[mirror_zfs-debian.git] / module / zfs / fletcher.c

/*
 * CDDL HEADER START
 *
 * The contents of this file are subject to the terms of the
 * Common Development and Distribution License (the "License").
 * You may not use this file except in compliance with the License.
 *
 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
 * or http://www.opensolaris.org/os/licensing.
 * See the License for the specific language governing permissions
 * and limitations under the License.
 *
 * When distributing Covered Code, include this CDDL HEADER in each
 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
 * If applicable, add the following below this CDDL HEADER, with the
 * fields enclosed by brackets "[]" replaced with your own identifying
 * information: Portions Copyright [yyyy] [name of copyright owner]
 *
 * CDDL HEADER END
 */
/*
 * Copyright 2009 Sun Microsystems, Inc.  All rights reserved.
 * Use is subject to license terms.
 */

/*
 * Fletcher Checksums
 * ------------------
 *
 * ZFS's 2nd and 4th order Fletcher checksums are defined by the following
 * recurrence relations:
 *
 *	a  = a    + f
 *	 i    i-1    i-1
 *
 *	b  = b    + a
 *	 i    i-1    i
 *
 *	c  = c    + b		(fletcher-4 only)
 *	 i    i-1    i
 *
 *	d  = d    + c		(fletcher-4 only)
 *	 i    i-1    i
 *
 * Where
 *	a_0 = b_0 = c_0 = d_0 = 0
 * and
 *	f_0 .. f_(n-1) are the input data.
 *
 * Using standard techniques, these translate into the following series:
 *
 *	     __n_			     __n_
 *	     \   |			     \   |
 *	a  =  >     f			b  =  >     i * f
 *	 n   /___|   n - i		 n   /___|	 n - i
 *	     i = 1			     i = 1
 *
 *
 *	     __n_			     __n_
 *	     \   |  i*(i+1)		     \   |  i*(i+1)*(i+2)
 *	c  =  >     ------- f		d  =  >     ------------- f
 *	 n   /___|     2     n - i	 n   /___|	  6	   n - i
 *	     i = 1			     i = 1
 *
 * For fletcher-2, the f_is are 64-bit, and [ab]_i are 64-bit accumulators.
 * Since the additions are done mod (2^64), errors in the high bits may not
 * be noticed.  For this reason, fletcher-2 is deprecated.
 *
 * For fletcher-4, the f_is are 32-bit, and [abcd]_i are 64-bit accumulators.
 * A conservative estimate of how big the buffer can get before we overflow
 * can be estimated using f_i = 0xffffffff for all i:
 *
 * % bc
 *  f=2^32-1;d=0; for (i = 1; d<2^64; i++) { d += f*i*(i+1)*(i+2)/6 }; (i-1)*4
 * 2264
 *  quit
 * %
 *
 * So blocks of up to 2k will not overflow.  Our largest block size is
 * 128k, which has 32k 4-byte words, so we can compute the largest possible
 * accumulators, then divide by 2^64 to figure the max amount of overflow:
 *
 * % bc
 *  a=b=c=d=0; f=2^32-1; for (i=1; i<=32*1024; i++) { a+=f; b+=a; c+=b; d+=c }
 *  a/2^64;b/2^64;c/2^64;d/2^64
 * 0
 * 0
 * 1365
 * 11186858
 *  quit
 * %
 *
 * So a and b cannot overflow.  To make sure each bit of input has some
 * effect on the contents of c and d, we can look at what the factors of
 * the coefficients in the equations for c_n and d_n are.  The number of 2s
 * in the factors determines the lowest set bit in the multiplier.  Running
 * through the cases for n*(n+1)/2 reveals that the highest power of 2 is
 * 2^14, and for n*(n+1)*(n+2)/6 it is 2^15.  So while some data may overflow
 * the 64-bit accumulators, every bit of every f_i effects every accumulator,
 * even for 128k blocks.
 *
 * If we wanted to make a stronger version of fletcher4 (fletcher4c?),
 * we could do our calculations mod (2^32 - 1) by adding in the carries
 * periodically, and store the number of carries in the top 32-bits.
 *
 * --------------------
 * Checksum Performance
 * --------------------
 *
 * There are two interesting components to checksum performance: cached and
 * uncached performance.  With cached data, fletcher-2 is about four times
 * faster than fletcher-4.  With uncached data, the performance difference is
 * negligible, since the cost of a cache fill dominates the processing time.
 * Even though fletcher-4 is slower than fletcher-2, it is still a pretty
 * efficient pass over the data.
 *
 * In normal operation, the data which is being checksummed is in a buffer
 * which has been filled either by:
 *
 *	1. a compression step, which will be mostly cached, or
 *	2. a bcopy() or copyin(), which will be uncached (because the
 *	   copy is cache-bypassing).
 *
 * For both cached and uncached data, both fletcher checksums are much faster
 * than sha-256, and slower than 'off', which doesn't touch the data at all.
 */

