Algorithmic Details

Deep technical write-ups of selected algorithms used inside Universal. These docs are for readers who want the math, the transfer functions, and the trade-off space rather than the API-level usage.

Available Documents

• LNS log-domain add/sub algorithms — the seven shipped algorithms for evaluating log2(1 + 2^d) and log2(1 - 2^d), with transfer-function plots, error envelopes, and a picker decision tree.
• Multi-component floating-point arithmetic — Priest’s error-free transformations, Bailey/Hida’s hand-crafted fixed-precision dd / qd, Shewchuk’s adaptive expansions, and how Universal’s floatcascade<N> building block ties them together.

Companion sections

• Number Systems — API-level reference for each arithmetic type.
• Design — design rationale and architectural decisions.