This is a reference manual for the Cloud Monitoring Monitoring Query Language. It covers the following topics:

The data model underlying the time series database that the Monitoring Query Language accesses.

The structure and semantics of queries.

A description of each of the operations and functions that a query is built from.

**Data Model**

Cloud Monitoring uses a time series database that contains all the measurements it has ingested about each thing it is monitoring (known as a monitored resource). This describes the logical structure of that database.

The fundamental element is a *time series* whose data consists of observations
of the monitored resource being monitored.

Time series in the database are logically organized into relational *tables*,
each containing time series with a common meaning and structure. The tables are
referenced by queries that return data, generate graphs, and compute alerts.

The database also includes *metadata*, which are slowly changing values
associated with a monitored resource and which are set by user configuration or
by the service that implements the monitored-resource type.

**Time series**

A *time series* is a named sequence of *points*, each being a measured value
and the time to which the value applies. A time series consists of three parts:
a type, which specifies the structure of the time series,
an identifier, which uniquely names the time series,
and a history, which contains the time series data.
Each of these three parts are explained in this section.

A **time series type** specifies the structure of the time series identifier and
the time series history. It consists of two parts:

A

**monitored-resource type**(listed here) that names a particular kind of monitored resource that is monitored, such as a Compute Engine instance (`gce_instance`

) or a cloud SQL database (`cloudsql_database`

). It has a set of label descriptors that uniquely identify an instance of that type of monitored resource.A

**metric type**(listed here) that describes a particular kind of measurement that can be taken on a monitored resource, for example bytes read from disk by a Compute Engine instance is measured by the metric named`compute.googleapis.com/instance/disk/read_bytes_count`

, and the data utilization of a cloud SQL database is measured by the metric named`cloudsql.googleapis.com/database/disk/bytes_used`

. The metric type specifies the type of measurement's value, the units of the measurement, and the kind of time series. It may specify label descriptors that distinguish time series measuring different aspects of the same thing. For example`command`

indicating what command is counted in the`appengine.googleapis.com/memcache/operation_count`

metric.

Note that a monitored resource type and a metric type are described by a
`MonitoredResourceDescriptor`

and a `MetricDescriptor`

, respectively. These
describe the types. They each contain a field named `type`

which contains the
name of that monitored resource or metric type.

A **time series identifier** is the name of the
time series, uniquely identifying it among all time series with the same type.
It consists of a set of values, one for
each of the label descriptors specified in the monitored resource and metric
types that make up the time series type.

The labels from the monitored-resource type uniquely identify the particular instance of the kind of monitored resource from which the measurements in the time series were taken. For example, the

`gce_instance`

monitored resource has labels`project_id`

,`instance_id`

, and`zone`

which uniquely identify a particular Google Compute Engine virtual machine.Each label from the metric type identifies which specific kind of measurement for the given metric is represented in the time series. For example

`status`

indicating the status of the commands counted in the`appengine.googleapis.com/memcache/operation_count`

metric might have value`'HIT'`

for one time series that counts hits and`'MISS'`

for another time series that counts misses.

A **time series history** is a time-ordered sequence of *points*, each
representing a simultaneous measurement of one, or, potentially, several
values (for example, CPU load or temperature and humidity) at some time or
over some time range. A point has two elements:

A point's

**extent**in time consists of an**end time**, which is always present, and a**start time**which may or may not be present. If the start time is not present, the point's extent is a single point in time given by the end time. If the start time is given, it must be before the end time and the point's extent is the time interval starting at the start time and ending at the end time.No two points in a time series can have the same extent. In addition, the extents of the points in a time series are constrained by the time series kind given by the metric type as described below.

A point's

**value**represents a simultaneous measurement of one, or, potentially, several values (for example, CPU load or temperature and humidity) that applies to the time given by the point's extent. The metric type describes each measurement value, giving it a name and a value type for each. If there are multiple measurement values, they are in a particular order and can be reference by their index in that order.A typical time series stored in the time series database has a single value in each point. The name of the metric in the time series type is a URI and the name of the single value is the part of the metric name after the last

`/`

. For example, the metric`appengine.googleapis.com/memcache/operation_count`

has a value column named`operation_count`

.A time series that is the output of a query may have multiple points whose type, name, and order are given by the query.

The metric type may also specify

*units of measurement*for the time series value if it is of type*Int*,*Double*, or*Distribution*. The units are given using a subset of the Unified Code for Units of Measure (UCUM). For example,`ms`

for milliseconds or`By`

for bytes. See Units of Measure for the details.

Each value in a point has a particular **value type**, which
is specified by the metric
type in the time series type. Also each label in the time series
identifier has a value type, given by the label descriptor
in the time series type's monitored resource or metric type. The value types are
as follows.

**Int**: A 64-bit signed integer.**String**: A UTF-8 encoded Unicode string.**Bool**: A boolean value.**Double**: A 64-bit IEEE floating point value.**Distribution**: A complex value containing a histogram and statistics that provide a summary description of a population (set) of*Double*values. The parts of this value are as follows:- A count of the number of values in the population.
- The sum of the values in the population.
- The sum of squared deviation of the values in the population.
- A bucket specification indicating the boundaries between buckets in the histogram. A bucket contains a count of the values that fall between the lower and upper bound of the bucket.
- A histogram giving the number of values that fall into each bucket.

These parts are enough to additionally compute the population mean, variance, standard deviation, and estimates of percentiles.

A point value's type may be any of the above. A time series identifier label
type may only be *String*, *Int*, or *Bool*

In addition to these types, there are two further types that are in the start and end time of a point or are used to describe times and durations in queries.

**Date**: A particular point in time measured as the distance since the Unix epoch. It is a time-zone-independent representation of a point in time. The start and end time of a point are of this type.**Duration**: A length of time. This time does not have a particular unit of measurement (although resolution is to the microsecond level) but takes on a particular unit (e.g. seconds) when converted to an*Int*or*Double*.

The set of values for each type (except *Date* and *Duration*) includes a
value called **no-value** which indicates that there is no
specific value. This is used in two cases:

When no specific value is known, for example when there is an error (such as dividing by 0) that prevents the computation of a value.

No-value will be the value of a label in a time series identifier when the label is required by the time series type but no value is known for it. This may happen in cases where no value is known when the metric is collected or if the time series was generated by a query and the computation generating the label value did not produce a value. Note that no-value is a distinct value and thus distinguishes the time series identifier from any other that has an actual value for the given label.

No-value is distinct from an IEEE NaN and from a string value that is the empty string. It is not possible for any value in a point to be no-value.

The **time series kind** describes the meaning of the
values of the points in a time series and constrains each
point's extents. There are three time series kinds:

**Gauge**: The value of a point in a*Gauge*time series is a measurement taken at the point's end time. A point in a*Gauge*stream does not have a start time so its extent is a single point in time. The value of a point may represent one of the following things:A

*sample*taken of some variable (such as the length of a queue or an amount of memory in use).A

*state*quality that is true at the point's time and will remain true until the time of the next point.A

*summary*of some quantity (mean, max, etc.) that applies to the period between the point and the next earlier point in the time series.

**Delta**: For numeric values (*Int*or*Double*), each point represents the change in some measured value over the point's extent, that is to say between the point's start time (if present), and end time. For a Distribution's value, it has a population of the numeric values that arose during the point's extent. A*Delta*time series kind must have a value type of*Int*,*Double*, or*Distribution*.For a

*Delta*time series, the extents of any two points cannot overlap, so each point represents an independent change in the measured value (numeric) or disjoint population of values (*Distribution*). Ideally, the extent of each point starts immediately after the extent of the next earlier point so the time series is a complete description of the range of time it covers.**Cumulative**: This can be thought of as a*Delta*time series with overlapping extents. The constraint is that, if two points have overlapping extents, they must have the same start time. Thus each point represents a cumulative increase in some measured value over the last point with a common start time.*Cumulative*metrics are a robust way to collect time series from an external source of data:The source is not required to reset counters or accumulators each time a value is collected and can be be easily monitored at multiple periods.

Accumulated counts are not lost if some points are missing; the next point has all the counts since the start time, including those from the missing point. Only temporal resolution is lost.

In queries, however, cumulative time series are not often observed. To make operations on time series returned from queries more straightforward, when a cumulative time series is fetched, it is automatically converted into a delta time series by making each point's extent start at the time of the next earlier point and making its value be the change since that next earlier point. This does not change the information present but makes each point independent of the others. (This can be overridden by

`fetch_cumulative`

.)For a time series whose points have more than one value, each value has a time series kind which can only be

*Gauge*or*Delta*. If any value has*Delta*kind, then the overall metric has*Delta*kind (and thus each point has a start and end time). Otherwise, the metric has*Gauge*kind (and only end time).

### Tables

All time series with the same time series type
(monitored-resource type and metric
type) are logically organized into a relational *table*. The table has
a *table name* which consists of the
monitored-resource type name followed by the metric type name.

A table has one row for each point in each of the time series included in it. The table has the following kinds of columns:

**Time series identifier**columns, One column for each time series identifier label as specified by the monitored resource and metric types. The name of the column is the name of the label (its key) and the type of the column is the value type of the label. If a monitored resource label and a metric label have the same name, the name of the metric label column has`metric.`

prepended to it.A time series is made up of all the rows in a table with the same value for each of the corresponding time series idenfiter columns.

**Time**column or columns, derived from the extent of the points in the time series. There is always one end time column that is accessed by the function`end()`

(we don't actually give the column a name). If the metric is of*Delta*time series kind, then there is a start time column accessed by the function`start()`

. (There is also a start time column for metrics with Cumulative time series kind.) Both columns have values of type*Date*.**Value**columns, one for each value in the value of the points of the time series. Each column has the name and type given of that value and the value columns are in the same order as that given by the metric type. If there is a monitored resource or metric label with the same name as a value name, the value name given by the metric type is prefixed with`value.`

to form the column name.

All the points in one time series have the same value in the time series identifier columns and these columns uniquely identify time series. The time series columns plus the end time column make up the table's primary key, uniquely identifying a row and thus a point.

The above describes a *stored table* consisting of time series that are stored
in the database. A query takes *stored tables* as the initial inputs and
performs successive table operations (filtering, aggregating, joining, etc),
yielding intermediate
*derived* tables as the output from these table operations.

A derived table has the same structure as a stored table with these differences:

The table will still be associated with a monitored-resource type if the transformation that produced it preserved all the monitored resource label columns. Otherwise it is not associated with a monitored-resource type. This is important for metadata (described in the next section).

The table is described by a table type rather than by a monitored-resource type and metric type. The table type is the same as a metric type except that the set of labels includes all the columns of the time series identifier. Depending on the actual derivation of the table, the time series identifier columns may have no relation to the columns specified by any actual monitored-resource type or metric type.

A derived table does not have a name.

### Metadata

A monitored-resource type
can have *metadata* types, each of which associates a
value with every instance of that particular monitored-resource type. Each metadata
type has a name and a value type (which is *String*, *Int*, or *Bool*).

There are two kinds of metadata:

**System metadata**which is created by the service that creates and manages the monitored resource. System metadata has a name of the form`metadata.system_labels.<key>`

, where`<key>`

identifies a specific kind of metadata.**User metadata**which is present when a service allows the user to attach labels to a specific monitored resource. User metadata has a name of the form`metadata.user_labels.<key>`

, where`<key>`

is the key of the label the user has attached to the entity. For example:`metadata.user_labels.my_key`

. The value of user metadata is always of type*String*.

A table (stored or derived) that is associated with a monitored resource can be considered to have additional virtual value columns, one for each metadata type associated with the monitored-resource type. For each row in the table, a metadata column has the value of that metadata at the time of the row's end time column. These additional metadata columns are not actually part of the table, but they can be referenced in query expressions as if they were by giving the name of the metadata in the expressions that operate on a table row.

### Alignment

A time series is *temporally aligned* (or just *aligned*) if the end time of
its points occur only at regular intervals. We say a time series is aligned
with respect to a particular alignment base time and period if every
point in the time series has an end time that is some multiple of the
alignment period before (or after) the alignment base time. For example,
with an alignment base time of 10:03 and an alignment period of 5 minutes,
09:48, 09:53, 09:58, 10:03, 10:08 would all be valid end times for points.

If a table's time series have *Delta* time series kind then the start time of
each point must be earlier than the end time by the duration of the period,
making the duration of every point be of equal length. A table with
*Cumulative* start times cannot be aligned because it is not, in general,
possible to make the start times of points line up between different time
series.

If all the time series that make up a table are aligned with respect to the same alignment time and period, then the table is aligned with respect to that time and period.

When a table is aligned, the points in different time series line up with each other in time. This makes it possible to do operations combining different time series. For example, if we want to get the time series that is the sum of some metric over all of our monitored resources, we need the points in the individual time series to 'line up', that is, have the same alignment. Then the value of points in the resulting time series is the sum of values of the points at the same time in the individual time series.

## Syntax and Semantics

### Lexical Elements

The text of a query is made up of a sequence of *tokens* which are described in
the following grammar with these rules:

- A token is described by one of the all-capitalized non-terminal symbols in the grammar below.
- A token other than
`base_string`

has no white space within it. White space is space, tab, newline, and comments. A comment is any text, not in a`base_string`

starting with`#`

and ending with a newline. - White space between tokens is ignored, other than to separate tokens.
- Two adjacent tokens must be separated by white space if this grammar would
allow them to be recognized as a single token other than
`BARE_NAME`

(which is only recognized in certain contexts).

```
ID : letter { letter_num_under } .
QUOTED_COLUMN : ( 'c' | 'C' ) base_string .
BARE_NAME : ( '/' | letter_num_under ) { letter_num_under | '.' | '/' | '-' } .
NUMBER : digit { digit } [ fraction | '.' ] [ exponent ] | fraction [exponent] .
STRING : [ 'r' | 'R' ] base_string .
DURATION : digit { digit } ( 's' | 'ms' | 'us' | 'm' | 'h' | 'd' | 'w' ) .
DATE : ( 'd' | 'D' ) base_string .
letter_num_under : letter | digit | '_' .
base_string : '\'' any-but-quote '\'' | '"' any-but-quote-quote '"' .
fraction : '.' digit { digit } .
exponent : ( 'e' | 'E' ) [ '-' | '+' ] digit { digit } .
letter - an ASCII letter
digit - an ASCII digit
any-but-quote - any Unicode character except the ASCII control codes or `'`.
any-but-quote-quote - any Unicode character except the ASCII control codes or `"'.
```

Identifiers (`ID`

) are used to name the builtin table operations and functions
that are part of the Monitoring Query Language and to name columns and metadata
in expressions. The syntax distinguishes between a place that an `ID`

can be a
table operation or function name and a place that an `ID`

can be a column name,
so there are no "reserved" identifiers that can't be used as column names. A
`QUOTED_COLUMN`

is used to give the name of a column that will not parse as an
identifier. Example: `c'total cpu'`

The `NUMBER`

, `STRING`

, `DURATION`

, and `DATE`

tokens identify literal values.
A `NUMBER`

can be followed by a `unit`

which gives the
units of measure of that literal value as a `STRING`

.
A `STRING`

may contain Unicode characters. If it is not prefixed by `r`

or
`R`

, the normal escape sequences will be recognized. The suffix of a `DURATION`

indicates how a time duration is being denominated: seconds, milliseconds,
microseconds, minutes, hours, days, or weeks. The `base_string`

in a date
contains a date in the form `2010/06/23-19:32:15-07:00`

, where the first `-`

can
be a space and the timezone (`-07:00`

) can be dropped (as can the seconds,
minutes, or hours).

The remaining tokens are punctuation and operator tokens that appear in quotes
in the grammar that follows (e.g. `'^'`

or `'<='`

).
These tokens are `^`

, `<=`

, `<`

, `==`

, `=`

`=~`

, `>=`

,
`>`

, `||`

, `|`

, `_`

, `-`

, `,`

,
`;`

, `::`

, `:`

, `!=`

, `<>`

, `!~`

,
`!`

, `//`

,
`/`

, `.`

, `(`

, `)`

, `[`

, `]`

,
`{`

, `}`

, `*`

, `&&`

, `%`

, `+`

.

### Query Structure

A query is made up of a sequence of table operations (`table_op`

),
joined together by pipe operators (`|`

). Each table operation
takes tables as inputs and produces tables as
output. The tables output by one table operation are piped into the next
table operation which consumes them to produce its own table output.

```
query : table_op { '|' table_op } .
table_op : basic_table_op | grouped_table_op | shortcut_table_op .
basic_table_op : ID [ arg { ',' arg } ] .
arg : table_name | expr | map .
grouped_table_op: '{' query { ';' query } '}' .
```

There are three kinds of table operations
(`table_op`

):

A

`basic_table_op`

starts with an`ID`

that names the kind of operation to be done (as described here). This is followed by arguments (`arg`

) which provide details about what the table operation will do. Each kind of`basic_table_op`

takes zero, one, or many tables as input and produces one table as output.A

`grouped_table_op`

consists of an ordered list of queries. Each of the queries produces one table and the result of the`grouped_table_op`

is an ordered list of these tables. Each of the queries takes as input the same zero or more input tables that are the input to the`grouped_table_op`

.A

`shortcut_table_op`

is a shortcut notation (described here) for a`basic_table_op`

.

The tables output by one `table_op`

are passed by the pipe operator (`|`

) as
input to the next `table_op`

. The following are the rules of passing tables
that are output by one table operation to the left of a pipe operator (called
the producer) to a table operation to the right of the pipe operator (called
the consumer):

A table operation that takes no table input cannot be a consumer.

For a producer that outputs a single table and a consumer that takes a single table, the producer output table is an input to the consumer.

For a producer that outputs multiple tables and a consumer that takes a single table, the consumer is applied separately to each input table and the output of the consumer table operation is one table for each input table.

For a producer that outputs multiple tables and a consumer that takes multiple tables, all the produced tables are input to the consumer.

For a producer that produces a single table and a consumer that is a

`grouped_table_op`

, the single table is the input to the first table operation of each`query`

in the`grouped_table_op`

.It is not valid for a

`grouped_table_op`

to be a consumer for a producer that produces multiple tables.The last

`table_op`

in each`query`

in a`grouped_table_op`

must produce only one table.

The table operation's 'arg' elements provide information to the table operation
about how it should process its input tables into an output table.
An `arg`

can be one of three things:

A table name (

`table_name`

), which names a table or is part of the name of a table that is to be fetched from the Cloud Monitoring database.An expression (

`expr`

), which is a formula for computing a value. This can be a literal value that is known statically or it can be a value computed from the column values of one or more rows from the input table or tables of the table operation.A map (

`map`

), which describes how to compute the columns in the output table of a table operation. A`map`

contains one or more`expr`

that compute the values of the columns.

### Table Names

A `table_name`

names a monitored-resource type, a
metric type, a group, or a table. These are used in
table operations that fetch tables from the time-series database for further
processing.

```
table_name : name { '::' name } .
name : string | BARE_NAME | ID .
```

A single `name`

refers to a monitored-resource type or a metric type, for example
the monitored-resource type
`gce_instance`

or `aws_dynamodb_table`

or the metric type
`loadbalancing.googleapis.com/http/backend_latencies`

.

A monitored-resource type can also be named using a group name or
by a monitored-resource type
name followed by `::`

and a group name. The former can be used when
the group specifies a single monitored-resource type and the latter is used when the
group does not.

A stored table is given by a monitored-resource type name followed by `::`

and a
metric type name. For example
`gce_instance :: loadbalancing.googleapis.com/http/backend_latencies`

.

### Expressions

An expression (`expr`

) is a formula for computing a value. It is used as an
argument to a table operation and helps describe the transformation
that the table operation will perform on its input table or tables. An `expr`

can be a literal expression or it can be a dynamic expression.

If an `expr`

is literal, it is composed only of literal values and simple
function calls whose arguments are literal values. The value of such an
expression is determined before the query is applied to any tables.

If an `expr`

is dynamic it can contain references to table columns
and is used to compute a value from one or more rows from the input table.
There are three kinds of dynamic expressions:

*Value*expression A value expression produces a value for each input table row that it is applied to. It may contain references to table columns and, when evaluated for one input row, those references evaluate to the corresponding column values in the row.*Aggregating*expression An aggregating expression produces a value for a set of input table rows. It can be decomposed into three parts:One or more value expressions that are applied individually to each input row to produce a value for each row. These value expressions are arguments to aggregation functions.

One or more aggregation functions which take a collection of input values produced by the value expression(s) and reduce them to a single resulting value.

An outer expression over the aggregation functions that take the values that result from the aggregation functions and produce the value of the expression as a whole.

