TinyMath functions

TinyMath provides a set of functions that can be used with the Canvas expression language to perform complex math calculations. Read on for detailed information about the functions available in TinyMath, including what parameters each function accepts, the return value of that function, and examples of how each function behaves.

Most of the functions accept arrays and apply JavaScript Math methods to each element of that array. For the functions that accept multiple arrays as parameters, the function generally does the calculation index by index.

Any function can be wrapped by another function as long as the return type of the inner function matches the acceptable parameter type of the outer function.

abs( a )

Calculates the absolute value of a number. For arrays, the function will be applied index-wise to each element.

Returns: number | Array.<number>. The absolute value of a. Returns an array with the absolute values of each element if a is an array.

Example

abs(-1) // returns 1
abs(2) // returns 2
abs([-1 , -2, 3, -4]) // returns [1, 2, 3, 4]

add( …​args )

Calculates the sum of one or more numbers/arrays passed into the function. If at least one array of numbers is passed into the function, the function will calculate the sum by index.

Returns: number | Array.<number>. The sum of all numbers in args if args contains only numbers. Returns an array of sums of the elements at each index, including all scalar numbers in args in the calculation at each index if args contains at least one array.

Throws: 'Array length mismatch' if args contains arrays of different lengths

Example

add(1, 2, 3) // returns 6
add([10, 20, 30, 40], 10, 20, 30) // returns [70, 80, 90, 100]
add([1, 2], 3, [4, 5], 6) // returns [(1 + 3 + 4 + 6), (2 + 3 + 5 + 6)] = [14, 16]

cbrt( a )

Calculates the cube root of a number. For arrays, the function will be applied index-wise to each element.

Returns: number | Array.<number>. The cube root of a. Returns an array with the cube roots of each element if a is an array.

Example

cbrt(-27) // returns -3
cbrt(94) // returns 4.546835943776344
cbrt([27, 64, 125]) // returns [3, 4, 5]

ceil( a )

Calculates the ceiling of a number, i.e., rounds a number towards positive infinity. For arrays, the function will be applied index-wise to each element.

Returns: number | Array.<number>. The ceiling of a. Returns an array with the ceilings of each element if a is an array.

Example

ceil(1.2) // returns 2
ceil(-1.8) // returns -1
ceil([1.1, 2.2, 3.3]) // returns [2, 3, 4]

clamp( …​a, min, max )

Restricts value to a given range and returns closed available value. If only min is provided, values are restricted to only a lower bound.

Returns: number | Array.<number>. The closest value between min (inclusive) and max (inclusive). Returns an array with values greater than or equal to min and less than or equal to max (if provided) at each index.

Throws:

• 'Array length mismatch' if a min and/or max are arrays of different lengths
• 'Min must be less than max' if max is less than min

Example

clamp(1, 2, 3) // returns 2
clamp([10, 20, 30, 40], 15, 25) // returns [15, 20, 25, 25]
clamp(10, [15, 2, 4, 20], 25) // returns [15, 10, 10, 20]
clamp(35, 10, [20, 30, 40, 50]) // returns [20, 30, 35, 35]
clamp([1, 9], 3, [4, 5]) // returns [clamp([1, 3, 4]), clamp([9, 3, 5])] = [3, 5]

count( a )

Returns the length of an array. Alias for size.

Returns: number. The length of the array.

Throws: 'Must pass an array' if a is not an array.

Example

count([]) // returns 0
count([-1, -2, -3, -4]) // returns 4
count(100) // returns 1

cube( a )

Calculates the cube of a number. For arrays, the function will be applied index-wise to each element.

Returns: number | Array.<number>. The cube of a. Returns an array with the cubes of each element if a is an array.

Example

cube(-3) // returns -27
cube([3, 4, 5]) // returns [27, 64, 125]

divide( a, b )

Divides two numbers. If at least one array of numbers is passed into the function, the function will be applied index-wise to each element.

Returns: number | Array.<number>. Returns the quotient of a and b if both are numbers. Returns an array with the quotients applied index-wise to each element if a or b is an array.

Throws:

• 'Array length mismatch' if a and b are arrays with different lengths
• 'Cannot divide by 0' if b equals 0 or contains 0

Example

divide(6, 3) // returns 2
divide([10, 20, 30, 40], 10) // returns [1, 2, 3, 4]
divide(10, [1, 2, 5, 10]) // returns [10, 5, 2, 1]
divide([14, 42, 65, 108], [2, 7, 5, 12]) // returns [7, 6, 13, 9]

exp( a )

Calculates e^x where e is Euler’s number. For arrays, the function will be applied index-wise to each element.

