Slew Constrained Minimum Cost Buffering

Abstract

A buffer insertion technique addresses slew constraints while minimizing buffer cost. The method builds initial solutions for the sinks, each having an associated cost, slew and capacitance. As a solution propagates toward a source, wire capacitance and wire slew arc added to the solution. When a buffer is selected for possible insertion, the slew of the solution is set to zero while the cost of the solution is incremented based on the selected buffer and the capacitance is set to an intrinsic capacitance of the buffer. The solutions of two intersecting wire branches are merged by adding branch capacitances and costs, and selecting the highest branch slew. The solution sets are updated by disregarding solutions which have a slew component greater than a slew constraint, and any solution that is dominated by another solution is eliminated. The solution having the smallest cost is selected as the final solution.

Description

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 diagram of a Steiner tree for a net of an integrated circuit design showing candidate buffer insertion points at regular intervals along the paths from a source to several sinks, according to the prior art van Ginneken algorithm;

FIG. 2 is a block diagram of a computer system programmed to carry out computer-aided design of an integrated circuit in accordance with one implementation of the present invention;

FIG. 3 is a schematic diagram illustrating an example of a circuit having various nets whose wiring is to be optimized as part of a physical synthesis process;

FIG. 4 is a chart illustrating the logical flow for a buffer assignment process in accordance with one implementation of the present invention;

FIG. 5 is a chart illustrating the logical flow for one implementation of a solution set update procedure that is used with the process of FIG. 4; and

FIGS. 6A-6D are schematics diagrams of a wire branch showing a progression for candidate buffer solutions in accordance with one example of the present invention.

The use of the same reference symbols in different drawings indicates similar or identical items.

DESCRIPTION OF THE PREFERRED EMBODIMENT(S)

The present invention provides a novel method for determining buffer insertion locations in a net of an integrated circuit design, and is generally applicable to any type of IC design, such as general-purpose microprocessors, memory units or special-purpose circuitry. The method may be implemented as part of a physical synthesis process which optimizes placement, timing, power consumption, crosstalk effects or other design parameters. As explained more fully below, an exemplary embodiment of the present invention provides a fast technique which can handle a large volume of nets to optimally solve slew buffering while also reducing buffering cost.

With reference now to the figures, and in particular with reference to FIG. 2, there is depicted one embodiment 10 of a computer system programmed to carry out the buffer insertion in accordance with one implementation of the present invention. System includes a central processing unit (CPU) 12 which carries out program instructions, firmware or read-only memory (ROM) 14 which stores the system's basic input/output logic, and a dynamic random access memory (DRAM) 16 which temporarily stores program instructions and operand data used by CPU 12. CPU 12, ROM 14 and DRAM 16 are all connected to a system bus 18. There may be additional structures in the memory hierarchy which are not depicted, such as on-board (L1) and second-level (L2) caches. In high performance implementations, system 10 may include multiple CPUs and a distributed system memory.

CPU 12, ROM 14 and DRAM 16 are coupled to a peripheral component interconnect (PCI) local bus 20 using a PCI host bridge 22. PCI host bridge 22 provides a low latency path through which processor 12 may access PCI devices mapped anywhere within bus memory or I/O address spaces. PCI host bridge 22 also provides a high bandwidth path to allow the PCI devices to access DRAM 16. Attached to PCI local bus 20 are a local area network (LAN) adapter 24, a small computer system interface (SCSI) adapter 26, an expansion bus bridge 28, an audio adapter 30, and a graphics adapter 32. LAN adapter 24 may be used to connect computer system 10 to an external computer network 34, such as the Internet. A small computer system interface (SCSI) adapter 26 is used to control high-speed SCSI disk drive 36. Disk drive 36 stores the program instructions and data in a more permanent state including the program which embodies the present invention as explained further below. Expansion bus bridge 28 is used to couple an industry standard architecture (ISA) expansion bus 38 to PCI local bus 20. As shown, several user input devices are connected to ISA bus 38, including a keyboard 40, a microphone 42, and a graphical pointing device (mouse) 44. Other devices may also be attached to ISA bus 38, such as a CD-ROM drive 46. Audio adapter 30 controls audio output to a speaker 48, and graphics adapter 32 controls visual output to a display monitor 50, to allow the user to carry out the buffer insertion as taught herein.

While the illustrative implementation provides the program instructions embodying the present invention on disk drive 36, those skilled in the art will appreciate that the invention can be embodied in a program product utilizing other computer-readable media, including transmission media. The program instructions may be written in the C++ programming language for an AIX environment. Computer system 10 carries out program instructions for an interconnect optimization process that uses novel buffer insertion techniques to manage timing requirements and electrical violations. Accordingly, a program embodying the invention may include conventional aspects of various placement and timing tools, and these details will become apparent to those skilled in the art upon reference to this disclosure.

The present invention provides an improved method of determining buffer insertion locations which may be used to optimize slew and buffer cost of a net. The invention may be understood with reference to the generalized circuit 60 depicted in FIG. 3. Circuit 60 has four driving elements or primary inputs 62a, 62b, 62c, 62d, and four output nodes or sinks 64a, 64b, 64c, 64d. The sources are interconnected to the sinks via gates 66a, 66b, 66c or other combinational logic 68. The gates 66 and logic 68 act as sinks for upstream nets, and act as sources for downstream nets, forming a total of nine nets. The layout shown in FIG. 3 is one example of how a placement tool might provide wiring between the input and outputs based on a netlist. Candidate buffer locations are established for a Steiner topology of the nets at some uniformly fixed distance apart, such as 250 μm. A finer spacing will provide better timing but increases analysis time. The invention may be used with a buffer library have various types of buffers, including smaller buffers 70a or larger buffers 70b. The following nomenclature is used to identify the various aspects of the net and its buffer solutions;

T—a routing tree of the net, T=(V, E);

V—the set of vertices (branch points v) in the routing tree;

E—the set of edges (wire sections e) in the routing tree;

C—capacitance;

W—buffer cost (area);

S—slew;

B—a buffer library;

b—a specific buffer (b₀=no buffer);

γ—a buffer assignment, or candidate solution for a buffer assignment;

Γ—a solution set;

α—a slew constraint.

The present invention introduces slew into the buffer assignment algorithm to collect delay information for slew rate computation so as to enable the invention to perform in a dynamic programming framework. A given buffer solution γ is represented by an associated three-tuple (C, S, W) where C denotes the downstream capacitance at the current node, S denotes the cumulative slew along a bottom-up computation, and W denotes the total cost of the solution, i.e., buffer area. An initial solution set is built by providing initial solutions γ_s for each sink of a given net, where the initial slew and cost are set to zero, and the capacitance is set to the intrinsic capacitance of the sink. A final solution for a wire branch propagates from one or more sinks toward an upstream source (postorder traversal). For example, in FIG. 3 the net having a source at gate 66a will have a solution that propagates from sink 64a and gate 66b toward gate 66a. As the solution propagates upstream, capacitance is increased by adding the capacitance of each wire section, and slew is increased by adding the slew of each wire section, which may be expressed according to Bakoglu's metric in terms of the Elmore delay. The invention generates sets of new solutions for each allowable buffer insertion location in respective wire branches, setting the new slew to zero when a buffer is inserted, incrementing the new cost based on the particular buffer selected, and setting the new capacitance to the intrinsic capacitance of the buffer. Solution sets for intersecting branches are merged by adding the branch capacitances and costs, and selecting the highest branch slew. Solutions are continually optimized with regard to the slew constraint, i.e., any candidate solutions which have a slew component greater than the slew constraint are disregarded, and dominated solutions are eliminated. When the progression reaches a source (e.g., gate 66a), the solution with the least cost is selected as the final solution for that net. The buffer insertion algorithm is repeated for each net in circuit 60.

The present invention may be understood in further detail with reference to the chart of FIG. 4, which illustrates the logical flow of a slew constrained minimum cost buffering process for a binary routing tree T in accordance with one implementation. The process begins (80) by building an initial solution set for each sink s where S(γ_s)=0, W(γ_s)=0, and C(γ_s)=C_s (the sink capacitance). Each branch point/driver v_t is iteratively examined (82) in the order given by a postorder traversal of T, and a wire e in one of the branches is further selected for analysis (84). Each candidate solution γ for the selected wire is updated (86) by setting C(γ)=C(γ)+C_e and S(γ)=S(γ)+1n9·D_e, where C_e is the edge capacitance and D_e is the Elmore delay for the current wire section (88). The Elmore delay can further be expressed as D_e=R_e(C_e/2+C(γ)) where R_e is the lumped resistance of the wire section. The solution set Γ′ corresponding to the branches T′ of the selected branch point/driver v_t is then updated (assuming no buffer insertion at the current location, b=b₀) to check whether any solutions violate the slew constraint and to see if any solutions are dominated (90). The solution set update procedure is described further below in conjunction with FIG. 5.

