diff options
Diffstat (limited to 'sys/cddl/contrib/opensolaris/uts/common/fs/zfs/fletcher.c')
| -rw-r--r-- | sys/cddl/contrib/opensolaris/uts/common/fs/zfs/fletcher.c | 104 |
1 files changed, 102 insertions, 2 deletions
diff --git a/sys/cddl/contrib/opensolaris/uts/common/fs/zfs/fletcher.c b/sys/cddl/contrib/opensolaris/uts/common/fs/zfs/fletcher.c index edda3c9..54247d7 100644 --- a/sys/cddl/contrib/opensolaris/uts/common/fs/zfs/fletcher.c +++ b/sys/cddl/contrib/opensolaris/uts/common/fs/zfs/fletcher.c @@ -19,11 +19,111 @@ * CDDL HEADER END */ /* - * Copyright 2006 Sun Microsystems, Inc. All rights reserved. + * Copyright 2009 Sun Microsystems, Inc. All rights reserved. * Use is subject to license terms. */ -#pragma ident "%Z%%M% %I% %E% SMI" +/* + * 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 <sys/types.h> #include <sys/sysmacros.h> |
