1219089Spjd/* 2219089Spjd * CDDL HEADER START 3219089Spjd * 4219089Spjd * The contents of this file are subject to the terms of the 5219089Spjd * Common Development and Distribution License (the "License"). 6219089Spjd * You may not use this file except in compliance with the License. 7219089Spjd * 8219089Spjd * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE 9219089Spjd * or http://www.opensolaris.org/os/licensing. 10219089Spjd * See the License for the specific language governing permissions 11219089Spjd * and limitations under the License. 12219089Spjd * 13219089Spjd * When distributing Covered Code, include this CDDL HEADER in each 14219089Spjd * file and include the License file at usr/src/OPENSOLARIS.LICENSE. 15219089Spjd * If applicable, add the following below this CDDL HEADER, with the 16219089Spjd * fields enclosed by brackets "[]" replaced with your own identifying 17219089Spjd * information: Portions Copyright [yyyy] [name of copyright owner] 18219089Spjd * 19219089Spjd * CDDL HEADER END 20219089Spjd */ 21219089Spjd/* 22219089Spjd * Copyright 2009 Sun Microsystems, Inc. All rights reserved. 23219089Spjd * Use is subject to license terms. 24219089Spjd */ 25219089Spjd 26219089Spjd/* 27219089Spjd * Fletcher Checksums 28219089Spjd * ------------------ 29219089Spjd * 30219089Spjd * ZFS's 2nd and 4th order Fletcher checksums are defined by the following 31219089Spjd * recurrence relations: 32219089Spjd * 33219089Spjd * a = a + f 34219089Spjd * i i-1 i-1 35219089Spjd * 36219089Spjd * b = b + a 37219089Spjd * i i-1 i 38219089Spjd * 39219089Spjd * c = c + b (fletcher-4 only) 40219089Spjd * i i-1 i 41219089Spjd * 42219089Spjd * d = d + c (fletcher-4 only) 43219089Spjd * i i-1 i 44219089Spjd * 45219089Spjd * Where 46219089Spjd * a_0 = b_0 = c_0 = d_0 = 0 47219089Spjd * and 48219089Spjd * f_0 .. f_(n-1) are the input data. 49219089Spjd * 50219089Spjd * Using standard techniques, these translate into the following series: 51219089Spjd * 52219089Spjd * __n_ __n_ 53219089Spjd * \ | \ | 54219089Spjd * a = > f b = > i * f 55219089Spjd * n /___| n - i n /___| n - i 56219089Spjd * i = 1 i = 1 57219089Spjd * 58219089Spjd * 59219089Spjd * __n_ __n_ 60219089Spjd * \ | i*(i+1) \ | i*(i+1)*(i+2) 61219089Spjd * c = > ------- f d = > ------------- f 62219089Spjd * n /___| 2 n - i n /___| 6 n - i 63219089Spjd * i = 1 i = 1 64219089Spjd * 65219089Spjd * For fletcher-2, the f_is are 64-bit, and [ab]_i are 64-bit accumulators. 66219089Spjd * Since the additions are done mod (2^64), errors in the high bits may not 67219089Spjd * be noticed. For this reason, fletcher-2 is deprecated. 68219089Spjd * 69219089Spjd * For fletcher-4, the f_is are 32-bit, and [abcd]_i are 64-bit accumulators. 