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 * Copyright 2013 Saso Kiselkov. All rights reserved.
27 */
28
29 /*
30 * Fletcher Checksums
31 * ------------------
32 *
33 * ZFS's 2nd and 4th order Fletcher checksums are defined by the following
34 * recurrence relations:
35 *
36 * a = a + f
37 * i i-1 i-1
38 *
39 * b = b + a
40 * i i-1 i
41 *
42 * c = c + b (fletcher-4 only)
43 * i i-1 i
44 *
45 * d = d + c (fletcher-4 only)
46 * i i-1 i
47 *
48 * Where
49 * a_0 = b_0 = c_0 = d_0 = 0
50 * and
51 * f_0 .. f_(n-1) are the input data.
52 *
53 * Using standard techniques, these translate into the following series:
54 *
55 * __n_ __n_
56 * \ | \ |
57 * a = > f b = > i * f
58 * n /___| n - i n /___| n - i
59 * i = 1 i = 1
60 *
61 *
62 * __n_ __n_
63 * \ | i*(i+1) \ | i*(i+1)*(i+2)
64 * c = > ------- f d = > ------------- f
65 * n /___| 2 n - i n /___| 6 n - i
66 * i = 1 i = 1
67 *
68 * For fletcher-2, the f_is are 64-bit, and [ab]_i are 64-bit accumulators.
69 * Since the additions are done mod (2^64), errors in the high bits may not
70 * be noticed. For this reason, fletcher-2 is deprecated.
71 *
72 * For fletcher-4, the f_is are 32-bit, and [abcd]_i are 64-bit accumulators.
73 * A conservative estimate of how big the buffer can get before we overflow
74 * can be estimated using f_i = 0xffffffff for all i:
75 *
76 * % bc
77 * f=2^32-1;d=0; for (i = 1; d<2^64; i++) { d += f*i*(i+1)*(i+2)/6 }; (i-1)*4
78 * 2264
79 * quit
80 * %
81 *
82 * So blocks of up to 2k will not overflow. Our largest block size is
83 * 128k, which has 32k 4-byte words, so we can compute the largest possible
84 * accumulators, then divide by 2^64 to figure the max amount of overflow:
85 *
86 * % bc
87 * a=b=c=d=0; f=2^32-1; for (i=1; i<=32*1024; i++) { a+=f; b+=a; c+=b; d+=c }
88 * a/2^64;b/2^64;c/2^64;d/2^64
89 * 0
90 * 0
91 * 1365
92 * 11186858
93 * quit
94 * %
95 *
96 * So a and b cannot overflow. To make sure each bit of input has some
97 * effect on the contents of c and d, we can look at what the factors of
98 * the coefficients in the equations for c_n and d_n are. The number of 2s
99 * in the factors determines the lowest set bit in the multiplier. Running
100 * through the cases for n*(n+1)/2 reveals that the highest power of 2 is
101 * 2^14, and for n*(n+1)*(n+2)/6 it is 2^15. So while some data may overflow
102 * the 64-bit accumulators, every bit of every f_i effects every accumulator,
103 * even for 128k blocks.
104 *
105 * If we wanted to make a stronger version of fletcher4 (fletcher4c?),
106 * we could do our calculations mod (2^32 - 1) by adding in the carries
107 * periodically, and store the number of carries in the top 32-bits.
108 *
109 * --------------------
110 * Checksum Performance
111 * --------------------
112 *
113 * There are two interesting components to checksum performance: cached and
114 * uncached performance. With cached data, fletcher-2 is about four times
115 * faster than fletcher-4. With uncached data, the performance difference is
116 * negligible, since the cost of a cache fill dominates the processing time.
117 * Even though fletcher-4 is slower than fletcher-2, it is still a pretty
118 * efficient pass over the data.
119 *
120 * In normal operation, the data which is being checksummed is in a buffer
121 * which has been filled either by:
122 *
123 * 1. a compression step, which will be mostly cached, or
124 * 2. a bcopy() or copyin(), which will be uncached (because the
125 * copy is cache-bypassing).
126 *
127 * For both cached and uncached data, both fletcher checksums are much faster
128 * than sha-256, and slower than 'off', which doesn't touch the data at all.
