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, 2001, 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 the GNU Lesser General Public License as published by
13 the Free Software Foundation; either version 3 of the License, or (at your
14 option) any later version.
15
16 The GNU MP Library is distributed in the hope that it will be useful, but
17 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
18 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
19 License for more details.
20
21 You should have received a copy of the GNU Lesser General Public License
22 along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
23
24
25 #include "gmp.h"
26 #include "gmp-impl.h"
27
28
29 /* Calculate a remainder from {p,n} divided by 2^(GMP_NUMB_BITS*3/4)-1.
30 The remainder is not fully reduced, it's any limb value congruent to
31 {p,n} modulo that divisor.
32
33 This implementation is only correct when GMP_NUMB_BITS is a multiple of
34 4.
35
36 FIXME: If GMP_NAIL_BITS is some silly big value during development then
37 it's possible the carry accumulators c0,c1,c2 could overflow.
38
39 General notes:
40
41 The basic idea is to use a set of N accumulators (N=3 in this case) to
42 effectively get a remainder mod 2^(GMP_NUMB_BITS*N)-1 followed at the end
43 by a reduction to GMP_NUMB_BITS*N/M bits (M=4 in this case) for a
44 remainder mod 2^(GMP_NUMB_BITS*N/M)-1. N and M are chosen to give a good
45 set of small prime factors in 2^(GMP_NUMB_BITS*N/M)-1.
46
47 N=3 M=4 suits GMP_NUMB_BITS==32 and GMP_NUMB_BITS==64 quite well, giving
48 a few more primes than a single accumulator N=1 does, and for no extra
49 cost (assuming the processor has a decent number of registers).
50
51 For strange nailified values of GMP_NUMB_BITS the idea would be to look
52 for what N and M give good primes. With GMP_NUMB_BITS not a power of 2
53 the choices for M may be opened up a bit. But such things are probably
54 best done in separate code, not grafted on here. */
55
56 #if GMP_NUMB_BITS % 4 == 0
57
58 #define B1 (GMP_NUMB_BITS / 4)
59 #define B2 (B1 * 2)
60 #define B3 (B1 * 3)
61
62 #define M1 ((CNST_LIMB(1) << B1) - 1)
63 #define M2 ((CNST_LIMB(1) << B2) - 1)
64 #define M3 ((CNST_LIMB(1) << B3) - 1)
65
66 #define LOW0(n) ((n) & M3)
67 #define HIGH0(n) ((n) >> B3)
68
69 #define LOW1(n) (((n) & M2) << B1)
70 #define HIGH1(n) ((n) >> B2)
71
72 #define LOW2(n) (((n) & M1) << B2)
73 #define HIGH2(n) ((n) >> B1)
74
75 #define PARTS0(n) (LOW0(n) + HIGH0(n))
76 #define PARTS1(n) (LOW1(n) + HIGH1(n))
77 #define PARTS2(n) (LOW2(n) + HIGH2(n))
78
79 #define ADD(c,a,val) \
80 do { \
81 mp_limb_t new_c; \
82 ADDC_LIMB (new_c, a, a, val); \
83 (c) += new_c; \
84 } while (0)
85
86 mp_limb_t
mpn_mod_34lsub1(mp_srcptr p,mp_size_t n)87 mpn_mod_34lsub1 (mp_srcptr p, mp_size_t n)
88 {
89 mp_limb_t c0 = 0;
90 mp_limb_t c1 = 0;
91 mp_limb_t c2 = 0;
92 mp_limb_t a0, a1, a2;
93
94 ASSERT (n >= 1);
95 ASSERT (n/3 < GMP_NUMB_MAX);
96
97 a0 = a1 = a2 = 0;
98 c0 = c1 = c2 = 0;
99
100 while ((n -= 3) >= 0)
101 {
102 ADD (c0, a0, p[0]);
103 ADD (c1, a1, p[1]);
104 ADD (c2, a2, p[2]);
105 p += 3;
106 }
107
108 if (n != -3)
109 {
110 ADD (c0, a0, p[0]);
111 if (n != -2)
112 ADD (c1, a1, p[1]);
113 }
114
115 return
116 PARTS0 (a0) + PARTS1 (a1) + PARTS2 (a2)
117 + PARTS1 (c0) + PARTS2 (c1) + PARTS0 (c2);
118 }
119
120 #endif
121