After updating the branch solution set, a determination is made as to whether a buffer is allowed at the current position (92). The position may be blocked by some design constraint such as a logic cell or gate. If a buffer is allowed, the process continues by selecting one of the available buffers b_i in the buffer library (94). For each branch solution (96), a new solution γ′ is generated by setting C(γ′)=C_bi, S(γ′)=0, and W(γ′)=W(γ)+W_bi, where C_bi is the intrinsic capacitance of the selected buffer and W_bi is the cost of the buffer (98). The branch solution set is again updated with b=b_i to check whether any new branch solutions violate the slew constraint and to see if any new branch solutions are dominated (100). New solutions are so generated and updated for each branch solution (102), and for each buffer type in the buffer library (104).

If no buffer is allowed at the current position, the buffer analysis is skipped and the process continues with merging of the two branches of the selected vertex ( 106) by first setting a merged solution set to an empty set, i.e., Γ=Ø. Each potential pair of branch solutions (one solution from each branch, i.e., each γ₁εΓ₁ and γ₂εΓ₂) are selected for analysis (108). A new merged solution γ′ is generated by setting C(γ′)=C(γ₁)+C(γ₂), W(γ′)=W(γ₁)+W(γ₂), and S(γ′)=max{S(γ₁),S(γ₂)} (110). The merged solution set is updated with b=b₀ to check whether any new merged solutions violate the slew constraint and to see if any new merged solutions are dominated (112). The process continues iteratively at step 108 for each pair of branch solutions (114). If there are more candidate solutions (116), the process continues iteratively at stop 86. Once all candidate solutions have been analyzed, the process continues iteratively at step 84 for other wire branches (118). Once all the wire branches for the selected vertex have been analyzed, the process continues iteratively at step 82 for other vertices (120). Once all vertices have been analyzed, infeasible solutions at the driver are eliminated (122), and the solution with the smallest cost is returned as the final solution (124).

Details of the solution set update procedure are shown in the flow chart of FIG. 5. The procedure receives as inputs a candidate solution γ′, an existing solution set Γ, a buffer type b, and a slew constraint α. A check is made to see whether the new solution violates the slew constraint, but the buffer type is first examined to see if any buffer is present (130). If no buffer is present at the current location (b=b₀), the slew constraint is simply compared to S(γ′) (132). If the slew for the new solution is greater than the constraint, the procedure returns the existing solution set without modification (134). If a buffer is present (136), the slew formula for the new solution is calculated as the root-mean square of the gate slew and the interconnect slew as taught in U.S. Pat. No. 6,868,533, i.e.,

Totalslew=√{square root over ((GateSlew)²+(WireSlew)²)}{square root over ((GateSlew)²+(WireSlew)²)}=[(R_bi·C(γ′)+K_bi)²+S(γ′)²]^1/2,

where R_bi and K_bi are empirical fitting parameters for the specific buffer type. If this slew calculation is greater than the constraint, the procedure again returns the existing solution set without modification (134).

If the slew for the new solution passes the slew constraint, an existing solution is selected for domination checks (138). The old solution is considered to dominate the new solution if the slew, cost and capacitance of the old solution are less than or equal to the slew, cost and capacitance of the new solution, i.e., if C(γ)≦C(γ′), S(γ)≦S(γ′) and W(γ)≦W(γ′). If the old solution dominates (140), the procedure returns the existing solution set without modification (134). If the old solution does not dominate, the procedure checks to see if the new solution dominates (142). The new solution is considered to dominate the old solution if the slew, cost and capacitance of the new solution are less than or equal to the slew, cost and capacitance of the old solution, i.e., if C(γ′)≦C(γ), S(γ′)≦S(γ) and W(γ′)≦W(γ). If the new solution dominates, the old solution is removed from the solution set (144). After the domination checks, the next existing solution is selected for analysis (146). If all existing solutions have been examined regarding domination and the new solution has not been eliminated, the new solution is inserted into the solution set (148), and the procedure returns the modified solution set (134).

FIGS. 6A-6D illustrate an example of how the invention is applied to a wire branch 150 having three wire sections 152, 154, 156 between an input source 158 and a sink 160, with two potential buffer insertion locations. In this example, the initial solution for sink 160 is given as (20, 0, 0), that is, a capacitance of 20, a slew of zero 7 and a cost of zero, as shown in FIG. 6A. These values represent theoretical designer units that correspond to actual measurements, but the specific units may vary according to designer preferences. In a typical implementation the delay and slew values would correspond to a measurement on the order of picoseconds, and the capacitance values would correspond to a measurement on the order of femtofarads.

