Math Functions¶

Mathematical and statistical functions.

Summary¶

Function	Signature	Description
`abs_fn`	`number -> number`	Absolute value
`acos`	`number -> number`	Arc cosine function (returns null for out-of-domain input)
`add`	`number, number -> number`	Add two numbers
`asin`	`number -> number`	Arc sine function (returns null for out-of-domain input)
`atan`	`number -> number`	Arc tangent function
`atan2`	`number, number -> number`	Arc tangent of y/x using the signs of both arguments to determine the quadrant
`ceil_fn`	`number -> number`	Round up to nearest integer
`clamp`	`number, number, number -> number`	Clamp value to range
`correlation`	`array, array -> number`	Compute Pearson correlation coefficient between two arrays
`cos`	`number -> number`	Cosine function
`covariance`	`array, array -> number`	Covariance between two arrays
`cumulative_sum`	`array -> array`	Calculate running cumulative sum of a numeric array
`deg_to_rad`	`number -> number`	Convert degrees to radians
`divide`	`number, number -> number`	Divide first number by second
`ewma`	`array, number -> array`	Exponential weighted moving average
`floor_fn`	`number -> number`	Round down to nearest integer
`format_number`	`number, number?, string? -> string`	Format number with separators and optional suffix
`histogram`	`array, number -> array[object]`	Compute histogram bins for an array of numbers
`kurtosis`	`array -> number`	Excess kurtosis (measure of tailedness) of a numeric array (normal distribution = 0)
`log`	`number -> number`	Natural logarithm
`mad`	`array -> number`	Median absolute deviation (robust measure of variability)
`median`	`array -> number`	Calculate median of array
`mod_fn`	`number, number -> number`	Modulo operation
`mode`	`array -> any`	Find the most common value in an array
`moving_avg`	`array, number -> array`	Simple moving average with window size
`multiply`	`number, number -> number`	Multiply two numbers
`normalize`	`array -> array`	Min-max normalize an array of numbers to [0, 1] range
`outliers_iqr`	`array, number? -> array`	Find outliers using IQR method (values outside Q1-1.5IQR to Q3+1.5IQR)
`outliers_zscore`	`array, number? -> array`	Find outliers using z-score method (values with \|z-score\| > threshold)
`percentile`	`array, number -> number`	Calculate percentile of array
`pow`	`number, number -> number`	Raise to power
`quantile`	`array, number -> number`	Nth quantile (generalized percentile, q in [0,1])
`quartiles`	`array -> object`	Calculate quartiles (Q1, Q2, Q3) and IQR of array
`rad_to_deg`	`number -> number`	Convert radians to degrees
`rate_of_change`	`array -> array`	Calculate percentage change between consecutive values
`round`	`number, number -> number`	Round to specified decimal places
`sign`	`number -> number`	Sign of a number (-1, 0, or 1)
`sin`	`number -> number`	Sine function
`skew`	`array -> number`	Skewness (measure of asymmetry) of a numeric array using Fisher-Pearson coefficient
`sqrt`	`number -> number`	Square root
`standardize`	`array -> array`	Standardize array to mean=0, std=1 (z-score normalization)
`stddev`	`array -> number`	Calculate standard deviation of array
`subtract`	`number, number -> number`	Subtract second number from first
`tan`	`number -> number`	Tangent function
`to_fixed`	`number, number -> string`	Format number with exact decimal places
`trend`	`array -> string`	Detect trend direction in a numeric array (increasing, decreasing, or stable)
`trend_slope`	`array -> number`	Calculate the linear regression slope of a numeric array
`variance`	`array -> number`	Calculate variance of array
`z_score`	`array -> array`	Compute z-scores (standard scores) for an array of numbers

Functions¶

abs_fn¶

Absolute value

Signature: number -> number

Examples:

# Negative to positive
abs_fn(`-5`) -> 5
# Already positive
abs_fn(`5`) -> 5
# Zero stays zero
abs_fn(`0`) -> 0
# Negative float
abs_fn(`-3.14`) -> 3.14

acos¶

Arc cosine function (returns null for out-of-domain input)