#include <sys/types.h>
#include <sys/sysmacros.h>
#include <sys/byteorder.h>
#include <sys/spa.h>

void
fletcher_2_native(const void *buf, uint64_t size, zio_cksum_t *zcp)
{
	const uint64_t *ip = buf;
	const uint64_t *ipend = ip + (size / sizeof (uint64_t));
	uint64_t a0, b0, a1, b1;

	for (a0 = b0 = a1 = b1 = 0; ip < ipend; ip += 2) {
		a0 += ip[0];
		a1 += ip[1];
		b0 += a0;
		b1 += a1;
	}

	ZIO_SET_CHECKSUM(zcp, a0, a1, b0, b1);
}

void
fletcher_2_byteswap(const void *buf, uint64_t size, zio_cksum_t *zcp)
{
	const uint64_t *ip = buf;
	const uint64_t *ipend = ip + (size / sizeof (uint64_t));
	uint64_t a0, b0, a1, b1;

	for (a0 = b0 = a1 = b1 = 0; ip < ipend; ip += 2) {
		a0 += BSWAP_64(ip[0]);
		a1 += BSWAP_64(ip[1]);
		b0 += a0;
		b1 += a1;
	}

	ZIO_SET_CHECKSUM(zcp, a0, a1, b0, b1);
}

void
fletcher_4_native(const void *buf, uint64_t size, zio_cksum_t *zcp)
{
	const uint32_t *ip = buf;
	const uint32_t *ipend = ip + (size / sizeof (uint32_t));
	uint64_t a, b, c, d;

	for (a = b = c = d = 0; ip < ipend; ip++) {
		a += ip[0];
		b += a;
		c += b;
		d += c;
	}

	ZIO_SET_CHECKSUM(zcp, a, b, c, d);
}

void
fletcher_4_byteswap(const void *buf, uint64_t size, zio_cksum_t *zcp)
{
	const uint32_t *ip = buf;
	const uint32_t *ipend = ip + (size / sizeof (uint32_t));
	uint64_t a, b, c, d;

	for (a = b = c = d = 0; ip < ipend; ip++) {
		a += BSWAP_32(ip[0]);
		b += a;
		c += b;
		d += c;
	}

	ZIO_SET_CHECKSUM(zcp, a, b, c, d);
}

void
fletcher_4_incremental_native(const void *buf, uint64_t size,
    zio_cksum_t *zcp)
{
	const uint32_t *ip = buf;
	const uint32_t *ipend = ip + (size / sizeof (uint32_t));
	uint64_t a, b, c, d;

	a = zcp->zc_word[0];
	b = zcp->zc_word[1];
	c = zcp->zc_word[2];
	d = zcp->zc_word[3];

	for (; ip < ipend; ip++) {
		a += ip[0];
		b += a;
		c += b;
		d += c;
	}

	ZIO_SET_CHECKSUM(zcp, a, b, c, d);
}

void
fletcher_4_incremental_byteswap(const void *buf, uint64_t size,
    zio_cksum_t *zcp)
{
	const uint32_t *ip = buf;
	const uint32_t *ipend = ip + (size / sizeof (uint32_t));
	uint64_t a, b, c, d;

	a = zcp->zc_word[0];
	b = zcp->zc_word[1];
	c = zcp->zc_word[2];
	d = zcp->zc_word[3];

	for (; ip < ipend; ip++) {
		a += BSWAP_32(ip[0]);
		b += a;
		c += b;
		d += c;
	}

