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 * Copyright 2013 Saso Kiselkov. All rights reserved. 27 */ 28 29 /* 30 * Fletcher Checksums 31 * ------------------ 32 * 33 * ZFS's 2nd and 4th order Fletcher checksums are defined by the following 34 * recurrence relations: 35 * 36 * a = a + f 37 * i i-1 i-1 38 * 39 * b = b + a 40 * i i-1 i 41 * 42 * c = c + b (fletcher-4 only) 43 * i i-1 i 44 * 45 * d = d + c (fletcher-4 only) 46 * i i-1 i 47 * 48 * Where 49 * a_0 = b_0 = c_0 = d_0 = 0 50 * and 51 * f_0 .. f_(n-1) are the input data. 52 * 53 * Using standard techniques, these translate into the following series: 54 * 55 * __n_ __n_ 56 * \ | \ | 57 * a = > f b = > i * f 58 * n /___| n - i n /___| n - i 59 * i = 1 i = 1 60 * 61 * 62 * __n_ __n_ 63 * \ | i*(i+1) \ | i*(i+1)*(i+2) 64 * c = > ------- f d = > ------------- f 65 * n /___| 2 n - i n /___| 6 n - i 66 * i = 1 i = 1 67 * 68 * For fletcher-2, the f_is are 64-bit, and [ab]_i are 64-bit accumulators. 69 * Since the additions are done mod (2^64), errors in the high bits may not 70 * be noticed. For this reason, fletcher-2 is deprecated. 71 * 72 * For fletcher-4, the f_is are 32-bit, and [abcd]_i are 64-bit accumulators. 73 * A conservative estimate of how big the buffer can get before we overflow 74 * can be estimated using f_i = 0xffffffff for all i: 75 * 76 * % bc 77 * f=2^32-1;d=0; for (i = 1; d<2^64; i++) { d += f*i*(i+1)*(i+2)/6 }; (i-1)*4 78 * 2264 79 * quit 80 * % 81 * 82 * So blocks of up to 2k will not overflow. Our largest block size is 83 * 128k, which has 32k 4-byte words, so we can compute the largest possible 84 * accumulators, then divide by 2^64 to figure the max amount of overflow: 85 * 86 * % bc 87 * a=b=c=d=0; f=2^32-1; for (i=1; i<=32*1024; i++) { a+=f; b+=a; c+=b; d+=c } 88 * a/2^64;b/2^64;c/2^64;d/2^64 89 * 0 90 * 0 91 * 1365 92 * 11186858 93 * quit 94 * % 95 * 96 * So a and b cannot overflow. To make sure each bit of input has some 97 * effect on the contents of c and d, we can look at what the factors of 98 * the coefficients in the equations for c_n and d_n are. The number of 2s 99 * in the factors determines the lowest set bit in the multiplier. Running 100 * through the cases for n*(n+1)/2 reveals that the highest power of 2 is 101 * 2^14, and for n*(n+1)*(n+2)/6 it is 2^15. So while some data may overflow 102 * the 64-bit accumulators, every bit of every f_i effects every accumulator, 103 * even for 128k blocks. 104 * 105 * If we wanted to make a stronger version of fletcher4 (fletcher4c?), 106 * we could do our calculations mod (2^32 - 1) by adding in the carries 107 * periodically, and store the number of carries in the top 32-bits. 108 * 109 * -------------------- 110 * Checksum Performance 111 * -------------------- 112 * 113 * There are two interesting components to checksum performance: cached and 114 * uncached performance. With cached data, fletcher-2 is about four times 115 * faster than fletcher-4. With uncached data, the performance difference is 116 * negligible, since the cost of a cache fill dominates the processing time. 117 * Even though fletcher-4 is slower than fletcher-2, it is still a pretty 118 * efficient pass over the data. 119 * 120 * In normal operation, the data which is being checksummed is in a buffer 121 * which has been filled either by: 122 * 123 * 1. a compression step, which will be mostly cached, or 124 * 2. a bcopy() or copyin(), which will be uncached (because the 125 * copy is cache-bypassing). 