海量数据,海明距离高效检索(smlar) - 阿里云RDS PosgreSQL最佳实践

司空健

2023-12-01

背景

http://www.cnblogs.com/lushilin/p/6549665.html

SimHash的应用

通过上面的步骤，我们可以利用SimHash算法为每一个网页生成一个向量指纹，那么问题来了，如何判断2篇文本的相似性？
这里面主要应用到是海明距离。

（1）什么是海明距离
两个码字的对应比特取值不同的比特数称为这两个码字的海明距离。在一个有效编码集中,任意两个码字的海明距离的最小值称为该编码集的海明距离。举例如下：10101和00110从第一位开始依次有第一位、第四、第五位不同，则海明距离为3。

（2）海明距离的几何意义
n位的码字可以用n维空间的超立方体的一个顶点来表示。两个码字之间的海明距离就是超立方体两个顶点之间的一条边，而且是这两个顶点之间的最短距离。

（3）海明距离的应用场景
用于编码的检错和纠错

经过SimHash算法提取来的指纹（Simhash对长文本500字+比较适用，短文本可能偏差较大，具体需要根据实际场景测试），最后使用海明距离，求相似，在google的论文给出的数据中，64位的签名，在海明距离为3的情况下，可认为两篇文档是相似的或者是重复的，当然这个值只是参考值，针对自己的应用可能又不同的测试取值

到这里相似度问题基本解决，但是按这个思路，在海量数据几百亿的数量下，效率问题还是没有解决的，因为数据是不断添加进来的，不可能每来一条数据，都要和全库的数据做一次比较，按照这种思路，处理速度会越来越慢，线性增长。

针对海量数据的去重效率，我们可以将64位指纹，切分为4份16位的数据块，根据抽屉原理在海明距离为3的情况，如果两个文档相似，那么它必有一个块的数据是相等的。

那么数据库是否支持这种高效率的检索呢？

反正PostgreSQL是支持的，通过黑科技smlar插件。

一、需求

二、架构设计

在PostgreSQL中，从海量数据中，搜索海明距离小于N的数据，有多种设计手段。每种方法的能耗比都不一样，读者可以按需选择。

1 暴力计算

1、单机多核并行计算，暴力扫描。采用阿里云RDS PostgreSQL 10提供的多核并行能力，暴力扫描。

2、多机多核并行计算，暴力扫描。采用阿里云HybridDB for PostgreSQL提供的多级并行计算能力，暴力扫描。

3、利用GPU、FPGA加速暴力运算。

PostgreSQL提供了扩展接口，可以利用GPU，FPGA的能力对数据进行计算。

4、利用CPU向量计算指令，暴力计算。

PostgreSQL提供了扩展接口，可以利用CPU向量计算指令的能力加速计算。

2 索引

索引是高效的做法，例如PostgreSQL smlar插件，在阿里的导购平台就有使用，用于实时导购文的海量相似度查询。

如果要让smlar加速海明距离的搜索，需要采用更科学的方法，比如切片。

直接使用位置，会有问题，因为smlar的第一道工序是块级收敛，而海明码是bit64的编码，在一个数据块中，有若干条记录，任何位置都可能同时出现0和1，任何数据块都包含0和1，因此无法完成第一道过滤。

我们可以采用切片，减少这种可能性。例如每2个BIT一片，或者每4个BIT一片，或者更多。

通常海明距离大于3的，就没有什么相关性了。

三、DEMO与性能

1 暴力计算

1、全扫，并行扫描

创建测试表

create table hm (  
  id int,        -- id  
  hmval bit(64)  -- 海明HASH  
);

写入1000万测试数据

postgres=# insert into hm select id, val::int8::bit(64) from (select id, sqrt(random())::numeric*9223372036854775807*2-9223372036854775807::numeric as val from generate_series(1,10000000) t(id)) t;  
INSERT 0 10000000  
  
postgres=# select * from hm limit 10;  
 id |                              hmval                                 
----+------------------------------------------------------------------  
  1 | 0000101001110110110101010111101011100110101010000111100011110111  
  2 | 0110011100110101101000001010101111010001011101100111111011001110  
  3 | 1010110111001011011110110000111111101101101111010111111100101110  
  4 | 0110011110110000001011000010010000101011100101010100111000101001  
  5 | 0101110100101111010110010110000000101110000010001011010110110000  
  6 | 0011010000100000101011011100000101111110010110111101100001100001  
  7 | 1011110011101101101000011101011101010111011001011010110111101000  
  8 | 1110010011000101001101110010001111110100001101010101111101110010  
  9 | 0110111111110011101001001000101101011011111100010010111010001111  
 10 | 0011100011000010101011010001111000000110100011100100111011011001  
(10 rows)

设置暴力并行度

postgres=# set force_parallel_mode = on;  
postgres=# set min_parallel_table_scan_size = 0;  
postgres=# set parallel_setup_cost = 0;  
postgres=# set parallel_tuple_cost = 0;  
postgres=# alter table hm set (parallel_workers = 128);  
postgres=# set max_parallel_workers_per_gather = 64;

并行查询海明距离小于4的记录，耗时463毫秒。

postgres=# select * from hm where length(replace(bitxor(bit'0011110001011010110010001011010101001000111110000111110010010110', hmval)::text,'0','')) < 4;  
 id |                              hmval                                 
----+------------------------------------------------------------------  
 16 | 0011110001011010110010001011010101001000111110000111110010010110  
(1 row)  
  
Time: 463.314 ms

非并行查询海明距离小于4的记录，耗时16秒。

postgres=# select * from hm where length(replace(bitxor(bit'0011110001011010110010001011010101001000111110000111110010010110', hmval)::text,'0','')) < 4;  
 id |                              hmval                                 
----+------------------------------------------------------------------  
 16 | 0011110001011010110010001011010101001000111110000111110010010110  
(1 row)  
  
Time: 16791.215 ms (00:16.791)

求两个BIT的不同位数，还有更高效率的方法。理论上可以达到100毫秒以内。

https://www.postgresql.org/message-id/flat/ab1ea6540903121110l2a3021d4h6632b206e2419898%40mail.gmail.com#ab1ea6540903121110l2a3021d4h6632b206e2419898@mail.gmail.com

2 索引

阿里云RDS PostgreSQL提供了一个smlar插件，用于高效率的求数组的相似度。

我们需要将海明HASH，转换为数组，根据前面的设计，我们采用8个BIT一片的切法，支持索引查询海明距离为8以内的值。

切之前，验证一下切片后的过滤性：

postgres=# select relpages from pg_class where relname='hm';  
 relpages   
----------  
    63695  
(1 row)  
  
1、单个片为1时，不用说，每个块都包含。  
  
postgres=# select count(*) from (select substring(ctid::text,'(\d+),') from hm where substring(hmval,1,1)='0' group by 1)t;  
 count   
-------  
 63695  
(1 row)  
  
2、单个片为8时，有接近一半的块包含。  
  
postgres=# select count(*) from (select substring(ctid::text,'(\d+),') from hm where substring(hmval,1,8)='00000000' group by 1)t;  
 count   
-------  
 29100  
(1 row)  
  
3、单个片为16时，只有100多个块包含了。  
  
postgres=# select count(*) from (select substring(ctid::text,'(\d+),') from hm where substring(hmval,1,16)='0000000000000000' group by 1)t;  
 count   
-------  
   160  
(1 row)

8片切法的性能验证

创建插件

create extension smlar;

创建测试表

create table hm1 (id int, hmval bit(64), hmarr text[]);

