Abstract:
A method is taught for determining a calibrated wire load model. The calibrated wire load model can be used to reach timing closure for an integrated circuit. The method includes; determining a reference timing description; determining a wire load model based on synthesis; determining a wire load model based connectivity; comparing the wire load model based on connectivity to the reference timing description. The method teaches adjusting the wire load model based on connectivity to determine a wire load model which faciliates timing closure. The method also teaches comparing the wire load model (based on synthesis) with the reference timing description. The disclosure contemplates a computer program product based upon the method taught. The disclosure further contemplates an integrated circuit designed based on the method taught. In another embodiment a computer system or another electronic system includes an integrated circuit designed by the method taught.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application relates to co-pending U.S. patent application Ser. No. 09/946,240, filed on Sep. 5, 2001, entitled “Timing Optimization and Timing Closure for Integrated Circuit Models” naming Wolfgang Roethig and Attila Kovacs-Birkas as inventors, which is assigned to the assignee of this application, the application being hereby incorporated herein by reference in its entirety. 
     This application relates to co-pending U.S. patent application Ser. No. 09/878,497, filed on Jun. 11, 2001, entitled “Cell Modeling In the Design of An Integrated Circuit” naming Attila Kovacs-Birkas as inventor, which is assigned to the assignee of this application, the application being hereby incorporated herein by reference in its entirety. 
     BACKGROUND OF THE INVENTION  
     Present day ultra-large-scale integration (ULSI) circuits may include millions of interconnected active electronic devices fabricated on a silicon substrate and operating at clock rates of 1 Ghz or more. A substantial amount of time and money is needed to design, fabricate, and test such integrated circuits. Electronic design automation (EDA) tools are used in the design phase of integrated circuits to simulate the functional behavior of integrated circuits prior to their fabrication. These tools are used to confirm that an integrated circuit will function properly prior to its fabrication. 
     EDA tools are becoming more sophisticated in estimating design parameters such as signal transmission delay and power dissipation. Accurate signal delay estimation now generally requires a stronger link between front-end EDA tools which synthesize a design into a netlist of cells (active devices) and back-end EDA tools which place and route the cells of the synthesis. Without such a link, deep-submicron designs of integrated circuits may have to undergo multiple design iterations to meet design specifications. This process can be expensive and time consuming. The number of layout iterations needed to optimize a design generally increases significantly as logic density and clock speed of the integrated circuit increases. A more accurate signal delay estimation during front-end design generally leads to fewer time-consuming layout iterations. 
     As the minimum feature sizes of integrated circuits continue to shrink and operating speeds increase, the effects on signal delay due to the resistive, capacitive, and inductive parasitics of nets (e.g., wiring) which interconnect the active devices of the integrated circuit become more critical and more difficult to characterize. Accordingly, a complete analysis of the functional behavior of modem integrated circuit designs typically must account for the resistive, capacitive and inductive effects on signal delay of the interconnect paths. In the past, these parasitic effects of interconnect nets could generally be disregarded when simulating the operation of an integrated circuit, because the active devices therein typically dominated the overall signal delay calculations while the delays associated with interconnect nets were typically considered negligible. However, as the minimum feature sizes of integrated circuits continue to shrink, the ratio of interconnect net delay to total delay has increased substantially. EDA tools that predict interconnect signal transmission delay or extract wiring parasitics for back annotation into the circuit typically use distributed RC equivalent networks to model the interconnects. 
       FIG. 1  illustrates the steps for designing an integrated circuit).  FIG. 1  shows subsequent design steps A, B, and C. As further discussed below, design step A includes design synthesis  110  performed by a synthesis tool. Design step B includes design placement  120  performed by a placement tool. Design step C includes design routing  130  performed by a routing tool. 
     Synthesis  110  transforms an abstract behavior description of an integrated circuit into a functionally equivalent structural description (i.e., a netlist of cells and wiring interconnect). The behavior description is represented in design database A. The netlist is represented in design database B. The components or cells from which the netlist is built are selected from a library. This library contains information necessary to perform embedded timing analysis on the netlist in design database B. More particularly, the library contains timing models for each of the cells therein. A timing model is a mathematical model of input-to-output delay of a path between an input pin and an output pin of the cell. Such a path is also called a timing arc. The library also contains a parasitic estimation model. The purpose of embedded timing analysis is to enable optimization within  110  until the integrated circuit meets the desired timing specification. The desired timing specification is represented by timing constraints and exceptions from the designer. 
