CN101770531A - Method for improving circuit emulation run speed - Google Patents

Abstract

The invention belongs to the integrated circuit CAD field. Newton iteration is a basic method for all circuit emulators to solve a system of nonlinear equations. In view of efficiency, various variables of Newton iteration are widely applied in reality, such as modified Newton iteration and damping Newton iteration, and to improve the efficiency of Newton iteration is also one of the key factors in emulator acceleration. Aiming at the step of computing Newton direction in the Newton iteration process, the invention provides a novel method for confirming intervals of LU decomposition times, improving the speed of computing Newton direction and optimizing the efficiency of computing Newton direction and Newton iteration.

Description

A kind of method that improves circuit emulation run speed

Technical field

The invention belongs to the integrated circuit CAD field.

Background technology

Circuit emulator is an important tool of circuit design front end, and its major function is before physical Design circuit to be carried out emulation, the checking mentality of designing.Its principle of work is to find the solution the equation of describing various circuit on computers, obtains the unknown quantitys such as voltage, electric current of each position in the middle of the circuit, in process of simulation, unavoidably will find the solution Nonlinear System of Equations.Newton iteration is a common method of finding the solution Nonlinear System of Equations, and each step iteration need be found the solution a system of linear equations with the method that LU decomposes, and when equation was on a grand scale, what LU decomposed will spend a large amount of time, has reduced the efficient of finding the solution.Therefore, people have created the modification of a lot of Newton iterations, such as revising Newton iteration, decline Newton iteration or the like, the minimizing that these methods have the number of times that decomposes of LU, the raising that has the convergence of Newton iteration, provide effective way for finding the solution Nonlinear System of Equations.

Summary of the invention

The present invention proposes a kind of LU that can optimize and decompose the Newton iteration method of number of times at interval, and provided its actual enforcement method.

Newton iteration is the effective ways of finding the solution Nonlinear System of Equations, and this method is carried out loop iteration according to following two steps, up to x _kSatisfy the condition of convergence:

(1) calculates F (x _k) and F ' (x _k), find the solution F ' (x _k) d _k=-F (x _k),

(2)x _k+1＝x _k+d _k，k＝k+1。

As can be seen, each step Newton iteration is all wanted computing function value F (x _k) and F ' (x _k), find the solution F ' (x then _k) d _k=-F (x _k), because to F ' (x _k) complexity of carrying out the LU decomposition method is that polynomial expression increases, and when circuit scale becomes big, can cause a step Newton iteration to take a long time.In order to improve iteration efficient, can determine a number of times M at interval in advance, after finishing a LU decomposition, no longer upgrade F ' (x in the later M step iteration _k), find the solution F ' (x and use existing LU to decompose _k) d _k=-F (x _k), can reduce like this and calculate d _kPrecision, but but reduced the number of times that LU decomposes, after interval M step iteration, upgrade F ' (x again _k), be LU again and decompose, Here it is revises the Newton iteration method.Because the number of times that LU decomposes has lacked, the efficient of Newton iteration is improved, and it circulates according to following steps:

$F^{\′}\left(x_k^0\right)d_k^m=-F\left(x_k^m\right),$

$x_k^{m+1}=x_k^m+d_k^m,m=\mathrm{0,1},...,M$

$x_{k+1}^0=x_k^M,k=\mathrm{0,1},...$

A free-revving engine revising Newton iteration is to improve finds the solution speed, and the key that the speed of finding the solution improves is that number of times M at interval, table 1 are time of finding the solution and the relation of M:

Table 1 is found the solution the variation of time with M

????M	????1	????2	????4	????5	????6	????8	????10	????12
									Time	????162.52	????103.97	????87.12	????88.27	????66.35	????66.62	????64.18	????65.22

As can be seen from Table 1, M not only can not improve the speed of finding the solution after being increased to a certain degree, and finds the solution speed and may reduce.Generally speaking, the interval number of times M that LU decomposes is selected before revising Newton iteration, and no longer changes along with the carrying out of Newton iteration later selected, does like this to be difficult to guarantee to realize that selected M can make the speed of finding the solution reach optimum.

Because the fixed intervals number of times can not make full use of the advantage of revising Newton iteration, therefore can consider to adopt the method for dynamic control interval number of times, make determined interval number of times M can improve the speed of finding the solution as far as possible.On the other hand, when circuit is done the time domain transient analysis, variation along with the time, circuit equation may change, at this time need to find the solution different Nonlinear System of Equations, and the interval number of times M that can optimize different equations is likely different, and therefore in making the process of transient analysis, M also should be along with the time changes.