As further seen in FIG. 6B, the first wire section 152 has an intrinsic capacitance of 10 and a delay of 150, and one buffer type is provided for possible insertion at the first buffer location (in the direction of postorder traversal) with that buffer having a capacitance of 5 and a delay of 30. Two new solutions are derived using the foregoing formulas, one for the buffer inserted at the first location and another for no buffer inserted at that location. If the butter is inserted, the capacitance becomes five, the slew stays at 0, and the cost is 1. If no buffer is inserted at the first location, the capacitance becomes 30, the slew 330, and the cost 0. These two solutions propagate toward source 158 as further shown in FIG. 6C. The second wire section 154 has a capacitance of 15, and a delay of 200 if no buffer was inserted at the first location, or a delay of 120 if a buffer was inserted. The buffer again has a capacitance of 5, and a delay of 50 if the previous location has no buffer, or a delay of 30 if the previous located is buffered. Four new solutions are then derived: one solution has no buffers at either location and results in a capacitance of 45, a slew of 770, and zero cost; another solution has a buffer at the second location but no buffer at the first location and results in a capacitance of 5, zero slew, and a cost of 1, another solution has a buffer at the first location but no buffer at the second location and results in a capacitance of 20, a slew of 264, and a cost of 1; the fourth solution has buffers at both locations and results in a capacitance of 5, zero slew, and a cost of 2.

At this point in the process some solutions might be eliminated depending upon the slew constraint. For example, if the slew limit is 500, then the first of these solutions is eliminated—the final slew when factoring in the gate slew of 200 from source 158 is 796. The solution (5, 0, 2) is also eliminated since it is dominated by solution (5, 0, 1). Alternatively, if the slew limit is 1000 the latter two solutions will be eliminated since they are dominated, i.e., solution (20, 264, 1) and solution (5, 0, 2) are both dominated by solution (5, 0, 1). This scenario is illustrated in FIG. 6D, which also shows the final propagation of the solutions to source 158. Assuming a capacitance of 10 for the third wire section 156, two solutions are derived: one solution has no buffers at either location and results in a capacitance of 55, a slew of 1430, and zero cost; another solution has a buffer at the second location but no buffer at the first location and results in a capacitance of 15, a slew of 198, and a cost of 1. The first of these solutions violates the slew limit and is eliminated, leaving the final solution of (15, 198, 1).

The buffering technique of the present invention may be used as part of a physical synthesis methodology which inserts buffers early in the process for electrical correction so that timing analysis uses legal slew constraints. Buffers on critical nets can later be removed and replaced. It is estimated that only a small fraction (5-10%) of the buffers in an IC net will need to be re-buffered for delay optimization, as most of the buffers derived from slew-based insertion are sufficient to meet the net's timing criteria. The invention is particularly beneficial since the designer does not need to know the required arrival times at sinks, so it can be used earlier in the design flow than traditional buffering techniques. The invention may be performed totally independent of the timing analysis, i.e., incremental timing is not required between buffering of individual nets.

For a single buffer type, an optimal linear solution is achievable and for multiple buffer types the present invention still produces an efficient solution. In an experimental computation of CPU requirements using the same buffer library, runtime was speeded up by a factor of 25-30, with up to a 21% buffer area reduction. In another experimental computation for area comparison with similar runtimes, buffer area was reduced by 41%-56% (timing buffering used four buffers and slew-based buffering uses 48 buffers, with runtimes of about 50 seconds). Thus, the present invention not only saves turn-around time, but also results in a buffered circuit that is smaller and consumes less power. The invention is especially efficient in the presence of blockages and its handling of multi-fanout nets.

Although the invention has been described with reference to specific embodiments, this description is not meant to be construed in a limiting sense. Various modifications of the disclosed embodiments, as well as alternative embodiments of the invention, will become apparent to persons skilled in the art upon reference to the description of the invention. For example, while the present invention has been disclosed in the context of a binary routing tree having only two branches at each vertex, it could easily he expanded to other tree structures. It is therefore contemplated that such modifications can be made without departing from the spirit or scope of the present invention as defined in the appended claims.

Claims

1. A method of providing a buffer tree for a net of an integrated circuit design, comprising: building an initial solution set for the buffer tree from initial solutions for sinks of the net wherein solutions have an associated cost, an associated slew and an associated capacitance;generating sets of candidate solutions for wire branches of the net which originate at the sinks and extend toward a source of the net wherein the candidate solutions include components from the initial solutions and from one or more buffers positioned along the wire branches;updating the candidate solution sets by disregarding any candidate solutions which have a slew component greater than a slew constraint; andselecting a final solution which has a smallest cost from updated candidate solution sets.

2. The method of claim 1 wherein: the buffers are selected from a buffer library having different buffer types; andthe candidate solutions are generated for more than one buffer type in the library.

3. The method of claim 1 wherein said updating includes eliminating any candidate solution whose associated cost, slew and capacitance are dominated by the associated cost, slew and capacitance of another candidate solution.

