  We have developed a software-based polarization spectrometer, PolariS, to
acquire full-Stokes spectra with a very high spectral resolution of 61 Hz. The
primary aim of PolariS is to measure the magnetic fields in dense star-forming
cores by detecting the Zeeman splitting of molecular emission lines. The
spectrometer consists of a commercially available digital sampler and a Linux
computer. The computer is equipped with a graphics processing unit (GPU) to
process FFT and cross-correlation using the CUDA (Compute Unified Device
Architecture) library developed by NVIDIA. Thanks to a high degree of precision
in quantization of the analog-to-digital converter and arithmetic in the GPU,
PolariS offers excellent performances in linearity, dynamic range, sensitivity,
bandpass flatness and stability. The software has been released under the MIT
License and is available to the public. In this paper, we report the design of
PolariS and its performance verified through engineering tests and
commissioning observations.
