Abstract: Methods and systems for determining a numerical delay model based on one or more discretized delay models are described. A discretized delay model is a delay model in which the delay behavior is represented using a set of discrete data points of delay behavior. A numerical delay model is a delay model that can be used by a numerical solver to optimize a cost function. In general, computing delay using a numerical delay model is significantly faster than computing delay using discretized delay models. This performance improvement is important when optimizing a design for various metrics like timing, area and leakage power, because repeated delay computations are required in circuit optimization approaches.

Abstract: Systems and techniques are described for performing numerical delay, area, and leakage power optimization on a circuit design. During operation, an embodiment can iteratively perform at least the following set of operations in a loop, wherein in each iteration a current threshold voltage value is progressively decreased: (a) perform numerical delay optimization on the circuit design using a numerical delay model that is generated using gates in a technology library whose threshold voltages are equal to the current threshold voltage; (b) perform a total negative slack based buffering optimization on the circuit design; and (c) perform a worst negative slack touchup optimization on the circuit design that uses gates whose threshold voltages are greater than or equal to the current threshold voltage. Next, the embodiment can perform combined area and leakage power optimization on the circuit design. The embodiment can then perform multiple iterations of worst negative slack touchup optimization.

Abstract: Systems and techniques are described for discretizing gate sizes during numerical synthesis. Some embodiments can receive an optimal input capacitance value for an input of an optimizable cell, wherein the input capacitance value is determined by a numerical solver that is optimizing the circuit design. Note that the circuit design may be optimized for different objective functions, e.g., best delay, minimal area under delay constraints, etc. Next, the embodiments can identify an initial library cell in a technology library whose input capacitance value is closest to the optimal input capacitance value. The embodiments can then use the initial library cell to attempt to identify a better (in terms of the objective function that is being optimized) library cell in the technology library. The delay computations used during this process are also minimized.

Abstract: Systems and techniques are described for performing numerical delay, area, and leakage power optimization on a circuit design. During operation, an embodiment can iteratively perform at least the following set of operations in a loop, wherein in each iteration a current threshold voltage value is progressively decreased: (a) perform numerical delay optimization on the circuit design using a numerical delay model that is generated using gates in a technology library whose threshold voltages are equal to the current threshold voltage; (b) perform a total negative slack based buffering optimization on the circuit design; and (c) perform a worst negative slack touchup optimization on the circuit design that uses gates whose threshold voltages are greater than or equal to the current threshold voltage. Next, the embodiment can perform combined area and leakage power optimization on the circuit design. The embodiment can then perform multiple iterations of worst negative slack touchup optimization.

Abstract: Systems and techniques are described for solving an optimization problem using a constraints solver. A set of constraints that correspond to the optimization problem can be generated. Next, a set of upper bound constraints can be added to the set of constraints, wherein the set of upper bound constraints imposes an upper bound on one or more variables that are used in an objective function of the optimization problem. Next, the embodiments can iteratively perform the following set of operations on a computer: (a) solve the set of constraints using the constraints solver; (b) responsive to the constraints solver returning a solution, decrease the upper bound; and (c) responsive to the constraints solver indicating that no solutions exist or that the constraints solver timed out, increase the upper bound. The solution with the lowest upper bound value can be outputted as the optimal solution for the optimization problem.

Abstract: Systems and techniques are described for performing area recovery on a circuit design. Some embodiments can select a gate for area recovery in accordance with a reverse-levelized processing order, wherein an output pin of a driver gate is electrically coupled to an input pin of the gate. Next, the embodiment can determine a maximum delay value from an input pin of the driver gate to an output pin of the gate that does not create new timing requirement violations or worsen existing timing requirement violations at any of the timing endpoints of the circuit design. The embodiment can then downsize the gate based on the maximum delay value, wherein said downsizing comprises inputting the maximum delay value in a closed-form expression. Timing margin computation can be used to ensure that timing violations are not worsened when the embodiment recovers area from non-timing-critical regions of the circuit design.

