247 lines
6.6 KiB
C
247 lines
6.6 KiB
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/zio.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);
|
|
}
|