126 * 127 * For both cached and uncached data, both fletcher checksums are much faster 128 * than sha-256, and slower than 'off', which doesn't touch the data at all. 129 */ 130 131 #include <sys/types.h> 132 #include <sys/sysmacros.h> 133 #include <sys/byteorder.h> 134 #include <sys/zio.h> 135 #include <sys/spa.h> 136 137 /*ARGSUSED*/ 138 void 139 fletcher_2_native(const void *buf, uint64_t size, 140 const void *ctx_template, zio_cksum_t *zcp) 141 { 142 const uint64_t *ip = buf; 143 const uint64_t *ipend = ip + (size / sizeof (uint64_t)); 144 uint64_t a0, b0, a1, b1; 145 146 for (a0 = b0 = a1 = b1 = 0; ip < ipend; ip += 2) { 147 a0 += ip[0]; 148 a1 += ip[1]; 149 b0 += a0; 150 b1 += a1; 151 } 152 153 ZIO_SET_CHECKSUM(zcp, a0, a1, b0, b1); 154 } 155 156 /*ARGSUSED*/ 157 void 158 fletcher_2_byteswap(const void *buf, uint64_t size, 159 const void *ctx_template, zio_cksum_t *zcp) 160 { 161 const uint64_t *ip = buf; 162 const uint64_t *ipend = ip + (size / sizeof (uint64_t)); 163 uint64_t a0, b0, a1, b1; 164 165 for (a0 = b0 = a1 = b1 = 0; ip < ipend; ip += 2) { 166 a0 += BSWAP_64(ip[0]); 167 a1 += BSWAP_64(ip[1]); 168 b0 += a0; 169 b1 += a1; 170 } 171 172 ZIO_SET_CHECKSUM(zcp, a0, a1, b0, b1); 173 } 174 175 /*ARGSUSED*/ 176 void 177 fletcher_4_native(const void *buf, uint64_t size, 178 const void *ctx_template, zio_cksum_t *zcp) 179 { 180 const uint32_t *ip = buf; 181 const uint32_t *ipend = ip + (size / sizeof (uint32_t)); 182 uint64_t a, b, c, d; 183 184 for (a = b = c = d = 0; ip < ipend; ip++) { 185 a += ip[0]; 186 b += a; 187 c += b; 188 d += c; 189 } 190 191 ZIO_SET_CHECKSUM(zcp, a, b, c, d); 192 } 193 194 /*ARGSUSED*/ 195 void 196 fletcher_4_byteswap(const void *buf, uint64_t size, 197 const void *ctx_template, zio_cksum_t *zcp) 198 { 199 const uint32_t *ip = buf; 200 const uint32_t *ipend = ip + (size / sizeof (uint32_t)); 201 uint64_t a, b, c, d; 202 203 for (a = b = c = d = 0; ip < ipend; ip++) { 204 a += BSWAP_32(ip[0]); 205 b += a; 206 c += b; 207 d += c; 208 } 209 210 ZIO_SET_CHECKSUM(zcp, a, b, c, d); 211 } 212 213 void 214 fletcher_4_incremental_native(const void *buf, uint64_t size, 215 zio_cksum_t *zcp) 216 { 217 const uint32_t *ip = buf; 218 const uint32_t *ipend = ip + (size / sizeof (uint32_t)); 219 uint64_t a, b, c, d; 220 221 a = zcp->zc_word[0]; 222 b = zcp->zc_word[1]; 223 c = zcp->zc_word[2]; 224 d = zcp->zc_word[3]; 225 226 for (; ip < ipend; ip++) { 227 a += ip[0]; 228 b += a; 229 c += b; 230 d += c; 231 } 232 233 ZIO_SET_CHECKSUM(zcp, a, b, c, d); 234 } 235 236 void 237 fletcher_4_incremental_byteswap(const void *buf, uint64_t size, 238 zio_cksum_t *zcp) 239 { 240 const uint32_t *ip = buf; 241 const uint32_t *ipend = ip + (size / sizeof (uint32_t)); 242 uint64_t a, b, c, d; 243 244 a = zcp->zc_word[0]; 245 b = zcp->zc_word[1]; 246 c = zcp->zc_word[2]; 247 d = zcp->zc_word[3]; 248 249 for (; ip < ipend; ip++) { 250 a += BSWAP_32(ip[0]); 251 b += a; 252 c += b; 253 d += c; 254 } 255 256 ZIO_SET_CHECKSUM(zcp, a, b, c, d); 257 } 258