text: In general, the number of multiplication operations required to compute  can be reduced to  by using exponentiation by squaring, where  denotes the number of s in the binary representation of . For some exponents (100 is not among them), the number of multiplications can be further reduced by computing and using the minimal addition-chain exponentiation. Finding the minimal sequence of multiplications (the minimal-length addition chain for the exponent) for  is a difficult problem, for which no efficient algorithms are currently known (see Subset sum problem), but many reasonably efficient heuristic algorithms are available. However, in practical computations, exponentiation by squaring is efficient enough, and much more easy to implement.
  Iterated functions
  Function composition is a binary operation that is defined on functions such that the codomain of the function written on the right is included in the domain of the function written on the left. It is denoted  and defined as
  for every  in the domain of .
  If the domain of a function  equals its codomain, one may compose the function with itself an arbitrary number of time, and this defines the th power of the function under composition, commonly called the th iterate of the function. Thus  denotes generally the th iterate of ; for example,  means