Bounded electrostatic target prototype

The optional placer.electrostatic configuration adds unseeded CPU target generation after the existing B2B/bisection placement has produced a legal baseline. The common retargeting, legalizer, detailed placement and legality check process the proposed targets. The final exact integer raw and weighted center HPWL must both be no worse than that baseline. A rejected proposal keeps the baseline and reports its reason.

Omitting the option preserves the legacy serialization and execution branch. Seeded placement retains its existing algorithm and records not_applied_seeded when this option is present. Seed refinement is outside this prototype. Combining anchor_isolated with the option is an explicit configuration error; retarget_isolated keeps its existing final targeting behavior.

For example, an experimental configuration can contain:

{
  "electrostatic": {
    "target_density_milli": 600,
    "max_iterations": 200,
    "max_evaluations": 512,
    "max_backtracks": 4,
    "workers": 4
  }
}

These parameters are heuristics requiring component and physical qualification. The target density is bounded by 700 milli-units. It is a numerical parameter; physical density, routing, timing and foundry rules have separate acceptance gates.

Numerical model

Stored design geometry and published positions remain integer DBU. The workspace adapter supplies the actual integer core rectangle. A bounded local integer view subtracts the core origin before any floating-point conversion. Both axes then use the same scale L=max(core_width,core_height). Supported integer differences are at most 2^52 DBU. Candidate legalization uses that local view and translates checked integer positions back to the original core.

Movable wire pins use physical cell centers and fixed pins retain the existing adapter coordinates. Net weights, repeated pins and the existing fanout cutoff keep their original meanings. The wire objective is weighted-average wirelength with shifted exponentials, shifted weighted means and analytic derivatives. Every inner reduction has a fixed order.

The grid is 64 by 64. Exact integer rectangle/bin intersections compute free capacity from the existing intervals, which already exclude taps, fixed halos and placement blockages. Cell spacing is enforced by the common legalizer. It is not subtracted again from capacity or applied between disconnected intervals.

Physical area is deposited with a uniform rectangle convolved with a unit-integral hat of one bin radius in each axis. Bin weights integrate that kernel. Truncated weights are normalized with the quotient-rule derivative, which preserves each object's total mass. Extremely thin normalized kernel extents are rejected explicitly. Numerical fillers carry the positive slack between target free capacity and real-cell area; they have no pins, are placed deterministically in capacity-bin order, and never enter the physical output.

Let q=M-target*C, rho=q/bin_area, with the arithmetic mean removed. The symmetric discrete finite-volume Neumann operator is solved by direct separable orthonormal cosine transforms. The constant mode is zero and every other eigenvalue is positive. Energy and force are

D = 0.5 * sum(q * phi)
dD/dcenter_i = area_i * sum(phi * dweight_i/dcenter_i)

The force is the adjoint of the same normalized deposition used in the energy. With normalized lengths, energy has length^4 units, its gradient length^3, and the weight in WA + lambda*D has length^-3. The three stages freeze smoothing and density weight separately. The initial density weight uses a guarded wire/density gradient-norm ratio. Stage changes restart momentum and secant history.

Projected accelerated steps use an area/weighted-degree diagonal preconditioner, bounded secant estimates, a majorization check and at most four backtracks. Objective increases restart momentum. Nonfinite state, failed mass/residual checks and insufficient trial budgets produce explicit fallback diagnostics. A bounded line-search stall after a strictly improved exact-target checkpoint retains that checkpoint for the common legalizer and final no-worse gate; a stall without it falls back. The iteration horizon is reported as a horizon, without a convergence-rate claim.

The mathematical basis is the published formulation in Lu et al., ePlace, TODAES 2015. This prototype uses its own fixed-grid discrete operator and differentiated deposition; it does not reproduce the paper's implementation or performance claims.

Admission and work

Quantity	Hard ceiling
Movable cells	100000
Numerical fillers	4096
Pin occurrences	1000000
Nets	100000
Free intervals	250000
Grid bins	4096
Touched bins/object	256
Forward plus adjoint interactions/evaluation	2000000
Accepted iterations	200
Objective evaluations	512
Backtracks per attempt	4
Numerical workers	4
New-state allowance	256 MiB
Total original placement work	20 billion

Additional counters bound cumulative pin evaluations, density interactions, transform terms and capacity intersections. Admission checks the requested evaluation envelope against each remaining budget. Common retargeting, legalization and detailed-placement work shares the additional-work ceiling. The opt-in unseeded baseline and refinement also share a hard 20-billion total ceiling even when a core caller supplies a larger placement limit. Maximum-sized inputs are not promised the maximum horizon. In particular, the conservative worst-case support admission may reject a design whose actual deposition would use fewer bins; the report identifies this budget fallback. Every trial recomputes the wire objective, deposition and full Poisson potential.

A conservative state estimate is 256*(cells+fillers)+64*pins+96*nets+112*intervals+1MiB, including the retained legal baseline, translated view, exact checkpoint, numerical histories, pin/net scratch and fixed grids. It is about 124 MiB at the simultaneous input ceilings, within the unchanged 256 MiB allowance. Loaded design, PDK and snapshot memory are separate. The intended Ibex experiment is estimated below 1 GiB total and requires a 2 GiB/512 MiB/180 s process guard. No cell-by-bin matrix or per-iteration transcript is retained.

Independent transform output jobs preserve fixed serial inner sums. Deposition and global scalar reductions use object/bin order. The caller's thread pool is bounded further to four active numerical jobs.

Qualification scope

Numerical acceptance requires an independently assembled finite-volume dense solve, independent high-precision wire/deposition expectations and step-refined finite differences, including boundary truncation, conservation and large common translations. These tests are separate from the EDA oracle.

Default physical outputs must retain exact dual-PDK identity. Opt-in physical acceptance requires an independent actual-pin DEF/LEF checker for site/row, orientation, overlaps, obstacles, displacement and density, followed by the original full foundry and timing gates. Surrogate energy and unlegalized wirelength do not establish physical QoR or the 1.0M um final HPWL goal.