	ZIO_SET_CHECKSUM(zcp, a, b, c, d);
}
Commit	Line	Data
34dc7c2f BB	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 += fi(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>
	131	#include <sys/spa.h>
	132
	133	void
	134	fletcher_2_native(const void buf, uint64_t size, zio_cksum_t zcp)
	135	{
	136	const uint64_t *ip = buf;
	137	const uint64_t *ipend = ip + (size / sizeof (uint64_t));
	138	uint64_t a0, b0, a1, b1;
	139
	140	for (a0 = b0 = a1 = b1 = 0; ip < ipend; ip += 2) {
	141	a0 += ip[0];
	142	a1 += ip[1];
	143	b0 += a0;
	144	b1 += a1;
	145	}
	146
	147	ZIO_SET_CHECKSUM(zcp, a0, a1, b0, b1);
	148	}
	149
	150	void
	151	fletcher_2_byteswap(const void buf, uint64_t size, zio_cksum_t zcp)
	152	{
	153	const uint64_t *ip = buf;
	154	const uint64_t *ipend = ip + (size / sizeof (uint64_t));
	155	uint64_t a0, b0, a1, b1;
	156
	157	for (a0 = b0 = a1 = b1 = 0; ip < ipend; ip += 2) {
	158	a0 += BSWAP_64(ip[0]);
	159	a1 += BSWAP_64(ip[1]);
	160	b0 += a0;
	161	b1 += a1;
	162	}
	163
	164	ZIO_SET_CHECKSUM(zcp, a0, a1, b0, b1);
	165	}
	166
	167	void
	168	fletcher_4_native(const void buf, uint64_t size, zio_cksum_t zcp)
	169	{
	170	const uint32_t *ip = buf;
	171	const uint32_t *ipend = ip + (size / sizeof (uint32_t));
	172	uint64_t a, b, c, d;
	173
	174	for (a = b = c = d = 0; ip < ipend; ip++) {
	175	a += ip[0];
	176	b += a;
	177	c += b;
	178	d += c;
	179	}
	180
	181	ZIO_SET_CHECKSUM(zcp, a, b, c, d);
	182	}
	183
	184	void
	185	fletcher_4_byteswap(const void buf, uint64_t size, zio_cksum_t zcp)
	186	{
	187	const uint32_t *ip = buf;
	188	const uint32_t *ipend = ip + (size / sizeof (uint32_t));
	189	uint64_t a, b, c, d;
	190
191	for (a = b = c = d = 0; ip < ipend; ip++) {
192	a += BSWAP_32(ip[0]);
193	b += a;
194	c += b;
195	d += c;
196	}
197
198	ZIO_SET_CHECKSUM(zcp, a, b, c, d);
199	}
200
201	void
202	fletcher_4_incremental_native(const void *buf, uint64_t size,
203	zio_cksum_t *zcp)
204	{
205	const uint32_t *ip = buf;
206	const uint32_t *ipend = ip + (size / sizeof (uint32_t));
207	uint64_t a, b, c, d;
208
209	a = zcp->zc_word[0];
210	b = zcp->zc_word[1];
211	c = zcp->zc_word[2];
212	d = zcp->zc_word[3];
213
214	for (; ip < ipend; ip++) {
215	a += ip[0];
216	b += a;
217	c += b;
218	d += c;
219	}
220
221	ZIO_SET_CHECKSUM(zcp, a, b, c, d);
222	}
223
224	void
225	fletcher_4_incremental_byteswap(const void *buf, uint64_t size,
226	zio_cksum_t *zcp)
227	{
228	const uint32_t *ip = buf;
229	const uint32_t *ipend = ip + (size / sizeof (uint32_t));
230	uint64_t a, b, c, d;
231
232	a = zcp->zc_word[0];
233	b = zcp->zc_word[1];
234	c = zcp->zc_word[2];
235	d = zcp->zc_word[3];
236
237	for (; ip < ipend; ip++) {
238	a += BSWAP_32(ip[0]);
239	b += a;
240	c += b;
241	d += c;
242	}
243
244	ZIO_SET_CHECKSUM(zcp, a, b, c, d);
245	}