4. The method of claim 1 wherein said generating includes merging solutions of two intersecting wire branches by adding branch capacitances and costs, and selecting a highest branch slew.

5. The method of claim 1 wherein a candidate solution is generated by: increasing the capacitance of an existing solution for the wire branch by adding a wire capacitance of a new wire section; andincreasing the slew of the existing solution by adding a wire slew of the new wire section.

6. The method of claim 1 wherein a candidate solution is generated by: selecting a buffer for insertion at a buffer insertion location along the wire branch;setting the slew of an existing solution for the wire branch to zero;incrementing the cost of the existing solution based on the selected butler; andsetting the capacitance of the existing solution to an intrinsic capacitance of the selected buffer.

7. A computer system comprising: one or more processors which process program instructions;a memory device connected to said one or more processors; andprogram instructions residing in said memory device for providing a buffer tree for a net of an integrated circuit design by building an initial solution set for the buffer tree from initial solutions for sinks of the net wherein solutions have an associated cost, an associated slew and an associated capacitance, generating sets of candidate solutions for wire branches of the net which originate at the sinks and extend toward a source of the net wherein the candidate solutions include components from the initial solutions and from one or more buffers positioned along the wire branches, updating the candidate solution sets by disregarding any candidate solutions which have a slew component greater than a slew constraint, and selecting a final solution which has a smallest cost from updated candidate solution sets.

8. The computer system of claim 7 wherein; the buffers are selected from a buffer library having different buffer types; andthe candidate solutions are generated for more than one buffer type in the library.

9. The computer system of claim 7 wherein the updating of the candidate solutions includes eliminating any candidate solution whose associated cost, slew and capacitance are dominated by the associated cost, slew and capacitance of another candidate solution.

10. The computer system of claim 7 wherein the generating of the sets of candidate solutions includes merging solutions of two intersecting wire branches by adding branch capacitances and costs, and selecting a highest branch slew.

11. The computer system of claim 7 wherein a candidate solution is generated by: increasing the capacitance of an existing solution for the wire branch by adding a wire capacitance of a new wire section; andincreasing the slew of the existing solution by adding a wire slew of the new wire section.

12. The computer system of claim 7 wherein a candidate solution is generated by: selecting a buffer for insertion at a buffer insertion location along the wire branch;setting the slew of an existing solution for the wire branch to zero;incrementing the cost of the existing solution based on the selected buffer; andsetting the capacitance of the existing solution to an intrinsic capacitance of the selected buffer.

13. The computer system of claim 7 wherein the initial solutions for sinks have a cost of zero, a slew of zero, and a capacitance corresponding to an intrinsic capacitance of the sink.

14. A computer program product comprising: a computer-readable medium; andprogram instructions residing in said medium for providing a buffer tree for a net of an integrated circuit design by building an initial solution set for the buffer tree from initial solutions for sinks of the net wherein solutions have an associated cost, an associated slew and an associated capacitance, generating sets of candidate solutions for wire branches of the net which originate at the sinks and extend toward a source of the net wherein the candidate solutions include components from the initial solutions and from one or more buffers positioned along the wire branches, updating the candidate solution sets by disregarding any candidate solutions which have a slew component greater than a slew constraint, and selecting a final solution which has a smallest cost from updated candidate solution sets.

15. The computer program product of claim 14 wherein: the buffers are selected from a bulkier library having different buffer types; andthe candidate solutions are generated for more than one buffer type in the library.

16. The computer program product of claim 14 wherein the updating of the candidate solutions includes eliminating any candidate solution whose associated cost, slew and capacitance are dominated by the associated cost, slew and capacitance of another candidate solution.

17. The computer program product of claim 14 wherein the generating of the sets of candidate solutions includes merging solutions of two intersecting wire branches by adding branch capacitances and costs, and selecting a highest branch slew.

18. The computer program product of claim 14 wherein a candidate solution is generated by: increasing the capacitance of an existing solution for the wire branch by adding a wire capacitance of a new wire section; andincreasing the slew of the existing solution by adding a wire slew of the new wire section.

19. The computer program product of claim 14 wherein a candidate solution is generated by: selecting a buffer for insertion at a buffer insertion location along the wire branch;setting the slew of an existing solution for the wire branch to zero;incrementing the cost of the existing solution based on the selected buffer; andsetting the capacitance of the existing solution to an intrinsic capacitance of the selected buffer.

20. The computer program product of claim 14 wherein the initial solutions for sinks have a cost of zero, a slew of zero, and a capacitance corresponding to an intrinsic capacitance of the sink.