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
134void
135fletcher_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
151void
152fletcher_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
168void
169fletcher_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
185void
186fletcher_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
202void
203fletcher_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
225void
226fletcher_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}
247