生成1000万测试数据，生成测试数据时，按切分手段进行切分，记录为TEXT数组。

insert into hm1   
select   
  id,   
  val::bit(64),   
  regexp_split_to_array('1_'||substring(val,1,8)||',2_'||substring(val,9,8)||',3_'||substring(val,17,8)||',4_'||substring(val,25,8)||',5_'||substring(val,33,8)||',6_'||substring(val,41,8)||',7_'||substring(val,49,8)||',8_'||substring(val,57,8), ',')    
from   
(select id, (sqrt(random())::numeric*9223372036854775807*2-9223372036854775807::numeric)::int8::bit(64)::text as val from generate_series(1,10000000) t(id)) t;  
  
postgres=# select * from hm1 limit 10;  
 id |                              hmval                               |                                           hmarr                                             
----+------------------------------------------------------------------+-------------------------------------------------------------------------------------------  
  1 | 0000001110101101100110011000100111100100001100100101101010010011 | {1_00000011,2_10101101,3_10011001,4_10001001,5_11100100,6_00110010,7_01011010,8_10010011}  
  2 | 0001001000010101001100100010101010111001001000000110101101100100 | {1_00010010,2_00010101,3_00110010,4_00101010,5_10111001,6_00100000,7_01101011,8_01100100}  
  3 | 0011111111010100011001001010110110100010101110101001101111010000 | {1_00111111,2_11010100,3_01100100,4_10101101,5_10100010,6_10111010,7_10011011,8_11010000}  
  4 | 1100110010011001001110101110111111111111010000100000010011000010 | {1_11001100,2_10011001,3_00111010,4_11101111,5_11111111,6_01000010,7_00000100,8_11000010}  
  5 | 0011000011010001011111010101010111100110000110000011101100000101 | {1_00110000,2_11010001,3_01111101,4_01010101,5_11100110,6_00011000,7_00111011,8_00000101}  
  6 | 0111101101111110101000010110101101110011011110100100010111011001 | {1_01111011,2_01111110,3_10100001,4_01101011,5_01110011,6_01111010,7_01000101,8_11011001}  
  7 | 0010001011111111100010101011110001001101001011100100011000010000 | {1_00100010,2_11111111,3_10001010,4_10111100,5_01001101,6_00101110,7_01000110,8_00010000}  
  8 | 1110001111100011011110110111101111010101000111000100111111111101 | {1_11100011,2_11100011,3_01111011,4_01111011,5_11010101,6_00011100,7_01001111,8_11111101}  
  9 | 0111110010111000010111001000000101111000000110110110000011101110 | {1_01111100,2_10111000,3_01011100,4_10000001,5_01111000,6_00011011,7_01100000,8_11101110}  
 10 | 0111001101100010001101101111000000100100000000010001010011100101 | {1_01110011,2_01100010,3_00110110,4_11110000,5_00100100,6_00000001,7_00010100,8_11100101}  
(10 rows)

创建smlar索引

postgres=# create index idx_hm1 on hm1 using gin(hmarr _text_sml_ops );

搜索海明距离小于等于1的VALUE。用到了smlar索引，耗时63毫秒。

postgres=# set smlar.type = overlap;  
postgres=# set smlar.threshold = 7;  
  
select    
    *,    
    smlar( hmarr, '{1_00000011,2_10101101,3_10011001,4_10001001,5_11100100,6_00110010,7_01011010,8_10010011}')    
  from    
    hm1    
  where    
    hmarr % '{1_00000011,2_10101101,3_10011001,4_10001001,5_11100100,6_00110010,7_01011010,8_10010011}'      
    and length(replace(bitxor(bit'0000001110101101100110011000100111100100001100100101101010010011', hmval)::text,'0','')) < 2  
  limit 100;  
  
  
postgres=# explain (analyze,verbose,timing,costs,buffers) select    
    *,    
    smlar( hmarr, '{1_00000011,2_10101101,3_10011001,4_10001001,5_11100100,6_00110010,7_01011010,8_10010011}')    
  from    
    hm1    
  where    
    hmarr % '{1_00000011,2_10101101,3_10011001,4_10001001,5_11100100,6_00110010,7_01011010,8_10010011}'      
    and length(replace(bitxor(bit'0000001110101101100110011000100111100100001100100101101010010011', hmval)::text,'0','')) < 2  
  limit 100;  
                                                                            QUERY PLAN                                                                               
-------------------------------------------------------------------------------------------------------------------------------------------------------------------  
 Limit  (cost=117.83..420.48 rows=100 width=169) (actual time=62.928..62.929 rows=1 loops=1)  
   Output: id, hmval, hmarr, (smlar(hmarr, '{1_00000011,2_10101101,3_10011001,4_10001001,5_11100100,6_00110010,7_01011010,8_10010011}'::text[]))  
   Buffers: shared hit=166  
   ->  Bitmap Heap Scan on public.hm1  (cost=117.83..10205.17 rows=3333 width=169) (actual time=62.927..62.927 rows=1 loops=1)  
         Output: id, hmval, hmarr, smlar(hmarr, '{1_00000011,2_10101101,3_10011001,4_10001001,5_11100100,6_00110010,7_01011010,8_10010011}'::text[])  
         Recheck Cond: (hm1.hmarr % '{1_00000011,2_10101101,3_10011001,4_10001001,5_11100100,6_00110010,7_01011010,8_10010011}'::text[])  
         Filter: (length(replace((bitxor(B'0000001110101101100110011000100111100100001100100101101010010011'::"bit", hm1.hmval))::text, '0'::text, ''::text)) < 2)  
         Heap Blocks: exact=1  
         Buffers: shared hit=166  
         ->  Bitmap Index Scan on idx_hm1  (cost=0.00..117.00 rows=10000 width=0) (actual time=62.898..62.898 rows=1 loops=1)  
               Index Cond: (hm1.hmarr % '{1_00000011,2_10101101,3_10011001,4_10001001,5_11100100,6_00110010,7_01011010,8_10010011}'::text[])  
               Buffers: shared hit=165  
 Planning time: 0.147 ms  
 Execution time: 62.975 ms  
(14 rows)  
  
postgres=# select                  
    *,    
    smlar( hmarr, '{1_00000011,2_10101101,3_10011001,4_10001001,5_11100100,6_00110010,7_01011010,8_10010011}')    
  from    
    hm1    
  where    
    hmarr % '{1_00000011,2_10101101,3_10011001,4_10001001,5_11100100,6_00110010,7_01011010,8_10010011}'      
    and length(replace(bitxor(bit'0000001110101101100110011000100111100100001100100101101010010011', hmval)::text,'0','')) < 2  
  limit 100;  
 id |                              hmval                               |                                           hmarr                                           | smlar   
----+------------------------------------------------------------------+-------------------------------------------------------------------------------------------+-------  
  1 | 0000001110101101100110011000100111100100001100100101101010010011 | {1_00000011,2_10101101,3_10011001,4_10001001,5_11100100,6_00110010,7_01011010,8_10010011} |     8  
(1 row)  
Time: 61.227 ms

如果我们只需要查询4以内的海明距离，实际上可以使用16的分组，或者我们可以使用混合切法。

6片混合切法的性能验证

切法为8,16,8,8,16,8。支持海明距离6以内的查询。

create table hm2 (id int, hmval bit(64), hmarr text[]);  
  
insert into hm2   
select   
  id,   
  val::bit(64),   
  regexp_split_to_array('1_'||substring(val,1,8)||',2_'||substring(val,9,16)||',3_'||substring(val,25,8)||',4_'||substring(val,33,8)||',5_'||substring(val,41,16)||',6_'||substring(val,57,8), ',')    
from   
(select id, (sqrt(random())::numeric*9223372036854775807*2-9223372036854775807::numeric)::int8::bit(64)::text as val from generate_series(1,10000000) t(id)) t;  
  