     Design step A produces a slack distribution  118  which is a representation of the result of embedded timing analysis. Slack is the difference between required signal arrival time and actual signal arrival time at a measurement point in the integrated circuit. A slack distribution histogram displays the number of points for which the slack has a given value within a given resolution. For example, if the X-axis of the histogram displays time with the resolution of one nanoseconds (“ns”) and the Y-axis of the histogram displays the value  300  for the time value  7 , then 300 points in the integrated circuit have a slack of 7 ns+/−0.5 ns. 
     Design step B specifies a physical location for each cell of the integrated circuit on a silicon substrate, printed circuit board, etc., based on the netlist in design database B. The result of design step B is represented in design database C. Placement performs embedded timing analysis and optimization. The timing models for arcs used in step B are similar to those used for design step A. However, the parasitic estimation model used in placement timing analysis and optimization is different than that used in step A. In design step A, parasitic estimation was based on structural circuit description only, whereas in design step B placement information is available for more accurate parasitic estimation. Slack distribution B  128 , again provides a representation of the result of embedded timing analysis. 
     Design step C specifies physical interconnect routes between the individual cells based on the structural integrated circuit information and placement information in design database C. The result of design step C is represented in reference design database  140 . Routing also performs embedded timing analysis and optimization. The timing model for arcs used in step C is similar to that used in design steps A and B. However, the parasitic estimation model used in placement timing analysis and optimization of step C is different than that used in steps A and B. The estimation model used in step C is more accurate than that used in design steps A and B because specific route information is available. Slack distribution  138  is generated and provides a representation of the result of embedded timing analysis. Slack distribution  138  again provides a representation of the result of embedded timing analysis for step C. 
     Reference timing analysis  142  is performed on design database  140  after step C to verify that the integrated circuit design meets the desired timing specification, based on. Reference timing analysis  142  performs embedded timing analysis and optimization. Timing models used in reference timing analysis  142  are similar to those used in design steps A, B, and C. However, the parasitic estimation model is different. Specific route information is available in reference design database  140  for all interconnections of the integrated circuit, whereas in design step C, only partial route information was available, as the routes were being specified. Therefore, the most accurate parasitic estimation model, also called parasitic extraction model, is chosen for timing analysis  142 . Slack distribution  148  is generated to provide a representation of the result of embedded timing analysis. 
       FIG. 2  illustrates relevant details on timing analysis used in the steps shown in  FIG. 1 . Design database  210  (which corresponds to databases A, B, C or reference design database  140 ) contains information about the implementation of the integrated circuit. Depending on the available implementation information, an appropriate parasitic estimation model  295  is chosen. The parasitic estimation engine  220  calculates parasitic data  270  based on design database  210  and parasitic estimation model  295 . The accuracy of the resulting parasitic data  270  depends on the available implementation information contained in database  210  and on the accuracy of the parasitic estimation model  295 . The accuracy of the resulting parasitic data  270  depends also on the parasitic estimation engine  220 . 
     Delay calculation engine  280  calculates timing data  290 . This timing data calculation is based on design database  210 , parasitic data  270 , and timing model for arc  260 . The accuracy of the resulting timing data  290  is limited by the accuracy of the parasitic data  270 . 
     Timing analysis engine  230  combines timing data  290  along each path as defined by the structure of the integrated circuit given in design database  210 . Timing analysis engine  230  compares the results of combining timing data  290  along each path against timing constraints and exceptions  250  to check whether the desired timing on the paths are met. The result is represented in slack distribution  240 . 
     Timing closure is the agreement between timing results in design steps A, B, and C and the result of timing analysis  142 . More particularly, timing closure is meet when the slack distributions resulting from embedded timing analyses in design steps A, B, and C, correlates with the slack distribution resulting from reference timing analysis. 
     The following conditions are necessary, but not sufficient, to achieve timing closure: similarity between the timing models for arc  260  used in steps A, B, and C; similarity between the delay calculation engines  280  used in steps A, B, and C; similarity between the timing analysis engines  230  used in steps A, B, and C, and; compatibility between timing constraints and exceptions  250  used in steps A, B, and. These conditions can be satisfied by choosing and qualifying appropriate EDA tools used in steps A, B, C and the reference timing analysis. For example: Design step A can be performed by the Design Compiler tool from Synopsys or by the BuildGates tool from Cadence; design step B can be performed by the Qplace tool from Cadence; and design step C can be performed by the Wroute tool from Cadence or by the Apollo tool from Avant!. Alternatively, a combination of design step A and design step B can be performed by the Physical Compiler tool from Synopsys, or the PKS tool from Cadence, etc. 
     Estimating the parasitics for each wire is one of the problems which arise during attempts to achieve timing closure in the design of an integrated circuit. In the front end of the design phase the placement, the length of each wire is not known. As such, the actual parasitic effects on signal delay cannot be accurately predicted at the front end of the design phase. A lumped resistance, capacitance, and inductance (RCL) is estimated for each wire at the front end of the design phase. Using a lumped RCL allows a designer to attempt to match the total distributed RCL on a wire which results in the back end of the design phase. But even if the estimated lumped RLC at the front end matches total RLC at the back end, the timing would not match, since the effect of distribution of the lumped RLC is neglected in the front end. Another problem is the lack of one-to-one correspondence of logical and physical wires. A logical wire may be broken into multiple physical wires by inserting buffers. 
     In theory, different timing engines analyzing a design under equivalent constraints should give matching results. However, for the following reasons the results must be verified for each design. Convergent timing arcs on a path may be handled algorithmically different by different engines. Timing exceptions (i.e. exclusion of non-relevant paths from analysis) may be handled differently by different engines, or the user may have made mistakes in specifying the intentionally equivalent timing exceptions in different tool-specific languages. This problem would be solved by using the same timing engine for each design step, but this is often not possible. A unique timing engine is embedded in each design tool. The unique timing engines cannot be exchanged between design tools. (As an analogy, a motor is an integral part of a car and cannot be arbitrarily replaced by a motor designed for a different car.) 
     Attempts in the related art to drive the EDA tools towards a common timing target by correlating the different factors of influence (e.g., electrical parasitics, timing characterization models, and timing engines) in isolation. In some instances, even with a large number of iterations, the timing correlation cannot be satisfied. As a consequence, the synthesis tool, the placement tool and the routing tool may anticipate a different timing result than the actually achieved timing result. Under design leads to excessive iterations, increasing the cost and delaying the production of the design. In the case of over design, the lack of timing correlation leads to a circuit which is larger, slower or consumes more power than necessary to accomplish the desired function. 
     SUMMARY OF THE INVENTION  
     A method is taught for correlating the timing target for each design tool. The method can determine a calibrated wire load model. The calibrated wire load model can be used to reach timing closure for an integrated circuit. The method includes; determining a reference timing description; determining a wire load model based on synthesis; determining a wire load model based connectivity; comparing the wire load model based on connectivity to the reference timing description. The method teaches adjusting the wire load model based on connectivity to determine a wire load model which faciliates timing closure. The method also teaches comparing the wire load model (based on synthesis) with the reference timing description. 
     The disclosure contemplates a computer program product based upon the method taught. The disclosure further contemplates an integrated circuit designed based on the method taught. In another embodiment a computer system or another electronic system includes an integrated circuit designed by the method taught. 
     The disclosure contains, by necessity, simplifications, generalizations and omissions of detail; consequently, those skilled in the art will appreciate that the disclosure is illustrative only and is not intended in any way to be limiting. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS  
       The present invention may be better understood, and its numerous objects, features, and advantages made apparent to those skilled in the art by referencing the accompanying drawings. 
         FIG. 1  is a flow diagram illustrating relevant steps of designing an integrated circuit. 
         FIG. 2  is a flow diagram illustrating relevant steps for performing timing analysis. 
         FIG. 3  is a flow diagram illustrating one implementation of the present invention. 
         FIG. 4  is an example of a placement solution diagram showing clusters of an integrated circuit generated in accordance with one implementation of the present invention. 
         FIG. 5  illustrate relevant aspects of wire load models. 
         FIG. 6  is a representation of a distributed cluster extracted from  FIG. 4 . 
         FIG. 7  is an example of a timing histogram. 
     
