CN102592013B - Optimization method for time delay and area of fixed-polarity Reed-Muller circuit - Google Patents
Optimization method for time delay and area of fixed-polarity Reed-Muller circuit Download PDFInfo
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Abstract
The invention discloses an optimization method for time delay and an area of a fixed-polarity Reed-Muller circuit, which is characterized by comprising the steps of simplifying a polarity expression through an algebraic method according to the characteristics of fixed-polarity Reed-Muller expression; calculating the time delay and area of the fixed-polarity Reed-Muller circuit based on a time delay and area module by means of time delay decomposition, and synthesizing the calculated time delay and area to obtain a function of polarity fitness; and building corresponding relationships between the fixed polarities and individuals of a particle swarm, referring to a list technology and performing polarity searches of optimum time delay and area of the fixed-polarity Reed-Muller circuit by means of a particle swarm optimization algorithm. Tests of Microelectronics Center of North Carolina (MCNC) Benchmark Circuit show that the optimization method for time delay and the area of the fixed-polarity Reed-Muller circuit has good optimization effects on large-scale fixed-polarity Reed-Muller circuits.
Description
Technical field
The present invention relates to a kind of optimization method of circuit, especially relate to the optimization method of a kind of fixed polarity Reed Muller circuit delay and area.
Background technology
Reed Muller (Reed-Muller, RM) logic based on AND/XOR or OR/XNOR computing is the another kind of circuit expressions mode that is different from Boolean logic.Research shows, than Boolean logic, the partial circuit based on RM logic (as functional circuits such as arithmetical circuit, parity checkers) has more compact structure
[1]with better measurability
[2].RM circuit delay and area-optimized be the important component part of circuit synthesis and optimisation technique, be subject to the generally attention of academia
[3-6].N variable R M logical function has 2
nindividual fixed polarity, corresponding 2
nindividual different fixed polarity Reed Muller (Fixed-Polarity Reed-Muller, FPRM) expression formula
[4].Each expression formula is complicated and simple to differ, and time delay and the area of its corresponding circuits are also not quite similar.While optimizing middle and small scale circuit, can utilize limit algorithm traversal and check each polarity, but to fairly large circuit, due to the sharply increase in its polarity space, exhaustive search strategy is difficult to the result that is optimized within the limited time.Therefore, need to find the search efficiency that a kind of effective intelligent algorithm improves polarity.
Particle group optimizing (Particle Swarm Optimization, PSO) algorithm is a kind of emerging evolutionary computation technique, and it comes from the research to flock of birds predation, is a kind of intelligent method based on population
[7].Than other intelligent algorithms, as genetic algorithm (Genetic Algorithm, GA)
[5], simulated annealing
[8]deng, PSO algorithm has the features such as principle is simple, parameter is less, fast convergence rate, and is easy to realize, and is therefore widely used in Continuous Nonlinear function, neural network, Solution of Nonlinear Optimal Problem etc.
[7,9].PSO algorithm, from initial solution, is found global optimum by following current optimal value warp by generation search, and this global optimum is corresponding with FPRM circuit delay and area optimum polarity.
[1]T.Hirayama，Y.Nishitani.Exact minimization of AND-EXOR expressions of practicalbenchmark functions[J].Journal of Circuits，Systems and Computers.2009，18(3)：465-486.
[2]H.Rahaman，D.K.Das，B.B.Bhattacharya.Testable design of AND-EXOR logicnetworks with universal test sets[J].Computers and Electrical Engineering.2009，35(5)：644-658.
[3]M.Yang，L.Wang，J.R.Tong，et al.Techniques for dual forms of Reed-Muller expansionconversion[J].Integration，the VLSI Journal.2008，41(1)：113-122.
[4] Wang Pengjun, Lu Jingang. the low-power consumption optimum polarity search [J] based on XNOR/OR logic. electronic letters, vol .2008,36 (5): 993-997.
[5] Li Hui, Wang Pengjun. the MPRM circuit low-power consumption optimisation technique [J] based on dynamic logic. Circuits and Systems journal .2010,15 (5): 99-105.
[6]T.K.Shahana，R.K.James，K.P.Jacob，et al.Automated synthesis of delay-reducedReed-muller universal logic module networks[C].in：Proceedings of 23rd NORCHIPConference.Oulu，2005，1-4.
[7]F.Mauger，C.Chandre，T.Uzer.Simulated annealing algorithm for finding periodic orbitsof multi-electron atomic systems[J].Communications in Nonlinear Science andNumerical Simulation.2011，16(7)：2845-2852.
[8]C.J.Liao，C.T.Tseng，P.Luarn.A discrete version of particle swarm optimization forflowshop scheduling problems[J].Computers and Operations Research.2007，34(10)：3099-3111.
[9]W.N.Chen，J.Zhang，H.S.H.Chung，et al.A novel set-based particle swarmoptimization method for discrete optimization problems[J].IEEE Transactions onEvolutionary Computation.2010，14(2)：278-300.
Summary of the invention
Technical matters to be solved by this invention is to provide a kind ofly has higher polarity search efficiency to fairly large fixed polarity Reed Muller circuit, and can within the limited time, be optimized the fixed polarity Reed Muller circuit delay of result and the optimization method of area.
The present invention solves the problems of the technologies described above adopted technical scheme: the optimization method of a kind of fixed polarity Reed Muller circuit delay and area, according to fixed polarity Reed Muller expression formula feature, utilizes algebraic approach to carry out abbreviation to polarity expression formula; Based on time delay and Area Model, utilize time delay to decompose to calculate time delay and the area of fixed polarity Reed Muller circuit, and comprehensively both obtain polarity fitness function again; Then set up the individual corresponding relation of fixed polarity and population, in conjunction with list technique, utilize particle swarm optimization algorithm to carry out optimum delay and the search of area polarity to fixed polarity Reed Muller circuit; Concrete steps are:
1) select evolutionary generation to be greater than for 100 generations, be less than for 150 generations, read in circuit, be expressed as function
n is function f (x
n-1, x
n-2..., x
k..., x
0) variable number, (x
n-1, x
n-2..., x
k..., x
0) be function f (x
n-1, x
n-2..., x
k..., x
0) n variable, ∑ is exclusive disjunction symbol; a
iminterm coefficient, and a
i{ 0,1}, i is minterm ordinal number to ∈, with binary number representation, is (i
n-1i
n-2i
ki
0), m
ibe minterm, represent n variable phase and, x wherein
kwith i
kpass be: work as i
k=1 o'clock, x
kfor positive variable, work as i
k=0 o'clock, x
kfor negative variable, wherein k is positive integer, and 0≤k≤n-1; Utilize list technique function to be converted to the fixed polarity Reed Muller expression formula of p polarity:
p is the polarity number of fixed polarity Reed Muller expression formula, with binary number representation, is (p
n-1p
n-2p
gp
0),
for xor operator; b
jfor with item coefficient, and b
j∈ { 0,1}; J is and item ordinal number, with binary number representation, is (j
n-1j
n-2j
gj
0), π
jfor with item, represent n variable phase and, x
gwith j
gand p
gpass be: work as j
g=0, p
g=0 o'clock, x
gbe 1; Work as j
g=1, p
g=0 o'clock, x
gfor positive variable; Work as j
g=0, p
g=1 o'clock, x
gbe 1; Work as j
g=1, p
g=1 o'clock, x
gfor negative variable, wherein g is positive integer, and 0≤g≤n-1;
2) initialization population: the space dimensionality that variable number n is defined as to population, polarity is defined as to the particle of population, polarity number p is defined as to the particle position of population, in n-dimensional space, choose arbitrarily initial position and the initial velocity of M particle random this M of generation particle, present speed using the initial velocity of each particle as this particle, current location using the initial position of each particle now as this particle, also be the current optimal location of particle simultaneously, current optimal location using the optimum initial position in the initial position of M particle as population, then select 1 as current evolutionary generation,
3) according to current evolutionary generation, select the current location of particle as the polarity number of fixed polarity Reed Muller expression formula, with algebraic approach, the fixed polarity Reed Muller expression formula of all polarity is carried out to abbreviation;
4) for the fixed polarity Reed Muller circuit after abbreviation, each many input gate of circuit are resolved into two input gates, and the shortest critical path time delay of definition is circuit delay, node in circuit adds up to circuit area, and circuit area and the circuit delay of fixed polarity Reed Muller circuit corresponding to m particle position are defined as respectively to A (X
m) and d (X
m), wherein 1≤m≤M, is defined as respectively A by the circuit area summation of initialization population and circuit delay summation
totaland d
total, defining m fitness function corresponding to particle position is fitness (X
m)=α * A (X
m)/A
total+ (1-α) * d (X
m)/d
total, in formula, α optimizes weighted value, represents area-optimized share shared in whole optimization, and its value is 0.1～0.9, the more present speed of new particle and current location, present speed using the most current speed of each particle as this particle, current location using the latest position of each particle as this particle, calculate the fitness function of all particles, the current optimal location of the current location of this particle and this particle is compared, select the corresponding particle position of fitness function smaller value as the new current optimal location of this particle, the new current optimal location of more all particles again, using the current optimal location with the corresponding particle of minimum fitness function as the new current optimal location of population,
5) judge whether current algebraically is maximum evolutionary generation, if not, forward step 3 to), otherwise enter step 6);
6) polarity of the new corresponding fixed polarity Reed of the current optimal location Muller expression formula of population is exported to optimum delay and the output of best area using the time delay of fixed polarity Reed Muller circuit corresponding to this optimum polarity and area as fixed polarity Reed Muller circuit as optimum polarity.
Utilize in list technique acquisition fixed polarity Reed Muller expression formula and with the concrete steps of item be:
1)-1 by f (x
n-1, x
n-2..., x
0) in minterm and the polarity of required conversion be expressed as binary number form;
1) if-2 polarity g positions are 0, select the minterm that g position is 0, produce this be 1 new; If polarity g position is 1, selecting g position is 1 minterm, and producing this is 0 new;
1)-3 compare new item with original minterm: if there be the minterm identical with new, delete this minterm; Otherwise new item is inserted in original minterm;
1)-4 repeating steps 1)-2 and 1)-3, until complete the operation of all positions;
1)-5 will be left all minterms carries out an xor operation with polarity, and the item obtaining i.e. the fixed polarity Reed Muller and item of this polarity.
By the concrete steps that algebraic approach carries out abbreviation to fixed polarity Reed Muller expression formula, be:
3)-1 will be expressed as binary number form with item, by the size of l to classifying with item, 0≤l≤n, method is: produce sequence number and be followed successively by 0 to n set, according to combinatorial formula
corresponding, put into set 0 to set n with item from small to large, for
with item, by l and n-l compared with corresponding being stored in small size set with item of decimal, plurality is corresponding puts into large size set with item;
3)-2 by the sorting from small to large with item of each set, makes r=n, s=n-1;
3) if-3 set r and s non-NULL all, by the minimum of set r and s with assignment respectively to u and w; Otherwise, jump to step 3) and-5;
3) whether-4 meet by checking with a u and w
if meet, in set, delete this two with, generate mixed term, and by next in set r and s with assignment respectively to u and w; Otherwise next by set in s is with an assignment to w, and u is constant;
3) if-5 set r for empty or completed in set r last with Reduction, make r=r-1, and pair set r makes the following judgment: 1. when r > 1 and set r non-NULL, by the minimum of set r with an assignment to u; 2. work as r=1, jump to step 3)-9; 3. when set r is empty, repeat current step;
3) if-6 set s for empty or completed in set s last with Reduction, make s=s-1, and pair set s makes the following judgment: 1. when s > 0 and set s non-NULL, by the minimum of set s with an assignment to w; 2. work as s=0, jump to step 3)-9; 3. when set s is empty, repeat current step;
3) if-7 r=s, s=s-1, and pair set s makes the following judgment: 1. when s > 0 and set s non-NULL, by the minimum of set s with an assignment to w; If 2. set s is empty, repeating step 3)-6;
3) if-8 r=1 or s=0 enter step 3)-9, otherwise return to step 3)-4;
3)-9 check whether set 0 has and item: if had, carry out with arbitrary not abbreviation and item
operation; Otherwise constant;
3)-10 algorithms finish, and currentitem comprises: not abbreviation with and mixed term.
For the fixed polarity Reed Muller circuit after abbreviation, the concrete steps that obtain circuit delay and circuit area are as follows:
4)-1 for mixed term
utilize class Huffman algorithm pair
the AND door of part decomposes, and is exported the input as u part; AND door to u part repeats aforesaid operations, and the input using the output with item as XOR gate;
4)-2 for abbreviation not with, utilize class Huffman to decompose AND door, the input using output as XOR gate;
4)-3 utilize class Huffman algorithm to complete the decomposition to XOR gate, and the shortest critical path nodes obtaining is circuit delay, and the node of whole circuit network adds up to circuit area.
Determine that the most current speed of particle and the concrete steps of latest position are: definition t is current evolutionary generation, and h is space dimensionality, 0≤h≤n-1, the most current speed of tieing up as evolution generation m particle h is v
mh(t) with function representation, be: v
mh(t)=v
mh(t-1)+c1*random1 () * (pbest
mh-x
mh(t-1))+c2*random2 () * (gbest
h-x
mh(t-1)), the latest position when evolution generation m particle h dimension is x
mh(t) with sigmoid function representation, be:
S(v
mh(t))=1/ (1+exp (v
mh(t))), wherein, v
mh(t-1) represent the present speed when the front h dimension of evolution generation m particle evolution, x
mh(t-1) represent that c1 and c2 represent speedup factor, c1, c2 ∈ [1,3], pbest when the current location of the front h dimension of evolution generation m particle evolution
mhrepresent the current optimal location when the front h dimension of evolution generation m particle evolution, gbest
hrepresent that random1 () and random2 () are the random number in (0,1) scope, v when the current optimal location of evolution for the front h dimension of population evolution
mh(t) concrete definite criterion is as follows: v
mh(t) ∈ [v
max, v
max], v
maxbe made as 4, work as v
mh(t)>=v
maxtime, make v
mh(t)=v
max, work as v
mh(t)≤-v
maxtime, make v
mh(t)=-v
max, when-v
max< v
mh(t) < v
maxtime, v
mh(t) be calculated value; x
mh(t) concrete definite criterion is as follows: x
mh(t) value is 0 or 1, establishes random3 () for the random number in (0,1) scope, as random3 () < s (v
mh(t)), make x
mh(t)=1, otherwise make x
mh(t)=0.
