Composability rather than computation sets the cost of an analog EML hardware fabric

Computer Science > Emerging Technologies
[Submitted on 15 Sep 2026]
Title:Composability rather than computation sets the cost of an analog EML hardware fabric
View PDF HTML (experimental)Abstract:The operator eml(x, y) = exp(x) - ln(y) with the constant 1 generates the elementary functions, a continuous counterpart to NAND. Whether it yields a useful fabric had not been asked of hardware. We ask in network models, circuit simulation and SkyWater 130 nm layout. Four bipolar junctions evaluate the operator for 13 fJ, beating a width-matched digital datapath by 4-134x. The fabric assembled from them is not cheap: it loses to resource-matched baselines, and over the reals its grammar excludes trigonometry. Amplifiers holding those junctions' operating points take 74.5% of a cell's current, so a cell costs 3000 times what they spend. Extracted non-idealities cost 2.6x when a cell must hold a value and nothing when it need only be repeatable. Sharing them across cells recovers two of the three orders. The premise was that a universal primitive licenses a uniform machine. It survives in the primitive and fails in the machine.
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Facts Only

* The operator $\text{eml}(x, y) = \exp(x) - \ln(y)$ with the constant 1 generates the elementary functions, serving as a continuous counterpart to NAND.
* Four bipolar junctions evaluate the operator for $13\text{ fJ}$.
* This performance beats a width-matched digital datapath by $4-134\text{x}$.
* The fabric assembled from these elements loses to resource-matched baselines.
* The grammar excludes trigonometry over the reals.
* Amplifiers holding junction operating points consume $74.5\%$ of a cell's current.
* A cell costs 3000 times what it spends on the junctions.
* Extracted non-idealities cost $2.6\text{x}$ when a cell must hold a value, and nothing when repeatable.
* Sharing elements recovers two of the three orders of magnitude.

Executive Summary

An operator $\text{eml}(x, y) = \exp(x) - \ln(y)$ with the constant 1 generates elementary functions, serving as a continuous counterpart to NAND logic. The operator was evaluated in network models, circuit simulations, and SkyWater 130 nm layout considerations. Four bipolar junctions evaluate the operator for $13 \text{ fJ}$, which is significantly faster than a width-matched digital datapath by a factor of $4-134\text{x}$. The resulting fabric assembled from these elements loses to resource-matched baselines, and the grammar excludes trigonometry. Amplifiers holding the junctions' operating points consume $74.5\%$ of a cell's current, making a single cell cost approximately 3000 times the energy spent on the junctions. Extracted non-idealities cost $2.6\text{x}$ when a cell must hold a value, but nothing when it only needs to be repeatable. Sharing these elements across cells recovers two of the three orders of magnitude. The underlying premise was that a universal primitive licenses a uniform machine, but this premise fails within the physical machine itself.

Full Take

The core argument pivots on the tension between abstract computational primitives (the universal primitive) and physical hardware constraints (the machine). The finding suggests that achieving theoretical efficiency in a system is insufficient if the underlying physical implementation introduces disproportionate costs and limitations. The transition from ideal mathematical functions to realizable hardware reveals that abstraction alone does not guarantee efficiency; rather, the specific nature of the physical realization—how non-idealities are managed—determines utility. The failure described is not in the mathematical operator itself but in the assumption that a universal primitive naturally licenses an efficient machine when confronted with real-world physics like current sharing and non-ideal extraction costs. This points to a systemic challenge where optimizing for theoretical elegance ignores the high cost associated with handling physical realities, suggesting that true system efficiency requires embedding resource management directly into the definition of the primitive rather than treating it as an external license. The implication is that future hardware development must account for the complexity of non-idealities from the outset to avoid massive divergence between potential and actual performance.

Composability rather than computation sets the cost of an analog EML hardware fabric

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