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