Abstract: Disclosed are methods and systems for specifying an analytical wirelength formulation that is continuous along with its derivative. One approach performs a wirelength estimate in which a continuous formulation is employed to identify and use a bounding box to enclose circuit elements of a net, and in which an attribute of the bounding box may be completely or partially diagonal. Such formulations are used for optimizing the wirelength using numerical approaches.

Abstract: 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: Function = ? n ? ? p ? ( n ) ? b i , j ? ( 1 2 ? ( ? + ( x i - x j ) 2 + ? + ( y i - y j ) 2 ) + ( 1 - 1 2 ) ? ? + ( x i - x j ) 2 + ( y i - y j ) 2 - 2 ? ( x i - x j ) 2 ? ( y i - y j ) 2 ? + ( x i - x j ) 2 ? ( y i - y j ) 2 ) 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 bi,j represents a weighting factor that biases the function based on the desired closeness of pins i and j.

Abstract: Disclosed are methods and systems for specifying an analytical wirelength formulation that is continuous along with its derivative. One approach performs a wirelength estimate in which a continuous formulation is employed to identify and use a bounding box to enclose circuit elements of a net, and in which an attribute of the bounding box may be completely or partially diagonal. Such formulations are used for optimizing the wirelength using numerical approaches.

Abstract: 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: Function = ? n ? ? p ? ( n ) ? b i , j ? ( 1 2 ? ( ? + ( x i - x j ) 2 + ? + ( y i - y j ) 2 ) + ( 1 - 1 2 ) ? ? + ( x i - x j ) 2 + ( y i - y j ) 2 - 2 ? ( x i - x j ) 2 ? ( y i - y j ) 2 ? + ( x i - x j ) 2 ? ( y i - y j ) 2 ) 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 bi,j represents a weighting factor that biases the function based on the desired closeness of pins i and j.

Abstract: Disclosed are methods and systems for formulating a wirelength estimate that takes into account whether any of the routing directions are unavailable. Under certain circumstances, one or more of the routing layers may not be available for routing a wire. If this occurs, then the bounding box that is determined for performing the wirelength estimate would take into account the unavailability of the layer.

Abstract: 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.