src/include/storage/checksum_impl.h

   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) 1996-2024, 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 {
 113         PageHeaderData phdr;
 114         uint32          data[BLCKSZ / (sizeof(uint32) * N_SUMS)][N_SUMS];
 115 } PGChecksummablePage;
 116
 117 /*
 118  * Base offsets to initialize each of the parallel FNV hashes into a
 119  * different initial state.
 120  */
 121 static const uint32 checksumBaseOffsets[N_SUMS] = {
 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
 146 pg_checksum_block(const PGChecksummablePage *page)
 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((Page) page));
 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 (uint16) ((checksum % 65535) + 1);
 215 }