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1 : /*-------------------------------------------------------------------------
2 : *
3 : * checksum_impl.h
4 : * Checksum implementation for data pages.
5 : *
6 : * This file exists for the benefit of external programs that may wish to
7 : * check Postgres page checksums. They can #include this to get the code
8 : * referenced by storage/checksum.h. (Note: you may need to redefine
9 : * Assert() as empty to compile this successfully externally.)
10 : *
11 : * Portions Copyright (c) 1996-2017, PostgreSQL Global Development Group
12 : * Portions Copyright (c) 1994, Regents of the University of California
13 : *
14 : * src/include/storage/checksum_impl.h
15 : *
16 : *-------------------------------------------------------------------------
17 : */
18 :
19 : /*
20 : * The algorithm used to checksum pages is chosen for very fast calculation.
21 : * Workloads where the database working set fits into OS file cache but not
22 : * into shared buffers can read in pages at a very fast pace and the checksum
23 : * algorithm itself can become the largest bottleneck.
24 : *
25 : * The checksum algorithm itself is based on the FNV-1a hash (FNV is shorthand
26 : * for Fowler/Noll/Vo). The primitive of a plain FNV-1a hash folds in data 1
27 : * byte at a time according to the formula:
28 : *
29 : * hash = (hash ^ value) * FNV_PRIME
30 : *
31 : * FNV-1a algorithm is described at http://www.isthe.com/chongo/tech/comp/fnv/
32 : *
33 : * PostgreSQL doesn't use FNV-1a hash directly because it has bad mixing of
34 : * high bits - high order bits in input data only affect high order bits in
35 : * output data. To resolve this we xor in the value prior to multiplication
36 : * shifted right by 17 bits. The number 17 was chosen because it doesn't
37 : * have common denominator with set bit positions in FNV_PRIME and empirically
38 : * provides the fastest mixing for high order bits of final iterations quickly
39 : * avalanche into lower positions. For performance reasons we choose to combine
40 : * 4 bytes at a time. The actual hash formula used as the basis is:
41 : *
42 : * hash = (hash ^ value) * FNV_PRIME ^ ((hash ^ value) >> 17)
43 : *
44 : * The main bottleneck in this calculation is the multiplication latency. To
45 : * hide the latency and to make use of SIMD parallelism multiple hash values
46 : * are calculated in parallel. The page is treated as a 32 column two
47 : * dimensional array of 32 bit values. Each column is aggregated separately
48 : * into a partial checksum. Each partial checksum uses a different initial
49 : * value (offset basis in FNV terminology). The initial values actually used
50 : * were chosen randomly, as the values themselves don't matter as much as that
51 : * they are different and don't match anything in real data. After initializing
52 : * partial checksums each value in the column is aggregated according to the
53 : * above formula. Finally two more iterations of the formula are performed with
54 : * value 0 to mix the bits of the last value added.
55 : *
56 : * The partial checksums are then folded together using xor to form a single
57 : * 32-bit checksum. The caller can safely reduce the value to 16 bits
58 : * using modulo 2^16-1. That will cause a very slight bias towards lower
59 : * values but this is not significant for the performance of the
60 : * checksum.
61 : *
62 : * The algorithm choice was based on what instructions are available in SIMD
63 : * instruction sets. This meant that a fast and good algorithm needed to use
64 : * multiplication as the main mixing operator. The simplest multiplication
65 : * based checksum primitive is the one used by FNV. The prime used is chosen
66 : * for good dispersion of values. It has no known simple patterns that result
67 : * in collisions. Test of 5-bit differentials of the primitive over 64bit keys
68 : * reveals no differentials with 3 or more values out of 100000 random keys
69 : * colliding. Avalanche test shows that only high order bits of the last word
70 : * have a bias. Tests of 1-4 uncorrelated bit errors, stray 0 and 0xFF bytes,
71 : * overwriting page from random position to end with 0 bytes, and overwriting
72 : * random segments of page with 0x00, 0xFF and random data all show optimal
73 : * 2e-16 false positive rate within margin of error.
74 : *
75 : * Vectorization of the algorithm requires 32bit x 32bit -> 32bit integer
76 : * multiplication instruction. As of 2013 the corresponding instruction is
77 : * available on x86 SSE4.1 extensions (pmulld) and ARM NEON (vmul.i32).
78 : * Vectorization requires a compiler to do the vectorization for us. For recent
79 : * GCC versions the flags -msse4.1 -funroll-loops -ftree-vectorize are enough
80 : * to achieve vectorization.
81 : *
82 : * The optimal amount of parallelism to use depends on CPU specific instruction
83 : * latency, SIMD instruction width, throughput and the amount of registers
84 : * available to hold intermediate state. Generally, more parallelism is better
85 : * up to the point that state doesn't fit in registers and extra load-store
86 : * instructions are needed to swap values in/out. The number chosen is a fixed
87 : * part of the algorithm because changing the parallelism changes the checksum
88 : * result.
89 : *
90 : * The parallelism number 32 was chosen based on the fact that it is the
91 : * largest state that fits into architecturally visible x86 SSE registers while
92 : * leaving some free registers for intermediate values. For future processors
93 : * with 256bit vector registers this will leave some performance on the table.
