A traditional query executor, such as the Postgres Pro Enterprise executor, deals with a single row of data at each moment of time. If it has to evaluate expression (x+y), it first fetches the value of "x", then the value of "y", performs the "+" operation, and returns the result value to the upper node. In contrast, a vectorized executor can process multiple values in one operation. In this case, "x" and "y" represent not just a single scalar value, but a vector of values. The returned result is also a vector of values. In vector execution model, interpretation and function call overhead is divided by the vector size. The price of performing a function call is the same, but as the function processes N values instead of a single one, this overhead becomes less critical. The larger the vector, the smaller the per-row overhead.

Thus, we can form a vector from all values of the corresponding table attribute. It is called vertical data model, or columnar storage. Unlike the classical horizontal data model where the data storing unit is a row (tuple), here we have vertical columns.

Columnar storage has the following advantages:

However, performing an operation on the whole column is not a very good idea. If the table is very large, the vector can also be very big and may not fit in memory. But even if it fits in memory, working with such large vectors prevents efficient utilization of CPU cache levels (L1, L2,...). So it is more efficient to split the column into relatively small chunks, or tiles — units of processing by vectorized executor. The size of such chunks is chosen to keep all operands of vector operations in cache, even for complex expressions. A typical size of chunk is from 100 to 1000 elements.

VOPS supports all basic Postgres Pro Enterprise numeric types: 1-, 2-, 4- ,8-byte integers and 4,8 bytes floats. Also it supports date and timestamp types but they are using the same implementation as int4 and int8, respectively.

VOPS does not support strings (char or varchar types), except for a single character. If strings are used as identifiers, in most cases it is preferable to place them in some dictionary and use integer identifiers instead of original strings.

VOPS provides implementation of all built-in SQL arithmetic operations for numeric types: + - / * Certainly it also implements all comparison operators: = <> > >= < <=. Operands of such operators can be either tiles or scalar constants: x=y or x=1.

Boolean operators AND, OR, NOT cannot be overloaded. Instead, VOPS provides operators & | !. Please notice that precedence of these operators is different from AND, OR, NOT operators. So you cannot write predicate as x=1 | x=2 - it will cause a syntax error. To solve this problem use parenthesis: (x=1) | (x=2).

Also VOPS provides analog of BETWEEN operator. In SQL expression (x BETWEEN a AND b) is equivalent to (x >= a AND x <= b). But as far as AND operator cannot be overloaded, such substitution will not work for VOPS tiles. This is why VOPS provides special function for range check. Unfortunately BETWEEN is reserved keyword, so no function with such name can be defined. This is why synonym BETWIXT is used.

Postgres Pro Enterprise requires predicate expression to have boolean type. But result of vector boolean operators is vops_bool, not bool. This is why compiler doesn't allow to use it in predicate. The problem can be solved by introducing special filter function. This function is given arbitrary vector boolean expression and returns normal boolean which ... is always true. So from Postgres Pro Enterprise executor point of view predicate value is always true. But filter function sets filter_mask which is actually used in subsequent operators to determine selected records. So query in VOPS looks something like this:

  select sum(price) from trades where filter(day >= '2017-01-01'::date);

Please notice one more difference from normal sequence: we have to use explicit cast of string constant to appreciate data type (date type in this example). For betwixt function it is not needed:

  select sum(price) from trades where filter(betwixt(day, '2017-01-01', '2017-02-01'));

For char, int2 and int4 types VOPS provides concatenation operator || which produces doubled integer type: (char || char) -> int2, (int2 || int2) -> int4, (int4 || int4) -> int8. Them can be used for grouping by several columns (see below).

OLAP queries usually perform some kind of aggregation of large volumes of data. These includes grand aggregates which are calculated for the whole table or aggregates with group by which are calculated for each group. VOPS implements all standard SQL aggregates: count, min, max, sum, avg, var_pop, var_sampl, variance, stddev_pop, stddev_samp, stddev. Them can be used exactly in the same way as in normal SQL queries:

select sum(l_extendedprice*l_discount) as revenue
from vops_lineitem
where filter(betwixt(l_shipdate, '1996-01-01', '1997-01-01')
        & betwixt(l_discount, 0.08, 0.1)
        & (l_quantity < 24));

Also VOPS provides weighted average aggregate VWAP which can be used to calculate volume-weighted average price:

select wavg(l_extendedprice,l_quantity) from vops_lineitem;

Using aggregation with group by is more complex. VOPS provides two functions for it: map and reduce. The work is actually done by map(group_by_expression, aggregate_list, expr {, expr }) VOPS implements aggregation using hash table, which entries collect aggregate states for all groups. And set returning function reduce just iterates through the hash table consrtucted by map. reduce function is needed because result of aggregate in Postgres Pro Enterprise can not be a set. So aggregate query with group by looks something like this:

select reduce(map(l_returnflag||l_linestatus, 'sum,sum,sum,sum,avg,avg,avg',
    l_quantity,
    l_extendedprice,
    l_extendedprice*(1-l_discount),
    l_extendedprice*(1-l_discount)*(1+l_tax),
    l_quantity,
    l_extendedprice,
    l_discount)) from vops_lineitem where filter(l_shipdate <= '1998-12-01'::date);

Here we use concatenation operator to perform grouping by two columns. Right now VOPS supports grouping only by integer type. Another serious restriction is that all aggregated expressions should have the same type, for example vops_float4. It is not possible to calculate aggregates for vops_float4 and vopd_int8 columns in one call of map function, because it accepts aggregation arguments as variadic array, so all elements of this array should have the same type.

Aggregate string in map function should contain list of requested aggregate functions, separated by colon. Standard lowercase names should be used: count, sum, agg, min, max. Count is executed for the particular column: count(x). There is no need to explicitly specify count(*) because number of records in each group is returned by reduce function in any case.

reduce function returns set of vops_aggregate type. It contains three components: value of group by expression, number of records in the group and array of floats with aggregate values. Please notice that values of all aggregates, including count and min/max, are returned as floats.

create type vops_aggregates as(group_by int8, count int8, aggs float8[]);
create function reduce(bigint) returns setof vops_aggregates;

But there is much simple and straightforward way of performing group aggregates using VOPS. We need to partition table by group by fields. In this case grouping keys will be stored in normal way and other fields - inside tiles. Now Postgres Pro Enterprise executor will execute VOPS aggregates for each group:

select
    l_returnflag,
    l_linestatus,
    sum(l_quantity) as sum_qty,
    sum(l_extendedprice) as sum_base_price,
    sum(l_extendedprice*(1-l_discount)) as sum_disc_price,
    sum(l_extendedprice*(1-l_discount)*(1+l_tax)) as sum_charge,
    avg(l_quantity) as avg_qty,
    avg(l_extendedprice) as avg_price,
    avg(l_discount) as avg_disc,
    countall(*) as count_order
from
    vops_lineitem_projection
where
    filter(l_shipdate <= '1998-12-01'::date)
group by
    l_returnflag,
    l_linestatus
order by
    l_returnflag,
    l_linestatus;

In this example l_returnflag and l_linestatus fields of table vops_lineitem_projection have "char" type while all other used fields - tile types (l_shipdate has type vops_date and other fields - vops_float4). The query above is executed even faster than query with reduce(map(...)). The main problem with this approach is that you have to create projection for each combination of group by keys you want to use in queries.

VOPS provides limited support of Postgres Pro Enterprise window functions. It implements count, sum, min, max, avg and lag functions. But unfortunately Postgres Pro Enterprise requires aggregates to have to similar final type for moving (window) and plain implementations. This is why VOPS has to choose define this aggregate under different names: mcount, msum, mmin, mmax, mavg.

There are also two important restrictions:

Example of using window functions with VOPS:

select unnest(t.*) from (select mcount(*) over w,mcount(x) over w,msum(x) over w,mavg(x) over w,mmin(x) over w,mmax(x) over w,x - lag(x) over w 
from v window w as (rows between unbounded preceding and current row)) t;

Analytic queries are usually performed on the data for which no indexes are defined. And columnar store vector operations are most efficient in this case. But it is still possible to use indexes with VOPS.

As far as each VOPS tile represents multiple values, index can be used only for some preliminary, non-precise filtering of data. It is something similar with BRIN indexes. VOPS provides four functions: first, last, high, low which can be used to obtain high/low boundary of values stored in the tile. First two functions first and last should be used for sorted data set. In this case first value is the smallest value in the tile and last value is the largest value in the tile. If data is not sorted, then lowhigh functions should be used, which are more expensive, because them need to inspect all tile values. Using this four function it is possible to construct functional indexes for VOPS table. BRIN index seems to be the best choice for VOPS table:

create index low_boundary on trades using brin(first(day)); -- trades table is ordered by day
create index high_boundary on trades using brin(last(day)); -- trades table is ordered by day

Now it is possible to use this indexes in query. Please notice that we have to recheck precise condition because index gives only approximate result:

select sum(price) from trades where first(day) >= '2015-01-01' and last(day) <= '2016-01-01'
                                               and filter(betwixt(day, '2015-01-01', '2016-01-01'));

The vops extension provides special functions to pre-process the data for VOPS queries, uniting attribute values of several rows inside one VOPS tile.

First of all you need to create table with columns having VOPS tile types. It can map all columns of the original table or just some most frequently used subset of them. This table can be treated as a projection of the original table. Projection should include columns which are most frequently used together in queries.

Original table from TPC-H benchmark:

create table lineitem(
   l_orderkey integer,
   l_partkey integer,
   l_suppkey integer,
   l_linenumber integer,
   l_quantity real,
   l_extendedprice real,
   l_discount real,
   l_tax real,
   l_returnflag char,
   l_linestatus char,
   l_shipdate date,
   l_commitdate date,
   l_receiptdate date,
   l_shipinstruct char(25),
   l_shipmode char(10),
   l_comment char(44));

VOPS projection of this table:

create table vops_lineitem(
   l_shipdate vops_date not null,
   l_quantity vops_float4 not null,
   l_extendedprice vops_float4 not null,
   l_discount vops_float4 not null,
   l_tax vops_float4 not null,
   l_returnflag vops_char not null,
   l_linestatus vops_char not null
);

Original table can be treated as the write-optimized storage (WOS). If it has not indexes, then Postgres Pro Enterprise is able to provide very fast insertion speed, comparable with raw disk write speed. Projection in VOPS format can be treated as the read-optimized storage (ROS), most efficient for execution of OLAP queries.

To transfer data from the original to the projected table, use the vops.populate function. For example:

select populate(destination := 'vops_lineitem'::regclass, source := 'lineitem'::regclass);

You can use populated table in queries performing sequential scan. VOPS operators can speed up filtering of records and calculation of aggregates. Aggregation with group by requires use of reduce + map functions. But as it was mentioned above in the section describing aggregates, it is possible to populate table in such way, that standard PostgreSQL grouping algorithm will be used.

We need to choose partitioning keys and sort original table by this keys. Combination of partitioning keys expected to be NOT unique - otherwise tiles can only increase used space and lead to performance degradation. But if there are a lot of duplicates, then "collapsing" them and storing other fields in tiles will help to reduce space and speed up queries. Let's create the following projection of lineitems table:

create table vops_lineitem_projection(
   l_shipdate vops_date not null,
   l_quantity vops_float4 not null,
   l_extendedprice vops_float4 not null,
   l_discount vops_float4 not null,
   l_tax vops_float4 not null,
   l_returnflag "char" not null,
   l_linestatus "char" not null
);

As you can see, in this table l_returnflag and l_linestatus fields are scalars, and other fields - tiles. This projection can be populated using the following command:

select populate(destination := 'vops_lineitem_projection'::regclass, source := 'lineitem_projection'::regclass, sort := 'l_returnflag,l_linestatus');

Now we can create normal index on partitioning keys, define standard predicates for them and use them in group by and order by clauses.

Sometimes it is not possible or not desirable to store two copies of the same dataset. VOPS allows to load data directly from CSV file into VOPS table with tiles, bypassing creation of normal (plain) table. It can be done using import function:

select import(destination := 'vops_lineitem'::regclass, csv_path := '/mnt/data/lineitem.csv', separator := '|');

import function is defined in this way:

create function import(destination regclass, 
                       csv_path cstring, 
                       separator cstring default ',', 
                       skip integer default 0) returns bigint;

It accepts name of target VOPS table, path to CSV file, optional separator (default is ',') and number of lines in CSV header (no header by default). The function returns number of imported rows.

A query from VOPS projection returns set of tiles. Output function of tile type is able to print content of the tile. But in some cases it is preferable to transfer result to normal (horizontal) format where each tuple represents one record. It can be done using unnest function:

postgres=# select unnest(l.*) from vops_lineitem l where filter(l_shipdate <= '1998-12-01'::date) limit 3;
                unnest                 
---------------------------------------
 (1996-03-13,17,33078.9,0.04,0.02,N,O)
 (1996-04-12,36,38306.2,0.09,0.06,N,O)
 (1996-01-29,8,15479.7,0.1,0.02,N,O)
(3 rows)

As it was mentioned in previous section, unnest function can scatter records with VOPS types into normal records with scalar types. So it is possible to use this records in arbitrary SQL queries. But there are two problems with unnest function:

Fortunately Postgres Pro Enterprise provides solution for both of this problem: foreign data wrappers (FDW). In our case data is not really "foreign": it is stored inside our own database. But in alternatives (VOPS) format. VOPS FDW allows to "hide" specific of VOPS format and run normal SQL queries on VOPS tables. FDW allows the following:

So, by placing VOPS projection under FDW, we can efficiently perform sequential scan and aggregation queries as if them will be explicitly written for VOPS table and at the same time be able to execute any other queries on this data, including joins, CTEs,... Query can be written in standard SQL without usage of any VOPS specific functions.

Below is an example of creating VOPS FDW and running some queries on it:

create foreign table lineitem_fdw  (
   l_suppkey int4 not null,
   l_orderkey int4 not null,
   l_partkey int4 not null,
   l_shipdate date not null,
   l_quantity float4 not null,
   l_extendedprice float4 not null,
   l_discount float4 not null,
   l_tax      float4 not null,
   l_returnflag "char" not null,
   l_linestatus "char" not null
) server vops_server options (table_name 'vops_lineitem');

explain select
   sum(l_extendedprice*l_discount) as revenue
from
   lineitem_fdw
where
   l_shipdate between '1996-01-01' and '1997-01-01'
   and l_discount between 0.08 and 0.1
   and l_quantity < 24;
                       QUERY PLAN                        
---------------------------------------------------------
 Foreign Scan  (cost=1903.26..1664020.23 rows=1 width=4)
(1 row)

-- Filter was pushed down to FDW

explain select
    n_name,
    count(*),
    sum(l_extendedprice * (1-l_discount)) as revenue
from
    customer_fdw join orders_fdw on c_custkey = o_custkey
    join lineitem_fdw on l_orderkey = o_orderkey
    join supplier_fdw on l_suppkey = s_suppkey
    join nation on c_nationkey = n_nationkey
    join region on n_regionkey = r_regionkey
where
    c_nationkey = s_nationkey
    and r_name = 'ASIA'
    and o_orderdate >= '1996-01-01'
    and o_orderdate < '1997-01-01'
group by
    n_name
order by
    revenue desc;
                                                              QUERY PLAN                                                              
--------------------------------------------------------------------------------------------------------------------------------------
 Sort  (cost=2337312.28..2337312.78 rows=200 width=48)
   Sort Key: (sum((lineitem_fdw.l_extendedprice * ('1'::double precision - lineitem_fdw.l_discount)))) DESC
   ->  GroupAggregate  (cost=2336881.54..2337304.64 rows=200 width=48)
         Group Key: nation.n_name
         ->  Sort  (cost=2336881.54..2336951.73 rows=28073 width=40)
               Sort Key: nation.n_name
               ->  Hash Join  (cost=396050.65..2334807.39 rows=28073 width=40)
                     Hash Cond: ((orders_fdw.o_custkey = customer_fdw.c_custkey) AND (nation.n_nationkey = customer_fdw.c_nationkey))
                     ->  Hash Join  (cost=335084.53..2247223.46 rows=701672 width=52)
                           Hash Cond: (lineitem_fdw.l_orderkey = orders_fdw.o_orderkey)
                           ->  Hash Join  (cost=2887.07..1786058.18 rows=4607421 width=52)
                                 Hash Cond: (lineitem_fdw.l_suppkey = supplier_fdw.s_suppkey)
                                 ->  Foreign Scan on lineitem_fdw  (cost=0.00..1512151.52 rows=59986176 width=16)
                                 ->  Hash  (cost=2790.80..2790.80 rows=7702 width=44)
                                       ->  Hash Join  (cost=40.97..2790.80 rows=7702 width=44)
                                             Hash Cond: (supplier_fdw.s_nationkey = nation.n_nationkey)
                                             ->  Foreign Scan on supplier_fdw  (cost=0.00..2174.64 rows=100032 width=8)
                                             ->  Hash  (cost=40.79..40.79 rows=15 width=36)
                                                   ->  Hash Join  (cost=20.05..40.79 rows=15 width=36)
                                                         Hash Cond: (nation.n_regionkey = region.r_regionkey)
                                                         ->  Seq Scan on nation  (cost=0.00..17.70 rows=770 width=40)
                                                         ->  Hash  (cost=20.00..20.00 rows=4 width=4)
                                                               ->  Seq Scan on region  (cost=0.00..20.00 rows=4 width=4)
                                                                     Filter: ((r_name)::text = 'ASIA'::text)
                           ->  Hash  (cost=294718.76..294718.76 rows=2284376 width=8)
                                 ->  Foreign Scan on orders_fdw  (cost=0.00..294718.76 rows=2284376 width=8)
                     ->  Hash  (cost=32605.64..32605.64 rows=1500032 width=8)
                           ->  Foreign Scan on customer_fdw  (cost=0.00..32605.64 rows=1500032 width=8)

-- filter on orders range is pushed to FDW