1 /* mpn_mod_34lsub1 -- remainder modulo 2^(GMP_NUMB_BITS*3/4)-1.
2
3 THE FUNCTIONS IN THIS FILE ARE FOR INTERNAL USE ONLY. THEY'RE ALMOST
4 CERTAIN TO BE SUBJECT TO INCOMPATIBLE CHANGES OR DISAPPEAR COMPLETELY IN
5 FUTURE GNU MP RELEASES.
6
7 Copyright 2000-2002 Free Software Foundation, Inc.
8
9 This file is part of the GNU MP Library.
10
11 The GNU MP Library is free software; you can redistribute it and/or modify
12 it under the terms of either:
13
14 * the GNU Lesser General Public License as published by the Free
15 Software Foundation; either version 3 of the License, or (at your
16 option) any later version.
17
18 or
19
20 * the GNU General Public License as published by the Free Software
21 Foundation; either version 2 of the License, or (at your option) any
22 later version.
23
24 or both in parallel, as here.
25
26 The GNU MP Library is distributed in the hope that it will be useful, but
27 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
28 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
29 for more details.
30
31 You should have received copies of the GNU General Public License and the
32 GNU Lesser General Public License along with the GNU MP Library. If not,
33 see https://www.gnu.org/licenses/. */
34
35
36 #include "gmp.h"
37 #include "gmp-impl.h"
38
39
40 /* Calculate a remainder from {p,n} divided by 2^(GMP_NUMB_BITS*3/4)-1.
41 The remainder is not fully reduced, it's any limb value congruent to
42 {p,n} modulo that divisor.
43
44 This implementation is only correct when GMP_NUMB_BITS is a multiple of
45 4.
46
47 FIXME: If GMP_NAIL_BITS is some silly big value during development then
48 it's possible the carry accumulators c0,c1,c2 could overflow.
49
50 General notes:
51
52 The basic idea is to use a set of N accumulators (N=3 in this case) to
53 effectively get a remainder mod 2^(GMP_NUMB_BITS*N)-1 followed at the end
54 by a reduction to GMP_NUMB_BITS*N/M bits (M=4 in this case) for a
55 remainder mod 2^(GMP_NUMB_BITS*N/M)-1. N and M are chosen to give a good
56 set of small prime factors in 2^(GMP_NUMB_BITS*N/M)-1.
57
58 N=3 M=4 suits GMP_NUMB_BITS==32 and GMP_NUMB_BITS==64 quite well, giving
59 a few more primes than a single accumulator N=1 does, and for no extra
60 cost (assuming the processor has a decent number of registers).
61
62 For strange nailified values of GMP_NUMB_BITS the idea would be to look
63 for what N and M give good primes. With GMP_NUMB_BITS not a power of 2
64 the choices for M may be opened up a bit. But such things are probably
65 best done in separate code, not grafted on here. */
66
67 #if GMP_NUMB_BITS % 4 == 0
68
69 #define B1 (GMP_NUMB_BITS / 4)
70 #define B2 (B1 * 2)
71 #define B3 (B1 * 3)
72
73 #define M1 ((CNST_LIMB(1) << B1) - 1)
74 #define M2 ((CNST_LIMB(1) << B2) - 1)
75 #define M3 ((CNST_LIMB(1) << B3) - 1)
76
77 #define LOW0(n) ((n) & M3)
78 #define HIGH0(n) ((n) >> B3)
79
80 #define LOW1(n) (((n) & M2) << B1)
81 #define HIGH1(n) ((n) >> B2)
82
83 #define LOW2(n) (((n) & M1) << B2)
84 #define HIGH2(n) ((n) >> B1)
85
86 #define PARTS0(n) (LOW0(n) + HIGH0(n))
87 #define PARTS1(n) (LOW1(n) + HIGH1(n))
88 #define PARTS2(n) (LOW2(n) + HIGH2(n))
89
90 #define ADD(c,a,val) \
91 do { \
92 mp_limb_t new_c; \
93 ADDC_LIMB (new_c, a, a, val); \
94 (c) += new_c; \
95 } while (0)
96
97 mp_limb_t
mpn_mod_34lsub1(mp_srcptr p,mp_size_t n)98 mpn_mod_34lsub1 (mp_srcptr p, mp_size_t n)
99 {
100 mp_limb_t c0 = 0;
101 mp_limb_t c1 = 0;
102 mp_limb_t c2 = 0;
103 mp_limb_t a0, a1, a2;
104
105 ASSERT (n >= 1);
106 ASSERT (n/3 < GMP_NUMB_MAX);
107
108 a0 = a1 = a2 = 0;
109 c0 = c1 = c2 = 0;
110
111 while ((n -= 3) >= 0)
112 {
113 ADD (c0, a0, p[0]);
114 ADD (c1, a1, p[1]);
115 ADD (c2, a2, p[2]);
116 p += 3;
117 }
118
119 if (n != -3)
120 {
121 ADD (c0, a0, p[0]);
122 if (n != -2)
123 ADD (c1, a1, p[1]);
124 }
125
126 return
127 PARTS0 (a0) + PARTS1 (a1) + PARTS2 (a2)
128 + PARTS1 (c0) + PARTS2 (c1) + PARTS0 (c2);
129 }
130
131 #endif
132