255 lines
6.8 KiB
C
255 lines
6.8 KiB
C
/*
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* CDDL HEADER START
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*
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* The contents of this file are subject to the terms of the
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* Common Development and Distribution License (the "License").
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* You may not use this file except in compliance with the License.
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*
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* You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
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* or http://www.opensolaris.org/os/licensing.
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* See the License for the specific language governing permissions
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* and limitations under the License.
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*
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* When distributing Covered Code, include this CDDL HEADER in each
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* file and include the License file at usr/src/OPENSOLARIS.LICENSE.
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* If applicable, add the following below this CDDL HEADER, with the
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* fields enclosed by brackets "[]" replaced with your own identifying
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* information: Portions Copyright [yyyy] [name of copyright owner]
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*
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* CDDL HEADER END
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*/
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/*
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* Copyright 2009 Sun Microsystems, Inc. All rights reserved.
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* Use is subject to license terms.
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*/
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/*
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* Fletcher Checksums
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* ------------------
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*
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* ZFS's 2nd and 4th order Fletcher checksums are defined by the following
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* recurrence relations:
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*
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* a = a + f
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* i i-1 i-1
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*
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* b = b + a
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* i i-1 i
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*
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* c = c + b (fletcher-4 only)
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* i i-1 i
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*
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* d = d + c (fletcher-4 only)
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* i i-1 i
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*
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* Where
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* a_0 = b_0 = c_0 = d_0 = 0
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* and
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* f_0 .. f_(n-1) are the input data.
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*
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* Using standard techniques, these translate into the following series:
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*
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* __n_ __n_
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* \ | \ |
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* a = > f b = > i * f
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* n /___| n - i n /___| n - i
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* i = 1 i = 1
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*
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*
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* __n_ __n_
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* \ | i*(i+1) \ | i*(i+1)*(i+2)
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* c = > ------- f d = > ------------- f
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* n /___| 2 n - i n /___| 6 n - i
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* i = 1 i = 1
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*
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* For fletcher-2, the f_is are 64-bit, and [ab]_i are 64-bit accumulators.
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* Since the additions are done mod (2^64), errors in the high bits may not
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* be noticed. For this reason, fletcher-2 is deprecated.
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*
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* For fletcher-4, the f_is are 32-bit, and [abcd]_i are 64-bit accumulators.
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* A conservative estimate of how big the buffer can get before we overflow
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* can be estimated using f_i = 0xffffffff for all i:
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*
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* % bc
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* f=2^32-1;d=0; for (i = 1; d<2^64; i++) { d += f*i*(i+1)*(i+2)/6 }; (i-1)*4
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* 2264
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* quit
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* %
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*
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* So blocks of up to 2k will not overflow. Our largest block size is
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* 128k, which has 32k 4-byte words, so we can compute the largest possible
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* accumulators, then divide by 2^64 to figure the max amount of overflow:
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*
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* % bc
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* a=b=c=d=0; f=2^32-1; for (i=1; i<=32*1024; i++) { a+=f; b+=a; c+=b; d+=c }
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* a/2^64;b/2^64;c/2^64;d/2^64
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* 0
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* 0
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* 1365
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* 11186858
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* quit
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* %
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*
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* So a and b cannot overflow. To make sure each bit of input has some
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* effect on the contents of c and d, we can look at what the factors of
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* the coefficients in the equations for c_n and d_n are. The number of 2s
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* in the factors determines the lowest set bit in the multiplier. Running
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* through the cases for n*(n+1)/2 reveals that the highest power of 2 is
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* 2^14, and for n*(n+1)*(n+2)/6 it is 2^15. So while some data may overflow
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* the 64-bit accumulators, every bit of every f_i effects every accumulator,
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* even for 128k blocks.
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*
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* If we wanted to make a stronger version of fletcher4 (fletcher4c?),
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* we could do our calculations mod (2^32 - 1) by adding in the carries
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* periodically, and store the number of carries in the top 32-bits.
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*
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* --------------------
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* Checksum Performance
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* --------------------
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*
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* There are two interesting components to checksum performance: cached and
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* uncached performance. With cached data, fletcher-2 is about four times
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* faster than fletcher-4. With uncached data, the performance difference is
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* negligible, since the cost of a cache fill dominates the processing time.
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* Even though fletcher-4 is slower than fletcher-2, it is still a pretty
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* efficient pass over the data.
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*
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* In normal operation, the data which is being checksummed is in a buffer
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* which has been filled either by:
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*
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* 1. a compression step, which will be mostly cached, or
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* 2. a bcopy() or copyin(), which will be uncached (because the
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* copy is cache-bypassing).
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*
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* For both cached and uncached data, both fletcher checksums are much faster
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* than sha-256, and slower than 'off', which doesn't touch the data at all.
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*/
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#include <sys/types.h>
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#include <sys/sysmacros.h>
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#include <sys/byteorder.h>
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#include <sys/spa.h>
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void
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fletcher_2_native(const void *buf, uint64_t size, zio_cksum_t *zcp)
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{
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const uint64_t *ip = buf;
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const uint64_t *ipend = ip + (size / sizeof (uint64_t));
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uint64_t a0, b0, a1, b1;
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for (a0 = b0 = a1 = b1 = 0; ip < ipend; ip += 2) {
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a0 += ip[0];
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a1 += ip[1];
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b0 += a0;
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b1 += a1;
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}
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ZIO_SET_CHECKSUM(zcp, a0, a1, b0, b1);
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}
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void
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fletcher_2_byteswap(const void *buf, uint64_t size, zio_cksum_t *zcp)
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{
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const uint64_t *ip = buf;
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const uint64_t *ipend = ip + (size / sizeof (uint64_t));
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uint64_t a0, b0, a1, b1;
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for (a0 = b0 = a1 = b1 = 0; ip < ipend; ip += 2) {
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a0 += BSWAP_64(ip[0]);
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a1 += BSWAP_64(ip[1]);
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b0 += a0;
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b1 += a1;
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}
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ZIO_SET_CHECKSUM(zcp, a0, a1, b0, b1);
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}
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void
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fletcher_4_native(const void *buf, uint64_t size, zio_cksum_t *zcp)
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{
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const uint32_t *ip = buf;
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const uint32_t *ipend = ip + (size / sizeof (uint32_t));
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uint64_t a, b, c, d;
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for (a = b = c = d = 0; ip < ipend; ip++) {
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a += ip[0];
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b += a;
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c += b;
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d += c;
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}
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ZIO_SET_CHECKSUM(zcp, a, b, c, d);
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}
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void
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fletcher_4_byteswap(const void *buf, uint64_t size, zio_cksum_t *zcp)
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{
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const uint32_t *ip = buf;
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const uint32_t *ipend = ip + (size / sizeof (uint32_t));
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uint64_t a, b, c, d;
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for (a = b = c = d = 0; ip < ipend; ip++) {
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a += BSWAP_32(ip[0]);
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b += a;
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c += b;
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d += c;
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}
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ZIO_SET_CHECKSUM(zcp, a, b, c, d);
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}
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void
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fletcher_4_incremental_native(const void *buf, uint64_t size,
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zio_cksum_t *zcp)
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{
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const uint32_t *ip = buf;
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const uint32_t *ipend = ip + (size / sizeof (uint32_t));
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uint64_t a, b, c, d;
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a = zcp->zc_word[0];
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b = zcp->zc_word[1];
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c = zcp->zc_word[2];
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d = zcp->zc_word[3];
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for (; ip < ipend; ip++) {
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a += ip[0];
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b += a;
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c += b;
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d += c;
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}
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ZIO_SET_CHECKSUM(zcp, a, b, c, d);
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}
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void
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fletcher_4_incremental_byteswap(const void *buf, uint64_t size,
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zio_cksum_t *zcp)
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{
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const uint32_t *ip = buf;
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const uint32_t *ipend = ip + (size / sizeof (uint32_t));
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uint64_t a, b, c, d;
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a = zcp->zc_word[0];
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b = zcp->zc_word[1];
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c = zcp->zc_word[2];
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d = zcp->zc_word[3];
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for (; ip < ipend; ip++) {
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a += BSWAP_32(ip[0]);
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b += a;
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c += b;
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d += c;
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}
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ZIO_SET_CHECKSUM(zcp, a, b, c, d);
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}
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#if defined(_KERNEL) && defined(HAVE_SPL)
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EXPORT_SYMBOL(fletcher_2_native);
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EXPORT_SYMBOL(fletcher_2_byteswap);
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EXPORT_SYMBOL(fletcher_4_native);
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EXPORT_SYMBOL(fletcher_4_byteswap);
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EXPORT_SYMBOL(fletcher_4_incremental_native);
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EXPORT_SYMBOL(fletcher_4_incremental_byteswap);
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#endif
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