CN107220463B - A kind of mixing polarity XNOR/OR circuit area optimization method - Google Patents
A kind of mixing polarity XNOR/OR circuit area optimization method Download PDFInfo
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Abstract
The invention discloses a kind of mixing polarity XNOR/OR circuit area optimization methods, the circuit of PLA format is read in first, using the function representation circuit, then function is converted to the expression formula of mixing polarity XNOR/OR circuit using polarity conversion method, then each parameter for mixing polarity XNOR/OR circuit area and optimizing each parameter and three value diversiform particle group's algorithms is associated and establishes fitness function, finally using three value diversiform particle group algorithm search to optimal polarity, obtain the optimal area under optimal polarity, in search process, increase extensive study thoughts and three value mutation operations；Advantage is can fast and accurately to search optimal polarity, and search capability is strong, and search efficiency is high.
Description
Technical field
The present invention relates to a kind of XNOR/OR circuit area optimization methods, more particularly, to a kind of mixing polarity XNOR/OR electricity
Accumulate optimization method in road surface.
Background technique
Digital Logical Circuits can both use the Boolean logic based on AND/OR/NOT operation, can also be with based on XOR/
Reed-Muller (RM) logic of AND or XNOR/OR operation is realized.Currently, the circuit face based on traditional Boolean logic
Optimisation technique comparable maturation is accumulated, establishes the Automated Design scheme of relative system, and be successfully applied to various business
Eda software, such as the product of Synopsys, Mentor and Graphics Cadence company.Research shows that using or part adopt
Greatly improving on available energy is designed with RM logic and is promoted.Compared with the circuit that Boolean logic is realized, RM is used
The partial circuit that form indicates has more compact structure, such as: arithmetical circuit, parity checker and telecommunication circuit；Use RM
The logic circuit that form is realized has good testability, this is especially suitable for the design in terms of testability, to be
It solves current IC test verifying problem and provides a set of realistic plan.
For the RM logic circuit using RM logical design, RM logic expansion generally includes fixed polarity RM
(Fixed-Polarity Reed-Muller, FPRM) expansion and mixing polarity RM (Mixed-Polarity Reed-
Muller, MPRM) two kinds of expansion.RM logic circuit is inputted for n, the polarity number of FPRM expansion is MPRM expansion
(2/3)n, and the polarity of MPRM expansion includes institute's polarized of FPRM expansion, the huge polarity search space of MPRM circuit
Also the Time & Space Complexity for causing its circuit performance to optimize all is higher than FPRM circuit, therefore, in the excellent of MPRM logic circuit
Change theory and there is an urgent need to new breakthroughs on method for solving.Enumerative technique and genetic algorithm are normal in current MPRM logic circuit optimization
Two methods.But enumerative technique is when optimizing extensive MPRM logic circuit, and it is infeasible in terms of run time, it searches
Rope efficiency is poor；When genetic algorithm optimizes extensive MPRM logic circuit, the diversity with population keeps mechanism poor,
Convergence rate is slow, and the defect that local optimal searching ability is weak etc..
In view of this, design that a kind of search capability is strong, the high mixing polarity XNOR/OR circuit area optimization method tool of search efficiency
It is significant.
Summary of the invention
Technical problem to be solved by the invention is to provide a kind of search capability is strong, the high mixing polarity of search efficiency
XNOR/OR circuit area optimization method.
