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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 | /* | |
9babb374 | 22 | * Copyright 2009 Sun Microsystems, Inc. All rights reserved. |
34dc7c2f BB |
23 | * Use is subject to license terms. |
24 | */ | |
25 | ||
9babb374 BB |
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 | */ | |
34dc7c2f BB |
127 | |
128 | #include <sys/types.h> | |
129 | #include <sys/sysmacros.h> | |
130 | #include <sys/byteorder.h> | |
428870ff | 131 | #include <sys/zio.h> |
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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 | } |