postgres=# select * from hm2 limit 10;  
 id |                              hmval                               |                                        hmarr                                          
----+------------------------------------------------------------------+-------------------------------------------------------------------------------------  
  1 | 1100111011000001100100100111111110100011100111111101101001101010 | {1_11001110,2_1100000110010010,3_01111111,4_10100011,5_1001111111011010,6_01101010}  
  2 | 0111111000101011000111010011011000000010010001111001000111011101 | {1_01111110,2_0010101100011101,3_00110110,4_00000010,5_0100011110010001,6_11011101}  
  3 | 0111111000101111000101011100100000001111011101101100110100000101 | {1_01111110,2_0010111100010101,3_11001000,4_00001111,5_0111011011001101,6_00000101}  
  4 | 0111010101010010100000110001100011110010111000001011000010010010 | {1_01110101,2_0101001010000011,3_00011000,4_11110010,5_1110000010110000,6_10010010}  
  5 | 1111101100110100101111000011001011111110111000100110101001100001 | {1_11111011,2_0011010010111100,3_00110010,4_11111110,5_1110001001101010,6_01100001}  
  6 | 0011110000100010101001000001100010000010111011100010011001000110 | {1_00111100,2_0010001010100100,3_00011000,4_10000010,5_1110111000100110,6_01000110}  
  7 | 0000111111001110100110011110000110001101110111111111111010111001 | {1_00001111,2_1100111010011001,3_11100001,4_10001101,5_1101111111111110,6_10111001}  
  8 | 0110100010010100111100110110000011101110101001001111010101011111 | {1_01101000,2_1001010011110011,3_01100000,4_11101110,5_1010010011110101,6_01011111}  
  9 | 0111001111001100101011001001100100000000111100000110110001000011 | {1_01110011,2_1100110010101100,3_10011001,4_00000000,5_1111000001101100,6_01000011}  
 10 | 1101111101011000111100101010101000100001101100101110100001111000 | {1_11011111,2_0101100011110010,3_10101010,4_00100001,5_1011001011101000,6_01111000}  
(10 rows)  
  
create index idx_hm2 on hm2 using gin(hmarr _text_sml_ops );

查询海明距离小于等于1的值，提高到2毫秒了。

postgres=# set smlar.type = overlap;  
postgres=# set smlar.threshold = 5;  
  
postgres=# select    
    *,    
    smlar( hmarr, '{1_11001110,2_1100000110010010,3_01111111,4_10100011,5_1001111111011010,6_01101010}')    
  from    
    hm2   
  where    
    hmarr % '{1_11001110,2_1100000110010010,3_01111111,4_10100011,5_1001111111011010,6_01101010}'      
    and length(replace(bitxor(bit'1100111011000001100100100111111110100011100111111101101001101010', hmval)::text,'0','')) < 2  
  limit 100;  
 id |                              hmval                               |                                        hmarr                                        | smlar   
----+------------------------------------------------------------------+-------------------------------------------------------------------------------------+-------  
  1 | 1100111011000001100100100111111110100011100111111101101001101010 | {1_11001110,2_1100000110010010,3_01111111,4_10100011,5_1001111111011010,6_01101010} |     6  
(1 row)  
Time: 1.954 ms  
  