The technical scheme of the invention to solve the technical problem is: a kind of mixing polarity XNOR/OR circuit area
Optimization method, comprising the following steps:
(1) circuit of PLA format is read in, which uses functionTable
Show, n is function f (xn-1,xn-2,…,xk,…,x0) input variable number, (xn-1,xn-2,…,xk,…,x0) it is function f (xn-1,
xn-2,…,xk,…,x0) n input variable, ∏ is AND operator, aiIt is maximum term coefficient, and ai∈ { 0,1 }, i are maximum
Ordinal number, with being represented in binary as in-1in-2…ik…i0, MiMaximal term, indicate n input variable phase or, k be positive integer,
And 0≤k≤n-1；
(2) use polarity conversion method by functionBe converted to mixing pole
The expression formula of property XNOR/OR circuit:Wherein, p is mixing polarity
The polarity number of XNOR/OR circuit, p are expressed as p with ternary formn-1pn-2…pg…p0, g is positive integer, and 0≤g≤n-1, ⊙
∏ is same or operator, SjExpression or item, djFor or term coefficient, and dj∈ { 0,1 }, j be or item ordinal number, and j is with being represented in binary as
jn-1jn-2…jg…j0, djIt indicates or whether item occurs in mixing polarity XNOR/OR expression formula, work as djWhen=0, expression or item Sj
Occur in the expression formula of mixing polarity XNOR/OR circuit, works as djWhen=1, expression or item SjNot in mixing polarity XNOR/OR electricity
Occur in the expression formula on road, wherein xgWith pgAnd jgRelationship are as follows: work as pg=0 and jgWhen=0, xgWith former occurrences；Work as pg=1
And jgWhen=0, xgOccur with contravariant；Work as pgWhen=2, xgOccur in the form of former variable and contravariant simultaneously, works as jgWhen=0,
xgWith former occurrences, work as jgWhen=1, xgOccur with contravariant；
(3) mixing polarity XNOR/OR circuit area is optimized to each parameter of each parameter Yu three value diversiform particle group's algorithms
It is associated: input variable number n is defined as to the search space dimension of three value diversiform particle groups, mixing polarity is defined as three
It is worth the particle of diversiform particle group, polarity number p is defined as particle position；Set the quantity of particle in three value diversiform particle groups
It is positive integer for M, M, total evolutionary generation of three value diversiform particle groups is tmax；
(4) fitness function is established: the fitness function fitness (p) of the corresponding particle position of polarity number p are as follows:
Fitness (p)=(1-w) * Earea(p)/Earea_max
Wherein, EareaIt (p) is the Class area estimation value that polarity XNOR/OR circuit is mixed at polarity p, EareaIt (p) is polarity p
The sum of the item number of same or item and/or item that the expression formula of lower mixing polarity XNOR/OR circuit includes, Earea_maxTo mix polarity
The maximum area estimated value of XNOR/OR circuit, and Earea_max=n*2n, n be input variable number, w be more than or equal to 0 and be less than etc.
In 1 coefficient, * is multiplication symbol ,/it is division operation symbol；
(5) population is initialized: the speed of each particle in three value diversiform particle group of random initializtion, position, particle
Current individual optimal location, three value diversiform particle groups current global optimum position and each particle position fitness value；
(6) equation of motion of particle in three value diversiform particle groups is established:
Wherein, t is the current evolutionary generation of three value diversiform particle groups, 1≤t≤tmax,It is m-th of particle in t
The speed of secondary iteration,It is m-th of particle in the position of the t times iteration, m=1,2 ..., M, d is integer and 1≤d≤n,
Round expression is rounded up to closest integer, speed of m-th of particle in the t+1 times iterationvmin,dThe minimum speed of m-th of particle is represented,
vmax,dRepresent the maximum speed of m-th of particle, the transposition of subscript T representing matrix；M-th of particle is in the position of the t+1 times iterationRdIndicate the lower limit of search space, SdIndicate search
The upper limit in space, c1, c2 and c3 are Studying factors, respectively indicate self adjustment capability and to the three optimal grains of value diversiform particle group
The ability of son study, wherein 0 < c1≤ 2,0 < c2≤ 2,0 < c3≤ 2,0 < r1≤ 1,0 < r2≤ 1,0 < r3≤ 1, h are inertia weight, andhstartFor initial inertia weight and 0.3≤hstart≤ 0.5, hendFor terminate inertia weight and
0.8≤hend≤ 1.0,Indicate the current individual optimal location before evolution m-th of particle evolution of generation,Expression is worked as
Evolution for random particles evolve before current individual optimal location,Indicate when evolution generation three value diversiform particle groups into
Current global optimum position before change；Set one third dimension respectively toWithStudy；N value is 3, σ
For weight, and 0 < σ≤1, randn () indicate standard normal distribution function, and e indicates the bottom of natural logrithm；
(7) each particle in three value diversiform particle groups is updated according to the equation of motion of particle in three value diversiform particle groups
Current location and present speed the latest position of particle is made using the most current speed of particle as the present speed of the particle
For the current location of the particle；
(8) with probability PmThree value variations, P are carried out to the current location of each particle in three value diversiform particle groupsmValue be
0.1, detailed process are as follows: generate one and be more than or equal to the 0 and random number b less than or equal to 1, if b < Pm, then working as the particle
0 in front position, which becomes 2,2, which becomes 1,1, becomes 0, and the value after the current location of the particle is made a variation is as the present bit of the particle
It sets；If b >=Pm, the current location of the particle remains unchanged；
(9) the corresponding fitness value in current location that current each particle is calculated according to fitness function, by the particle
The corresponding fitness value in current location fitness value corresponding with the current individual optimal location of the particle is compared, and selection is suitable
The current individual optimal location that answer angle value lesser new as the particle, then the optimal position of current individual that more all particles are new
It sets, using the current individual optimal location for having the particle of minimum fitness value new as the new current of three value diversiform particle groups
Global optimum position；
(10) judge whether current evolutionary generation is maximum evolutionary generation, if it is not, going to step (7) starts next round
It evolves, otherwise enters step (11)；
(11) the new current global optimum position of three value diversiform particle groups is exported as optimal polarity, this is optimal
The area of the corresponding mixing polarity XNOR/OR circuit of polarity is exported as optimal area.
