nx_latency_metric_test.nx

nx_latency_metric_test.nx -- proves the HONEST latency-metric organ and uses it to race three divider TOPOLOGIES at W=16: radix-2 (W stages), radix-4 (W/2 stages), and the scalar-equivalent Newton-Raphson reciprocal structure (~log W iterations of multiply-heavy work). WHAT THIS PROVES (FAIL LOUD on every leg): (1) The organ's UNIT metric matches the functional sim's implicit depth-1 model: on a tiny hand-built chain whose longest path is known by hand, nx_lat_unit returns exactly that hand-counted op-depth. (2) The HONEST metric does NOT treat a multiplier as depth-1: a single MUL cell costs 2*ceil(log2 W) gate levels, an ADD costs ceil(log2 W), a boolean costs 1 -- asserted directly against nx_lat_kind_weight, and asserted on a one-MUL chain whose honest depth > its unit depth. (3) THE RACE, told HONESTLY across WIDTH -- the trap, and where it flips. The SAME Newton topology is measured with a DEEP multiplier (the real nx_mul_wide 32-bit-limb schoolbook) and a SHALLOW one (single-cell Wallace model, 2*logW), at W=16 and W=64. The MEASURED honest critical paths are: W=16: radix-2=181 radix-4=139 Newton-deep=363 Newton-shallow=166 W=64: radix-2=967 radix-4=743 Newton-deep=709 Newton-shallow=320 So, honestly: - At SMALL width (W=16) the multiplicative method does NOT pay off: radix-4 wins; the DEEP-multiplier Newton is the WORST (363); and even the SHALLOW-multiplier Newton (166) still loses to radix-4 (139). The naive "log(W) multiplies beats W subtracts" LATENCY claim is FALSE here. - At LARGE width (W=64) the log(W) FRONTIER appears: BOTH Newton variants beat BOTH radix dividers (320 and 709 vs 743 and 967), because the radix dividers' stage count grows linearly in W while Newton's iteration count grows only ~log W. Ordering: shallow-Newton < deep-Newton < r4 < r2. - THE CROSSOVER is the headline: the SAME shallow-multiplier Newton goes from LOSING to radix-4 at W=16 to BEATING it at W=64. That measured sign- flip IS the multiplicative-divider latency win -- and the honest metric refuses to award it at a width where it is not real. Invariant independent of width + multiplier: radix-4 (W/2 stages) always beats radix-2 (W stages). All orderings are ASSERTED, not assumed. Known-answer lines (printed for the gate): four honest critical paths at W=16, then at W=64, then the kind-weight spot-checks. exit 0 iff all asserts hold. HONESTY SCOPE: the Newton network here is the algorithm's STRUCTURAL skeleton (the exact operator dependency chain of nx_alu_divider_newton.nx: normalize ->