94 : * When vectorization is not available it might be beneficial to restructure
95 : * the computation to calculate a subset of the columns at a time and perform
96 : * multiple passes to avoid register spilling. This optimization opportunity
97 : * is not used. Current coding also assumes that the compiler has the ability
98 : * to unroll the inner loop to avoid loop overhead and minimize register
99 : * spilling. For less sophisticated compilers it might be beneficial to
100 : * manually unroll the inner loop.
101 : */
102 :
103 : #include "storage/bufpage.h"
104 :
105 : /* number of checksums to calculate in parallel */
106 : #define N_SUMS 32
107 : /* prime multiplier of FNV-1a hash */
108 : #define FNV_PRIME 16777619
109 :
110 : /*
111 : * Base offsets to initialize each of the parallel FNV hashes into a
112 : * different initial state.
113 : */
114 : static const uint32 checksumBaseOffsets[N_SUMS] = {
115 : 0x5B1F36E9, 0xB8525960, 0x02AB50AA, 0x1DE66D2A,
116 : 0x79FF467A, 0x9BB9F8A3, 0x217E7CD2, 0x83E13D2C,
117 : 0xF8D4474F, 0xE39EB970, 0x42C6AE16, 0x993216FA,
118 : 0x7B093B5D, 0x98DAFF3C, 0xF718902A, 0x0B1C9CDB,
119 : 0xE58F764B, 0x187636BC, 0x5D7B3BB1, 0xE73DE7DE,
120 : 0x92BEC979, 0xCCA6C0B2, 0x304A0979, 0x85AA43D4,
121 : 0x783125BB, 0x6CA8EAA2, 0xE407EAC6, 0x4B5CFC3E,
122 : 0x9FBF8C76, 0x15CA20BE, 0xF2CA9FD3, 0x959BD756
123 : };
124 :
125 : /*
126 : * Calculate one round of the checksum.
127 : */
128 : #define CHECKSUM_COMP(checksum, value) \
129 : do { \
130 : uint32 __tmp = (checksum) ^ (value); \
131 : (checksum) = __tmp * FNV_PRIME ^ (__tmp >> 17); \
132 : } while (0)
133 :
134 : /*
135 : * Block checksum algorithm. The data argument must be aligned on a 4-byte
136 : * boundary.
137 : */
138 : static uint32
139 0 : pg_checksum_block(char *data, uint32 size)
140 : {
141 : uint32 sums[N_SUMS];
142 0 : uint32 (*dataArr)[N_SUMS] = (uint32 (*)[N_SUMS]) data;
143 0 : uint32 result = 0;
144 : uint32 i,
145 : j;
146 :
147 : /* ensure that the size is compatible with the algorithm */
148 0 : Assert((size % (sizeof(uint32) * N_SUMS)) == 0);
149 :
150 : /* initialize partial checksums to their corresponding offsets */
151 0 : memcpy(sums, checksumBaseOffsets, sizeof(checksumBaseOffsets));
152 :
153 : /* main checksum calculation */
154 0 : for (i = 0; i < size / sizeof(uint32) / N_SUMS; i++)
155 0 : for (j = 0; j < N_SUMS; j++)
156 0 : CHECKSUM_COMP(sums[j], dataArr[i][j]);
157 :
158 : /* finally add in two rounds of zeroes for additional mixing */
159 0 : for (i = 0; i < 2; i++)
160 0 : for (j = 0; j < N_SUMS; j++)
161 0 : CHECKSUM_COMP(sums[j], 0);
162 :
163 : /* xor fold partial checksums together */
164 0 : for (i = 0; i < N_SUMS; i++)
165 0 : result ^= sums[i];
166 :
167 0 : return result;
168 : }
169 :
170 : /*
171 : * Compute the checksum for a Postgres page. The page must be aligned on a
172 : * 4-byte boundary.
173 : *
174 : * The checksum includes the block number (to detect the case where a page is
175 : * somehow moved to a different location), the page header (excluding the
176 : * checksum itself), and the page data.
177 : */
178 : uint16
179 0 : pg_checksum_page(char *page, BlockNumber blkno)
180 : {
181 0 : PageHeader phdr = (PageHeader) page;
182 : uint16 save_checksum;
183 : uint32 checksum;
184 :
185 : /* We only calculate the checksum for properly-initialized pages */
186 0 : Assert(!PageIsNew(page));
187 :
188 : /*
189 : * Save pd_checksum and temporarily set it to zero, so that the checksum
190 : * calculation isn't affected by the old checksum stored on the page.
191 : * Restore it after, because actually updating the checksum is NOT part of
192 : * the API of this function.
193 : */
194 0 : save_checksum = phdr->pd_checksum;
195 0 : phdr->pd_checksum = 0;
196 0 : checksum = pg_checksum_block(page, BLCKSZ);
197 0 : phdr->pd_checksum = save_checksum;
198 :
199 : /* Mix in the block number to detect transposed pages */
200 0 : checksum ^= blkno;
201 :
202 : /*
203 : * Reduce to a uint16 (to fit in the pd_checksum field) with an offset of
204 : * one. That avoids checksums of zero, which seems like a good idea.
205 : */
206 0 : return (checksum % 65535) + 1;
207 : }
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