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 /* 22 * Copyright 2009 Sun Microsystems, Inc. All rights reserved. 23 * Use is subject to license terms. 24 */ 25 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 += f*i*(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 */ 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 } 246