151 add_ssaaaa (ph, pl, ph, pl, ch, cl);
152
153 umul_ppmm (ch, cl, rl, B4modb);
154 add_ssaaaa (ph, pl, ph, pl, ch, cl);
155
156 umul_ppmm (rh, rl, rh, B5modb);
157 add_ssaaaa (rh, rl, rh, rl, ph, pl);
158 }
159
160 umul_ppmm (rh, cl, rh, B1modb);
161 add_ssaaaa (rh, rl, rh, rl, CNST_LIMB(0), cl);
162
163 cnt = cps[1];
164 bi = cps[0];
165
166 r = (rh << cnt) | (rl >> (GMP_LIMB_BITS - cnt));
167 udiv_rnnd_preinv (r, r, rl << cnt, b, bi);
168
169 return r >> cnt;
170 }