    
    
     The use of the same reference symbols in different drawings indicates identical items unless otherwise noted. 
     DETAILED DESCRIPTION  
     The following sets forth a detailed description of a mode for carrying out the invention. The description is intended to be illustrative of the invention and should not be taken to be limiting. As previously described, accurate timing management throughout the design process is necessary for an integrated circuit to operate correctly. The length of net connections in an integrated circuit determines the operating frequency, or speed, of the chip. The objective is a design with the shortest possible connections. Similarly, an integrated circuit with shorter net connections will be a smaller chip. A method to select the shortest possible connections will result in a design with the optimum solution for area and timing. The desired solution for area and timing produces a minimum of timing slacks with no timing violations. 
     The present invention provides timing correlation before and after layout and balances timing margins. Balancing the timing margin of an integrated circuit produces a design which operates as specified at a higher speed without errors being introduced by too small timing margin. The present invention provides a design with sufficient timing margin to prevent operational errors but a small enough timing margin to prevent overdesign (i.e., a circuit which is too large and too expensive to manufacture). 
     The present invention provides a method for managing the timing margin added before layout to ensure correct operation after layout. A large timing margin results in a circuit operating at less than its optimum speed. A small timing margin results in signals that arrive at their intended destination after they are expected. Signals which arrive after they have been predicted to arrive can introduce errors in the function of the circuit and can further create errors in a design resulting in a manufactured integrated circuit which does not perform as intended. 
     The delay of a signal traversing a path in an integrated circuit must be between specified upper and lower bounds. The upper and lower bounds of each path are derived from constraints. Timing analysis tools thus derive the upper and lower bounds from the constraints and calculate the delay on each path and report the difference between the upper and lower bound and the actual delay. In order to calculate the delay on each path, electrical parasitics must be estimated or extracted and delay on each timing arc must be calculated. This calculation uses timing models supplied in a characterization library. Timing analysis checks the delay against those bounds and reports slack as the difference between the actual delay and the respective bound. 
     Timing histograms are a statistical way of representing time slack. Negative time slack is also called “violation.” Positive time slack is often called “slack” for shortness. Eliminating violations is necessary to produce a design, which functions as intended. However, eliminating violations produces slack. Ideally, the time slack should be zero. Positive slack indicates overdesign, i.e. a circuit that is too large and/or too expensive and operates slower than intended. 
     Without calibration, histograms taken at different design phases (e.g. before placement, before routing, after routing) will show a significantly different slack distribution. Different slack distributions are due to different estimated parasitics. In the front end of the design phase only lumped estimated parasitics are available. In later design phases more accurate, distributed parasitics are available. Parasitic estimation varies from EDA tool to EDA tool. However, histograms taken as snapshots by different timing analysis tools at the same design phase will also show differences. 
     Calibrating all histograms to a common reference provides each EDA tool in the design flow the most realistic view of the actual timing. Adjusting the design based on statistical interpretation of the histogram allows a faster design without violations. Previously, no formal method has been available to statistically analyze the histograms. 
     In a flat (or hierarchical) design the appropriate parasitic estimation model for a given block and a given design step will be chosen. The definition of “block” may vary for different design steps. For example, synthesis may be performed on several blocks which may later be merged into one block for flat layout. Timing analysis will be done after each design step for each block. The results will be displayed in sets of timing histograms and compared (as described further below) to a set of reference timing histograms. The set of reference timing histograms are based on the last design step in the trial design flow using a reference parasitic extraction tool, reference timing analysis tool and reference timing models. The set of reference timing histograms can contain one timing histogram per block as defined in the last design step. Even if the previous design steps (e.g. synthesis) are performed on sub-blocks, the timing analysis results related to the previous design steps must be merged to reflect a histogram for the entire block. 
