Mathematical functions

Learn how to use and combine different mathematical functions in APL

The table summarizes the mathematical functions available in APL.

Name	Description
abs	Calculates the absolute value of the input.
acos	Returns the angle whose cosine is the specified number (the inverse operation of cos()).
asin	Returns the angle whose sine is the specified number (the inverse operation of sin()).
atan	Returns the angle whose tangent is the specified number (the inverse operation of tan()).
atan2	Calculates the angle, in radians, between the positive x-axis and the ray from the origin to the point (y, x).
cos	Returns the cosine function.
degrees	Converts angle value in radians into value in degrees, using formula degrees = (180 / PI) * angle-in-radians.
exp	The base-e exponential function of x, which is e raised to the power x: e^x.
exp10	The base-10 exponential function of x, which is 10 raised to the power x: 10^x.
exp2	The base-2 exponential function of x, which is 2 raised to the power x: 2^x.
gamma	Computes gamma function.
isinf	Returns whether input is an infinite (positive or negative) value.
isint	Returns whether input is an integer (positive or negative) value
isnan	Returns whether input is Not-a-Number (NaN) value.
log	Returns the natural logarithm function.
log10	Returns the common (base-10) logarithm function.
log2	Returns the base-2 logarithm function.
loggamma	Computes log of absolute value of the gamma function.
max_of	Returns the largest of the provided values.
min_of	Returns the smallest of the provided values.
not	Reverses the value of its bool argument.
pi	Returns the constant value of Pi (π).
pow	Returns a result of raising to power.
radians	Converts angle value in degrees into value in radians, using formula radians = (PI / 180) * angle-in-degrees.
round	Returns the rounded source to the specified precision.
set_difference	Returns the difference between two arrays.
set_has_element	Determines if a set contains a specific value.
set_intersect	Returns the intersection of two arrays.
set_union	Returns the union of two arrays.
sign	Sign of a numeric expression.
sin	Returns the sine function.
sqrt	Returns the square root function.
tan	Returns the tangent function.

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

abs(x)

abs(80.5) == 80.5

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

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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

acos(x)

acos(-1) == 3.141592653589793

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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

asin(x)

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

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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

atan(x)

atan(-1) == -0.7853981633974483

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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

atan2(y,x)

atan2(-1, 1) == -0.7853981633974483

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cos

Returns the cosine function.

Arguments

x: A real number.

Returns

The result of cos(x)

Examples

cos(x)

cos(-1) == 0.5403023058681398

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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

degrees(a)

degrees(3.14) == 179.9087476710785

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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.
• For exponential functions of base-2 and base-10 logarithms, see exp2, exp10

Examples

exp(x)

exp(1) == 2.718281828459045

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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.
• For exponential functions of base-e and base-10 logarithms, see exp, exp10

Examples

exp2(x)

| project base_2_exponential_value = exp2(req_duration_ms)

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gamma

Computes gamma function

Arguments

• x: Parameter for the gamma function

Returns

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

Examples

gamma(x)

gamma(4) == 6

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isinf

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

Example

isinf(x)

isinf(45.56) == false

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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

isnan(x)

isnan(45.56) == false

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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

log(x)

log(1) == 0

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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

log10(x)

log10(4) == 0.6020599913279624

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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

log2(x)

log2(6) == 2.584962500721156

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loggamma

Computes log of absolute value of the 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

loggamma(x)

```kusto
loggamma(16) == 27.89927138384089

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not

Reverses the value of its bool argument.

Examples

not(expr)

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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

pi()

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

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pow

Returns a result of raising to power

Examples

pow(base, exponent )

pow(2, 6) == 64

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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

radians(a)

radians(60) == 1.0471975511965976

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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

round(source [, Precision])

round(25.563663) == 26

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sign

Sign of a numeric expression

Examples

sign(x)

sign(25.563663) == 1

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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

sin(x)

sin(25.563663) == 0.41770848373492825

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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

sqrt(x)

sqrt(25.563663) == 5.0560521160288685

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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

tan(x)

tan(25.563663) == 0.4597371460602336

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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

exp10(x)

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

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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.
• For exponential functions of base-e and base-2 logarithms, see exp, 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

isint(expression)

isint(resp_body_size_bytes) == true 

isint(25.563663) == false

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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

isfinite(number)

isfinite(25.563663) == true

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