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We present $\mathcal{O}(N^2)$ estimators for the small-scale power spectrumand bispectrum in cosmological simulations. In combination with traditionalmethods, these allow spectra to be efficiently computed across a vast range ofscales, requiring orders of magnitude less computation time than Fast FourierTransform based approaches alone. These methods are applicable to any tracer;simulation particles, halos or galaxies, and take advantage of the simplegeometry of the box and periodicity to remove almost all dependence on largerandom particle catalogs. By working in configuration-space, both power spectraand bispectra can be computed via a weighted sum of particle pairs up to someradius, which can be reduced at larger $k$, leading to algorithms withdecreasing complexity on small scales. These do not suffer from aliasing orshot-noise, allowing spectra to be computed to arbitrarily large wavenumbers.The estimators are rigorously derived and tested against simulations, and theircovariances discussed. The accompanying code, HIPSTER, has been publiclyreleased, incorporating these algorithms. Such estimators will be of great usein the analysis of large sets of high-resolution simulations.

A Faster Fourier Transform? Computing Small-Scale Power Spectra and Bispectra for Cosmological Simulations in $\mathcal{O}(N^2)$ Time