spinsfast is a fast spin-s spherical harmonic transform algorithm, which is flexible and exact for band-limited functions. It permits the computation of several distinct spin transforms simultaneously. Specifically, only one set of special functions is computed for transforms of quantities with any spin, namely the Wigner d matrices evaluated at π/2, which may be computed with efficient recursions. For any spin, the computation scales as O(L^3), where L is the band limit of the function.