Population sum M is preferably the positive integer between 30～50.
Compared with prior art, the invention has the advantages that in conjunction with particle swarm optimization algorithm and list technique, and use the algebraic approach based on AND/XOR computing to carry out and item abbreviation fixed polarity Reed Muller circuit expressions formula, fixed polarity Reed Muller circuit delay and area are optimized, by MCNC Benchmark circuit test is shown, fairly large fixed polarity Reed Muller circuit is had to good effect of optimization.
Embodiment
Below in conjunction with embodiment, the present invention is described in further detail.
Embodiment: the optimization method of a kind of fixed polarity Reed Muller circuit delay and area, according to fixed polarity Reed Muller expression formula feature, utilizes algebraic approach to carry out abbreviation to polarity expression formula; Based on time delay and Area Model, utilize time delay to decompose to calculate time delay and the area of fixed polarity Reed Muller circuit, and comprehensively both obtain polarity fitness function again; Then set up the individual corresponding relation of fixed polarity and population, in conjunction with list technique, utilize particle swarm optimization algorithm to carry out optimum delay and the search of area polarity to fixed polarity Reed Muller circuit; Concrete steps are:
1) selecting evolutionary generation was 120 generations, read in circuit, was expressed as function
n is function f (x
n-1, x
n-2..., x
k..., x
0) variable number, (x
n-1, x
n-2..., x
k..., x
0) be function f (x
n-1, x
n-2..., x
k..., x
0) n variable, ∑ is exclusive disjunction symbol; a
iminterm coefficient, and a
i{ 0,1}, i is minterm ordinal number to ∈, with binary number representation, is (i
n-1i
n-2i
ki
0), m
ibe minterm, represent n variable phase and, x wherein
kwith i
kpass be: work as i
k=1 o'clock, x
kfor positive variable, work as i
k=0 o'clock, x
kfor negative variable, wherein k is positive integer, and 0≤k≤n-1; Utilize list technique function to be converted to the fixed polarity Reed Muller expression formula of p polarity:
p is the polarity number of fixed polarity Reed Muller expression formula, with binary number representation, is (p
n-1p
n-2p
gp
0),
for xor operator; b
jfor with item coefficient, and b
j∈ { 0,1}; J is and item ordinal number, with binary number representation, is (j
n-1j
n-2j
gj
0), π
jfor with item, represent n variable phase and, x
gwith j
gand p
gpass be: work as j
g=0, p
g=0 o'clock, x
gbe 1; Work as j
g=1, p
g=0 o'clock, x
gfor positive variable; Work as j
g=0, p
g=1 o'clock, x
gbe 1; Work as j
g=1, p
g=1 o'clock, x
gfor negative variable, wherein g is positive integer, and 0≤g≤n-1; And utilize list technique to obtain in fixed polarity Reed Muller expression formula, with the concrete steps of item be:
1)-1 by f (x
n-1, x
n-2..., x
0) in minterm and the polarity of required conversion be expressed as binary number form;
1) if-2 polarity g positions are 0, select the minterm that g position is 0, produce this be 1 new; If polarity g position is 1, selecting g position is 1 minterm, and producing this is 0 new;
1)-3 compare new item with original minterm: if there be the minterm identical with new, delete this minterm; Otherwise new item is inserted in original minterm;
1)-4 repeating steps 1)-2 and 1)-3, until complete the operation of all positions;
1)-5 will be left all minterms carries out an xor operation with polarity, and the item obtaining i.e. the fixed polarity Reed Muller and item of this polarity.
2) initialization population: the space dimensionality that variable number n is defined as to population, polarity is defined as to the particle of population, polarity number p is defined as to the particle position of population, in n-dimensional space, choose arbitrarily 40 particles (being population sum M=40), and generate at random initial position and the initial velocity of these 40 particles, present speed using the initial velocity of each particle as this particle, current location using the initial position of each particle now as this particle, also be the current optimal location of particle simultaneously, current optimal location using the optimum initial position in the initial position of M particle as population, then select 1 as current evolutionary generation,
3) according to current evolutionary generation, select the current location of particle as the polarity number of fixed polarity Reed Muller expression formula, with algebraic approach, the fixed polarity Reed Muller expression formula of all polarity is carried out to abbreviation, concrete steps are:
3)-1 will be expressed as binary number form with item, by the size of l to classifying with item, 0≤l≤n, method is: produce sequence number and be followed successively by 0 to n set, according to combinatorial formula
corresponding, put into set 0 to set n with item from small to large, for
with item, by l and n-l compared with corresponding being stored in small size set with item of decimal, plurality is corresponding puts into large size set with item;
3)-2 by the sorting from small to large with item of each set, makes r=n, s=n-1;
3) if-3 set r and s non-NULL all, by the minimum of set r and s with assignment respectively to u and w; Otherwise, jump to step 3) and-5;
3) whether-4 meet by checking with a u and w
if meet, in set, delete this two with, generate mixed term, and by next in set r and s with assignment respectively to u and w; Otherwise next by set in s is with an assignment to w, and u is constant;
3) if-5 set r for empty or completed in set r last with Reduction, make r=r-1, and pair set r makes the following judgment: 1. when r > 1 and set r non-NULL, by the minimum of set r with an assignment to u; 2. work as r=1, jump to step 3)-9; 3. when set r is empty, repeat current step;
3) if-6 set s for empty or completed in set s last with Reduction, make s=s-1, and pair set s makes the following judgment: 1. when s > 0 and set s non-NULL, by the minimum of set s with an assignment to w; 2. work as s=0, jump to step 3)-9; 3. when set s is empty, repeat current step;
3) if-7 r=s, s=s-1, and pair set s makes the following judgment: 1. when s > 0 and set s non-NULL, by the minimum of set s with an assignment to w; If 2. set s is empty, repeating step 3)-6;
3) if-8 r=1 or s=0 enter step 3)-9, otherwise return to step 3)-4;
3)-9 check whether set 0 has and item: if had, carry out with arbitrary not abbreviation and item
operation; Otherwise constant;
3)-10 algorithms finish, and currentitem comprises: not abbreviation with and mixed term.
