Mathematical software for the Fast Fourier Transform We present a library for computing the Fast Fourier Transform (FFT) with an interface that fully embraces the principles of modern C++. We support half, single, and double precision; in-place and out-of-place transforms; scaling; arbitrary dimensions; and both complex and real time domain data. We currently support AVX2 and AVX512 hardware. The API of hpkfft is based on the abstract factory design pattern. We have different types for in-place and out-of-place and template on both precision and domain types to allow static type checking at compilation time. Scaled and unscaled functions have distinct names, and the scale factor is provided at each call site, not beforehand. FFT compute objects are immutable, thread-safe, fully initialized at construction, and managed by smart pointers. Our results are overall more accurate than the leading vendor library. For half precision, only 58 FFT lengths are vendor supported, and on those, we have slightly lower error: a little better than 3% using the geometric mean. Our error for AVX512 single precision is 15% lower in the mean; for AVX512 double precision, 25% lower. Furthermore, our performance is generally higher. In AVX512 half precision, our geometric mean performance on the vendor supported sizes is 15% higher. That grows to 20% when evaluated using a small batch. For single and double precision, our AVX512 performance is over 30% higher in the mean. For AVX2, it is over 40% higher.