math

Exponentials, logarithms, square roots and trigonometry. Import it with IMPORT math.

The functions are lowercase wrappers around the built-in LN, SQRT, ASIN and so on. Where the built-in stops with an error on bad input, the wrapper gives NOTHING, so the result is a MAYBE NUMBER.

Example:

-- Math Example: Mathematical functions with safe error handling
IMPORT math

-- Euler's constant
#EVAL EULER  -- 2.718281828459045

-- Exponential function
DECIDE `exponential growth` IS exp 2
#EVAL `exponential growth`  -- e^2 ≈ 7.389

-- Safe logarithms (return MAYBE to handle domain errors)
DECIDE `valid natural log` IS ln 10
#EVAL `valid natural log`  -- JUST 2.302...

DECIDE `invalid natural log` IS ln (0 MINUS 5)
#EVAL `invalid natural log`  -- NOTHING (negative input)

DECIDE `base 10 logarithm` IS log10 100
#EVAL `base 10 logarithm`  -- JUST 2

-- Safe square root
DECIDE `valid square root` IS sqrt 16
#EVAL `valid square root`  -- JUST 4

DECIDE `invalid square root` IS sqrt (0 MINUS 4)
#EVAL `invalid square root`  -- NOTHING (negative input)

-- Absolute value
DECIDE `absolute of positive` IS absNumber 42
#EVAL `absolute of positive`  -- 42

DECIDE `absolute of negative` IS absNumber (0 MINUS 42)
#EVAL `absolute of negative`  -- 42

-- Trigonometric functions (angles in radians)
DECIDE `sine of zero` IS sin 0
#EVAL `sine of zero`  -- JUST 0

DECIDE `cosine of zero` IS cos 0
#EVAL `cosine of zero`  -- JUST 1

-- Tangent with asymptote protection
DECIDE `tangent of zero` IS tan 0
#EVAL `tangent of zero`  -- JUST 0

-- Inverse trig with domain checking
DECIDE `valid arcsine` IS asin 0.5
#EVAL `valid arcsine`  -- JUST 0.523... (π/6)

DECIDE `invalid arcsine` IS asin 2
#EVAL `invalid arcsine`  -- NOTHING (|x| > 1)

-- Using fromMaybe to extract with default
DECIDE `safe extracted value` IS fromMaybe 0 (sqrt 25)
#EVAL `safe extracted value`  -- 5

DECIDE `value with default` IS fromMaybe 0 (sqrt (0 MINUS 1))
#EVAL `value with default`  -- 0 (used default)

Constants

Constant	Value
EULER	Euler's number, 2.718281828459045
TAN_EPSILON	0.000000001, the threshold below which tan treats the cosine as zero

Functions

Function	Input	Gives	What it does
exp	x: NUMBER	NUMBER	e to the power x
ln	x: NUMBER	MAYBE NUMBER	Natural logarithm; NOTHING if x is 0 or less
log10	x: NUMBER	MAYBE NUMBER	Base-10 logarithm; NOTHING if x is 0 or less
sqrt	x: NUMBER	MAYBE NUMBER	Square root; NOTHING if x is negative
absNumber	x: NUMBER	NUMBER	Absolute value
sin	x: NUMBER	MAYBE NUMBER	Sine; always JUST
cos	x: NUMBER	MAYBE NUMBER	Cosine; always JUST
tan	x: NUMBER	MAYBE NUMBER	Tangent; NOTHING where the cosine is almost zero
asin	x: NUMBER	MAYBE NUMBER	Arc sine; NOTHING outside -1 to 1
acos	x: NUMBER	MAYBE NUMBER	Arc cosine; NOTHING outside -1 to 1
atan	x: NUMBER	MAYBE NUMBER	Arc tangent; always JUST

Angles are in radians.