Abstract: Systems and techniques are described for solving a gate-sizing optimization problem using a constraints solver. Some embodiments can create a constraints problem based on a gate-sizing optimization problem for a portion of a circuit design. Specifically, the constraints problem can comprise a set of upper bound constraints that impose an upper bound on one or more variables that are used in the objective function of the gate-sizing optimization problem. Next, the embodiments can solve the gate-sizing optimization problem by repeatedly solving the constraints problem using a constraints solver. Specifically, prior to each invocation of the constraints solver, the upper bound can be increased or decreased based at least on a result returned by a previous invocation of the constraints solver.

Abstract: Methods and systems for excluding library cells are described. Some embodiments receive a generic logical effort value and optionally a generic parasitic delay value for a timing arc of a library cell type. Next, library cells of the library cell type are excluded whose specific logical effort values for the timing arc are greater than the generic logical effort value by more than a first threshold and/or optionally whose specific parasitic delay values for the timing arc are greater than the generic parasitic delay value by more than a second threshold. A new generic logical effort value and optionally a new generic parasitic delay value can be determined based on at least some of the remaining library cells. The process of excluding library cells and determining new generic logical effort values and optionally new generic parasitic delay values can be performed iteratively.

Abstract: Systems and techniques are described for estimating optimal gate sizes in a circuit design using numerical delay models of cells and cell types in a technology library. Gate sizes are optimized in the circuit design in a reverse-levelized processing order. Gates that are at the same level in the reverse-levelized processing order, and whose inputs are electrically connected to the same driver output are optimized together. A closed-form expression is used to determine the optimized size for each gate in a set of gates that are optimized together. Some embodiments perform multiple optimization iterations, wherein in each optimization iteration all of the gates in the circuit design are processed in the reverse-levelized processing order. The iterative optimization process terminates when one or more termination conditions are met.

Abstract: Systems and techniques are described for optimizing a circuit design by using a numerical solver. Some embodiments construct a set of lower bound expressions for a parameter that is used in an approximation of an objective function. Next, the embodiments evaluate the set of lower bound expressions to obtain a set of lower bound values. The embodiments then determine a maximum lower bound value from the set of lower bound values. Next, while solving a gate sizing problem using the numerical solver, the embodiments evaluate the approximate objective function and the partial derivatives of the approximate objective function by using the maximum lower bound value of the parameter. The maximum lower bound value of this parameter determines the accuracy of the approximation of the objective function.

Abstract: Systems and techniques are described for optimizing a circuit design by using a numerical solver. The gates sizes are optimized by modeling a set of gate optimization problems and solving the set of gate optimization problems by using a numerical solver. The optimization can be performed iteratively, wherein in each iteration a gate optimization problem can be modeled for the portion of the circuit design based on circuit information for the portion of the circuit design. An objective function can be created, wherein the objective function includes at least one penalty function that imposes a lower and/or upper bound on at least one variable that is being optimized. In some embodiments, gradients of the objective function, which includes the penalty function, can be computed to enable the use of a conjugate-gradient-based numerical solver.

Abstract: Methods and systems for determining a numerical delay model based on one or more discretized delay models are described. A discretized delay model is a delay model in which the delay behavior is represented using a set of discrete data points of delay behavior. A numerical delay model is a delay model that can be used by a numerical solver to optimize a cost function. In general, computing delay using a numerical delay model is significantly faster than computing delay using discretized delay models. This performance improvement is important when optimizing a design for various metrics like timing, area and leakage power, because repeated delay computations are required in circuit optimization approaches.

Abstract: Systems and techniques are described for efficiently and accurately identifying candidate nets that would benefit from buffering. A buffering process can then be performed only on the identified candidate nets. Embodiments described herein can quickly and accurately identify nets for which performing buffering optimization would most likely waste computational time (so they can be skipped for the buffering transformation), thereby improving the overall performance of buffering optimization and overall physical synthesis optimization. Some embodiments use a buffer topology generating process to generate a buffer topology for a net and then use a numerical sizing process to size the buffers in the buffer topology and the driver gate.

Abstract: Methods and systems for determining a numerical delay model based on one or more discretized delay models are described. A discretized delay model is a delay model in which the delay behavior is represented using a set of discrete data points of delay behavior. A numerical delay model is a delay model that can be used by a numerical solver to optimize a cost function. In general, computing delay using a numerical delay model is significantly faster than computing delay using discretized delay models. This performance improvement is important when optimizing a design for various metrics like timing, area and leakage power, because repeated delay computations are required in circuit optimization approaches.

