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Math Module

The math module provides common floating-point math functions and constants. Checked operations return MathError, with read-only kind and detail fields plus message() and to_string().

Import​

Mux
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Constants​

  • math.pi returns float
  • math.e returns float

Unary Functions​

All unary math functions take one float and return a float:

  • math.sqrt(x)
  • math.sin(x)
  • math.cos(x)
  • math.tan(x)
  • math.asin(x)
  • math.acos(x)
  • math.atan(x)
  • math.ln(x)
  • math.log2(x)
  • math.log10(x)
  • math.exp(x)
  • math.abs(x)
  • math.floor(x)
  • math.ceil(x)
  • math.round(x)
  • math.trunc(x)
  • math.fract(x)
  • math.sinh(x)
  • math.cosh(x)
  • math.tanh(x)
  • math.asinh(x)
  • math.acosh(x)
  • math.atanh(x)
  • math.to_radians(x)
  • math.to_degrees(x)
  • math.exp2(x)
  • math.exp_m1(x) (computes exp(x) - 1 accurately near zero)
  • math.ln_1p(x)
  • math.cbrt(x)
  • math.signum(x)
  • math.erf(x)
  • math.gamma(x)

Sequence reductions take list<float> and return result<float, MathError>. math.sum(values) uses Neumaier compensation; math.product(values) retains the rounding error of each finite multiplication. Empty inputs use the usual identities (0.0 and 1.0). A non-float element is reported as an error.

Classification helpers return bool: math.is_nan(x), math.is_infinite(x), and math.is_finite(x).

Integer helpers take and return int: math.gcd(a, b), math.lcm(a, b), and math.isqrt(x). isqrt returns zero for non-positive inputs; overflowing integer results saturate at the largest representable int.

Binary Functions​

All binary math functions take two float values and return a float:

  • math.atan2(y, x)
  • math.log(x, base)
  • math.min(a, b)
  • math.max(a, b)
  • math.hypot(a, b)
  • math.pow(base, exp)

Interpolation and Integer Helpers​

  • math.clamp(value, lower, upper) returns the value limited to the inclusive range. Reversed bounds are normalized; math.clamp_checked reports them as an error instead.
  • math.lerp(start, end, amount) linearly interpolates without restricting amount to 0..1.
  • math.inverse_lerp(start, end, value) returns a result<float, MathError> and rejects equal endpoints.
  • math.smoothstep(edge0, edge1, value) returns a clamped cubic interpolation and rejects non-increasing edges.
  • math.factorial(n), math.combinations(n, k), and math.permutations(n, k) return result<int, MathError> and report negative, out-of-range, or overflowing inputs.

Example​

math_example.mux
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