1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
|
// Copyright (c) 2009-2011, Wilson W.L. Fung, Tor M. Aamodt, Ali Bakhoda,
// The University of British Columbia
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
// Redistributions of source code must retain the above copyright notice, this
// list of conditions and the following disclaimer.
// Redistributions in binary form must reproduce the above copyright notice,
// this list of conditions and the following disclaimer in the documentation
// and/or other materials provided with the distribution. Neither the name of
// The University of British Columbia nor the names of its contributors may be
// used to endorse or promote products derived from this software without
// specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
// POSSIBILITY OF SUCH DAMAGE.
#include <math.h>
#include <string.h>
#include "../abstract_hardware_model.h"
#include "gpu-cache.h"
unsigned ipoly_hash_function(new_addr_type higher_bits, unsigned index,
unsigned bank_set_num) {
/*
* Set Indexing function from "Pseudo-randomly interleaved memory."
* Rau, B. R et al.
* ISCA 1991
* http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=348DEA37A3E440473B3C075EAABC63B6?doi=10.1.1.12.7149&rep=rep1&type=pdf
*
* equations are corresponding to IPOLY(37) and are adopted from:
* "Sacat: streaming-aware conflict-avoiding thrashing-resistant gpgpu
* cache management scheme." Khairy et al. IEEE TPDS 2017.
*
* equations for 16 banks are corresponding to IPOLY(5)
* equations for 32 banks are corresponding to IPOLY(37)
* equations for 64 banks are corresponding to IPOLY(67)
* To see all the IPOLY equations for all the degrees, see
* http://wireless-systems.ece.gatech.edu/6604/handouts/Peterson's%20Table.pdf
*
* We generate these equations using GF(2) arithmetic:
* http://www.ee.unb.ca/cgi-bin/tervo/calc.pl?num=&den=&f=d&e=1&m=1
*
* We go through all the strides 128 (10000000), 256 (100000000),... and
* do modular arithmetic in GF(2) Then, we create the H-matrix and group
* each bit together, for more info read the ISCA 1991 paper
*
* IPOLY hashing guarantees conflict-free for all 2^n strides which widely
* exit in GPGPU applications and also show good performance for other
* strides.
*/
if (bank_set_num == 16) {
std::bitset<64> a(higher_bits);
std::bitset<4> b(index);
std::bitset<4> new_index(index);
new_index[0] =
a[11] ^ a[10] ^ a[9] ^ a[8] ^ a[6] ^ a[4] ^ a[3] ^ a[0] ^ b[0];
new_index[1] =
a[12] ^ a[8] ^ a[7] ^ a[6] ^ a[5] ^ a[3] ^ a[1] ^ a[0] ^ b[1];
new_index[2] = a[9] ^ a[8] ^ a[7] ^ a[6] ^ a[4] ^ a[2] ^ a[1] ^ b[2];
new_index[3] = a[10] ^ a[9] ^ a[8] ^ a[7] ^ a[5] ^ a[3] ^ a[2] ^ b[3];
return new_index.to_ulong();
} else if (bank_set_num == 32) {
std::bitset<64> a(higher_bits);
std::bitset<5> b(index);
std::bitset<5> new_index(index);
new_index[0] =
a[13] ^ a[12] ^ a[11] ^ a[10] ^ a[9] ^ a[6] ^ a[5] ^ a[3] ^ a[0] ^ b[0];
new_index[1] = a[14] ^ a[13] ^ a[12] ^ a[11] ^ a[10] ^ a[7] ^ a[6] ^ a[4] ^
a[1] ^ b[1];
new_index[2] =
a[14] ^ a[10] ^ a[9] ^ a[8] ^ a[7] ^ a[6] ^ a[3] ^ a[2] ^ a[0] ^ b[2];
new_index[3] =
a[11] ^ a[10] ^ a[9] ^ a[8] ^ a[7] ^ a[4] ^ a[3] ^ a[1] ^ b[3];
new_index[4] =
a[12] ^ a[11] ^ a[10] ^ a[9] ^ a[8] ^ a[5] ^ a[4] ^ a[2] ^ b[4];
return new_index.to_ulong();
} else if (bank_set_num == 64) {
std::bitset<64> a(higher_bits);
std::bitset<6> b(index);
std::bitset<6> new_index(index);
new_index[0] = a[18] ^ a[17] ^ a[16] ^ a[15] ^ a[12] ^ a[10] ^ a[6] ^ a[5] ^
a[0] ^ b[0];
new_index[1] = a[15] ^ a[13] ^ a[12] ^ a[11] ^ a[10] ^ a[7] ^ a[5] ^ a[1] ^
a[0] ^ b[1];
new_index[2] = a[16] ^ a[14] ^ a[13] ^ a[12] ^ a[11] ^ a[8] ^ a[6] ^ a[2] ^
a[1] ^ b[2];
new_index[3] = a[17] ^ a[15] ^ a[14] ^ a[13] ^ a[12] ^ a[9] ^ a[7] ^ a[3] ^
a[2] ^ b[3];
new_index[4] = a[18] ^ a[16] ^ a[15] ^ a[14] ^ a[13] ^ a[10] ^ a[8] ^ a[4] ^
a[3] ^ b[4];
new_index[5] =
a[17] ^ a[16] ^ a[15] ^ a[14] ^ a[11] ^ a[9] ^ a[5] ^ a[4] ^ b[5];
return new_index.to_ulong();
} else { /* Else incorrect number of channels for the hashing function */
assert(
"\nmemory_partition_indexing error: The number of "
"channels should be "
"16, 32 or 64 for the hashing IPOLY index function. other banks "
"numbers are not supported. Generate it by yourself! \n" &&
0);
return 0;
}
}
unsigned bitwise_hash_function(new_addr_type higher_bits, unsigned index,
unsigned bank_set_num) {
return (index) ^ (higher_bits & (bank_set_num - 1));
}
unsigned PAE_hash_function(new_addr_type higher_bits, unsigned index,
unsigned bank_set_num) {
// Page Address Entropy
// random selected bits from the page and bank bits
// similar to
// Liu, Yuxi, et al. "Get Out of the Valley: Power-Efficient Address
if (bank_set_num == 32) {
std::bitset<64> a(higher_bits);
std::bitset<5> b(index);
std::bitset<5> new_index(index);
new_index[0] = a[13] ^ a[10] ^ a[9] ^ a[5] ^ a[0] ^ b[3] ^ b[0] ^ b[0];
new_index[1] = a[12] ^ a[11] ^ a[6] ^ a[1] ^ b[3] ^ b[2] ^ b[1] ^ b[1];
new_index[2] = a[14] ^ a[9] ^ a[8] ^ a[7] ^ a[2] ^ b[1] ^ b[2];
new_index[3] = a[11] ^ a[10] ^ a[8] ^ a[3] ^ b[2] ^ b[3] ^ b[3];
new_index[4] = a[12] ^ a[9] ^ a[8] ^ a[5] ^ a[4] ^ b[1] ^ b[0] ^ b[4];
return new_index.to_ulong();
} else {
assert(0);
return 0;
}
}
|