     The timing histograms can be analyzed by matching the total number of paths in each histogram corresponding to each block. A mismatch would be due to major discrepancies in timing exception handling by the different timing engines. Therefore, such discrepancy can be detected and corrected by modifying the timing constraint specifications. After such correction, timing analysis is applied again. Although the number of wires can vary, the number of paths does not change significantly during the design steps. This is because the number of wires is mainly governed by electrical and physical design implementation requirements, whereas the number of paths is mainly governed by the logical functionality of the circuit, which by definition does not change during the trial design flow. 
     Once the number of paths matches, the profile of the timing histograms is compared using a mathematical method. The profiles should match within a certain tolerance. A major mismatch in profile would indicate either a poor choice of parasitic estimation models for sub-blocks or a poor choice of partitioning into blocks and sub-blocks in the first place. Therefore, such poor choices can be detected and corrected. Then the relevant design steps are applied again on the newly partitioned blocks 
     A mathematical method is applied to calibrate the parasitic estimation models with the effect that the timing histograms will be shifted until they all match the reference timing histogram within a certain tolerance. In this step, the differences in parasitic estimation models, timing characterization models and timing analysis algorithms are implicitly compensated for. Explicit knowledge about the significance or preponderance of a particular difference is not required, because the calibration is self-adaptive. 
       FIG. 3  shows a method of selecting a wire load model in accordance with one embodiment of the present invention. More specifically,  FIG. 3  shows the three factors which may be considered in calibrating a wire load model. As shown in  FIG. 3 , one factor is a reference and two factors are variables (connectivity and synthesis). Connectivity depends on the size and shape of the silicon chip. Connectivity determines the timing behavior of the integrated circuit. Synthesis depends on a netlist which describes the desired function of the manufactured integrated circuit. An initial synthesis (not shown in  FIG. 3 ) initializes the synthesis tool with embedded timing analysis and optimization using auto wire load. A hardware description language (HDL) such as Verilog can be used to describe the function of an integrated circuit. In parallel with the HDL description (not shown) a standard delay format (SDF) can be used to describe the timing of the integrated circuit. 
     Now referring to  FIG. 3 , the software application discussed in the preceding paragraph is the input of steps  305 ,  3100  and  320 . The first iteration begins with an initial wire load model as further discussed in  FIG. 4 . From initial synthesis the method proceeds to non-timing driven placement  305 . Non-timing driven placement  305  (or non TD placement) is placement without embedded timing analysis. Non TD Placement  305  includes connectivity optimization without any specific determination for placement (e.g., grouping or predefining placement). Connectivity optimization minimizes the total wire length of the design as further discussed in  FIG. 4 . WLM selection  311  (or “wire load model selection”) identifies one of several wire load models to use in the design of interest. (Identifying one of several wire load models is further described in  FIG. 5 .) Standard delay format (SDF)  315  represents the results of a calculation of timing data for arc based on the wire load model selected in WLM selection  311 . Timing data for arc represented in SDF  315  can be similar to logical event  290  previously shown in  FIG. 2 . From generation of SDF  315  the logical method proceeds to STA  320 . STA  320  produces a histogram  325  generated from the wire load model selected in WLM selection  311 . The method proceeds to consider the synthesis factor (as described below) before considering the reference factor. 
     Considering synthesis includes data generated from an external software application (not shown) which used automatic wire load selection based on actual block size. From initial synthesis  310  the method proceeds to WLM calibration  370 . In subsequent iterations, WLM Calibration  370  speaks to calibrating a model of wire loads available in a database. From WLM  370  the method proceeds to SDF  380 . SDF  380  represents timing data for a timing arc based on the wire load model from logical step  370 . SDF  380  can be similar to Timing Data for arc  290  as previously shown in  FIG. 2 . From SDF  380  the method proceeds to STA  390 . STA  390  produces a timing histogram  395  which can be compared to a histogram  365  subsequently calibrated. The method can proceed from synthesis data to considering reference data, as described in the paragraph below. 