For example in the aggregating expression

`sum(if(status >= 500, val(), 0)) / sum(val())`

the parts are as follows:The value expressions are

`if(status >= 500, val(), 0)`

and`val()`

. These will be applied to each input row to create two collections of values.The aggregators are the two

`sum`

function calls, each taking as input the collections of values produced by the value expression that is its argument.The outer expression is the division operator (

`/`

) which will be applied to the final output of each of the`sum`

aggregation functions to produce the value of the overall expression.

*Aligning*expression; An aligning expression consists of a single call on an aligning function. The aligning function produces an output value from an input time series and is used by the`align`

to produce an aligned table.

Each expression is composed of `opnd`

elements (defined below))
connected by operators.

```
expr : term { infix_op term } .
term : { prefix_op } opnd .
infix_op : '&&' | '||' | '^'
| '==' | '=' | '!=' | '<>' | '<' | '>' | '<=' | '>=' | '=~' | '!~'
| '+' | '-'
| '*' | '/' | '//' | '%' .
prefix_op : '+' | '-' | '!' .
```

The operators behave in the usual way according to precedence. The following table arranges operators in five groups. All the operators in a group have the same precedence, with higher groups binding more tightly. Operators of the same precedence are applied left to right. Each operator corresponds to a function, given in the table, which is applied to its operands.

operator | function | operation |
---|---|---|

`*` `/` `//` `%` |
`mul` `div` `div` `rem` |
Multiplication Division Integer Division Integer Remainder |

`+` `-` |
`add` `sub` |
Addition Subtraction |

`==` `=` `!=` `<>` `<=` `>=` `>` `<` `=~` `!~` |
`eq` `ne` `le` `ge` `gt` `lt` `re_full_match` `! re_full_match` |
Equality comparison Inequality comparison Less than or equal comparison Greater than or equal comparison Greater than comparison Less than comparison Regular expression full match Regular expression not full match |

`&&` |
`and` |
Logical and |

`||` |
`or` |
Logical or |

The prefix operators `+`

, `-`

, and `!`

correspond to the unary functions
`pos`

, `neg`

, and `not`

respectively
and are applied before any infix operator.

Thus `a < b && a + b + c / -d == 5`

is equivalent to
`(a < b) && (((a + b) + (c / (-d))) == 5)`

, which in turn is equivalent to
`and(lt(a, b), eq(add(add(a, b), div(c, neg(d))), 5))`

.

The operators operate on operands (`opnd`

).

```
opnd : literal | column_meta_name | '_' | '(' expr ')' | call_chain .
literal : NUMBER [ unit ] | string | DURATION | DATE .
unit : STRING
string : STRING { STRING } .
column_meta_name : id { '.' id } .
id : ID | QUOTED_COLUMN .
```

Each `opnd`

corresponds to a particular way of computing a value.

`literal`

is the value of the given literal token.A NUMBER literal can be followed by a

`unit`

which gives the units of measure of the literal value, for example`33 'By'`

for 33 bytes.A

`string`

is made up of one or more`STRING`

tokens that are concatenated into one string value. Thus`'a-' 'b'`

has the same value as`'a-b'`

.

`column_meta_name`

names a column or a virtual metadata column in the input table and evaluates to the value of that column in the input row the expression is applied to.`_`

represents the default value. This can only be given as an actual argument to an optional formal argument.`'(' expr ')'`

is a parenthesized expression that is just the value of the`expr`

.`call_chain`

is one or more chained function calls:

```
call_chain : [ ID arg_list ] { '.' call } .
arg_list : '(' [ expr { ',' expr } [ ',' ] ] ')' .
call : ID [ arg_list ] .
```

Each `ID`

in a call_chain names a function that is applied to
zero or more arguments. The arguments to a function call can come from the
value columns of the input table, from the result of an earlier `call`

in the
call chain, or from the value of `expr`

in an `arg_list`

.

If the call chain starts with an

`ID`

(and no`.`

before it), then the arguments to the called function are given by the`expr`

in the following`arg_list`

.For example,

`add(error_count, 1)`

applies the function`add`

to two arguments: the`column_meta_name`

`error_count`

and the`literal`

`1`

. This would be equivalent to`error_count + 1`

.If a

`call_chain`

starts with a`'.' call`

, then the value columns of the input table are the first argument to the called function. If the`call`

has an`arg_list`

, then the`arg_list`

provides additional arguments.For example,

`.div`

applied to a table with value columns`num`

and`den`

would be equivalent to`div(num, den)`

or just`num / den`

. The expression`.add(3)`

applied to a table with a single value column`count`

would be equivalent to`add(count, 3)`

or just`count + 3`

The function called by a

`call`

other than the first in a call chain takes as its first argument, the output of the previously called function in the call chain. If the`call`

has an`arg_list`

, then the`arg_list`

provides additional arguments.For example

`.mul(3).div(4)`

applied to a table with a single value column`error_count`

would be equivalent to`div(.mul(3), 4)`

which is equivalent to`div(mul(error_count, 3), 4)`

which is equivalent to`error_count * 3 / 4`

or`(error_count * 3) / 4`

.

Note that the end and start time columns in a table do not have column names.
The value of the time columns are accessed using the `end`

and `start`

functions.

### Maps

A `map`

computes values for columns in an output row and gives them names.
Depending on where the `map`

is used, it will either be a time series identifier
`map`

that computes the time series identifier columns of the output row or a
value `map`

that computes the value columns of the output row.

```
map : [ modifier ] '[' [ maplet { ',' maplet } ] ']' .
modifier : ID .
maplet : [ column_name ':' ] expr .
column_name : ID | QUOTED_COLUMN .
```

Each `expr`

in the `maplet`

computes the value of an output column and the
`column_name`

gives the name of the column. If no `column_name`

is given,
one is constructed from the `expr`

. If the `expr`

is just the name of an
input column, the `column_name`

is the same. If functions are applied,
these are added to the name. For example `sum(error_count / 3)`

would get the
name `error_count_div_sum`

.

The output columns that the `map`

computes (time series identifier or value)
come from the `maplet`

s in the `map`

and from the corresponding kind of columns
(time series identifier or value) in the input table. How this is done depends
on the `modifier`

:

No

`modifier`

The corresponding columns of the output row consist of exactly those columns specified by a`maplet`

in the`map`

. The name of the column either is explicitly given by an`ID`

or`QUOTED_COLUMN`

or is derived from the form of the`expr`

. The value of the column in the output row is the value of the`expr`

.Each

`maplet`

must have a column name (explicit or derived) that is unique among all the columns in the output table.For example, applying

`[ratio: num/den]`

as a value column`map`

to a table with value columns`num`

and`den`

would result in an output table with value column`ratio`

, where the`ratio`

column value is the ratio of the two input colums.Applying

`[zone]`

as a time series identifier`map`

to a table with time series identifier columns`project_id`

,`zone`

, and`instance`

would result in a table with just a`zone`

time series identifier column whose value is the same as the`zone`

input table column.All of the columns of the corresponding kind (time series identifier or value) of the input row are included in the output row. In addition, for each`add`

`maplet`

in the`map`

, there is an additional output column whose name and value are given by the`maplet`

.Each

`maplet`

must have a column name (explicit or derived) that is unique among all the columns in the output table.For example, applying

`add[ratio: num/den]`

as a value`map`

to a table with value columns`num`

and`den`

would result in an output table with value columns`num`

,`den`

, and`ratio`

, where the`ratio`

column value is the ratio of the other two columns.All of the columns of the corresponding kind (time series identifier or value) of the input row whose column name is not the same as that of a`update`

`maplet`

in the`map`

are included in the output row. In addition, for each`maplet`

in the`map`

, there is an additional output column whose name and value are given by the`maplet`

.Each

`maplet`

must have a column name (explicit or derived) that is unique among all the columns in the output table. It may name a column of the corresponding kind in the input that it is replacing.For example, the following is a time series identifier

`map`

:`update[job: re_extract(job, '[^-]*-(.*)', r'\1'), kind: re_extract(job, '([^-]*)-.*', r'\1')]`

When used on a table with time series identifier columns

`user`

,`job`

, and`zone`

would result in an output table with time series identifier column`user`

,`job`

,`zone`

, and`kind`

.Each`drop`

`maplet`

must consist of an`expr`

that is just the name of an input column of the corresponding kind. The output columns consist of all the input columns of the corresponding kind except those that are named in an`expr`

in the`maplet`

.Each

`maplet`

must not have a`column_name`

and the`expr`

must simply name a column of the corresponding kind in the input table.For example, applying

`drop [job, user]`

as a time series identifier`map`

to a table with time series identifier columns`user`

,`job`

, and`zone`

would result in an output table with time series identifier column`zone`

.Each`ignore`

`maplet`

must consist of an`expr`

that is just a column name. If the name is the name of an input column of the corresponding kind, that column does not appear in the output columns. If the`maplet`

column name does not name an input table column of the corresponding kind, that`maplet`

has no effect. Thus, the output columns consist of all the input columns of the corresponding kind except those that are named in the`expr`

in the`maplet`

.Each

`maplet`

must not have a`column_name`

and the`expr`

must simply be a column name, but it does not have to be the name of a column in the input table. If the`maplet`

does not name a column in the input table, it is ignored.For example, applying

`ignore [job, instance]`

as a time series identifier`map`

to a table with time series identifier columns`user`

,`job`

, and`zone`

would result in an output table with time series identifier columns`user`

and`zone`

(with the maplet`instance`

ignored).Each`rename`

`maplet`

must have an explicit`column_name`

and must have an`expr`

that just references a column of the corresponding kind in the input table. The output columns are all the columns of the corresponding kind in the input table but if referenced in a`maplet`

with a new name given by the`column_name`

in the`maplet`

.The

`column_name`

in each`maplet`

must be unique among the column names of the output table.For example, applying

`rename[numerator : num, denominator : den]`

as a value column`map`

to an input table with value columns`num`

,`den`

, and`ratio`

would result in an output table with value columns`numerator`

,`denominator`

, and`ratio`

.

### Units of Measure

Every numeric value (*Int*, *Double*, and *Distribution*) can have a unit of
measure associated with it indicating the unit of measurement used by that
value. Units are represented by strings that follow a subset of the Unified Code for
Units of Measure (UCUM). For example a value
denoting a number of bytes will have unit 'By' and another, denoting a rate of
bytes transferred, unit 'By/s'.

Units attach to the columns of tables produced by table operations and to the value of expressions. They are statically associated with the column or expression in the same way that the type is. Any column or expression with a numeric type can have units associated with it but does not have to.

The units attached to columns in tables come from these sources:

Metric descriptors can specify the units for the value of a metric and these are seen in the documentation that describes metrics (for example, here). The value columns of tables produced by

`fetch`

and`metric`

table operations have the units specified by the metric descriptor.Output table columns that are just a copy of the column from the input table have the same units as the input table column. So, for example, the

`filter`

table operation does not change the units on any columns of its input table and passes them on to the output.The

`union`

table operation combines multiple tables into one, and all the tables must have the same columns. Each value column in an input table must have either no units attached or units that are equivalent to the units, if any, attached to that column in every other input table. If units are given for a column in any of the input tables, that column has those units in the output table. If none of the input tables have units specified for a column, that column has no units in the output.For table operations that contain an

`expr`

that computes an output table column value, the units on the output column have the units attached to that`expr`

as described below.

The units attached to an `expr`

depend on the form of the `expr`

:

Literal values by themselves do not have units. But numeric (

*Int*or*Double*) literals can be given units by following the value with a string specifying the unit. Thus`3 "By"`

is an`expr`

with value 3, whose type is*Int*, and whose unit is bytes (`By`

).Column reference expressions get units from the named column in the input table, if it has units.

Functions and operators derive the unit of measurement for their output values from the unit of their input values. So, if

`amount`

has unit`By`

and`time`

has unit`s`

, then`amount / time`

has unit`By/s`

. Functions that take two numeric arguments typically require both arguments to have units or neither argument to have units. The documentation for each function describes the treatment of units of measurement by that function.Many functions have a requirement about unit agreement. For example

`add`

requires both of its operands, if they have units, to have the same unit. These requirements are described in the documentation for each function.The functions

`scale`

and`cast_units`

have functionality specific to units.The

`scale`

function will multiply a value with one unit by a scale factor that converts it to a value with a different unit. So for`expr`

`ev`

with unit "KiBy" (kibi-bytes),`scale(ev, "By")`

will result in multiplying`ev`

by 1024 and giving the result unit`By`

. It is equivalent to`ev * 1024 'By/KiBy'`

.The

`cast_units`

function returns its argument with a given unit regardless of the argument's original unit, if any. So`cast_units(ev, 'By/s')`

results in the value of`ev`

, unchanged but with the unit`By/s`

.

The subset of UCUM units supported by MQL is given by string values that follow this grammar:

```
digit : '0' | '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9'
exponent : [ '+' | '-' ] { digit }
simple_unit : [ PREFIX_SYMBOL ] ATOM_SYMBOL
annotatable : '10^' exponent | simple_unit
component : annotatable [ annotation ] | '1'
annotation : “{” ANNOTATION-STRING “}” | annotatable | annotation
unit : component { '.' component } { '/' component }
```

A `simple_unit`

specifies a unit given by an `ATOM_SYMBOL`

optionally prefixed
by a scaling factor given by a `PREFIX_SYMBOL`

An `ATOM_SYMBOL`

gives a basic unit of measure:

text | meaning |
---|---|

s | second |

min | minute (60 seconds) |

h | hour (60 minutes) |

d | day (24 hours) |

wk | week (7 days) |

bit | bit |

By | byte (8 bits) |

% | 10^-2 (dimensionless ratio scaled to %) |

m | meter |

g | gram |

K | kelvin |

C | coulomb |

Hz | hertz (1/s) |

J | joule (kg.m.m/s/s) |

W | watt (kg.m.m/s/s/s) (J/s) |

A | amp (C/s) |

V | volt (kg.m.m/s/s/C) (J/C) |

A `PREFIX_SYMBOL`

gives a scale factor for the basic unit it precedes:

text | meaning | scale |
---|---|---|

k | kilo | 10^3 |

M | mega | 10^6 |

G | giga | 10^9 |

T | tera | 10^12 |

P | peta | 10^15 |

E | exa | 10^18 |

Z | zetta | 10^21 |

Y | yotta | 10^24 |

m | milli | 10^-3 |

u | micro | 10^-6 |

n | nano | 10^-9 |

p | pico | 10^-12 |

f | femto | 10^-15 |

a | atto | 10^-18 |

z | zepto | 10^-21 |

y | yocto | 10^-24 |

Ki | kibi | 2^10 |

Mi | mebi | 2^20 |

Gi | gibi | 2^30 |

Ti | tebi | 2^40 |

Pi | pebi | 2^50 |

A dimensionless unit can be given as `1`

or as a power of 10 (`10^ exponent`

such as `10^2`

). The unit `1`

is the unit given to most counter metrics. This
also supports the dimensionless ratio scaled to percent `%`

. So `10^-2`

and
`%`

are the same units. To put it another way, adding 3 to a percentage is
the same as adding .03 to the corresponding ratio. The `exponent`

is limited to
the range of -128 to 127.

An `annotation`

is a comment that may be attached to an `annotatable`

(`simple_unit`

or power of 10) and does not change the meaning of the unit. An
annotation not attached to a unit is treated as if it was attached to the unit
`1`

. Thus `{queries}/s`

is equivalent to `1/s`

, with the `1`

unit decorated
with `{queries}`

.

A unit string can be made up of multiple `component`

strings, connected by `.`

or `/`

. The `.`

connector indicates multiplication of the units and the `/`

connector, division. The multiplication and division are applied left to
right. The subset of UCUM units that MQL supports requires all division
connectors to come after multiplication connectors. This avoids the problem of
writing the units of acceleration as `m/s.s`

when `m/s/s`

is what is wanted.
Note that in UCUM units, `m/s.s`

is the same as `m.s/s`

or just `m`

.

Two unit strings are *equivalent* if they have the same *dimension* and
*scale*, regardless of annotations. The dimension and scale are determined in
the conventional way:

Each

`component`

is either dimensionless or has a dimension that is some combination of*time*,*length*,*data*,*mass*, or*charge*. For example both`bit`

and`By`

have dimension*data*. The dimensions of a unit string are found by converting each annotatable to its dimension, multiplying and dividing these as given by the unit string, and canceling dimensions that appear in the numerator and denominator. Thus`b.h/s`

(bit-hour per second) has dimension*data*times*time*divided by*time*, and the*time*dimension cancels to leave dimension*data*.Each annotatable has a scale relative to the basic units of its dimension. For example

`h`

(hour) has dimension*time*with basic unit`s`

and a scale factor of 3600 (every hour is 3600 seconds). The scale factor of a unit string is the combination of the scale factors of each`component`

combined by multiplication and division.

Numeric literals can be given units by following the value with the string for
the desired unit of measurement. So `3 "m/s"`

is the value `3`

with unit `m/s`

and `10.8 "km/h"`

represents the same speed as the value `10.8`

with unit
`km/h`

.

A value with one unit can be scaled to have a different unit with the same
dimension using the `scale`

function. For example, `MiBy`

and
`By`

have the dimension *data* with scale factor 8*1024 and 8 respectively
(relative to the base unit of dimension *data*, which is `bit`

). A value `x`

having unit `MiBy`

can be scaled to a value having unit `By`

by the
expression `scale(x, "By")`

. This multiplies `x`

by 1024 and results in a
value with unit `By`

. It is equivalent to the expression `x * 1024 "By/MiBy"`

,
`size * 1024 "By/MiBy"`

and the unit of the resulting expression is
`MiBy.By/MiBy`

or just `By`

.

The `scale`

function checks that the unit requested has
the same dimension as the unit of the value being scaled.

If `size`

is a column whose value has
unit "KiBy", then the expression `scale(size, "By")`

is the same as
`size * 1024 "By/KiBy"`

and the unit of the resulting expression is
`MiBy.By/MiBy`

or just `By`

.

There are a limited number of cases where MQL will automatically adjust or supply units for a value.

For a function

*f*that require two arguments with equivalent units (`add`

,`sub`

, any of the numeric comparison operators,`if`

, and`or_else`

), one of the arguments may be a call on the`scale`

function without the second unit argument. If the unit of the other argument to*f*has the same dimension as the unit of the argument to the`scale`

function, then the`scale`

function's second argument will be automatically set to the units of the other argument to*f*. This causes the units of two arguments to*f*to be equivalent and*f*will be able to operate.For example, The

`+`

operator requires its arguments to have equivalent units because it makes no sense to add two numbers with different units. If`cache_size`

has unit`By`

and`heap_size`

has unit`MiBy`

, then the expression`scale(cache_size) + heap_size`

is equivalent to the expression`scale(cache_size, "MiBy") + heap_size`

For any comparison function, if one argument is a literal with a unit having the same dimension but different scale than the other argument, the literal is scaled to have the same scale.

For example, if 'cache_size' has unit

`By`

, the expression`cache_size < 3 "KiBy"`

is equivalent to the expression`cache_size < 3072 "By"`

. Note that this is not the same as`cache_size < scale(3 "KiBy", "By")`

if`cache_size`

is type*Int*, because`scale`

will convert its result to type*Double*which might reduce the precision of the comparison. The integer scaling in this case takes into account proper rounding and handling of overflow for the particular comparison done.For either argument of

`mul`

or the divisor of`div`

, a literal without a unit will be given unit '1'. This takes into account scaling operations that are*not*intended to change units (for example, asking what if the rate were double what it is). To change units, it is best to use`scale`

, which will automatically select the right scale factor for the conversion.

Unit errors are treated as warnings when evaluating a query, so the query will still produce results. When defining an alert, unit errors are are treated as real errors and will prevent the alert from being defined.

It is important to realize that *Duration* and *Date* are NOT numeric types and
do not have units. The *Duration* value `60s`

is a non-numeric length of time,
exactly the same length of time as `1m`

or `60000ms`

. The expression
`60s`

== `60000ms`

is valid and true.

A numeric value with unit of time is different. The numbers `3 'min'`

and `180 's'`

are two different numeric values (3 and 180) with different units. Without
scaling, it is not valid to compare them.

The `scale`

function will convert *Duration* and *Date* values to *Double*
values with units. For example `scale(60s, "min")`

, `scale(1m, "min")`

, and
`scale(60000ms, "min")`

will all return the double value `1.0`

with unit `min`

.

### Table Operation Shortcuts

A shortcut is a simplified way of specifying a basic table operation.

```
shortcut_table_op : shortcut { ',' arg } .
shortcut : table_name | '(' expr ')' | map | DURATION .
```

There are a number of forms of shortcut table operations, each of which designates a kind of basic table operation:

A function promotion shortcut looks like a normal table operation, but the table operation starts with an

`ID`

that names a function instead of a table operation and the`arg`

elements that follow (which are all`expr`

form) are the arguments to the function.The function is

*promoted*by providing a table operation that the function becomes an argument for. The value column or columns of the input table become the first arguments to the function, as if it had been preceded by a`.`

operator. The specific promotions are as follows:An ordinary function becomes the argument of a

`value`

table operation, computing the single value column of its output table.For example,

`| add 3`

is a shortcut for`value [.add(3)]`

and`| div`

is a shortcut for`| value [.div]`

.An aggregating function becomes the second argument of a

`group_by`

table operation whose first argument is the empty`map`

(`[ ]`

). Thus the function computes the single value column of an output table with no time series identifier columns (a table with a single time series).For example

`| min`

is a shortcut for`| group_by [], [.min]`

.An aligning function becomes the argument to an

`align`

table operation, thus performing its designated kind of alignment on the time-series of the input table.For example,

`| delta 10m`

is a shortcut for the table operation`| align [.delta(10m)]`

.

A naming shortcut starts with a

`table_name`

which is used as the argument to`resource`

,`metric`

, or`fetch`

table operation, depending on what kind of thing the`table_name`

names.For example,

`| gce_instance`

is a shortcut for the table operation`| resource gce_instance`

and`| gce_instance :: compute/instance/cpu/usage_time`

is shortcut for`| fetch gce_instance :: compute/instance/cpu/usage_time`

.A filtering shortcut consists of a parenthesized

`expr`

which becomes the predicate in a`filter`

table operation.For example,

`| (job == 'search')`

is a shortcut for`| filter job == 'search'`

.A grouping shortcut starts with a

`map`

which becomes the first argument to a`group_by`

table operation. It may be followed by an`arg`

that is a`map`

that describes the aggregation that computes the value columns of the output table.For example,

`| [zone]`

is a shortcut for`| group_by [zone]`

,A windowing shortcut starts with a

`DURATION`

which becomes the first argument to a`group_by`

table operation. It must be followed by an`arg`

that is a`map`

that describes the aggregation that computes the value columns of the output table.For example,,

`| 10m, [.sum]`

is a shortcut for`| group_by 10m, [.sum]`

A duration shortcut starts with a

`DURATION`

with no following`arg`

. It becomes a`for`

table operation, giving the overall extent in time of the query operation.For example,

`| 10m`

is a shortcut for`| for 10m`

.

### Table Operation and Function Descriptions

Each Monitoring Query Language table operation and function description starts with a documentation signature indicating the table inputs (for table operations) and the types of arguments that can be given for the table operation or function. This section describes the form of these signatures.

Note that these signatures are NOT part of the Monitoring Query Language itself. They are used to describe the Monitoring Query Language.

A table operation signature optionally starts with a type that describes the
input table(s) to the table operations followed by the name of the table
operation followed by an argument list describing the valid arguments to the
table operation. For example the signature of the `pick`

table operation:

*Table* `| pick`

*lit-Int*`,`

*[ TSIDSel ]*`,`

*[ Windowed(Num) ]*

This table operation takes a `Table`

as input (the most common case), and has 3
potential arguments, described by *lit-Int*, *[ TSIDSel ]*, and *[
Windowed(Num) ]*.

The input table and `|`

are optional and if not given the table operation does
not take an input table. The input table specification is one of the following:

*Table*The input to the table operation is a single table.*Table++*The table operation takes two or more tables as input.*Resource*The table operation takes a collection of tables specified by a monitored-resource type (all tables containing time series whose type includes a particular monitored-resource type).*ResourceOrTable*Either*Table*or*Resource*is allowed as input.

Each argument descriptor in the argument list that follows the name of the table operation has the following parts:

It may be enclosed in

`[`

`]`

, in which case it is optional and the actual argument can be given as`_`

or omitted if the actual argument is positioned after all explicitly given arguments.It may have a

`lit-`

prefix that indicates the argument value must be a constant value known before we evaluate the query.It always has the name of a value type or a class of types (described below) that describes the allowed type of the actual argument.

It may have a suffix giving a time series kind which constrains the time series kind of the input value.

The argument descriptor type name may be one of the actual types described
here: *Bool*, *Int*, *Double*, *Distribution*, *String*,
*Duration*,
or *Date*. In that case the actual argument must be an expression of the same
type.

The following indicate that the actual argument must be a
`table_name`

that
names a metric, monitored resource, or table, respectivly:

*MetricName**ResourceName**TableName*

An argument descriptor may name a category that indicates the actual argument may be an expression of one of varisous types:

*Num*Either an*Int*or*Double*.*Summable*Types of values that can be summed:*Int*,*Double*, or*Distribution*.*Comparable*: Types of values that can be compared:*Int*,*Double*,*String*,*Bool*,*Duration*,*Date*.*ColumnValue*: Types that are a valid column values:*Int*,*Double*,*String*,*Bool*, or*Distribution*.*Windowed(Num)*A*Num*, potentially annotated by`within`

,`ago`

, or`bottom`

functions.*WindowDuration*A*Duration*, potentially annotated by`window`

or`sliding`

.*BucketSpecification*A bucket specification for a*Distribution*.

A table operation may require a `map`

argument specifying the output
row time series identifier columns or value columns. This is indicated by one
of the following:

*RowToTSID*A map describing the time series identifier columns of the output table.*TSIDSel*A map naming time series identifier columns to be retained. Each`maplet`

in the`map`

must consist only of an`expr`

that names a column (`ID`

or`column_name`

). For example,`[zone, name]`

causes the output columns to consist only of the input time series identifier columns`zone`

and`name`

, with all other input columns dropped.*RowToVal*A map describing output table value columns. If a non-map expression is given as an actual argument, it is promoted to be a single-element map with that expression.*RowSetToVal*A map describing output table value columns by aggregation. If a non-map expression is given as an actual argument, it is promoted to be a single-element map with that expression.*DefaultColumns*A map describing default value columns for an`outer_join`

. If a non-map expression is given as an actual argument, it is promoted to be a single-element map with that expression.

A function signature starts with the name of the function followed by a
parenthesized argument list describing the valid arguments to the function
followed by a return type describing the value returned by the function. For
example, the signature of the `fraction_less_than`

function:

`fraction_less_than(`

*Summable*`,`

*lit-Num*`)`

→
*Double*

This function takes two arguments described by *Summable* and *lit-Num* and
returns a value of type *Double*. The argument list has the same elements
described above for table operations. The return type can be a specific
value type, indicating the returned value will be of that type,
or one of the following:

*Num*- If any of the arguments to the function are*Double*, then*Double*, otherwise,*Int*.*ColumnValue*- The same type as the first actual argument to the function.*LastArgType*- The same type as the last actual argument to the function.*Windowed()*- The same type as the*Windowed*actual argument, annotated with the*Windowed*type. (If the*Windowed*actual argument was type*Int*, then the return type is*Windowed(Int)*. (See`within`

,`ago`

, or`bottom`

functions.)

A function argument descriptor or return type may have an indicator controlling the time series kind of the argument or result. These appear as one of the following suffixes to the type:

*.Cumulative*,*.Delta*, or*.Gauge*indicate the actual argument must have the given time series kind.*.CumulativeOK*means that an actual argument can be*Cumulative*.*.FirstArgKind*means, for return types only, the same time series kind as the first argument to the function.

If an argument has no time series kind suffix, the argument must be *Gauge* or
*Delta* time series kind. If a return type has no time series kind suffix, it
will be *Gauge*.

A function signature may also have one or more of the following notes:

*(implicit row input)*This indicates the function takes the whole row as an implicit input. For example, the`hash_tsid`

function produces a hash of the time series identifier columns of its input row, but does not take those column values as explicit arguments.*(temporal only)*This is used on the signature of aggregation functions to indicate the function signature only applies when doing temporal aggregation. (Other signatures for the function apply otherwise.) Note that this includes the case of both temporal aggregation and spatial aggregation are being done in the same table operation.*(sliding temporal only)*This is used on the signature of aggregation functions to indicate the function signature only applies when doing sliding temporal aggregation. (Other signatures for the function apply otherwise.) Note that this includes the case of both sliding temporal aggregation and spatial aggregation are being done in the same table operation.

## Table Operations

This section describes each of the basic table operations in the Monitoring Query Language.

- Fetching
`fetch`

Produces a table from the database.`metric`

Produces the table for a specific metric type from a set of tables.`fetch_cumulative`

Produces a table of*Cumulative*time series from the database.

- Selection
`filter`

Filters rows from an input table by a predicate.`top`

Selects the top time series by a sort-value expression.`bottom`

Selects the bottom time series by a sort-value expression.`top_by`

Selects time series by a sort-value expression in different groups.`bottom_by`

Selects time series by a sort-value expression in different groups.

- Row Modification
`map`

Rewrites the time series identifier and value columns of each row in a table.`value`

Rewrites the value columns of each row in a table.`time_shift`

Shift time series forward in time.

- Time Series Alignment
`align`

Produces an aligned table using an alignment function.

- Aggregation
`group_by`

Aggregates rows by mapped time series identifier and time window.`union_group_by`

Aggregates rows from multiple tables.`unaligned_group_by`

Aggregates rows by mapped time series identifier without alignment.

- Union and Join
`join`

Natural join of multiple tables.`outer_join`

Outer natural join of two tables.`union`

Union of multiple tables.

- Time Horizon and Period
`every`

Specifies the period for aligned table output.`within`

Specifies the time range of the query output.`graph_period`

Specifies the preferred output period for drawing time series graphs.`window`

Specifies the window for alignment operations.

- Alerting
`condition`

Add a boolean condition column to the input table.`absent_for`

Create a condition for the absence of input.

- Miscellaneous
`ident`

Identity table operation: no change to the input table.`ratio`

Computes the ratio of value columns of two aligned input tables.`filter_ratio`

Computes the ratio of two filtered sums of the input value column.`filter_ratio_by`

Computes a grouped ratio of two filtered sums of the input value column.

### Fetching

The output of a `fetch`

table operation is a table retrieved by name
from the Cloud Monitoring time series data base.

The `resource`

table operation's output is the set of all tables
that have the named monitored-resource type in their name. Each `resource`

must eventually be followed by a `metric`

table operation that selects the
single table whose name contains that metric. Prior to the `metric`

table
operation, there may be `filter`

table operations that restrict the rows
included in the resulting tables.

`fetch`

Produces a table from the database.

Signature:
`fetch`

*lit-TableName*

The `fetch`

operation fetches from the time series database the table
whose name is the table name given in the *TableName*
argument.
It is an error if the table name contains an unknown monitored-resource type
or metric type name.

This table will be empty if no metric of the given type was collected from the monitored resource of the given type.

If the metric is *Cumulative*, the time series that make up the table are
effectively converted to *Delta* time series, where each point represents
the change in value since the next-earlier point.

The `fetch`

operation can also fetch the set of all tables that are based on
a particular monitored resource by just giving the name of the monitored resource and not
giving a metric name. Such a `fetch`

operation must be followed by a
`metric`

operation that selects the specific table
containing the data for a specific metric. The only operation that may come
between such a `fetch`

and the subsequent `metric`

is a
`filter`

operation, that filters based on the monitored resource
columns.

This form of `fetch`

is useful if we wish to fetch more than one
metric for a given monitored resource as in this example:

```
fetch gce_instance | filter zone = 'asia-east1-a' |
{ metric compute.googleapis.com/instance/cpu/utilization ;
metric compute.googleapis.com/instance/cpu/reserved_cores
} | join | div
gce_instance | (zone = 'asia-east1-a') |
{ compute.googleapis.com/instance/cpu/utilization ;
compute.googleapis.com/instance/cpu/reserved_cores
} | join | div
```

This is equivalent to

```
{ fetch gce_instance :: compute.googleapis.com/instance/cpu/utilization ;
fetch gce_instance :: compute.googleapis.com/instance/cpu/reserved_cores
} | filter zone = 'asia-east1-a' | join | div
```

`metric`

Produces the table for a specific metric type from a set of tables.

Signature:
*Resource* `| metric`

*lit-MetricName*

The `metric`

table operation takes in a set of tables produced by a
`fetch`

table operation that did not give a metric name.
It selects the one table holding data for the metric given by the
*lit-MetricName* argument and produces that table as its output.
It is an error if there is no metric definition with the given name. It
produces an empty table if there is no input table with data for the given
metric name.

`fetch_cumulative`

Produces a table of *Cumulative* time series from the database.

Signature:
`fetch_cumulative`

*lit-TableName*

The `fetch_cumulative`

table operation is the same as the
`fetch`

table operation except that *Cumulative* metrics are
not automatically converted to *Delta* metrics when fetched.

### Selection

The selection table operations select rows from the input table for inclusion in the output table. The type of the output table is exactly the same as that of the input table.

`filter`

Filters rows from an input table by a predicate.

Signature:
*ResourceOrTable* `| filter`

*Bool*

The `filter`

operation evaluates its argument *Bool* expression for each
row in a single input table or in the collection of tables named by
a `resource`

operation. Exactly those rows in the input table or tables for which this
expression evaluates to true are retained in the output table or tables.

If the input is a collection of tables, only the monitored resource labels (which are common to all the tables) can be referenced in the predicate.

`top`

Selects the top time series by a sort-value expression.

Signature:
*Table* `| top`

*lit-Int*`,`

*[ Windowed(Num) ]*

The `top`

table operation computes a sort value for each time series in its
input table and selects the number of time series given by its *Int*
argument with the largest sort value. The *Windowed* argument espression
computes the sort value.

The *Windowed(Num)* argument is applied to rows in a time series that fall
within a value time window. The default value time window is the same as
the query time window. If the expression is an aggregating expression
(e.g. `.min`

), it is an aggregation over all the rows whose end timestamp is
within the value window. If the expression is a value expression
(e.g. `.val(0)/.val(1)`

), it is applied to the youngest row, if any, within
the value window. If there are no rows within the value window
for a time series, or if the *Windowed(Num)* argument does not produce a
value for a time series, that time series is not considered for inclusion
in the output.

The `within`

function can be used in the *Windowed(Num)*
argument to modify the value window by giving a a starting time, a duration,
and/or an ending time for the window.

Examples:

```
| top 3
```

Select 3 time series with the largest value for the youngest point in the time series.

```
| top 7, .max
```

Select 7 time series with the largest value for the maximum of all the points in the time series within the query window.

```
| top 3, .min.within(-10h, 1h)
```

This selects 3 time series with the largest value of the `min`

reducer
applied to the rows in each time series that fall in a window starting 10
hours ago and lasting for 1 hour.

`bottom`

Selects the bottom time series by a sort-value expression.

Signature:
*Table* `| bottom`

*lit-Int*`,`

*[ Windowed(Num) ]*

The `bottom`

table operation computes a sort value for each time series in
its input table and selects the number of time series given by its *Int*
argument with the smallest sort value. The *Windowed* argument espression
computes the sort value.

The *Windowed(Num)* argument is applied to rows in a time series that fall
within a value time window. The default value time window is the same as
the query time window. If the expression is an aggregating expression
(e.g. `.min`

), it is an aggregation over all the rows whose end timestamp is
within the value window. If the expression is a value expression
(e.g. `.val(0)/.val(1)`

), it is applied to the youngest row, if any, within
the value window. If there are no rows within the value window
for a time series, or if the *Windowed(Num)* argument does not produce a
value for a time series, that time series is not considered for inclusion
in the output.

The `within`

function can be used in the *Windowed(Num)*
argument to modify the value window by giving a a starting time, a duration,
and/or an ending time for the window.

Examples:

```
| bottom 3
```

Select 3 time series with the smallest value for the youngest point in the time series.

```
| bottom 7, .min
```

Select 7 time series with the smallest value for the minimum of all the points in the time series within the query window.

```
| bottom 3, .max.within(10h)
```

This selects 3 time series with the smallest value of the `max`

reducer
applied to the rows in each time series that fall in a window starting 10
hours ago and lasting until now.

`top_by`

Selects time series by a sort-value expression in different groups.

Signature:
*Table* `| top_by`

*TSIDSel*`,`

*lit-Int*`,`

*[ Windowed(Num) ]*

The `top_by`

table operation groups time series together that have the same
time series identifier computed by the *TSIDSel* argument. Within each
group it selects time series by the same method that `top`

does when given
the same *Int* and *Windowed* arguments. For each group, it computes a sort
value for each time series in a group and selects the number of time series
given by its *Int* argument with the largest sort value. The *Windowed*
argument espression computes the sort value.

The *Windowed(Num)* argument is applied to rows in a time series that fall
within a value time window. The default value time window is the same as
the query time window. If the expression is an aggregating expression
(e.g. `.min`

), it is an aggregation over all the rows whose end timestamp is
within the value window. If the expression is a value expression
(e.g. `.val(0)/.val(1)`

), it is applied to the youngest row, if any, within
the value window. If there are no rows within the value window
for a time series, or if the *Windowed(Num)* argument does not produce a
value for a time series, that time series is not considered for inclusion
in the output.

The `within`

function can be used in the *Windowed(Num)*
argument to modify the value window by giving a a starting time, a duration,
and/or an ending time for the window.

Examples:

```
| top_by [zone], 1
```

For each group of time series with the same value of the 'zone' column, this selects the time series with the largest value for the youngest point in the time series.

```
| top_by [project_id], 2, .max
```

For each group of time series with the same value of the 'project_id' column, this this selects the 2 time series with the largest value for the maximum of all the points in the time series within the query window.

```
| top_by [zone], 1, .min.within(-10h, 1h)
```

For each group of time series with the same value of the 'zone' column, this
selects the time series with the largest value of the `min`

reducer applied
to the rows in each time series that fall in a window starting 10 hours ago
and lasting for 1 hour.

`bottom_by`

Selects time series by a sort-value expression in different groups.

Signature:
*Table* `| bottom_by`

*TSIDSel*`,`

*lit-Int*`,`

*[ Windowed(Num) ]*

The `bottom_by`

table operation groups time series together that have the
same time series identifier computed by the *TSIDSel* argument. Within each
group it selects time series by the same method that `bottom`

does when given
the same *Int* and *Windowed* arguments. For each group, it computes a sort
value for each time series in a group and selects the number of time series
given by its *Int* argument with the smallest sort value. The *Windowed*
argument espression computes the sort value.

*Windowed(Num)* argument is applied to rows in a time series that fall
within a value time window. The default value time window is the same as
the query time window. If the expression is an aggregating expression
(e.g. `.min`

), it is an aggregation over all the rows whose end timestamp is
within the value window. If the expression is a value expression
(e.g. `.val(0)/.val(1)`

), it is applied to the youngest row, if any, within
the value window. If there are no rows within the value window
for a time series, or if the *Windowed(Num)* argument does not produce a
value for a time series, that time series is not considered for inclusion
in the output.

`within`

function can be used in the *Windowed(Num)*
argument to modify the value window by giving a a starting time, a duration,
and/or an ending time for the window.

Examples:

```
| bottom_by [zone], 1
```

For each group of time series with the same value of the 'zone' column, this selects the time series with the smallest value for the youngest point in the time series.

```
| bottom_by [project_id], 2, .max
```

For each group of time series with the same value of the 'project_id' column, this this selects the 2 time series with the smallest value for the maximum of all the points in the time series within the query window.

```
| bottom_by [zone], 1, .min.within(1h)
```

For each group of time series with the same value of the 'zone' column, this
selects the time series with the smallest value of the `min`

reducer applied
to the rows in each time series that fall in a window starting 10 hours ago
and lasting for 1 hour.

### Row Modification

`map`

Rewrites the time series identifier and value columns of each row in a table.

Signature:
*Table* `| map`

*[ RowToTSID ]*`,`

*[ RowToVal ]*

For each row in the input *Table* two transformations are applied:

If the

*RowToTSID*map is given, it is applied to the time series identifier columns of that row to produce the time series identifier columns of the corresponding output row. If the*RowToTSID*map is not given (or given as`_`

), then the output time series identifier columns are the same as the input.If the

*RowToVal*map is given, it is applied to the value columns of the input row to produce the value columns of the output row. If the*RowToVal*map is not given, then the output value columns are the same as the input.

It is a dynamic error if rows from two different time series in the input are mapped to the same time series in the output. In this case, the rows derived from one of the input time series are dropped from the output and an error message will be given.

If the *RowToTSID* map contains references to value columns or time columns,
then it is possible that it will split single input time series into
multiple output time series. For this reason, when the *RowToTSID* map
contains references to value columns or time columns, it is only allowed to
apply it to tables whose value columns are *Gauge* or *Delta* time series
kind.

`value`

Rewrites the value columns of each row in a table.

Signature:
*Table* `| value`

*RowToVal*

For each row in the input *Table*, the *RowToVal* map is applied to the
columns of that row to produce the value columns of the corresponding output
row. Each output row has the same time series identifier and time columns
as the input row it was produced from and has the value columns produced by
the *RowToVal* map.

`time_shift`

Shift time series forward in time.

Signature:
*Table* `| time_shift`

*lit-Duration*

Each row in the input table has the amount given by the *Duration* argument
added to its time column or columns. This has the effect of shifting each
time series in the table forward in time.

If the input table is aligned, then the shift amount must be an even multiple of the alignment period, which maintains the input table alignment.

### Time Series Alignment

`align`

Produces an aligned table using an alignment function.

Signature:
*Table* `| align`

*[ Aligner ]*

The `align`

table operation uses the alignment function
given for its *Aligner* argument to
make an aligned time series from each time series in its
input table, producing the times series in its output table.

The alignment base time is the end time of the query window and the alignment period is set by one of the three following things:

An

`every`

table operation that sets the period for this`align`

table operation.The aligner function requires that the alignment period be equal to its window width (see the

`delta`

).An external graphics interface requires a particular alignment period.

The particular method of producing aligned time series is described for
the alignment function given to the *Aligner* argument.

### Aggregation

An aggregation table operation divides the rows of the input table into groups. For each group of input rows it computes a common time series identifier and time columns for the group, aggregate the input rows to create the value output columns, and outputs a single row with the resulting time series identifier, time, and value columns.

There are three kinds of aggregation

*Spatial aggregation*. This form of aggregation computes new time series id columns for each input row and groups all the rows with the same new time series id columns and end time together. This kind of aggregation typically requires aligned input so that rows from different time series will line up in time to be grouped together.*Temporal aggregation*. This form of aggregation computes a set of valid aligned output times and computes a new end time for each row giving it the oldest aligned end time that is no earlier than the row's original end time. Rows with the same time series identifier and end time are grouped together.*Sliding temporal aggregation*. This form of aggregation is similar to temporal aggregation except that a row may be included in more than one group. This computes a set of time windows, each having an later edge at a valid aligned end time and each having the same fixed width. A row is given an end time that is the later edge of each window it falls within and the row is grouped with any other rows having the same time series identifier and new end time. When the windows overlap, a row may be given more than one new end time and thus may be included in more than one group.

It is possible to combine spatial aggregation with one of the two forms of temporal aggregation in one table operation.

An important distinction between sliding and non-sliding temporal
aggregation is that some aggregators (e.g. sum) will produce
values with *Delta* time series kind for non-sliding temporal aggregation
but *Gauge* kind for sliding temporal aggregation. The reason for this is
the time extents for two points in a *Delta* time series cannot overlap,
so the overlapping input windows of slinding temporal aggregation cannot be
represented in the time columns of *Delta* time series output rows.

When a new time series identifier is computed for a row, the new time series identifier is computed by a map argument. The value columns for the output row are computed by a map argument with an aggregating expression computing each value column.

`group_by`

Aggregates rows by mapped time series identifier and time window.

Signature:
*Table* `| group_by`

*RowToTSID*`,`

*[ RowSetToVal ]*

*Table* `| group_by`

*RowToTSID*`,`

*lit-WindowDuration*`,`

*[ RowSetToVal ]*

*Table* `| group_by`

*lit-WindowDuration*`,`

*[ RowSetToVal ]*

The `group_by`

table operation groups rows together by mapping the time
series identifier columns, time columns, or both:

If the

*RowToTSID*argument is given and the*WindowDuration*argument is not, it computes the time series identifier produced by that map argument for each row in the input table and groups together all rows with the same produced time series identifier and end time.In this case

`group_by`

requires an aligned table as input so that different time series have points with the same end time. If the input table is not aligned, then an`align`

table operation will automatically be inserted to provide alignment.If the

*WindowDuration*argument is given and the*RowToTSID*argument is not, a group of rows is produced for each time series identifier and every aligned period output point. The rows in one group are all the rows with the given time series identifier whose end time falls in a window between the output time and the time that is the duration earlier.If the

*Duration*argument has a`sliding`

function call (e.g.`sliding(1h)`

), then the window may be different than the alignment period. Otherwise, the*Duration*argument must be the same as the alignment period. The expression`window()`

represents a duration that is the same as the alignment period. If a non-sliding*Duration*is given explicitly, it forces the period to be the same if no period was given explicitly.If both the

*RowToTSID*and*WindowDuration*arguments are given, a new mapped time series identifier is computed for each row and a group is created for all the rows with the same mapped time series identifier whose end time falls in a window between the output time and the time that is the duration earlier.

An output row is produced for each group with the common time series
identifier of the rows in the group and a timestamp that is the output point
time of the group (*WindowDuration* was given) or the common end time of the
rows in the group (*WindowDuration* was not given). The value columns in
the group are produced by the *RowSetToVal* argument. Each aggregating
expression is applied to the rows in the set and the result is the output
row value column.

Some aggregating expressions (e.g. `sum`

) will produce output
value columns with *Delta* or *Gauge* time series kind, depending on the
kind of aggregation being done. This depends on whether or not sliding or
non-sliding temporal aggregation is being done. For this purpose,
aggregation is treated as temporal aggregation if it combines both temporal
and spatial aggregation.

A `group_by`

table operation always produces aligned output tables. If no
*WindowDuration* argument is given, then the input table must be aligned and
the output table will have the same alignment. If the *WindowDuration*
argument is given, then an output point is only produced at an alignment
time point and the output table is aligned.

Note that if the *RowToTSID* map argument includes value or time columns in
its expressions, it is possible that time series in the input table will be
fractured into multiple time series in the output table.

`union_group_by`

Aggregates rows from multiple tables.

Signature:
*Table++* `| union_group_by`

*RowToTSID*`,`

*[ RowSetToVal ]*

*Table++* `| union_group_by`

*RowToTSID*`,`

*lit-WindowDuration*`,`

*[ RowSetToVal ]*

*Table++* `| union_group_by`

*lit-WindowDuration*`,`

*[ RowSetToVal ]*

The `union_group_by`

function aggregates input rows exactly like the
`group_by`

function except that it takes its input rows from multiple
input tables.

All the input tables input to a `union_group_by`

must have the same columns
(same name, same type, and, for value columns, same time series kind). If
aligned input tables are required by the arguments to 'union_group_by' (no
*WindowDuration* argument given), then all the input tables must be aligned
with the same period.

`unaligned_group_by`

Aggregates rows by mapped time series identifier without alignment.

Signature:
*Table* `| unaligned_group_by`

*TSIDSel*`,`

*[ RowSetToVal ]*

The `unaligned_group_by`

table operation does the same thing as the
`group_by`

table operation, but does not require its input table to be
aligned.

This computes the time series identifier produced by *TSIDSel* for each row
in the input table and groups together all rows with the same resulting time
series identifier and end time. All the rows in the group have the same end
time and should have the same start time. If any two rows in a group have
different start time, issue a dynamic error and arbitrarily choose one of
the rows and remove it from the group.

Produces an output row for each group of the above group of rows. The
output row has the time series identifier produced by *TSIDSel* map argument
and the same end time and (if present) start time as the input rows in the
group. It has value columns produced by the *RowSetToVal* map argument
applied to all the rows in the group.

The `unaligned_group_by`

table operation does not require its input table to
be aligned, which may mean that it is unlikely for there to be multiple rows
in a group to aggregate. It does require that the rows collected into one
output time series (all having the same time series identifier) do not have
end times whose density gives more than one row per second.

### Union and Join

`join`

Natural join of multiple tables.

Signature:
*Table++* `| join`

The `join`

table operation takes two or more input tables and combines the
rows in these table into rows in a single output table by doing a natural
inner join on the time series identifier and end time columns of the input
tables.

Besides being aligned, the input tables must all be aligned with the same
period and must all be of *Delta* or *Gauge* time series kind.

The output table will have the following elements:

One time series identifier column for every unique time series identifier column in any of the input tables. Each column will have the same type as the corresponding column in the input tables. If two tables have time series identifier columns with the same name but different types, that is an error.

An end time column. If any of the input tables is

*Delta*time series kind, the output table will also be*Delta*time series kind and have a start time column.A value column for each input table value columns. The order is the order of the input tables in the

`grouped_table_op`

that produced them. It is an error if two different input tables have value columns with the same name.

The join considers every tuple consisting of one row from each input table. For each such tuple that meets the following conditions, an output row is created:

For each time series identifier column name that appears in any of the input tables that column has the same value for each row in the tuple that has that column.

Every row in the tuple has the same end time.

Each such output row will have the following column values:

Each time series column will have the value for that column as each row in the tuple that has that column.

Each time column will have the same value as the rows in the input tuple.

Each value column will have the same value as the row in the tuple that value column came from.

`outer_join`

Outer natural join of two tables.

Signature:
*Table++* `| outer_join`

*[ DefaultColumns ]*`,`

*[ DefaultColumns ]*

The `outer_join`

table operation takes two input tables and combines the
rows in these table into rows in a single output table by doing a natural
outer join on the time series identifier and end time columns of the input
tables.

One or both of the *DefaultColumns* arguments must be given. Each
corresponds to one input table and when given for a table, that table will
have rows created if it does not have some row that matches a row in the
other table. The *DefaultColumns* specify the value columns of the created
row. If a *DefaultColumns* is given for a table, then the time series
identifier columns in that table must be a subset of the time series of
those of the other table and it can only have *Delta* time series kind if
the other table has *Delta* time series kind.

Besides being aligned, the input tables must all be aligned with the same
period and must all be of *Delta* or *Gauge* time series kind.

As with `join`

the output table will have the following elements:

One time series identifier column for every unique time series identifier column in any of the input tables. Each column will have the same type as the corresponding column in the input tables. If two tables have time series identifier columns with the same name but different types, that is an error.

An end time column. If any of the input tables is

*Delta*time series kind, the output table will also be*Delta*time series kind and have a start time column.A value column for each input table value columns. The order is the order of the input tables in the

`grouped_table_op`

that produced them. It is an error if two different input tables have value columns with the same name.

The join considers every pair consisting of one row from each input table. For each such pair that meets the following conditions, an output row is created:

For each time series identifier column name that appears in either of the input tables that column has the same value for each row in the pair that has that column.

Each row in the pair has the same end time.

Each such output row will have the following column values:

Each time series column will have the value for that column as each row in the pair that has that column.

Each time column will have the same value as the rows in the input pair.

Each value column will have the same value as the row in the pair that value column came from.

In addition to the pairs above, if a row in one table does cannot form a
pair with any row in the other table and the other table has a
*DefaultColumns* given, then a pair is created with the row from the first
table and a default row for the other table. The default row is constructed
as follows:

Each of its time series identifier columns and time columns has the same value as the corresponding column in the first table row.

The default row's value columns are constructed by the

*DefaultColumns*`map`

That`map`

must specify a value for each value column in the default table.

`union`

Union of multiple tables.

Signature:
*Table++* `| union`

The `union`

table operation takes two or more input tables and produces a
single output table containing rows from all the input tables.

The input tables must have the same columns (same name, same type, and, for value columns, same time series kind). The produced output table will have the same columns as the input tables. The output table is aligned only if all input tables are aligned with a common period.

It is a dynamic error if streams from two or more different tables have the same time series identifier. In this case, one of the streams with a duplicate time series identifier is chosen arbitrarily to be included in the output and the remainder are dropped.

### Time Horizon and Period

The period to use when aligning the time series in the table is set by
the `every`

command.

The query will produce all its results as points whose end time falls within
a *query window*. The duration of the query window is set by the `within`

table operation, which can specify any of a starting time, ending time, or
duration.

`every`

Specifies the period for aligned table output.

Signature:
*Table* `| every`

*lit-Duration*

The `every`

table operation requires an input table that is
aligned with an
input period given by the *Duration* argument. This is handled in one of
the following ways:

If the input table is not aligned, then an

`align`

operation is inserted with an appropriate aligner function for the input table. The*Duration*argument to the aligner function is the default value for the given period.If the table is aligned but does not have a specific required period, the query that is input to the

`every`

table operation is adjusted to to produce that period.It is an error if the input table is aligned with a specific period and that period is different from the one specified by the

*Duration*argument.

`within`

Specifies the time range of the query output.

Signature:
*Table* `| within`

*lit-DateOrDuration*`,`

*[ lit-DateOrDuration ]*

The `within`

table operation specifies the time range of the query output.
This is done by specifying one or two out of three of the values: the
oldest (starting) time of the window, the youngest (ending) time of the
window, or the duration of the window.

If either of the two arguments of `within`

is a positive *Duration*, then
that sets the width of the window. At most one of the arguments can be
a positive *Duration*.

If the first argument is a *Date*, then that specifies the starting time.
If the second argument is a *Date*, that specifies the ending time. If both
are *Date* values, the second must be after than the first. A *Date*
argument can be given as a *Date* literal or with a negative *Duration*
literal. In the later case, the time is the specified *Duration* before the
time the query was issued (now).

If only one argument is given, the second argument defaults to the time the
query was issued (now). In this case, the first argument must be a positive
*Duration* or a *Date* that is earlier than the time the query is issued.

`graph_period`

Specifies the preferred output period for drawing time series graphs.

Signature:
*Table* `| graph_period`

*lit-Duration*

The `graph_period`

table operation transforms its input table to make it
suitable for presentation as a graph. Its *Duration* argument indicates
the period between points suitable for the graph.

This operation is automatically inserted in queries that are given to
Metrics Explorer if the user does not explicitly add one to the query. In
either event, Metrics Explorer sets the value of the *Duration* argument to
be appropriate for the actual time window of the chart. Explicitly giving
adding `graph_period`

as part of a query only makes sense if the query is
being given to the API.

The `graph_period`

operation compares its *Duration* argument with the
period of the input table and does one of the following:

If the period of the input table is less than half the

*Duration*argument, then the`graph_period`

operation acts as a temporal reducer whose window and output period are given by the*Duration*argument. Each value column in the input table is aggregated according to its type.For a value column of numeric type, three columns are placed in the output table, each produced by aggregating the input column with the

`min`

,`mean`

, and`max`

aggregators. The output column names are the input column name with, respectively,`.min`

,`.mean`

, and`.max`

appended.For a value column of type

*Bool*, three columns are placed in the output table, each produced by aggregating the input column with the`min`

,`mean`

, and`max`

aggregators. The output column names are the input column name with, respectively,`.all_true`

,`.mean`

, and`.any_true`

append.For a column of type

*Distribution*, a single column with the same name is created using`distribution`

aggregation to combine the populations of all the distribution input values that fall in each graph period window.

If the input table period is more than twice the

*Duration*argument, then for each point in the input table, copies are made for the time points required by the output period.If the input table period is less than twice the

*Duration*argument and more than half the*Duration*argument, the input table is just copied to the output.

Note that if the input table has more than one value column or has a
*String* value column, its behavior is undefined. Metrics Explorer might
only display a single column or give an error if there is no displayable
column.

`window`

Specifies the window for alignment operations.

Signature:
*Table* `| window`

*lit-Duration*

The `window`

table operation requires an input table that is
aligned by an aligner function whose window
*Duration* argument is the same as the *Duration* argument given on
this `window`

table operation. This is handled in one of the following ways:

If the input table is not aligned, then an

`align`

operation is inserted with an appropriate aligner function for the input table. The*Duration*argument to the aligner function is given by this`window`

table operation's*Duration*argument.If the table is aligned but the table operation that aligned it does not have a specific alignment window, the

*Duration*from this`window`

argument is used as the aligner window argument.It is an error if the input table is aligned and the table operation that aligned specifies a window

*Duration*that is different from the Duration argument of this`window`

table operation.

### Alerting

Alerting operations are used to define alert policies. Use these operations only to install alerts, not as part of a query.

Abstractly, these operations provide ways to create queries that result in a table with two value columns: a boolean indicating whether or not the alert should be in a firing state and a value of the same type as the input giving the most recent value of the input.

`condition`

Add a boolean condition column to the input table.

Signature:
*Table* `| condition`

*Bool*

The `condition`

table operation adds a boolean value column to each
input table row to create its output table. The value of this column is
the value of the *Bool* argument applied to the row.

This can be used to create an alerting query. The output table has a a boolean column indicating that the alert condition is satisfied. The alerting facility will use this to determine if and when an alert should fire or stop firing.

The `condition`

operation requires its input table to be aligned and to be
generated by a query with an explicit alignment window. This is supplied
by a window argument to an align operation (e.g. `| align rate(10m)`

) or
by a `window`

table operation.

Examples:

```
fetch gce_instance :: compute.googleapis.com/instance/cpu/usage_time
| window 5m
| condition val() < .5
```

This will produce a table with two value columns. The first column is a
*Bool* column that will be true if the input table `usage_time`

value
column is less than `.5`

. The second column is a copy of the `usage_time`

value column from the input.

`absent_for`

Create a condition for the absence of input.

Signature:
*Table* `| absent_for`

*lit-Duration*

The `absent_for`

table operation generates a table with two value columns,
`active`

and `signal`

. The `active`

column is true when there is data
missing from the table input and false otherwise. This is useful for
creating a condition query to be used to alert on the absence of inputs.

For each input time series, `absent_for`

creates an aligned output time
series with the same time series identifier as the input. The alignment
period is either given by a following `every`

or is the
default period.

The *Duration* argument gives a time limit. The `active`

column for an
output point will be false if there is a point in the input time series that
is within this time limit earlier than the time of the output point. If
there is no such input point, the `active`

column will be true, indicating
an absence of input within the time limit.

If the input table has value columns, the `signal`

column will contain the
value of first value column of the most recent input point
(within the limit or not) in the input time series. If the input table has
no value columns, the `signal`

column in the output point will be an integer
giving the number of minutes since the last input point.

For each output point time, the `absent_for`

table operation will look back
24 hours before that time for an input point. If there is no input point in
the prior 24 hours no point will be output for that time.

Examples:

```
fetch gce_instance :: compute.googleapis.com/instance/cpu/usage_time
| absent_for 8h
```

For each `usage_time`

time series from a virtual machine (`gce_instance`

)
the `absent_for`

will generate an aligned time series whose output points
will have an `active`

column that is true if there is an input point within
the last 24 hours but no points within the last 8 hours (`8h`

). This is a
suitable alerting query.

```
fetch gce_instance :: compute.googleapis.com/instance/cpu/usage_time
| value [] | absent_for 8h
```

This is similar to the previous example, but the `| value []`

removes the
value columns from the input to the `absent_for`

operation, so the `signal`

column is set to the time (in minutes) since the last input point.

### Miscellaneous

`ident`

Identity table operation: no change to the input table.

Signature:
*Table* `| ident`

The `ident`

table operation produces an input table, unchanged.

Example:

```
fetch gce_instance :: compute.googleapis.com/instance/cpu/usage_time |
{ ident ; group_by [zone] } |
join | value [zone_fraction: val(0) / val(1)]
```

For each row in the given table, compute the ratio of its value to the total of that value over all instances in the zone it is in.

`ratio`

Computes the ratio of value columns of two aligned input tables.

Signature:
*Table++* `| ratio`

The `ratio`

table operation takes two aligned input tables, the numerator
table input and the denominator table input, respectively. Both table inputs
should have exactly one value column of a numeric type.

The time series identifier columns of the denominator table must be a subset of the time series identifier columns of hte numerator table. If both tables have the same time series identifier columns (name and type) then a default value of zero will be used for the numerator when calculating ratios.

`filter_ratio`

Computes the ratio of two filtered sums of the input value column.

Signature:
*Table* `| filter_ratio`

*Bool*`,`

*[ Bool ]*

The `filter_ratio`

table operation takes one input table that has exactly
one value column of a numeric type. If the input table is not aligned, then
an `align`

table operation will automatically be inserted to provide
alignment.

The `filter_ratio`

operation aggregates all input rows at a given timestamp,
computes a numerator and denominator sum, and produces a time series with
the ratio of these sums at each timestamp. The first *Bool* argument
controls what goes into the numerator sum and the second *Bool* argument
controls what goes into the denominator sum. The second argument is
optional and defaults to `true`

if not given.

The *Bool* arguments are evaluated for each row and if true the value
column for that row is included in the numerator (first *Bool*) or
denominator (second *Bool*) sum.

`filter_ratio_by`

Computes a grouped ratio of two filtered sums of the input value column.

Signature:
*Table* `| filter_ratio_by`

*RowToTSID*`,`

*Bool*`,`

*[ Bool ]*

The `filter_ratio_by`

table operation takes one input table that has exactly
one value column of a numeric type. If the input table is not aligned, then
an `align`

table operation will automatically be inserted to provide
alignment.

The `filter_ratio_by`

operation groups rows together that have the same time
series identifier computed by the *RowToTSID* argument. For each group it
computes a numerator and denominator sum, and produces a time series with
the ratio of these sums at each timestamp. The first *Bool* argument
controls what goes into the numerator sum and the second *Bool* argument
controls what goes into the denominator sum. The second argument is
optional and defaults to `true`

if not given.

The *Bool* arguments are evaluated for each row and if true the value
column for that row is included in the numerator (first *Bool*) or
denominator (second *Bool*) sum.

One times series is computed for each group, with the time series identifier computed by the RowToTSID argument.

## Functions

This section describes each of the functions that can be used in expressions
(`expr`

) in the Monitoring Query Language.

- Input Row Columns
`val`

A value column's value in the input point (row).`end`

The ending time of the input point (row).`start`

The starting time of the input point (row).`older`

A value from the next-earlier point (row) in a time series.`adjacent_delta`

The change in value between an input point and next-earlier point.`adjacent_rate`

The rate of change between the input and next-earlier points (rows).`hash_tsid`

Return a hash of the time series identifier columns.

- Logical
`not`

The logical negation of a boolean value.`and`

The logical and of two boolean values.`or`

The logical or of two boolean values.`true`

The boolean value true.`false`

The boolean value false.`has`

True if a set argument contains a particular value.`has_value`

True if an argument expression computes a value.`if`

A value conditionally chosen from two values.`or_else`

A value or, if it is not a value, another value.

- Comparison
- Arithmetic
`add`

The sum of two numbers.`sub`

The difference of two numbers.`mul`

The product of two numbers.`div`

The ratio of two numbers.`int_div`

The quotient from the division of two integers.`abs`

Absolute value.`neg`

The negative of a number.`pos`

Identity for numeric inputs.`rem`

The remainder from the division of two integers.

- Math
- String
`concatenate`

String concatenation.`string_to_double`

Convert*String*to*Double*.`string_to_int64`

Convert*String*to*Int*.`ascii_to_lower`

Change ASCII upper case letter characters to lower case.`ascii_to_upper`

Change ASCII lower case letter characters to upper case.`utf8_normalize`

Unicode string suitable for case-folding comparison.

- Regular Expressions
`re_full_match`

True if a regular expression matches the whole of a string value.`re_partial_match`

True if a regular expression matches some part of string value.`re_extract`

Extract values matched by a regular expression in another string.`re_replace`

Replace the first match of a regular expression in another string.`re_global_replace`

Replace all matches of a regular expression in another string.

- Aggregation
`sum`

The sum of a group of numeric values.`distribution`

A distribution from a group of numeric or distribution values.`count`

The count of the number of values in a group of values.`row_count`

The number of input rows encountered.`count_true`

The number of true values in a group of boolean values.`min`

The minimum of a group of numeric values.`max`

The maximum of a group of numeric values.`diameter`

The maximum minus the minimum of a group of numeric values.`mean`

The mean of a group of numeric values.`stddev`

The standard deviation of a group of values.`variance`

The variance of a group of numeric values.`covariance`

The covariance of a group of pairs of values.`median`

The median of a group of numeric or distribution values.`percentile`

A percentile of a group of numeric or distribution values.`fraction_less_than`

The fraction of a group of values less than a fixed value.`fraction_true`

The fraction of a group of boolean values that are true.`any_true`

The disjunction of a group of boolean values.`all_true`

The conjunction of a group of boolean values.`pick_any`

The value of any element of a group of values (chosen arbitrarily).`singleton`

The value of the element of a group of values with only one element.`unique`

The common value of a group of values (which must all be the same).`aggregate`

Default aggregate value from a group of values of any type.`weighted_distribution`

A distribution from a group of weighted values.

- Aligning
`rate`

Compute a rate of change at aligned points in time.`delta`

Compute the change in value at aligned points in time.`any_true_aligner`

Align a*Bool*time series by finding any true value in a window.`count_true_aligner`

Align a*Bool*time series by counting the true values in a window.`delta_gauge`

Compute the change in value at aligned points in time as a*Gauge*time series.`fraction_true_aligner`

Align a*Bool*time series with the fraction of true values in a window.`int_mean_aligner`

Align by finding the mean of*Int*values in a window.`interpolate`

Compute interpolated values at aligned points in time.`mean_aligner`

Align by finding the mean of values in a window.`next_older`

Aligned points in time by moving from an earlier to later time.`next_younger`

Aligned points in time by moving from a later to earlier time.

- Manipulating Units
`scale`

Scale a value to a different unit of measure.`cast_units`

Set the unit of measure of a value.

- Periodic Window
- Distribution
`count_from`

The number of values in a distribution value.`sum_from`

The sum of the values in a distribution value.`mean_from`

The mean of the values in a distribution value.`stddev_from`

The standard deviation of the values in a distribution value.`variance_from`

The variance of the values in a distribution value.`median_from`

The median of the values in a distribution value.`percentile_from`

A percentile of the values in a distribution value.`fraction_less_than_from`

The fraction of values in a distribution that are less than a fixed value.`bounded_percentile_from`

A percentile of the values within a bound in a distribution value.`rebucket`

Distribution value converted to a new bucket specification.

- Bucket Specifier
`powers_of`

A bucket specification with exponentially increasing bucket boundaries.`fixed_width`

A bucket specification with equal-sized buckets.`custom`

A bucket specification from a list of bucket boundaries.`num_buckets`

Sets the number of buckets in a bucket specification.`bounds`

Sets the lower bound of the first bucket and upper bound of the last.`lower`

Sets the lower bound of the first bucket in a bucket specification.

- Miscellaneous
`cast_double`

Convert*Int*value to*Double*.`cast_gauge`

Cast a*Cumulative*or*Delta*time series value to*Gauge*.`within`

Specifies the window of the sort value calculation.

### Input Row Columns

The expressions in a query operate on the columns of an input row. A column is normally accessed by giving its name. The functions in this section provide alternative ways to access columns.

The time columns do not have column names and are accessed by the `start`

and `end`

functions.

The value columns can be accessed by name or by position using the `val`

function.

The `older`

function gives access to a column in the next-earlier row in a
time series.

`val`

A value column's value in the input point (row).

Signature:
*ImplicitRowInput* `val(`

*[ lit-Int ]* `)`

→
*InputType* *(implicit row input)*

The `val`

function provides an alternative to using the column name when
accessing the value columns of an input row. Its *Int*
argument (default value 0) indexes the ordered set of value columns
(starting with 0 for the first value column) and returns the value of
the indexed value column. This is the same value that results from using
the value column name.

It is a static error if the `val`

function indicates an index that is
negative or is the same or larger than or equal to the number of value
columns.

`end`

The ending time of the input point (row).

Signature:
*ImplicitRowInput* `end(`

`)`

→
*Date.Gauge* *(implicit row input)*

The `end`

function returns the Date value in the end time column of the
current input row.

`start`

The starting time of the input point (row).

Signature:
*ImplicitRowInput* `start(`

`)`

→
*Date.Gauge* *(implicit row input)*

The `start`

function returns the Date value in the start time column of the
current input row. If the row does not have a start time (because it
contains only *Gauge* data), start time returns
no-value.

`older`

A value from the next-earlier point (row) in a time series.

Signature:
`older(`

*ColumnValue.CumulativeOK* `)`

→
*FirstArgType.FirstArgKind*

`older(`

*Date* `)`

→ *Date.FirstArgKind*

The argument to `older`

must be a column name or a function that designates
a column value (`val`

, `end`

, `start`

). The value returned is the value of
that column in the row that is next-earlier to the input row in the
same time series. If there is no such earlier row in the same time series,
`older`

returns no-value.

The column referenced may be a value, time, or time series identifier
column. If it is a time series identifier column `older`

will return
the same value as the argument expression would even if there is no
earlier row in the same time series.

`adjacent_delta`

The change in value between an input point and next-earlier point.

Signature:
*ImplicitRowInput* `adjacent_delta(`

`)`

→
*InputType* *(implicit row input)*

The `adjacent_delta`

function operates on tables with a single numeric
(*Int* or *Double*) or Distribution value column.

If applied to a *Gauge* time series, `adjacent_delta`

returns
the difference between the value of the value column in current input row
and the value column in the next-earlier row in the same time series, if
any. If there is no next-earlier row in the same time series,
`adjacent_delta`

returns no-value. The result has *Gauge*
time series kind.

If applied to a *Delta* time series, `adjacent_delta`

returns the value of
the value column, which remains a *Delta* time series kind. Each output
point has the same value, start time, and end time as the input point it was
generated from.

Although *Cumulative* time series are rarely used in queries, if applied to
a *Cumulative* time series, `adjacent_delta`

returns one of two values:

If the input point's start time is before the end time of the next earlier point,

`adjacent_delta`

returns the value of the input point minus the value of the next-earlier point.If the input point's start time is later than the end time of the next-earlier point,

`adjacent_delta`

returns the input points value (effective subtracting a value of 0 at the start time).

The resulting time series has a *Delta* time series kind and each point a
start time that is its original start time or the end time of the next
earlier input point, whichever is later.

`adjacent_rate`

The rate of change between the input and next-earlier points (rows).

Signature:
*ImplicitRowInput* `adjacent_rate(`

`)`

→
*Double.Gauge* *(implicit row input)*

The `adjacent_rate`

function operates on tables with a single numeric
(*Int* or *Double*) or Distribution value column.

If applied to a *Gauge* or *Cumulative* time series, `adjacent_rate`

returns
the rate of change between the value of the value column in current input
row and the value column in the next-earlier row in the same time series, if
any. This is the difference in values divided by the difference in end time
of the two rows. If there is no next-earlier row in the same time series,
`adjacent_rate`

return no-value. The result has *Gauge* time
series kind.

If applied to a *Delta* time series, `adjacent_rate`

returns the value
column of the current input row divided by the difference between the start
time and the end time of that row.

`hash_tsid`

Return a hash of the time series identifier columns.

Signature:
*ImplicitRowInput* `hash_tsid(`

*[ lit-Int ]* `)`

→ *Int* *(implicit row input)*

The `hash_tsid`

function returns a hash of the values in the fields of
the time series identifier of the current input row. If it is given an
argument, that is used as a seed to the hash.

### Logical

`not`

The logical negation of a boolean value.

Signature:
`not(`

*Bool* `)`

→ *Bool*

The `not`

function takes a boolean value and returns true if that argument
is false and returns false if that argument is true. If the input
argument is
no-value, that is the result.

`and`

The logical and of two boolean values.

Signature:
`and(`

*Bool*`,`

*Bool* `)`

→ *Bool*

The `and`

function returns true if both of its inputs are true, and false
otherwise. If either input is
no-value, `and`

always returns no-value.

`or`

The logical or of two boolean values.

Signature:
`or(`

*Bool*`,`

*Bool* `)`

→ *Bool*

The `or`

function returns true if either of its inputs are true, and false
otherwise. If either input is
no-value, `or`

always returns no-value.

`true`

The boolean value true.

Signature:
*ImplicitRowInput* `true(`

`)`

→
*lit-Bool* *(implicit row input)*

This function returns the literal *Bool* value `true`

.

`false`

The boolean value false.

Signature:
*ImplicitRowInput* `false(`

`)`

→
*lit-Bool* *(implicit row input)*

This function returns the literal *Bool* value `false`

.

`has`

True if a set argument contains a particular value.

Signature:
`has(`

*Set*`,`

*lit-ColumnValue* `)`

→ *Bool*

The `has`

function returns true if its first argument set has the second
argument as an element.

`has_value`

True if an argument expression computes a value.

Signature:
`has_value(`

*ColumnValue* `)`

→ *Bool*

The `has_value`

function returns true if its argument evaluates to a value
and returns false if it evaluates to
no-value.

`if`

A value conditionally chosen from two values.

Signature:
`if(`

*Bool*`,`

*ColumnValue.Delta*`,`

*ColumnValue.Delta**(same)* `)`

→
*LastArgType.Delta*

`if(`

*Bool*`,`

*ColumnValue*`,`

*ColumnValue**(same)* `)`

→ *LastArgType*

The `if`

function returns its second or third argument, depending on the
value (`true`

or `false`

) of its first argument.

`if`

evaluates its first *Bool* argument. If it is
no-value,
then no-value is the result. If the first argument is true, then the
second argument is returned and if the first argument is false, then
the third argument is returned.

Either the second or third argument may be no-value, but the result of
`if`

will only be no-value if the *Bool* argument is no-value or if the
argument returned is no-value. The argument that is not selected may be
no-value without the result being no-value.

If the second and third arguments of `if`

are numeric and either argument
has units, then both arguments must have units. If the
arguments have units, they must either be equivalent
or the rules given here must allow one of the
arguments to be scaled before applying `if`

so the units are equivalent.
It is an error if only one argument has units or if both arguments have
units that cannot be made equivalent.

The result of the `if`

has the unit of its second argument, possibly scaled.

`or_else`

A value or, if it is not a value, another value.

Signature:
`or_else(`

*ColumnValue*`,`

*ColumnValue**(same)* `)`

→ *LastArgType*

The `or_else`

function returns the value of its first argument unless it
is no-value, in which case the value of its second argument is
returned.

The `or_else`

function only returns no-value if both its arguments are
no-value.

If the arguments of `or_else`

are numeric and either argument has
units, then both arguments must have units. If the
arguments have units, they must either be equivalent
or the rules given here must allow one of the
arguments to be scaled before applying `or_else`

so the units are equivalent.
It is an error if only one argument has units or if both arguments have
units that cannot be made equivalent.

The result of the `or_else`

has the unit of the first argument, possibly scaled.

### Comparison

The comparison operators compare two values of the same type or two
numeric (*Int* or *Double) values and return a *Bool* value. Unlike most
functions, comparison operators never return
no-value. If an input is
no-value, it is considered to be a specific value that is larger than any
other value.

`eq`

Equal.

Signature:
`eq(`

*Num*`,`

*Num* `)`

→ *Bool*

`eq(`

*Comparable*`,`

*Comparable**(same)* `)`

→ *Bool*

This compares its first *Comparable* argument to the second
*Comparable* argument and returns `true`

if they are the same and `false`

if
they are not the same. If one argument is *Int* and the other *Double*,
the *Int* argument is converted to a *Double* value before comparing.

If either input is no-value, the comparison is done and
a *Bool* argument is returned, `true`

if both values are
no-value and
`false`

otherwise. (This treats no-value as equal to itself.)

For a comparison on numeric arguments, if
either argument has units, then both
arguments must have units and the units must be
equivalent. The result, being type *Bool* will not
have units.
If the arguments to `eq`

have non-equivalent units that have the same dimension,
then one argument may have its unit scaled
automatically to make the units of both arguments be
equivalent.

If the arguments of `eq`

are numeric and either argument has
units, then both arguments must have units. If the
arguments have units, they must either be equivalent
or the rules given here must allow one of the
arguments to be scaled before applying `eq`

so the units are equivalent.
It is an error if only one argument has units or if both arguments have
units that cannot be made equivalent.

The result of 'eq', being type *Bool*, will not have units.

A comparison between the `resource.project_id`

column and a literal string
has special treatment to deal with the difference between project numbers
and project names, as described in
Matching the `resource.project_id`

column.

`ne`

Not equal.

Signature:
`ne(`

*Num*`,`

*Num* `)`

→ *Bool*

`ne(`

*Comparable*`,`

*Comparable**(same)* `)`

→ *Bool*

This compares its first *Comparable* argument to the second
*Comparable* argument and returns `false`

if they are the same and `true`

if
they are not the same. If one argument is *Int* and the other *Double*,
the *Int* argument is converted to a *Double* value before comparing.

If either input is no-value, the comparison is done and
a *Bool* argument is returned, `false`

if both values are
no-value and `false`

otherwise. (This treats no-value as equal to itself.)

If the arguments of `ne`

are numeric and either argument has
units, then both arguments must have units. If the
arguments have units, they must either be equivalent
or the rules given here must allow one of the
arguments to be scaled before applying `ne`

so the units are equivalent.
It is an error if only one argument has units or if both arguments have
units that cannot be made equivalent.

The result of 'ne', being type *Bool*, will not have units.

A comparison between the `resource.project_id`

column and a literal string
has special treatment to deal with the difference between project numbers
and project names, as described in
Matching the `resource.project_id`

column.

`ge`

Greater than or equal.

Signature:
`ge(`

*Num*`,`

*Num* `)`

→ *Bool*

`ge(`

*Comparable*`,`

*Comparable**(same)* `)`

→ *Bool*

This compares its first *Comparable* argument to the second *Comparable*
argument and returns `true`

if the first is greater than or equal to
the second
and `false`

otherwise. If one argument is *Int* and the other *Double*, the
*Int* argument is converted to a *Double* value before comparing.

If either input is no-value, the comparison is done and
a *Bool* argument is returned, `true`

if the first value is
no-value and
`false`

otherwise. (This treats no-value as greater than any other value.)

If the arguments of `ge`

are numeric, then, if either argument has
units, both arguments must have units. If the
arguments have units, then the units must be
equivalent. If the units are not equivalent but have
the same dimension, then one of the arguments **may** be
automatically scaled to have the same units as the other as described
here. It is an error if only one of the arguments has
units or if the arguments have non-equivalent units and no scaling is done.

The result of 'ge', being type *Bool*, will not have units.

`gt`

Greater than.

Signature:
`gt(`

*Num*`,`

*Num* `)`

→ *Bool*

`gt(`

*Comparable*`,`

*Comparable**(same)* `)`

→ *Bool*

This compares its first *Comparable* argument to the second *Comparable*
argument and returns `true`

if the first is greater than the second
and `false`

otherwise. If one argument is *Int* and the other *Double*, the
*Int* argument is converted to a *Double* value before comparing.

If either input is no-value, the comparison is done and
a *Bool* argument is returned, `false`

if the second value is
no-value and
`true`

otherwise. (This treats no-value as greater than any other value.)

If the arguments of `gt`

are numeric and either argument has
units, then both arguments must have units. If the
arguments have units, they must either be equivalent
or the rules given here must allow one of the
arguments to be scaled before applying `gt`

so the units are equivalent.
It is an error if only one argument has units or if both arguments have
units that cannot be made equivalent.

The result of 'gt', being type *Bool*, will not have units.

`le`

Less than or equal.

Signature:
`le(`

*Num*`,`

*Num* `)`

→ *Bool*

`le(`

*Comparable*`,`

*Comparable**(same)* `)`

→ *Bool*

This compares its first *Comparable* argument to the second *Comparable*
argument and returns `true`

if the first is less than or equal to the second
and `false`

otherwise. If one argument is *Int* and the other *Double*, the
*Int* argument is converted to a *Double* value before comparing.

If either input is no-value, the comparison is done and
a *Bool* argument is returned, `true`

if the second value is
no-value and
`false`

otherwise. (This treats no-value as greater than any other value.)

If the arguments of `le`

are numeric and either argument has
units, then both arguments must have units. If the
arguments have units, they must either be equivalent
or the rules given here must allow one of the
arguments to be scaled before applying `le`

so the units are equivalent.
It is an error if only one argument has units or if both arguments have
units that cannot be made equivalent.

The result of 'le', being type *Bool*, will not have units.

`lt`

Less than.

Signature:
`lt(`

*Num*`,`

*Num* `)`

→ *Bool*

`lt(`

*Comparable*`,`

*Comparable**(same)* `)`

→ *Bool*

This compares its first *Comparable* argument to the second
*Comparable* argument and returns `true`

if the first is less than the
second and `false`

otherwise. If one argument is *Int* and the other
*Double*, the *Int* argument is converted to a *Double* value before
comparing.

If either input is no-value, the comparison is done and
a *Bool* argument is returned, `false`

if the first value is
no-value and
`true`

otherwise. (This treats no-value as greater than any other value.)

If the arguments of `lt`

are numeric and either argument has
units, then both arguments must have units. If the
arguments have units, they must either be equivalent
or the rules given here must allow one of the
arguments to be scaled before applying `lt`

so the units are equivalent.
It is an error if only one argument has units or if both arguments have
units that cannot be made equivalent.

The result of 'lt', being type *Bool*, will not have units.

### Arithmetic

Functions implementing the arithmetic operators.

`add`

The sum of two numbers.

Signature:
`add(`

*Num.Delta*`,`

*Num.Delta* `)`

→
*Num.Delta*

`add(`

*Num*`,`

*Num* `)`

→ *Num*

`add(`

*Duration*`,`

*Duration* `)`

→
*Duration*

`add(`

*Date*`,`

*Duration* `)`

→ *Date*

`add(`

*Duration*`,`

*Date* `)`

→ *Date*

The `add`

function on two *Num* arguments returns the sum of its arguments,
as a *Double* value if either input is a *Double* value and as an *Int*
value otherwise. If both inputs are *Delta* time series kind, then the
output is *Delta* time series kind. Otherwise the output is *Gauge* time
series kind.

The `add`

function on two *Duration* arguments returns the duration that is
their sum.

The `add`

function on a *Date* and *Duration* argument returns the Date that
is the *Duration* later than the *Date* argument. If the *Duration* is
negative, the result will be earlier than the input *Date* (goes back in
time).

If the arguments of `add`

are numeric and either argument has
units, then both arguments must have units. If the
arguments have units, they must either be equivalent
or the rules given here must allow one of the
arguments to be scaled before applying `add`

so the units are equivalent.
It is an error if only one argument has units or if both arguments have
units that cannot be made equivalent.

The result of the `add`

has the unit of the first argument, possibly scaled.

`sub`

The difference of two numbers.

Signature:
`sub(`

*Num.Delta*`,`

*Num.Delta* `)`

→
*Num.Delta*

`sub(`

*Num*`,`

*Num* `)`

→ *Num*

`sub(`

*Duration*`,`

*Duration* `)`

→
*Duration*

`sub(`

*Date*`,`

*Duration* `)`

→ *Date*

`sub(`

*Date*`,`

*Date* `)`

→ *Duration*

The `sub`

function on two *Num* arguments returns the first argument minus
the second argument, as a *Double* value if either input is a *Double* value
and as an *Int* otherwise. If both inputs are *Delta* time series kind,
then the output is *Delta* time series kind. Otherwise the output is
*Gauge* time series kind.

The `sub`

function two *Duration* arguments returns the duration that is
their numeric difference.

The `sub`

function on a *Date* and *Duration* argument returns the Date
that is the *Duration* earlier than the *Date* argument. If the *Duration*
argument is negative, the result is later than the *Date* argument.

If the arguments of `sub`

are numeric and either argument has
units, then both arguments must have units. If the
arguments have units, they must either be equivalent
or the rules given here must allow one of the
arguments to be scaled before applying `sub`

so the units are equivalent.
It is an error if only one argument has units or if both arguments have
units that cannot be made equivalent.

The result of the `sub`

has the unit of the first argument, possibly scaled.

`mul`

The product of two numbers.

Signature:
`mul(`

*Num.Delta*`,`

*lit-Num* `)`

→
*Num.Delta*

`mul(`

*lit-Num*`,`

*Num.Delta* `)`

→
*Num.Delta*

`mul(`

*Num*`,`

*Num* `)`

→ *Num*

`mul(`

*Duration*`,`

*Num* `)`

→ *Duration*

`mul(`

*Num*`,`

*Duration* `)`

→ *Duration*

The `mul`

function on two *Num* arguments returns the product of the two
arguments, as a *Double* value if either input is a *Double* value and as an
*Int* value otherwise. If one inputs is *Delta* time series kind and the
other
input is a literal, then the output is *Delta* time series kind. Otherwise
the output is *Gauge* time series kind.

The `mul`

function on a *Num* and *Duration* is the *Duration* multiplied by
the *Num* as a *Duration* type.

If either numeric argument has units, then both
arguments must have units and the units must be
equivalent. The unit of the result, if the arguments
have units, will be the product of the units of the two arguments. The one
exception is multiplication by a literal: the literal may not have a unit of
measure given explicitly, so if the other argument has a unit of measure,
the unit `1`

will be given to the literal, causing the result to have the
units of the other argument.

`div`

The ratio of two numbers.

Signature:
`div(`

*Num.Delta*`,`

*lit-Num* `)`

→
*Double.Delta*

`div(`

*Num*`,`

*Num* `)`

→ *Double*

`div(`

*Duration*`,`

*Num* `)`

→ *Duration*

`div(`

*Duration*`,`

*Duration* `)`

→ *Double*

`div(`

*Date*`,`

*Duration* `)`

→ *Double*

The `div`

function divides its first *Num* argument by its second *Num*
argument, returning the ratio as a *Double* value.

It does not produce a result if the second *Num* argument is 0.

The `div`

function divides its first argument by its second
argument, returning the ratio as an *Double* value. When an argument is a
*Date* or *Duration*, the value is represented as a double value that is
the *Date* or *Duration* in units that represent the full internal precision
of such values. If the result is a Date or Duration, the ratio
is interpreted as a value with the same units, rounded to the nearest
value that a *Date* or *Duration* can represent.

In the case of a *Date* value being divided by a *Duration* value, the
result is the *Double* value that is the number of that *Duration* periods
since the Unix epoch (`d'1970/01/01-00:00:00+00:00'`

). So
`d'2020/06/01-01:20:03' / 1s`

is the number of seconds since
`d'1970/01/01-00:00:00+00:00'`

at `d'2020/06/01-01:20:03'`

.

The `div`

function does not produce a result if the second
argument is 0.

If either numeric argument has units, then both
arguments must have units. The unit of the result, if the arguments
have units, will be the division of the unit of the first argument by the
unit of the second. The one exception is division by a literal: the literal
may not have a unit of measure given explicitly, so if the other argument
has a unit of measure, the unit `1`

will be given to the literal, causing
the result to have the units of the other argument.

`int_div`

The quotient from the division of two integers.

Signature:
`int_div(`

*Int*`,`

*Int* `)`

→ *Int*

`int_div(`

*Duration*`,`

*Int* `)`

→
*Duration*

`int_div(`

*Duration*`,`

*Duration* `)`

→
*Int*

`int_div(`

*Date*`,`

*Duration* `)`

→ *Int*

The `int_div`

function divides its first argument by its second
argument, returning the quotient as an *Int* value. When an argument is a
*Date* or *Duration*, the value is represented as an integer value that is
the *Date* or *Duration* in units that represent the full internal precision
of such values. If the result is a Date or Duration, the numeric quotient
is interpreted as a value with the same units.

In the case of a *Date* value being divided by a *Duration* value, the
result is the *Int* value that is the number of that *Duration* periods
since the Unix epoch (`d'1970/01/01-00:00:00+00:00'`

). So
`d'2020/06/01-01:20:03' / 1s`

is the number of seconds since
`d'1970/01/01-00:00:00+00:00'`

at `d'2020/06/01-01:20:03'`

.

The `int_div`

function does not produce a result if the second
argument is 0.

If either numeric argument has units, then both
arguments must have units. The unit of the result, if the arguments
have units, will be the division of the unit of the first argument by the
unit of the second. The one exception is division by a literal: the literal
may not have a unit of measure given explicitly, so if the other argument
has a unit of measure, the unit `1`

will be given to the literal, causing
the result to have the units of the other argument.

`abs`

Absolute value.

Signature:
`abs(`

*Num* `)`

→ *Num*

The `abs`

function takes a numeric (*Int* or *Double) input and returns a
value of the same type that has the same magnitude as the input and is
non-negative.

The result of `abs`

has the same unit of measure.

`neg`

The negative of a number.

Signature:
`neg(`

*Num* `)`

→ *Num*

`neg(`

*Duration* `)`

→ *Duration*

The `neg`

function returns the negative of its argument.

`pos`

Identity for numeric inputs.

Signature:
`pos(`

*Num* `)`

→ *Num*

`pos(`

*Duration* `)`

→ *Duration*

The `pos`

function returns its one argument

`rem`

The remainder from the division of two integers.

Signature:
`rem(`

*Int*`,`

*Int* `)`

→ *Int*

`rem(`

*Duration*`,`

*Duration* `)`

→
*Duration*

The `rem`

function divides its first *Int* argument by its second *Int*
argument, returning the remainder as a *Int* value.

It does not produce a result if the second *Num* argument is 0.

The unit of measure attached to the result of `Rem`

is the same as the unit, if any, of the first argument.

### Math

Some mathematical functions.

`sqrt`

Square root.

Signature:
`sqrt(`

*Num* `)`

→ *Double*

The `sqrt`

function returns the square root of the *Num* argument as
a *Double* value.

The `sqrt`

does not produce a result if the *Num* argument is less than 0.

The result of `sqrt`

does not have a unit of measure.

`log`

Natural logarithm.

Signature:
`log(`

*Num* `)`

→ *Double*

The `log`

function returns the natural logarithm of the *Num* argument as
a *Double* value.

The `log`

does not produce a result if the *Num* argument is less than or
equal to 0.

The result of `log`

does not have a unit of measure.

`exp`

e raised to a power.

Signature:
`exp(`

*Num* `)`

→ *Double*

The `exp`

returns e (the base of natural logarithms)
raised to the power of the *Num* argument as a *Double* value.

The `exp`

functions returns the Double value infinity on overflow.

The result of `exp`

does not have a unit of measure.

`power`

One number to the power of another.

Signature:
`power(`

*Num*`,`

*Num* `)`

→ *Double*

This returns the value of the first *Num* argument, raised to the power
of the second *Num* argument, represented as a *Double* value. If either
argument is an *Int*, it is converted to a *Double* before the operation.

The result of `power`

does not have a unit of measure.

`int_round`

Nearest integer.

Signature:
`int_round(`

*Double* `)`

→ *Int*

The `int_round`

function takes a *Double* value, rounds it to the nearest
integer value and returns it as an *Int* value. If the input is not a value
or the result cannot be represent as an *Int* value, the result is
no-value.

The result of `int_round`

has the same unit of measure
as its input.

`int_floor`

Lower bound integer.

Signature:
`int_floor(`

*Double* `)`

→ *Int*

The `int_floor`

function takes a *Double* value, rounds it toward minus
infinity to the nearest integer value and returns it as an *Int* value. If
the input is not a value or the result cannot be represent as an *Int*
value, the result is
no-value.

The result of `int_floor`

has the same unit of measure
as its input.

`int_ceil`

Upper bound integer.

Signature:
`int_ceil(`

*Double* `)`

→ *Int*

The `int_ceil`

function takes a *Double* value, rounds it toward infinity to
the nearest integer value and returns it as an *Int* value. If the input
is no-valueor the result cannot be represent as an *Int* value,
the result is no-value.

The result of `int_ceil`

does not have a unit of measure.

### String

Functions processing *String* values.

`concatenate`

String concatenation.

Signature:
`concatenate(`

*String*`,`

*String* `)`

→
*String*

The `concatenate`

function returns the concatenation of its two *String*
arguments.

`string_to_double`

Convert *String* to *Double*.

Signature:
`string_to_double(`

*String* `)`

→ *Double*

The `string_to_double`

function parses its input *String* argument as a
floating point number and returns the result as a *Double* value.
If the string is not a valid floating point value, the result is
no-value.

The result of `string_to_double`

does not have a unit of measure.

`string_to_int64`

Convert *String* to *Int*.

Signature:
`string_to_int64(`

*String* `)`

→ *Int*

The `string_to_int64`

function parses its input *String* argument as an
integer number and returns the result as an *Int* value. If the string is
not a valid integer value or cannot be represented as an *Int* value, the
result is
no-value.

The result of `string_to_int64`

does not have a unit of measure.

`ascii_to_lower`

Change ASCII upper case letter characters to lower case.

Signature:
`ascii_to_lower(`

*String* `)`

→ *String*

The `ascii_to_upper`

function takes a *String* argument and returns a
*String* value that is the same except that each upper-case ASCII letter has
been converted to the corresponding lower-case ASCII letter. All other
characters are left unchanged.

`ascii_to_upper`

Change ASCII lower case letter characters to upper case.

Signature:
`ascii_to_upper(`

*String* `)`

→ *String*

The `ascii_to_upper`

function takes a *String* argument and returns a
*String* value that is the same except that each lower-case ASCII letter has
been converted to the corresponding upper-case ASCII letter. All other
characters are left unchanged.

`utf8_normalize`

Unicode string suitable for case-folding comparison.

Signature:
`utf8_normalize(`

*String* `)`

→ *String*

The `utf8_normalize`

function takes a *String* argument and returns an
*String* value suitable for case-folding comparison of the input value under
the assumption the input is a valid utf8-encoded string.

### Regular Expressions

Functions that do matching, extraction, and modification using RE2 regular expressions.

`re_full_match`

True if a regular expression matches the whole of a string value.

Signature:
`re_full_match(`

*String*`,`

*lit-String* `)`

→
*Bool*

The `re_partial_match`

function takes a string input and a literal string
regular expression and returns `true`

if the whole of the input string is
matched by the regular expression. It returns `false`

otherwise, even if
the input string argument is
no-value.

A regular expression match on the `resource.project_id`

column has special
treatment to deal with the difference between project numbers and project
names, as described in Matching the `resource.project_id`

column.

`re_partial_match`

True if a regular expression matches some part of string value.

Signature:
`re_partial_match(`

*String*`,`

*lit-String* `)`

→ *Bool*

The `re_partial_match`

function takes a string input and a literal string
regular expression and returns `true`

if any part of the input string is
matched by the regular expression. It returns `false`

otherwise, even if
the string argument is
no-value.

`re_extract`

Extract values matched by a regular expression in another string.

Signature:
`re_extract(`

*String*`,`

*[ lit-String ]*`,`

*[ lit-String ]* `)`

→ *String*

The `re_extract`

function takes an input *String* argument and two literal
*String* arguments: a regular expression and a replacement string. The
result is formed by matching the input string to the regular expression and
the substituting capture groups in the expression in the replacement string.
The replacement string with the capture groups substituted is the result.

If the regular expression argument is not given, it defaults to "(.*)", thus including the whole first argument string in one capture group.

If the replacement string argument is not given, it defaults to R"\1", thus making the first replacement group be the output string.

If the input string is no-value, if the regular expression did not match, or the substitution of capture groups did not work, no-value is returned.

`re_replace`

Replace the first match of a regular expression in another string.

Signature:
`re_replace(`

*String*`,`

*lit-String*`,`

*lit-String* `)`

→ *String*

The `re_replace`

function takes an input *String* argument and two literal
*String* arguments: a regular expression and a replacement value. If the
regular expression matches any part of the input string, the returned value
is formed by replacing the first such match in the input string with the
replacement string.

If the input string is no-valueor if there is no match, the input string is the returned value.

`re_global_replace`

Replace all matches of a regular expression in another string.

Signature:
`re_global_replace(`

*String*`,`

*lit-String*`,`

*lit-String* `)`

→ *String*

The `re_global_replace`

function takes an input *String* argument and two
literal *String* arguments: a regular expression and a replacement value.
The result is formed from the input string by replacing each disjoint match
of the regular expression (from left to right) with the replacement string.

If the input string is no-valueor if there is no match, the input string is the returned value.

### Aggregation

An aggregation function combines a set of input values into a final output value. They are used when a number of input rows are grouped together and aggregated into a single output row.

An aggregation function maintains an internal aggregation state. The argument expression to the aggregation function is evaluated once for each of the grouped input rows and the resulting value (if any) is passed to the aggregation function to be accumulated in its internal state. Once this has been done for all rows in the group, the aggregation function produces its output value to be used in creating value columns in the single output row.

For example, `mean(memory_usage)`

applied to a set of rows with a
`memory_usage`

column, evaluates the argument expression,
`memory_usage`

, for each row, and incorporates the resulting value (if
one is produced) in the internal state of the `mean`

aggregation
function (which might be a sum of values and a count of values).
Once all the rows have been processed, the `mean`

reducer produces
a value from its internal state (the sum divided by the count).

Most aggregation functions that operate on numeric or *Distribution*
values give the unit of measure of their input to
the output. The exceptions are:

`count`

and`row_count`

whose output has unit`1`

.`variance`

whose output is the square of input?`covariance`

whose output is the product of the units of the two inputs.`fraction_less_than`

and`fraction_true`

give unit`10^2.%`

to their output.

`sum`

The sum of a group of numeric values.

Signature:
`sum(`

*Num* `)`

→ *Num.Delta*
*(temporal only)*

`sum(`

*Distribution* `)`

→ *Double.Delta*
*(temporal only)*

`sum(`

*Num* `)`

→ *Num.Gauge*
*(sliding temporal only)*

`sum(`

*Distribution* `)`

→ *Double.Gauge*
*(sliding temporal only)*

`sum(`

*Num* `)`

→ *Num.FirstArgKind*

`sum(`

*Distribution* `)`

→ *Double.FirstArgKind*

If the argument expression is numeric (*Int* or *Double), this returns the
sum of the values that are passed to it.

If the argument expression is a *Distribution* value, this returns the sum
of the population values in all the *Distribution* values that are passed to
it.

If, for some input row, the argument expression does not evaluate to a value
or evaluates to a non-finite *Double* value, that input row does not affect
the sum.

For numeric (*Int* or *Double) input, the result is the same type (*Int* or
*Double*) as the input expression. For *Distribution* input values, the
result type is *Double*.

The output has *Delta* time series kind if
non-sliding temporal aggregations
is being done or if only spatial aggregation is being done and the input
time series kind is also *Delta*.

The unit of measure attached to the result of `sum`

is the same as the unit of the input.

`distribution`

A distribution from a group of numeric or distribution values.

Signature:
`distribution(`

*Num*`,`

*lit-BucketSpecification* `)`

→ *Distribution.Delta*
*(temporal only)*

`distribution(`

*Num*`,`

*lit-BucketSpecification* `)`

→ *Distribution.Gauge*

`distribution(`

*Distribution* `)`

→
*Distribution.Delta* *(temporal only)*

`distribution(`

*Distribution* `)`

→
*Distribution.Gauge* *(sliding temporal only)*

`distribution(`

*Distribution* `)`

→
*Distribution.FirstArgKind*

If the first argument is a *Num* value, the input values are collected
into a distribution result whose bucket specification is given by the
*lit-Bucketer* argument.

If the first argument is a *Distribution* value, the distributions are
merged into a distribution result that includes the population of all the
input distributions. The resulting distribution bucket specification is
determined from the input distribution bucket specifications. If the bucket
specifications are all the same, then that bucket specification is used. If
there are different bucket specification, a new merged bucket specification
is used. This merged specification is typically no more accurate than
least-accurate input bucket specification.

If, for some input row, the first argument expression does not evaluate to a
value or evaluates to a non-finite *Double*, that input row does not affect
the percentile.

The unit of measure attached to the result of
`distribution`

is the same as the unit of the input.

`count`

The count of the number of values in a group of values.

Signature:
`count(`

*ColumnValue* `)`

→ *Int.Delta*
*(temporal only)*

`count(`

*ColumnValue* `)`

→ *Int.Gauge*

Returns the count of the number of values that have been passed to it. If
the argument expression does not evaluate to a value for some input row or
evaluates to a non-finite *Double* value, it is not counted.

The output will have *Delta* time series kind when
non-sliding temporal
aggregation is being done.

The unit of measure attached to the result of `count`

is `1`

.

`row_count`

The number of input rows encountered.

Signature:
*ImplicitRowSetInput* `row_count(`

`)`

→
*Int.Delta* *(temporal only)*

*ImplicitRowSetInput* `row_count(`

`)`

→
*Int.Gauge*

The `row_count`

aggregation function returns the count of the number of
rows that this is aggregating over. Unlike `count`

, `row_count`

does not
take an argument and does not care if a value could be calculated from
the row.

The output will have *Delta* time series kind when
non-sliding temporal
aggregation is being done.

The unit of measure attached to the result of `count`

is `1`

.

`count_true`

The number of true values in a group of boolean values.

Signature:
`count_true(`

*Bool* `)`

→ *Int.Delta*
*(temporal only)*

`count_true(`

*Bool* `)`

→ *Int*

The input boolean values are collected and the result is the number of input values that are true.

If, for some input row, the argument expression does not evaluate to a value, that input row does not affect the result.

The output will have *Delta* time series kind when
non-sliding temporal
aggregation is being done.

The unit of measure attached to the result of
`count_true`

is `1`

.

`min`

The minimum of a group of numeric values.

Signature:
`min(`

*Num* `)`

→ *Num*

This collects the numeric values that are passed to it and returns the minimum value. If result type is the same as the input type.

If, for some input row, the argument expression does not evaluate to a value, that input row does not affect the result.

The unit of measure attached to the result of
`min`

is the same as the unit of the input.

`max`

The maximum of a group of numeric values.

Signature:
`max(`

*Num* `)`

→ *Num*

This collects the numeric values that are passed to it and returns the maximum value. If result type is the same as the input type.

If, for some input row, the argument expression does not evaluate to a value, that input row does not affect the result.

The unit of measure attached to the result of
`max`

is the same as the unit of the input.

`diameter`

The maximum minus the minimum of a group of numeric values.

Signature:
`diameter(`

*Num* `)`

→ *Num*

This collects the numeric values that are passed to it and returns the
difference between the maximum of the values and the minimum of the values.
If result type is the same as the input type (*Int* or *Double*).

The unit of measure attached to the result of
`diameter`

is the same as the unit of the input.

`mean`

The mean of a group of numeric values.

Signature:
`mean(`

*Summable* `)`

→ *Double*

If the argument expression is numeric (*Int* or *Double), this returns the
mean of the values that are passed to it.

If the argument expression is of type *Distribution*, this returns the mean
of all the values in all the distributions.

If, for some input row, the argument expression does not evaluate to a value
or evaluates to a non-finite *Double* value, that input row does not affect
the mean.

The unit of measure attached to the result of `mean`

is the same as the unit of the input.

`stddev`

The standard deviation of a group of values.

Signature:
`stddev(`

*Summable* `)`

→ *Double*

If the argument expression is numeric (*Int* or *Double), this returns the
standard deviation of the values that are passed to it.

If the argument expression is a *Distribution* value, this returns the
standard deviation of all the values in all the distributions.

If, for some input row, the argument expression does not evaluate to a value
or evaluates to a non-finite *Double* value, that input row does not affect
the standard deviation.

The unit of measure attached to the result of `stddev`

is the same as the unit of the input.

`variance`

The variance of a group of numeric values.

Signature:
`variance(`

*Summable* `)`

→ *Double*

If the argument expression is numeric (*Int* or *Double), this returns the
variance of the values that are passed to it.

If the argument expression is of type *Distribution*, this returns the
variance of all the values in all the distributions.

If, for some input row, the argument expression does not evaluate to a value
or evaluates to a non-finite *Double* value, that input row does not affect
the variance.

There is no unit of measure attached to the result of
`variance`

function.

`covariance`

The covariance of a group of pairs of values.

Signature:
`covariance(`

*Num*`,`

*Num* `)`

→ *Double*

This returns the covariance of the pairs of numeric (*Int* or *Double)
values that are passed to it.

If, for some input row, either argument expression does not evaluate to a
value or evaluates to a non-finite *Double* value, that input row does not
affect the covariance.

There is no unit of measure attached to the result of
`covariance`

function.

`median`

The median of a group of numeric or distribution values.

Signature:
`median(`

*Summable* `)`

→ *Double*

If the argument expression is numeric (*Int* or *Double), this returns an
estimate of the median of the population of values that are passed to it.
The median is computed by creating a distribution value from the values in
the population with bucket boundaries that are 10% apart, which bounds the
error in the estimate by that amount.

The bucket specification used to accumlate a *Distribution* value from
numeric input to estimate a meidan is
`powers_of(1.05).num_buckets(500).lower(.01)`

. This includes a range of
values from `.01`

to about `4e+8`

. While this handles many use cases, it
might be necessary to use the `scale`

function to adjust the input, for
example from `By`

to `MiBy`

or 'MBy' if the range of number of bytes is
going to be in the gigabyte or terabyte range.

If the argument expression is a *Distribution* value, this returns an
estimate of the median of the merged population of values from all the
distributions. The median is computed by merging all the input
distributions into one distribution and estimating the median. The accuracy
of the median will depend on the bucket boundaries of the input
distributions.

If, for some input row, the argument expression does not evaluate to a value
or evaluates to a non-finite *Double* value, that input row does not affect
the standard deviation.

The unit of measure attached to the result of `median`

is the same as the unit of the input.

`percentile`

A percentile of a group of numeric or distribution values.

Signature:
`percentile(`

*Summable*`,`

*lit-Num* `)`

→
*Double*

The *lit-Num* argument gives a percentile (in the range 0 to 100).

If the first argument expression is numeric (*Int* or *Double*), this
returns an estimate of that percentile of the population of values that are
passed to it. The percentile is computed by creating a distribution value
from the values in the population with bucket boundaries that are 10% apart,
which bounds the error in the estimate by that amount.

The bucket specification used to accumlate a *Distribution* value from
numeric input to estimate a percentile is
`powers_of(1.05).num_buckets(500).lower(.01)`

. This includes a range of
values from `.01`

to about `4e+8`

. While this handles many use cases, it
might be necessary to use the `scale`

function to adjust the input, for
example from `By`

to `MiBy`

or 'MBy' if the range of number of bytes is
going to be in the gigabyte or terabyte range.

If the argument expression is a *Distribution* value, this returns an
estimate of the percentile of the merged population of values from all the
distributions. The percentile is computed by merging all the input
distributions into one distribution and estimating the percentile. The
accuracy of the percentile will depend on the bucket boundaries of the input
distributions.

If, for some input row, the first argument expression does not evaluate to a
value or evaluates to a non-finite *Double*, that input row does not affect
the percentile.

The unit of measure attached to the result of
`percentile`

is the same as the unit of the input.

`fraction_less_than`

The fraction of a group of values less than a fixed value.

Signature:
`fraction_less_than(`

*Summable*`,`

*lit-Num* `)`

→ *Double*

If the first argument is a numeric (*Int* or *Double) value, this returns
the fraction of the collection of values passed to the first argument that
are less than the *lit-Num* argument. In computing this fraction, it
ignores non-finite *Double* values and not-a-value *Int* and *Double*
values.

If the first argument is a *Distribution* value, this combines the
populations of all the Distributions it is passed and makes an estimate of
the fraction of the values in the population of that aggregated distribution
that are less than the value of the *lit-Num* argument.

The unit of measure attached to the result of
`fraction_less_than`

is `10^2.%`

.

`fraction_true`

The fraction of a group of boolean values that are true.

Signature:
`fraction_true(`

*Bool* `)`

→ *Double*

The input boolean values are collected and the result is a *Double* in the
range 0 to 1 that is the fraction of input values that are true.

The unit of measure attached to the result of
`fraction_true`

is `10^2.%`

.

`any_true`

The disjunction of a group of boolean values.

Signature:
`any_true(`

*Bool* `)`

→ *Bool*

The `any_true`

function calculates the value `true`

if all of its input
values are `true`

and returns `false`

otherwise.

`all_true`

The conjunction of a group of boolean values.

Signature:
`all_true(`

*Bool* `)`

→ *Bool*

The `all_true`

function calculates the value `true`

if all its input values
are `true`

and returns `false`

otherwise.

`pick_any`

The value of any element of a group of values (chosen arbitrarily).

Signature:
`pick_any(`

*ColumnValue* `)`

→ *FirstArgType*

This functions returns one of the values given to it, chosen arbitrarily.

The unit of measure attached to the result of
`pick_any`

is the same as the unit of the input, if any.

`singleton`

The value of the element of a group of values with only one element.

Signature:
`singleton(`

*ColumnValue* `)`

→ *FirstArgType*

This function returns its argument expression value as evaluated on a single row. It is an error if its argument expression is evaluated and produces a value for more than one row, even if it evaluates to a previously produced value.

The unit of measure attached to the result of
`singleton`

is the same as the unit of the input.

`unique`

The common value of a group of values (which must all be the same).

Signature:
`unique(`

*Comparable* `)`

→ *FirstArgType*

The `unique`

function returns the value that is the same as every value
that was given to it. If there is no such value (this was given at least
two different values), then it generates an error and returns one of the
values given to it.

The unit of measure attached to the result of `unique`

is the same as the unit of the input.

`aggregate`

Default aggregate value from a group of values of any type.

Signature:
`aggregate(`

*Num* `)`

→ *Num.Delta*
*(temporal only)*

`aggregate(`

*Distribution* `)`

→
*Distribution.Delta* *(temporal only)*

`aggregate(`

*Num* `)`

→ *Num.Gauge*
*(sliding temporal only)*

`aggregate(`

*Distribution* `)`

→
*Distribution.Gauge* *(sliding temporal only)*

`aggregate(`

*Num* `)`

→ *Num.FirstArgKind*

`aggregate(`

*Distribution* `)`

→
*Distribution.FirstArgKind*

`aggregate(`

*Bool* `)`

→ *Bool*

`aggregate(`

*String* `)`

→ *String*

The `aggregate`

function does an aggregation that depends on the type of
the input.

For

*Int*and*Double*input, it is the same as the`sum`

aggregator.For

*Distribution*input, it is the same as the`distribution`

aggregator.For

*Bool*input, it is the same as the`any_true`

aggregator.For

*String*input, it is the same as the`pick_any`

aggregator.

`weighted_distribution`

A distribution from a group of weighted values.

Signature:
`weighted_distribution(`

*Num*`,`

*Int*`,`

*lit-BucketSpecification* `)`

→
*Distribution.Delta* *(temporal only)*

`weighted_distribution(`

*Num*`,`

*Int*`,`

*lit-BucketSpecification* `)`

→
*Distribution.Gauge*

The input values are collected into a distribution result whose bucket
specification is given by *lit-Bucketer* argument. The first argument is
the value to be added to the distribution and the second argument is the
weight of that value. A value `N`

with a weight of `M`

is represented by
`M`

instances of value `N`

in the distribution.

If, for some input row, the first or the second argument expression does not
evaluate to a value or evaluates to a non-finite *Double*, that input row
does not affect the percentile.

The unit of measure attached to the result of
`weighted_distribution`

is the same as the unit of the input.

### Aligning

Aligning functions are use by the `align`

table operation
to produce an aligned table, one whose time
series have points with timestamps at regular intervals.

In addition to its explicit *Duration* argument, an aligner function
takes an input time series and a point in time
and produces an output point for that particular time.

The `interpolate`

alignment function produces a value at a given time by
interpolating a value from two adjacent input points whose timestamps
straddle the output timestamp.

The `next_older`

and `next_younger`

alignment functions produce the value
from the single point in the input time series whose timestamp is next
is just prior to or just after the output timestamp.

The `delta`

, `rate`

, and `delta_gauge`

aligner functions compute their
output based on the change in the value of the input time series over the
time window between the output point end time and the *Duration* argument
earlier. That change in value is computed as follows:

Thus the value of the input time series at any given time can be computed by linear interpolation between the nearest point before and the nearest point after the output time. The change in value over a given window is the difference between the interpolated value at the earlier edge of the window and the later edge.

The amount of change in the window is the sum of the value of all points whose extent is entirely within the window and the pro-rata share of the value of the points whose extent partially overlaps the window.

For a

*Cumulative*time series, interpolation of a value between two adjacent points with the same start time is done by linear interpolation between the two values. Interpolation between two adjacent points with different start times (so the start time of the later point is between the end times of the two points) is handled this way:If the output time is between the earlier point's end time and the later point's start time, the result is the earlier point's value. (No change between the earlier point and the reset time.)

If the output time is between the later points start and end time, then the value is the linear interpolation between zero (at the start time) and the point's value.

For a

*Cumulative*time series, the change in value over a given window is the difference between the interpolated value at the earlier edge of the window and the later edge plus a correction for resets. For each reset time that falls within the window, the value of the point just before that reset time is added to the change value to account for the time series value being reset to 0 at that time.The aggregating aligner functions,

`mean_aligner`

,`int_mean_aligner`

, apply an aggregation function to the input points that fall in a time window whose width is given by the*Duration*argument and whose later edge is the timestamp of the output point. The result of that aggregation is the value of the output point.The unit of measure of the output of an aligning function is usually the same as that of the input. The exceptions are:

The output of

`rate`

has the unit of its input divided by the unit 's'.The output of

`count_true_aligner`

has unit`1`

.The output of

`fraction_true_aligner`

has unit`10^2.%`

`rate`

Compute a rate of change at aligned points in time.

Signature:
*ImplicitRowInput* `rate(`

*[ lit-Duration ]* `)`

→ *Double.Gauge* *(implicit row input)*

The `rate`

aligner operates on input time series with a single value column
of numeric (*Int* or *Double) type. It always produces an output table with
a single value column of *Double* type and *Gauge* time series kind .

The `rate`

aligner computes the change in value of the time series over its
window (as described here) and divides that by the
width of the window in seconds. The window extends from the output point
time to the *Duration* parameter time earlier.

The default value for the *Duration* argument is the alignment period.
Unlike the 'delta' aligner function, there is no requirement
that the alignment period and window width match.

`delta`

Compute the change in value at aligned points in time.

Signature:
*ImplicitRowInput* `delta(`

*[ lit-Duration ]* `)`

→ *InputType.Delta*
*(implicit row input)*

The `delta`

aligner operates on input time series with a single value
column of *Summable* type (*Int*, *Double*, or *Distribution*) and the
output is a time series whose value column is of the same type but has a
*Delta* time series kind.

The 'delta_gauge' aligner computes the change in value of the input time
series over the time window between the output time and the *Duration*
argument earlier. The output point's start time is the *Duration* argument
earlier than the output time (the point's end time).

The `delta`

aligner has the requirement that its *Duration* argument is the
same as the alignment period it is used to align to. The default value for
the *Duration* argument is that alignment period.

`any_true_aligner`

Align a *Bool* time series by finding any true value in a window.

Signature:
*ImplicitRowInput*
`any_true_aligner(`

*[ lit-Duration ]* `)`

→
*Bool.Gauge* *(implicit row input)*

The `any_true_aligner`

function operates on an input table with a single
value column of *Bool* type and produces an output table with a single value
column of *Bool* type and *Gauge* time series kind.

The *Duration* argument gives the width of a time window for each output
point that ends at the time of that output point. If the *Duration*
argument is not given, it defaults to the alignment period. The value of an
output point is `true`

if any input point in the window is true and is
`false`

otherwise.

`count_true_aligner`

Align a *Bool* time series by counting the true values in a window.

Signature:
*ImplicitRowInput*
`count_true_aligner(`

*[ lit-Duration ]* `)`

→
*Int.Gauge* *(implicit row input)*

The `count_true_aligner`

function operates on an input table with a single
value column of *Bool* type and produces an output table with a single value
column of *Int* type and *Gauge* time series kind.

The *Duration* argument gives the width of a time window for each output
point that ends at the time of that output point. If the *Duration*
argument is not given, it defaults to the alignment period. The value of an
output point is the number of input points in the window with value `true`

.

`delta_gauge`

Compute the change in value at aligned points in time as a *Gauge* time series.

Signature:
*ImplicitRowInput* `delta_gauge(`

*[ lit-Duration ]* `)`

→ *InputType.Gauge*
*(implicit row input)*

The `delta_gauge`

aligner operates on input time series with a single value
column of *Summable* type (*Int*, *Double*, or *Distribution*) and the
output is a time series whose value column is of the same type but has a
*Gauge* time series kind.

The `delta_gauge`

aligner computes the change in value of the input time
series over its window (as described here). The
window extends from the output point time to the *Duration* parameter time
earlier.

The default value for the *Duration* argument is the alignment period.
Unlike the 'delta' aligner function, there is no requirement
that the alignment period and window width match.

`fraction_true_aligner`

Align a *Bool* time series with the fraction of true values in a window.

Signature:
*ImplicitRowInput*
`fraction_true_aligner(`

*[ lit-Duration ]* `)`

→
*Double.Gauge* *(implicit row input)*

The `fraction_true_aligner`

function operates on an input table with a
single value column of *Bool* type and produces an output table with a
single value column of *Double* type and *Gauge* time series kind.

The *Duration* argument gives the width of a time window for each output
point that ends at the time of that output point. If the *Duration*
argument is not given, it defaults to the alignment period. The value of an
output point is the fraction of all input points in the window that have
the value `true`

.

`int_mean_aligner`

Align by finding the mean of *Int* values in a window.

Signature:
*ImplicitRowInput*
`int_mean_aligner(`

*[ lit-Duration ]* `)`

→
*Int.Gauge* *(implicit row input)*

The `int_mean_aligner`

function operates on an input table with a single
value column of *Int* type and *Gauge* or *Delta* time series kind. It
produces an output table with a single value column of *Int* type and
*Gauge* time series kind.

The *Duration* argument gives the width of a time window for each output
point that ends at the time of that output point. If the *Duration*
argument is not given, it defaults to the alignment period. The value of an
output point is the mean of the input table value points that fall within
this above window, rounded to the nearest integer value.

`interpolate`

Compute interpolated values at aligned points in time.

Signature:
*ImplicitRowInput* `interpolate(`

*[ lit-Duration ]* `)`

→ *InputType.Gauge*
*(implicit row input)*

The `interpolate`

aligner operates on an input table with a single value
column of numeric (*Int* or *Double) type and *Gauge* time series kind.
It produces an output table with a single
value column of the same type and time series kind.

If the output time for the `interpolate`

aligner function is the same as the
end time of a point in the input time series, that is used for the output
point. Otherwise, the `interpolate`

aligner considers the input points
whose end time are are the nearest earlier and later points to the output
time. If these points are within the
*Duration* argument of one another, the output value is the linear
interpolation between those to points at the output time. If there is no
input point earlier than the output time or no input point later than the
output time or if the two input points are not within *Duration* argument
of each other, no output value is produced.

The default for the *Duration* argument is twice the alignment period.

`mean_aligner`

Align by finding the mean of values in a window.

Signature:
*ImplicitRowInput* `mean_aligner(`

*[ lit-Duration ]* `)`

→ *Double.Gauge* *(implicit row input)*

The `mean_aligner`

function operates on an input table with a single value
column of numeric type. (*Int* or *Double*) and *Gauge* or *Delta* time
series kind. It produces an output table with a single value column of
*Double* type and *Gauge* time series kind.

The *Duration* argument gives the width of a time window for each output
point that ends at the time of that output point. If the *Duration*
argument is not given, it defaults to the alignment period. The value of an
output point is the mean of the input table value points that fall within
this above window.

`next_older`

Aligned points in time by moving from an earlier to later time.

Signature:
*ImplicitRowInput* `next_older(`

*[ lit-Duration ]* `)`

→ *InputType.Gauge*
*(implicit row input)*

The `next_older`

aligner operates on time series with any number of value
columns of any type, but all with *Gauge* time series kind. It
produces an output columns of the same type and time series kind.

The `next_older`

aligner creates an output point at by finding the
latest input point whose end time is no later than the output time and
whose end time is no further away from the output time than the *Duration*
argument. If there is no such input point, no output point is created.

The default for the *Duration* argument is twice the alignment period.

`next_younger`

Aligned points in time by moving from a later to earlier time.

Signature:
*ImplicitRowInput* `next_younger(`

*[ lit-Duration ]* `)`

→ *InputType.Gauge*
*(implicit row input)*

The `next_younger`

aligner operates on time series with any number of value
columns of any type, but all with *Gauge* time series kind. It
produces an output columns of the same type and time series kind.

The `next_younger`

aligner creates an output point at by finding the
earliest input point whose end time is no earlier than the output time and
whose end time is no further away from the output time than the *Duration*
argument. If there is no such input point, no output point is created.

The default for the *Duration* argument is twice the alignment period.

### Manipulating Units

These functions change the units of the expressions they are applied to.

`scale`

Scale a value to a different unit of measure.

Signature:
`scale(`

*Num*`,`

*[ lit-String ]* `)`

→
*Double*

`scale(`

*Duration*`,`

*[ lit-String ]* `)`

→
*Double*

`scale(`

*Date*`,`

*[ lit-String ]* `)`

→
*Double*

The `scale`

function returns the value of the first argument, converted to
double, if necessary, and possibly scaled so it has the units given by the
second argument.

If the second argument is not given, then the `scale`

function merely
converts its first argument to double, without changing its units except in
cases where automatic scaling is invoked as described
here. In that case, the second argument is supplied
implicitly, and `scale`

behaves as it normally does with two arguments.

The second argument, if given, must be a valid UCUM code string for the unit that the first argument is to be scaled to. In this case, the returned value denotes the same physical quantity as the input value but expressed in the units given by the second argument. This is done by multiplying the argument by the appropriate scaling factor.

For example, the expression `scale(3 "min", "s")`

will convert the value `3`

with units minutes (`min`

) to the value `180`

with units seconds (`s`

). The
same amount of time, expressed in different units.

It is an error if the first argument has no unit or if the unit of the first argument does not have the same dimension as the unit code given as the second argument, if given. If they do not have the same dimension, it is not possible to scale the first argument to have the dimension given by the second argument.

For example, it is an error to say `scale(3 "km", "m/s")`

, which asks
to scale 3 kilometers into some number of meters per second, because
kilometers has the dimension "distance" and meters per second has the
dimension "distance per time" (speed). There is no scale factor that can
turn distance into speed. One would need to divide the distance by some
value with units of time to make this work. For example ```
scale(3 "km" / 10
"min", "m/s")
```

will scale `.3 "km/min"`

to `5 "m/s"`

.

If the first argument is a *Date* or *Duration* argument, then the second
argument must give a unit of time (for example `"s"`

, `"h"`

, or `"wk"`

).
The returned value will be a *Double* value designating the amount of time
of the first argument value in the units given by the second argument. For
a *Date* value, this will be the length of time since the Unix epoch.

For example, `scale(1m, "s")`

will result in a value of `60.0`

with units
`s`

, and `scale(d'1970/01/01-01:00:00+00', "h")`

results in a value of `1.0`

with units `h' (one hour into the Unix epoch).

`cast_units`

Set the unit of measure of a value.

Signature:
`cast_units(`

*Summable*`,`

*lit-String* `)`

→
*FirstArgType*

The `cast_units`

function returns the unchanged value of the first argument
but sets the unit of measure for that value to be that given by the second
argument string.

The string must be a value UCUM code string for the desired unit. Any unit the first argument may have had before applying this function is ignored.

### Periodic Window

The periodic window functions are used to annotate a *Duration* actual
argument passed to a *WindowDuration* argument
that specifies a window width used to select input points to a periodic
calculation. Such an argument is passed to the
`group_by`

table operation which outputs
aligned time series. The `window`

and `sliding`

functions constrain the input widow width according to the output
alignment period.

The `window`

function indicates that the alignment period and the widow
width must be the same, making the input point windows be
non-overlapping.

The `sliding`

function indicates that the alignment period can be smaller
than the window width, causing input windows to overlap.

`window`

Indicates a window that is the same as the alignment period.

Signature:
`window(`

*[ lit-Duration ]* `)`

→
*lit-WindowDuration*

The `window`

function annotates a
*Duration* actual
argument passed to a *WindowDuration* argument
that specifies a window width used in a calculation that produces
aligned time series. It requires that the window width and
the output alignment period both be the same as its *Duration* argument.
If the
*Duration* argument is not given, then it specifies that the window width
be the output alignment period, however that is defined.

For example, the table operation
`|`

`group_by`

`window(5m), .mean`

produces
output points that are the mean value of inputs points falling within a 5m
window of the output end time. The `window`

function annotates the `5m`

window width to require that the alignment period of the `group_by`

be 5
minutes as well. The table operation `| group_by window(), .mean`

also
requires the window width to be the same as the output alignment period, but
does not specify what that must be.

`sliding`

Indicates a window that is sliding (overlapping) rather than disjoint.

Signature:
`sliding(`

*lit-Duration* `)`

→ *lit-SlidingDuration*

The `sliding`

function annotates a *Duration* actual
argument passed to a *WindowDuration* argument
that specifies a window width used in a calculation that produces
aligned time series. It requires that the window width be
its *Duration* argument and requires that the alignment period be no larger
(but allows it to be smaller).

For example, the table operation
`|`

`group_by`

`sliding(5m), .mean`

produces
output points that are the mean value of inputs points falling within a 5m
window of the output end time. The `sliding`

function annotating the `5m`

window width indicates that alignment period of the `group_by`

can be any
time no larger than 5 minutes. If there is an `| every 1m`

table operation
indicating 1 minute alignment, then the 4 minutes of each 5 minute window
will overlap the window of the next-earlier output point.

### Distribution

`count_from`

The number of values in a distribution value.

Signature:
`count_from(`

*Distribution.CumulativeOK* `)`

→
*Int.FirstArgKind*

The `count_from`

function returns the size of the population of values in
its input Distribution value.

The unit of measure attached to the result of
`count_from`

is `1`

.

`sum_from`

The sum of the values in a distribution value.

Signature:
`sum_from(`

*Distribution.CumulativeOK* `)`

→
*Double.FirstArgKind*

The `sum_from`

function returns the sum of all the values contained in
its input Distribution value.

The result of `sum_from`

has the same unit of
measure as the input.

`mean_from`

The mean of the values in a distribution value.

Signature:
`mean_from(`

*Distribution* `)`

→ *Double*

The `mean_from`

function returns the arithmetic mean of all the values
contained in its input Distribution value.

The result of `mean_from`

has the same unit of
measure as the input.

`stddev_from`

The standard deviation of the values in a distribution value.

Signature:
`stddev_from(`

*Distribution* `)`

→ *Double*

The `stddev_from`

function returns the variance of the population the
values contained in its input Distribution value.

The result of `stddev_from`

has the same unit of
measure as the input.

`variance_from`

The variance of the values in a distribution value.

Signature:
`variance_from(`

*Distribution* `)`

→ *Double*

The `variance_from`

function returns the variance of the population the
values contained in its input Distribution value.

The result of the 'variance_from' function has no unit of measure.

`median_from`

The median of the values in a distribution value.

Signature:
`median_from(`

*Distribution* `)`

→ *Double*

The `median_from`

function returns an estimate of the median of the
population the values contained in its input Distribution value.

The result of `median_from`

has the same unit of
measure as the input.

`percentile_from`

A percentile of the values in a distribution value.

Signature:
`percentile_from(`

*Distribution*`,`

*lit-Num* `)`

→ *Double*

The `percentile_from`

function returns an estimate of the percentile of the
population the values contained in its input Distribution value. The
*Num* argument gives the percentile to estimate as a number between 0 and
100.

The result of `percentile_from`

has the same unit of
measure as the input.

`fraction_less_than_from`

The fraction of values in a distribution that are less than a fixed value.

Signature:
`fraction_less_than_from(`

*Distribution*`,`

*lit-Num* `)`

→ *Double*

The `fraction_less_than_from`

function returns an estimate of the fraction
of the population the values contained in its input Distribution value
that are less than its *Num* argument.

The unit of measure attached to the result of
`fraction_less_than`

is `10^2.%`

.

`bounded_percentile_from`

A percentile of the values within a bound in a distribution value.

Signature:
`bounded_percentile_from(`

*Distribution*`,`

*lit-Num*`,`

*[ lit-Num ]*`,`

*[ lit-Num ]* `)`

→
*Double*

The `bounded_percentile_from`

function operates on a subset of the value
contained in the input Distribution. An estimate is made of the population
of values that are greater than the second *Num* parameter, if given, and
less than or equal to the third *Num* parameter, if given. At least one
or the other of the second and third *Num* arguments must be given and, if
both are given, the second must be less than the third.

This returns an estimate of the percentile of that estimated population of
values. The first *Num* argument gives the percentile to estimate as a
number between 0 and 100.

The result of `bounded_percentile_from`

has the same unit of
measure as the input.

`rebucket`

Distribution value converted to a new bucket specification.

Signature:
`rebucket(`

*Distribution*`,`

*lit-BucketSpecification* `)`

→ *Distribution*

This converts the input Distribution value to a Distribution value whose
bucket specification is that given in the second argument
*BucketSpecification*.

This distributes the counts from each bucket in the input Distribution to the buckets of the output Distribution under the assumption that the values counted in a bucket are evenly distributed across the range of the bucket. The output Distribution has the same total count as the input Distribution but the counts are distributed differently across the output Distribution buckets. The output Distribution has the same sum, mean, and standard deviation as the input Distribution.

### Bucket Specifier

A Distribution value has a histogram made up of buckets. Each bucket is associated with a range of values and contains a count of the values in the Distribution that fall within that range. Every Distribution has a Bucket Specification that describes the boundaries for the buckets in a Distribution value. The functions in this section generate Bucket Specifications.

`powers_of`

A bucket specification with exponentially increasing bucket boundaries.

Signature:
`powers_of(`

*lit-Num* `)`

→
*lit-BucketSpecification*

The `powers_of`

function returns a bucket specifications where the upper
bound of each bucket is fixed factor (given by the *Num* argument) times the
lower bound. Thus the bucket size is exponentially increasing and the error
for computing percentiles is a bounded by a constant factor of the true
value.

This does not set the number of buckets or the lower bound of the first
bucket, both of which must either be specified (by 'num_buckets' and
'lower') or will take the default values (30 buckets, lower bound of 1.0).
If the bucket specification is given by `powers_of`

, the lower bound must be
greater than 0.

The following example gives a bucket specification with 50 buckets whose size grows exponentially at a rate of 1.1, starting at the value 100. So the bucket boundaries are 1, 1.1, 1.21, 1.331, and so on.

```
powers_of(1.1).num_buckets(30).lower(100.0)
```

`fixed_width`

A bucket specification with equal-sized buckets.

Signature:
`fixed_width(`

*lit-Num* `)`

→
*lit-BucketSpecification*

The `fixed_width`

function returns a bucket specifications where the upper
bound of each bucket is fixed amount (given by the *Num* argument) more than
the lower bound. Thus the bucket size is fixed.

This does not set the number of buckets or the lower bound of the first bucket, both of which must either be specified (by 'num_buckets' and 'lower') or will take the default values (30 buckets, lower bound of 1.0).

The following example gives a bucket specification with 100 buckets of size 1, staring at 1. This is a good specification for a distribution of percentage values.

```
fixed_width(1).num_buckets(100)
```

`custom`

A bucket specification from a list of bucket boundaries.

Signature:
`custom(`

*lit-Num**...* `)`

→
*lit-BucketSpecification*

The `custom`

function returns a bucket specification with explicitly given
bucket bounds. The function takes multiple numeric arguments which must be
given in increasing order. The lower bound of the first bucket is given by
the first argument and the upper bound of the last bucket is given by the
last argument. Each intermediate argument gives the upper bound of the
previous bucket and the upper bound of the next bucket.

This completely determines the bucket specification, giving the number of buckets and the exact bound of each.

The following example gives a bucket specification with 3 buckets. The first has boundary 3 and 27, the second 27 and 105, and the third 105 and 277.

```
custom(3,27,105,277)
```

`num_buckets`

Sets the number of buckets in a bucket specification.

Signature:
`num_buckets(`

*lit-BucketSpecification*`,`

*lit-Num* `)`

→ *lit-BucketSpecification*

When applied to a bucket specification that does not have the number of
buckets determined, the `num_buckets`

function returns a bucket
specification with a number of buckets given by its *Num* argument. All the
other aspects of the input bucket specification are preserved.

It is an error to apply `num_buckets`

to a bucket specification that already
has the number of buckets determined.

`bounds`

Sets the lower bound of the first bucket and upper bound of the last.

Signature:
`bounds(`

*lit-BucketSpecification*`,`

*lit-Num*`,`

*lit-Num* `)`

→ *lit-BucketSpecification*

When applied to a bucket specification that does not have the lower bound of
the first bucket or the upper bound of the last bucket determined,
the `bounds`

function returns a bucket
specification with the lower bound of its first bucket given by its first
*Num* argument and the upper bound of its last bucket given by the second
*Num* argument. All the other aspects of the input bucket specification are
preserved.

It is an error to apply `bounds`

to a bucket specification that already
has either the lower bound of the first bucket or upper bound of the last
bucket determined.

`lower`

Sets the lower bound of the first bucket in a bucket specification.

Signature:
`lower(`

*lit-BucketSpecification*`,`

*lit-Num* `)`

→ *lit-BucketSpecification*

When applied to a bucket specification that does not have the lower bound of
the first bucket determined, the `num_buckets`

function returns a bucket
specification with the lower bound of its first bucket given by its *Num*
argument. All the other aspects of the input bucket specification are
preserved.

It is an error to apply `lower`

to a bucket specification that already
has the lower bound of the first bucket determined.

### Miscellaneous

`cast_double`

Convert *Int* value to *Double*.

Signature:
`cast_double(`

*Num.CumulativeOK* `)`

→
*Double.FirstArgKind*

The `cast_double`

function takes a single *Int* argument and returns
the nearest *Double* value.

The result of `cast_double`

has the same unit of
measure as the input.

`cast_gauge`

Cast a *Cumulative* or *Delta* time series value to *Gauge*.

Signature:
`cast_gauge(`

*ColumnValue.CumulativeOK* `)`

→
*FirstArgType.Gauge*

The `cast_gauge`

functions returns the value of its argument but changes
the time series kind of the value to *Gauge*.

If this results in an output table without value columns that have *Delta*
time series kind, the output table will have no start time column.

The result of `cast_gauge`

has the same unit of
measure as the input.

`within`

Specifies the window of the sort value calculation.

Signature:
`within(`

*ColumnValue*`,`

*[ lit-DateOrDuration ]*`,`

*[ lit-DateOrDuration ]* `)`

→
*Windowed.FirstArgKind*

The `within`

function decorates the expression bound to the *Windowed(Num)*
sort value argument of the `top`

or `bottom`

table operation. It specifies the window in which the sort value expression
is evaluated by specifying one or two out of three of the values: the
oldest (starting) time of the window, the youngest (ending) time of the
window, or the duration of the window.

If either of the two arguments of `within`

is a positive *Duration*, then
that sets the width of the window. At most one of the arguments can be such
a *Duration*.

If the first argument is a *Date*, then that specifies the starting time.
If the second argument is a *Date*, that specifies the ending time. If both
are *Date* values, the second must be later in time than the first. A
*Date* argument can be given as a *Date* literal or with a negative
*Duration* literal. In the later case, the time is the specified *Duration*
before the ending time of the outer query window (see the
`within`

table operation).

If the first argument is not given, it defaults to the starting time of the outer query window. If the second argument is not given, it defaults to the ending time of the outer query window.

For example `.mean().within(1h,-2h)`

indicates that the `max`

reducer
should be applied to all the points in the input time series whose end time
is within a window of 1 hour width, ending 2 hours ago.
The `mean`

aggregator is applied to all input points whose
end time is in this window.

For example `max(val()).within(10m)`

indicates that the `max`

reducer
should be applied to all the in the input time series whose end time falls
within the time range between the query end time and 10 minutes earlier.
The `max`

aggregator is applied to all input points whose
end time is in this window.

## Index of Table Operations and Functions

An index to all the table operations and functions.

`abs`

Absolute value.`absent_for`

Create a condition for the absence of input.`add`

The sum of two numbers.`adjacent_delta`

The change in value between an input point and next-earlier point.`adjacent_rate`

The rate of change between the input and next-earlier points (rows).`aggregate`

Default aggregate value from a group of values of any type.`align`

Produces an aligned table using an alignment function.`all_true`

The conjunction of a group of boolean values.`and`

The logical and of two boolean values.`any_true`

The disjunction of a group of boolean values.`any_true_aligner`

Align a*Bool*time series by finding any true value in a window.`ascii_to_lower`

Change ASCII upper case letter characters to lower case.`ascii_to_upper`

Change ASCII lower case letter characters to upper case.`bottom`

Selects the bottom time series by a sort-value expression.`bottom_by`

Selects time series by a sort-value expression in different groups.`bounded_percentile_from`

A percentile of the values within a bound in a distribution value.`bounds`

Sets the lower bound of the first bucket and upper bound of the last.`cast_double`

Convert*Int*value to*Double*.`cast_gauge`

Cast a*Cumulative*or*Delta*time series value to*Gauge*.`cast_units`

Set the unit of measure of a value.`concatenate`

String concatenation.`condition`

Add a boolean condition column to the input table.`count`

The count of the number of values in a group of values.`count_from`

The number of values in a distribution value.`count_true`

The number of true values in a group of boolean values.`count_true_aligner`

Align a*Bool*time series by counting the true values in a window.`covariance`

The covariance of a group of pairs of values.`custom`

A bucket specification from a list of bucket boundaries.`delta`

Compute the change in value at aligned points in time.`delta_gauge`

Compute the change in value at aligned points in time as a*Gauge*time series.`diameter`

The maximum minus the minimum of a group of numeric values.`distribution`

A distribution from a group of numeric or distribution values.`div`

The ratio of two numbers.`end`

The ending time of the input point (row).`eq`

Equal.`every`

Specifies the period for aligned table output.`exp`

e raised to a power.`false`

The boolean value false.`fetch`

Produces a table from the database.`fetch_cumulative`

Produces a table of*Cumulative*time series from the database.`filter`

Filters rows from an input table by a predicate.`filter_ratio`

Computes the ratio of two filtered sums of the input value column.`filter_ratio_by`

Computes a grouped ratio of two filtered sums of the input value column.`fixed_width`

A bucket specification with equal-sized buckets.`fraction_less_than`

The fraction of a group of values less than a fixed value.`fraction_less_than_from`

The fraction of values in a distribution that are less than a fixed value.`fraction_true`

The fraction of a group of boolean values that are true.`fraction_true_aligner`

Align a*Bool*time series with the fraction of true values in a window.`ge`

Greater than or equal.`graph_period`

Specifies the preferred output period for drawing time series graphs.`group_by`

Aggregates rows by mapped time series identifier and time window.`gt`

Greater than.`has`

True if a set argument contains a particular value.`has_value`

True if an argument expression computes a value.`hash_tsid`

Return a hash of the time series identifier columns.`ident`

Identity table operation: no change to the input table.`if`

A value conditionally chosen from two values.`int_ceil`

Upper bound integer.`int_div`

The quotient from the division of two integers.`int_floor`

Lower bound integer.`int_mean_aligner`

Align by finding the mean of*Int*values in a window.`int_round`

Nearest integer.`interpolate`

Compute interpolated values at aligned points in time.`join`

Natural join of multiple tables.`le`

Less than or equal.`log`

Natural logarithm.`lower`

Sets the lower bound of the first bucket in a bucket specification.`lt`

Less than.`map`

Rewrites the time series identifier and value columns of each row in a table.`max`

The maximum of a group of numeric values.`mean`

The mean of a group of numeric values.`mean_aligner`

Align by finding the mean of values in a window.`mean_from`

The mean of the values in a distribution value.`median`

The median of a group of numeric or distribution values.`median_from`

The median of the values in a distribution value.`metric`

Produces the table for a specific metric type from a set of tables.`min`

The minimum of a group of numeric values.`mul`

The product of two numbers.`ne`

Not equal.`neg`

The negative of a number.`next_older`

Aligned points in time by moving from an earlier to later time.`next_younger`

Aligned points in time by moving from a later to earlier time.`not`

The logical negation of a boolean value.`num_buckets`

Sets the number of buckets in a bucket specification.`older`

A value from the next-earlier point (row) in a time series.`or`

The logical or of two boolean values.`or_else`

A value or, if it is not a value, another value.`outer_join`

Outer natural join of two tables.`percentile`

A percentile of a group of numeric or distribution values.`percentile_from`

A percentile of the values in a distribution value.`pick_any`

The value of any element of a group of values (chosen arbitrarily).`pos`

Identity for numeric inputs.`power`

One number to the power of another.`powers_of`

A bucket specification with exponentially increasing bucket boundaries.`rate`

Compute a rate of change at aligned points in time.`ratio`

Computes the ratio of value columns of two aligned input tables.`re_extract`

Extract values matched by a regular expression in another string.`re_full_match`

True if a regular expression matches the whole of a string value.`re_global_replace`

Replace all matches of a regular expression in another string.`re_partial_match`

True if a regular expression matches some part of string value.`re_replace`

Replace the first match of a regular expression in another string.`rebucket`

Distribution value converted to a new bucket specification.`rem`

The remainder from the division of two integers.`row_count`

The number of input rows encountered.`scale`

Scale a value to a different unit of measure.`singleton`

The value of the element of a group of values with only one element.`sliding`

Indicates a window that is sliding (overlapping) rather than disjoint.`sqrt`

Square root.`start`

The starting time of the input point (row).`stddev`

The standard deviation of a group of values.`stddev_from`

The standard deviation of the values in a distribution value.`string_to_double`

Convert*String*to*Double*.`string_to_int64`

Convert*String*to*Int*.`sub`

The difference of two numbers.`sum`

The sum of a group of numeric values.`sum_from`

The sum of the values in a distribution value.`time_shift`

Shift time series forward in time.`top`

Selects the top time series by a sort-value expression.`top_by`

Selects time series by a sort-value expression in different groups.`true`

The boolean value true.`unaligned_group_by`

Aggregates rows by mapped time series identifier without alignment.`union`

Union of multiple tables.`union_group_by`

Aggregates rows from multiple tables.`unique`

The common value of a group of values (which must all be the same).`utf8_normalize`

Unicode string suitable for case-folding comparison.`val`

A value column's value in the input point (row).`value`

Rewrites the value columns of each row in a table.`variance`

The variance of a group of numeric values.`variance_from`

The variance of the values in a distribution value.`weighted_distribution`

A distribution from a group of weighted values.`window`

Indicates a window that is the same as the alignment period.`window`

Specifies the window for alignment operations.`within`

Specifies the window of the sort value calculation.`within`

Specifies the time range of the query output.