Version: 23.4

# Arithmetic Calculations in SenseTalk

You can perform mathematical operations in SenseTalk by using mathematical operators as well as a variety of commands and functions. For detailed information about using operators, see the Expressions page, which describes the basics of using expressions in SenseTalk and links to pages for specific mathematical operators (+, -, *, and other operators) and other useful concepts such as comparisons and logical operators.

SenseTalk's arithmetic commands and functions also provide useful tools for working with numbers. Arithmetic Commands can be used to modify numeric values stored in containers. These commands perform the same arithmetic functions as the +, -, *, and / operators. The difference is that these commands take one of their operands from a container and store the result of the calculation back into that container. Arithmetic Functions operate on numbers. You can use these functions to manipulate numbers in a variety of ways.

In a topic related to arithmetic calculations, Points and Rectangles describes how SenseTalk understands the concepts of geometric points and rectangles. Any list of two numbers, or a text string consisting of two numbers separated by a comma, can be treated as a point. The functions explained on the Points and Rectangles page can be used to extract the various component values of a point or rectangle.

## Arithmetic Commands​

There are four arithmetic commands:

Use them to modify values stored in containers. These commands perform the same arithmetic functions as the +, -, *, and / operators. The difference is that these commands take one of their operands from a container and store the result of the calculation back into that container.

### `Add` Command​

Behavior: Use the `add` command when you want to add a number to the value in a container, replacing the value in the container by the sum. Lists of values can be added, provided that both the source and destination lists contain the same number of items. Each item from the source list is added to the corresponding item of the destination container. NumExpr is a source expression. It can be a number, any formula, or another container. Chunk is a chunk expression describing part of a container (lines, words, items, or characters). Container is any container.

Syntax:
add numExpr to {chunk of} container

#### Examples​

``add amount to dollarsVariableadd 37 to item 2 of line 3 of scoresadd speed * time to item 1 of distancesadd [10,5] to centerPoint``

Related:

### `Subtract` Command​

Behavior: Use the `subtract` command when you want to subtract a number from the value in a container, replacing the value in the container by the result. Lists of values can be subtracted, provided that both the source and destination lists contain the same number of items. Each item from the source list is subtracted from the corresponding item of the destination container. NumExpr is a source expression. It can be a number, any formula, or another container. Chunk is a chunk expression describing part of a container (lines, words, items, or characters). Container is any container.

Syntax:
subtract numExpr from {chunk of} container

#### Examples​

``subtract checkAmt from accountBalancesubtract 1 from property CountDown of gameControllersubtract rate * pmt from line 4 of amortizationsubtract [1,2] from boxDimensions``

Related:

### `Multiply` Command​

Behavior: Use the `multiply` command when you want to multiply a value in a container by another number, replacing the value in the container by the product. Lists of values can be multiplied, provided that both the source and destination lists contain the same number of items, or that the source is a single value. Each item in the destination container is multiplied by the corresponding item of the source list, or by the source value. NumExpr is a source expression. It can be a number, any formula, or another container. Chunk is a chunk expression describing part of a container (lines, words, items, or characters). Container is any container.

Syntax:
multiply {chunk of} container by numExpr

#### Examples​

``multiply score by weightingFactormultiply accountBalance by 1 + interestRatemultiply item 3 of line x of table by 2``

Related:

### `Divide` Command​

Behavior: Use the `divide` command when you want to divide a value in a container by another number, replacing the value in the container by the quotient. Lists of values can be divided, provided that both the source and destination lists contain the same number of items, or that the source is a single value. Each item in the destination container is divided by the corresponding item of the source list, or by the source value. NumExpr is a source expression. It can be a number, any formula, or another container. Chunk is a chunk expression describing part of a container (lines, words, items, or characters). Container is any container.

Syntax:
divide {chunk of} container by numExpr

#### Examples​

``divide score by totalCountdivide item 1 of balances by 12``

Related:

## Arithmetic Functions​

Use these functions to manipulate numbers.

### `Abs`, `As a positive number`, `As a negative number` Functions​

Behavior: Returns the absolute value of its numeric parameter. The absolute value is the magnitude of a number regardless of its sign — it is always positive or zero. `As a positive number` returns the absolute value. `As a negative number` returns the negative absolute value.

Syntax:
abs( numExpr )
the abs of numFactor
numFactor as a positive number
numFactor as a negative number

#### Examples​

``put abs(-11) --> 11put the abs of -11 --> 11``

#### Example​

``if height is a negative number then put abs(height) into height``

#### Examples​

``put (3 - 16) as a positive number --> 13put 500 as a negative number --> -500``

### `ACos` Function​

Behavior: Calculates the trigonometric arc cosine of a value and returns the result as an angle expressed in radians.

Syntax:
acos( numExpr )
{the} acos of numFactor

#### Examples​

``put acos(0) --> 1.570796 radiansput the acos of 0 --> 1.570796 radiansput acos(0.5) as degrees --> 60 degrees``

Related:

### `ACosh` Function​

Behavior: Calculates the inverse hyperbolic cosine of a value and returns the result as an angle expressed in radians.

Syntax:
acosh( numExpr )
{the} acosh of numFactor

#### Examples​

``put acosh(2.509178) rounded to the nearest degree --> 90 degreesput the acosh of 1 --> 0 radians``

Related:

### `Annuity` Function​

Behavior: Calculates the present value of an ordinary annuity with payments of one unit, based on the specified interest rate per period and the number of periods.

Syntax:
annuity( interest, periods )

#### Example​

``put annuity(1%, 32) --> 27.269589``

Related:

### `ASin` Function​

Behavior: Calculates the trigonometric arc sine of a value and returns the result as an angle expressed in radians.

Syntax:
asin( numExpr )
{the} asin of numFactor

#### Examples​

``put asin(0) --> 0 radiansput asin of 1 --> 1.570796 radiansput asin(0.5) as degrees --> 30 degrees``

Related:

### `ASinh` Function​

Behavior: Calculates the inverse hyperbolic sine of a value and returns the result as an angle expressed in radians.

Syntax:
asinh( numExpr )
{the} asinh of numFactor

#### Examples​

``put asinh(0) --> 0 radiansput the asinh of 2.301299 rounded to the nearest degree --> 90 degrees``

Related:

### `ATan` Function​

Behavior: Returns the trigonometric arctangent of its parameter as an angle expressed in radians.

Syntax:
atan( numExpr )
the atan of numFactor

#### Examples​

``put atan(19) --> 1.518213 radiansput the atan of 5 --> 1.373401 radians``

Related:

### `ATanh` Function​

Behavior: Calculates the inverse hyperbolic tangent of a value and returns the result as an angle expressed in radians.

Syntax:
atanh( numExpr )
{the} atanh of numFactor

#### Examples​

``put atanh(0.917152) rounded to the nearest degree --> 90 degreesput the atanh of 0 --> 0 radians``

Related:

### `ATanPt` Function​

Behavior: Calculates the trigonometric arc tangent of a point and returns the result as an angle expressed in radians.

Syntax:
atanPt( aPoint )
atanPt( xCoord , yCoord )
{the} atanPt of aPoint

note

The `atanPt` function provides the same functionality as the atan2 function in other languages, but accepts either a point, or coordinates in x,y order as parameters, rather than y,x.

#### Examples​

``put atanPt(123,0) --> 0 radiansput the atanPt of [11,56] --> 1.376837 radians``

#### Example​

``set myPoint to [50,50]put atanPt(myPoint) as degrees --> 45 degrees``

Related:

### `Average` Function​

Behavior: Returns the average of its parameters.

Syntax:
average( numList )
{the} average of numList

The parameter numList may be a list of numbers, an expression which evaluates to a list of numbers separated by commas, or a combination of these, nested to any depth.

#### Examples​

``put average(8, 10, 12) --> 10put the average of [3,7,15,84,6,42,11] --> 24``

#### Example​

note

This example is an incomplete portion of code meant to illustrate how the feature may be used

``if the average of [x,y,z] is greater than z then  put "Z is below average!"end if``

Related:

### `Compound` Function​

Behavior: Computes the principal plus accrued interest on an investment of 1 unit, based on the specified interest rate and the number of periods.

Syntax:
compound( interest, periods )

#### Example​

``put compound(7.25%, 6) --> 1.521892``

#### Example​

``put 10 into initialinvestmentput initialInvestment * compound(6.7%, 12) into currentValueput currentvalue --> 21.775746``

Related:

### `Cos` Function​

Behavior: Returns the trigonometric cosine of its parameter, which is an angle expressed in radians.

Syntax:
cos( numExpr )
{the} cos of numFactor

#### Examples​

``put cos(18) --> 0.660317put the cos of 18 --> 0.660317``

Related:

### `Cosh` Function​

Behavior: Returns the hyperbolic cosine of its parameter, which is an angle expressed in radians.

Syntax:
cosh( numExpr )
{the} cosh of numFactor

#### Examples​

``put cosh(0) --> 1  (no units specified, so 0 radians assumed)put cosh of 90 degrees --> 2.509178``

Related:

### `Cube Root`, `CbRt` Function​

Behavior: Computes the cube root of its parameter.

Syntax:
cube root( number )
{the} cube root of number
cbrt( numExpr )

#### Examples​

``put cube root (27) --> 3put the cube root of 8 --> 2put cbrt(125) --> 5``

Related:

### `Exp` Function​

Behavior: Returns the natural exponential of its parameter (that is, the mathematical constant e raised to the power of the parameter).

Syntax:
exp( numExpr )
{the} exp of numFactor

#### Examples​

``put exp(2) --> 7.389056put the exp of 1 --> 2.718282``

Related:

### `Exp1` Function​

Behavior: Returns one less than the natural exponential of its parameter (that is, the mathematical constant e raised to the power of the parameter, minus 1).

Syntax:
exp1( numExpr )
{the} exp1 of numFactor

#### Examples​

``put exp1(2) --> 6.389056put the exp1 of 2 --> 6.389056``

Related:

### `Exp2` Function​

Behavior: Returns 2 raised to the power of its parameter.

Syntax:
exp2( numExpr )
{the} exp2 of numFactor

#### Examples​

``put exp2(8) --> 256put exp2 of 10 --> 1024``

Related:

### `Frac` Function​

Behavior: Returns the fractional part of a number. Use the `trunc` function to get the whole number part of a value. The `trunc` and `frac` functions are defined such that `trunc(x) + frac(x)` is always equal to `x`.

Syntax:
frac( numExpr )
{the} frac of numFactor

#### Examples​

``put frac(81.236) --> 0.236put frac of 8.125 --> 0.125``

Related:

### `Ln` Function​

Behavior: Returns the natural logarithm of its parameter.

Syntax:
ln( numExpr )
{the} ln of numFactor

#### Examples​

``put ln(2) --> 0.693147put the ln of 4 --> 1.386294``

Related:

### `Ln1` Function​

Behavior: Returns the natural logarithm of 1 more than its parameter.

Syntax:
ln1( numExpr )
{the} ln1 of numFactor

#### Examples​

``put ln1(2) --> 1.098612put the ln1 of 8 --> 2.197225``

Related:

### `Log10` Function​

Behavior: Returns the base 10 logarithm of its parameter.

Syntax:
log10( numExpr )
{the} log10 of numFactor

#### Examples​

``put log10(100) --> 2put the log10 of one million --> 6``

Related:

### `Log2` Function​

Behavior: Returns the base 2 logarithm of its parameter.

Syntax:
log2( numExpr )
{the} log2 of numFactor

#### Examples​

``put log2(256) --> 8put the log2 of 8 --> 3``

Related:

### `Maximum`, `Max`, `HighestValue`, `LargestValue` Functions​

Behavior: Returns the highest number from a list. The `maximum` function may be abbreviated as `max` or expressed using one of the synonyms `highestValue` or `largestValue`.

Syntax:
[max | maximum | highestValue | largestValue]( numList )
{the} [max | maximum | highest value | largest value] of numList

The parameter numList may be a list of numbers, an expression which evaluates to a list of numbers separated by commas, or a combination of these, nested to any depth.

#### Examples​

``put max(4, 6, 5, 7, 3) --> 7put largestValue of [2,23,45,76] --> 76put the highest value of [3,42,9,13,21] --> 42``

#### Example​

note

This example is an incomplete portion of code meant to illustrate how the feature may be used

``if the maximum of [x,y,z] is z then  put "Z is the greatest!"end if``

Related:

### `Median` Function​

Behavior: Returns the median (middle value) of its parameters when arranged in numeric order, or the average of the two middle values.

Syntax:
median( numList )
{the} median of numList

The parameter numList may be a list of numbers, an expression which evaluates to a list of numbers separated by commas, or a combination of these, nested to any depth. If numList contains an odd number of numbers, the median is the middle value of the sorted list of numbers, otherwise it is the average of the two middle values.

#### Examples​

``put median(1, 2, 8, 9, 12) --> 8put the median of "2,7,8,10" --> 7.5``

Related:

### `Minimum`, `Min`, `LowestValue`, `SmallestValue` Functions​

Behavior: Returns the lowest number from a list. The `minimum` function may be abbreviated as `min` or given as one of the synonyms `lowestValue` or `smallestValue`.

Syntax:
[min | minimum | lowestValue | smallestValue]( numList )
{the} [min | minimum | lowest value | smallest value] of numList

The parameter numList may be a list of numbers, an expression which evaluates to a list of numbers separated by commas, or a combination of these, nested to any depth.

#### Examples​

``put min(4,6,5,7,3) --> 3put lowestValue of [3,9,13,21,42] --> 3put smallest value of [9,13,21,56,72] --> 9``

#### Example​

note

This example is an incomplete portion of code meant to illustrate how the feature may be used

``if the min of [x,y,z] is z then put "Z is the smallest!"``

Related:

### `Payment` Function​

Behavior: Returns the payment amount of a loan, given a loan amount, interest rate, term, and frequency of payments.

Syntax:
payment( loanProperties )
payment( principal, rate, term {, frequency} )

{the} {daily | weekly | monthly | quarterly | yearly | annual} payment on {a} {loan of} principal {loan} at {a rate of} rate {interest} for {a term of} term { {with} [ [payments | paid] frequency | frequency payments] }

If loanProperties is given as a property list, it should include:

• Principal or Amountprincipal amount of the loan (may be specified with a currency unit)
• Rate — interest rate of the loan (may be specified as percent per year, calendarQuarter, month, week, day — if per period is not specified, annual interest rate is assumed)
• Term — the term length of the loan (may be given as a duration of time or as a number of payments. If a number of payments is used (with no duration units), then frequency parameter is required)
• Frequency — the frequency of loan payments (optional if loan term is given as a duration) — may be one of these terms: monthly, months, calendarMonths, quarterly, calendarQuarters, annual, annually, yearly, years, calendarYears, decades, calendarDecades

If the principal is given in units of a particular currency, then the payment amount returned will have the same units. If term is specified with units of duration and frequency is omitted, then the term's units will be used as the frequency of payments.

#### Examples​

``put payment(\$10000,7.5%,60,"months") --> \$200.379486put payment(amount:\$1000, rate: 6.5% per year, term:60 months) --> \$19.566148``

#### Examples​

``put the monthly payment on a ten thousand dollar loan at 4.5% yearly for 10 years --> \$103.638409put payment on a loan of \$50000 at 7 percent interest for 60 months rounded to 2 places --> \$990.06``

Related:

### `Random` Function​

Behavior: Returns a randomly generated integer between 1 and the value of its parameter, or between two values, inclusive.

Syntax:
random( numExpr {, secondExpr} )
{the} random of numFactor

#### Examples​

``put random(12) -- returns any number from 1 to 12put random(20,30) -- gets a number from 20 to 30, inclusiveput (random(100) / 100) into randomPercentage``

Related:

### `Reset Random` Command​

Behavior: Resets the random number generator sequence used by the `random` function and whenever SenseTalk selects things at random. By setting a specific seedExpr value for the random number generator, you can obtain a repeatable sequence of "random" events. This can be very useful for testing purposes. Use the `reset random` command without a seed value to get an unpredictable sequence.

Syntax:
reset random {{with | from} {seed} seedExpr}

#### Example​

``reset random with seed 27``

#### Example​

``reset random``

#### Example​

``reset random 2repeat 10 times  put 1..10 into NumberRange  put any item of NumberRange into ReplaceitemNumber  log ReplaceitemNumber // Using reset random [#] as shown in line 1 results in the same list every time you run the loop.[#] can be any seed number.  // Commenting out "reset random 2" in line 1 and running the repeat loop multiple times results in a different list every time you run the loop.end repeat``

Related:

### `Round` Function​

Behavior: Returns the value of its parameter rounded to the nearest whole number. An optional second parameter may be supplied to specify the number of decimal places to round to. A negative number of places will round to the left of the decimal point.

Syntax:
round( numExpr {, decimalPlaces} )
{the} round of numFactor

#### Examples​

``put round(6.5) --> 7put round(6.49) --> 6put round(6.49 , 1) --> 6.5put round(2389 , -2) --> 2400``

Related:

### `RoundToNearest` Function​

Behavior: Returns the value of its first parameter rounded to the nearest whole multiple of its second parameter.

Syntax:
roundToNearest( numExpr, nearestMultiple )
numExpr rounded to {the} nearest {multiple of} nearestMultiple

#### Examples​

``put roundToNearest(643,100) --> 600put roundToNearest(643,25) --> 650put 12.16 rounded to the nearest multiple of .25 --> 12.25``

Related:

### `Sin` Function​

Behavior: Returns the trigonometric sine of its parameter, which is an angle expressed in radians.

Syntax:
sin( numExpr )
{the} sin of numFactor

#### Examples​

``put sin(18) --> -0.750987put the sin of 8 --> 0.989358``

Related:

### `Sinh` Function​

Behavior: Returns the hyperbolic sine of its parameter, which is an angle expressed in radians.

Syntax:
sinh( numExpr )
{the} sinh of numFactor

#### Examples​

``put sinh(0) --> 0  (no units specified, so 0 radians assumed)put sinh of 90 degrees --> 2.301299``

Related:

### `Square Root` , `SqRt` Function​

Behavior: Returns the square root of its parameter.

Syntax:
sqrt( numExpr )
{the} [square root | sqrt] of numFactor

#### Examples​

``put sqrt(16) --> 4put the square root of nine --> 3``

Related:

### `Sum` Function​

Behavior: Returns the sum of its parameters.

Syntax:
sum( numList )
{the} sum of numList

The parameter numList may be a list of numbers, an expression which evaluates to a list of numbers separated by commas, or a combination of these, nested to any depth.

#### Example​

``put sum("8,1", [10,11], 12) --> 42``

#### Example​

note

This example does not run as written and must be modified to execute

``if the sum of [x,y,z] is more than 100 then  put "The sum exceeds 100"end if``

Related:

### `Tan` Function​

Behavior: Returns the trigonometric tangent of its parameter, which is an angle expressed in radians.

Syntax:
tan( numExpr )
{the} tan of numFactor

#### Examples​

``put tan(18) --> -1.137314put tan of 10 --> 0.648361``

Related:

### `Tanh` Function​

Behavior: Returns the hyperbolic tangent of its parameter, which is an angle expressed in radians.

Syntax:
tanh( numExpr )
{the} tanh of numFactor

#### Examples​

``put tanh(0) --> 0  (no units specified, so 0 radians assumed)put tanh of 90 degrees --> 0.917152``

Related:

### `Trunc` Function​

Behavior: Truncates a number, returning the integer part of its parameter, and discarding any fractional part. Use the `frac` function to get the fractional part of a value. The `trunc` and `frac` functions are defined such that `trunc(x) + frac(x)` is always equal to `x`.

Syntax:
trunc( numExpr )
{the} trunc of numFactor

#### Examples​

``put trunc(6.8) --> 6put trunc(6.49) --> 6``

Related: