diff options
Diffstat (limited to 'src/include/storage/checksum_impl.h')
| -rw-r--r-- | src/include/storage/checksum_impl.h | 215 |
1 files changed, 215 insertions, 0 deletions
diff --git a/src/include/storage/checksum_impl.h b/src/include/storage/checksum_impl.h new file mode 100644 index 0000000..364acfa --- /dev/null +++ b/src/include/storage/checksum_impl.h @@ -0,0 +1,215 @@ +/*------------------------------------------------------------------------- + * + * 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) 1996-2020, 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); +} |