@math

Import this module with import @math.

Unless noted otherwise, all math functions accept any integer or float type (i8–i64, u8–u64, f32, f64). Functions that return the same type as their input are marked with -> T below; others specify their return type explicitly.

Basic Arithmetic

Function	Signature	Description
abs	(n T) -> T	Absolute value
neg	(n T) -> T	Negation
sign	(n T) -> i64	Sign (-1, 0, or 1)
mod	(x f64, y f64) -> f64	Floating-point remainder, carrying the sign of x
copysign	(x f64, y f64) -> f64	Magnitude of x with the sign of y
fma	(x f64, y f64, z f64) -> f64	Fused multiply-add: x * y + z with a single rounding step
modf	(x f64) -> (f64, f64)	Integer and fractional parts of x, both carrying its sign. Both values must be captured: mut whole, frac = math.modf(x)

Min/Max/Clamp

Function	Signature	Description
min	(a T, b T) -> T	Minimum of two values. T is the arguments’ common type, as a binary operator would type them (see Sized Types)
max	(a T, b T) -> T	Maximum of two values; T as for min
clamp	(value T, min T, max T) -> T	Clamp value to range [min, max]; T as for min

Rounding

Function	Signature	Description
floor	(n T) -> f64	Round down to nearest integer (returns f64)
ceil	(n T) -> f64	Round up to nearest integer (returns f64)
round	(n T) -> f64	Round to nearest integer (returns f64)
trunc	(n T) -> f64	Truncate toward zero (returns f64)

Powers and Roots

Function	Signature	Description
pow	(base T, exp T) -> f64	Raise base to exponent
sqrt	(n T) -> f64	Square root
cbrt	(n T) -> f64	Cube root
hypot	(x T, y T) -> f64	Hypotenuse (sqrt(x^2 + y^2))
exp	(n T) -> f64	e raised to the power n
exp2	(n T) -> f64	2 raised to the power n

Logarithms

Function	Signature	Description
log	(n T) -> f64	Natural logarithm
log2	(n T) -> f64	Base 2 logarithm
log10	(n T) -> f64	Base 10 logarithm
log_base	(value T, base T) -> f64	Logarithm with custom base

Trigonometry

Function	Signature	Description
sin	(rad T) -> f64	Sine
cos	(rad T) -> f64	Cosine
tan	(rad T) -> f64	Tangent
asin	(n T) -> f64	Arc sine
acos	(n T) -> f64	Arc cosine
atan	(n T) -> f64	Arc tangent
atan2	(y T, x T) -> f64	Arc tangent of y/x
sinh	(n T) -> f64	Hyperbolic sine
cosh	(n T) -> f64	Hyperbolic cosine
tanh	(n T) -> f64	Hyperbolic tangent
deg_to_rad	(deg T) -> f64	Degrees to radians
rad_to_deg	(rad T) -> f64	Radians to degrees

Statistical

Function	Signature	Description
factorial	(n i64) -> i64	Factorial (n must be non-negative)
gcd	(a i64, b i64) -> i64	Greatest common divisor
lcm	(a i64, b i64) -> i64	Least common multiple

Number Properties

Function	Signature	Description
is_prime	(n i64) -> bool	Check if prime
is_even	(n i64) -> bool	Check if even
is_odd	(n i64) -> bool	Check if odd
is_infinite	(n f64) -> bool	Check if infinite
is_nan	(n f64) -> bool	Check if NaN
is_finite	(n f64) -> bool	Check if finite (not infinite or NaN)
is_power_of_two	(n i64) -> bool	Check if a positive power of two; zero and negatives are not
next_power_of_two	(n i64) -> i64	Smallest power of two >= n, or 1 when n <= 0. Panics (P0106) above 2^62, where the result would exceed MAX_I64

Utility

Function	Signature	Description
lerp	(a T, b T, t T) -> f64	Linear interpolation between a and b by factor t
remap	(v f64, in_lo f64, in_hi f64, out_lo f64, out_hi f64) -> f64	Linearly map v from [in_lo, in_hi] onto [out_lo, out_hi] without clamping; panics (P0122) if in_lo == in_hi
approx_equal	(a f64, b f64, epsilon f64) -> bool	True if abs(a - b) <= epsilon
distance	(x1 T, y1 T, x2 T, y2 T) -> f64	Euclidean distance between two 2D points

Constants

• PI - Pi (3.14159…)
• E - Euler’s number (2.71828…)
• PHI - Golden ratio (1.61803…)
• SQRT2 - Square root of 2
• LN2 - Natural log of 2
• LN10 - Natural log of 10
• TAU - Tau (2*Pi)
• INF - Positive infinity
• NEG_INF - Negative infinity
• EPSILON - Smallest representable f64 difference
• MAX_I64 - Largest value an i64 can hold (9223372036854775807)
• MIN_I64 - Smallest value an i64 can hold (-9223372036854775808)
• MAX_F64 - Largest finite value an f64 can hold (1.7976931348623157e308)
• MIN_F64 - Smallest, i.e. most negative, finite value an f64 can hold (-1.7976931348623157e308)