Use polarity conversion method by function in the step (2)
Be converted to the specific steps of the expression formula of mixing polarity XNOR/OR circuit are as follows:
A. by f (xn-1,xn-2,…,xk,…,x0) in maximal term indicate in binary form；
B. the mixing polarity number p of required conversion is indicated with ternary form；
If C. mixing polar g is 1, g are selected as 1 maximal term, xor operation is carried out to the position, is obtained
New item does not operate if g are 0 or 2；
If D. mix it is polar g be 0 or 1 when, select the value of q position for 1 new item, with these positions be it is unrelated
, then generate all 2q- 1 new item, and update the item number in concordance list, if mixing polar g when being 2, it keeps not
Become, 0≤q≤n；
E. step D is repeated, until having operated all new items, obtaining the item that concordance list middle term ordinal number is odd number is the mixing
Corresponding same or/or item of polarity.
The lower limit R of the search spacedValue be 0, the upper limit S of the search spacedValue be 2, vmin,d
Value be -6, vmax,dValue be 6, total population M be 20-30, maximum evolutionary generation tmaxValue be 100 or more.
Compared with the prior art, the advantages of the present invention are as follows using three value diversiform particle group algorithms to particle rapidity and
During particle position is updated, extensive study thoughts and three value mutation operations are increased, thus keep three value diversity
The population diversity strategy of population, to be asked efficiently against the Premature Convergence of three traditional value diversiform particle group's algorithms
Topic, fast and accurately searches optimal polarity, and search capability is strong, and search efficiency is high；Experimental verification, using method of the invention into
When row is area-optimized, averagely saving circuit area is 15.1%.
Detailed description of the invention
Fig. 1 is the contrast curve chart that method of the invention and existing method optimize the area performance of circuit.
Specific embodiment
The present invention will be described in further detail below with reference to the embodiments of the drawings.
A kind of embodiment one: mixing polarity XNOR/OR circuit area optimization method, comprising the following steps:
(1) circuit of PLA format is read in, which uses functionTable
Show, n is function f (xn-1,xn-2,…,xk,…,x0) input variable number, (xn-1,xn-2,…,xk,…,x0) it is function f (xn-1,
xn-2,…,xk,…,x0) n input variable, ∏ is AND operator, aiIt is maximum term coefficient, and ai∈ { 0,1 }, i are maximum
Ordinal number, with being represented in binary as in-1in-2…ik…i0, MiMaximal term, indicate n input variable phase or, k be positive integer,
And 0≤k≤n-1；
(2) use polarity conversion method by functionBe converted to mixing pole
The expression formula of property XNOR/OR circuit:Wherein, p is mixing polarity
The polarity number of XNOR/OR circuit, p are expressed as p with ternary formn-1pn-2…pg…p0, g is positive integer, and 0≤g≤n-1, ⊙
∏ is same or operator, SjExpression or item, djFor or term coefficient, and dj∈ { 0,1 }, j be or item ordinal number, and j is with being represented in binary as
jn-1jn-2…jg…j0, djIt indicates or whether item occurs in mixing polarity XNOR/OR expression formula, work as djWhen=0, expression or item Sj
Occur in the expression formula of mixing polarity XNOR/OR circuit, works as djWhen=1, expression or item SjNot in mixing polarity XNOR/OR electricity
Occur in the expression formula on road, wherein xgWith pgAnd jgRelationship are as follows: work as pg=0 and jgWhen=0, xgWith former occurrences；Work as pg=1
And jgWhen=0, xgOccur with contravariant；Work as pgWhen=2, xgOccur in the form of former variable and contravariant simultaneously, works as jgWhen=0,
xgWith former occurrences, work as jgWhen=1, xgOccur with contravariant；
(3) mixing polarity XNOR/OR circuit area is optimized to each parameter of each parameter Yu three value diversiform particle group's algorithms
It is associated: input variable number n is defined as to the search space dimension of three value diversiform particle groups, mixing polarity is defined as three
It is worth the particle of diversiform particle group, polarity number p is defined as particle position；Set the quantity of particle in three value diversiform particle groups
It is positive integer for M, M, total evolutionary generation of three value diversiform particle groups is tmax；
(4) fitness function is established: the fitness function fitness (p) of the corresponding particle position of polarity number p are as follows:
Fitness (p)=(1-w) * Earea(p)/Earea_max
Wherein, EareaIt (p) is the Class area estimation value that polarity XNOR/OR circuit is mixed at polarity p, EareaIt (p) is polarity p
The sum of the item number of same or item and/or item that the expression formula of lower mixing polarity XNOR/OR circuit includes, Earea_maxTo mix polarity
The maximum area estimated value of XNOR/OR circuit, and Earea_max=n*2n, n be input variable number, w be more than or equal to 0 and be less than etc.
In 1 coefficient, * is multiplication symbol ,/it is division operation symbol；
(5) population is initialized: the speed of each particle in three value diversiform particle group of random initializtion, position, particle
Current individual optimal location, three value diversiform particle groups current global optimum position and each particle position fitness value；
(6) equation of motion of particle in three value diversiform particle groups is established:
Wherein, t is the current evolutionary generation of three value diversiform particle groups, 1≤t≤tmax,It is m-th of particle in t
The speed of secondary iteration,It is m-th of particle in the position of the t times iteration, m=1,2 ..., M, d is integer and 1≤d≤n,
Round expression is rounded up to closest integer, speed of m-th of particle in the t+1 times iterationvmin,dThe minimum speed of m-th of particle is represented,
vmax,dRepresent the maximum speed of m-th of particle, the transposition of subscript T representing matrix；M-th of particle is in the position of the t+1 times iterationRdIndicate the lower limit of search space, SdIndicate that search is empty
Between the upper limit, c1, c2 and c3 are Studying factors, respectively indicate self adjustment capability and to three value diversiform particle group's optimal particles
The ability of study, wherein 0 < c1≤ 2,0 < c2≤ 2,0 < c3≤ 2,0 < r1≤ 1,0 < r2≤ 1,0 < r3≤ 1, h are inertia weight, andhstartFor initial inertia weight and 0.3≤hstart≤ 0.5, hendFor terminate inertia weight and
0.8≤hend≤ 1.0,Indicate the current individual optimal location before evolution m-th of particle evolution of generation,Expression is worked as
Evolution for random particles evolve before current individual optimal location,Indicate when evolution generation three value diversiform particle groups into
Current global optimum position before change；Set one third dimension respectively toWithStudy；N value is 3,
σ is weight, and 0 < σ≤1, randn () indicate standard normal distribution function, and e indicates the bottom of natural logrithm；
(7) each particle in three value diversiform particle groups is updated according to the equation of motion of particle in three value diversiform particle groups
Current location and present speed the latest position of particle is made using the most current speed of particle as the present speed of the particle
For the current location of the particle；
(8) with probability PmThree value variations, P are carried out to the current location of each particle in three value diversiform particle groupsmValue be
0.1, detailed process are as follows: generate one and be more than or equal to the 0 and random number b less than or equal to 1, if b < Pm, then working as the particle
0 in front position, which becomes 2,2, which becomes 1,1, becomes 0, and the value after the current location of the particle is made a variation is as the present bit of the particle
It sets；If b >=Pm, the current location of the particle remains unchanged；
(9) the corresponding fitness value in current location that current each particle is calculated according to fitness function, by the particle
The corresponding fitness value in current location fitness value corresponding with the current individual optimal location of the particle is compared, and selection is suitable
The current individual optimal location that answer angle value lesser new as the particle, then the optimal position of current individual that more all particles are new
It sets, using the current individual optimal location for having the particle of minimum fitness value new as the new current of three value diversiform particle groups
Global optimum position；
(10) judge whether current evolutionary generation is maximum evolutionary generation, if it is not, going to step (7) starts next round
It evolves, otherwise enters step (11)；
(11) the new current global optimum position of three value diversiform particle groups is exported as optimal polarity, this is optimal
The area of the corresponding mixing polarity XNOR/OR circuit of polarity is exported as optimal area.
