Frontier Systems
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RTL Design PPA Attribution
Chip PPA Optimization
How large is the post-placement PPA gap across 16 formally equivalent multiplier pairs, and does its sign agree between two independent flows in 14 of 16 pairs?
THE QUESTION
Can an AI generate an RTL Montgomery-multiplier block that passes formal equivalence AND beats commercial synthesis on reference-normalised PPA-product — against agentic pass rates of 94% on RTLLM v2.0, where functional correctness is already saturating and PPA is the unmeasured axis? · Verifier: Formal equivalence check plus synthesis and timing report, minutes
WORK ORDER
Post-placement power-performance-area gaps between formally equivalent modular multiplier descriptions
BACKGROUND
What this Apodex Lab is
Hardware accelerators and secure cryptoprocessors rely on dedicated modular arithmetic units, such as Montgomery multipliers, to execute large-integer calculations. When engineers or automated systems write the register-transfer-level source code for these blocks, they select structural architectures to minimise power consumption, propagation delay, and silicon area. Yet whether structural choices in the source text govern the completed physical circuit depends on the synthesis and physical-design tools that map logic gates into standard-cell layouts. If commercial tools routinely absorb or overwrite source-level decisions, apparent architectural advantages disappear before fabrication.
Functional correctness on hardware generation benchmarks has reached pass rates around 94 percent, shifting attention to power, performance, and area metrics where evidence is unresolved. Published evaluations score designs on a single synthesis run in one standard-cell library, rarely advancing past synthesis to post-placement timing closure. Because no systematic cross-facility replication exists, the share of an architectural gap that survives physical implementation has never been quantified. For formally equivalent Montgomery multipliers at operand widths of 1024 and 2048 bits differing in carry-save accumulation, Booth recoding, pipeline depth, or processing-element array topology, the field lacks ground truth on whether power-performance-area gains reflect the source code or the specific tool configuration.
The Chip PPA Optimization Apodex Lab measures the post-placement power-performance-area-product gap across 16 baseline-variant multiplier pairs evaluated independently by two implementation houses. Across 32 pair evaluations reporting square micrometres, milliwatts, and nanoseconds, the protocol resolves mean axis gaps within a 95 percent confidence interval of 12 percentage points and tests whether the sign of the gap agrees across organisations. If measured differences fail to replicate or fall near chance rather than agreeing in at least 14 of 16 pairs, teams can defund custom source-level datapath authoring and redirect effort to synthesis-recipe optimization.
WHY NOW
Why the field is spending on an assumption
Evaluations of arithmetic hardware descriptions routinely report reference-normalised power, performance, and area labels using a single synthesis flow in one standard-cell library, mostly stopping before placement. Functional equivalence checks now settle functional correctness in minutes, and fast surrogate estimators predict implementation outcomes at scale. However, published benchmarks cannot show whether an architectural advantage written into register-transfer-level source survives physical placement and timing closure. They also cannot determine whether reported improvements reflect true circuit advantages or the quirks of a single proprietary tool chain.
WHAT WE’D BUY
What we would ask a laboratory to run
We are not buying the answer. We are buying a measurement with an interval — and the bars it will be compared against.
Two independent ASIC design facilities implement ten formally verified register-transfer-level descriptions of a Montgomery modular multiplier at operand widths of 1024 and 2048 bits. The sets comprise one baseline architecture, eight single-axis structural variants, and one cosmetic duplicate. Both facilities execute sealed pre-implementation estimates, six synthesis configurations, and three post-placement timing-closure runs using their own licensed tool chains. They measure raw cell area, power under fixed stimulus, and worst achieved clock period. The deliverable is the mean post-placement power-performance-area gap across 32 baseline-variant pair comparisons, returned with a pooled 95 percent confidence interval no wider than 12 percentage points total, alongside cross-house sign agreement resolved to within about ±15 percentage points and the mean signed error of the pre-implementation estimate.
SCOPE & LIMITS
The results reflect unattended post-placement timing closure on 1024-bit and 2048-bit Montgomery multipliers rather than full routing with parasitic extraction or hand-tuned tape-out implementations.
WHO EXECUTES
The kind of lab that can run this
An independent silicon design-services house or university ASIC group holding licensed commercial synthesis and place-and-route tools plus a signed-off standard-cell library and formal equivalence checker, staffed by engineers who did not author any of the candidate register-transfer-level descriptions.
EXECUTOR KIND
independent-reimplementation
WAYS IN
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