Discrete or continuous.
Would prefer a discrete function f(t) that takes on the values -1, 1 for integer t.
Let's say F(t) is the sum from f(0) to f(t).
Preferably F(t) should look like an example of a random walk. And ideally there is a way to generate a family of functions for f(t), where each F(t) looks like a different sample of a random walk.
And the sum from 0 to t of f, is some easily calculated, or closed form solution, where the time it takes to calculate the sum is less than linear with respect to t.