prometheus/docs/querying/operators.md

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Operators	2

Operators

Binary operators

Prometheus's query language supports basic logical and arithmetic operators. For operations between two instant vectors, the matching behavior can be modified.

Arithmetic binary operators

The following binary arithmetic operators exist in Prometheus:

• + (addition)
• - (subtraction)
• * (multiplication)
• / (division)
• % (modulo)
• ^ (power/exponentiation)

Binary arithmetic operators are defined between scalar/scalar, vector/scalar, and vector/vector value pairs. They follow the usual IEEE 754 floating point arithmetic, including the handling of special values like NaN, +Inf, and -Inf.

Between two scalars, the behavior is obvious: they evaluate to another scalar that is the result of the operator applied to both scalar operands.

Between an instant vector and a scalar, the operator is applied to the value of every data sample in the vector. If the data sample is a float, the operation performed on the data sample is again obvious, e.g. if an instant vector of float samples is multiplied by 2, the result is another vector of float samples in which every sample value of the original vector is multiplied by 2. For vector elements that are histogram samples, the behavior is the following: For *, all bucket populations and the count and the sum of observations are multiplied by the scalar. For /, the histogram sample has to be on the left hand side (LHS), followed by the scalar on the right hand side (RHS). All bucket populations and the count and the sum of observations are then divided by the scalar. A division by zero results in a histogram with no regular buckets and the zero bucket population and the count and sum of observations all set to +Inf, -Inf, or NaN, depending on their values in the input histogram (positive, negative, or zero/NaN, respectively). For / with a scalar on the LHS and a histogram sample on the RHS, and similarly for all other arithmetic binary operators in any combination of a scalar and a histogram sample, there is no result and the corresponding element is removed from the resulting vector. Such a removal is flagged by an info-level annotation.

Between two instant vectors, a binary arithmetic operator is applied to each entry in the LHS vector and its matching element in the RHS vector. The result is propagated into the result vector with the grouping labels becoming the output label set. Entries for which no matching entry in the right-hand vector can be found are not part of the result. If two float samples are matched, the behavior is obvious. If a float sample is matched with a histogram sample, the behavior follows the same logic as between a scalar and a histogram sample (see above), i.e. * and / (the latter with the histogram sample on the LHS) are valid operations, while all others lead to the removal of the corresponding element from the resulting vector. If two histogram samples are matched, only + and - are valid operations, each adding or substracting all matching bucket populations and the count and the sum of observations. All other operations result in the removal of the corresponding element from the output vector, flagged by an info-level annotation.

In any arithmetic binary operation involving vectors, the metric name is dropped.

Trigonometric binary operators

The following trigonometric binary operators, which work in radians, exist in Prometheus:

• atan2 (based on https://pkg.go.dev/math#Atan2)

Trigonometric operators allow trigonometric functions to be executed on two vectors using vector matching, which isn't available with normal functions. They act in the same manner as arithmetic operators. They only operate on float samples. Operations involving histogram samples result in the removal of the corresponding vector elements from the output vector, flagged by an info-level annotation.

Comparison binary operators

The following binary comparison operators exist in Prometheus:

• == (equal)
• != (not-equal)
• > (greater-than)
• < (less-than)
• >= (greater-or-equal)
• <= (less-or-equal)

Comparison operators are defined between scalar/scalar, vector/scalar, and vector/vector value pairs. By default they filter. Their behavior can be modified by providing bool after the operator, which will return 0 or 1 for the value rather than filtering.

Between two scalars, the bool modifier must be provided and these operators result in another scalar that is either 0 (false) or 1 (true), depending on the comparison result.

Between an instant vector and a scalar, these operators are applied to the value of every data sample in the vector, and vector elements between which the comparison result is false get dropped from the result vector. These operation only work with float samples in the vector. For histogram samples, the corresponding element is removed from the result vector, flagged by an info-level annotation.

Between two instant vectors, these operators behave as a filter by default, applied to matching entries. Vector elements for which the expression is not true or which do not find a match on the other side of the expression get dropped from the result, while the others are propagated into a result vector with the grouping labels becoming the output label set. Matches between two float samples work as usual, while matches between a float sample and a histogram sample are invalid. The corresponding element is removed from the result vector, flagged by an info-level annotation. Between two histogram samples, == and != work as expected, but all other comparison binary operations are again invalid.

In any comparison binary operation involving vectors, providing the bool modifier changes the behavior in the following way: Vector elements that would be dropped instead have the value 0 and vector elements that would be kept have the value 1. Additionally, the metric name is dropped. (Note that invalid operations involving histogram samples still return no result rather than the value 0.)

Logical/set binary operators

These logical/set binary operators are only defined between instant vectors:

• and (intersection)
• or (union)
• unless (complement)

vector1 and vector2 results in a vector consisting of the elements of vector1 for which there are elements in vector2 with exactly matching label sets. Other elements are dropped. The metric name and values are carried over from the left-hand side vector.

vector1 or vector2 results in a vector that contains all original elements (label sets + values) of vector1 and additionally all elements of vector2 which do not have matching label sets in vector1.

vector1 unless vector2 results in a vector consisting of the elements of vector1 for which there are no elements in vector2 with exactly matching label sets. All matching elements in both vectors are dropped.

As these logical/set binary operators do not interact with the sample values, they work in the same way for float samples and histogram samples.

Vector matching

Operations between vectors attempt to find a matching element in the right-hand side vector for each entry in the left-hand side. There are two basic types of matching behavior: One-to-one and many-to-one/one-to-many.

Vector matching keywords

These vector matching keywords allow for matching between series with different label sets providing:

• on
• ignoring

Label lists provided to matching keywords will determine how vectors are combined. Examples can be found in One-to-one vector matches and in Many-to-one and one-to-many vector matches

Group modifiers

These group modifiers enable many-to-one/one-to-many vector matching:

• group_left
• group_right

Label lists can be provided to the group modifier which contain labels from the "one"-side to be included in the result metrics.

Many-to-one and one-to-many matching are advanced use cases that should be carefully considered. Often a proper use of ignoring(<labels>) provides the desired outcome.

Grouping modifiers can only be used for comparison and arithmetic. Operations as and, unless and or operations match with all possible entries in the right vector by default.

One-to-one vector matches

One-to-one finds a unique pair of entries from each side of the operation. In the default case, that is an operation following the format vector1 <operator> vector2. Two entries match if they have the exact same set of labels and corresponding values. The ignoring keyword allows ignoring certain labels when matching, while the on keyword allows reducing the set of considered labels to a provided list:

<vector expr> <bin-op> ignoring(<label list>) <vector expr>
<vector expr> <bin-op> on(<label list>) <vector expr>

Example input:

method_code:http_errors:rate5m{method="get", code="500"}  24
method_code:http_errors:rate5m{method="get", code="404"}  30
method_code:http_errors:rate5m{method="put", code="501"}  3
method_code:http_errors:rate5m{method="post", code="500"} 6
method_code:http_errors:rate5m{method="post", code="404"} 21

method:http_requests:rate5m{method="get"}  600
method:http_requests:rate5m{method="del"}  34
method:http_requests:rate5m{method="post"} 120

Example query:

method_code:http_errors:rate5m{code="500"} / ignoring(code) method:http_requests:rate5m

This returns a result vector containing the fraction of HTTP requests with status code of 500 for each method, as measured over the last 5 minutes. Without ignoring(code) there would have been no match as the metrics do not share the same set of labels. The entries with methods put and del have no match and will not show up in the result:

{method="get"}  0.04            //  24 / 600
{method="post"} 0.05            //   6 / 120

Many-to-one and one-to-many vector matches

Many-to-one and one-to-many matchings refer to the case where each vector element on the "one"-side can match with multiple elements on the "many"-side. This has to be explicitly requested using the group_left or group_right modifiers, where left/right determines which vector has the higher cardinality.

<vector expr> <bin-op> ignoring(<label list>) group_left(<label list>) <vector expr>
<vector expr> <bin-op> ignoring(<label list>) group_right(<label list>) <vector expr>
<vector expr> <bin-op> on(<label list>) group_left(<label list>) <vector expr>
<vector expr> <bin-op> on(<label list>) group_right(<label list>) <vector expr>

The label list provided with the group modifier contains additional labels from the "one"-side to be included in the result metrics. For on a label can only appear in one of the lists. Every time series of the result vector must be uniquely identifiable.

Example query:

method_code:http_errors:rate5m / ignoring(code) group_left method:http_requests:rate5m

In this case the left vector contains more than one entry per method label value. Thus, we indicate this using group_left. The elements from the right side are now matched with multiple elements with the same method label on the left:

{method="get", code="500"}  0.04            //  24 / 600
{method="get", code="404"}  0.05            //  30 / 600
{method="post", code="500"} 0.05            //   6 / 120
{method="post", code="404"} 0.175           //  21 / 120

Aggregation operators

Prometheus supports the following built-in aggregation operators that can be used to aggregate the elements of a single instant vector, resulting in a new vector of fewer elements with aggregated values:

• sum (calculate sum over dimensions)

• avg (calculate the arithmetic average over dimensions)

• min (select minimum over dimensions)

• max (select maximum over dimensions)

• bottomk (smallest k elements by sample value)

• topk (largest k elements by sample value)

• limitk (sample k elements, experimental, must be enabled with --enable-feature=promql-experimental-functions)

• limit_ratio (sample a pseudo-randem ratio r of elements, experimental, must be enabled with --enable-feature=promql-experimental-functions)

• group (all values in the resulting vector are 1)

• count (count number of elements in the vector)

• count_values (count number of elements with the same value)

• stddev (calculate population standard deviation over dimensions)

• stdvar (calculate population standard variance over dimensions)

• quantile (calculate φ-quantile (0 ≤ φ ≤ 1) over dimensions)

These operators can either be used to aggregate over all label dimensions or preserve distinct dimensions by including a without or by clause. These clauses may be used before or after the expression.

<aggr-op> [without|by (<label list>)] ([parameter,] <vector expression>)

or

<aggr-op>([parameter,] <vector expression>) [without|by (<label list>)]

label list is a list of unquoted labels that may include a trailing comma, i.e. both (label1, label2) and (label1, label2,) are valid syntax.

without removes the listed labels from the result vector, while all other labels are preserved in the output. by does the opposite and drops labels that are not listed in the by clause, even if their label values are identical between all elements of the vector.

parameter is only required for topk, bottomk, limitk, limit_ratio, quantile, and count_values. It is used as the value for k, r, φ, or the name of the additional label, respectively.

Detailed explanations

sum sums up sample values in the same way as the + binary operator does between two values. Similarly, avg divides the sum by the number of aggregated samples in the same way as the / binary operator. Therefore, all sample values aggregation into a single resulting vector element must either be float samples or histogram samples. An aggregation of a mix of both is invalid, resulting in the removeal of the corresponding vector element from the output vector, flagged by a warn-level annotation.

min and max only operate on float samples, following IEEE 754 floating point arithmetic, which in particular implies that NaN is only ever considered a minimum or maximum if all aggregated values are NaN. Histogram samples in the input vector are ignored, flagged by an info-level annotation.

topk and bottomk are different from other aggregators in that a subset of the input samples, including the original labels, are returned in the result vector. by and without are only used to bucket the input vector. Similar to min and max, they only operate on float samples, considering NaN values to be farthest from the top or bottom, respectively. Histogram samples in the input vector are ignored, flagged by an info-level annotation.

limitk and limit_ratio also return a subset of the input samples, including the original labels in the result vector. The subset is selected in a deterministic pseudo-random way. limitk picks k samples, while limit_ratio picks a ratio r of samples (each determined by parameter). This happens independent of the sample type. Therefore, it works for both float samples and histogram samples. r can be between +1 and -1. The absolute value of r is used as the selection ratio, but the selection order is inverted for a negative r, which can be used to select complements. For example, limit_ratio(0.1, ...) returns a deterministic set of approximatiely 10% of the input samples, while limit_ratio(-0.9, ...) returns precisely the remaining approximately 90% of the input samples not returned by limit_ratio(0.1, ...).

group and count do not do not interact with the sample values, they work in the same way for float samples and histogram samples.

count_values outputs one time series per unique sample value. Each series has an additional label. The name of that label is given by the aggregation parameter, and the label value is the unique sample value. The value of each time series is the number of times that sample value was present. count_values works with both float samples and histogram samples. For the latter, a compact string representation of the histogram sample value is used as the label value.

stddev and stdvar only work with float samples, following IEEE 754 floating point arithmetic. Histogram samples in the input vector are ignored, flagged by an info-level annotation.

quantile calculates the φ-quantile, the value that ranks at number φ*N among the N metric values of the dimensions aggregated over. φ is provided as the aggregation parameter. For example, quantile(0.5, ...) calculates the median, quantile(0.95, ...) the 95th percentile. For φ = NaN, NaN is returned. For φ < 0, -Inf is returned. For φ > 1, +Inf is returned.

Examples

If the metric http_requests_total had time series that fan out by application, instance, and group labels, we could calculate the total number of seen HTTP requests per application and group over all instances via:

sum without (instance) (http_requests_total)

Which is equivalent to:

 sum by (application, group) (http_requests_total)

If we are just interested in the total of HTTP requests we have seen in all applications, we could simply write:

sum(http_requests_total)

To count the number of binaries running each build version we could write:

count_values("version", build_version)

To get the 5 largest HTTP requests counts across all instances we could write:

topk(5, http_requests_total)

To sample 10 timeseries, for example to inspect labels and their values, we could write:

limitk(10, http_requests_total)

Binary operator precedence

The following list shows the precedence of binary operators in Prometheus, from highest to lowest.

1. ^
2. *, /, %, atan2
3. +, -
4. ==, !=, <=, <, >=, >
5. and, unless
6. or

Operators on the same precedence level are left-associative. For example, 2 * 3 % 2 is equivalent to (2 * 3) % 2. However ^ is right associative, so 2 ^ 3 ^ 2 is equivalent to 2 ^ (3 ^ 2).