4) for the fixed polarity Reed Muller circuit after abbreviation, each many input gate of circuit are resolved into two input gates, and the shortest critical path time delay of definition is circuit delay, the node in circuit adds up to circuit area, and the concrete steps that obtain circuit delay and circuit area are as follows:
4)-1 for mixed term
utilize class Huffman algorithm pair
the AND door of part decomposes, and is exported the input as u part; AND door to u part repeats aforesaid operations, and the input using the output with item as XOR gate;
4)-2 for abbreviation not with, utilize class Huffman to decompose AND door, the input using output as XOR gate;
4)-3 utilize class Huffman algorithm to complete the decomposition to XOR gate, and the shortest critical path nodes obtaining is circuit delay, and the node of whole circuit network adds up to circuit area.
Estimate circuit area and the circuit delay of the fixed polarity Reed Muller circuit that each particle position is corresponding, circuit area and the circuit delay of fixed polarity Reed Muller circuit corresponding to m particle position are defined as respectively to A (X
m) and d (X
m), wherein 1≤m≤40, are defined as respectively A by the circuit area summation of initialization population and circuit delay summation
totaland d
total; Defining m fitness function corresponding to particle position is fitness (X
m)=α * A (X
m)/A
total+ (1-α) * d (X
m)/d
total, in formula, α optimizes weighted value, represents area-optimized share shared in whole optimization, gets α=0.5; The more present speed of new particle and current location, present speed using the most current speed of each particle as this particle, current location using the latest position of each particle as this particle, determine that the most current speed of particle and the concrete steps of latest position are: definition t is current evolutionary generation, h is space dimensionality, 0≤h≤n-1, the most current speed of tieing up as evolution generation m particle h is v
mh(t) with function representation, be:
V
mh(t)=v
mh(t-1)+c1*random1 () * (pbest
mh-x
mh(t-1))+c2*random2 () * (gbest
h-x
mh(t-1)), the latest position when evolution generation m particle h dimension is x
mh(t) with sigmoid function representation, be:
S(v
mh(t))=1/ (1+exp (v
mh(t))), wherein, v
mh(t-1) represent the present speed when the front h dimension of evolution generation m particle evolution, x
mh(t-1) represent that c1 and c2 represent speedup factor, c1, c2 ∈ [1,3], pbest when the current location of the front h dimension of evolution generation m particle evolution
mhrepresent the current optimal location when the front h dimension of evolution generation m particle evolution, gbest
hrepresent that random1 () and random2 () are the random number in (0,1) scope, v when the current optimal location of evolution for the front h dimension of population evolution
mh(t) concrete definite criterion is as follows: v
mh(t) ∈ [v
max, v
max], v
maxbe made as 4, work as v
mh(t)>=v
maxtime, make v
mh(t)=v
max, work as v
mh(t)≤-v
maxtime, make v
mh(t)=-v
max, when-v
max< v
mh(t) < v
maxtime, v
mh(t) be calculated value; x
mh(t) concrete definite criterion is as follows: x
mh(t) value is 0 or 1, establishes random3 () for the random number in (0,1) scope, as random3 () < s (v
mh(t)), make x
mh(t)=1, otherwise make x
mh(t)=0; Calculate again the fitness function of all particles, the current optimal location of the current location of this particle and this particle is compared, select the corresponding particle position of fitness function smaller value as the new current optimal location of this particle, the new current optimal location of more all particles again, using the current optimal location with the corresponding particle of minimum fitness function as the new current optimal location of population;
5) judge whether current algebraically was 120 generations, if not, forward step 3 to), otherwise enter step 6);
6) polarity of the new corresponding fixed polarity Reed of the current optimal location Muller expression formula of population is exported to optimum delay and the output of best area using the time delay of fixed polarity Reed Muller circuit corresponding to this optimum polarity and area as fixed polarity Reed Muller circuit as optimum polarity.
