Print this page
3741 zfs needs better comments
Submitted by: Will Andrews <willa@spectralogic.com>
Submitted by: Justin Gibbs <justing@spectralogic.com>
Submitted by: Alan Somers <alans@spectralogic.com>
Reviewed by: Matthew Ahrens <mahrens@delphix.com>
| Split |
Close |
| Expand all |
| Collapse all |
--- old/usr/src/common/zfs/zfs_fletcher.c
+++ new/usr/src/common/zfs/zfs_fletcher.c
1 1 /*
2 2 * CDDL HEADER START
3 3 *
4 4 * The contents of this file are subject to the terms of the
5 5 * Common Development and Distribution License (the "License").
6 6 * You may not use this file except in compliance with the License.
7 7 *
8 8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9 9 * or http://www.opensolaris.org/os/licensing.
10 10 * See the License for the specific language governing permissions
11 11 * and limitations under the License.
12 12 *
13 13 * When distributing Covered Code, include this CDDL HEADER in each
14 14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15 15 * If applicable, add the following below this CDDL HEADER, with the
16 16 * fields enclosed by brackets "[]" replaced with your own identifying
17 17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 18 *
19 19 * CDDL HEADER END
20 20 */
21 21 /*
22 22 * Copyright 2009 Sun Microsystems, Inc. All rights reserved.
23 23 * Use is subject to license terms.
24 24 */
25 25
26 26 /*
27 27 * Fletcher Checksums
28 28 * ------------------
29 29 *
30 30 * ZFS's 2nd and 4th order Fletcher checksums are defined by the following
31 31 * recurrence relations:
32 32 *
33 33 * a = a + f
34 34 * i i-1 i-1
35 35 *
36 36 * b = b + a
37 37 * i i-1 i
38 38 *
39 39 * c = c + b (fletcher-4 only)
40 40 * i i-1 i
41 41 *
42 42 * d = d + c (fletcher-4 only)
43 43 * i i-1 i
44 44 *
45 45 * Where
46 46 * a_0 = b_0 = c_0 = d_0 = 0
47 47 * and
48 48 * f_0 .. f_(n-1) are the input data.
49 49 *
50 50 * Using standard techniques, these translate into the following series:
51 51 *
52 52 * __n_ __n_
53 53 * \ | \ |
54 54 * a = > f b = > i * f
55 55 * n /___| n - i n /___| n - i
56 56 * i = 1 i = 1
57 57 *
58 58 *
59 59 * __n_ __n_
60 60 * \ | i*(i+1) \ | i*(i+1)*(i+2)
61 61 * c = > ------- f d = > ------------- f
62 62 * n /___| 2 n - i n /___| 6 n - i
63 63 * i = 1 i = 1
64 64 *
65 65 * For fletcher-2, the f_is are 64-bit, and [ab]_i are 64-bit accumulators.
66 66 * Since the additions are done mod (2^64), errors in the high bits may not
67 67 * be noticed. For this reason, fletcher-2 is deprecated.
68 68 *
69 69 * For fletcher-4, the f_is are 32-bit, and [abcd]_i are 64-bit accumulators.
70 70 * A conservative estimate of how big the buffer can get before we overflow
71 71 * can be estimated using f_i = 0xffffffff for all i:
72 72 *
73 73 * % bc
74 74 * f=2^32-1;d=0; for (i = 1; d<2^64; i++) { d += f*i*(i+1)*(i+2)/6 }; (i-1)*4
75 75 * 2264
76 76 * quit
77 77 * %
78 78 *
79 79 * So blocks of up to 2k will not overflow. Our largest block size is
80 80 * 128k, which has 32k 4-byte words, so we can compute the largest possible
81 81 * accumulators, then divide by 2^64 to figure the max amount of overflow:
82 82 *
83 83 * % bc
84 84 * a=b=c=d=0; f=2^32-1; for (i=1; i<=32*1024; i++) { a+=f; b+=a; c+=b; d+=c }
85 85 * a/2^64;b/2^64;c/2^64;d/2^64
86 86 * 0
87 87 * 0
88 88 * 1365
89 89 * 11186858
90 90 * quit
91 91 * %
92 92 *
93 93 * So a and b cannot overflow. To make sure each bit of input has some
94 94 * effect on the contents of c and d, we can look at what the factors of
95 95 * the coefficients in the equations for c_n and d_n are. The number of 2s
96 96 * in the factors determines the lowest set bit in the multiplier. Running
97 97 * through the cases for n*(n+1)/2 reveals that the highest power of 2 is
98 98 * 2^14, and for n*(n+1)*(n+2)/6 it is 2^15. So while some data may overflow
99 99 * the 64-bit accumulators, every bit of every f_i effects every accumulator,
100 100 * even for 128k blocks.
101 101 *
102 102 * If we wanted to make a stronger version of fletcher4 (fletcher4c?),
103 103 * we could do our calculations mod (2^32 - 1) by adding in the carries
104 104 * periodically, and store the number of carries in the top 32-bits.
105 105 *
106 106 * --------------------
107 107 * Checksum Performance
108 108 * --------------------
109 109 *
110 110 * There are two interesting components to checksum performance: cached and
111 111 * uncached performance. With cached data, fletcher-2 is about four times
112 112 * faster than fletcher-4. With uncached data, the performance difference is
113 113 * negligible, since the cost of a cache fill dominates the processing time.
114 114 * Even though fletcher-4 is slower than fletcher-2, it is still a pretty
115 115 * efficient pass over the data.
