Interdependent Latch Setup/Hold Time Characterization via Euler-Newton Curve Tracing on State-Transition Equations

Interdependent characterization of latch setup/hold times is a core component of techniques for pessimism reduction via Setup/Hold Interdependence Aware Static Timing Analysis (SHIA-STA) [1], [2]. We present an efficient and novel method for such characterization, by formulating the interdependent setup-hold time problem as an underdetermined nonlinear equation h(zeta_s,zeta_h) = 0, which we derive from the latch´s state-transition function. We solve this equation numerically using a Moore-Penrose Newton method. Further, we use null-space information from the Newton´s Jacobian matrix to efficiently find constant-clock-to-Q contours (in the setup/hold time plane), via an Euler-Newton curve tracing procedure. We validate the method on TSPC and C²MOS registers, obtaining speedups of more than 20 x over prior approaches while achieving superior accuracy. This speedup increases linearly with the precision with which curve tracing is desired. In view of the importance and large computational expense of latch characterization in industry today, the new technique represents a significant enabling technology for dramatically speeding up industrial timing closure flows.