Returns: number | Array.<number>. Returns an array with the values of e^x evaluated where x is each element of a if a is an array.

Example

exp(2) // returns e^2 = 7.3890560989306495
exp([1, 2, 3]) // returns [e^1, e^2, e^3] = [2.718281828459045, 7.3890560989306495, 20.085536923187668]

first( a )

Returns the first element of an array. If anything other than an array is passed in, the input is returned.

Returns: *. The first element of a. Returns a if a is not an array.

Example

first(2) // returns 2
first([1, 2, 3]) // returns 1

fix( a )

Calculates the fix of a number, i.e., rounds a number towards 0. For arrays, the function will be applied index-wise to each element.

Returns: number | Array.<number>. The fix of a. Returns an array with the fixes for each element if a is an array.

Example

fix(1.2) // returns 1
fix(-1.8) // returns -1
fix([1.8, 2.9, -3.7, -4.6]) // returns [1, 2, -3, -4]

floor( a )

Calculates the floor of a number, i.e., rounds a number towards negative infinity. For arrays, the function will be applied index-wise to each element.

Returns: number | Array.<number>. The floor of a. Returns an array with the floor of each element if a is an array.

Example

floor(1.8) // returns 1
floor(-1.2) // returns -2
floor([1.7, 2.8, 3.9]) // returns [1, 2, 3]

last( a )

Returns the last element of an array. If anything other than an array is passed in, the input is returned.

Returns: *. The last element of a. Returns a if a is not an array.

Example

last(2) // returns 2
last([1, 2, 3]) // returns 3

log( a, b )

Calculates the logarithm of a number. For arrays, the function will be applied index-wise to each element.

Returns: number | Array.<number>. The logarithm of a. Returns an array with the the logarithms of each element if a is an array.

Throws:

• 'Base out of range' if b ⇐ 0
• 'Must be greater than 0' if a > 0

Example

log(1) // returns 0
log(64, 8) // returns 2
log(42, 5) // returns 2.322344707681546
log([2, 4, 8, 16, 32], 2) // returns [1, 2, 3, 4, 5]

log10( a )

Calculates the logarithm base 10 of a number. For arrays, the function will be applied index-wise to each element.

Returns: number | Array.<number>. The logarithm of a. Returns an array with the the logarithms base 10 of each element if a is an array.

Throws: 'Must be greater than 0' if a < 0

Example

log(10) // returns 1
log(100) // returns 2
log(80) // returns 1.9030899869919433
log([10, 100, 1000, 10000, 100000]) // returns [1, 2, 3, 4, 5]

max( …​args )

Finds the maximum value of one of more numbers/arrays of numbers passed into the function. If at least one array of numbers is passed into the function, the function will find the maximum by index.

Returns: number | Array.<number>. The maximum value of all numbers if args contains only numbers. Returns an array with the the maximum values at each index, including all scalar numbers in args in the calculation at each index if args contains at least one array.

Throws: 'Array length mismatch' if args contains arrays of different lengths

Example

max(1, 2, 3) // returns 3
max([10, 20, 30, 40], 15) // returns [15, 20, 30, 40]
max([1, 9], 4, [3, 5]) // returns [max([1, 4, 3]), max([9, 4, 5])] = [4, 9]

mean( …​args )

Finds the mean value of one of more numbers/arrays of numbers passed into the function. If at least one array of numbers is passed into the function, the function will find the mean by index.

Returns: number | Array.<number>. The mean value of all numbers if args contains only numbers. Returns an array with the the mean values of each index, including all scalar numbers in args in the calculation at each index if args contains at least one array.

Example

mean(1, 2, 3) // returns 2
mean([10, 20, 30, 40], 20) // returns [15, 20, 25, 30]
mean([1, 9], 5, [3, 4]) // returns [mean([1, 5, 3]), mean([9, 5, 4])] = [3, 6]

median( …​args )

Finds the median value(s) of one of more numbers/arrays of numbers passed into the function. If at least one array of numbers is passed into the function, the function will find the median by index.

Returns: number | Array.<number>. The median value of all numbers if args contains only numbers. Returns an array with the the median values of each index, including all scalar numbers in args in the calculation at each index if args contains at least one array.