For an interval number of times is the correction Newton iteration of M, and its definitions of efficiency is

$e=\frac{\ln (M+1)}{W},$

Wherein W is the working time of finishing a Newton iteration, and this time mainly spends in two aspects, the one, calculate current iteration value x _kPairing functional value F (x _k) time t _f, the 2nd, find the solution F ' (x _k) d _k=-F (x _k) time t _s, the efficient of therefore revising Newton iteration is

$e=\frac{\ln (M+1)}{{\mathrm{Mt}}_f+t_s},$

After finishing a LU decomposition, make the M of e maximum to revise Newton iteration as the interval number of times.

Thus, the present invention proposes to determine to revise the Newton iteration method of number of times at interval, as shown in Figure 1, steps of the method are:

(1) gets initial value x ₀, iteration interval M=1, iterations k=0;

(2) computing function value F (x _k) and F ' (x _k), preserve the time t that is spent _f

(3) if satisfy the condition of convergence, stop, otherwise carry out (4);

(4), carry out (5), otherwise carry out (7) if M is divided exactly k;

(5) find the solution F ' (x _k) d _k=-F (x _k), preserve the time t that is spent _s

(6) calculating makes

Maximum M carries out (8);

(7) utilize existing LU decomposition computation d _k

(8) x _K+1=x _k+ d _x, k=k+1 carries out (2).

Description of drawings

Fig. 1 the present invention proposes the process flow diagram of the at interval inferior counting method of the positive Newton iteration of periodical repair really

Fig. 2 RTLINV circuit

Fig. 3 ECLGATE circuit

Fig. 4 RCA3040 circuit

Concrete implementation step

From input net table extraction circuit relation, employing is revised node analysis method (Modified Nodal Analysis) and is set up circuit equation, when each iteration provides equation, is extracted in x _kThe relation of the parameter of each device and input/output variable in the dot circuit, thus calculate current functional value F (x _k) and its residual error, to each node in the circuit, set up conservation equation, and utilize the approximate calculating F (x of finite difference method by annexation and electric current conservation (KCL) _k) to the partial derivative of each variable, set up BCR (Branch Constitutive Relation) equation, obtain F ' (x _k), preserve computing function value F (x simultaneously _k) and F ' (x _k) time t _f, judge according to residual error whether iteration restrains.

The present invention adopts direct method to guarantee numerical stability.If the current iteration number of times is the multiple of iteration interval number of times, matrix is carried out LU decompose, back substitution is found the solution then, and preserves and find the solution time t _s, need to calculate new best iteration interval number of times then; Otherwise directly utilize the back substitution of existing LU decomposition result to obtain separating of system of linear equations, need not upgrade number of times at interval this moment.Utilize separating of system of linear equations to upgrade location variable and obtain next Newton iteration point x _K+1

If the current iteration number of times is the multiple of interval number of times, before carrying out next iteration, should recomputate best iteration interval number of times.In the middle of actual computation, the value of M can not be too big, otherwise that the convergence of Newton iteration will become will be very poor, and the present invention seeks best M in 1～10 scope, according to the expression formula of iteration efficient

Calculate and make the M of e maximum get final product.

With RTLINV circuit (Fig. 2), ECLGATE circuit (Fig. 3), RCA3040 circuit (Fig. 4) are verified the validity of the method that provides as an example, and it the results are shown in Table 2.

The result of three test circuits of table 2 relatively

As can be seen from Table 2, new alternative manner has reduced significantly finds the solution the number of times that LU decomposes in the nonlinear equation process, can improve the travelling speed of circuit emulator.

Claims (2)

1. method that improves circuit emulation run speed, it is characterized in that determining that by circuit emulator the LU that revises Newton iteration decomposes number of times at interval, optimize the efficient of Newton iteration by the number of times that LU in the dynamic control Newton iteration process decomposes, thereby reach the purpose that improves circuit emulation run speed.

2. a kind of method that improves circuit emulation run speed according to claim 1 is characterized in that the certain number of times in every interval recomputates circuit matrix, carry out LU and decompose, and number of times is dynamically control at interval, determines that wherein the step of number of times is as follows at interval:

(1) gets initial value x ₀, interval number of times M=1, iterations k=0;

(2) computing function value F (x _k) and F ' (x _k), preserve the time t that is spent _f

(3) if satisfy the condition of convergence, stop, otherwise carry out (4);

(4), carry out (5), otherwise carry out (7) if M is divided exactly k;

(5) find the solution F ' (x _k) d _k=-F (x _k), preserve the time t that is spent _s

(6) calculating makes

Maximum M carries out (8);

(7) utilize existing LU decomposition computation d _k

(8) x _K+1=x _k+ d _k, k=k+1 carries out (2).

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