Analytical placement method and apparatus

摘要

Some embodiments provide an analytical placement method that considers diagonal wiring. This method formulates an objective function that accounts for the use of diagonal wiring during routing. Some embodiments use horizontal, vertical, and ±45° diagonal lines. For such a wiring model, some embodiments use the following objective function: $\mathrm{Function}=\sum _n\sum _{p\left(n\right)}{b}_{i,j}\left(\begin{array}{c}\frac{1}{\sqrt{2}}\left(\sqrt{\mathrm{beta}+{\left(x_i-x_j\right)}^2}+\sqrt{\mathrm{beta}+{\left(y_i-y_j\right)}^2}\right)+\\ \left(1-\frac{1}{\sqrt{2}}\right)\sqrt{\begin{array}{c}\mathrm{beta}+{\left(x_i-x_j\right)}^2+{\left(y_i-y_j\right)}^2-\\ \frac{2{\left(x_i-x_j\right)}^2{\left(y_i-y_j\right)}^2}{\sqrt{\mathrm{beta}+{\left(x_i-x_j\right)}^2{\left(y_i-y_j\right)}^2}}\end{array}}\end{array}\right)$ In this equation, n represents a net, p(n) represents a unique pair of pins i and j of the net n, x and y represent the x-, and y-coordinates of a particular pin, and b_i,j represents a weighting factor that biases the function based on the desired closeness of pins i and j.