/* * 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 #include #include #include 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); }