Methods For Computing Addition Chains
Calculating an addition chain of minimal length is not easy; a generalized version of the problem, in which one must find a chain that simultaneously forms each of a sequence of values, is NP-complete. There is no known algorithm which can calculate a minimal addition chain for a given number with any guarantees of reasonable timing or small memory usage. However, several techniques to calculate relatively short chains exist. One very well known technique to calculate relatively short addition chains is the binary method, similar to exponentiation by squaring. Other well-known methods are the factor method and window method.
Read more about this topic: Addition Chain
Famous quotes containing the words methods, addition and/or chains:
“There are souls that are incurable and lost to the rest of society. Deprive them of one means of folly, they will invent ten thousand others. They will create subtler, wilder methods, methods that are absolutely DESPERATE. Nature herself is fundamentally antisocial, it is only by a usurpation of powers that the organized body of society opposes the natural inclination of humanity.”
—Antonin Artaud (1896–1948)
“The force of truth that a statement imparts, then, its prominence among the hordes of recorded observations that I may optionally apply to my own life, depends, in addition to the sense that it is argumentatively defensible, on the sense that someone like me, and someone I like, whose voice is audible and who is at least notionally in the same room with me, does or can possibly hold it to be compellingly true.”
—Nicholson Baker (b. 1957)
“Let the saints be joyful in glory: let them sing aloud upon their beds. Let the high praises of God be in their mouth, and a two-edged sword in their hand; to execute vengeance upon the heathen, and punishments upon the people; to bind their kings with chains and their nobles with fetters of iron; to execute upon them the judgment written.”
—Bible: Hebrew Psalms 149:5-9.