Volder: CORDIC shift-add coordinate rotation and vectoring

What changed

Volder presents signed binary shift-add coordinate operations for real-time trigonometric rotation and vectoring, with a fixed gain correction and finite-word navigation implementation.

Scientific scope

Volder presents signed binary shift-add coordinate operations for real-time trigonometric rotation and vectoring, with a fixed gain correction and finite-word navigation implementation. Exact 1959 IRE Trans. Electron. Comput. EC-8(3),330-334, authorized reprint PDF 1-5 all technical text read; reprint pagination differs from original. First quadrant-handling step swaps/signs coordinates by 90 degrees; subsequent signed shift-add pseudo-rotations provide rotation/vectoring with constant gain only when scheduled steps are retained. Gain compensation and finite word/truncation error remain; navigation example includes two multiplication routines, not an entirely multiplication-free application. Own ideal 23-step gain 1.64676025812105 differs from printed 1.646760255 by 3.12 e-9: initial 1 e-9 equality check failed and is preserved, original finite-precision coefficient/table glyphs unreconstructed. No binary-table/hardware-time replication. Similar multiply/divide/hyperbolic/log routines are mentioned but not derived here; later unified methods remain separate. No all-domain optimality or independent certification.

Evidence

Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.

Contributors

Jack E. Volder · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

Full scientific record · Browse contribution grades · Request a correction