A kind of embodiment two: mixing polarity XNOR/OR circuit area optimization method, comprising the following steps:
(1) circuit of PLA format is read in, which uses functionTable
Show, n is function f (xn-1,xn-2,…,xk,…,x0) input variable number, (xn-1,xn-2,…,xk,…,x0) it is function f (xn-1,
xn-2,…,xk,…,x0) n input variable, ∏ is AND operator, aiIt is maximum term coefficient, and ai∈ { 0,1 }, i are maximum
Ordinal number, with being represented in binary as in-1in-2…ik…i0, MiMaximal term, indicate n input variable phase or, k be positive integer,
And 0≤k≤n-1；
(2) use polarity conversion method by functionBe converted to mixing
The expression formula of polarity XNOR/OR circuit:Wherein, p is mixing polarity
The polarity number of XNOR/OR circuit, p are expressed as p with ternary formn-1pn-2…pg…p0, g is positive integer, and 0≤g≤n-1, ⊙
∏ is same or operator, SjExpression or item, djFor or term coefficient, and dj∈ { 0,1 }, j be or item ordinal number, and j is with being represented in binary as
jn-1jn-2…jg…j0, djIt indicates or whether item occurs in mixing polarity XNOR/OR expression formula, work as djWhen=0, expression or item Sj
Occur in the expression formula of mixing polarity XNOR/OR circuit, works as djWhen=1, expression or item SjNot in mixing polarity XNOR/OR electricity
Occur in the expression formula on road, wherein xgWith pgAnd jgRelationship are as follows: work as pg=0 and jgWhen=0, xgWith former occurrences；Work as pg=1
And jgWhen=0, xgOccur with contravariant；Work as pgWhen=2, xgOccur in the form of former variable and contravariant simultaneously, works as jgWhen=0,
xgWith former occurrences, work as jgWhen=1, xgOccur with contravariant；
(3) mixing polarity XNOR/OR circuit area is optimized to each parameter of each parameter Yu three value diversiform particle group's algorithms
It is associated: input variable number n is defined as to the search space dimension of three value diversiform particle groups, mixing polarity is defined as three
It is worth the particle of diversiform particle group, polarity number p is defined as particle position；Set the quantity of particle in three value diversiform particle groups
It is positive integer for M, M, total evolutionary generation of three value diversiform particle groups is tmax；
(4) fitness function is established: the fitness function fitness (p) of the corresponding particle position of polarity number p are as follows:
Fitness (p)=(1-w) * Earea(p)/Earea_max
Wherein, EareaIt (p) is the Class area estimation value that polarity XNOR/OR circuit is mixed at polarity p, EareaIt (p) is polarity p
The sum of the item number of same or item and/or item that the expression formula of lower mixing polarity XNOR/OR circuit includes, Earea_maxTo mix polarity
The maximum area estimated value of XNOR/OR circuit, and Earea_max=n*2n, n be input variable number, w be more than or equal to 0 and be less than etc.
