1 /* mpn_mod_1s_3p (ap, n, b, cps)
2 Divide (ap,,n) by b. Return the single-limb remainder.
3 Requires that b < B / 3.
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, 2013 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_3p_cps (mp_limb_t cps[6], mp_limb_t b)
45 {
46 mp_limb_t bi;
47 mp_limb_t B1modb, B2modb, B3modb, B4modb;
48 int cnt;
49
50 ASSERT (b <= (~(mp_limb_t) 0) / 3);
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 #if WANT_ASSERT
74 {
75 int i;
76 b = cps[2];
77 for (i = 3; i <= 5; i++)
78 {
79 b += cps[i];
80 ASSERT (b >= cps[i]);
81 }
82 }
83 #endif
84 }
85
86 mp_limb_t
87 mpn_mod_1s_3p (mp_srcptr ap, mp_size_t n, mp_limb_t b, const mp_limb_t cps[6])
88 {
89 mp_limb_t rh, rl, bi, ph, pl, ch, cl, r;
90 mp_limb_t B1modb, B2modb, B3modb, B4modb;
91 mp_size_t i;
92 int cnt;
93
94 ASSERT (n >= 1);
95
96 B1modb = cps[2];
97 B2modb = cps[3];
98 B3modb = cps[4];
99 B4modb = cps[5];
100
101 /* We compute n mod 3 in a tricky way, which works except for when n is so
102 close to the maximum size that we don't need to support it. The final
103 cast to int is a workaround for HP cc. */
104 switch ((int) ((mp_limb_t) n * MODLIMB_INVERSE_3 >> (GMP_NUMB_BITS - 2)))
105 {
106 case 0:
107 umul_ppmm (ph, pl, ap[n - 2], B1modb);
108 add_ssaaaa (ph, pl, ph, pl, CNST_LIMB(0), ap[n - 3]);
109 umul_ppmm (rh, rl, ap[n - 1], B2modb);
110 add_ssaaaa (rh, rl, rh, rl, ph, pl);
111 n -= 3;
112 break;
113 default: /* n mod 3 = 1; (case 2)*/
114 rh = 0;
115 rl = ap[--n];
116 break;
117 case 1: /* n mod 3 = 2 */
118 rh = ap[n - 1];
119 rl = ap[n - 2];
120 n -= 2;
121 break;
122 }
123
124 for (i = n - 3; i >= 0; i -= 3)
125 {
126 /* rr = ap[i] < B
127 + ap[i+1] * (B mod b) <= (B-1)(b-1)
128 + ap[i+2] * (B^2 mod b) <= (B-1)(b-1)
129 + LO(rr) * (B^3 mod b) <= (B-1)(b-1)
130 + HI(rr) * (B^4 mod b) <= (B-1)(b-1)
131 */
132 umul_ppmm (ph, pl, ap[i + 1], B1modb);
133 add_ssaaaa (ph, pl, ph, pl, CNST_LIMB(0), ap[i + 0]);
134
135 umul_ppmm (ch, cl, ap[i + 2], B2modb);
136 add_ssaaaa (ph, pl, ph, pl, ch, cl);
137
138 umul_ppmm (ch, cl, rl, B3modb);
139 add_ssaaaa (ph, pl, ph, pl, ch, cl);
140
141 umul_ppmm (rh, rl, rh, B4modb);
142 add_ssaaaa (rh, rl, rh, rl, ph, pl);
143 }
144
145 umul_ppmm (rh, cl, rh, B1modb);
146 add_ssaaaa (rh, rl, rh, rl, CNST_LIMB(0), cl);
147
148 cnt = cps[1];
149 bi = cps[0];
150
151 r = (rh << cnt) | (rl >> (GMP_LIMB_BITS - cnt));
152 udiv_rnnd_preinv (r, r, rl << cnt, b, bi);
153
154 return r >> cnt;
155 }