Abstract
We designed a VLSI (Very Large Scale Integrated circuit) chip of FFT multiplier using a floating-point representation with optimal data length based on an experimental error analysis. Using the hardware implementation, we can perform 2^5 to 2^<13> hexadecimal digit (39 to 9,831 decimal digit) multiplication 25.1 to 45.6 times (33.9 times in average) faster than using FFTW3, at an area cost of 9.05mm^2. The hardware FFT multiplier has 64 times faster performance than exflib (a multi-digit arithmetic library using Karatsuba method) for longer than 2^<21> hexadecimal digit (≒2,520,000 decimal digit) multiplication. Considering the wide applications of its FFT modules, the performance and cost of the FFT multiplier justifies the VLSI implementation.
