This paper presents the fastest fast Fourier transform (FFT) hardware architectures so far. The architectures are based on a fully parallel implementation of the FFT algorithm. In order to obtain the highest throughput while keeping the resource utilization low, we base our design on making use of advanced shift-and-add techniques to implement the rotators and on selecting the most suitable FFT algorithms for these architectures. Apart from high throughput and resource efficiency, we also guarantee high accuracy in the proposed architectures. For the implementation, we have developed an automatic tool that generates the architectures as a function of the FFT size, input word length and accuracy of the rotations. We provide experimental results covering various FFT sizes, FFT algorithms, and field-programmable gate array boards. These results show that it is possible to break the barrier of 100 GS/s for FFT calculation.