Module Math.Math

module Math: sig .. end

Math contains many common mathematical functions.

val abs : int -> int

abs i is the absolute value of i.

val absf : float -> float

absf f is the absolute value of f.

val ceil : float -> int

ceil f is the integer closest to f in the direction of positive infinity.

val floor : float -> int

floor f is the integer closest to f in the direction of negative infinity.

val constrain : int -> int -> int -> int

constrain i min max is min if i <= min, max if i >= max, or i otherwise. The behavior is undefined if min > max.

val constrainf : float -> float -> float -> float

constrainf f min max is min if f <= min, max if f >= max, or f otherwise. The behavior is undefined if min > max.

val dist : int -> int -> int -> int -> float

dist x1 y1 x2 y2 is the distance between the points (x1, y1) and (x2, y2).

val distf : float -> float -> float -> float -> float

distf x1 y1 x2 y2 is the distance between the points (x1, y1) and (x2, y2).

val mag : int -> int -> float

mag x y is dist x y 0 0.

val magf : float -> float -> float

magf x y is distf x y 0 0.

val lerp : int -> int -> float -> int

lerp a b t is the linear interpolation from a to b by t, where t is in [0, 1].

val lerpf : float -> float -> float -> float

lerpf a b t is the linear interpolation from a to b by t, where t is in [0, 1].

val log : float -> float -> float

log f b is the base-b logarithm of f.

val map : int -> int -> int -> int -> int -> int

map i low1 high1 low2 high2 is i mapped from the range [low1, high1] to the range [low2, high2].

val mapf : float -> float -> float -> float -> float -> float

mapf f low1 high1 low2 high2 is f mapped from the range [low1, high1] to the range [low2, high2].

val max : int -> int -> int

max a b is the maximum of a and b.

val maxf : float -> float -> float

maxf a b is the maximum of a and b.

val min : int -> int -> int

min a b is the minimum of a and b.

val minf : float -> float -> float

minf a b is the minimum of a and b.

val norm : int -> int -> int -> float

norm i low high is map i low high 0 1.

val normf : float -> float -> float -> float

normf f low high is mapf f low high 0. 1..

val round : float -> int

round f is the integer closest to f; 0.5 rounds up.

val sqrt : float -> float

sqrt f is the square root of f.

Trigonometry

All functions in this section expect angles in radians.

val acos : float -> float

acos f is the inverse cosine of f. f is in [-1, 1] and acos f is in [0, pi].

val asin : float -> float

asin f is the inverse sine of f. f is in [-1, 1] and asin f is in [-pi/2, pi/2].

val atan : float -> float

atan f is the inverse tangent of f. f is in [-infinity, infinity] and atan f is in [-pi/2, pi/2].

val atan2 : float -> float -> float

atan2 y x is the angle from the origin to (y, x). This function uses the signs of x and y to determine the correct quadrant.

val cos : float -> float

cos theta is the cosine of theta.

val sin : float -> float

sin theta is the sine of theta.

val tan : float -> float

tan theta is the tangent of theta.

Angle Conversion

val degrees : float -> float

degrees theta is theta, which is in radians, converted to degrees.

val radians : float -> float

radians d is d, which is in degrees, converted to radians.

Angle Manipulation

All functions in this section expect angles in radians.

val angle_avg : float -> float -> float

angle_avg theta1 theta2 is the average angle between theta1 and theta2.

val angle_sum : float -> float -> float

angle_sum theta1 theta2 is the sum of the angles theta1 and theta2.

val angle_diff : float -> float -> float

angle_diff theta1 theta2 is the difference between the angles theta1 and theta2.

Mathematical Constants

val pi : float

pi is the constant pi. pi = 3.1415926535...

val half_pi : float

half_pi is pi /. 2.. half_pi = 1.5707963267...

val two_pi : float

two_pi is pi *. 2.. two_pi = 6.2831853071...

val e : float

e is the constant e. e = 2.7182818284...

Random

val random_int : ?lower_bound:int -> int -> int

random_int bound is a random integer between 0 (inclusive) and bound (exclusive).

val random_float : ?lower_bound:float -> float -> float

random_float bound is a random float between 0. (inclusive) and bound (exclusive).

val random_bool : unit -> bool

random_bool () is either true or false with an equal probability of either.