Abstract: Systems and techniques are described for optimizing a circuit design. Specifically, gate sizes in the circuit design are optimized by iteratively performing a set of operations that include, but are not limited to: selecting a portion of the circuit design (e.g., according to a reverse-levelized processing order), selecting an input-to-output arc of a driver gate in the portion of the circuit design, selecting gates in the portion of the circuit design for optimization, modeling a gate optimization problem based on the selected input-to-output arc of the driver gate and the selected gates, solving the gate optimization problem to obtain a solution using one or more solvers, and discretizing the solution. Discretizing the solution involves identifying library cells that exactly or closely match the gate sizes specified in the solution. These library cells can then be used to model other gate optimization problems in the current or subsequent iterations.

Abstract: Some embodiments of the present invention provide techniques and systems for performing scenario reduction using a dominance relation on a set of corners. During operation, the system can receive a design library which specifies gate characteristics at each corner in a set of corners. Next, the system can use the design library to determine a dominance relation on the set of corners for each gate type. The dominance relations can be stored with the design library. The system can then receive a set of scenarios over which a circuit design is to be optimized. Next, the system can determine a subset of the set of scenarios using one or more dominance relations on the set of corners. The system can then optimize the circuit design over the subset of the set of scenarios.

Abstract: Techniques and systems for optimizing a circuit design are described. In some embodiments, a sequential cell is selected for optimization. Next, the system iterates through a set of candidate sequential cells that are functionally equivalent to the sequential cell that is being optimized. The system evaluates the global timing impact of each candidate sequential cell in a highly efficient manner. For each candidate sequential cell that is evaluated, a non-timing metric and a timing metric for a candidate sequential cell are compared with the corresponding non-timing metric and timing metric for the current best sequential cell. If a candidate sequential cell improves the timing metric, or maintains the timing metric and has better non-timing metric(s), then the candidate sequential cell is stored as the current best sequential cell. Once the process completes, the current best sequential cell is the optimized cell size for the sequential cell.

Abstract: Systems and techniques are described for optimizing a circuit design. Specifically, gate sizes in the circuit design are optimized by iteratively performing a set of operations that include, but are not limited to: selecting a portion of the circuit design (e.g., according to a reverse-levelized processing order), selecting an input-to-output arc of a driver gate in the portion of the circuit design, selecting gates in the portion of the circuit design for optimization, modeling a gate optimization problem based on the selected input-to-output arc of the driver gate and the selected gates, solving the gate optimization problem to obtain a solution using one or more solvers, and discretizing the solution. Discretizing the solution involves identifying library cells that exactly or closely match the gate sizes specified in the solution. These library cells can then be used to model other gate optimization problems in the current or subsequent iterations.

Abstract: Systems and techniques are described for optimizing a circuit design by using a numerical solver. Some embodiments construct a set of lower bound expressions for a parameter that is used in an approximation of an objective function. Next, the embodiments evaluate the set of lower bound expressions to obtain a set of lower bound values. The embodiments then determine a maximum lower bound value from the set of lower bound values. Next, while solving a gate sizing problem using the numerical solver, the embodiments evaluate the approximate objective function and the partial derivatives of the approximate objective function by using the maximum lower bound value of the parameter. The maximum lower bound value of this parameter determines the accuracy of the approximation of the objective function.

Abstract: Systems and techniques are described for optimizing a circuit design by using a numerical solver. The gates sizes are optimized by modeling a set of gate optimization problems and solving the set of gate optimization problems by using a numerical solver. The optimization can be performed iteratively, wherein in each iteration a gate optimization problem can be modeled for the portion of the circuit design based on circuit information for the portion of the circuit design. An objective function can be created, wherein the objective function includes at least one penalty function that imposes a lower and/or upper bound on at least one variable that is being optimized. In some embodiments, gradients of the objective function (which includes the penalty function) can be computed to enable the use of a conjugate-gradient-based numerical solver.