70219089Spjd * A conservative estimate of how big the buffer can get before we overflow 71219089Spjd * can be estimated using f_i = 0xffffffff for all i: 72219089Spjd * 73219089Spjd * % bc 74219089Spjd * f=2^32-1;d=0; for (i = 1; d<2^64; i++) { d += f*i*(i+1)*(i+2)/6 }; (i-1)*4 75219089Spjd * 2264 76219089Spjd * quit 77219089Spjd * % 78219089Spjd * 79219089Spjd * So blocks of up to 2k will not overflow. Our largest block size is 80219089Spjd * 128k, which has 32k 4-byte words, so we can compute the largest possible 81219089Spjd * accumulators, then divide by 2^64 to figure the max amount of overflow: 82219089Spjd * 83219089Spjd * % bc 84219089Spjd * a=b=c=d=0; f=2^32-1; for (i=1; i<=32*1024; i++) { a+=f; b+=a; c+=b; d+=c } 85219089Spjd * a/2^64;b/2^64;c/2^64;d/2^64 86219089Spjd * 0 87219089Spjd * 0 88219089Spjd * 1365 89219089Spjd * 11186858 90219089Spjd * quit 91219089Spjd * % 92219089Spjd * 93219089Spjd * So a and b cannot overflow. To make sure each bit of input has some 94219089Spjd * effect on the contents of c and d, we can look at what the factors of 95219089Spjd * the coefficients in the equations for c_n and d_n are. The number of 2s 96219089Spjd * in the factors determines the lowest set bit in the multiplier. Running 97219089Spjd * through the cases for n*(n+1)/2 reveals that the highest power of 2 is 98219089Spjd * 2^14, and for n*(n+1)*(n+2)/6 it is 2^15. So while some data may overflow 99219089Spjd * the 64-bit accumulators, every bit of every f_i effects every accumulator, 100219089Spjd * even for 128k blocks. 101219089Spjd * 102219089Spjd * If we wanted to make a stronger version of fletcher4 (fletcher4c?), 103219089Spjd * we could do our calculations mod (2^32 - 1) by adding in the carries 104219089Spjd * periodically, and store the number of carries in the top 32-bits. 105219089Spjd * 106219089Spjd * -------------------- 107219089Spjd * Checksum Performance 108219089Spjd * -------------------- 109219089Spjd * 110219089Spjd * There are two interesting components to checksum performance: cached and 111219089Spjd * uncached performance. With cached data, fletcher-2 is about four times 112219089Spjd * faster than fletcher-4. With uncached data, the performance difference is 113219089Spjd * negligible, since the cost of a cache fill dominates the processing time. 114219089Spjd * Even though fletcher-4 is slower than fletcher-2, it is still a pretty 115219089Spjd * efficient pass over the data. 116219089Spjd * 117219089Spjd * In normal operation, the data which is being checksummed is in a buffer 118219089Spjd * which has been filled either by: 119219089Spjd * 120219089Spjd * 1. a compression step, which will be mostly cached, or 121219089Spjd * 2. a bcopy() or copyin(), which will be uncached (because the 122219089Spjd * copy is cache-bypassing). 123219089Spjd * 124219089Spjd * For both cached and uncached data, both fletcher checksums are much faster 125219089Spjd * than sha-256, and slower than 'off', which doesn't touch the data at all. 126219089Spjd */ 127219089Spjd 128219089Spjd#include <sys/types.h> 129219089Spjd#include <sys/sysmacros.h> 130219089Spjd#include <sys/byteorder.h> 131219089Spjd#include <sys/zio.h> 132219089Spjd#include <sys/spa.h> 133219089Spjd 134219089Spjdvoid 135219089Spjdfletcher_2_native(const void *buf, uint64_t size, zio_cksum_t *zcp) 136219089Spjd{ 137219089Spjd const uint64_t *ip = buf; 138219089Spjd const uint64_t *ipend = ip + (size / sizeof (uint64_t)); 139219089Spjd uint64_t a0, b0, a1, b1; 140219089Spjd 141219089Spjd for (a0 = b0 = a1 = b1 = 0; ip < ipend; ip += 2) { 142219089Spjd a0 += ip[0]; 143219089Spjd a1 += ip[1]; 144219089Spjd b0 += a0; 145219089Spjd b1 += a1; 146219089Spjd } 147219089Spjd 148219089Spjd ZIO_SET_CHECKSUM(zcp, a0, a1, b0, b1); 149219089Spjd} 150219089Spjd 151219089Spjdvoid 152219089Spjdfletcher_2_byteswap(const void *buf, uint64_t size, zio_cksum_t *zcp) 153219089Spjd{ 154219089Spjd const uint64_t *ip = buf; 155219089Spjd const uint64_t *ipend = ip + (size / sizeof (uint64_t)); 156219089Spjd uint64_t a0, b0, a1, b1; 157219089Spjd 158219089Spjd for (a0 = b0 = a1 = b1 = 0; ip < ipend; ip += 2) { 159219089Spjd a0 += BSWAP_64(ip[0]); 160219089Spjd a1 += BSWAP_64(ip[1]); 161219089Spjd b0 += a0; 162219089Spjd b1 += a1; 163219089Spjd } 164219089Spjd 165219089Spjd ZIO_SET_CHECKSUM(zcp, a0, a1, b0, b1); 166219089Spjd} 167219089Spjd 168219089Spjdvoid 169219089Spjdfletcher_4_native(const void *buf, uint64_t size, zio_cksum_t *zcp) 170219089Spjd{ 171219089Spjd const uint32_t *ip = buf; 172219089Spjd const uint32_t *ipend = ip + (size / sizeof (uint32_t)); 173219089Spjd uint64_t a, b, c, d; 174219089Spjd 175219089Spjd for (a = b = c = d = 0; ip < ipend; ip++) { 176219089Spjd a += ip[0]; 177219089Spjd b += a; 178219089Spjd c += b; 179219089Spjd d += c; 180219089Spjd } 181219089Spjd 182219089Spjd ZIO_SET_CHECKSUM(zcp, a, b, c, d); 183219089Spjd} 184219089Spjd 185219089Spjdvoid 186219089Spjdfletcher_4_byteswap(const void *buf, uint64_t size, zio_cksum_t *zcp) 187219089Spjd{ 188219089Spjd const uint32_t *ip = buf; 189219089Spjd const uint32_t *ipend = ip + (size / sizeof (uint32_t)); 190219089Spjd uint64_t a, b, c, d; 191219089Spjd 192219089Spjd for (a = b = c = d = 0; ip < ipend; ip++) { 193219089Spjd a += BSWAP_32(ip[0]); 194219089Spjd b += a; 195219089Spjd c += b; 196219089Spjd d += c; 197219089Spjd } 198219089Spjd 199219089Spjd ZIO_SET_CHECKSUM(zcp, a, b, c, d); 200219089Spjd} 201219089Spjd 202219089Spjdvoid 203219089Spjdfletcher_4_incremental_native(const void *buf, uint64_t size, 204219089Spjd zio_cksum_t *zcp) 205219089Spjd{ 206219089Spjd const uint32_t *ip = buf; 207219089Spjd const uint32_t *ipend = ip + (size / sizeof (uint32_t)); 208219089Spjd uint64_t a, b, c, d; 209219089Spjd 210219089Spjd a = zcp->zc_word[0]; 211219089Spjd b = zcp->zc_word[1]; 212219089Spjd c = zcp->zc_word[2]; 213219089Spjd d = zcp->zc_word[3]; 214219089Spjd 215219089Spjd for (; ip < ipend; ip++) { 216219089Spjd a += ip[0]; 217219089Spjd b += a; 218219089Spjd c += b; 219219089Spjd d += c; 220219089Spjd } 221219089Spjd 222219089Spjd ZIO_SET_CHECKSUM(zcp, a, b, c, d); 223219089Spjd} 224219089Spjd 225219089Spjdvoid 226219089Spjdfletcher_4_incremental_byteswap(const void *buf, uint64_t size, 227219089Spjd zio_cksum_t *zcp) 228219089Spjd{ 229219089Spjd const uint32_t *ip = buf; 230219089Spjd const uint32_t *ipend = ip + (size / sizeof (uint32_t)); 231219089Spjd uint64_t a, b, c, d; 232219089Spjd 233219089Spjd a = zcp->zc_word[0]; 234219089Spjd b = zcp->zc_word[1]; 235219089Spjd c = zcp->zc_word[2]; 236219089Spjd d = zcp->zc_word[3]; 237219089Spjd 238219089Spjd for (; ip < ipend; ip++) { 239219089Spjd a += BSWAP_32(ip[0]); 240219089Spjd b += a; 241219089Spjd c += b; 242219089Spjd d += c; 243219089Spjd } 244219089Spjd 245219089Spjd ZIO_SET_CHECKSUM(zcp, a, b, c, d); 246219089Spjd} 247