PhasorFlow: A Python Library for Unit Circle Based Computing

We present PhasorFlow, an open-source Python library for computing on the S^1 unit circle. Inputs are encoded as complex phasors z=e^{iϕ} on the N-torus (\mathbb{T}^N); as computation proceeds through unitary wave-interference gates, global norm is preserved while components drift into \mathbb{C}^N, letting algorithms leverage continuous geometric gradients. PhasorFlow makes three contributions. First, we formalize the Phasor Circuit model (N threads, M gates) with a 22-gate library spanning standard-unitary, non-linear, neuromorphic, and encoding operations under full matrix-algebra simulation. Second, we introduce the Variational Phasor Circuit (VPC), a trainable phase-native classifier analogous to variational quantum circuits. Third, we introduce the Phasor Transformer block and Large Phasor Model (LPM), replacing QK^TV attention with a parameter-free DFT token-mixing layer. We validate the framework on financial volatility detection, neuromorphic associative memory, neural binding, period finding, and algorithmic logic applications that are unique to the library. This positions unit-circle computing as a deterministic, lightweight paradigm on classical hardware. Available at https://github.com/mindverse-computing/phasorflow.