GRG Computational Cost and Hardware

Binary sector indices and power-of-two scaling motivate investigation of digital implementations. They do not establish a performance advantage for the complete calculation.

Define the Task

Kernel evaluation, generation of radial nodes, drawing a raster boundary, filling a disk, and building a volume are different tasks. Their complexity depends on the output representation and implementation.

Count Complete Costs

Include generation or retrieval of geometric ratios, arithmetic precision, divisions and square roots, precomputation, memory access, and output generation. A final multiplication alone does not describe the complete cost.

Hardware Directions

Possible directions include fixed-point arithmetic, lookup tables, vectorisation, parallel execution, and programmable hardware. Each requires an implementation and measurements; their availability is not a claim that GRG already outperforms alternatives.

Evidence Required

Use the benchmark protocol and publish comparisons at equal achieved accuracy. Test rounding, cancellation, overflow, and refinement limits. State what is geometric identity and what is numerical approximation.

Current Status

The current formulation supplies geometric kernels and accuracy proofs. This page makes no unsupported claim of speed, stability, throughput superiority, or three-dimensional scaling.