In 1 coefficient, * is multiplication symbol ,/it is division operation symbol；
(5) population is initialized: the speed of each particle in three value diversiform particle group of random initializtion, position, particle
Current individual optimal location, three value diversiform particle groups current global optimum position and each particle position fitness value；
(6) equation of motion of particle in three value diversiform particle groups is established:
Wherein, t is the current evolutionary generation of three value diversiform particle groups, 1≤t≤tmax,It is m-th of particle in t
The speed of secondary iteration,It is m-th of particle in the position of the t times iteration, m=1,2 ..., M, d is integer and 1≤d≤n,
Round expression is rounded up to closest integer, speed of m-th of particle in the t+1 times iterationvmin,dThe minimum speed of m-th of particle is represented,
vmax,dRepresent the maximum speed of m-th of particle, the transposition of subscript T representing matrix；M-th of particle is in the position of the t+1 times iterationRdIndicate the lower limit of search space, SdIndicate search
The upper limit in space, c1, c2 and c3 are Studying factors, respectively indicate self adjustment capability and to the three optimal grains of value diversiform particle group
The ability of son study, wherein 0 < c1≤ 2,0 < c2≤ 2,0 < c3≤ 2,0 < r1≤ 1,0 < r2≤ 1,0 < r3≤ 1, h are inertia weight, andhstartFor initial inertia weight and 0.3≤hstart≤ 0.5, hendFor terminate inertia weight and
0.8≤hend≤ 1.0,Indicate the current individual optimal location before evolution m-th of particle evolution of generation,Expression is worked as
Evolution for random particles evolve before current individual optimal location,Indicate when evolution generation three value diversiform particle groups into
Current global optimum position before change；Set one third dimension respectively toWithStudy；N value is 3, σ
For weight, and 0 < σ≤1, randn () indicate standard normal distribution function, and e indicates the bottom of natural logrithm；
(7) each particle in three value diversiform particle groups is updated according to the equation of motion of particle in three value diversiform particle groups
Current location and present speed the latest position of particle is made using the most current speed of particle as the present speed of the particle
For the current location of the particle；
(8) with probability PmThree value variations, P are carried out to the current location of each particle in three value diversiform particle groupsmValue be
0.1, detailed process are as follows: generate one and be more than or equal to the 0 and random number b less than or equal to 1, if b < Pm, then working as the particle
0 in front position, which becomes 2,2, which becomes 1,1, becomes 0, and the value after the current location of the particle is made a variation is as the present bit of the particle
It sets；If b >=Pm, the current location of the particle remains unchanged；
(9) the corresponding fitness value in current location that current each particle is calculated according to fitness function, by the particle
The corresponding fitness value in current location fitness value corresponding with the current individual optimal location of the particle is compared, and selection is suitable
The current individual optimal location that answer angle value lesser new as the particle, then the optimal position of current individual that more all particles are new
It sets, using the current individual optimal location for having the particle of minimum fitness value new as the new current of three value diversiform particle groups
Global optimum position；
(10) judge whether current evolutionary generation is maximum evolutionary generation, if it is not, going to step (7) starts next round
It evolves, otherwise enters step (11)；
(11) the new current global optimum position of three value diversiform particle groups is exported as optimal polarity, this is optimal
The area of the corresponding mixing polarity XNOR/OR circuit of polarity is exported as optimal area.
In the present embodiment, use polarity conversion method by function in step (2)Be converted to the specific steps of the expression formula of mixing polarity XNOR/OR circuit
Are as follows:
A. by f (xn-1,xn-2,…,xk,…,x0) in maximal term indicate in binary form；
B. the mixing polarity number p of required conversion is indicated with ternary form；
If C. mixing polar g is 1, g are selected as 1 maximal term, xor operation is carried out to the position, is obtained
New item does not operate if g are 0 or 2；
If D. mix it is polar g be 0 or 1 when, select the value of q position for 1 new item, with these positions be it is unrelated
, then generate all 2q- 1 new item, and update the item number in concordance list, if mixing polar g when being 2, it keeps not
Become, 0≤q≤n；
E. step D is repeated, until having operated all new items, obtaining the item that concordance list middle term ordinal number is odd number is the mixing
Corresponding same or/or item of polarity.
In the present embodiment, the lower limit R of search spacedValue be 0, the upper limit S of search spacedValue be 2, vmin,d's
Value is -6, vmax,dValue be 6, total population M be 20-30, maximum evolutionary generation tmaxValue be 100 or more.
In order to verify the superiority of method of the invention in mixing polarity XNOR/OR circuit area optimization, document is used
YU Hai-zhen,WANG Peng-jun,WANG Di-shen.Discrete ternary particle swarm
optimization for area optimization of MPRM circuits[J].Journal of
Semiconductors, 2013,34 (2): 025011-1-025011-6. is compared with proposed algorithm.In an experiment, originally
The parameter setting of invention are as follows: initial inertia weight hstart=0.9, terminate inertia weight hend=0.4, linear decrease strategy, study
The factor c1=c2=c3=1.8, σ=0.2, vmax=6.0, total population M are 20-30, maximum evolutionary generation tmaxIt is 200.Its
Optimum results are as shown in table 1 below, wherein " benchmark " indicates the title of test circuit, " inputs " indicates test circuit
Input variable number；" DTPSO " indicates the result that circuit area optimization is carried out with discrete three values particle swarm algorithm；" TDPSO " table
Show that the present invention carries out the result of circuit area optimization；Coefficient w value is 0.0,0.25,0.5,0.75,1.0.
The correlation curve that method of the invention and existing method optimize the area performance of circuit is as shown in Figure 1.
In Fig. 1, abscissa is coefficient w, and ordinate is the average value of 10 circuit areas.As shown in Figure 1, method of the invention is significantly excellent
In existing method, averagely saving circuit area is 15.1%.
Claims (3)
1. a kind of mixing polarity XNOR/OR circuit area optimization method, it is characterised in that the following steps are included:
(1) circuit of PLA format is read in, which uses functionIt indicates, n
For function f (xn-1,xn-2,…,xk,…,x0) input variable number, (xn-1,xn-2,…,xk,…,x0) it is function f (xn-1,
xn-2,…,xk,…,x0) n input variable, ∏ is AND operator, aiIt is maximum term coefficient, and ai∈ { 0,1 }, i are maximum
Ordinal number, with being represented in binary as in-1in-2…ik…i0, MiMaximal term, indicate n input variable phase or, k be positive integer,
And 0≤k≤n-1；
(2) use polarity conversion method by functionBe converted to mixing polarity
The expression formula of XNOR/OR circuit:Wherein, p is mixing polarity
The polarity number of XNOR/OR circuit, p are expressed as p with ternary formn-1pn-2…pg…p0, g is positive integer, and 0≤g≤n-1, ⊙
∏ is same or operator, SjExpression or item, djFor or term coefficient, and dj∈ { 0,1 }, j be or item ordinal number, and j is with being represented in binary as
jn-1jn-2…jg…j0, djIt indicates or whether item occurs in mixing polarity XNOR/OR expression formula, work as djWhen=0, expression or item Sj
Occur in the expression formula of mixing polarity XNOR/OR circuit, works as djWhen=1, expression or item SjNot in mixing polarity XNOR/OR electricity
Occur in the expression formula on road, wherein xgWith pgAnd jgRelationship are as follows: work as pg=0 and jgWhen=0, xgWith former occurrences；Work as pg=1
And jgWhen=0, xgOccur with contravariant；Work as pgWhen=2, xgOccur in the form of former variable and contravariant simultaneously, works as jgWhen=0,
xgWith former occurrences, work as jgWhen=1, xgOccur with contravariant；
(3) each parameter progress that polarity XNOR/OR circuit area optimizes each parameter with three value diversiform particle group's algorithms will be mixed
Input variable number n: being defined as the search space dimension of three value diversiform particle groups by association, and it is more that mixing polarity is defined as three values
Polarity number p is defined as particle position by the particle of sample population；The quantity of particle in three value diversiform particle groups is set as M,
M is positive integer, and total evolutionary generation of three value diversiform particle groups is tmax；
(4) fitness function is established: the fitness function fitness (p) of the corresponding particle position of polarity number p are as follows:
Fitness (p)=(1-w) * Earea(p)/Earea_max
Wherein, EareaIt (p) is the Class area estimation value that polarity XNOR/OR circuit is mixed at polarity p, EareaIt (p) is mixed under polarity p
The sum of the item number of same or item and/or item that the expression formula of conjunction polarity XNOR/OR circuit includes, Earea_maxTo mix polarity XNOR/OR
The maximum area estimated value of circuit, and Earea_max=n*2n, n is input variable number, and w is to be more than or equal to 0 and less than or equal to 1
Number, * are multiplication symbol ,/it is division operation symbol；
(5) initialize population: the speed of each particle in three value diversiform particle group of random initializtion, position, particle it is current
Personal best particle, three value diversiform particle groups current global optimum position and each particle position fitness value；
(6) equation of motion of particle in three value diversiform particle groups is established:
Wherein, t is the current evolutionary generation of three value diversiform particle groups, 1≤t≤tmax,It changes for m-th of particle at the t times