postgres=# explain (analyze,verbose,timing,costs,buffers) select    
    *,    
    smlar( hmarr, '{1_11001110,2_1100000110010010,3_01111111,4_10100011,5_1001111111011010,6_01101010}')    
  from    
    hm2   
  where    
    hmarr % '{1_11001110,2_1100000110010010,3_01111111,4_10100011,5_1001111111011010,6_01101010}'      
    and length(replace(bitxor(bit'1100111011000001100100100111111110100011100111111101101001101010', hmval)::text,'0','')) < 2  
  limit 100;  
                                                                            QUERY PLAN                                                                               
-------------------------------------------------------------------------------------------------------------------------------------------------------------------  
 Limit  (cost=103.83..406.06 rows=100 width=153) (actual time=2.414..2.416 rows=1 loops=1)  
   Output: id, hmval, hmarr, (smlar(hmarr, '{1_11001110,2_1100000110010010,3_01111111,4_10100011,5_1001111111011010,6_01101010}'::text[]))  
   Buffers: shared hit=102  
   ->  Bitmap Heap Scan on public.hm2  (cost=103.83..10177.17 rows=3333 width=153) (actual time=2.414..2.415 rows=1 loops=1)  
         Output: id, hmval, hmarr, smlar(hmarr, '{1_11001110,2_1100000110010010,3_01111111,4_10100011,5_1001111111011010,6_01101010}'::text[])  
         Recheck Cond: (hm2.hmarr % '{1_11001110,2_1100000110010010,3_01111111,4_10100011,5_1001111111011010,6_01101010}'::text[])  
         Filter: (length(replace((bitxor(B'1100111011000001100100100111111110100011100111111101101001101010'::"bit", hm2.hmval))::text, '0'::text, ''::text)) < 2)  
         Heap Blocks: exact=1  
         Buffers: shared hit=102  
         ->  Bitmap Index Scan on idx_hm2  (cost=0.00..103.00 rows=10000 width=0) (actual time=2.374..2.374 rows=1 loops=1)  
               Index Cond: (hm2.hmarr % '{1_11001110,2_1100000110010010,3_01111111,4_10100011,5_1001111111011010,6_01101010}'::text[])  
               Buffers: shared hit=101  
 Planning time: 0.149 ms  
 Execution time: 2.463 ms  
(14 rows)

4片切法的性能验证

create table hm3 (id int, hmval bit(64), hmarr text[]);  
  
insert into hm3   
select   
  id,   
  val::bit(64),   
  regexp_split_to_array('1_'||substring(val,1,16)||',2_'||substring(val,17,16)||',3_'||substring(val,33,16)||',4_'||substring(val,41,16), ',')    
from   
(select id, (sqrt(random())::numeric*9223372036854775807*2-9223372036854775807::numeric)::int8::bit(64)::text as val from generate_series(1,10000000) t(id)) t;  
  
postgres=# select * from hm3 limit 10;  
 id |                              hmval                               |                                     hmarr                                       
----+------------------------------------------------------------------+-------------------------------------------------------------------------------  
  1 | 0101011111111010000001001011101101100011111101111101101100000011 | {1_0101011111111010,2_0000010010111011,3_0110001111110111,4_1111011111011011}  
  2 | 1101011000010000000000000000111011011111011101110100000010101011 | {1_1101011000010000,2_0000000000001110,3_1101111101110111,4_0111011101000000}  
  3 | 0101000010110110110010001010100010101001001010111111011000110011 | {1_0101000010110110,2_1100100010101000,3_1010100100101011,4_0010101111110110}  
  4 | 0111000111100011111000100111000011101111110000011110101101000100 | {1_0111000111100011,2_1110001001110000,3_1110111111000001,4_1100000111101011}  
  5 | 0010111010101011111010011110110010011110111111110011101110010011 | {1_0010111010101011,2_1110100111101100,3_1001111011111111,4_1111111100111011}  
  6 | 0110111110011100100110010111010000000011100011000011110001010110 | {1_0110111110011100,2_1001100101110100,3_0000001110001100,4_1000110000111100}  
  7 | 0100110100111001110011011110100111101110101001000101010110110110 | {1_0100110100111001,2_1100110111101001,3_1110111010100100,4_1010010001010101}  
  8 | 0110010111001100111000011011011100001100111111101111011010100010 | {1_0110010111001100,2_1110000110110111,3_0000110011111110,4_1111111011110110}  
  9 | 0110111010110000001010101111000101110000010011100011100101000100 | {1_0110111010110000,2_0010101011110001,3_0111000001001110,4_0100111000111001}  
 10 | 0101101000000110100101100011111111000101110001010011100110101011 | {1_0101101000000110,2_1001011000111111,3_1100010111000101,4_1100010100111001}  
(10 rows)  
  
create index idx_hm3 on hm3 using gin(hmarr _text_sml_ops );

