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-impl.h"
37
38
39 /* Calculate a remainder from {p,n} divided by 2^(GMP_NUMB_BITS*3/4)-1.
40 The remainder is not fully reduced, it's any limb value congruent to
41 {p,n} modulo that divisor.
42
43 This implementation is only correct when GMP_NUMB_BITS is a multiple of
44 4.
45
46 FIXME: If GMP_NAIL_BITS is some silly big value during development then
47 it's possible the carry accumulators c0,c1,c2 could overflow.
48
49 General notes:
50
51 The basic idea is to use a set of N accumulators (N=3 in this case) to
52 effectively get a remainder mod 2^(GMP_NUMB_BITS*N)-1 followed at the end
53 by a reduction to GMP_NUMB_BITS*N/M bits (M=4 in this case) for a
54 remainder mod 2^(GMP_NUMB_BITS*N/M)-1. N and M are chosen to give a good
55 set of small prime factors in 2^(GMP_NUMB_BITS*N/M)-1.
56
57 N=3 M=4 suits GMP_NUMB_BITS==32 and GMP_NUMB_BITS==64 quite well, giving
58 a few more primes than a single accumulator N=1 does, and for no extra
59 cost (assuming the processor has a decent number of registers).
60
61 For strange nailified values of GMP_NUMB_BITS the idea would be to look
62 for what N and M give good primes. With GMP_NUMB_BITS not a power of 2
63 the choices for M may be opened up a bit. But such things are probably
64 best done in separate code, not grafted on here. */
65
66 #if GMP_NUMB_BITS % 4 == 0
67
68 #define B1 (GMP_NUMB_BITS / 4)
69 #define B2 (B1 * 2)
70 #define B3 (B1 * 3)
71
72 #define M1 ((CNST_LIMB(1) << B1) - 1)
73 #define M2 ((CNST_LIMB(1) << B2) - 1)
74 #define M3 ((CNST_LIMB(1) << B3) - 1)
75
76 #define LOW0(n) ((n) & M3)
77 #define HIGH0(n) ((n) >> B3)
78
79 #define LOW1(n) (((n) & M2) << B1)
80 #define HIGH1(n) ((n) >> B2)
81
82 #define LOW2(n) (((n) & M1) << B2)
83 #define HIGH2(n) ((n) >> B1)
84
85 #define PARTS0(n) (LOW0(n) + HIGH0(n))
86 #define PARTS1(n) (LOW1(n) + HIGH1(n))
87 #define PARTS2(n) (LOW2(n) + HIGH2(n))
88
89 #define ADD(c,a,val) \
90 do { \
91 mp_limb_t new_c; \
92 ADDC_LIMB (new_c, a, a, val); \
93 (c) += new_c; \
94 } while (0)
95
96 mp_limb_t
97 mpn_mod_34lsub1 (mp_srcptr p, mp_size_t n)
98 {
99 mp_limb_t c0, c1, c2;
100 mp_limb_t a0, a1, a2;
101
102 ASSERT (n >= 1);
103 ASSERT (n/3 < GMP_NUMB_MAX);
104
105 a0 = a1 = a2 = 0;
106 c0 = c1 = c2 = 0;
107
108 while ((n -= 3) >= 0)
109 {
110 ADD (c0, a0, p[0]);
111 ADD (c1, a1, p[1]);
112 ADD (c2, a2, p[2]);
113 p += 3;
114 }
115
116 if (n != -3)
117 {
118 ADD (c0, a0, p[0]);
119 if (n != -2)
120 ADD (c1, a1, p[1]);
121 }
122
123 return
124 PARTS0 (a0) + PARTS1 (a1) + PARTS2 (a2)
125 + PARTS1 (c0) + PARTS2 (c1) + PARTS0 (c2);
126 }
127
128 #endif