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checksum_impl.h
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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) 1996-2019, 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 /* Use a union so that this code is valid under strict aliasing */
111 typedef union
112 {
114  uint32 data[BLCKSZ / (sizeof(uint32) * N_SUMS)][N_SUMS];
116 
117 /*
118  * Base offsets to initialize each of the parallel FNV hashes into a
119  * different initial state.
120  */
122  0x5B1F36E9, 0xB8525960, 0x02AB50AA, 0x1DE66D2A,
123  0x79FF467A, 0x9BB9F8A3, 0x217E7CD2, 0x83E13D2C,
124  0xF8D4474F, 0xE39EB970, 0x42C6AE16, 0x993216FA,
125  0x7B093B5D, 0x98DAFF3C, 0xF718902A, 0x0B1C9CDB,
126  0xE58F764B, 0x187636BC, 0x5D7B3BB1, 0xE73DE7DE,
127  0x92BEC979, 0xCCA6C0B2, 0x304A0979, 0x85AA43D4,
128  0x783125BB, 0x6CA8EAA2, 0xE407EAC6, 0x4B5CFC3E,
129  0x9FBF8C76, 0x15CA20BE, 0xF2CA9FD3, 0x959BD756
130 };
131 
132 /*
133  * Calculate one round of the checksum.
134  */
135 #define CHECKSUM_COMP(checksum, value) \
136 do { \
137  uint32 __tmp = (checksum) ^ (value); \
138  (checksum) = __tmp * FNV_PRIME ^ (__tmp >> 17); \
139 } while (0)
140 
141 /*
142  * Block checksum algorithm. The page must be adequately aligned
143  * (at least on 4-byte boundary).
144  */
145 static uint32
147 {
148  uint32 sums[N_SUMS];
149  uint32 result = 0;
150  uint32 i,
151  j;
152 
153  /* ensure that the size is compatible with the algorithm */
154  Assert(sizeof(PGChecksummablePage) == BLCKSZ);
155 
156  /* initialize partial checksums to their corresponding offsets */
157  memcpy(sums, checksumBaseOffsets, sizeof(checksumBaseOffsets));
158 
159  /* main checksum calculation */
160  for (i = 0; i < (uint32) (BLCKSZ / (sizeof(uint32) * N_SUMS)); i++)
161  for (j = 0; j < N_SUMS; j++)
162  CHECKSUM_COMP(sums[j], page->data[i][j]);
163 
164  /* finally add in two rounds of zeroes for additional mixing */
165  for (i = 0; i < 2; i++)
166  for (j = 0; j < N_SUMS; j++)
167  CHECKSUM_COMP(sums[j], 0);
168 
169  /* xor fold partial checksums together */
170  for (i = 0; i < N_SUMS; i++)
171  result ^= sums[i];
172 
173  return result;
174 }
175 
176 /*
177  * Compute the checksum for a Postgres page.
178  *
179  * The page must be adequately aligned (at least on a 4-byte boundary).
180  * Beware also that the checksum field of the page is transiently zeroed.
181  *
182  * The checksum includes the block number (to detect the case where a page is
183  * somehow moved to a different location), the page header (excluding the
184  * checksum itself), and the page data.
185  */
186 uint16
187 pg_checksum_page(char *page, BlockNumber blkno)
188 {
189  PGChecksummablePage *cpage = (PGChecksummablePage *) page;
190  uint16 save_checksum;
191  uint32 checksum;
192 
193  /* We only calculate the checksum for properly-initialized pages */
194  Assert(!PageIsNew(&cpage->phdr));
195 
196  /*
197  * Save pd_checksum and temporarily set it to zero, so that the checksum
198  * calculation isn't affected by the old checksum stored on the page.
199  * Restore it after, because actually updating the checksum is NOT part of
200  * the API of this function.
201  */
202  save_checksum = cpage->phdr.pd_checksum;
203  cpage->phdr.pd_checksum = 0;
204  checksum = pg_checksum_block(cpage);
205  cpage->phdr.pd_checksum = save_checksum;
206 
207  /* Mix in the block number to detect transposed pages */
208  checksum ^= blkno;
209 
210  /*
211  * Reduce to a uint16 (to fit in the pd_checksum field) with an offset of
212  * one. That avoids checksums of zero, which seems like a good idea.
213  */
214  return (checksum % 65535) + 1;
215 }
static const uint32 checksumBaseOffsets[N_SUMS]
static uint32 pg_checksum_block(const PGChecksummablePage *page)
uint32 BlockNumber
Definition: block.h:31
uint16 pd_checksum
Definition: bufpage.h:156
unsigned short uint16
Definition: c.h:357
unsigned int uint32
Definition: c.h:358
uint16 pg_checksum_page(char *page, BlockNumber blkno)
uint32 data[BLCKSZ/(sizeof(uint32) *N_SUMS)][N_SUMS]
#define Assert(condition)
Definition: c.h:732
#define N_SUMS
#define PageIsNew(page)
Definition: bufpage.h:229
int i
#define CHECKSUM_COMP(checksum, value)
PageHeaderData phdr