查询海明距离小于等于1的值，提高到0.2毫秒了。

postgres=# set smlar.type = overlap;  
postgres=# set smlar.threshold = 3;  
  
postgres=# select    
    *,    
    smlar( hmarr, '{1_0101011111111010,2_0000010010111011,3_0110001111110111,4_1111011111011011}')    
  from    
    hm3  
  where    
    hmarr % '{1_0101011111111010,2_0000010010111011,3_0110001111110111,4_1111011111011011}'      
    and length(replace(bitxor(bit'0101011111111010000001001011101101100011111101111101101100000011', hmval)::text,'0','')) < 2  
  limit 100;  
 id |                              hmval                               |                                     hmarr                                     | smlar   
----+------------------------------------------------------------------+-------------------------------------------------------------------------------+-------  
  1 | 0101011111111010000001001011101101100011111101111101101100000011 | {1_0101011111111010,2_0000010010111011,3_0110001111110111,4_1111011111011011} |     4  
(1 row)  
  
  
postgres=# explain (analyze,verbose,timing,costs,buffers) select    
    *,    
    smlar( hmarr, '{1_0101011111111010,2_0000010010111011,3_0110001111110111,4_1111011111011011}')    
  from    
    hm3  
  where    
    hmarr % '{1_0101011111111010,2_0000010010111011,3_0110001111110111,4_1111011111011011}'      
    and length(replace(bitxor(bit'0101011111111010000001001011101101100011111101111101101100000011', hmval)::text,'0','')) < 2  
  limit 100;  
                                                                            QUERY PLAN                                                                               
-------------------------------------------------------------------------------------------------------------------------------------------------------------------  
 Limit  (cost=99.83..401.19 rows=100 width=134) (actual time=0.169..0.170 rows=1 loops=1)  
   Output: id, hmval, hmarr, (smlar(hmarr, '{1_0101011111111010,2_0000010010111011,3_0110001111110111,4_1111011111011011}'::text[]))  
   Buffers: shared hit=14  
   ->  Bitmap Heap Scan on public.hm3  (cost=99.83..10144.17 rows=3333 width=134) (actual time=0.168..0.169 rows=1 loops=1)  
         Output: id, hmval, hmarr, smlar(hmarr, '{1_0101011111111010,2_0000010010111011,3_0110001111110111,4_1111011111011011}'::text[])  
         Recheck Cond: (hm3.hmarr % '{1_0101011111111010,2_0000010010111011,3_0110001111110111,4_1111011111011011}'::text[])  
         Filter: (length(replace((bitxor(B'0101011111111010000001001011101101100011111101111101101100000011'::"bit", hm3.hmval))::text, '0'::text, ''::text)) < 2)  
         Heap Blocks: exact=1  
         Buffers: shared hit=14  
         ->  Bitmap Index Scan on idx_hm3  (cost=0.00..99.00 rows=10000 width=0) (actual time=0.145..0.145 rows=1 loops=1)  
               Index Cond: (hm3.hmarr % '{1_0101011111111010,2_0000010010111011,3_0110001111110111,4_1111011111011011}'::text[])  
               Buffers: shared hit=13  
 Planning time: 0.101 ms  
 Execution time: 0.200 ms  
(14 rows)

查询海明距离小于等于4的，依旧在毫秒返回。

postgres=# set smlar.type = overlap;  
postgres=# set smlar.threshold = 0;  
  
postgres=# select    
    *,    
    smlar( hmarr, '{1_0101011111111010,2_0000010010111011,3_0110001111110111,4_1111011111011011}')    
  from    
    hm3  
  where    
    hmarr % '{1_0101011111111010,2_0000010010111011,3_0110001111110111,4_1111011111011011}'      
    and length(replace(bitxor(bit'0101011111111010000001001011101101100011111101111101101100000011', hmval)::text,'0','')) < 5  
  limit 100;  
 id |                              hmval                               |                                     hmarr                                     | smlar   
----+------------------------------------------------------------------+-------------------------------------------------------------------------------+-------  
  1 | 0101011111111010000001001011101101100011111101111101101100000011 | {1_0101011111111010,2_0000010010111011,3_0110001111110111,4_1111011111011011} |     4  
(1 row)  
Time: 6.983 ms

不使用索引，23秒。

postgres=# select * from hm3 where length(replace(bitxor(bit'0101011111111010000001001011101101100011111101111101101100000011', hmval)::text,'0','')) < 5;  
 id |                              hmval                               |                                     hmarr                                       
----+------------------------------------------------------------------+-------------------------------------------------------------------------------  
  1 | 0101011111111010000001001011101101100011111101111101101100000011 | {1_0101011111111010,2_0000010010111011,3_0110001111110111,4_1111011111011011}  
(1 row)  
  
Time: 22954.686 ms

相比没有索引的情况，性能从23秒提升到了0.2毫秒。提升了11.48万倍。

自动切分

有人会说，怎么自动生成simhash切分后的数组呢？

不用担心，PostgreSQL提供了强大的UDF功能，可以建立UDF和TRIGGER，在写入数据时，自动生成切分后的数组。

例子

create table hm4 (id int, hmval bit(64), hmarr text[]);  

create or replace function sp(val bit(64)) returns text[] as $$
select regexp_split_to_array('1_'||substring(val::text,1,10)||',2_'||substring(val::text,11,10)||',3_'||substring(val::text,21,10)||',4_'||substring(val::text,31,10)||',5_'||substring(val::text,41,10)||',6_'||substring(val::text,51,14), ',') ;            
$$ language sql strict;

postgres=# select sp(123::bit(64));
                                         sp                                          
-------------------------------------------------------------------------------------
 {1_0000000000,2_0000000000,3_0000000000,4_0000000000,5_0000000000,6_00000001111011}
(1 row)

-- 写入1亿记录

insert into hm4  
select   
  id,   
  val::bit(64),   
  sp(val::bit(64))    
from   
(select id, (sqrt(random())::numeric*9223372036854775807*2-9223372036854775807::numeric)::int8::bit(64)::text as val from generate_series(1,100000000) t(id)) t;  

-- 索引

create index idx_hm4 on hm4 using gin(hmarr _text_sml_ops );  

-- 查询海明距离小于等于1的记录，性能杠杠的

postgres=# set smlar.type = overlap;  
postgres=# set smlar.threshold = 5; 

select    
    *,    
    smlar( hmarr, sp(123::bit(64)))     -- 查询与123::bit(64)海明距离小于2的记录
  from    
    hm3  
  where    
    hmarr % sp(123::bit(64))      -- 查询与123::bit(64)海明距离小于2的记录
    and length(replace(bitxor(123::bit(64), hmval)::text,'0','')) < 2      -- 查询与123::bit(64)海明距离小于2的记录
  limit 100;

创建触发器，写入simhash时，自动写入切分数组

create or replace function tg() returns trigger as $$
declare
begin
  NEW.hmarr := sp(NEW.hmval);
  return NEW;
end;
$$ language plpgsql strict;

postgres=# create trigger tg before insert or update on hm4 for each row execute procedure tg();
CREATE TRIGGER

-- 效果很赞

postgres=# truncate hm4;
TRUNCATE TABLE
postgres=# insert into hm4 values (1,1::bit(64));
INSERT 0 1
postgres=# select * from hm4;
 id |                              hmval                               |                                        hmarr                                        
----+------------------------------------------------------------------+-------------------------------------------------------------------------------------
  1 | 0000000000000000000000000000000000000000000000000000000000000001 | {1_0000000000,2_0000000000,3_0000000000,4_0000000000,5_0000000000,6_00000000000001}
(1 row)

postgres=# update hm4 set hmval=123456::bit(64);
UPDATE 1
postgres=# select * from hm4;
 id |                              hmval                               |                                        hmarr                                        
----+------------------------------------------------------------------+-------------------------------------------------------------------------------------
  1 | 0000000000000000000000000000000000000000000000011110001001000000 | {1_0000000000,2_0000000000,3_0000000000,4_0000000000,5_0000000111,6_10001001000000}
(1 row)

爽就点个赞吧。