The content of the present embodiment realizes with C++ programming, under Windows XP operating system, by VC6.0, compiles, and program running environment is Intel Pentium (R) Dual-Core CPU 2.70GHZ, 2G RAM.
For the high efficiency of checking particle swarm optimization algorithm, by the exhaustive search based on Gray code order and particle swarm optimization algorithm be applied to respectively circuit time delay and area-optimized in, experimental result is as shown in table 1.Wherein, " name " and " input " is respectively circuit name and variable number, and " area " and " delay " is respectively circuit area and the time delay of optimum polarity, " t
gray" and " t
pSO" be respectively limit algorithm based on Gray code order and the program runtime of particle swarm optimization algorithm.As seen from the data in Table 1, for middle and small scale circuit, the limit algorithm based on Gray code order just can search optimum, and program runtime is fast compared with particle swarm optimization algorithm.But, when circuit scale is larger, t
graysurpass 1 hour, and particle swarm optimization algorithm can, in the situation that keeping precision, shorten program runtime greatly.
The limit algorithm of table 1 based on Gray code order and the search efficiency contrast of particle swarm optimization algorithm
| name | input | area | delay | t Gray [4]/s | t PSO/s |
| bw | 5 | 23 | 5 | ～0 | 0.125 |
| inc | 7 | 27 | 6 | 0.015 | 0.157 |
| rd84 | 8 | 55 | 6 | 0.031 | 0.516 |
| 9sym | 9 | 616 | 10 | 0.672 | 5.797 |
| ex1010 | 10 | 2136 | 12 | 7.062 | 29.625 |
| misex3 | 14 | 1888 | 12 | 615.57 | 21.812 |
| table3 | 14 | 5762 | 14 | 4254.3 | 151.5 |
| pdc | 16 | 156 | 8 | 3697.3 | 11.968 |
For further verifying the Optimal performance of particle swarm optimization algorithm, choose at random the test circuit that 14 variable numbers are 16～26, utilize respectively genetic algorithm (population scale and maximum evolutionary generation are respectively 40 and 120) and particle swarm optimization algorithm to carry out circuit delay and area-optimized to fixed polarity Reed Muller circuit.Specific experiment result is as shown in table 2, wherein " name " and " input " is respectively title and the variable number of test circuit, " GA " and " PSO " is respectively the optimum results based on genetic algorithm and particle swarm optimization algorithm, and " area ", " delay " and " time " represent respectively fixed polarity Reed Muller circuit area, time delay and the program runtime of optimum polarity.The experimental data of analytical table 2 is known, compare with genetic algorithm, most of circuit has reduction in various degree through circuit delay or the circuit area of particle swarm optimization algorithm optimization, wherein the circuit delay of " bcc " and circuit area are saved respectively up to 25% and 67.8%, and the circuit delay of 14 test circuits and circuit area are on average saved and be respectively 6.6% and 11.1%.
The fairly large fixed polarity Reed of table 2 Muller circuit delay and area-optimized result
Claims (6)
1. an optimization method for fixed polarity Reed Muller circuit delay and area, is characterized in that, according to fixed polarity Reed Muller expression formula feature, utilizing algebraic approach to carry out abbreviation to polarity expression formula; Based on time delay and Area Model, utilize time delay to decompose to calculate time delay and the area of fixed polarity Reed Muller circuit, and comprehensively both obtain polarity fitness function again; Then set up the individual corresponding relation of fixed polarity and population, in conjunction with list technique, utilize particle swarm optimization algorithm to carry out optimum delay and the search of area polarity to fixed polarity Reed Muller circuit; Concrete steps are:
1) select evolutionary generation to be greater than for 100 generations, be less than for 150 generations, read in circuit, be expressed as function
n is function f (x
n-1, x
n-2..., x
k..., x
0) variable number, (x
n-1, x
n-2..., x
k..., x
0) be function f (x
n-1, x
n-2..., x
k..., x
0) n variable, ∑ is exclusive disjunction symbol; a
iminterm coefficient, and a
i{ 0,1}, i is minterm ordinal number to ∈, with binary number representation, is (i
n-1i
n-2i
ki
0), m
ibe minterm, represent n variable phase and, x wherein
kwith i
kpass be: work as i
k=1 o'clock, x
kfor positive variable, work as i
k=0 o'clock, x
kfor negative variable, wherein k is positive integer, and 0≤k≤n-1; Utilize list technique function to be converted to the fixed polarity Reed Muller expression formula of p polarity:
p is the polarity number of fixed polarity Reed Muller expression formula, with binary number representation, is (p
n-1p
n-2p
gp
0),
∑ is xor operator; b
jfor with item coefficient, and b
j∈ { 0,1}; J is and item ordinal number, with binary number representation, is (j
n-1j
n-2j
gj
0), π
jfor with item, represent n variable phase and, x
gwith j
gand p
gpass be: work as j
g=0, p
g=0 o'clock, x
gbe 1; Work as j
g=1, p
g=0 o'clock, x
gfor positive variable; Work as j
g=0, p
g=1 o'clock, x
gbe 1; Work as j
g=1, p
g=1 o'clock, x
gfor negative variable, wherein g is positive integer, and 0≤g≤n-1;
2) initialization population: the space dimensionality that variable number n is defined as to population, polarity is defined as to the particle of population, polarity number p is defined as to the particle position of population, in n-dimensional space, choose arbitrarily initial position and the initial velocity of M particle random this M of generation particle, present speed using the initial velocity of each particle as this particle, current location using the initial position of each particle now as this particle, also be the current optimal location of particle simultaneously, current optimal location using the optimum initial position in the initial position of M particle as population, then select 1 as current evolutionary generation,
3) according to current evolutionary generation, select the current location of particle as the polarity number of fixed polarity Reed Muller expression formula, with algebraic approach, the fixed polarity Reed Muller expression formula of all polarity is carried out to abbreviation;
4) for the fixed polarity Reed Muller circuit after abbreviation, each many input gate of circuit are resolved into two input gates, and the shortest critical path time delay of definition is circuit delay, node in circuit adds up to circuit area, estimate circuit area and the circuit delay of the fixed polarity Reed Muller circuit that each particle position is corresponding, circuit area and the circuit delay of fixed polarity Reed Muller circuit corresponding to m particle position are defined as respectively to A (X
m) and d (X
m), wherein 1≤m≤M, is defined as respectively A by the circuit area summation of initialization population and circuit delay summation
totaland d
total, defining m fitness function corresponding to particle position is fitness (X
m)=α * A (X
m)/A
total+ (1-α) * d (X
m)/d
total, in formula, α optimizes weighted value, represents area-optimized share shared in whole optimization, and its value is 0.1～0.9, calculate the fitness function of all particles, the more present speed of new particle and current location, present speed using the most current speed of each particle as this particle, current location using the latest position of each particle as this particle, the current optimal location of the current location of this particle and this particle is compared, select the corresponding particle position of fitness function smaller value as the new current optimal location of this particle, the new current optimal location of more all particles again, using the current optimal location with the corresponding particle of minimum fitness function as the new current optimal location of population,
5) judge whether current algebraically is maximum evolutionary generation, if not, forward step 3) to, otherwise enter step 6);
6) polarity of the new corresponding fixed polarity Reed of the current optimal location Muller expression formula of population is exported to optimum delay and the output of best area using the time delay of fixed polarity Reed Muller circuit corresponding to this optimum polarity and area as fixed polarity Reed Muller circuit as optimum polarity.
2. the optimization method of a kind of fixed polarity Reed Muller circuit delay as claimed in claim 1 and area, is characterized in that utilizing list technique to obtain in fixed polarity Reed Muller expression formula with the concrete steps of item being:
1)-1 by f (x
n-1, x
n-2..., x
0) in minterm and the polarity of required conversion be expressed as binary number form;
1) if-2 polarity g positions are 0, select the minterm that g position is 0, produce this be 1 new; If polarity g position is 1, selecting g position is 1 minterm, and producing this is 0 new;
1)-3 compare new item with original minterm: if there be the minterm identical with new, delete this minterm; Otherwise new item is inserted in original minterm;
1)-4 repeating steps 1)-2 and 1)-3, until complete the operation of all positions;
1)-5 will be left all minterms carries out an xor operation with polarity, and the item obtaining i.e. the fixed polarity Reed Muller and item of this polarity.
3. the optimization method of a kind of fixed polarity Reed Muller circuit delay as claimed in claim 1 and area, is characterized in that by the concrete steps that algebraic approach carries out abbreviation to fixed polarity Reed Muller expression formula being:
3)-1 will be expressed as binary number form with item, by the size of l to classifying with item, 0≤l≤n, method is: produce sequence number and be followed successively by 0 to n set, according to combinatorial formula
corresponding, put into set 0 to set n with item from small to large, for
with item, by l and n-l compared with corresponding being stored in small size set with item of decimal, plurality is corresponding puts into large size set with item;
3)-2 by the sorting from small to large with item of each set, makes r=n, s=n-1;
3) if-3 set r and s non-NULL all, by the minimum of set r and s with assignment respectively to u and w; Otherwise, jump to step 3)-5;
3) whether-4 meet by checking with a u and w
if meet, in set, delete this two with, generate mixed term, and by next in set r and s with assignment respectively to u and w; Otherwise next by set in s is with an assignment to w, and u is constant;
3) if-5 set r for empty or completed in set r last with Reduction, make r=r-1, and pair set r makes the following judgment: 1. when r>1 and set r non-NULL, by the minimum of set r with an assignment to u; 2. work as r=1, jump to step 3)-9; 3. when set r is empty, repeat current step;
3) if-6 set s for empty or completed in set s last with Reduction, make s=s-1, and pair set s makes the following judgment: 1. when s>0 and set s non-NULL, by the minimum of set s with an assignment to w; 2. work as s=0, jump to step 3)-9; 3. when set s is empty, repeat current step;
3) if-7 r=s, s=s-1, and pair set s makes the following judgment: 1. when s>0 and set s non-NULL, by the minimum of set s with an assignment to w; If 2. set s is empty, repeating step 3)-6;
3) if-8 r=1 or s=0 enter step 3)-9, otherwise return to step 3)-4;
3)-9 check whether set 0 has and item: if had, carry out with arbitrary not abbreviation and item
operation; Otherwise constant;
3)-10 algorithms finish, and currentitem comprises: not abbreviation with and mixed term.
4. the optimization method of a kind of fixed polarity Reed Muller circuit delay as claimed in claim 1 and area, is characterized in that for the fixed polarity Reed Muller circuit after abbreviation, and the concrete steps that obtain circuit delay and circuit area are as follows:
4)-1 for mixed term
utilize class Huffman algorithm pair
the AND door of part decomposes, and is exported the input as u part; Utilize class Huffman algorithm to decompose the AND door of u part, and the input using the output with item as XOR gate;
4)-2 for abbreviation not with, utilize class Huffman to decompose AND door, the input using output as XOR gate;
4)-3 utilize class Huffman algorithm to complete the decomposition to XOR gate, and the shortest critical path nodes obtaining is circuit delay, and the node of whole circuit network adds up to circuit area.
5. the optimization method of a kind of fixed polarity Reed Muller circuit delay as claimed in claim 1 and area, it is characterized in that determining that the most current speed of particle and the concrete steps of latest position are: definition t is current evolutionary generation, h is space dimensionality, 0≤h≤n-1, the most current speed of tieing up as evolution generation m particle h is vmh (t), is: v with function representation
mh(t)=v
mh(t-1)+c1*random1 () * (pbest
mh-x
mh(t-1))+c2*random2 () * (gbest
h-x
mh(t-1)), the latest position when evolution generation m particle h dimension is x
mh(t) with sigmoid function representation, be: s (v
mh(t))=1/ (1+exp (v
mh(t))), wherein, v
mh(t-1) represent the present speed when the front h dimension of evolution generation m particle evolution, x
mh(t-1) represent that c1 and c2 represent speedup factor, c1, c2 ∈ [1,3], pbest when the current location of the front h dimension of evolution generation m particle evolution
mhrepresent the current optimal location when the front h dimension of evolution generation m particle evolution, gbest
hrepresent that random1 () and random2 () are the random number in (0,1) scope, v when the current optimal location of evolution for the front h dimension of population evolution
mh(t) concrete definite criterion is as follows: v
mh(t) ∈ [v
max, v
max], v
maxbe made as 4, work as v
mh(t)>=v
maxtime, make v
mh(t)=v
max, work as v
mh(t)≤-v
maxtime, make v
mh(t)=-v
max, when-v
max<v
mh(t) <v
maxtime, v
mh(t) be calculated value; x
mh(t) concrete definite criterion is as follows: x
mh(t) value is 0 or 1, establishes random3 () for the random number in (0,1) scope, as random3 () <s (v
mh(t)), make x
mh(t)=1, otherwise make x
mh(t)=0.
6. the optimization method of a kind of fixed polarity Reed Muller circuit delay as claimed in claim 1 and area, is characterized in that M is the positive integer between 30～50.
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| CN105187051B (en) * | 2015-07-14 | 2017-12-05 | 北京航空航天大学 | One kind is used to not exclusively determine Reed Muller circuit power consumptions and area-optimized method based on NSGA II |
| CN106027032A (en) * | 2016-05-20 | 2016-10-12 | 北京航空航天大学 | RM logic circuit delay optimization method in unit delay model |
| CN107194023B (en) * | 2017-03-30 | 2019-07-12 | 宁波大学 | A kind of FPRM circuit area and delay Optimization method |
| CN107220463B (en) * | 2017-06-28 | 2019-07-09 | 宁波大学 | A kind of mixing polarity XNOR/OR circuit area optimization method |
| CN107515964B (en) * | 2017-07-27 | 2019-07-12 | 宁波大学 | A kind of area-optimized method of fixed polarity RM circuit |
| CN107748912B (en) * | 2017-09-13 | 2020-11-27 | 宁波大学 | Three-value FPRM circuit delay optimization method utilizing bat algorithm |
| CN107679326B (en) * | 2017-10-10 | 2019-07-09 | 宁波大学 | A kind of two-value FPRM circuit area and the comprehensive optimization method that is delayed |
| CN107862132B (en) * | 2017-11-06 | 2020-11-27 | 电子科技大学 | Automatic node deletion method for circuit approximate calculation |
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