Mathematical functions

Learn how to use and combine different mathematical functions in APL

Mathematical functions

Function 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.
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.
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.
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.
sign()	Sign of a numeric expression.
sin()	Returns the sine function.
sqrt()	Returns the square root function.
tan()	Returns the tangent function.
exp10()	The base-10 exponential function of x, which is 10 raised to the power x: 10^x.
isint()	Returns whether input is an integer (positive or negative) value
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

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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