     From initial synthesis (not shown) the method can proceed to timing driven layout (TDL)  320 . TDL  320  can be similar to placement step  120  shown in  FIG. 1 . TDL  330  includes placement with embedded timing analysis and optimization. TDL  330  can further include routing with embedded timing analysis and optimization. Thus, TDL  320  can also include a logical function similar to logical function  130  shown previously in  FIG. 1 . Extraction  340  can include a parasitic model such as discussed earlier (refer to  FIG. 2 ). As discussed earlier (refer to  FIG. 2 ) the accuracy of extraction  340  can depend on the accuracy of the parasitic estimation model such as parasitic estimation model  295  (shown previously in  FIG. 2 ). 
     From extraction  340  the method proceeds to SDF  350 . SDF  350  can include the actual wire length of the design of interest. SDF  350  can also include delay such as a delay considered in Timing Data for Arc  290  previously shown in  FIG. 2 . From SDF  350  the method can proceed to STA  360 . STA  360  generates a reference timing histogram  365 . 
     Reference timing histogram  365  can be similar to slack distribution  240 . Integrated circuits can be tested after manufacture. The results of the test can be gathered into a data file, sometimes called a library. For example, the data file can be similar to Timing Model for Arc  260  (previously shown in  FIG. 2 ). In addition, the data library can include data such as found in Parasitic Estimation Model,  295  (previously shown in  FIG. 2 ). 
     Still referring to  FIG. 3 , compare and adjust  326  compares data from histogram  325  and histogram  365 . Compare and adjust  326  adjusts the histogram data by adjusting the position of clusters. At least 50% of the blocks will be placed as compact clusters. Therefore automatic wire load selection is used. The remaining blocks will be placed as disjoint clusters. Wire load models will be assigned to those blocks based on the area of a bounding box around the clusters (refer to  FIG. 6 ). Compare and adjust  396  compares data from histogram  365  and histogram  395 . Compare and adjust  395  adjusts histogram data using the method described in co-pending patent application Ser. No. 09/946,240 entitled “TIMING OPTIMIZATION AND TIMING CLOSURE FOR INTEGRATED CIRCUIT MODELS.” Step  398  combines the data from step  326  and step  396 . Step  399  includes the results describing a calibrated wire load model. The calibrated wire load model is used to start the synthesis and timing driven layout. Using the calibrated wire load model with synthesis and timing driven layout facilitates timing closure. 
       FIG. 4  shows the placement of cells within an integrated circuit. The placement was done by a software application tool called placement tool. The different colors highlight sub-circuits or blocks. If no constraints are given to the placement tool, sub-circuits will be placed as compact clusters, if the connectivity within the block (intra-block connectivity) is stronger than the connectivity between blocks (inter-block connectivity). However, there are blocks with weak intra-block connectivity. These blocks will be placed in scattered clusters. A floor plan drawn by the designer of the integrated circuit could force such blocks also to be placed in compact clusters. However, such a manually forced placement would not be as optimal as the unconstraint automatic placement. 
       FIG. 5  is an example of wire load model.  FIG. 5  is an example of linear wire load models for specific die sizes and specific module sizes. (Specifically, the top curve shown in  FIG. 5  represents a wire load for grid size is 1000.) The wire load models shown are adjusted by the method taught. Another adjustment to the wire load model can be made based on the offset of the histograms. One method of determining an offset of histograms is given in Equation 1 and Equation 2, below. 
       FIG. 6  shows a block placed in scattered clusters. This block is extracted from  FIG. 4 . For the purpose of optimizing the timing of a block in the integrated circuit, a wire load model is assigned to the block. This wire load model enables prediction of delay due to wiring. The delay due to wiring depends on the estimated length of the wire, which is statistically related to the area enclosing the block. In the case of compact clusters, the enclosing area is simply the area covered by the block itself. In the case of scattered clusters, the enclosing area also covers empty space (i.e. space occupied by components which are not members of the block), as illustrated in  FIG. 6 . 
       FIG. 7  is an example of a timing histogram. As previously shown (refer to  FIG. 3 , step  326  and  396 ) a histogram can be used for comparison. Referring to  FIG. 7 , the histogram shows the result of the wire load model selection. The wire load model shown in the histogram can be calibrated to a second histogram. The second histogram (not shown) can include clock trees, routing and cross-talk effects. 
     Comparing histograms and adjusting design based on timing histogram results provides the necessary method to calibrate an integrated circuit design. A slack histogram is a graphical representation of a slack distribution. Slack distribution can be represented as a discrete function P(S), where P is the number of paths with a given slack S. The autocorrelation function C p (T) for P(S) is defined by equation 1, below. 
     