Signature: number -> number

Examples:

# Arccos of 1
acos(`1`) -> 0
# Arccos of 0 (pi/2)
acos(`0`) -> ~1.5708
# Out of domain (|n| > 1)
acos(`2`) -> null

add¶

Add two numbers

Signature: number, number -> number

Examples:

# Add integers
add(`2`, `3`) -> 5
# Add floats
add(`1.5`, `2.5`) -> 4.0
# With negative
add(`-5`, `3`) -> -2
# Add zero
add(`0`, `10`) -> 10

asin¶

Arc sine function (returns null for out-of-domain input)

Signature: number -> number

Examples:

# Arcsin of 0
asin(`0`) -> 0
# Arcsin of 1 (pi/2)
asin(`1`) -> ~1.5708
# Out of domain (|n| > 1)
asin(`2`) -> null

atan¶

Arc tangent function

Signature: number -> number

Examples:

# Arctan of 0
atan(`0`) -> 0
# Arctan of 1 (pi/4)
atan(`1`) -> ~0.7854

atan2¶

Arc tangent of y/x using the signs of both arguments to determine the quadrant

Signature: number, number -> number

Examples:

# Arctan2 of (0, 1)
atan2(`0`, `1`) -> 0
# Arctan2 of (1, 1) (pi/4)
atan2(`1`, `1`) -> ~0.7854

ceil_fn¶

Round up to nearest integer

Signature: number -> number

Examples:

# Round up fraction
ceil_fn(`3.2`) -> 4
# Round up high fraction
ceil_fn(`3.9`) -> 4
# Already integer
ceil_fn(`3.0`) -> 3
# Negative rounds toward zero
ceil_fn(`-3.2`) -> -3

clamp¶

Clamp value to range

Signature: number, number, number -> number

Examples:

# Above max
clamp(`15`, `0`, `10`) -> 10
# Below min
clamp(`-5`, `0`, `10`) -> 0
# Within range
clamp(`5`, `0`, `10`) -> 5
# Custom range
clamp(`100`, `50`, `75`) -> 75

correlation¶

Compute Pearson correlation coefficient between two arrays

Signature: array, array -> number

Examples:

# Perfect positive
correlation([1, 2, 3], [1, 2, 3]) -> 1.0
# Perfect negative
correlation([1, 2, 3], [3, 2, 1]) -> -1.0

cos¶

Cosine function

Signature: number -> number

Examples:

# Cos of 0
cos(`0`) -> 1
# Cos of pi
cos(`3.14159`) -> -1
# Cos of pi/2
cos(`1.5708`) -> ~0
# Cos of 2*pi
cos(`6.28318`) -> 1

covariance¶

Covariance between two arrays

Signature: array, array -> number

Examples:

# Perfect positive
covariance([1, 2, 3], [1, 2, 3]) -> 0.666...
# Perfect negative
covariance([1, 2, 3], [3, 2, 1]) -> -0.666...
# No correlation
covariance([1, 2, 3], [1, 1, 1]) -> 0
# From arrays
covariance(x_values, y_values) -> number

cumulative_sum¶

Calculate running cumulative sum of a numeric array

Signature: array -> array

Examples:

# Running total
cumulative_sum([1, 2, 3, 4]) -> [1, 3, 6, 10]
# With negatives
cumulative_sum([10, -5, 3]) -> [10, 5, 8]
# Single element
cumulative_sum([100]) -> [100]

deg_to_rad¶

Convert degrees to radians

Signature: number -> number

Examples:

# 0 degrees
deg_to_rad(`0`) -> 0
# 180 degrees (pi)
deg_to_rad(`180`) -> ~3.14159

divide¶

Divide first number by second

Signature: number, number -> number

Examples:

# Integer division
divide(`10`, `2`) -> 5
# Fractional result
divide(`7`, `2`) -> 3.5
# Repeating decimal
divide(`1`, `3`) -> 0.333...
# Negative dividend
divide(`-10`, `2`) -> -5

ewma¶

Exponential weighted moving average

Signature: array, number -> array

Examples:

