Adaptive Physical Layer Exploitation for CRT-Packed Arithmetic

Abstract

Shannon's radix economy establishes base‑3 as the most efficient representation for numerical information, yet binary logic dominates hardware. Recent work circumvented this barrier by using the Chinese Remainder Theorem (CRT) over Eisenstein integers to pack six independent complex numbers into a 64‑bit register, achieving 48 real operations per cycle with sub‑0.005% overhead. This computational density shifts the bottleneck to the DRAM Physical Layer (PHY), where standard worst‑case timing margins waste 30‑40% of available bandwidth. This work presents a two‑tier optimisation suite that leverages the structured data patterns of CRT‑packed arithmetic. The static tier provides four reconfigurations—72‑bit bus exploitation via ECC pin hijacking, Data Bus Inversion (DBI) for thermal headroom, CTLE equaliser hard‑tuning, and six‑stream burst aggregation—yielding a 24% bandwidth gain. The adaptive tier repurposes the native XOR parity lane (Lane 6) as a live signal‑to‑noise sensor, feeding a hardware PID controller that continuously adjusts DRAM clock frequency and transmit voltage to maintain a user‑configurable error target. The closed‑loop system delivers a net 40‑45% bandwidth increase, 10‑15% per‑operation energy reduction, and transforms reliability from a fixed MTBF into a tunable deployment parameter. Integration requires BIOS support, a reordered memory scheduler, and on‑die PMICs. The architecture operates at the absolute physical boundary of binary silicon, limited only by the speed of light on copper interconnects.