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# 5 Mathematical functions

All functions listed here are supported in:

Mathematical functions are supported with float and integer value types, unless stated otherwise.

Some general notes on function parameters:

• Function parameters are separated by a comma
• Expressions are accepted as parameters
• Optional function parameters (or parameter parts) are indicated by `<` `>`
FUNCTION
abs (value)
The absolute value of a value. value - value to check Supported value types: float, int, str, text, log

For strings returns:
0 - values are equal
1 - values differ

Example:
=> abs(last(/host/key))>10

Absolute numeric difference will be calculated, as seen with these incoming example values ('previous' and 'latest' value = absolute difference):
'1' and '5' = `4`
'3' and '1' = `2`
'0' and '-2.5' = `2.5`
acos (value)
The arccosine of a value as an angle, expressed in radians. value - value to check The value must be between -1 and 1.

For example, the arccosine of a value '0.5' will be '2.0943951'.

Example:
=> acos(last(/host/key))
asin (value)
The arcsine of a value as an angle, expressed in radians. value - value to check The value must be between -1 and 1.

For example, the arcsine of a value '0.5' will be '-0.523598776'.

Example:
=> asin(last(/host/key))
atan (value)
The arctangent of a value as an angle, expressed in radians. value - value to check For example, the arctangent of a value '1' will be '0.785398163'.

Example:
=> atan(last(/host/key))
atan2 (value,abscissa)
The arctangent of the ordinate (exprue) and abscissa coordinates specified as an angle, expressed in radians. value - value to check
abscissa - abscissa value
For example, the arctangent of the ordinate and abscissa coordinates of a value '1' will be '2.21429744'.

Example:
=> atan2(last(/host/key),2)
avg (<value1>,<value2>,...)
Average value of the referenced item values. valueX - value returned by one of history functions Example:
=> avg(avg(/host/key),avg(/host2/key2))
cbrt (value)
Cube root of a value. value - value to check For example, the cube root of '64' will be '4', of '63' will be '3.97905721'.

Example:
=> cbrt(last(/host/key))
ceil (value)
Round the value up to the nearest greater integer. value - value to check For example, '2.4' will be rounded up to '3'.

Example:
=> ceil(last(/host/key))

cos (value)
The cosine of a value, where the value is an angle expressed in radians. value - value to check For example, the cosine of a value '1' will be '0.54030230586'.

Example:
=> cos(last(/host/key))
cosh (value)
The hyperbolic cosine of a value. value - value to check For example, the hyperbolic cosine of a value '1' will be '1.54308063482'.

Returns value as a real number, not as scientific notation.

Example:
=> cosh(last(/host/key))
cot (value)
The cotangent of a value, where the value is an angle, expressed in radians. value - value to check For example, the cotangent of a value '1' will be '0.54030230586'.

Example:
=> cot(last(/host/key))
degrees (value)
Converts a value from radians to degrees. value - value to check For example, a value '1' converted to degrees will be '57.2957795'.

Example:
=> degrees(last(/host/key))
e
Euler's number (2.718281828459045). Example:
=> e()
exp (value)
Euler's number at a power of a value. value - value to check For example, Euler's number at a power of a value '2' will be '7.38905609893065'.

Example:
=> exp(last(/host/key))
expm1 (value)
Euler's number at a power of a value minus 1. value - value to check For example, Euler's number at a power of a value '2' minus 1 will be '6.38905609893065'.

Example:
=> expm1(last(/host/key))
floor (value)
Round the value down to the nearest smaller integer. value - value to check For example, '2.6' will be rounded down to '2'.

Example:
=> floor(last(/host/key))

log (value)
Natural logarithm. value - value to check For example, the natural logarithm of a value '2' will be '0.69314718055994529'.

Example:
=> log(last(/host/key))
log10 (value)
Decimal logarithm. value - value to check For example, the decimal logarithm of a value '5' will be '0.69897000433'.

Example:
=> log10(last(/host/key))
max (<value1>,<value2>,...)
Highest value of the referenced item values. valueX - value returned by one of history functions Example:
=> max(avg(/host/key),avg(/host2/key2))
min (<value1>,<value2>,...)
Lowest value of the referenced item values. valueX - value returned by one of history functions Example:
=> min(avg(/host/key),avg(/host2/key2))
mod (value,denominator)
Division remainder. value - value to check
denominator - division denominator
For example, division remainder of a value '5' with division denominator '2' will be '1'.

Example:
=> mod(last(/host/key),2)
pi
Pi constant (3.14159265358979). Example:
=> pi()
power (value,power value)
The power of a value. value - value to check
power value - the Nth power to use
For example, the 3rd power of a value '2' will be '8'.

Example:
=> power(last(/host/key),3)
Convert a value from degrees to radians. value - value to check For example, a value '1' converted to radians will be '0.0174532925'.

Example:
rand
Return a random integer value. A pseudo-random generated number using time as seed (enough for mathematical purposes, but not cryptography).

Example:
=> rand()
round (value,decimal places)
Round the value to decimal places. value - value to check
decimal places - specify decimal places for rounding (0 is also possible)
For example, a value '2.5482' rounded to 2 decimal places will be '2.55'.

Example:
=> round(last(/host/key),2)
signum (value)
Returns '-1' if a value is negative, '0' if a value is zero, '1' if a value is positive. value - value to check Example:
=> signum(last(/host/key))
sin (value)
The sine of a value, where the value is an angle expressed in radians. value - value to check For example, the sine of a value '1' will be '0.8414709848'.

Example:
=> sin(last(/host/key))
sinh (value)
The hyperbolical sine of a value. value - value to check For example, the hyperbolical sine of a value '1' will be '1.17520119364'.

Example:
=> sinh(last(/host/key))
sqrt (value)
Square root of a value. value - value to check This function will fail with a negative value.

For example, the square root of a value '3.5' will be '1.87082869339'.

Example:
=> sqrt(last(/host/key))
sum (<value1>,<value2>,...)
Sum of the referenced item values. valueX - value returned by one of history functions Example:
=> sum(avg(/host/key),avg(/host2/key2))
tan (value)
The tangent of a value. value - value to check For example, the tangent of a value '1' will be '1.55740772465'.

Example:
=> tan(last(/host/key))
truncate (value,decimal places)
Truncate the value to decimal places. value - value to check
decimal places - specify decimal places for truncating (0 is also possible)
Example:
=> truncate(last(/host/key),2)

### Function details

Some general notes on function parameters:

• Function parameters are separated by a comma
• Expressions are accepted as parameters
• Optional function parameters (or parameter parts) are indicated by `<` `>`
##### abs(value)

The absolute value of a value.
Supported value types: Float, Integer, String, Text, Log.
For strings returns: 0 - the values are equal; 1 - the values differ.

Parameter:

• value - the value to check

The absolute numeric difference will be calculated, as seen with these incoming example values ('previous' and 'latest' value = absolute difference): '1' and '5' = `4`; '3' and '1' = `2`; '0' and '-2.5' = `2.5`

Example:

``abs(last(/host/key))>10``
##### acos(value)

The arccosine of a value as an angle, expressed in radians.

Parameter:

• value - the value to check

The value must be between -1 and 1. For example, the arccosine of a value '0.5' will be '2.0943951'.

Example:

``acos(last(/host/key))``
##### asin(value)

The arcsine of a value as an angle, expressed in radians.

Parameter:

• value - the value to check

The value must be between -1 and 1. For example, the arcsine of a value '0.5' will be '-0.523598776'.

Example:

``asin(last(/host/key)) ``
##### atan(value)

The arctangent of a value as an angle, expressed in radians.

Parameter:

• value - the value to check

The value must be between -1 and 1. For example, the arctangent of a value '1' will be '0.785398163'.

Example:

``atan(last(/host/key))``
##### atan2(value,abscissa)

The arctangent of the ordinate (exprue) and abscissa coordinates specified as an angle, expressed in radians.

Parameter:

• value - the value to check;
• abscissa - the abscissa value.

For example, the arctangent of the ordinate and abscissa coordinates of a value '1' will be '2.21429744'.

Example:

``atan(last(/host/key),2)``
##### avg(<value1>,<value2>,...)

The average value of the referenced item values.

Parameter:

• valueX - the value returned by one of the history functions.

Example:

``avg(avg(/host/key),avg(/host2/key2))``
##### cbrt(value)

The cube root of a value.

Parameter:

• value - the value to check

For example, the cube root of '64' will be '4', of '63' will be '3.97905721'.

Example:

``cbrt(last(/host/key))``
##### ceil(value)

Round the value up to the nearest greater or equal integer.

Parameter:

• value - the value to check

For example, '2.4' will be rounded up to '3'. See also floor().

Example:

``ceil(last(/host/key))``
##### cos(value)

The cosine of a value, where the value is an angle expressed in radians.

Parameter:

• value - the value to check

For example, the cosine of a value '1' will be '0.54030230586'.

Example:

``cos(last(/host/key))``
##### cosh(value)

The hyperbolic cosine of a value. Returns the value as a real number, not as scientific notation.

Parameter:

• value - the value to check

For example, the hyperbolic cosine of a value '1' will be '1.54308063482'.

Example:

``cosh(last(/host/key))``
##### cot(value)

The cotangent of a value, where the value is an angle expressed in radians.

Parameter:

• value - the value to check

For example, the cotangent of a value '1' will be '0.54030230586'.

Example:

``cot(last(/host/key))``
##### degrees(value)

Converts a value from radians to degrees.

Parameter:

• value - the value to check

For example, a value '1' converted to degrees will be '57.2957795'.

Example:

``degrees(last(/host/key))``
##### e

The Euler's number (2.718281828459045).

Example:

``e()``
##### exp(value)

The Euler's number at a power of a value.

Parameter:

• value - the value to check

For example, Euler's number at a power of a value '2' will be '7.38905609893065'.

Example:

``exp(last(/host/key))``
##### expm1(value)

The Euler's number at a power of a value minus 1.

Parameter:

• value - the value to check

For example, Euler's number at a power of a value '2' minus 1 will be '6.38905609893065'.

Example:

``expm1(last(/host/key))``
##### floor(value)

Round the value down to the nearest smaller or equal integer.

Parameter:

• value - the value to check

For example, '2.6' will be rounded down to '2'. See also ceil().

Example:

``floor(last(/host/key))``
##### log(value)

The natural logarithm.

Parameter:

• value - the value to check

For example, the natural logarithm of a value '2' will be '0.69314718055994529'.

Example:

``log(last(/host/key))``
##### log10(value)

The decimal logarithm.

Parameter:

• value - the value to check

For example, the decimal logarithm of a value '5' will be '0.69897000433'.

Example:

``log10(last(/host/key))``
##### max(<value1>,<value2>,...)

The highest value of the referenced item values.

Parameter:

• valueX - the value returned by one of the history functions.

Example:

``max(avg(/host/key),avg(/host2/key2))``
##### min(<value1>,<value2>,...)

The lowest value of the referenced item values.

Parameter:

• valueX - the value returned by one of the history functions.

Example:

``min(avg(/host/key),avg(/host2/key2))``
##### mod(value,denominator)

The division remainder.

Parameter:

• value - the value to check;
• denominator - the division denominator.

For example, division remainder of a value '5' with division denominator '2' will be '1'.

Example:

``mod(last(/host/key),2)``
##### pi

The Pi constant (3.14159265358979).

Example:

``pi()``
##### power(value,power value)

The power of a value.

Parameter:

• value - the value to check;
• power value - the Nth power to use.

For example, the 3rd power of a value '2' will be '8'.

Example:

``power(last(/host/key),3)``

Converts a value from degrees to radians.

Parameter:

• value - the value to check

For example, a value '1' converted to radians will be '0.0174532925'.

Example:

``radians(last(/host/key))``
##### rand

Return a random integer value. A pseudo-random generated number using time as seed (enough for mathematical purposes, but not cryptography).

Example:

``rand()``
##### round(value,decimal places)

Round the value to decimal places.

Parameter:

• value - the value to check;
• decimal places - specify decimal places for rounding (0 is also possible).

For example, a value '2.5482' rounded to 2 decimal places will be '2.55'.

Example:

``round(last(/host/key),2)``
##### signum(value)

Returns '-1' if a value is negative, '0' if a value is zero, '1' if a value is positive.

Parameter:

• value - the value to check.

For example, a value '2.5482' rounded to 2 decimal places will be '2.55'.

Example:

``signum(last(/host/key))``
##### sin(value)

The sine of a value, where the value is an angle expressed in radians.

Parameter:

• value - the value to check

For example, the sine of a value '1' will be '0.8414709848'.

Example:

``sin(last(/host/key))``
##### sinh(value)

The hyperbolical sine of a value, where the value is an angle expressed in radians.

Parameter:

• value - the value to check

For example, the hyperbolical sine of a value '1' will be '1.17520119364'.

Example:

``sinh(last(/host/key))``
##### sqrt(value)

The square root of a value.
This function will fail with a negative value.

Parameter:

• value - the value to check

For example, the square root of a value '3.5' will be '1.87082869339'.

Example:

``sqrt(last(/host/key))``
##### sum(<value1>,<value2>,...)

The sum of the referenced item values.

Parameter:

• valueX - the value returned by one of the history functions.

Example:

``sum(avg(/host/key),avg(/host2/key2))``
##### tan(value)

The tangent of a value.

Parameter:

• value - the value to check

For example, the tangent of a value '1' will be '1.55740772465'.

Example:

``tan(last(/host/key))``
##### truncate(value,decimal places)

Truncate the value to decimal places.

Parameter:

• value - the value to check;
• decimal places - specify decimal places for truncating (0 is also possible).

For example, a value '2.5482' truncated to 2 decimal places will be '2.54'.

Example:

``truncate(last(/host/key),2)``
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