FPFS (Fourier Power Function Shaplets) is a fast, accurate shear estimator for the shear responses of galaxy shape, flux, and detection. Utilizing leading-order perturbations of shear (a vector perturbation) and image noise (a tensor perturbation), the code determines shear and noise responses for both measurements and detections. Unlike methods that distort each observed galaxy repeatedly, the software employs analytical shear responses of select basis functions, including Shapelets basis and peak basis. FPFS is efficient and can process approximately 1,000 galaxies within a single CPU second, and maintains a multiplicative shear estimation bias below 0.5% even amidst blending challenges.