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
7 THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY
8 SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
9 GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
10
11 Copyright 2008, 2009 Free Software Foundation, Inc.
12
13 This file is part of the GNU MP Library.
14
15 The GNU MP Library is free software; you can redistribute it and/or modify
16 it under the terms of the GNU Lesser General Public License as published by
17 the Free Software Foundation; either version 3 of the License, or (at your
18 option) any later version.
19
20 The GNU MP Library is distributed in the hope that it will be useful, but
21 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
22 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
23 License for more details.
24
25 You should have received a copy of the GNU Lesser General Public License
26 along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
27
28 #include "gmp.h"
29 #include "gmp-impl.h"
30 #include "longlong.h"
31
32 void
mpn_mod_1s_2p_cps(mp_limb_t cps[5],mp_limb_t b)33 mpn_mod_1s_2p_cps (mp_limb_t cps[5], mp_limb_t b)
34 {
35 mp_limb_t bi;
36 mp_limb_t B1modb, B2modb, B3modb;
37 int cnt;
38
39 ASSERT (b <= (~(mp_limb_t) 0) / 2);
40
41 count_leading_zeros (cnt, b);
42
43 b <<= cnt;
44 invert_limb (bi, b);
45
46 B1modb = -b * ((bi >> (GMP_LIMB_BITS-cnt)) | (CNST_LIMB(1) << cnt));
47 ASSERT (B1modb <= b); /* NB: not fully reduced mod b */
48 udiv_rnd_preinv (B2modb, B1modb, b, bi);
49 udiv_rnd_preinv (B3modb, B2modb, b, bi);
50
51 cps[0] = bi;
52 cps[1] = cnt;
53 cps[2] = B1modb >> cnt;
54 cps[3] = B2modb >> cnt;
55 cps[4] = B3modb >> cnt;
56
57 #if WANT_ASSERT
58 {
59 int i;
60 b = cps[2];
61 for (i = 3; i <= 4; i++)
62 {
63 b += cps[i];
64 ASSERT (b >= cps[i]);
65 }
66 }
67 #endif
68 }
69
70 mp_limb_t
mpn_mod_1s_2p(mp_srcptr ap,mp_size_t n,mp_limb_t b,mp_limb_t cps[5])71 mpn_mod_1s_2p (mp_srcptr ap, mp_size_t n, mp_limb_t b, mp_limb_t cps[5])
72 {
73 mp_limb_t rh, rl, bi, q, ph, pl, ch, cl, r;
74 mp_limb_t B1modb, B2modb, B3modb;
75 mp_size_t i;
76 int cnt;
77
78 ASSERT (n >= 1);
79
80 B1modb = cps[2];
81 B2modb = cps[3];
82 B3modb = cps[4];
83
84 if ((n & 1) != 0)
85 {
86 if (n == 1)
87 {
88 rl = ap[n - 1];
89 bi = cps[0];
90 cnt = cps[1];
91 udiv_qrnnd_preinv (q, r, rl >> (GMP_LIMB_BITS - cnt),
92 rl << cnt, b, bi);
93 return r >> cnt;
94 }
95
96 umul_ppmm (ph, pl, ap[n - 2], B1modb);
97 add_ssaaaa (ph, pl, ph, pl, 0, ap[n - 3]);
98 umul_ppmm (rh, rl, ap[n - 1], B2modb);
99 add_ssaaaa (rh, rl, rh, rl, ph, pl);
100 n--;
101 }
102 else
103 {
104 umul_ppmm (rh, rl, ap[n - 1], B1modb);
105 add_ssaaaa (rh, rl, rh, rl, 0, ap[n - 2]);
106 }
107
108 for (i = n - 4; i >= 0; i -= 2)
109 {
110 /* rr = ap[i] < B
111 + ap[i+1] * (B mod b) <= (B-1)(b-1)
112 + LO(rr) * (B^2 mod b) <= (B-1)(b-1)
113 + HI(rr) * (B^3 mod b) <= (B-1)(b-1)
114 */
115 umul_ppmm (ph, pl, ap[i + 1], B1modb);
116 add_ssaaaa (ph, pl, ph, pl, 0, ap[i + 0]);
117
118 umul_ppmm (ch, cl, rl, B2modb);
119 add_ssaaaa (ph, pl, ph, pl, ch, cl);
120
121 umul_ppmm (rh, rl, rh, B3modb);
122 add_ssaaaa (rh, rl, rh, rl, ph, pl);
123 }
124
125 bi = cps[0];
126 cnt = cps[1];
127
128 #if 1
129 umul_ppmm (rh, cl, rh, B1modb);
130 add_ssaaaa (rh, rl, rh, rl, 0, cl);
131 r = (rh << cnt) | (rl >> (GMP_LIMB_BITS - cnt));
132 #else
133 udiv_qrnnd_preinv (q, r, rh >> (GMP_LIMB_BITS - cnt),
134 (rh << cnt) | (rl >> (GMP_LIMB_BITS - cnt)), b, bi);
135 ASSERT (q <= 2); /* optimize for small quotient? */
136 #endif
137
138 udiv_qrnnd_preinv (q, r, r, rl << cnt, b, bi);
139
140 return r >> cnt;
141 }
142