129 */
130
131 #include <sys/types.h>
132 #include <sys/sysmacros.h>
133 #include <sys/byteorder.h>
134 #include <sys/zio.h>
135 #include <sys/spa.h>
136
137 /*ARGSUSED*/
138 void
139 fletcher_2_native(const void *buf, uint64_t size, const zio_cksum_salt_t *salt,
140 const void *ctx_template, zio_cksum_t *zcp)
141 {
142 const uint64_t *ip = buf;
143 const uint64_t *ipend = ip + (size / sizeof (uint64_t));
144 uint64_t a0, b0, a1, b1;
145
146 for (a0 = b0 = a1 = b1 = 0; ip < ipend; ip += 2) {
147 a0 += ip[0];
148 a1 += ip[1];
149 b0 += a0;
150 b1 += a1;
151 }
152
153 ZIO_SET_CHECKSUM(zcp, a0, a1, b0, b1);
154 }
155
156 /*ARGSUSED*/
157 void
158 fletcher_2_byteswap(const void *buf, uint64_t size,
159 const zio_cksum_salt_t *salt, const void *ctx_template, zio_cksum_t *zcp)
160 {
161 const uint64_t *ip = buf;
162 const uint64_t *ipend = ip + (size / sizeof (uint64_t));
163 uint64_t a0, b0, a1, b1;
164
165 for (a0 = b0 = a1 = b1 = 0; ip < ipend; ip += 2) {
166 a0 += BSWAP_64(ip[0]);
167 a1 += BSWAP_64(ip[1]);
168 b0 += a0;
169 b1 += a1;
170 }
171
172 ZIO_SET_CHECKSUM(zcp, a0, a1, b0, b1);
173 }
174
175 /*ARGSUSED*/
176 void
177 fletcher_4_native(const void *buf, uint64_t size, const zio_cksum_salt_t *salt,
178 const void *ctx_template, zio_cksum_t *zcp)
179 {
180 const uint32_t *ip = buf;
181 const uint32_t *ipend = ip + (size / sizeof (uint32_t));
182 uint64_t a, b, c, d;
183
184 for (a = b = c = d = 0; ip < ipend; ip++) {
185 a += ip[0];
186 b += a;
187 c += b;
188 d += c;
189 }
190
191 ZIO_SET_CHECKSUM(zcp, a, b, c, d);
192 }
193
194 /*ARGSUSED*/
195 void
196 fletcher_4_byteswap(const void *buf, uint64_t size,
197 const zio_cksum_salt_t *salt, const void *ctx_template, zio_cksum_t *zcp)
198 {
199 const uint32_t *ip = buf;
200 const uint32_t *ipend = ip + (size / sizeof (uint32_t));
201 uint64_t a, b, c, d;
202
203 for (a = b = c = d = 0; ip < ipend; ip++) {
204 a += BSWAP_32(ip[0]);
205 b += a;
206 c += b;
207 d += c;
208 }
209
210 ZIO_SET_CHECKSUM(zcp, a, b, c, d);
211 }
212
213 void
214 fletcher_4_incremental_native(const void *buf, uint64_t size,
215 zio_cksum_t *zcp)
216 {
217 const uint32_t *ip = buf;
218 const uint32_t *ipend = ip + (size / sizeof (uint32_t));
219 uint64_t a, b, c, d;
220
221 a = zcp->zc_word[0];
222 b = zcp->zc_word[1];
223 c = zcp->zc_word[2];
224 d = zcp->zc_word[3];
225
226 for (; ip < ipend; ip++) {
227 a += ip[0];
228 b += a;
229 c += b;
230 d += c;
231 }
232
233 ZIO_SET_CHECKSUM(zcp, a, b, c, d);
234 }
235
236 void
237 fletcher_4_incremental_byteswap(const void *buf, uint64_t size,
238 zio_cksum_t *zcp)
239 {
240 const uint32_t *ip = buf;
241 const uint32_t *ipend = ip + (size / sizeof (uint32_t));
242 uint64_t a, b, c, d;
243
244 a = zcp->zc_word[0];
245 b = zcp->zc_word[1];
246 c = zcp->zc_word[2];
247 d = zcp->zc_word[3];
248
249 for (; ip < ipend; ip++) {
250 a += BSWAP_32(ip[0]);
251 b += a;
252 c += b;
253 d += c;
254 }
255
256 ZIO_SET_CHECKSUM(zcp, a, b, c, d);
257 }