The speed in generation,It is m-th of particle in the position of the t times iteration, m=1,2 ..., M, d is integer and 1≤d≤n, round
Expression is rounded up to closest integer, speed of m-th of particle in the t+1 times iterationvmin,dThe minimum speed of m-th of particle is represented,
vmax,dRepresent the maximum speed of m-th of particle, the transposition of subscript T representing matrix；M-th of particle is in the position of the t+1 times iterationRdIndicate the lower limit of search space, SdIndicate search
The upper limit in space, c1, c2 and c3 are Studying factors, respectively indicate self adjustment capability and to the three optimal grains of value diversiform particle group
The ability of son study, wherein 0 < c1≤ 2,0 < c2≤ 2,0 < c3≤ 2,0 < r1≤ 1,0 < r2≤ 1,0 < r3≤ 1, h are inertia weight, andhstartFor initial inertia weight and 0.3≤hstart≤ 0.5, hendFor terminate inertia weight and
0.8≤hend≤ 1.0,Indicate the current individual optimal location before evolution m-th of particle evolution of generation,Expression is worked as
Evolution for random particles evolve before current individual optimal location,Indicate when evolution generation three value diversiform particle groups into
Current global optimum position before change；Set one third dimension respectively to WithStudy；N value is 3, σ
For weight, and 0 < σ≤1, randn () indicate standard normal distribution function, and e indicates the bottom of natural logrithm；
(7) each particle in three value diversiform particle groups is updated according to the equation of motion of particle in three value diversiform particle groups to work as
Front position and present speed, using the most current speed of particle as the present speed of the particle, using the latest position of particle as this
The current location of particle；
(8) with probability PmThree value variations, P are carried out to the current location of each particle in three value diversiform particle groupsmValue be 0.1,
Detailed process are as follows: generate one and be more than or equal to the 0 and random number b less than or equal to 1, if b < Pm, then by the present bit of the particle
0 in setting, which becomes 2,2, which becomes 1,1, becomes 0, and the value after the current location of the particle is made a variation is as the current location of the particle；
If b >=Pm, the current location of the particle remains unchanged；
(9) the corresponding fitness value in current location that current each particle is calculated according to fitness function, by the current of the particle
The corresponding fitness value in position fitness value corresponding with the current individual optimal location of the particle is compared, and selects fitness
It is worth the lesser current individual optimal location new as the particle, then the current individual optimal location that more all particles are new, it will
The new current overall situation of the new current individual optimal location of particle with minimum fitness value as three value diversiform particle groups
Optimal location；
(10) judge whether current evolutionary generation is maximum evolutionary generation, if it is not, go to step (7) start next round into
Change, otherwise enters step (11)；
(11) the new current global optimum position of three value diversiform particle groups is exported as optimal polarity, by the optimal polarity
The area of corresponding mixing polarity XNOR/OR circuit is exported as optimal area.
2. a kind of mixing polarity XNOR/OR circuit area optimization method according to claim 1, it is characterised in that described
Use polarity conversion method by function in step (2)Be converted to mixing pole
The specific steps of the expression formula of property XNOR/OR circuit are as follows:
A. by f (xn-1,xn-2,…,xk,…,x0) in maximal term indicate in binary form；
B. the mixing polarity number p of required conversion is indicated with ternary form；
If C. mixing polar g is 1, g are selected as 1 maximal term, xor operation is carried out to the position, is obtained new
, if g are 0 or 2, do not operate；
If D. mix it is polar g be 0 or 1 when, select the value of q position for 1 new item, using these positions as outlier,
All 2 are generated againq- 1 new item, and update the item number in concordance list, if mixing polar g when being 2, it remains unchanged, 0
≤q≤n；
E. step D is repeated, until having operated all new items, obtaining the item that concordance list middle term ordinal number is odd number is the mixing polarity
Corresponding same or/or item.
3. a kind of mixing polarity XNOR/OR circuit area optimization method according to claim 1, it is characterised in that described
The lower limit R of search spacedValue be 0, the upper limit S of the search spacedValue be 2, vmin,dValue be -6, vmax,d
Value be 6, total population M be 20-30, maximum evolutionary generation tmaxValue be 100 or more.
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