In my Aug 28 post<\/a> I brought up exponentiation and a straightforward algorithm that uses a loop. However, there is a less straightforward, yet more efficient, algorithm for it:<\/p>\n $orbase=ARGV[0];#reads original base as a param. from function call<\/span> while($exp>0){<\/p>\n if($exp%2==1){#checks if the exponent is odd<\/span> $exp=int($exp\/2);#for example: int(11\/2)=5<\/span><\/p>\n if($exp>0){ }#end while loop<\/span> Let’s assume this file is named exp.txt<\/span>. To call it and ask it to evalute 2<\/b>10<\/sup>, one would type at the command prompt<\/p>\n perl exp.txt 2 10<\/span> <\/p>\n This algorithm is more efficient than the looping one because it can square the base, then halve the number of times it needs to be multiplied by itself. Furthermore, it can separate the expression into even and odd segments, then tackle the even one(s) as just described.<\/p>\n I’ll be talking more about the details of this algorithm in future posts:)<\/p>\n Source:<\/p>\n Grimaldi, Ralph P. Discrete and Combinatorial Mathematics<\/u>. Addison-Wesley: Toronto,
\n$orexp=ARGV[1];#the original exponent<\/span>
\n$exp=$orexp;
\n$base=$orbase;#this program changes the exponent and base<\/span>
\n$res=1;#this variable will become the result<\/span><\/p>\n
\n$res*=$base;
\n}<\/p>\n
\n$base*=$base;
\n}<\/p>\n
\nprint “$orbase to the exponent of $orexp is $res\\n\\n”;\n<\/div>\n
1994.<\/p>\n