Branchless Computation - A Systematic Framework for Eliminating Conditional Branching via the Absolute Value Function

Presentation of a systematic framework for eliminating conditional branching from computational code by expressing traditionally branch-dependent mathematical functions as closed-form arithmetic expressions grounded in the absolute value function. We demonstrate that abs(·) constitutes a universal, branchless primitive for conditional logic: its hardware implementation is a single unconditional bit operation, and all standard conditional constructs - sign extraction, maximum, minimum, clamping, thresholding, half-wave rectification, and others can be derived from it without any logical evaluation.