Low-Latency Parallel Digit Decomposition and Sign Evaluation for CKKS

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Nonlinear functions such as sign, comparison, and ReLU are commonly evaluated in CKKS by approximating them with polynomials. The sign jumps at zero, so inputs on the two sides of zero, however close, must be mapped to outputs that differ by a constant. Comparison is the sign of a difference, and ReLU and max inherit this requirement when computed through the sign at high output precision. To distinguish inputs separated by about $2^{-p}$, polynomial approximation needs $\Theta(p)$ multiplicativ