`std/gradient`

Automatic differentiation: the derivative of a function written in ordinary arithmetic, computed alongside its value and exact to the scalar's own precision, with no step size and no symbolic algebra.

Dual is the forward mode. It carries a value and the rate at which that value changes, and because it is itself a Real it runs through every function that is generic over Real - geometry, animation, physics - without that function being written for it. The package is pure TorbScript: no foreign functions, and no dependency on std/tensor.

Modules

std/gradient/dual[Dual], a value together with the rate at which it changes, and [derivative], the one-call form of forward-mode differentiation.

Everything

fn derivativeThe derivative of a function of one variable, at a point: the function is called once with a [Dual.variable] and the rate of what it answers is the derivative.
type DualA number and its rate of change: the primal part is the value a plain Scalar would have, and the rate part is how fast that value changes with the variable being differentiated.
extend Dual<Scalar> with Power<Int64>A whole power: the rate is n * f ** (n - 1) * f', and zero for n == 0.