1 /* mpn_mod_1s_4p (ap, n, b, cps)
2 Divide (ap,,n) by b. Return the single-limb remainder.
3 Requires that d < 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.h"
41 #include "gmp-impl.h"
42 #include "longlong.h"
43
44 void
mpn_mod_1s_4p_cps(mp_limb_t cps[7],mp_limb_t b)45 mpn_mod_1s_4p_cps (mp_limb_t cps[7], mp_limb_t b)
46 {
47 mp_limb_t bi;
48 mp_limb_t B1modb, B2modb, B3modb, B4modb, B5modb;
49 int cnt;
50
51 ASSERT (b <= (~(mp_limb_t) 0) / 4);
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 udiv_rnnd_preinv (B4modb, B3modb, CNST_LIMB(0), b, bi);
72 cps[5] = B4modb >> cnt;
73
74 udiv_rnnd_preinv (B5modb, B4modb, CNST_LIMB(0), b, bi);
75 cps[6] = B5modb >> cnt;
76
77 #if WANT_ASSERT
78 {
79 int i;
80 b = cps[2];
81 for (i = 3; i <= 6; i++)
82 {
83 b += cps[i];
84 ASSERT (b >= cps[i]);
85 }
86 }
87 #endif
88 }
89
90 mp_limb_t
mpn_mod_1s_4p(mp_srcptr ap,mp_size_t n,mp_limb_t b,const mp_limb_t cps[7])91 mpn_mod_1s_4p (mp_srcptr ap, mp_size_t n, mp_limb_t b, const mp_limb_t cps[7])
92 {
93 mp_limb_t rh, rl, bi, ph, pl, ch, cl, r;
94 mp_limb_t B1modb, B2modb, B3modb, B4modb, B5modb;
95 mp_size_t i;
96 int cnt;
97
98 ASSERT (n >= 1);
99
100 B1modb = cps[2];
101 B2modb = cps[3];
102 B3modb = cps[4];
103 B4modb = cps[5];
104 B5modb = cps[6];
105
106 switch (n & 3)
107 {
108 case 0:
109 umul_ppmm (ph, pl, ap[n - 3], B1modb);
110 add_ssaaaa (ph, pl, ph, pl, CNST_LIMB(0), ap[n - 4]);
111 umul_ppmm (ch, cl, ap[n - 2], B2modb);
112 add_ssaaaa (ph, pl, ph, pl, ch, cl);
113 umul_ppmm (rh, rl, ap[n - 1], B3modb);
114 add_ssaaaa (rh, rl, rh, rl, ph, pl);
115 n -= 4;
116 break;
117 case 1:
118 rh = 0;
119 rl = ap[n - 1];
120 n -= 1;
121 break;
122 case 2:
123 rh = ap[n - 1];
124 rl = ap[n - 2];
125 n -= 2;
126 break;
127 case 3:
128 umul_ppmm (ph, pl, ap[n - 2], B1modb);
129 add_ssaaaa (ph, pl, ph, pl, CNST_LIMB(0), ap[n - 3]);
130 umul_ppmm (rh, rl, ap[n - 1], B2modb);
131 add_ssaaaa (rh, rl, rh, rl, ph, pl);
132 n -= 3;
133 break;
134 }
135
136 for (i = n - 4; i >= 0; i -= 4)
137 {
138 /* rr = ap[i] < B
139 + ap[i+1] * (B mod b) <= (B-1)(b-1)
140 + ap[i+2] * (B^2 mod b) <= (B-1)(b-1)
141 + ap[i+3] * (B^3 mod b) <= (B-1)(b-1)
142 + LO(rr) * (B^4 mod b) <= (B-1)(b-1)
143 + HI(rr) * (B^5 mod b) <= (B-1)(b-1)
144 */
145 umul_ppmm (ph, pl, ap[i + 1], B1modb);
146 add_ssaaaa (ph, pl, ph, pl, CNST_LIMB(0), ap[i + 0]);
147
148 umul_ppmm (ch, cl, ap[i + 2], B2modb);
149 add_ssaaaa (ph, pl, ph, pl, ch, cl);
150
151 umul_ppmm (ch, cl, ap[i + 3], B3modb);
152 add_ssaaaa (ph, pl, ph, pl, ch, cl);
153
154 umul_ppmm (ch, cl, rl, B4modb);
155 add_ssaaaa (ph, pl, ph, pl, ch, cl);
156
157 umul_ppmm (rh, rl, rh, B5modb);
158 add_ssaaaa (rh, rl, rh, rl, ph, pl);
159 }
160
161 umul_ppmm (rh, cl, rh, B1modb);
162 add_ssaaaa (rh, rl, rh, rl, CNST_LIMB(0), cl);
163
164 cnt = cps[1];
165 bi = cps[0];
166
167 r = (rh << cnt) | (rl >> (GMP_LIMB_BITS - cnt));
168 udiv_rnnd_preinv (r, r, rl << cnt, b, bi);
169
170 return r >> cnt;
171 }
172