1 /* mpn_divexact_by3c -- mpn exact division by 3.
2
3 Copyright 2000-2003, 2008 Free Software Foundation, Inc.
4
5 This file is part of the GNU MP Library.
6
7 The GNU MP Library is free software; you can redistribute it and/or modify
8 it under the terms of either:
9
10 * the GNU Lesser General Public License as published by the Free
11 Software Foundation; either version 3 of the License, or (at your
12 option) any later version.
13
14 or
15
16 * the GNU General Public License as published by the Free Software
17 Foundation; either version 2 of the License, or (at your option) any
18 later version.
19
20 or both in parallel, as here.
21
22 The GNU MP Library is distributed in the hope that it will be useful, but
23 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
24 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
25 for more details.
26
27 You should have received copies of the GNU General Public License and the
28 GNU Lesser General Public License along with the GNU MP Library. If not,
29 see https://www.gnu.org/licenses/. */
30
31 #include "gmp-impl.h"
32
33 #if DIVEXACT_BY3_METHOD == 0
34
35 mp_limb_t
36 mpn_divexact_by3c (mp_ptr rp, mp_srcptr up, mp_size_t un, mp_limb_t c)
37 {
38 mp_limb_t r;
39 r = mpn_bdiv_dbm1c (rp, up, un, GMP_NUMB_MASK / 3, GMP_NUMB_MASK / 3 * c);
40
41 /* Possible bdiv_dbm1 return values are C * (GMP_NUMB_MASK / 3), 0 <= C < 3.
42 We want to return C. We compute the remainder mod 4 and notice that the
43 inverse of (2^(2k)-1)/3 mod 4 is 1. */
44 return r & 3;
45 }
46
47 #endif
48
49 #if DIVEXACT_BY3_METHOD == 1
50
51 /* The algorithm here is basically the same as mpn_divexact_1, as described
52 in the manual. Namely at each step q = (src[i]-c)*inverse, and new c =
53 borrow(src[i]-c) + high(divisor*q). But because the divisor is just 3,
54 high(divisor*q) can be determined with two comparisons instead of a
55 multiply.
56
57 The "c += ..."s add the high limb of 3*l to c. That high limb will be 0,
58 1 or 2. Doing two separate "+="s seems to give better code on gcc (as of
59 2.95.2 at least).
60
61 It will be noted that the new c is formed by adding three values each 0
62 or 1. But the total is only 0, 1 or 2. When the subtraction src[i]-c
63 causes a borrow, that leaves a limb value of either 0xFF...FF or
64 0xFF...FE. The multiply by MODLIMB_INVERSE_3 gives 0x55...55 or
65 0xAA...AA respectively, and in those cases high(3*q) is only 0 or 1
66 respectively, hence a total of no more than 2.
67
68 Alternatives:
69
70 This implementation has each multiply on the dependent chain, due to
71 "l=s-c". See below for alternative code which avoids that. */
72
73 mp_limb_t
74 mpn_divexact_by3c (mp_ptr restrict rp, mp_srcptr restrict up, mp_size_t un, mp_limb_t c)
75 {
76 mp_limb_t l, q, s;
77 mp_size_t i;
78
79 ASSERT (un >= 1);
80 ASSERT (c == 0 || c == 1 || c == 2);
81 ASSERT (MPN_SAME_OR_SEPARATE_P (rp, up, un));
82
83 i = 0;
84 do
85 {
86 s = up[i];
87 SUBC_LIMB (c, l, s, c);
88
89 q = (l * MODLIMB_INVERSE_3) & GMP_NUMB_MASK;
90 rp[i] = q;
91
92 c += (q >= GMP_NUMB_CEIL_MAX_DIV3);
93 c += (q >= GMP_NUMB_CEIL_2MAX_DIV3);
94 }
95 while (++i < un);
96
97 ASSERT (c == 0 || c == 1 || c == 2);
98 return c;
99 }
100
101
102 #endif
103
104 #if DIVEXACT_BY3_METHOD == 2
105
106 /* The following alternative code re-arranges the quotient calculation from
107 (src[i]-c)*inverse to instead
108
109 q = src[i]*inverse - c*inverse
110
111 thereby allowing src[i]*inverse to be scheduled back as far as desired,
112 making full use of multiplier throughput and leaving just some carry
113 handing on the dependent chain.
114
115 The carry handling consists of determining the c for the next iteration.
116 This is the same as described above, namely look for any borrow from
117 src[i]-c, and at the high of 3*q.
118
119 high(3*q) is done with two comparisons as above (in c2 and c3). The
120 borrow from src[i]-c is incorporated into those by noting that if there's
121 a carry then then we have src[i]-c == 0xFF..FF or 0xFF..FE, in turn
122 giving q = 0x55..55 or 0xAA..AA. Adding 1 to either of those q values is
123 enough to make high(3*q) come out 1 bigger, as required.
124
125 l = -c*inverse is calculated at the same time as c, since for most chips
126 it can be more conveniently derived from separate c1/c2/c3 values than
127 from a combined c equal to 0, 1 or 2.
128
129 The net effect is that with good pipelining this loop should be able to
130 run at perhaps 4 cycles/limb, depending on available execute resources
131 etc.
132
133 Usage:
134
135 This code is not used by default, since we really can't rely on the
136 compiler generating a good software pipeline, nor on such an approach
137 even being worthwhile on all CPUs.
138
139 Itanium is one chip where this algorithm helps though, see
140 mpn/ia64/diveby3.asm. */
141
142 mp_limb_t
143 mpn_divexact_by3c (mp_ptr restrict rp, mp_srcptr restrict up, mp_size_t un, mp_limb_t cy)
144 {
145 mp_limb_t s, sm, cl, q, qx, c2, c3;
146 mp_size_t i;
147
148 ASSERT (un >= 1);
149 ASSERT (cy == 0 || cy == 1 || cy == 2);
150 ASSERT (MPN_SAME_OR_SEPARATE_P (rp, up, un));
151
152 cl = cy == 0 ? 0 : cy == 1 ? -MODLIMB_INVERSE_3 : -2*MODLIMB_INVERSE_3;
153
154 for (i = 0; i < un; i++)
155 {
156 s = up[i];
157 sm = (s * MODLIMB_INVERSE_3) & GMP_NUMB_MASK;
158
159 q = (cl + sm) & GMP_NUMB_MASK;
160 rp[i] = q;
161 qx = q + (s < cy);
162
163 c2 = qx >= GMP_NUMB_CEIL_MAX_DIV3;
164 c3 = qx >= GMP_NUMB_CEIL_2MAX_DIV3 ;
165
166 cy = c2 + c3;
167 cl = (-c2 & -MODLIMB_INVERSE_3) + (-c3 & -MODLIMB_INVERSE_3);
168 }
169
170 return cy;
171 }
172
173 #endif