> ## Documentation Index
> Fetch the complete documentation index at: https://axiom-mano-sample-app.mintlify.site/llms.txt
> Use this file to discover all available pages before exploring further.

# Mathematical functions

> Learn how to use and combine different mathematical functions in APL

## Mathematical functions

| **Function Name**       | **Description**                                                                                                |
| ----------------------- | -------------------------------------------------------------------------------------------------------------- |
| [abs()](#abs)           | Calculates the absolute value of the input.                                                                    |
| [acos()](#acos)         | Returns the angle whose cosine is the specified number (the inverse operation of cos()).                       |
| [asin()](#asin)         | Returns the angle whose sine is the specified number (the inverse operation of sin()).                         |
| [atan()](#atan)         | Returns the angle whose tangent is the specified number (the inverse operation of tan()).                      |
| [atan2()](#atan2)       | Calculates the angle, in radians, between the positive x-axis and the ray from the origin to the point (y, x). |
| [cos()](#cos)           | Returns the cosine function.                                                                                   |
| [degrees()](#degrees)   | Converts angle value in radians into value in degrees, using formula degrees = (180 / PI) \* angle-in-radians. |
| [exp()](#exp)           | The base-e exponential function of x, which is e raised to the power x: e^x.                                   |
| [exp2()](#exp2)         | The base-2 exponential function of x, which is 2 raised to the power x: 2^x.                                   |
| [gamma()](#gamma)       | Computes gamma function.                                                                                       |
| [isinf()](#isinf)       | Returns whether input is an infinite (positive or negative) value.                                             |
| [isnan()](#isnan)       | Returns whether input is Not-a-Number (NaN) value.                                                             |
| [log()](#log)           | Returns the natural logarithm function.                                                                        |
| [log10()](#log10)       | Returns the common (base-10) logarithm function.                                                               |
| [log2()](#log2)         | Returns the base-2 logarithm function.                                                                         |
| [loggamma()](#loggamma) | Computes log of absolute value of the gamma function.                                                          |
| [not()](#not)           | Reverses the value of its bool argument.                                                                       |
| [pi()](#pi)             | Returns the constant value of Pi (π).                                                                          |
| [pow()](#pow)           | Returns a result of raising to power.                                                                          |
| [radians()](#radians)   | Converts angle value in degrees into value in radians, using formula radians = (PI / 180) \* angle-in-degrees. |
| [round()](#round)       | Returns the rounded source to the specified precision.                                                         |
| [sign()](#sign)         | Sign of a numeric expression.                                                                                  |
| [sin()](#sin)           | Returns the sine function.                                                                                     |
| [sqrt()](#sqrt)         | Returns the square root function.                                                                              |
| [tan()](#tan)           | Returns the tangent function.                                                                                  |
| [exp10()](#exp10)       | The base-10 exponential function of x, which is 10 raised to the power x: 10^x.                                |
| [isint()](#isint)       | Returns whether input is an integer (positive or negative) value                                               |
| [isfinite()](#isfinite) | Returns whether input is a finite value (is neither infinite nor NaN).                                         |

## abs()

Calculates the absolute value of the input.

### Arguments

| **Name** | **Type**              | **Required or Optional** | **Description**            |
| -------- | --------------------- | ------------------------ | -------------------------- |
| x        | int, real or timespan | Required                 | The value to make absolute |

### Returns

* Absolute value of x.

### Examples

```kusto
abs(x)
```

```kusto
abs(80.5) == 80.5
```

```kusto
['sample-http-logs']
| project absolute_value = abs(req_duration_ms)
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20absolute_value%20%3D%20abs%28req_duration_ms%29%22%7D)

## acos()

Returns the angle whose cosine is the specified number (the inverse operation of cos()) .

### Arguments

| **Name** | **Type** | **Required or Optional** | **Description**                  |
| -------- | -------- | ------------------------ | -------------------------------- |
| x        | real     | Required                 | A real number in range \[-1,. 1] |

### Returns

* The value of the arc cosine of x
* `null` if `x` \< -1 or `x` > 1

### Examples

```kusto
acos(x)
```

```kusto
acos(-1) == 3.141592653589793
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20cosine_angle%20%3D%20acos%28-1%29%22%7D)

## asin()

Returns the angle whose sine is the specified number (the inverse operation of sin()) .

### Arguments

| **Name** | **Type** | **Required or Optional** | **Description**                  |
| -------- | -------- | ------------------------ | -------------------------------- |
| x        | real     | Required                 | A real number in range \[-1,. 1] |

* x: A real number in range \[-1, 1].

### Returns

* The value of the arc sine of x
* null if x \< -1 or x > 1

### Examples

```kusto
asin(x)
```

```kusto
['sample-http-logs']
| project inverse_sin_angle = asin(-1)
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20inverse_sin_angle%20%3D%20asin%28-1%29%22%7D)

## atan()

Returns the angle whose tangent is the specified number (the inverse operation of tan()) .

### Arguments

x: A real number.

### Returns

The value of the arc tangent of x

### Examples

```kusto
atan(x)
```

```kusto
atan(-1) == -0.7853981633974483
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20inverse_tan_angle%20%3D%20atan%28-1%29%22%7D)

## atan2()

Calculates the angle, in radians, between the positive x-axis and the ray from the origin to the point (y, x).

### Arguments

x: X coordinate (a real number).
y: Y coordinate (a real number).

### Returns

The angle, in radians, between the positive x-axis and the ray from the origin to the point (y, x).

### Examples

```kusto
atan2(y,x)
```

```kusto
atan2(-1, 1) == -0.7853981633974483
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20angle_in_rads%20%3D%20atan2%28-1%2C%201%29%22%7D)

## cos()

Returns the cosine function.

### Arguments

x: A real number.

### Returns

The result of cos(x)

### Examples

```kusto
cos(x)
```

```kusto
cos(-1) == 0.5403023058681398
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20cosine_function%20%3D%20cos%28-1%29%22%7D)

## degrees()

Converts angle value in radians into value in degrees, using formula degrees = (180 / PI ) \* angle\_in\_radians

### Arguments

| **Name** | **Type** | **Required or Optional** | **Description**   |
| -------- | -------- | ------------------------ | ----------------- |
| a        | real     | Required                 | Angle in radians. |

### Returns

The corresponding angle in degrees for an angle specified in radians.

### Examples

```kusto
degrees(a)
```

```kusto
degrees(3.14) == 179.9087476710785
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20degree_rads%20%3D%20degrees%283.14%29%22%7D)

## exp()

The base-e exponential function of x, which is e raised to the power x: e^x.

### Arguments

| **Name** | **Type**    | **Required or Optional** | **Description**        |
| -------- | ----------- | ------------------------ | ---------------------- |
| x        | real number | Required                 | Value of the exponent. |

### Returns

* Exponential value of x.
* For natural (base-e) logarithms, see [log()](/apl/scalar-functions/mathematical-functions#log\(\)).
* For exponential functions of base-2 and base-10 logarithms, see [exp2()](/apl/scalar-functions/mathematical-functions#exp2\(\)), [exp10()](/apl/scalar-functions/mathematical-functions#exp10\(\))

### Examples

```kusto
exp(x)
```

```kusto
exp(1) == 2.718281828459045
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20exponential_value%20%3D%20exp%281%29%22%7D)

## exp2()

The base-2 exponential function of x, which is 2 raised to the power x: 2^x.

### Arguments

| **Name** | **Type**    | **Required or Optional** | **Description**        |
| -------- | ----------- | ------------------------ | ---------------------- |
| x        | real number | Required                 | Value of the exponent. |

### Returns

* Exponential value of x.
* For natural (base-2) logarithms, see [log2()](/apl/scalar-functions/mathematical-functions#log2\(\)).
* For exponential functions of base-e and base-10 logarithms, see [exp()](/apl/scalar-functions/mathematical-functions#exp\(\)), [exp10()](/apl/scalar-functions/mathematical-functions#exp10\(\))

### Examples

```kusto
exp2(x)
```

```kusto
| project base_2_exponential_value = exp2(req_duration_ms)
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20base_2_exponential_value%20%3D%20exp2%28req_duration_ms%29%22%7D)

## gamma()

Computes [gamma function](https://en.wikipedia.org/wiki/Gamma_function)

### Arguments

* x: Parameter for the gamma function

### Returns

* Gamma function of x.
* For computing log-gamma function, see loggamma().

### Examples

```kusto
gamma(x)
```

```kusto
gamma(4) == 6
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20gamma_function%20%3D%20gamma%284%29%22%7D)

## isinf()

Returns whether input is an infinite (positive or negative) value.

### Example

```kusto
isinf(x)
```

```kusto
isinf(45.56) == false
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20infinite_value%20%3D%20isinf%2845.56%29%22%7D)

### Arguments

x: A real number.

### Returns

A non-zero value (true) if x is a positive or negative infinite; and zero (false) otherwise.

## isnan()

Returns whether input is Not-a-Number (NaN) value.

### Arguments

x: A real number.

### Returns

A non-zero value (true) if x is NaN; and zero (false) otherwise.

### Examples

```kusto
isnan(x)
```

```kusto
isnan(45.56) == false
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20nan%20%3D%20isnan%2845.56%29%22%7D)

## log()

log() returns the natural logarithm function.

### Arguments

| **Name** | **Type** | **Required or Optional** | **Description**    |
| -------- | -------- | ------------------------ | ------------------ |
| x        | real     | Required                 | A real number > 0. |

### Returns

The natural logarithm is the base-e logarithm: the inverse of the natural exponential function (exp).
null if the argument is negative or null or can’t be converted to a real value.

### Examples

```kusto
log(x)
```

```kusto
log(1) == 0
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20natural_log%20%3D%20log%281%29%22%7D)

## log10()

log10() returns the common (base-10) logarithm function.

### Arguments

| **Name** | **Type** | **Required or Optional** | **Description**    |
| -------- | -------- | ------------------------ | ------------------ |
| x        | real     | Required                 | A real number > 0. |

### Returns

The common logarithm is the base-10 logarithm: the inverse of the exponential function (exp) with base 10.
null if the argument is negative or null or can’t be converted to a real value.

### Examples

```kusto
log10(x)
```

```kusto
log10(4) == 0.6020599913279624
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20base10%20%3D%20log10%284%29%22%7D)

## log2()

log2() returns the base-2 logarithm function.

### Arguments

| **Name** | **Type** | **Required or Optional** | **Description**    |
| -------- | -------- | ------------------------ | ------------------ |
| x        | real     | Required                 | A real number > 0. |

### Returns

The logarithm is the base-2 logarithm: the inverse of the exponential function (exp) with base 2.
null if the argument is negative or null or can’t be converted to a real value.

### Examples

```kusto
log2(x)
```

```kusto
log2(6) == 2.584962500721156
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20base2_log%20%3D%20log2%286%29%22%7D)

## loggamma()

Computes log of absolute value of the [gamma function](https://en.wikipedia.org/wiki/Gamma_function)

### Arguments

x: Parameter for the gamma function

### Returns

* Returns the natural logarithm of the absolute value of the gamma function of x.

### Examples

````kusto
loggamma(x)

```kusto
loggamma(16) == 27.89927138384089
````

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20gamma_function%20%3D%20loggamma%2816%29%22%7D)

## not()

Reverses the value of its bool argument.

### Examples

```kusto
not(expr)
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20reverse%20%3D%20not%28false%29%22%7D)

### Arguments

| **Name** | **Type** | **Required or Optional** | **Description**                     |
| -------- | -------- | ------------------------ | ----------------------------------- |
| Expr     | bool     | Required                 | A `bool` expression to be reversed. |

### Returns

Returns the reversed logical value of its bool argument.

## pi()

Returns the constant value of Pi.

### Returns

* The double value of Pi (3.1415926...)

### Examples

```kusto
pi()
```

```kusto
['sample-http-logs']
| project pie = pi()
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20pie%20%3D%20pi%28%29%22%7D)

## pow()

Returns a result of raising to power

### Examples

```kusto
pow(base, exponent )
```

```kusto
pow(2, 6) == 64
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20power%20%3D%20pow%282%2C%206%29%22%7D)

### Arguments

* *base:* Base value.
* *exponent:* Exponent value.

### Returns

Returns base raised to the power exponent: base ^ exponent.

## radians()

Converts angle value in degrees into value in radians, using formula `radians = (PI / 180 ) * angle_in_degrees`

### Arguments

| **Name** | **Type** | **Required or Optional** | **Description**                   |
| -------- | -------- | ------------------------ | --------------------------------- |
| a        | real     | Required                 | Angle in degrees (a real number). |

### Returns

The corresponding angle in radians for an angle specified in degrees.

### Examples

```kusto
radians(a)
```

```kusto
radians(60) == 1.0471975511965976
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20radians%20%3D%20radians%2860%29%22%7D)

## round()

Returns the rounded source to the specified precision.

### Arguments

* source: The source scalar the round is calculated on.
* Precision: Number of digits the source will be rounded to.(default value is 0)

### Returns

The rounded source to the specified precision.

### Examples

```kusto
round(source [, Precision])
```

```kusto
round(25.563663) == 26
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20rounded_value%20%3D%20round%2825.563663%29%22%7D)

## sign()

Sign of a numeric expression

### Examples

```kusto
sign(x)
```

```kusto
sign(25.563663) == 1
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20numeric_expression%20%3D%20sign%2825.563663%29%22%7D)

### Arguments

* x: A real number.

### Returns

* The positive (+1), zero (0), or negative (-1) sign of the specified expression.

## sin()

Returns the sine function.

### Examples

```kusto
sin(x)
```

```kusto
sin(25.563663) == 0.41770848373492825
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20sine_function%20%3D%20sin%2825.563663%29%22%7D)

### Arguments

| **Name** | **Type** | **Required or Optional** | **Description** |
| -------- | -------- | ------------------------ | --------------- |
| x        | real     | Required                 | A real number.  |

### Returns

The result of sin(x)

## sqrt()

Returns the square root function.

### Examples

```kusto
sqrt(x)
```

```kusto
sqrt(25.563663) == 5.0560521160288685
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20squareroot%20%3D%20sqrt%2825.563663%29%22%7D)

### Arguments

| **Name** | **Type** | **Required or Optional** | **Description**     |
| -------- | -------- | ------------------------ | ------------------- |
| x        | real     | Required                 | A real number >= 0. |

### Returns

* A positive number such that \_sqrt(x) \_ sqrt(x) == x\*
* null if the argument is negative or cannot be converted to a real value.

## tan()

Returns the tangent function.

### Examples

```kusto
tan(x)
```

```kusto
tan(25.563663) == 0.4597371460602336
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20tangent_function%20%3D%20tan%2825.563663%29%22%7D)

### Argument

| **Name** | **Type** | **Required or Optional** | **Description** |
| -------- | -------- | ------------------------ | --------------- |
| x        | real     | Required                 | A real number.  |

### Returns

* The result of `tan(x)`

## exp10()

The base-10 exponential function of x, which is 10 raised to the power x: 10^x.

### Examples

```kusto
exp10(x)
```

```kusto
exp10(25.563663) == 36,615,333,994,520,800,000,000,000
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20base_10_exponential%20%3D%20pow%2810%2C%2025.563663%29%22%7D)

### Arguments

| **Name** | **Type** | **Required or Optional** | **Description**                       |
| -------- | -------- | ------------------------ | ------------------------------------- |
| x        | real     | Required                 | A real number, value of the exponent. |

### Returns

* Exponential value of x.
* For natural (base-10) logarithms, see [log10()](/apl/scalar-functions/mathematical-functions#log10\(\)).
* For exponential functions of base-e and base-2 logarithms, see [exp()](/apl/scalar-functions/mathematical-functions#exp\(\)), [exp2()](/apl/scalar-functions/mathematical-functions#exp2\(\))

## isint()

Returns whether input is an integer (positive or negative) value.

### Arguments

* Expr: expression value which can be a real number

### Returns

A non-zero value (true) if expression is a positive or negative integer; and zero (false) otherwise.

### Examples

```kusto
isint(expression)
```

```kusto
isint(resp_body_size_bytes) == true 
```

```kusto
isint(25.563663) == false
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20integer_value%20%3D%20isint%2825.563663%29%22%7D)

## isfinite()

Returns whether input is a finite value (is neither infinite nor NaN).

### Arguments

* number: A real number.

### Returns

A non-zero value (true) if x is finite; and zero (false) otherwise.

### Examples

```kusto
isfinite(number)
```

```kusto
isfinite(25.563663) == true
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B%27sample-http-logs%27%5D%5Cn%7C%20project%20isfinite_value%20%3D%20isfinite%2825.563663%29%22%7D)