Chain Length
Let denote the smallest s so that there exists an addition chain of length s which computes n. It is known that
- ,
where is Hamming weight of binary expansion of n.
It is clear that l(2n) ≤ l(n)+1. Strict inequality is possible, as l(382) = l(191) = 11, observed by Knuth.
Read more about this topic: Addition Chain
Famous quotes containing the words chain and/or length:
“From Nature’s chain whatever link you strike,
Tenth or ten thousandth, breaks the chain alike.”
—Alexander Pope (1688–1744)
“To find the length of an object, we have to perform certain
physical operations. The concept of length is therefore fixed when the operations by which length is measured are fixed: that is, the concept of length involves as much as and nothing more than the set of operations by which length is determined.”
—Percy W. Bridgman (1882–1961)