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/*-------------------------------------------------------------------------
*
* checksum_impl.h
* Checksum implementation for data pages.
*
* This file exists for the benefit of external programs that may wish to
* check Postgres page checksums. They can #include this to get the code
* referenced by storage/checksum.h. (Note: you may need to redefine
* Assert() as empty to compile this successfully externally.)
*
* Portions Copyright (c) 1996-2021, PostgreSQL Global Development Group
* Portions Copyright (c) 1994, Regents of the University of California
*
* src/include/storage/checksum_impl.h
*
*-------------------------------------------------------------------------
*/
/*
* The algorithm used to checksum pages is chosen for very fast calculation.
* Workloads where the database working set fits into OS file cache but not
* into shared buffers can read in pages at a very fast pace and the checksum
* algorithm itself can become the largest bottleneck.
*
* The checksum algorithm itself is based on the FNV-1a hash (FNV is shorthand
* for Fowler/Noll/Vo). The primitive of a plain FNV-1a hash folds in data 1
* byte at a time according to the formula:
*
* hash = (hash ^ value) * FNV_PRIME
*
* FNV-1a algorithm is described at http://www.isthe.com/chongo/tech/comp/fnv/
*
* PostgreSQL doesn't use FNV-1a hash directly because it has bad mixing of
* high bits - high order bits in input data only affect high order bits in
* output data. To resolve this we xor in the value prior to multiplication
* shifted right by 17 bits. The number 17 was chosen because it doesn't
* have common denominator with set bit positions in FNV_PRIME and empirically
* provides the fastest mixing for high order bits of final iterations quickly
* avalanche into lower positions. For performance reasons we choose to combine
* 4 bytes at a time. The actual hash formula used as the basis is:
*
* hash = (hash ^ value) * FNV_PRIME ^ ((hash ^ value) >> 17)
*
* The main bottleneck in this calculation is the multiplication latency. To
* hide the latency and to make use of SIMD parallelism multiple hash values
* are calculated in parallel. The page is treated as a 32 column two
* dimensional array of 32 bit values. Each column is aggregated separately
* into a partial checksum. Each partial checksum uses a different initial
* value (offset basis in FNV terminology). The initial values actually used
* were chosen randomly, as the values themselves don't matter as much as that
* they are different and don't match anything in real data. After initializing
* partial checksums each value in the column is aggregated according to the
* above formula. Finally two more iterations of the formula are performed with
* value 0 to mix the bits of the last value added.
*
* The partial checksums are then folded together using xor to form a single
* 32-bit checksum. The caller can safely reduce the value to 16 bits
* using modulo 2^16-1. That will cause a very slight bias towards lower
* values but this is not significant for the performance of the
* checksum.
*
* The algorithm choice was based on what instructions are available in SIMD
* instruction sets. This meant that a fast and good algorithm needed to use
* multiplication as the main mixing operator. The simplest multiplication
* based checksum primitive is the one used by FNV. The prime used is chosen
* for good dispersion of values. It has no known simple patterns that result
* in collisions. Test of 5-bit differentials of the primitive over 64bit keys
* reveals no differentials with 3 or more values out of 100000 random keys
* colliding. Avalanche test shows that only high order bits of the last word
* have a bias. Tests of 1-4 uncorrelated bit errors, stray 0 and 0xFF bytes,
* overwriting page from random position to end with 0 bytes, and overwriting
* random segments of page with 0x00, 0xFF and random data all show optimal
* 2e-16 false positive rate within margin of error.
*
* Vectorization of the algorithm requires 32bit x 32bit -> 32bit integer
* multiplication instruction. As of 2013 the corresponding instruction is
* available on x86 SSE4.1 extensions (pmulld) and ARM NEON (vmul.i32).
* Vectorization requires a compiler to do the vectorization for us. For recent
* GCC versions the flags -msse4.1 -funroll-loops -ftree-vectorize are enough
* to achieve vectorization.
*
* The optimal amount of parallelism to use depends on CPU specific instruction
* latency, SIMD instruction width, throughput and the amount of registers
* available to hold intermediate state. Generally, more parallelism is better
* up to the point that state doesn't fit in registers and extra load-store
* instructions are needed to swap values in/out. The number chosen is a fixed
* part of the algorithm because changing the parallelism changes the checksum
* result.
*
* The parallelism number 32 was chosen based on the fact that it is the
* largest state that fits into architecturally visible x86 SSE registers while
* leaving some free registers for intermediate values. For future processors
* with 256bit vector registers this will leave some performance on the table.
