Abstract: Delay look-up table（LUT） of standard logic circuits are useful in applications such as auto-synthesis and static timing analysis.The accuracy along with numerical convexity and smoothness of LUT will influence the final circuit design greatly.A convex smoothing algorithm suitable for real application of such circuits is proposed in this paper.It employs tensor-product B-spline technique originated from computer-aided geometric design to approximate the delay function in LUT and retains convexity by regulating the B-spline coefficients.The solution process of these coefficients is formulated as a semidefinite programming，and hence the final model has the globally minimized fitting error.To demonstrate the efficiency and accuracy，the delay LUT of standard library cells are used as numerical examples.

Key words: delay look-up table, B-spline, convex, smoothness, semidefinite programming

摘要： 门电路延时参数的查找表在电路逻辑综合及静态时序分析中均有重要应用。其精度及数学上的凸特性和平滑程度对电路最终的设计结果有较大的影响。基于绝大多数门电路延时模型的实际特性，提出了一种在给定查找表的基础上进行凸平滑的算法。该算法使用了计算机辅助几何设计中的张量积B样条技术，并通过调整样条系数使平滑后得到的延时模型为凸函数。为了使新延时模型的构造快速且准确，样条系数的求解过程被描述为一个半定规划问题，因此得到的新模型具有全局最小的拟合误差。最后以标准单元库门电路通过SPICE仿真得到的查找表数据为实例，并与其他方法进行对照，验证了该方法的有效性和精度。

关键词: 延时查找表, B样条, 凸函数, 平滑, 半定规划