       
         
           
             
               
                 
                   
                     
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     A measure for matching slack distribution is the normalized error between the data points C p (T=0), given in Equation 2, below. 
     
       
         
           
             
               
                 
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     Another measure for matching slack distribution is the normalized error between the autocorrelation functions, given by Equation 3, below. 
     
       
         
           
             
               
                 
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     If the error is outside an acceptable bound (e.g., 10%), a poor structural hierarchy of the integrated circuit is the cause. This can be corrected by choosing a different structural hierarchy and repeating all design steps required for creation of design database and reference design database. If the error is within an acceptable bound (e.g., 10%), the intercorrelation function between slack distribution and reference slack distribution is calculated. The intercorrelation function between two slack distributions P 1 (S) and P 2 (S) is defined in equation 4, below. 
     
       
         
           
             
               
                 
                   
                     
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                     ) 
                   
                 
               
             
           
         
       
     
     This intercorrelation function has an absolute maximum for a particular value of T. This maximum is compared to the datapoint CP(T=0) from the reference slack distribution. If there is a significant mismatch, a different parasitic estimation model must be selected and all design steps required for creation of design database and reference design database must be repeated. 
     Co-pending patent application Ser. No. 09/946,240 illustrates the calibration method, applied to the parasitic estimation model. As shown in co-pending patent application Ser. No. 09/946,240, slack distribution resulting from embedded timing analysis performed on the design database is compared with the reference slack distribution from reference the timing analysis performed on the reference design database. In case where N sub-blocks in the design database correspond to one block in reference design database, the slack distribution represents a collapsed slack distribution, corresponding to the collapsed slack distribution. A determination is made if the intercorrelation function has its maximum at T=0. If the maximum is at T max , where T max  is different from zero, a global scaling factor A shift  is applied to the parasitic estimation model. Embedded timing analysis is performed again, based on the scaled parasitic estimation model. The new slack distribution based on embedded timing analysis will have a similar shape as the previous one, but it will be shifted by T shift . The goal is to equate T shift  with −T max . As a result, the new intercorrelation function will have its maximum at T=0. The Newton-Rhapson method can be applied between subsequent iterations.
 
 A   shift   ≈T   shift   *ΔA/ΔT   Equation 5
 
     In Equation 5, ΔA is the difference between A shift  in subsequent iterations and ΔT is the difference between T shift  in subsequent iterations. A shift  will converge to zero, therefore T shift  will also converge to zero. 
     The operations described above and modules thereof may be executed on a computer system configured to execute the operations of the method and/or may be executed from computer-readable media. The method may be embodied in a machine-readable and/or computer-readable medium for configuring a computer system to execute the method. 
     While particular embodiments of the present invention have been shown and described, it will be recognized to those skilled in the art that, based upon the teachings herein, further changes and modifications may be made without departing from this invention and its broader aspects, and thus, the appended claims are to encompass within their scope all such changes and modifications as are within the true spirit and scope of this invention.