* When vectorization is not available it might be beneficial to restructure
* the computation to calculate a subset of the columns at a time and perform
* multiple passes to avoid register spilling. This optimization opportunity
* is not used. Current coding also assumes that the compiler has the ability
* to unroll the inner loop to avoid loop overhead and minimize register
* spilling. For less sophisticated compilers it might be beneficial to
* manually unroll the inner loop.
*/
#include "storage/bufpage.h"
/* number of checksums to calculate in parallel */
#define N_SUMS 32
/* prime multiplier of FNV-1a hash */
#define FNV_PRIME 16777619
/* Use a union so that this code is valid under strict aliasing */
typedef union
{
PageHeaderData phdr;
uint32 data[BLCKSZ / (sizeof(uint32) * N_SUMS)][N_SUMS];
} PGChecksummablePage;
/*
* Base offsets to initialize each of the parallel FNV hashes into a
* different initial state.
*/
static const uint32 checksumBaseOffsets[N_SUMS] = {
0x5B1F36E9, 0xB8525960, 0x02AB50AA, 0x1DE66D2A,
0x79FF467A, 0x9BB9F8A3, 0x217E7CD2, 0x83E13D2C,
0xF8D4474F, 0xE39EB970, 0x42C6AE16, 0x993216FA,
0x7B093B5D, 0x98DAFF3C, 0xF718902A, 0x0B1C9CDB,
0xE58F764B, 0x187636BC, 0x5D7B3BB1, 0xE73DE7DE,
0x92BEC979, 0xCCA6C0B2, 0x304A0979, 0x85AA43D4,
0x783125BB, 0x6CA8EAA2, 0xE407EAC6, 0x4B5CFC3E,
0x9FBF8C76, 0x15CA20BE, 0xF2CA9FD3, 0x959BD756
};
/*
* Calculate one round of the checksum.
*/
#define CHECKSUM_COMP(checksum, value) \
do { \
uint32 __tmp = (checksum) ^ (value); \
(checksum) = __tmp * FNV_PRIME ^ (__tmp >> 17); \
} while (0)
/*
* Block checksum algorithm. The page must be adequately aligned
* (at least on 4-byte boundary).
*/
static uint32
pg_checksum_block(const PGChecksummablePage *page)
{
uint32 sums[N_SUMS];
uint32 result = 0;
uint32 i,
j;
/* ensure that the size is compatible with the algorithm */
Assert(sizeof(PGChecksummablePage) == BLCKSZ);
/* initialize partial checksums to their corresponding offsets */
memcpy(sums, checksumBaseOffsets, sizeof(checksumBaseOffsets));
/* main checksum calculation */
for (i = 0; i < (uint32) (BLCKSZ / (sizeof(uint32) * N_SUMS)); i++)
for (j = 0; j < N_SUMS; j++)
CHECKSUM_COMP(sums[j], page->data[i][j]);
/* finally add in two rounds of zeroes for additional mixing */
for (i = 0; i < 2; i++)
for (j = 0; j < N_SUMS; j++)
CHECKSUM_COMP(sums[j], 0);
/* xor fold partial checksums together */
for (i = 0; i < N_SUMS; i++)
result ^= sums[i];
return result;
}
/*
* Compute the checksum for a Postgres page.
*
* The page must be adequately aligned (at least on a 4-byte boundary).
* Beware also that the checksum field of the page is transiently zeroed.
*
* The checksum includes the block number (to detect the case where a page is
* somehow moved to a different location), the page header (excluding the
* checksum itself), and the page data.
*/
uint16
pg_checksum_page(char *page, BlockNumber blkno)
{
PGChecksummablePage *cpage = (PGChecksummablePage *) page;
uint16 save_checksum;
uint32 checksum;
/* We only calculate the checksum for properly-initialized pages */
Assert(!PageIsNew(&cpage->phdr));
/*
* Save pd_checksum and temporarily set it to zero, so that the checksum
* calculation isn't affected by the old checksum stored on the page.
* Restore it after, because actually updating the checksum is NOT part of
* the API of this function.
*/
save_checksum = cpage->phdr.pd_checksum;
cpage->phdr.pd_checksum = 0;
checksum = pg_checksum_block(cpage);
cpage->phdr.pd_checksum = save_checksum;
/* Mix in the block number to detect transposed pages */
checksum ^= blkno;
/*
* Reduce to a uint16 (to fit in the pd_checksum field) with an offset of
* one. That avoids checksums of zero, which seems like a good idea.
*/
return (uint16) ((checksum % 65535) + 1);
}
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