116 116 *
117 117 * In normal operation, the data which is being checksummed is in a buffer
|
↓ open down ↓ |
117 lines elided |
↑ open up ↑ |
118 118 * which has been filled either by:
119 119 *
120 120 * 1. a compression step, which will be mostly cached, or
121 121 * 2. a bcopy() or copyin(), which will be uncached (because the
122 122 * copy is cache-bypassing).
123 123 *
124 124 * For both cached and uncached data, both fletcher checksums are much faster
125 125 * than sha-256, and slower than 'off', which doesn't touch the data at all.
126 126 */
127 127
128 +/*
129 + * TODO: vectorize these functions
130 + * All of these functions are written so that each iteration of the loop
131 + * depends on the value of the previous iteration. Also, in the fletcher_4
132 + * functions, each statement of the loop body depends on the previous
133 + * statement. These dependencies prevent the compiler from vectorizing the
134 + * code to take advantage of SIMD extensions (unless GCC is far smarter than I
135 + * think). It would be easy to rewrite the loops to be amenable to
136 + * autovectorization.
137 + */
138 +
128 139 #include <sys/types.h>
129 140 #include <sys/sysmacros.h>
130 141 #include <sys/byteorder.h>
131 142 #include <sys/zio.h>
132 143 #include <sys/spa.h>
133 144
134 145 void
135 146 fletcher_2_native(const void *buf, uint64_t size, zio_cksum_t *zcp)
136 147 {
137 148 const uint64_t *ip = buf;
138 149 const uint64_t *ipend = ip + (size / sizeof (uint64_t));
139 150 uint64_t a0, b0, a1, b1;
140 151
141 152 for (a0 = b0 = a1 = b1 = 0; ip < ipend; ip += 2) {
142 153 a0 += ip[0];
143 154 a1 += ip[1];
144 155 b0 += a0;
145 156 b1 += a1;
146 157 }
147 158
148 159 ZIO_SET_CHECKSUM(zcp, a0, a1, b0, b1);
149 160 }
150 161
151 162 void
152 163 fletcher_2_byteswap(const void *buf, uint64_t size, zio_cksum_t *zcp)
153 164 {
154 165 const uint64_t *ip = buf;
155 166 const uint64_t *ipend = ip + (size / sizeof (uint64_t));
156 167 uint64_t a0, b0, a1, b1;
157 168
158 169 for (a0 = b0 = a1 = b1 = 0; ip < ipend; ip += 2) {
159 170 a0 += BSWAP_64(ip[0]);
160 171 a1 += BSWAP_64(ip[1]);
161 172 b0 += a0;
162 173 b1 += a1;
163 174 }
164 175
165 176 ZIO_SET_CHECKSUM(zcp, a0, a1, b0, b1);
166 177 }
167 178
168 179 void
169 180 fletcher_4_native(const void *buf, uint64_t size, zio_cksum_t *zcp)
170 181 {
171 182 const uint32_t *ip = buf;
172 183 const uint32_t *ipend = ip + (size / sizeof (uint32_t));
173 184 uint64_t a, b, c, d;
174 185
175 186 for (a = b = c = d = 0; ip < ipend; ip++) {
176 187 a += ip[0];
177 188 b += a;
178 189 c += b;
179 190 d += c;
180 191 }
181 192
182 193 ZIO_SET_CHECKSUM(zcp, a, b, c, d);
183 194 }
184 195
185 196 void
186 197 fletcher_4_byteswap(const void *buf, uint64_t size, zio_cksum_t *zcp)
187 198 {
188 199 const uint32_t *ip = buf;
189 200 const uint32_t *ipend = ip + (size / sizeof (uint32_t));
190 201 uint64_t a, b, c, d;
191 202
192 203 for (a = b = c = d = 0; ip < ipend; ip++) {
193 204 a += BSWAP_32(ip[0]);
194 205 b += a;
195 206 c += b;
196 207 d += c;
197 208 }
198 209
199 210 ZIO_SET_CHECKSUM(zcp, a, b, c, d);
200 211 }
201 212
202 213 void
203 214 fletcher_4_incremental_native(const void *buf, uint64_t size,
204 215 zio_cksum_t *zcp)
205 216 {
206 217 const uint32_t *ip = buf;
207 218 const uint32_t *ipend = ip + (size / sizeof (uint32_t));
208 219 uint64_t a, b, c, d;
209 220
210 221 a = zcp->zc_word[0];
211 222 b = zcp->zc_word[1];
212 223 c = zcp->zc_word[2];
213 224 d = zcp->zc_word[3];
214 225
215 226 for (; ip < ipend; ip++) {
216 227 a += ip[0];
217 228 b += a;
218 229 c += b;
219 230 d += c;
220 231 }
221 232
222 233 ZIO_SET_CHECKSUM(zcp, a, b, c, d);
223 234 }
224 235
225 236 void
226 237 fletcher_4_incremental_byteswap(const void *buf, uint64_t size,
227 238 zio_cksum_t *zcp)
228 239 {
229 240 const uint32_t *ip = buf;
230 241 const uint32_t *ipend = ip + (size / sizeof (uint32_t));
231 242 uint64_t a, b, c, d;
232 243
233 244 a = zcp->zc_word[0];
234 245 b = zcp->zc_word[1];
235 246 c = zcp->zc_word[2];
236 247 d = zcp->zc_word[3];
237 248
238 249 for (; ip < ipend; ip++) {
239 250 a += BSWAP_32(ip[0]);
240 251 b += a;
241 252 c += b;
242 253 d += c;
243 254 }
244 255
245 256 ZIO_SET_CHECKSUM(zcp, a, b, c, d);
246 257 }
|
↓ open down ↓ |
109 lines elided |
↑ open up ↑ |
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX