use math

Mathematical functions and constants.

Constants

Functions

fn abs

Absolute value.

Signature: (x:f64 -- result:f64)

Example:

-5.0 math::abs print  // 5.0

fn acos

Arc cosine (inverse cosine).

Signature: (x:f64 -- result:f64)

Example:

1.0 math::acos print  // 0.0

fn asin

Arc sine (inverse sine).

Signature: (x:f64 -- result:f64)

Example:

0.0 math::asin print  // 0.0

fn atan2

Two-argument arc tangent. Returns the angle in radians between the positive x-axis and the point (x, y). More useful than atan for computing angles because it handles all quadrants.

Signature: (y:f64 x:f64 -- result:f64)

Example:

1.0 1.0 math::atan2 print  // ~0.785 (π/4)

fn atan

Arc tangent (inverse tangent).

Signature: (x:f64 -- result:f64)

Example:

0.0 math::atan print  // 0.0

fn cbrt

Cube root.

Signature: (x:f64 -- result:f64)

Example:

8.0 math::cbrt print  // 2.0

fn cb

Cube a number.

Signature: (x:f64 -- result:f64)

Example:

2.0 math::cb print  // 8.0

fn ceil

Ceiling (round up).

Signature: (x:f64 -- result:f64)

Example:

2.3 math::ceil print  // 3.0

fn clamp

Clamp value to range.

Signature: (x:f64 min_val:f64 max_val:f64 -- result:f64)

Example:

15.0 0.0 10.0 math::clamp print  // 10.0

fn cos

Cosine of angle in radians.

Signature: (x:f64 -- result:f64)

Example:

0.0 math::cos print  // 1.0

fn dec

Decrement integer by 1.

Signature: (x:i64 -- result:i64)

Example:

5 math::dec print  // 4

fn deg_to_rad

Convert degrees to radians.

Signature: (degrees:f64 -- radians:f64)

Example:

180.0 math::deg_to_rad print  // ~3.14159

fn exp

Exponential function (e^x).

Signature: (x:f64 -- result:f64)

Example:

1.0 math::exp print  // ~2.718 (e)

fn fac

Factorial (n!).

Signature: (n:i64 -- result:i64)

Example:

5 math::fac print  // 120

fn floor

Floor (round down).

Signature: (x:f64 -- result:f64)

Example:

2.7 math::floor print  // 2.0

fn fmod

Floating-point modulo (remainder). Returns the remainder of x/y with the same sign as x.

Signature: (x:f64 y:f64 -- result:f64)

Example:

5.5 2.0 math::fmod print  // 1.5

fn hypot

Hypotenuse (Euclidean distance). Computes sqrt(x² + y²) without intermediate overflow or underflow.

Signature: (x:f64 y:f64 -- result:f64)

Example:

3.0 4.0 math::hypot print  // 5.0

fn inc

Increment integer by 1.

Signature: (x:i64 -- result:i64)

Example:

5 math::inc print  // 6

fn inv

Reciprocal (1/x).

Signature: (x:f64 -- result:f64)

Example:

4.0 math::inv print  // 0.25

fn lerp

Linear interpolation between two values.

Signature: (a:f64 b:f64 t:f64 -- result:f64)

Example:

0.0 10.0 0.5 math::lerp print  // 5.0

fn ln

Natural logarithm (base e).

Signature: (x:f64 -- result:f64)

Example:

2.718281828 math::ln print  // ~1.0

fn log10

Base-10 logarithm.

Signature: (x:f64 -- result:f64)

Example:

100.0 math::log10 print  // 2.0

fn log

Logarithm with arbitrary base.

Signature: (x:f64 base:f64 -- result:f64)

Example:

8.0 2.0 math::log print  // 3.0

fn max

Maximum of two values.

Signature: (a:any b:any -- result:any)

Example:

3 7 math::max print  // 7

fn min

Minimum of two values.

Signature: (a:any b:any -- result:any)

Example:

3 7 math::min print  // 3

fn pow

Power function.

Signature: (base:f64 exp:f64 -- result:f64)

Example:

2.0 3.0 math::pow print  // 8.0

fn rad_to_deg

Convert radians to degrees.

Signature: (radians:f64 -- degrees:f64)

Example:

3.141592653589793 math::rad_to_deg print  // 180.0

fn round

Round to nearest integer.

Signature: (x:f64 -- result:f64)

Example:

2.5 math::round print  // 3.0

fn sin

Sine of angle in radians.

Signature: (x:f64 -- result:f64)

Example:

0.0 math::sin print  // 0.0

fn sqrt

Square root.

Signature: (x:f64 -- result:f64)

Example:

4.0 math::sqrt print  // 2.0

fn sq

Square a number.

Signature: (x:f64 -- result:f64)

Example:

3.0 math::sq print  // 9.0

fn tan

Tangent of angle in radians.

Signature: (x:f64 -- result:f64)

Example:

0.0 math::tan print  // 0.0

fn within

Check if value is within range (inclusive).

Signature: (x:any min_val:any max_val:any -- result:i64)

Example:

5 0 10 math::within print  // 1

fn sinh

Hyperbolic sine.

Signature: (x:f64 -- result:f64)

Example:

1.0 math::sinh print  // ~1.175

fn cosh

Hyperbolic cosine.

Signature: (x:f64 -- result:f64)

Example:

0.0 math::cosh print  // 1.0

fn tanh

Hyperbolic tangent.

Signature: (x:f64 -- result:f64)

Example:

0.0 math::tanh print  // 0.0

fn asinh

Inverse hyperbolic sine.

Signature: (x:f64 -- result:f64)

Example:

0.0 math::asinh print  // 0.0

fn acosh

Inverse hyperbolic cosine.

Signature: (x:f64 -- result:f64)

Example:

1.0 math::acosh print  // 0.0

fn atanh

Inverse hyperbolic tangent.

Signature: (x:f64 -- result:f64)

Example:

0.0 math::atanh print  // 0.0

fn log2

Base-2 logarithm.

Signature: (x:f64 -- result:f64)

Example:

8.0 math::log2 print  // 3.0

fn exp2

Exponential base 2 (2^x).

Signature: (x:f64 -- result:f64)

Example:

3.0 math::exp2 print  // 8.0

fn trunc

Truncate toward zero.

Signature: (x:f64 -- result:f64)

Example:

-2.7 math::trunc print  // -2.0

fn sign

Sign function.

Signature: (x:f64 -- result:f64)

Example:

-5.0 math::sign print  // -1.0

Mat4

4x4 matrix in column-major order (OpenGL compatible).

Struct

Constructors

fn mat4_identity

Create identity Mat4.

Signature: ( -- m:Mat4)

Example:

math::mat4_identity  // m

fn mat4_rotation_x

Create rotation Mat4 around X axis.

Signature: (angle:f64 -- m:Mat4)

Example:

1.57 math::mat4_rotation_x  // m

fn mat4_rotation_y

Create rotation Mat4 around Y axis.

Signature: (angle:f64 -- m:Mat4)

Example:

1.57 math::mat4_rotation_y  // m

fn mat4_rotation_z

Create rotation Mat4 around Z axis.

Signature: (angle:f64 -- m:Mat4)

Example:

1.57 math::mat4_rotation_z  // m

fn mat4_scaling

Create scale Mat4.

Signature: (sx:f64 sy:f64 sz:f64 -- m:Mat4)

Example:

2.0 2.0 2.0 math::mat4_scaling  // m

fn mat4_translation

Create translation Mat4.

Signature: (x:f64 y:f64 z:f64 -- m:Mat4)

Example:

1.0 2.0 3.0 math::mat4_translation  // m

fn mat4_zero

Create zero Mat4.

Signature: ( -- m:Mat4)

Example:

math::mat4_zero  // m

fn mat4_look_at

Create a look-at view matrix.

Signature: (eye:Vec3 target:Vec3 up:Vec3 -- m:Mat4)

Example:

eye target up math::mat4_look_at -> view

fn mat4_perspective

Create a perspective projection matrix.

Signature: (fov:f64 aspect:f64 near:f64 far:f64 -- m:Mat4)

Example:

1.047 1.777 0.1 100.0 math::mat4_perspective -> proj

fn mat4_orthographic

Create an orthographic projection matrix.

Signature: (left:f64 right:f64 bottom:f64 top:f64 near:f64 far:f64 -- m:Mat4)

Example:

-1.0 1.0 -1.0 1.0 0.1 100.0 math::mat4_orthographic -> proj

fn mat4_from_quat

Create rotation matrix from quaternion.

Signature: (q:Quat -- m:Mat4)

Example:

q math::mat4_from_quat -> rot_mat

Methods

fn mul

Matrix multiplication.

Signature: (m:Mat4) mul(other:Mat4 -- result:Mat4)

Example:

other m mul -> product

fn determinant

Matrix determinant.

Signature: (m:Mat4) determinant( -- result:f64)

Example:

m determinant -> det

fn inverse

Matrix inverse.

Signature: (m:Mat4) inverse( -- result:Mat4)

Example:

m inverse -> m_inv

fn transpose

Transpose this matrix.

Signature: (m:Mat4) transpose( -- result:Mat4)

Example:

m transpose  // m_t

fn transform_point

Transform a Vec3 point by this matrix (w=1).

Signature: (m:Mat4) transform_point(v:Vec3 -- result:Vec3)

Example:

point m transform_point -> transformed

fn transform_vec4

Transform a Vec4 by this matrix.

Signature: (m:Mat4) transform_vec4(v:Vec4 -- result:Vec4)

Example:

vec m transform_vec4 -> transformed

Quat

Quaternion for representing rotations. Stored as (w, x, y, z) where w is the scalar part.

Struct

Constructors

fn quat_identity

Create identity quaternion (no rotation).

Signature: ( -- q:Quat)

Example:

math::quat_identity  // q

fn quat_from_axis_angle

Create quaternion from axis and angle.

Signature: (axis:Vec3 angle:f64 -- result:Quat)

Example:

axis 1.57 math::quat_from_axis_angle -> q

fn quat_from_euler

Create quaternion from Euler angles (XYZ order).

Signature: (pitch:f64 yaw:f64 roll:f64 -- result:Quat)

Example:

0.0 1.57 0.0 math::quat_from_euler -> q

Methods

fn conjugate

Conjugate of this quaternion.

Signature: (q:Quat) conjugate( -- result:Quat)

Example:

q conjugate  // q_conj

fn dot

Dot product with another quaternion.

Signature: (q:Quat) dot(other:Quat -- result:f64)

Example:

other q dot  // d

fn length

Length (magnitude) of this quaternion.

Signature: (q:Quat) length( -- result:f64)

Example:

q length  // len

fn mul

Quaternion multiplication.

Signature: (q:Quat) mul(other:Quat -- result:Quat)

Example:

other q mul  // product

fn normalize

Normalize this quaternion to unit length.

Signature: (q:Quat) normalize( -- result:Quat)

Example:

q normalize  // unit_q

fn inverse

Inverse of this quaternion.

Signature: (q:Quat) inverse( -- result:Quat)

Example:

q inverse -> q_inv

fn length_sq

Squared length of quaternion.

Signature: (q:Quat) length_sq( -- result:f64)

Example:

q length_sq -> len_sq

fn slerp

Spherical linear interpolation to another quaternion.

Signature: (q:Quat) slerp(other:Quat t:f64 -- result:Quat)

Example:

other 0.5 q slerp -> mid

fn rotate_vec3

Rotate a Vec3 by this quaternion.

Signature: (q:Quat) rotate_vec3(v:Vec3 -- result:Vec3)

Example:

v q rotate_vec3 -> rotated

Vec2

2D vector with x and y components.

Struct

Constructors

fn vec2_one

Create a Vec2 with all components set to one.

Signature: ( -- v:Vec2)

Example:

math::vec2_one  // v

fn vec2_zero

Create a Vec2 with all components set to zero.

Signature: ( -- v:Vec2)

Example:

math::vec2_zero  // v

Methods

fn add

Add another Vec2 to this vector.

Signature: (v:Vec2) add(other:Vec2 -- result:Vec2)

Example:

other v add  // sum

fn dot

Dot product with another Vec2.

Signature: (v:Vec2) dot(other:Vec2 -- result:f64)

Example:

other v dot  // d

fn length_sq

Squared length of this vector (avoids sqrt).

Signature: (v:Vec2) length_sq( -- result:f64)

Example:

v length_sq  // len_sq

fn length

Length (magnitude) of this vector.

Signature: (v:Vec2) length( -- result:f64)

Example:

v length  // len

fn lerp

Linear interpolation to another Vec2.

Signature: (v:Vec2) lerp(other:Vec2 t:f64 -- result:Vec2)

Example:

other 0.5 v lerp  // mid

fn neg

Negate this vector.

Signature: (v:Vec2) neg( -- result:Vec2)

Example:

v neg  // neg_v

fn normalize

Normalize this vector to unit length.

Signature: (v:Vec2) normalize( -- result:Vec2)

Example:

v normalize  // unit

fn scale

Multiply this vector by a scalar.

Signature: (v:Vec2) scale(s:f64 -- result:Vec2)

Example:

2.0 v scale  // scaled

fn subtract

Subtract another Vec2 from this vector.

Signature: (v:Vec2) subtract(other:Vec2 -- result:Vec2)

Example:

other v subtract  // diff

fn distance

Distance to another Vec2.

Signature: (v:Vec2) distance(other:Vec2 -- result:f64)

Example:

other v distance -> d

fn angle

Angle of this vector from positive X axis.

Signature: (v:Vec2) angle( -- result:f64)

Example:

v angle -> a

fn rotate

Rotate this vector by an angle.

Signature: (v:Vec2) rotate(angle:f64 -- result:Vec2)

Example:

1.57 v rotate -> rotated

fn perpendicular

Get perpendicular vector (90° counterclockwise rotation).

Signature: (v:Vec2) perpendicular( -- result:Vec2)

Example:

v perpendicular -> perp

Vec3

3D vector with x, y, and z components.

Struct

Constructors

fn vec3_one

Create a Vec3 with all components set to one.

Signature: ( -- v:Vec3)

Example:

math::vec3_one  // v

fn vec3_unit_x

Unit vector along the X axis.

Signature: ( -- v:Vec3)

Example:

math::vec3_unit_x  // v

fn vec3_unit_y

Unit vector along the Y axis.

Signature: ( -- v:Vec3)

Example:

math::vec3_unit_y  // v

fn vec3_unit_z

Unit vector along the Z axis.

Signature: ( -- v:Vec3)

Example:

math::vec3_unit_z  // v

fn vec3_zero

Create a Vec3 with all components set to zero.

Signature: ( -- v:Vec3)

Example:

math::vec3_zero  // v

Methods

fn add

Add another Vec3 to this vector.

Signature: (v:Vec3) add(other:Vec3 -- result:Vec3)

Example:

other v add  // sum

fn cross

Cross product with another Vec3.

Signature: (v:Vec3) cross(other:Vec3 -- result:Vec3)

Example:

other v cross  // c

fn dot

Dot product with another Vec3.

Signature: (v:Vec3) dot(other:Vec3 -- result:f64)

Example:

other v dot  // d

fn length_sq

Squared length of this vector (avoids sqrt).

Signature: (v:Vec3) length_sq( -- result:f64)

Example:

v length_sq  // len_sq

fn length

Length (magnitude) of this vector.

Signature: (v:Vec3) length( -- result:f64)

Example:

v length  // len

fn lerp

Linear interpolation to another Vec3.

Signature: (v:Vec3) lerp(other:Vec3 t:f64 -- result:Vec3)

Example:

other 0.5 v lerp  // mid

fn neg

Negate this vector.

Signature: (v:Vec3) neg( -- result:Vec3)

Example:

v neg  // neg_v

fn normalize

Normalize this vector to unit length.

Signature: (v:Vec3) normalize( -- result:Vec3)

Example:

v normalize  // unit

fn reflect

Reflect this vector around a normal.

Signature: (v:Vec3) reflect(n:Vec3 -- result:Vec3)

Example:

normal v reflect  // reflected

fn scale

Multiply this vector by a scalar.

Signature: (v:Vec3) scale(s:f64 -- result:Vec3)

Example:

2.0 v scale  // scaled

fn subtract

Subtract another Vec3 from this vector.

Signature: (v:Vec3) subtract(other:Vec3 -- result:Vec3)

Example:

other v subtract  // diff

fn distance

Distance to another Vec3.

Signature: (v:Vec3) distance(other:Vec3 -- result:f64)

Example:

other v distance -> d

fn angle_between

Angle between this vector and another.

Signature: (v:Vec3) angle_between(other:Vec3 -- result:f64)

Example:

other v angle_between -> a

Vec4

4D vector with x, y, z, and w components.

Struct

Constructors

fn vec4_one

Create a Vec4 with all components set to one.

Signature: ( -- v:Vec4)

Example:

math::vec4_one  // v

fn vec4_zero

Create a Vec4 with all components set to zero.

Signature: ( -- v:Vec4)

Example:

math::vec4_zero  // v

Methods

fn add

Add another Vec4 to this vector.

Signature: (v:Vec4) add(other:Vec4 -- result:Vec4)

Example:

other v add  // sum

fn dot

Dot product with another Vec4.

Signature: (v:Vec4) dot(other:Vec4 -- result:f64)

Example:

other v dot  // d

fn length

Length (magnitude) of this vector.

Signature: (v:Vec4) length( -- result:f64)

Example:

v length  // len

fn normalize

Normalize this vector to unit length.

Signature: (v:Vec4) normalize( -- result:Vec4)

Example:

v normalize  // unit

fn scale

Multiply this vector by a scalar.

Signature: (v:Vec4) scale(s:f64 -- result:Vec4)

Example:

2.0 v scale  // scaled

fn subtract

Subtract another Vec4 from this vector.

Signature: (v:Vec4) subtract(other:Vec4 -- result:Vec4)

Example:

other v subtract  // diff

fn length_sq

Squared length of this vector (avoids sqrt).

Signature: (v:Vec4) length_sq( -- result:f64)

Example:

v length_sq -> len_sq

fn neg

Negate this vector.

Signature: (v:Vec4) neg( -- result:Vec4)

Example:

v neg -> neg_v

fn lerp

Linear interpolation to another Vec4.

Signature: (v:Vec4) lerp(other:Vec4 t:f64 -- result:Vec4)

Example:

other 0.5 v lerp -> mid