# Alpha 0.5
ewma([1, 2, 3, 4, 5], `0.5`) -> [1, 1.5, 2.25, ...]
# Smooth stock prices
ewma(prices, `0.3`) -> smoothed prices
# High alpha
ewma([10, 20, 30], `0.9`) -> fast response
# Low alpha
ewma([10, 20, 30], `0.1`) -> slow response

floor_fn¶

Round down to nearest integer

Signature: number -> number

Examples:

# Round down high fraction
floor_fn(`3.7`) -> 3
# Round down low fraction
floor_fn(`3.2`) -> 3
# Already integer
floor_fn(`3.0`) -> 3
# Negative rounds away from zero
floor_fn(`-3.2`) -> -4

format_number¶

Format number with separators and optional suffix

Signature: number, number?, string? -> string

Examples:

# With commas
format_number(`1234567`, `0`) -> \"1,234,567\"
# With decimals
format_number(`1234.56`, `2`) -> \"1,234.56\"
# Million
format_number(`1000000`, `0`) -> \"1,000,000\"
# Small number
format_number(`99.9`, `1`) -> \"99.9\"

histogram¶

Compute histogram bins for an array of numbers

Signature: array, number -> array[object]

Examples:

# 3 bins
histogram([1, 2, 3, 4, 5], `3`) -> [{min: 1.0, max: 2.33, count: 2}, ...]
# 2 bins
histogram([10, 20, 30], `2`) -> [{min: 10.0, max: 20.0, count: 2}, {min: 20.0, max: 30.0, count: 1}]

kurtosis¶

Excess kurtosis (measure of tailedness) of a numeric array (normal distribution = 0)

Signature: array -> number

Examples:

# Platykurtic (light tails)
kurtosis([1, 2, 3, 4, 5]) -> -1.3
# Uniform-like distribution
kurtosis([1, 1, 5, 5]) -> -2.0

log¶

Natural logarithm

Signature: number -> number

Examples:

# Log of e
log(`2.718`) -> ~1
# Log of 1
log(`1`) -> 0
# Log of 10
log(`10`) -> 2.302...
# Log of 100
log(`100`) -> 4.605...

mad¶

Median absolute deviation (robust measure of variability)

Signature: array -> number

Examples:

# MAD of simple array
mad([1, 2, 3, 4, 5]) -> 1.0
# MAD with outlier
mad([1, 1, 1, 100]) -> 0.0

median¶

Calculate median of array

Signature: array -> number

Examples:

# Odd count
median([1, 2, 3, 4, 5]) -> 3
# Even count
median([1, 2, 3, 4]) -> 2.5
# Middle value
median([10, 20, 30]) -> 20
# Single element
median([5]) -> 5

mod_fn¶

Modulo operation

Signature: number, number -> number

Examples:

# Remainder of 10/3
mod_fn(`10`, `3`) -> 1
# Evenly divisible
mod_fn(`15`, `5`) -> 0
# Odd check
mod_fn(`7`, `2`) -> 1
# Larger numbers
mod_fn(`100`, `7`) -> 2

mode¶

Find the most common value in an array

Signature: array -> any

Examples:

# Most frequent
mode([1, 2, 2, 3]) -> 2
# String mode
mode(['a', 'b', 'a', 'a']) -> 'a'
# Tie returns first
mode([1, 1, 2, 2, 3]) -> 1 or 2
# Single element
mode([5]) -> 5

moving_avg¶

Simple moving average with window size

Signature: array, number -> array

Examples:

# Window of 3
moving_avg([1, 2, 3, 4, 5], `3`) -> [null, null, 2, 3, 4]
# Window of 2
moving_avg([10, 20, 30, 40], `2`) -> [null, 15, 25, 35]
# 7-day moving avg
moving_avg(prices, `7`) -> weekly average
# Window of 1
moving_avg([1, 2, 3], `1`) -> [1, 2, 3]

multiply¶

Multiply two numbers

Signature: number, number -> number

Examples:

# Basic multiplication
multiply(`4`, `3`) -> 12
# With decimals
multiply(`2.5`, `4`) -> 10
# With negative
multiply(`-3`, `4`) -> -12
# Multiply by zero
multiply(`0`, `100`) -> 0

normalize¶

Min-max normalize an array of numbers to [0, 1] range

Signature: array -> array

Examples:

# Basic normalization
normalize([1, 3, 5]) -> [0.0, 0.5, 1.0]
# All same values
normalize([10, 10, 10]) -> [0, 0, 0]

outliers_iqr¶

Find outliers using IQR method (values outside Q1-1.5IQR to Q3+1.5IQR)

Signature: array, number? -> array

Examples:

# Detect outlier
outliers_iqr([1, 2, 3, 4, 100]) -> [100]
# No outliers
outliers_iqr([1, 2, 3, 4, 5]) -> []
# Custom multiplier
outliers_iqr(values, `3.0`) -> extreme outliers only
# Find anomalies
outliers_iqr(measurements) -> anomalies

outliers_zscore¶

Find outliers using z-score method (values with |z-score| > threshold)

Signature: array, number? -> array

Examples:

# Detect outlier
outliers_zscore([1, 2, 3, 4, 100]) -> [100]
# No outliers
outliers_zscore([1, 2, 3, 4, 5]) -> []
# Custom threshold
outliers_zscore(values, `3.0`) -> extreme outliers only
# Lower threshold
outliers_zscore(measurements, `1.5`) -> more sensitive detection

percentile¶

Calculate percentile of array

Signature: array, number -> number

Examples:

# 50th percentile (median)
percentile([1, 2, 3, 4, 5], `50`) -> 3
# 25th percentile
percentile([1, 2, 3, 4, 5], `25`) -> 2
# 75th percentile
percentile([1, 2, 3, 4, 5], `75`) -> 4
# 90th percentile
percentile(scores, `90`) -> top 10% threshold

pow¶

Raise to power

Signature: number, number -> number

Examples:

# 2 cubed
pow(`2`, `3`) -> 8
# 10 squared
pow(`10`, `2`) -> 100
# 2^10
pow(`2`, `10`) -> 1024
# Square root via power
pow(`4`, `0.5`) -> 2

quantile¶

Nth quantile (generalized percentile, q in [0,1])

Signature: array, number -> number

Examples:

# Median (0.5)
quantile([1, 2, 3, 4, 5], `0.5`) -> 3
# First quartile
quantile([1, 2, 3, 4, 5], `0.25`) -> 2
# Third quartile
quantile([1, 2, 3, 4, 5], `0.75`) -> 4
# 90th quantile
quantile(values, `0.9`) -> 90th quantile

quartiles¶

Calculate quartiles (Q1, Q2, Q3) and IQR of array

Signature: array -> object

Examples:

# Basic quartiles
quartiles([1, 2, 3, 4, 5]) -> {min: 1, q1: 2, q2: 3, q3: 4, max: 5, iqr: 2}
# Get IQR
quartiles([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]).iqr -> 4.5
# Q2 equals median
quartiles(values).q2 == median(values) -> true
# Distribution analysis
quartiles(scores) -> full distribution stats

rad_to_deg¶

Convert radians to degrees

Signature: number -> number

Examples:

# 0 radians
rad_to_deg(`0`) -> 0
# pi radians
rad_to_deg(`3.14159`) -> ~180

rate_of_change¶

Calculate percentage change between consecutive values

Signature: array -> array

Examples:

# 10% growth
rate_of_change([100, 110, 121]) -> [10.0, 10.0]
# 50% decline
rate_of_change([100, 50, 25]) -> [-50.0, -50.0]
# Varying rate
rate_of_change([1, 2, 3]) -> [100.0, 50.0]

round¶

Round to specified decimal places

Signature: number, number -> number

Examples:

# Two decimals
round(`3.14159`, `2`) -> 3.14
# Round to integer
round(`3.5`, `0`) -> 4
# Round up
round(`2.555`, `2`) -> 2.56
# One decimal
round(`123.456`, `1`) -> 123.5

sign¶

Sign of a number (-1, 0, or 1)

Signature: number -> number

Examples:

# Negative number
sign(`-5`) -> -1
# Zero
sign(`0`) -> 0
# Positive number
sign(`42`) -> 1

sin¶

Sine function

Signature: number -> number

Examples:

# Sin of 0
sin(`0`) -> 0
# Sin of pi/2
sin(`1.5708`) -> 1
# Sin of pi
sin(`3.14159`) -> ~0
# Sin of 2*pi
sin(`6.28318`) -> ~0

skew¶

Skewness (measure of asymmetry) of a numeric array using Fisher-Pearson coefficient

Signature: array -> number

Examples:

# Symmetric distribution
skew([1, 2, 3, 4, 5]) -> 0.0
# Right-skewed
skew([1, 1, 1, 10]) -> 1.15...

sqrt¶

Square root

Signature: number -> number

Examples:

# Perfect square
sqrt(`16`) -> 4
# Irrational result
sqrt(`2`) -> 1.414...
# Larger number
sqrt(`100`) -> 10
# Zero
sqrt(`0`) -> 0

standardize¶

Standardize array to mean=0, std=1 (z-score normalization)

Signature: array -> array

Examples:

# Basic z-scores
standardize([10, 20, 30]) -> [-1.22, 0, 1.22]
# Normalize values
standardize([1, 2, 3, 4, 5]) -> normalized
# Standardize scores
standardize(scores) -> z-scores
# Identical values
standardize([5, 5, 5]) -> [0, 0, 0]

stddev¶

Calculate standard deviation of array

Signature: array -> number

Examples:

# Basic stddev
stddev([1, 2, 3, 4, 5]) -> 1.414...
# No variation
stddev([10, 10, 10]) -> 0
# High variation
stddev([1, 100]) -> ~49.5
# Measure spread
stddev(values) -> spread measure

subtract¶

Subtract second number from first

Signature: number, number -> number

Examples:

# Basic subtraction
subtract(`5`, `3`) -> 2
# Negative result
subtract(`10`, `15`) -> -5
# With decimals
subtract(`3.5`, `1.5`) -> 2
# From zero
subtract(`0`, `5`) -> -5

tan¶

Tangent function

Signature: number -> number

Examples:

# Tan of 0
tan(`0`) -> 0
# Tan of pi/4
tan(`0.7854`) -> ~1
# Tan of pi
tan(`3.14159`) -> ~0
# Calculate tangent
tan(angle) -> ratio

to_fixed¶

Format number with exact decimal places

Signature: number, number -> string

Examples:

# Two decimals
to_fixed(`3.14159`, `2`) -> \"3.14\"
# Pad with zeros
to_fixed(`5`, `2`) -> \"5.00\"
# Round to integer
to_fixed(`99.9`, `0`) -> \"100\"
# Extra precision
to_fixed(`1.5`, `3`) -> \"1.500\"

trend¶

Detect trend direction in a numeric array (increasing, decreasing, or stable)

Signature: array -> string

Examples:

# Upward trend
trend([1, 2, 3, 4, 5]) -> "increasing"
# Downward trend
trend([5, 4, 3, 2, 1]) -> "decreasing"
# No change
trend([3, 3, 3, 3]) -> "stable"

trend_slope¶

Calculate the linear regression slope of a numeric array

Signature: array -> number

Examples:

# Perfect linear increase
trend_slope([1, 2, 3, 4, 5]) -> 1.0
# Perfect linear decrease
trend_slope([5, 4, 3, 2, 1]) -> -1.0
# Noisy upward
trend_slope([1, 3, 2, 4]) -> ~0.7

variance¶

Calculate variance of array

Signature: array -> number

Examples:

# Basic variance
variance([1, 2, 3, 4, 5]) -> 2
# No variation
variance([10, 10, 10]) -> 0
# High variation
variance([1, 100]) -> 2450.25
# Squared spread
variance(values) -> spread^2

z_score¶

Compute z-scores (standard scores) for an array of numbers

Signature: array -> array

Examples:

# Basic z-scores
z_score([1, 3, 5]) -> [-1.22, 0.0, 1.22]
# Middle value is 0
z_score([10, 20, 30])[1] -> 0.0