CN105306075B - A kind of three value FPRM circuit power consumption optimum polarity search methods - Google Patents
A kind of three value FPRM circuit power consumption optimum polarity search methods Download PDFInfo
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Abstract
The invention discloses a kind of three value FPRM circuit power consumption optimum polarity search methods, three value FPRM logical functions under p polarity are used to be indicated in three value FPRM circuits first, then the multi-input operational contained in three value FPRM logical functions is decomposed, the multiple two input moulds 3 plus door and multiple two inputs moulds 3 obtained under p polarity multiply door, the two input Jia Men of mould 3 and two input moulds 3 are multiplied into power consumption caused by door as the power consumption of three value FPRM circuits under p polarity, build the power estim ation model for obtaining three value FPRM circuits, power consumption optimum polarity search is finally carried out to three value FPRM circuits using Genetic Simulated Annealing Algorithm, obtain the search of power consumption optimum polarity and minimum power consumption；Advantage is to realize that three value FPRM circuit power consumptions optimum polarities are searched for, so as to realize that three value FPRM circuit power consumptions optimize；Random to carry out simulating, verifying using 13 MCNC Benchmark circuits, power consumption optimum polarity and 0 Polarity comparision that the present invention is searched, mould 3 plus door quantity averagely save 57.64%, and mould 3 multiplies a quantity and averagely saves 46.25%, and power consumption averagely saves 73.98%.
Description
Technical field
The present invention relates to a kind of three value FPRM circuit power consumption optimization methods, more particularly, to a kind of three value FPRM circuit power consumptions
Optimum polarity search method.
Background technology
With continuing to develop for footprint and integrated level, digital circuit inherently meets with power consumption, area and speed
The problems such as.Traditional digital circuit mostly uses two-valued function, but low turn into of binary signal information content restricts integrated electricity
The principal element of road development.And MULTI-VALUED LOGIC CIRCUIT adds the ability that single line carries information, space or time can be effectively improved
Utilization rate, reduce the line of digital display circuit, save circuit area and cost.The three-valued logic that radix is 3 is in multi valued logic generation
Radix is minimum in number system, easily realizes, representative.
Any logical function can be represented with Boolean logic and Reed-Muller (RM) logics, with traditional boolean
Logic circuit is compared, and the circuit based on RM logics has the advantage in terms of three below：First, in some functional circuits (as led to
Believe circuit, parity checker, computing circuit etc.) in, with the circuit of RM logical expressions in terms of power consumption, area and speed body
Big advantage is revealed；Secondly, it is strong with the circuit measurability of RM logical expressions；Finally, with the circuit structure of RM logical expressions
It is compacter.RM logical functions are generally using fixed polarity (Fixed-polarity Reed-Muller, FPRM) and mixing pole
Property (Mixed-polarity Reed-Muller, MPRM) two kinds of expression ways.Have in three value FPRM logical functions of n variables
3nIndividual fixed polarity, 3nIndividual fixed polarity is to that should have 3nIndividual three different value FPRM expression formulas, three value FPRM expression formulas it is simple with
It is no to be determined by its corresponding polarity, and the whether simple power consumption for directly determining three value FPRM circuits of three value FPRM expression formulas and
The performance indications such as area, therefore, polarity have a huge impact to performance indications such as power consumption, the areas of FPRM circuits.
Due to multi valued logic and the plurality of advantages of RM logics, domestic and international many experts and scholars are ground to multivalue RM logics
Study carefully.But experts and scholars mainly concentrate research multivalue RM logic circuit polarity conversion technologies both at home and abroad, for multivalue RM circuits
Low power technology is not studied.In view of this, based on Genetic Simulated Annealing Algorithm, a kind of three value FPRM circuit power consumptions of design are optimal
Polarity search method searches for the power consumption optimum polarity of three value FPRM circuits, has important meaning to the optimization of three value FPRM circuit power consumptions
Justice.
The content of the invention
The technical problems to be solved by the invention are to provide a kind of three value FPRM circuit power consumption optimum polarity search methods.Should
Method can be with fast search to power consumption optimum polarity, so as to realize the optimization of power consumption.
The present invention solve the technical scheme that is used of above-mentioned technical problem for：A kind of three value FPRM circuit power consumption optimum polarities
Searching method, comprises the following steps：
1. the power estim ation model of three value FPRM circuits is set up：
1. -1 three value FPRM circuits are expressed as form using three value FPRM logical functions：
Wherein, n is function fp(xn-1,xn-2,…,x0) input variable quantity, xn-1,xn-2,…,x0Representative function fp
(xn-1,xn-2,…,x0) n input variable, p representative functions fp(xn-1,xn-2,…,x0) polarity, polarity p ternary shapes
Formula is expressed as pn-1pn-2…p0, pj∈ { 0,1,2 }, j=0,1,2 ..., n-1,Mould 3 plus computing are represented, ∑ is summation sign, symbol
Number " * " is multiplication symbol, subscript i=0,1,2 ..., 3n- 1, i are expressed as i with ternary formn-1in-2…i0, aiFor FPRM
Coefficient；ai∈{0,1,2}；∏ represents the multiplication of mould 3,Its expansion be：Wherein ij∈{0,
1,2},Polarity p and subscript i decision variablesRepresentation；
1. three value FPRM logical functions under -2p polarity include two class multi-input operationals, and two class multi-input operationals are respectively
Multi input mould 3 plus computing and the multiplication of multi input mould 3, according to three value FPRM logical functions expansions by three value FPRM logical functions
Multiple multi input moulds 3 plus computing and multiple multiplications of multi input mould 3 are decomposed into, then each multi-input operational is separately disassembled into
Two input computings, obtain two input moulds 3 plus computing and the two input multiplications of mould 3, and specific decomposable process is：
It regard the 1st input variable and the 2nd input variable of multi-input operational as first two input computing two
Input variable, obtains the output variable of first two input computing；The output variable and multi input for inputting computing by first two
3rd input variable of computing obtains second two and inputs computing as two input variables of second two input computing
Output variable；The output variable and the 4th input variable of multi-input operational for inputting computing using second two are used as the 3rd two
Two input variables of computing are inputted, the output variable of the 3rd two input computing is obtained；The rest may be inferred, until all how defeated
Enter the input variable of computing as the input variable of two input computings, complete the decomposition of multi-input operational；
Multiple multi input moulds 3 plus computing and multiple multi inputs will be obtained after three value FPRM Logic function decompositions under p polarity
The multiplication of mould 3, multi input mould 3 plus computing are also referred to as multi input mould 3 plus door, and the multiplication of multi input mould 3 is also referred to as multi input mould 3 and multiplied
Door, N is designated as by the quantity of the multi input mould 3 after three value FPRM Logic function decompositions under p polarity plus door, by three value under p polarity
The quantity that multi input mould 3 after FPRM Logic function decompositions multiplies door is designated as W；Obtained after each multi input mould 3 plus computing are decomposed
Multiple two input moulds 3 plus computing, obtain multiple two inputs multiplications of mould 3, two inputs after each multiplication of multi input mould 3 is decomposed
Mould 3 plus computing are also referred to as two input moulds 3 plus door, and the two input multiplications of mould 3 are also referred to as two input moulds 3 and multiply door；By the H multi input
Two input moulds 3 after mould 3 plus door are decomposed add the quantity of door to be designated as NH, H=1,2 ..., N；O-th of multi input mould 3 is multiplied into a decomposition
The quantity that two input moulds 3 afterwards multiply door is designated as Wo, o=1,2 ..., W；
1. -3 the Jia Men of mould 3 and two inputs are inputted by obtained after three value FPRM Logic function decompositions under p polarity all two
Mould 3 multiplies power consumption caused by door as the power consumption of three value FPRM circuits under p polarity, and two input moulds 3 plus power consumption caused by door are used
Its switch activity represents that two input moulds 3 are multiplied power consumption caused by door and represented using its switch activity, the switch activity of gate circuit
Property represented with the output variable probability of its output end, two input moulds 3 plus power consumption caused by door use its output end output variable
Probability represents that two input moulds 3 are multiplied power consumption caused by door and represented using the output variable probability of its output end；
1. -4 k-th two input moulds 3 after the H multi input mould 3 plus door decomposition are calculated according to formula (2), (3) and (4)
Plus the output variable probability of door；K=1,2 ..., NH；
P1(k)H=Pky11*Pky20+Pky10*Pky21+Pky12*Pky22 (2)
P2(k)H=Pky12*Pky20+Pky11*Pky21+Pky10*Pky22 (3)
P0(k)H=1-P1(k)H-P2(k)H (4)
Multiply g-th two input moulds 3 after a decomposition according to formula (5), (6) and (7) o-th of multi input mould 3 of calculating and multiply door
Output variable probability, g=1,2 ..., Wo：
Q1(g)o=Qgr11*Qgr21+Qgr12*Qgr22 (5)
Q2(g)o=Qgr11*Qgr22+Qgr12*Qgr21 (6)
Q0(g)o=1-Q1(g)o-Q2(g)o (7)
Wherein, P1(k)HRepresent that k-th two input moulds 3 plus door output variable after the H multi input mould 3 plus door decomposition are 1
Probability, P2(k)HRepresent the H multi input mould 3 plus door decompose after k-th two input moulds 3 plus door output variable for 2 it is general
Rate, P0(k)HRepresent k-th two input moulds 3 after the H multi input mould 3 plus door decomposition plus the probability that door output variable is 0, y1
Represent two input variables of two input moulds 3 plus door with y2, m ∈ { 0,1,2 }, as k=1, Pky1mFor multi input mould 3 plus computing
The 1st input variable be m probability, Pky2mThe probability for being m for the 2nd input variable of multi input mould 3 plus computing, works as k>1
When, Pky1mThe probability that mould 3 plus door output variable are m, Pk are inputted for kth -1 twoy2mKth+1 for multi input mould 3 plus door is defeated
Enter the probability that variable is m；
Q1(g)oRepresent o-th of multi input mould 3 multiply g-th two input moulds 3 after decomposing multiply an output variable for 1 it is general
Rate, Q2(g)oRepresent that o-th of multi input mould 3 multiplies g-th two input moulds 3 after a decomposition and multiply the probability that an output variable is 2, Q0
(g)oRepresent that o-th of multi input mould 3 multiplies g-th two input moulds 3 after a decomposition and multiply the probability that an output variable is 0, r1 and r2
Represent that two input two input variables that mould 3 multiplies door；As g=1, Qgr1mFor the 1st input variable of the multiplication of multi input mould 3
For m probability, Qgr2mThe probability for being m for the 2nd input variable of the multiplication of multi input mould 3, works as g>When 1, Qgr1mFor g-1
Two input moulds 3 multiply the probability that an output variable is m, Qgr2mMultiply the probability that the g+1 input variable of door is m for multi input mould 3；
Input variable xjFor 1 and 2 probability be by function immediately produce probability to (P1, P2), P0=1-P1-P2；P0,
P1 and P2 are respectively some value between 0 to 1, and P0 represents the probability that input variable is 0, and P1 represents the probability that input variable is 1, P2
Represent the probability that input variable is 2；
1. -5 the output variable probability calculation that moulds 3 multiply door is inputted according to two input moulds 3 plus the output variable probability of door and two
The power consumption of three value FPRM circuits, the power estim ation model of three value FPRM circuits is expressed as：
Wherein, EswdThe power consumption of three value FPRM circuits under p polarity is represented, N is three value FPRM Logic function decompositions under p polarity
Multi input mould 3 afterwards plus the quantity of door, W multiply the number of door for the multi input mould 3 after three value FPRM Logic function decompositions under p polarity
Amount；
2. it is used for the fitness function for calculating individual adaptation degree in setting Genetic Simulated Annealing Algorithm：
According to power estim ation model, the fitness function of individual adaptation degree is calculated in setting Genetic Simulated Annealing Algorithm：
In Genetic Simulated Annealing Algorithm, fitness is bigger, and the adaptability for representing individual is stronger, but power consumption optimum polarity requires that power consumption is got over
It is small better, therefore, combined for the ease of both, reciprocal using power consumption represents fitness, obtains fitness function as follows：
Fitness=α/Eswd
Wherein, symbol "/" represents division operation symbol, and fitness represents the fitness size of individual；EswdIndication circuit work(
Consumption；α is amplification coefficient, and value is the natural number more than or equal to 1000；
3. three value FPRM circuits and the corresponding relation of Genetic Simulated Annealing Algorithm are set up：
Genetic Simulated Annealing Algorithm includes following key element：Maximum of individual, the fitness of individual, fitness
Body, maximum adaptation degree, crossover operation, mutation operation, annealing selection operation；
The optimization of three value FPRM circuit power consumptions includes following key element：Polarity, the power consumption of corresponding polarity, optimal pole
Property, the exchange of minimum power consumption, polarity, polarity mutation, reversal；
Individual is mapped to the optimization of three value FPRM circuit power consumptions, polarity is expressed as；The fitness of individual is mapped to three values
FPRM circuit power consumptions optimize, and are expressed as the power consumption of corresponding polarity；The maximum individual of fitness is mapped to three value FPRM circuit work(
Consumption optimization, is expressed as optimum polarity；Maximum adaptation degree is mapped to the optimization of three value FPRM circuit power consumptions, minimum power consumption is expressed as；
Crossover operation is mapped to the optimization of three value FPRM circuit power consumptions, polarity exchange is expressed as；Mutation operation is mapped to three value FPRM
Circuit power consumption optimizes, and is expressed as polarity mutation；Annealing selection operation is mapped to the optimization of three value FPRM circuit power consumptions, pole is expressed as
Property conversion；
4. Genetic Simulated Annealing Algorithm relevant parameter is set：
Genetic Simulated Annealing Algorithm need to set 4 parameters：Individual scale w, individual iterations z, gene mutation probability q,
Initial temperature T0；The individual scale w=50 of order, individual iterations z=20, gene mutation probability q=0.01, initial temperature T0=
100℃；
5. the maximum individual of fitness and maximum adaptation degree are obtained using Genetic Simulated Annealing Algorithm, fitness maximum individual is
For the power consumption optimum polarity of three value FPRM circuits；Maximum adaptation degree is the minimum power consumption of three value FPRM circuits.
5. middle use Genetic Simulated Annealing Algorithm obtains the maximum individual tool with maximum adaptation degree of fitness to described step
Body process is：
5. -1 the w individuals represented with n ternarys are produced with random function rand (), w individual are designated as P1 respectively,
P2 ..., Pw；
5. -2 fitness for calculating v-th of individual Pv by fitness function, v=1,2,3 ..., w obtain individual P1,
P2 ..., Pw fitness；
5. -3 compare individual P1, and P2 ..., Pw fitness filters out the maximum individual of fitness maximum as fitness
Individual, the maximum individual of record fitness and maximum adaptation degree；
5. -4 couples of individuals P1, P2 ..., Pw carry out crossover operation generation individual F1, F2 ..., Fw：If w is even number, by P1 and
P2, P3 and P4 ..., Pw-1 and Pw carry out crossover operation respectively two-by-two；If w be odd number, by P1 and P2, P3 and P4 ..., Pw-2 and
Pw-1 carries out crossover operation respectively two-by-two, and Pw is not involved in crossover operation, and Fw directly inherits Pw；Two individual Pe and Pu are intersected
Operation produces individual Fe and Fu, and detailed process is：The individual Pe for carrying out crossover operation is assigned to fe, individual Pu is assigned to fu,
A n binary codes are randomly generated, the n binary code is designated as A, fe and fu is updated according to binary code A, works as binary system
When h of code A are 1, fe h holdings are constant, and fu h holdings are constant；When h of binary code A being 0,
H of fe h succession fu, h of fu h succession fe, h=1,2,3 ..., n, after the completion of crossover operation
The fu that are designated as after the completion of Fe, crossover operation of fe be designated as Fu；Wherein u=e+1, when w is even number, e=1,3,5 ..., w-1；u
=2,4,6 ..., w；When w is odd number, e=1,3,5 ..., w-2；U=2,4,6 ..., w-1；
5. -5 by fitness function calculate v-th of individual Fv fitness, obtain individual F1, F2 ..., Fw adaptation
Degree；
5. -6 individual F1, F2 ..., Fw fitness and the maximum individual fitness of current fitness are compared, more
The new maximum individual of fitness and maximum adaptation degree；
5. -7 individual F1, F2 ..., Fw are subjected to mutation operation：To Fv each with random function rand () produce
Value between one 0 to 1, if this value is less than gene mutation probability q, the corresponding position of this value is exactly Fv change dystopy, right
Fv change dystopy is made a variation, and variation rule is " 0 → 1,1 → 2,2 → 0 "；
5. -8 according to step 5. -5~5. -6 couples of individual F1, F2 ..., Fw processing, the fitness after being updated is most
Big individual and maximum adaptation degree；
5. -9 according to the size of fitness value to individual P1, P2 ..., Pw is ranked up, according to the size pair of fitness value
Individual F1, F2 ..., Fw are ranked up；Fitness value is each selected in individual P1, P2 ..., Pw and individual F1, F2 ..., Fw
2w/3 optimal individual, constitutes one group of new individual, and new individual contains 4w/3 individual；
5. -10 pairs one group new individual carries out many wheel annealing selections：In each round annealing selection, first according to formula (9)
An annealing temperature is produced, for the annealing temperature, probability P (c) is selected by what formula (10) calculated each individual successively, together
When produce a screening probability t, 0 with random function rand ()<t<1；When individual when being selected probability more than screening probability,
The individual is chosen in this wheel annealing selection, and selected individual is no longer participate in next round annealing selection, and other are not chosen
The individual selected enters next round annealing selection, is updated until filtering out w individual after individual P1, P2 ..., Pw, annealing selection knot
Beam；
Tl=1/ln (l/T0+1) (9)
Wherein, TlRepresent the annealing temperature of l wheels, l=1,2 ...；During first round annealing selection, l=1, the second wheel annealing
During selection, l=2, by that analogy；Ln represents log operations；T0Represent initial temperature；P (c) represents individual c probability；F (c) tables
Show the fitness value of c-th of individual in new individual；C=1,2,3 ..., 4w/3；D-th of individual in the new individual of f (d) expressions
Fitness value；D=1,2,3 ..., 4w/3；
5. -11 according to step 5. -2~individual P1 after 5. 5. -3 pairs of steps are updated in -10, P2 ..., Pw processing,
Obtain the maximum individual of fitness and maximum adaptation degree；
5. -12 repeat steps 5. -4~5. -11, until meeting individual iterations z, algorithm terminates, and obtains fitness most
Big individual and maximum adaptation degree；
5. the maximum individual of -13 fitness for obtaining last time and maximum adaptation degree are exported, and fitness maximum individual is
For the optimum polarity of three value FPRM circuits；Maximum adaptation degree is the minimum power consumption of three value FPRM circuits.
Compared with prior art, the advantage of the invention is that three value FPRM circuits are used into three values under p polarity first
FPRM logical functions are indicated, and are then decomposed the three input computings contained in three value FPRM logical functions, are obtained under p polarity
Multiple two input moulds 3 plus door and multiple two inputs moulds 3 multiply door, and the two input Jia Men of mould 3 and two input moulds 3 are multiplied into power consumption caused by door
As the power consumption of three value FPRM circuits under p polarity, the power estim ation model for obtaining three value FPRM circuits is built, finally using mould
Intend Annealing-Genetic Algorithm and power consumption optimum polarity search is carried out to three value FPRM circuits, obtain the search of power consumption optimum polarity and least work
Consumption；The power estim ation models coupling Genetic Simulated Annealing Algorithms of the method three value FPRM circuits that pass through foundation of the present invention is realized
Three value FPRM circuit power consumptions optimum polarities are searched for, so as to realize the optimised power consumption of three value FPRM circuits；It is random to use 13 MCNC
Benchmark circuits carry out simulating, verifying, and power consumption optimum polarity and 0 Polarity comparision that the present invention is searched, mould 3 plus door quantity are put down
57.64% is saved, mould 3 multiplies a quantity and averagely saves 46.25%, and power consumption averagely saves 73.98%.
Embodiment
The present invention is described in further detail with reference to embodiments.
Embodiment one：A kind of three value FPRM circuit power consumption optimum polarity search methods, comprise the following steps：
1. the power estim ation model of three value FPRM circuits is set up：
1. -1 three value FPRM circuits are expressed as form using three value FPRM logical functions：
Wherein, n is function fp(xn-1,xn-2,…,x0) input variable quantity, xn-1,xn-2,…,x0Representative function fp
(xn-1,xn-2,…,x0) n input variable, p representative functions fp(xn-1,xn-2,…,x0) polarity, polarity p ternary shapes
Formula is expressed as pn-1pn-2…p0, pj∈ { 0,1,2 }, j=0,1,2 ..., n-1,Mould 3 plus computing are represented, ∑ is summation sign, symbol
Number " * " is multiplication symbol, subscript i=0,1,2 ..., 3n- 1, i are expressed as i with ternary formn-1in-2…i0, aiFor FPRM
Coefficient；ai∈{0,1,2}；∏ represents the multiplication of mould 3,Its expansion be：Wherein ij∈{0,
1,2},Polarity p and subscript i decision variablesRepresentation；
1. three value FPRM logical functions under -2p polarity include two class multi-input operationals, and two class multi-input operationals are respectively
Multi input mould 3 plus computing and the multiplication of multi input mould 3, according to three value FPRM logical functions expansions by three value FPRM logical functions
Multiple multi input moulds 3 plus computing and multiple multiplications of multi input mould 3 are decomposed into, then each multi-input operational is separately disassembled into
Two input computings, obtain two input moulds 3 plus computing and the two input multiplications of mould 3, and specific decomposable process is：
It regard the 1st input variable and the 2nd input variable of multi-input operational as first two input computing two
Input variable, obtains the output variable of first two input computing；The output variable and multi input for inputting computing by first two
3rd input variable of computing obtains second two and inputs computing as two input variables of second two input computing
Output variable；The output variable and the 4th input variable of multi-input operational for inputting computing using second two are used as the 3rd two
Two input variables of computing are inputted, the output variable of the 3rd two input computing is obtained；The rest may be inferred, until all how defeated
Enter the input variable of computing as the input variable of two input computings, complete the decomposition of multi-input operational；
Multiple multi input moulds 3 plus computing and multiple multi inputs will be obtained after three value FPRM Logic function decompositions under p polarity
The multiplication of mould 3, multi input mould 3 plus computing are also referred to as multi input mould 3 plus door, and the multiplication of multi input mould 3 is also referred to as multi input mould 3 and multiplied
Door, N is designated as by the quantity of the multi input mould 3 after three value FPRM Logic function decompositions under p polarity plus door, by three value under p polarity
The quantity that multi input mould 3 after FPRM Logic function decompositions multiplies door is designated as W；Obtained after each multi input mould 3 plus computing are decomposed
Multiple two input moulds 3 plus computing, obtain multiple two inputs multiplications of mould 3, two inputs after each multiplication of multi input mould 3 is decomposed
Mould 3 plus computing are also referred to as two input moulds 3 plus door, and the two input multiplications of mould 3 are also referred to as two input moulds 3 and multiply door；By the H multi input
Two input moulds 3 after mould 3 plus door are decomposed add the quantity of door to be designated as NH, H=1,2 ..., N；O-th of multi input mould 3 is multiplied into a decomposition
The quantity that two input moulds 3 afterwards multiply door is designated as Wo, o=1,2 ..., W；
1. -3 the Jia Men of mould 3 and two inputs are inputted by obtained after three value FPRM Logic function decompositions under p polarity all two
Mould 3 multiplies power consumption caused by door as the power consumption of three value FPRM circuits under p polarity, and two input moulds 3 plus power consumption caused by door are used
Its switch activity represents that two input moulds 3 are multiplied power consumption caused by door and represented using its switch activity, the switch activity of gate circuit
Property represented with the output variable probability of its output end, two input moulds 3 plus power consumption caused by door use its output end output variable
Probability represents that two input moulds 3 are multiplied power consumption caused by door and represented using the output variable probability of its output end；
1. -4 k-th two input moulds 3 after the H multi input mould 3 plus door decomposition are calculated according to formula (2), (3) and (4)
Plus the output variable probability of door；K=1,2 ..., NH；
P1(k)H=Pky11*Pky20+Pky10*Pky21+Pky12*Pky22 (2)
P2(k)H=Pky12*Pky20+Pky11*Pky21+Pky10*Pky22 (3)
P0(k)H=1-P1(k)H-P2(k)H (4)
Multiply g-th two input moulds 3 after a decomposition according to formula (5), (6) and (7) o-th of multi input mould 3 of calculating and multiply door
Output variable probability, g=1,2 ..., Wo：
Q1(g)o=Qgr11*Qgr21+Qgr12*Qgr22 (5)
Q2(g)o=Qgr11*Qgr22+Qgr12*Qgr21 (6)
Q0(g)o=1-Q1(g)o-Q2(g)o (7)
Wherein, P1(k)HRepresent that k-th two input moulds 3 plus door output variable after the H multi input mould 3 plus door decomposition are 1
Probability, P2(k)HRepresent the H multi input mould 3 plus door decompose after k-th two input moulds 3 plus door output variable for 2 it is general
Rate, P0(k)HRepresent k-th two input moulds 3 after the H multi input mould 3 plus door decomposition plus the probability that door output variable is 0, y1
Represent two input variables of two input moulds 3 plus door with y2, m ∈ { 0,1,2 }, as k=1, Pky1mFor multi input mould 3 plus computing
The 1st input variable be m probability, Pky2mThe probability for being m for the 2nd input variable of multi input mould 3 plus computing, works as k>1
When, Pky1mThe probability that mould 3 plus door output variable are m, Pk are inputted for kth -1 twoy2mKth+1 for multi input mould 3 plus door is defeated
Enter the probability that variable is m；
Q1(g)oRepresent o-th of multi input mould 3 multiply g-th two input moulds 3 after decomposing multiply an output variable for 1 it is general
Rate, Q2(g)oRepresent that o-th of multi input mould 3 multiplies g-th two input moulds 3 after a decomposition and multiply the probability that an output variable is 2, Q0
(g)oRepresent that o-th of multi input mould 3 multiplies g-th two input moulds 3 after a decomposition and multiply the probability that an output variable is 0, r1 and r2
Represent that two input two input variables that mould 3 multiplies door；As g=1, Qgr1mFor the 1st input variable of the multiplication of multi input mould 3
For m probability, Qgr2mThe probability for being m for the 2nd input variable of the multiplication of multi input mould 3, works as g>When 1, Qgr1mFor g-1
Two input moulds 3 multiply the probability that an output variable is m, Qgr2mMultiply the probability that the g+1 input variable of door is m for multi input mould 3；
Input variable xjFor 1 and 2 probability be by function immediately produce probability to (P1, P2), P0=1-P1-P2；P0,
P1 and P2 are respectively some value between 0 to 1, and P0 represents the probability that input variable is 0, and P1 represents the probability that input variable is 1, P2
Represent the probability that input variable is 2；
1. -5 the output variable probability calculation that moulds 3 multiply door is inputted according to two input moulds 3 plus the output variable probability of door and two
The power consumption of three value FPRM circuits, the power estim ation model of three value FPRM circuits is expressed as：
Wherein, EswdThe power consumption of three value FPRM circuits under p polarity is represented, N is three value FPRM Logic function decompositions under p polarity
Multi input mould 3 afterwards plus the quantity of door, W multiply the number of door for the multi input mould 3 after three value FPRM Logic function decompositions under p polarity
Amount；
2. it is used for the fitness function for calculating individual adaptation degree in setting Genetic Simulated Annealing Algorithm：
According to power estim ation model, the fitness function of individual adaptation degree is calculated in setting Genetic Simulated Annealing Algorithm：
In Genetic Simulated Annealing Algorithm, fitness is bigger, and the adaptability for representing individual is stronger, but power consumption optimum polarity requires that power consumption is got over
It is small better, therefore, combined for the ease of both, reciprocal using power consumption represents fitness, obtains fitness function as follows：
Fitness=α/Eswd
Wherein, symbol "/" represents division operation symbol, and fitness represents the fitness size of individual；EswdIndication circuit work(
Consumption；α is amplification coefficient, and value is the natural number more than or equal to 1000；
3. three value FPRM circuits and the corresponding relation of Genetic Simulated Annealing Algorithm are set up：
Genetic Simulated Annealing Algorithm includes following key element：Maximum of individual, the fitness of individual, fitness
Body, maximum adaptation degree, crossover operation, mutation operation, annealing selection operation；
The optimization of three value FPRM circuit power consumptions includes following key element：Polarity, the power consumption of corresponding polarity, optimal pole
Property, the exchange of minimum power consumption, polarity, polarity mutation, reversal；
Individual is mapped to the optimization of three value FPRM circuit power consumptions, polarity is expressed as；The fitness of individual is mapped to three values
FPRM circuit power consumptions optimize, and are expressed as the power consumption of corresponding polarity；The maximum individual of fitness is mapped to three value FPRM circuit work(
Consumption optimization, is expressed as optimum polarity；Maximum adaptation degree is mapped to the optimization of three value FPRM circuit power consumptions, minimum power consumption is expressed as；
Crossover operation is mapped to the optimization of three value FPRM circuit power consumptions, polarity exchange is expressed as；Mutation operation is mapped to three value FPRM
Circuit power consumption optimizes, and is expressed as polarity mutation；Annealing selection operation is mapped to the optimization of three value FPRM circuit power consumptions, pole is expressed as
Property conversion；
4. Genetic Simulated Annealing Algorithm relevant parameter is set：
Genetic Simulated Annealing Algorithm need to set 4 parameters：Individual scale w, individual iterations z, gene mutation probability q,
Initial temperature T0；The individual scale w=50 of order, individual iterations z=20, gene mutation probability q=0.01, initial temperature T0=
100℃；
5. the maximum individual of fitness and maximum adaptation degree are obtained using Genetic Simulated Annealing Algorithm, fitness maximum individual is
For the power consumption optimum polarity of three value FPRM circuits；Maximum adaptation degree is the minimum power consumption of three value FPRM circuits.
In the present embodiment, Genetic Simulated Annealing Algorithm uses ripe algorithm of the prior art.
Embodiment two：A kind of three value FPRM circuit power consumption optimum polarity search methods, comprise the following steps：
1. the power estim ation model of three value FPRM circuits is set up：
1. -1 three value FPRM circuits are expressed as form using three value FPRM logical functions：
Wherein, n is function fp(xn-1,xn-2,…,x0) input variable quantity, xn-1,xn-2,…,x0Representative function fp
(xn-1,xn-2,…,x0) n input variable, p representative functions fp(xn-1,xn-2,…,x0) polarity, polarity p ternary shapes
Formula is expressed as pn-1pn-2…p0, pj∈ { 0,1,2 }, j=0,1,2 ..., n-1,Mould 3 plus computing are represented, ∑ is summation sign, symbol
Number " * " is multiplication symbol, subscript i=0,1,2 ..., 3n- 1, i are expressed as i with ternary formn-1in-2…i0, aiFor FPRM
Coefficient；ai∈{0,1,2}；∏ represents the multiplication of mould 3,Its expansion be：Wherein ij∈{0,
1,2},Polarity p and subscript i decision variablesRepresentation；
1. three value FPRM logical functions under -2p polarity include two class multi-input operationals, and two class multi-input operationals are respectively
Multi input mould 3 plus computing and the multiplication of multi input mould 3, according to three value FPRM logical functions expansions by three value FPRM logical functions
Multiple multi input moulds 3 plus computing and multiple multiplications of multi input mould 3 are decomposed into, then each multi-input operational is separately disassembled into
Two input computings, obtain two input moulds 3 plus computing and the two input multiplications of mould 3, and specific decomposable process is：
It regard the 1st input variable and the 2nd input variable of multi-input operational as first two input computing two
Input variable, obtains the output variable of first two input computing；The output variable and multi input for inputting computing by first two
3rd input variable of computing obtains second two and inputs computing as two input variables of second two input computing
Output variable；The output variable and the 4th input variable of multi-input operational for inputting computing using second two are used as the 3rd two
Two input variables of computing are inputted, the output variable of the 3rd two input computing is obtained；The rest may be inferred, until all how defeated
Enter the input variable of computing as the input variable of two input computings, complete the decomposition of multi-input operational；
Multiple multi input moulds 3 plus computing and multiple multi inputs will be obtained after three value FPRM Logic function decompositions under p polarity
The multiplication of mould 3, multi input mould 3 plus computing are also referred to as multi input mould 3 plus door, and the multiplication of multi input mould 3 is also referred to as multi input mould 3 and multiplied
Door, N is designated as by the quantity of the multi input mould 3 after three value FPRM Logic function decompositions under p polarity plus door, by three value under p polarity
The quantity that multi input mould 3 after FPRM Logic function decompositions multiplies door is designated as W；Obtained after each multi input mould 3 plus computing are decomposed
Multiple two input moulds 3 plus computing, obtain multiple two inputs multiplications of mould 3, two inputs after each multiplication of multi input mould 3 is decomposed
Mould 3 plus computing are also referred to as two input moulds 3 plus door, and the two input multiplications of mould 3 are also referred to as two input moulds 3 and multiply door；By the H multi input
Two input moulds 3 after mould 3 plus door are decomposed add the quantity of door to be designated as NH, H=1,2 ..., N；O-th of multi input mould 3 is multiplied into a decomposition
The quantity that two input moulds 3 afterwards multiply door is designated as Wo, o=1,2 ..., W；
1. -3 the Jia Men of mould 3 and two inputs are inputted by obtained after three value FPRM Logic function decompositions under p polarity all two
Mould 3 multiplies power consumption caused by door as the power consumption of three value FPRM circuits under p polarity, and two input moulds 3 plus power consumption caused by door are used
Its switch activity represents that two input moulds 3 are multiplied power consumption caused by door and represented using its switch activity, the switch activity of gate circuit
Property represented with the output variable probability of its output end, two input moulds 3 plus power consumption caused by door use its output end output variable
Probability represents that two input moulds 3 are multiplied power consumption caused by door and represented using the output variable probability of its output end；
1. -4 k-th two input moulds 3 after the H multi input mould 3 plus door decomposition are calculated according to formula (2), (3) and (4)
Plus the output variable probability of door；K=1,2 ..., NH；
P1(k)H=Pky11*Pky20+Pky10*Pky21+Pky12*Pky22 (2)
P2(k)H=Pky12*Pky20+Pky11*Pky21+Pky10*Pky22 (3)
P0(k)H=1-P1(k)H-P2(k)H (4)
Multiply g-th two input moulds 3 after a decomposition according to formula (5), (6) and (7) o-th of multi input mould 3 of calculating and multiply door
Output variable probability, g=1,2 ..., Wo：
Q1(g)o=Qgr11*Qgr21+Qgr12*Qgr22 (5)
Q2(g)o=Qgr11*Qgr22+Qgr12*Qgr21 (6)
Q0(g)o=1-Q1(g)o-Q2(g)o (7)
Wherein, P1(k)HRepresent that k-th two input moulds 3 plus door output variable after the H multi input mould 3 plus door decomposition are 1
Probability, P2(k)HRepresent the H multi input mould 3 plus door decompose after k-th two input moulds 3 plus door output variable for 2 it is general
Rate, P0(k)HRepresent k-th two input moulds 3 after the H multi input mould 3 plus door decomposition plus the probability that door output variable is 0, y1
Represent two input variables of two input moulds 3 plus door with y2, m ∈ { 0,1,2 }, as k=1, Pky1mFor multi input mould 3 plus computing
The 1st input variable be m probability, Pky2mThe probability for being m for the 2nd input variable of multi input mould 3 plus computing, works as k>1
When, Pky1mThe probability that mould 3 plus door output variable are m, Pk are inputted for kth -1 twoy2mKth+1 for multi input mould 3 plus door is defeated
Enter the probability that variable is m；
Q1(g)oRepresent o-th of multi input mould 3 multiply g-th two input moulds 3 after decomposing multiply an output variable for 1 it is general
Rate, Q2(g)oRepresent that o-th of multi input mould 3 multiplies g-th two input moulds 3 after a decomposition and multiply the probability that an output variable is 2, Q0
(g)oRepresent that o-th of multi input mould 3 multiplies g-th two input moulds 3 after a decomposition and multiply the probability that an output variable is 0, r1 and r2
Represent that two input two input variables that mould 3 multiplies door；As g=1, Qgr1mFor the 1st input variable of the multiplication of multi input mould 3
For m probability, Qgr2mThe probability for being m for the 2nd input variable of the multiplication of multi input mould 3, works as g>When 1, Qgr1mFor g-1
Two input moulds 3 multiply the probability that an output variable is m, Qgr2mMultiply the probability that the g+1 input variable of door is m for multi input mould 3；
Input variable xjFor 1 and 2 probability be by function immediately produce probability to (P1, P2), P0=1-P1-P2；P0,
P1 and P2 are respectively some value between 0 to 1, and P0 represents the probability that input variable is 0, and P1 represents the probability that input variable is 1, P2
Represent the probability that input variable is 2；
1. -5 the output variable probability calculation that moulds 3 multiply door is inputted according to two input moulds 3 plus the output variable probability of door and two
The power consumption of three value FPRM circuits, the power estim ation model of three value FPRM circuits is expressed as：
Wherein, EswdThe power consumption of three value FPRM circuits under p polarity is represented, N is three value FPRM Logic function decompositions under p polarity
Multi input mould 3 afterwards plus the quantity of door, W multiply the number of door for the multi input mould 3 after three value FPRM Logic function decompositions under p polarity
Amount；
2. it is used for the fitness function for calculating individual adaptation degree in setting Genetic Simulated Annealing Algorithm：
According to power estim ation model, the fitness function of individual adaptation degree is calculated in setting Genetic Simulated Annealing Algorithm：
In Genetic Simulated Annealing Algorithm, fitness is bigger, and the adaptability for representing individual is stronger, but power consumption optimum polarity requires that power consumption is got over
It is small better, therefore, combined for the ease of both, reciprocal using power consumption represents fitness, obtains fitness function as follows：
Fitness=α/Eswd
Wherein, symbol "/" represents division operation symbol, and fitness represents the fitness size of individual；EswdIndication circuit work(
Consumption；α is amplification coefficient, and value is the natural number more than or equal to 1000；
3. three value FPRM circuits and the corresponding relation of Genetic Simulated Annealing Algorithm are set up：
Genetic Simulated Annealing Algorithm includes following key element：Maximum of individual, the fitness of individual, fitness
Body, maximum adaptation degree, crossover operation, mutation operation, annealing selection operation；
The optimization of three value FPRM circuit power consumptions includes following key element：Polarity, the power consumption of corresponding polarity, optimal pole
Property, the exchange of minimum power consumption, polarity, polarity mutation, reversal；
Individual is mapped to the optimization of three value FPRM circuit power consumptions, polarity is expressed as；The fitness of individual is mapped to three values
FPRM circuit power consumptions optimize, and are expressed as the power consumption of corresponding polarity；The maximum individual of fitness is mapped to three value FPRM circuit work(
Consumption optimization, is expressed as optimum polarity；Maximum adaptation degree is mapped to the optimization of three value FPRM circuit power consumptions, minimum power consumption is expressed as；
Crossover operation is mapped to the optimization of three value FPRM circuit power consumptions, polarity exchange is expressed as；Mutation operation is mapped to three value FPRM
Circuit power consumption optimizes, and is expressed as polarity mutation；Annealing selection operation is mapped to the optimization of three value FPRM circuit power consumptions, pole is expressed as
Property conversion；
4. Genetic Simulated Annealing Algorithm relevant parameter is set：
Genetic Simulated Annealing Algorithm need to set 4 parameters：Individual scale w, individual iterations z, gene mutation probability q,
Initial temperature T0；The individual scale w=50 of order, individual iterations z=20, gene mutation probability q=0.01, initial temperature T0=
100℃；
5. the maximum individual of fitness and maximum adaptation degree are obtained using Genetic Simulated Annealing Algorithm, fitness maximum individual is
For the power consumption optimum polarity of three value FPRM circuits；Maximum adaptation degree is the minimum power consumption of three value FPRM circuits.
In the present embodiment, 5. middle use Genetic Simulated Annealing Algorithm obtains the maximum individual of fitness and maximum adaptation degree to step
Detailed process be：
5. -1 the w individuals represented with n ternarys are produced with random function rand (), w individual are designated as P1 respectively,
P2 ..., Pw；
5. -2 fitness for calculating v-th of individual Pv by fitness function, v=1,2,3 ..., w obtain individual P1,
P2 ..., Pw fitness；
5. -3 compare individual P1, and P2 ..., Pw fitness filters out the maximum individual of fitness maximum as fitness
Individual, the maximum individual of record fitness and maximum adaptation degree；
5. -4 couples of individuals P1, P2 ..., Pw carry out crossover operation generation individual F1, F2 ..., Fw：If w is even number, by P1 and
P2, P3 and P4 ..., Pw-1 and Pw carry out crossover operation respectively two-by-two；If w be odd number, by P1 and P2, P3 and P4 ..., Pw-2 and
Pw-1 carries out crossover operation respectively two-by-two, and Pw is not involved in crossover operation, and Fw directly inherits Pw；Two individual Pe and Pu are intersected
Operation produces individual Fe and Fu, and detailed process is：The individual Pe for carrying out crossover operation is assigned to fe, individual Pu is assigned to fu,
A n binary codes are randomly generated, the n binary code is designated as A, fe and fu is updated according to binary code A, works as binary system
When h of code A are 1, fe h holdings are constant, and fu h holdings are constant；When h of binary code A being 0,
H of fe h succession fu, h of fu h succession fe, h=1,2,3 ..., n, after the completion of crossover operation
The fu that are designated as after the completion of Fe, crossover operation of fe be designated as Fu；Wherein u=e+1, when w is even number, e=1,3,5 ..., w-1；u
=2,4,6 ..., w；When w is odd number, e=1,3,5 ..., w-2；U=2,4,6 ..., w-1；
5. -5 by fitness function calculate v-th of individual Fv fitness, obtain individual F1, F2 ..., Fw adaptation
Degree；
5. -6 individual F1, F2 ..., Fw fitness and the maximum individual fitness of current fitness are compared, more
The new maximum individual of fitness and maximum adaptation degree；
5. -7 individual F1, F2 ..., Fw are subjected to mutation operation：To Fv each with random function rand () produce
Value between one 0 to 1, if this value is less than gene mutation probability q, the corresponding position of this value is exactly Fv change dystopy, right
Fv change dystopy is made a variation, and variation rule is " 0 → 1,1 → 2,2 → 0 "；
5. -8 according to step 5. -5~5. -6 couples of individual F1, F2 ..., Fw processing, the fitness after being updated is most
Big individual and maximum adaptation degree；
5. -9 according to the size of fitness value to individual P1, P2 ..., Pw is ranked up, according to the size pair of fitness value
Individual F1, F2 ..., Fw are ranked up；Fitness value is each selected in individual P1, P2 ..., Pw and individual F1, F2 ..., Fw
2w/3 optimal individual, constitutes one group of new individual, and new individual contains 4w/3 individual；
5. -10 pairs one group new individual carries out many wheel annealing selections：In each round annealing selection, first according to formula (9)
An annealing temperature is produced, for the annealing temperature, probability P (c) is selected by what formula (10) calculated each individual successively, together
When produce a screening probability t, 0 with random function rand ()<t<1；When individual when being selected probability more than screening probability,
The individual is chosen in this wheel annealing selection, and selected individual is no longer participate in next round annealing selection, and other are not chosen
The individual selected enters next round annealing selection, is updated until filtering out w individual after individual P1, P2 ..., Pw, annealing selection knot
Beam；
Tl=1/ln (l/T0+1) (9)
Wherein, TlRepresent the annealing temperature of l wheels, l=1,2 ...；During first round annealing selection, l=1, the second wheel annealing
During selection, l=2, by that analogy；Ln represents log operations；T0Represent initial temperature；P (c) represents individual c probability；F (c) tables
Show the fitness value of c-th of individual in new individual；C=1,2,3 ..., 4w/3；D-th of individual in the new individual of f (d) expressions
Fitness value；D=1,2,3 ..., 4w/3；
5. -11 according to step 5. -2~individual P1 after 5. 5. -3 pairs of steps are updated in -10, P2 ..., Pw processing,
Obtain the maximum individual of fitness and maximum adaptation degree；
5. -12 repeat steps 5. -4~5. -11, until meeting individual iterations z, algorithm terminates, and obtains fitness most
Big individual and maximum adaptation degree；
5. the maximum individual of -13 fitness for obtaining last time and maximum adaptation degree are exported, and fitness maximum individual is
For the optimum polarity of three value FPRM circuits；Maximum adaptation degree is the minimum power consumption of three value FPRM circuits.
The power consumption optimum polarity search method of the present invention is in the bit manipulation systems of Windows 7 64, Intel (R) Core (TM)
Under i3-2130 CPU 3.40GHZ, 4G RAM running environment, compiled and realized by VC6.0 with C language, it is random to use 13
MCNC Benchmark circuits carry out simulating, verifying, the power consumption optimum polarity that the method using the present invention is searched and 0 polarity
It is compared.To calculate the switch activity of three value FPRM circuits, 15 groups of input signal probability are randomly generated：(P1, P2)=
(0.21,0.53), (0.49,0.30), (0.33,0.24), (0.68,0.13), (0.15,0.26), (0.57,0.22),
(0.18,0.51), (0.71,0.24), (0.08,0.35), (0.57,0.32), (0.46,0.28), (0.17,0.05),
(0.32,0.43), (0.14,0.72), (0.25,0.61) }.
The result for carrying out optimum polarity search using the power consumption optimum polarity search method of the present invention is as shown in table 1.In table,
The indication circuit title of row 1, row 2 represent input/output variable number；Row 3, row 4 and row 5 represent under 0 polarity that two is defeated respectively successively
Enter mould 3 plus door quantity, the two door quantity that multiply of input moulds 3 and circuit power consumption；Row 6, row 7, row 8 and row 9 represent to adopt successively respectively
Three value FPRM circuits two input mould 3 plus door quantity, two under the optimum polarity and optimum polarity that are searched with the method for the present invention
Input mould 3 multiplies a quantity and power consumption.
The value FPRM circuit optimum polarity search results of table 1 three
Compared with 0 polarity, optimum polarity mould 3 plus door quantity, the door quantity that multiplies of mould 3 and power consumption on the percentage saved
Than as shown in table 2.The percentage of door quantity, the door quantity that mould 3 multiplies and Save power consumption that mould 3 adds is defined as follows：
Wherein, SaveMod3-A、SaveMod3-MAnd SavePowerRepresent respectively successively mould 3 plus door quantity, mould 3 multiply a quantity and
The saving of power consumption；Mod3-A0、Mod3-M0And Power0Represent respectively successively under 0 polarity mould 3 plus door quantity, mould 3 multiply a quantity and
Power consumption size；Mod3-ASAGA、Mod3-MSAGAAnd SASAGARepresent mould 3 under the optimum polarity that the inventive method is searched respectively successively
Plus door quantity, mould 3 multiply a quantity and power consumption size.Using the method for the present invention, three value FPRM gates numbers and Save power consumption hundred
Divide than as shown in table 2.
The value FPRM gates number of table 2 three and Save power consumption percentage
Knowable to analyze data, the power consumption optimum polarity searched using the method for the present invention effect of optimization compared with 0 polarity
Substantially, wherein clpl circuits multiply a quantity and power consumption and save 80.00%, 66.67% and respectively in mould 3 plus door quantity, mould 3
89.78%, 13 test circuits multiply a quantity and power consumption and averagely save 57.64%, 46.25% and in mould 3 plus door quantity, mould 3
73.98%.
Claims (2)
1. a kind of three value FPRM circuit power consumption optimum polarity search methods, it is characterised in that comprise the following steps：
1. the power estim ation model of three value FPRM circuits is set up：
1. -1 three value FPRM circuits are expressed as form using three value FPRM logical functions：
Wherein, n is function fp(xn-1,xn-2,…,x0) input variable quantity, xn-1,xn-2,…,x0Representative function fp(xn-1,
xn-2,…,x0) n input variable, p representative functions fp(xn-1,xn-2,…,x0) polarity, polarity p represents with ternary form
For pn-1pn-2…p0, pj∈ { 0,1,2 }, j=0,1,2 ..., n-1,Mould 3 plus computing are represented, ∑ is summation sign, symbol " * "
For multiplication symbol, subscript i=0,1,2 ..., 3n- 1, i are expressed as i with ternary formn-1in-2…i0, aiFor FPRM coefficients；
ai∈{0,1,2}；∏ represents the multiplication of mould 3,Its expansion be：Wherein ij∈{0,1,2},Polarity p and subscript i decision variablesRepresentation；
1. three value FPRM logical functions under -2 p polarity include two class multi-input operationals, and how defeated two class multi-input operationals be respectively
Enter mould 3 plus computing and the multiplication of multi input mould 3, according to three value FPRM logical functions expansions by three value FPRM Logic function decompositions
For multiple multi input moulds 3 plus computing and multiple multiplications of multi input mould 3, each multi-input operational is then separately disassembled into two defeated
Enter computing, obtain two input moulds 3 plus computing and the two input multiplications of mould 3, specific decomposable process is：
Inputted the 1st input variable and the 2nd input variable of multi-input operational as two of first two input computing
Variable, obtains the output variable of first two input computing；The output variable and multi-input operational for inputting computing by first two
The 3rd input variable as second two input computing two input variables, obtain second two input computing output
Variable；The output variable and the 4th input variable of multi-input operational for inputting computing using second two are used as the 3rd two input
Two input variables of computing, obtain the output variable of the 3rd two input computing；The rest may be inferred, until all multi inputs are transported
The input variable of calculation completes the decomposition of multi-input operational as the input variable of two input computings；
Multiple multi input moulds 3 plus computing will be obtained after three value FPRM Logic function decompositions under p polarity and multiple multi input moulds 3 multiply
Computing, multi input mould 3 plus computing are also referred to as multi input mould 3 plus door, and the multiplication of multi input mould 3 is also referred to as multi input mould 3 and multiplies door, will
The quantity of multi input mould 3 plus door under p polarity after three value FPRM Logic function decompositions is designated as N, by three value FPRM logics under p polarity
The quantity that multi input mould 3 after function decomposition multiplies door is designated as W；It is defeated that multiple two are obtained after each multi input mould 3 plus computing are decomposed
Enter mould 3 plus computing, multiple two inputs multiplications of mould 3, two input moulds 3 plus fortune are obtained after each multiplication of multi input mould 3 is decomposed
Also referred to as two input moulds 3 plus door are calculated, the two input multiplications of mould 3 are also referred to as two input moulds 3 and multiply door；By the H multi input mould 3 plus door
The quantity of two input moulds 3 plus door after decomposition is designated as NH, H=1,2 ..., N；O-th of multi input mould 3 is multiplied to two after a decomposition
The quantity that input mould 3 multiplies door is designated as Wo, o=1,2 ..., W；
1. -3 multiply all two input Jia Men of mould 3 obtained after three value FPRM Logic function decompositions under p polarity and two input moulds 3
Power consumption caused by door is as the power consumption of three value FPRM circuits under p polarity, and two input moulds 3 plus power consumption caused by door are switched using it
Activity represents that two input moulds 3 multiply power consumption caused by door and represent that the switch activity of gate circuit uses it using its switch activity
The output variable probability of output end represents that two input moulds 3 add power consumption caused by door using the output variable probability tables of its output end
Show, two input moulds 3 are multiplied power consumption caused by door and represented using the output variable probability of its output end；
1. -4 k-th two input moulds 3 plus door after the H multi input mould 3 plus door decomposition are calculated according to formula (2), (3) and (4)
Output variable probability；K=1,2 ..., NH；
P1(k)H=Pky11*Pky20+Pky10*Pky21+Pky12*Pky22 (2)
P2(k)H=Pky12*Pky20+Pky11*Pky21+Pky10*Pky22 (3)
P0(k)H=1-P1(k)H-P2(k)H (4)
Multiply g-th two input moulds 3 after a decomposition according to formula (5), (6) and (7) o-th of multi input mould 3 of calculating and multiply the defeated of door
Go out variable probability, g=1,2 ..., Wo：
Q1(g)o=Qgr11*Qgr21+Qgr12*Qgr22 (5)
Q2(g)o=Qgr11*Qgr22+Qgr12*Qgr21 (6)
Q0(g)o=1-Q1(g)o-Q2(g)o (7)
Wherein, P1(k)HRepresent the H multi input mould 3 plus door decompose after k-th two input moulds 3 plus door output variable for 1 it is general
Rate, P2(k)HRepresent k-th two input moulds 3 after the H multi input mould 3 plus door decomposition plus the probability that door output variable is 2, P0
(k)HRepresent k-th two input moulds 3 after the H multi input mould 3 plus door decomposition plus the probability that door output variable is 0, y1 and y2
Two input variables of the input moulds 3 of expression two plus door, m ∈ { 0,1,2 }, as k=1, Pky1mFor the of multi input mould 3 plus computing
The probability that 1 input variable is m, Pky2mThe probability for being m for the 2nd input variable of multi input mould 3 plus computing, works as k>When 1,
Pky1mThe probability that mould 3 plus door output variable are m, Pk are inputted for kth -1 twoy2mFor+1 input of kth of multi input mould 3 plus door
Variable is m probability；
Q1(g)oRepresent that o-th of multi input mould 3 multiplies g-th two input moulds 3 after a decomposition and multiply the probability that an output variable is 1, Q2
(g)oRepresent that o-th of multi input mould 3 multiplies g-th two input moulds 3 after a decomposition and multiply the probability that an output variable is 2, Q0(g)oTable
Show that o-th of multi input mould 3 multiplies g-th two input moulds 3 after a decomposition and multiply the probability that an output variable is 0, r1 and r2 represent two
Input mould 3 multiplies two input variables of door；As g=1, Qgr1mIt is m's for the 1st input variable of the multiplication of multi input mould 3
Probability, Qgr2mThe probability for being m for the 2nd input variable of the multiplication of multi input mould 3, works as g>When 1, Qgr1mIt is defeated for g-1 individual two
Enter mould 3 and multiply the probability that an output variable is m, Qgr2mMultiply the probability that the g+1 input variable of door is m for multi input mould 3；
Input variable xjFor 1 and 2 probability be by function immediately produce probability to (P1, P2), P0=1-P1-P2；P0, P1 and
P2 is respectively some value between 0 to 1, and P0 represents the probability that input variable is 0, and P1 represents the probability that input variable is 1, and P2 is represented
Input variable is 2 probability；
1. -5 the value of output variable probability calculation three that moulds 3 multiply door is inputted according to two input moulds 3 plus the output variable probability of door and two
The power consumption of FPRM circuits, the power estim ation model of three value FPRM circuits is expressed as：
Wherein, EswdThe power consumption of three value FPRM circuits under p polarity is represented, after N is three value FPRM Logic function decomposition under p polarity
The quantity of multi input mould 3 plus door, W multiplies the quantity of door for the multi input mould 3 after three value FPRM Logic function decompositions under p polarity；
2. it is used for the fitness function for calculating individual adaptation degree in setting Genetic Simulated Annealing Algorithm：
According to power estim ation model, the fitness function of individual adaptation degree is calculated in setting Genetic Simulated Annealing Algorithm：In simulation
In Annealing-Genetic Algorithm, fitness is bigger, and the adaptability for representing individual is stronger, but power consumption optimum polarity requires that power consumption is smaller more
It is good, therefore, combined for the ease of both, reciprocal using power consumption represents fitness, obtains fitness function as follows：
Fitness=α/Eswd
Wherein, symbol "/" represents division operation symbol, and fitness represents the fitness size of individual；EswdIndication circuit power consumption；α
For amplification coefficient, value is the natural number more than or equal to 1000；
3. three value FPRM circuits and the corresponding relation of Genetic Simulated Annealing Algorithm are set up：
Genetic Simulated Annealing Algorithm includes following key element：The maximum individual of individual, the fitness of individual, fitness,
Maximum adaptation degree, crossover operation, mutation operation, annealing selection operation；
The optimization of three value FPRM circuit power consumptions includes following key element：Polarity, the power consumption of corresponding polarity, optimum polarity, most
Low power consumption, polarity exchange, polarity mutation, reversal；
Individual is mapped to the optimization of three value FPRM circuit power consumptions, polarity is expressed as；The fitness of individual is mapped to three value FPRM
Circuit power consumption optimizes, and is expressed as the power consumption of corresponding polarity；The maximum individual of fitness is mapped to three value FPRM circuit power consumptions excellent
Change, be expressed as optimum polarity；Maximum adaptation degree is mapped to the optimization of three value FPRM circuit power consumptions, minimum power consumption is expressed as；It will hand over
Fork operation is mapped to the optimization of three value FPRM circuit power consumptions, is expressed as polarity exchange；Mutation operation is mapped to three value FPRM circuits
Optimised power consumption, is expressed as polarity mutation；Annealing selection operation is mapped to the optimization of three value FPRM circuit power consumptions, polarity change is expressed as
Change；
4. Genetic Simulated Annealing Algorithm relevant parameter is set：
Genetic Simulated Annealing Algorithm need to set 4 parameters：Individual scale w, individual iterations z, gene mutation probability q, starting
Temperature T0；The individual scale w=50 of order, individual iterations z=20, gene mutation probability q=0.01, initial temperature T0=100
℃；
5. the maximum individual of fitness and maximum adaptation degree are obtained using Genetic Simulated Annealing Algorithm, the maximum individual of fitness is three
The power consumption optimum polarity of value FPRM circuits；Maximum adaptation degree is the minimum power consumption of three value FPRM circuits.
2. a kind of three values FPRM circuit power consumption optimum polarity search methods according to claim 1, it is characterised in that described
The step of 5. it is middle use Genetic Simulated Annealing Algorithm obtain the detailed process of the maximum individual of fitness and maximum adaptation degree for：
5. -1 the w individuals represented with n ternarys are produced with random function rand (), w individual are designated as P1 respectively,
P2 ..., Pw；
5. -2 fitness for calculating v-th of individual Pv by fitness function, v=1,2,3 ..., w obtain individual P1, P2 ...,
Pw fitness；
5. -3 compare individual P1, and P2 ..., Pw fitness filters out the maximum individual of fitness as the maximum individual of fitness,
Record the maximum individual of fitness and maximum adaptation degree；
5. -4 couples of individuals P1, P2 ..., Pw carry out crossover operation generation individual F1, F2 ..., Fw：If w be even number, by P1 and P2,
P3 and P4 ..., Pw-1 and Pw carry out crossover operation respectively two-by-two；If w is odd number, by P1 and P2, P3 and P4 ..., Pw-2 and Pw-
1 carries out crossover operation respectively two-by-two, and Pw is not involved in crossover operation, and Fw directly inherits Pw；Two individual Pe and Pu carry out intersection behaviour
Make to produce individual Fe and Fu, detailed process is：The individual Pe for carrying out crossover operation is assigned to fe, individual Pu is assigned to fu, with
Machine produces a n binary codes, and the n binary code is designated as into A, updates fe and fu according to binary code A, works as binary code
When h of A are 1, fe h holdings are constant, and fu h holdings are constant；When h of binary code A being 0, fe
H successions h of fu, h of fu inherit fe h, h=1,2,3 ..., n, after the completion of crossover operation
The fu that fe is designated as after the completion of Fe, crossover operation is designated as Fu；Wherein u=e+1, when w is even number, e=1,3,5 ..., w-1；U=
2,4,6 ..., w；When w is odd number, e=1,3,5 ..., w-2；U=2,4,6 ..., w-1；
5. -5 by fitness function calculate v-th of individual Fv fitness, obtain individual F1, F2 ..., Fw fitness；
5. -6 individual F1, F2 ..., Fw fitness and the maximum individual fitness of current fitness are compared, update suitable
The maximum individual of response and maximum adaptation degree；
5. -7 individual F1, F2 ..., Fw are subjected to mutation operation：To Fv each with random function rand () produce one 0
Value between to 1, if this value is less than gene mutation probability q, the corresponding position of this value is exactly Fv change dystopy, the change to Fv
Dystopy enters row variation, and variation rule is " 0 → 1,1 → 2,2 → 0 "；
5. -8 according to step 5. -5~5. -6 couples of individuals F1, F2 ..., Fw processing, maximum of the fitness after being updated
Body and maximum adaptation degree；
5. -9 according to the size of fitness value to individual P1, P2 ..., Pw is ranked up, according to the size of fitness value to individual
F1, F2 ..., Fw are ranked up；Each select fitness value optimal in individual P1, P2 ..., Pw and individual F1, F2 ..., Fw
2w/3 individual, constitute one group of new individual, new individual contain 4w/3 it is individual；
5. -10 pairs one group new individual carries out many wheel annealing selections：In each round annealing selection, produced first according to formula (9)
One annealing temperature, for the annealing temperature, probability P (c) is selected by what formula (10) calculated each individual successively, while with
Random function rand () produces a screening probability t, 0<t<1；When individual when being selected probability more than screening probability, this
Body is chosen in this wheel annealing selection, and selected individual is no longer participate in next round annealing selection, and other are non-selected
Individual enters next round annealing selection, is updated until filtering out w individual after individual P1, P2 ..., Pw, annealing selection terminates；
Tl=1/ln (l/T0+1) (9)
Wherein, TlRepresent the annealing temperature of l wheels, l=1,2 ...；During first round annealing selection, l=1, the second wheel annealing selection
When, l=2, by that analogy；Ln represents log operations；T0Represent initial temperature；P (c) represents individual c probability；F (c) represents new
Individual in c-th individual fitness value；C=1,2,3 ..., 4w/3；F (d) represents in new individual the suitable of d-th individual
Answer angle value；D=1,2,3 ..., 4w/3；
5. -11 according to step 5. -2~individual P1 after 5. 5. -3 pairs of steps are updated in -10, P2 ..., Pw processing obtains
The maximum individual of fitness and maximum adaptation degree；
5. -12 repeat steps 5. -4~5. -11, until meeting individual iterations z, algorithm terminates, and obtains maximum of fitness
Body and maximum adaptation degree；
5. the maximum individual of -13 fitness for obtaining last time and maximum adaptation degree are exported, and the maximum individual of fitness is three
The optimum polarity of value FPRM circuits；Maximum adaptation degree is the minimum power consumption of three value FPRM circuits.
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