Struct CurveParams

pub struct CurveParams<F>
where
    F: FixedPointNumber,
{
    pub l: F,
    pub k: F,
    pub x0: F,
}

Defines parameters for a logistic (sigmoid) curve used in piecewise reward modeling.

Concept: Logistic Curve Parameterization

The curve follows:

f(x) = L / (1 + e^(-k*(x - x0)))

where:

• L = maximum value (upper asymptote)
• k = steepness (growth rate; positive for a growing S-curve)
• x0 = midpoint / inflection point

Type Requirements

FixedPoint must implement [FixedSignedCast<Signed = FixedI128>]. Both unsigned and signed fixed-point types satisfy this bound. Signed arithmetic (x - x0 when x < x0, and the negated exponent) is performed in the concrete FixedI128 workspace and projected back.

Fields

l: F

Maximum reward level (L): upper asymptotic bound of the curve

k: F

Steepness factor (k): controls how sharply the curve transitions.

• k > 0: growing S-curve (output increases with x)
• k < 0: decaying S-curve (output decreases with x)
• k = 0: constant L/2 for all inputs

x0: F

Inflection point (x0): input value where the curve is steepest.

At x = x0: f(x0) = L / 2.

Implementations

impl<FixedPoint> CurveParams<FixedPoint>

where FixedPoint: FixedPointNumber + FixedSignedCast<Signed = FixedI128>,

pub fn evaluate(&self, x: FixedPoint) -> FixedPoint

Evaluates the logistic curve at input x.

Formula

f(x) = L / (1 + e^(-k*(x - x0)))

Signed intermediates (x - x0, k*(x - x0), and its negation) are computed in FixedI128 via FixedSignedCast so the method works correctly for both signed and unsigned FixedPoint types..