Design and Performance Report

This report describes the current Luna-Flow/floating/decimal_gda@0.7.1 benchmark run.

Contract

Both libraries consume identical coefficient-and-scale fixtures. arithmetic_only times only the public operation; full_path additionally parses both canonical operand strings. Validation, canonicalization, calibration, and reporting stay outside timing. Division uses exact terminating divisors. Performance is paired only where both implementations pass the independent exact-finite BigInt oracle.

Correctness

The scaling corpus produced 1,476 validations. Floating GDA passed all 738 of its rows; DzmingLi passed 630 and failed 108. Failures start at 4,096 coefficient digits for add, subtract, multiply, and divide. Compare remains correct through 20,000 digits.

The official GDA audit executes 17,651 legal rows from 23 arithmetic/base files; floating GDA passes all of them. DzmingLi passes every shared arithmetic operation, comparison, and apply, but fails 329 toSci rows because formatting does not apply active precision and rounding. Official finite operands reach only 64 coefficient digits, so decTest cannot replace the large-coefficient oracle.

The scalable layer covers 19 exact operations. The 14 newly added operations run through 1,024 digits; exp, ln, and log10 remain decTest-only because identity-only timing would not measure their algorithms and general results need a separate independent transcendental oracle.

DzmingLi's digit_count evaluates bit_length * 30103 in signed Int. On the current native target it can overflow near 21,475 coefficient digits. Product, square, FMA, and integer-power results may double coefficient length and cross the boundary from inputs near 10,738 digits. Multiplication completes at 10,000 digits and non-product operations at 20,000; 32,768 and 65,536 digits reproduce the abort. These are analytical and observed bounds, not one universal exact first-failure point.

Performance

DzmingLi generally leads the arithmetic-only scope at 1–64 digits, while the full-path scope is mixed because parsing and construction are included. At 256 digits, floating GDA leads all five tested operations in both timing scopes. At 1,024 digits, where both remain correct, floating GDA is approximately 3.54–95.44× faster depending on operation and scope. At invalid larger arithmetic sizes, reports retain validated GDA latency but omit paired speedup decisions.

Limits

Results are from one Apple M4 native release run with uncontrolled CPU frequency. The corpus has three deterministic scale profiles and division uses small terminating divisors. These results are regression evidence, not a universal implementation ranking.