1 /* mpn_mod_1s_3p (ap, n, b, cps)
2 Divide (ap,,n) by b. Return the single-limb remainder.
3 Requires that d < B / 3.
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, 2010 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_3p_cps(mp_limb_t cps[6],mp_limb_t b)33 mpn_mod_1s_3p_cps (mp_limb_t cps[6], mp_limb_t b)
34 {
35 mp_limb_t bi;
36 mp_limb_t B1modb, B2modb, B3modb, B4modb;
37 int cnt;
38
39 ASSERT (b <= (~(mp_limb_t) 0) / 3);
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 udiv_rnd_preinv (B4modb, B3modb, b, bi);
51
52 cps[0] = bi;
53 cps[1] = cnt;
54 cps[2] = B1modb >> cnt;
55 cps[3] = B2modb >> cnt;
56 cps[4] = B3modb >> cnt;
57 cps[5] = B4modb >> cnt;
58
59 #if WANT_ASSERT
60 {
61 int i;
62 b = cps[2];
63 for (i = 3; i <= 5; i++)
64 {
65 b += cps[i];
66 ASSERT (b >= cps[i]);
67 }
68 }
69 #endif
70 }
71
72 mp_limb_t
mpn_mod_1s_3p(mp_srcptr ap,mp_size_t n,mp_limb_t b,mp_limb_t cps[6])73 mpn_mod_1s_3p (mp_srcptr ap, mp_size_t n, mp_limb_t b, mp_limb_t cps[6])
74 {
75 mp_limb_t rh, rl, bi, q, ph, pl, ch, cl, r;
76 mp_limb_t B1modb, B2modb, B3modb, B4modb;
77 mp_size_t i;
78 int cnt;
79
80 ASSERT (n >= 1);
81
82 B1modb = cps[2];
83 B2modb = cps[3];
84 B3modb = cps[4];
85 B4modb = cps[5];
86
87 /* We compute n mod 3 in a tricky way, which works except for when n is so
88 close to the maximum size that we don't need to support it. The final
89 cast to int is a workaround for HP cc. */
90 switch ((int) ((mp_limb_t) n * MODLIMB_INVERSE_3 >> (GMP_NUMB_BITS - 2)))
91 {
92 case 0:
93 umul_ppmm (ph, pl, ap[n - 2], B1modb);
94 add_ssaaaa (ph, pl, ph, pl, 0, ap[n - 3]);
95 umul_ppmm (rh, rl, ap[n - 1], B2modb);
96 add_ssaaaa (rh, rl, rh, rl, ph, pl);
97 n -= 3;
98 break;
99 case 2: /* n mod 3 = 1 */
100 rh = 0;
101 rl = ap[n - 1];
102 n -= 1;
103 break;
104 case 1: /* n mod 3 = 2 */
105 umul_ppmm (ph, pl, ap[n - 1], B1modb);
106 add_ssaaaa (rh, rl, ph, pl, 0, ap[n - 2]);
107 n -= 2;
108 break;
109 }
110
111 for (i = n - 3; i >= 0; i -= 3)
112 {
113 /* rr = ap[i] < B
114 + ap[i+1] * (B mod b) <= (B-1)(b-1)
115 + ap[i+2] * (B^2 mod b) <= (B-1)(b-1)
116 + LO(rr) * (B^3 mod b) <= (B-1)(b-1)
117 + HI(rr) * (B^4 mod b) <= (B-1)(b-1)
118 */
119 umul_ppmm (ph, pl, ap[i + 1], B1modb);
120 add_ssaaaa (ph, pl, ph, pl, 0, ap[i + 0]);
121
122 umul_ppmm (ch, cl, ap[i + 2], B2modb);
123 add_ssaaaa (ph, pl, ph, pl, ch, cl);
124
125 umul_ppmm (ch, cl, rl, B3modb);
126 add_ssaaaa (ph, pl, ph, pl, ch, cl);
127
128 umul_ppmm (rh, rl, rh, B4modb);
129 add_ssaaaa (rh, rl, rh, rl, ph, pl);
130 }
131
132 bi = cps[0];
133 cnt = cps[1];
134
135 #if 1
136 umul_ppmm (rh, cl, rh, B1modb);
137 add_ssaaaa (rh, rl, rh, rl, 0, cl);
138 r = (rh << cnt) | (rl >> (GMP_LIMB_BITS - cnt));
139 #else
140 udiv_qrnnd_preinv (q, r, rh >> (GMP_LIMB_BITS - cnt),
141 (rh << cnt) | (rl >> (GMP_LIMB_BITS - cnt)), b, bi);
142 ASSERT (q <= 3); /* optimize for small quotient? */
143 #endif
144
145 udiv_qrnnd_preinv (q, r, r, rl << cnt, b, bi);
146
147 return r >> cnt;
148 }
149