Example

median(1, 1, 2, 3) // returns 1.5
median(1, 1, 2, 2, 3) // returns 2
median([10, 20, 30, 40], 10, 20, 30) // returns [15, 20, 25, 25]
median([1, 9], 2, 4, [3, 5]) // returns [median([1, 2, 4, 3]), median([9, 2, 4, 5])] = [2.5, 4.5]

min( …​args )

Finds the minimum value of one of more numbers/arrays of numbers passed into the function. If at least one array of numbers is passed into the function, the function will find the minimum by index.

Returns: number | Array.<number>. The minimum value of all numbers if args contains only numbers. Returns an array with the the minimum values of each index, including all scalar numbers in args in the calculation at each index if a is an array.

Throws: 'Array length mismatch' if args contains arrays of different lengths.

Example

min(1, 2, 3) // returns 1
min([10, 20, 30, 40], 25) // returns [10, 20, 25, 25]
min([1, 9], 4, [3, 5]) // returns [min([1, 4, 3]), min([9, 4, 5])] = [1, 4]

mod( a, b )

Remainder after dividing two numbers. If at least one array of numbers is passed into the function, the function will be applied index-wise to each element.

Returns: number | Array.<number>. The remainder of a divided by b if both are numbers. Returns an array with the the remainders applied index-wise to each element if a or b is an array.

Throws:

• 'Array length mismatch' if a and b are arrays with different lengths
• 'Cannot divide by 0' if b equals 0 or contains 0

Example

mod(10, 7) // returns 3
mod([11, 22, 33, 44], 10) // returns [1, 2, 3, 4]
mod(100, [3, 7, 11, 23]) // returns [1, 2, 1, 8]
mod([14, 42, 65, 108], [5, 4, 14, 2]) // returns [5, 2, 9, 0]

mode( …​args )

Finds the mode value(s) of one of more numbers/arrays of numbers passed into the function. If at least one array of numbers is passed into the function, the function will find the mode by index.

Returns: number | Array.<Array.<number>>. An array of mode value(s) of all numbers if args contains only numbers. Returns an array of arrays with mode value(s) of each index, including all scalar numbers in args in the calculation at each index if args contains at least one array.

Example

mode(1, 1, 2, 3) // returns [1]
mode(1, 1, 2, 2, 3) // returns [1,2]
mode([10, 20, 30, 40], 10, 20, 30) // returns [[10], [20], [30], [10, 20, 30, 40]]
mode([1, 9], 1, 4, [3, 5]) // returns [mode([1, 1, 4, 3]), mode([9, 1, 4, 5])] = [[1], [4, 5, 9]]

multiply( a, b )

Multiplies two numbers. If at least one array of numbers is passed into the function, the function will be applied index-wise to each element.

Returns: number | Array.<number>. The product of a and b if both are numbers. Returns an array with the the products applied index-wise to each element if a or b is an array.

Throws: 'Array length mismatch' if a and b are arrays with different lengths

Example

multiply(6, 3) // returns 18
multiply([10, 20, 30, 40], 10) // returns [100, 200, 300, 400]
multiply(10, [1, 2, 5, 10]) // returns [10, 20, 50, 100]
multiply([1, 2, 3, 4], [2, 7, 5, 12]) // returns [2, 14, 15, 48]

pow( a, b )

Calculates the cube root of a number. For arrays, the function will be applied index-wise to each element.

Returns: number | Array.<number>. a raised to the power of b. Returns an array with the each element raised to the power of b if a is an array.

Throws: 'Missing exponent' if b is not provided

Example

pow(2,3) // returns 8
pow([1, 2, 3], 4) // returns [1, 16, 81]

random( a, b )

Generates a random number within the given range where the lower bound is inclusive and the upper bound is exclusive. If no numbers are passed in, it will return a number between 0 and 1. If only one number is passed in, it will return a number between 0 and the number passed in.

Returns: number. A random number between 0 and 1 if no numbers are passed in. Returns a random number between 0 and a if only one number is passed in. Returns a random number between a and b if two numbers are passed in.

Throws: 'Min must be greater than max' if a < 0 when only a is passed in or if a > b when both a and b are passed in

Example

random() // returns a random number between 0 (inclusive) and 1 (exclusive)
random(10) // returns a random number between 0 (inclusive) and 10 (exclusive)
random(-10,10) // returns a random number between -10 (inclusive) and 10 (exclusive)

range( …​args )

Finds the range of one of more numbers/arrays of numbers passed into the function. If at least one array of numbers is passed into the function, the function will find the range by index.

Returns: number | Array.<number>. The range value of all numbers if args contains only numbers. Returns an array with the range values at each index, including all scalar numbers in args in the calculation at each index if args contains at least one array.

Example

range(1, 2, 3) // returns 2
range([10, 20, 30, 40], 15) // returns [5, 5, 15, 25]
range([1, 9], 4, [3, 5]) // returns [range([1, 4, 3]), range([9, 4, 5])] = [3, 5]

range( …​args )

Finds the range of one of more numbers/arrays of numbers into the function. If at least one array of numbers is passed into the function, the function will find the range by index.

Returns: number | Array.<number>. The range value of all numbers if args contains only numbers. Returns an array with the the range values at each index, including all scalar numbers in args in the calculation at each index if args contains at least one array.

Example

range(1, 2, 3) // returns 2
range([10, 20, 30, 40], 15) // returns [5, 5, 15, 25]
range([1, 9], 4, [3, 5]) // returns [range([1, 4, 3]), range([9, 4, 5])] = [3, 5]

round( a, b )

Rounds a number towards the nearest integer by default, or decimal place (if passed in as b). For arrays, the function will be applied index-wise to each element.

Returns: number | Array.<number>. The rounded value of a. Returns an array with the the rounded values of each element if a is an array.

Example

round(1.2) // returns 2
round(-10.51) // returns -11
round(-10.1, 2) // returns -10.1
round(10.93745987, 4) // returns 10.9375
round([2.9234, 5.1234, 3.5234, 4.49234324], 2) // returns [2.92, 5.12, 3.52, 4.49]

size( a )

Returns the length of an array. Alias for count.

Returns: number. The length of the array.

Throws: 'Must pass an array' if a is not an array

Example

size([]) // returns 0
size([-1, -2, -3, -4]) // returns 4
size(100) // returns 1

sqrt( a )

Calculates the square root of a number. For arrays, the function will be applied index-wise to each element.

Returns: number | Array.<number>. The square root of a. Returns an array with the the square roots of each element if a is an array.

Throws: 'Unable find the square root of a negative number' if a < 0

Example

sqrt(9) // returns 3
sqrt(30) //5.477225575051661
sqrt([9, 16, 25]) // returns [3, 4, 5]

square( a )

Calculates the square of a number. For arrays, the function will be applied index-wise to each element.

Returns: number | Array.<number>. The square of a. Returns an array with the the squares of each element if a is an array.

Example

square(-3) // returns 9
square([3, 4, 5]) // returns [9, 16, 25]

subtract( a, b )

Subtracts two numbers. If at least one array of numbers is passed into the function, the function will be applied index-wise to each element.

Returns: number | Array.<number>. The difference of a and b if both are numbers, or an array of differences applied index-wise to each element.

Throws: 'Array length mismatch' if a and b are arrays with different lengths

Example

subtract(6, 3) // returns 3
subtract([10, 20, 30, 40], 10) // returns [0, 10, 20, 30]
subtract(10, [1, 2, 5, 10]) // returns [9, 8, 5, 0]
subtract([14, 42, 65, 108], [2, 7, 5, 12]) // returns [12, 35, 52, 96]

sum( …​args )

Calculates the sum of one or more numbers/arrays passed into the function. If at least one array is passed, the function will sum up one or more numbers/arrays of numbers and distinct values of an array. Sum accepts arrays of different lengths.

Returns: number. The sum of one or more numbers/arrays of numbers including distinct values in arrays

Example

sum(1, 2, 3) // returns 6
sum([10, 20, 30, 40], 10, 20, 30) // returns 160
sum([1, 2], 3, [4, 5], 6) // returns sum(1, 2, 3, 4, 5, 6) = 21
sum([10, 20, 30, 40], 10, [1, 2, 3], 22) // returns sum(10, 20, 30, 40, 10, 1, 2, 3, 22) = 138

unique( a )

Counts the number of unique values in an array.

Returns: number. The number of unique values in the array. Returns 1 if a is not an array.

Example

unique(100) // returns 1
unique([]) // returns 0
unique([1, 2, 3, 4]) // returns 4
unique([1, 2, 3, 4, 2, 2, 2, 3, 4, 2, 4, 5, 2, 1, 4, 2]) // returns 5

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