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Tag Archives: repeated
Efficiency of repeated squaring: another proof
In my previous post I proved that the “binary algorithm” (corresponding to the binary expansion of a number ) is the most efficient way to build using only doubling and incrementing steps. Today I want to explain another nice proof, … