A New Subexpression Elimination Algorithm Using Zero-Dominant Set

Al-Hasani, Firas; Hayes, Michael; Bainbridge-Smith, Andrew

doi:10.1109/delta.2011.18

Cited by 5 publications

(4 citation statements)

References 17 publications

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“…The time required to generate the demand graph is denoted by t g and that required to search the graph is denoted by t s . The MMAS algorithm was compared with the pattern preservation algorithm (PPA) [4], subexpression tree algorithm (STA) [5], difference based adder graph (DBAG) [23], and Yao [47], using a set of 100 MCM with N = 5. The wordlength was changed in steps starting from L = 6 to 15 and for each wordlength the average LO, LD, and time (t) are calculated as shown in Fig.…”

Section: Resultsmentioning

confidence: 99%

“…The PPA algorithm was excluded from the comparison because of its relatively long run time as compared with the other algorithms. Figure 13: (a)The average number of LO versus wordlength obtained when the algorithms PPA [4], MMAS, STA [5], DBAG [23], and Yao [47] used to synthesize random MCMs of 10 coefficients. The LD was constrained to the minimum in the case of Yao, STA, and MMAS algorithms.…”

Section: Resultsmentioning

confidence: 99%

“…The LD was constrained to the minimum in the case of Yao, STA, and MMAS algorithms. (b) The average number of LD versus wordlength obtained when the algorithms PPA [4], MMAS, and DBAG [23] used to synthesize random MCMs of 10 coefficients. The LD was constrained to the minimum in the case MMAS algorithm.…”

Section: Resultsmentioning

confidence: 99%

“…The LD was constrained to the minimum in the case MMAS algorithm. (c) Comparison between the run time of the algorithms PPA [4], MMAS, STA [5], DBAG [23], and Yao [47] used to synthesize random MCMs of 10 coefficients.…”

Section: Resultsmentioning

confidence: 99%

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Developing a combinatorial model for the multiple constant multiplication

Al-Hasani¹

2015

IJET

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A combinatoric model for the multiple constant multiplication (MCM) operation is developed. The model is found by decomposing each coefficient using the A−operation into two subexpressions. The constituted subexpressions are, in turn, decomposed using the A−operation. Connecting all of the decompositions results the decomposition graph which represents the solution space. The decomposition graph itself is not feasible for routing to find the minimum solutions. Therefore, a transformation on the A−operation is proposed to make the decomposition graph routable. In this case, the A−operation is transformed into a subexpression operation by replacing the shift information attached to the arcs by the other subexpression information which is called the demand. A demand that attached to an arc will represent its cost. The resulting transformed graph is called the demand graph. The demand graph is augmented with deadheading arcs to make it routable. Deadheading arcs are with zero demand. Similarly, traversing an arc with synthesized demand is of zero cost. Enumerating all of the routes that start from the signal vertex and visit all the coefficients gives all the solutions of the MCM problem. The routing technique requires redirecting the route when encountering an unsynthesized demand. The route in this case backtrack to the first encountered synthesized ancestors for this demand. This routing style analogous to the dynamic capacitated arc routing. To prevent exhaust routing, ant colony optimization (ACO) meta-heuristics is proposed to traverse the augmented demand graph. The solution space contains all the possible solutions that can be obtained from using both of the common subexpression elimination (CSE) and graph dependent heuristics that traditionally used to solve the MCM operation.

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