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The nonuniform fast Fourier transform (NUFFT) generalizes the FFT to off-griddata. Its many applications include image reconstruction, data analysis, andthe numerical solution of differential equations. We present FINUFFT, anefficient parallel library for type 1 (nonuiform to uniform), type 2 (uniformto nonuniform), or type 3 (nonuniform to nonuniform) transforms, in dimensions1, 2, or 3. It uses minimal RAM, requires no precomputation or plan steps, andhas a simple interface to several languages. We perform the expensivespreading/interpolation between nonuniform points and the fine grid via asimple new kernel---the `exponential of semicircle' $e^{\beta \sqrt{1-x^2}}$ in$x\in[-1,1]$---in a cache-aware load-balanced multithreaded implementation. Thedeconvolution step requires the Fourier transform of the kernel, for which wepropose efficient numerical quadrature. For types 1 and 2, rigorous errorbounds asymptotic in the kernel width approach the fastest known exponentialrate, namely that of the Kaiser--Bessel kernel. We benchmark against severalpopular CPU-based libraries, showing favorable speed and memory footprint,especially in three dimensions when high accuracy and/or clustered pointdistributions are desired.

A parallel non-uniform fast Fourier transform library based on an "exponential of semicircle" kernel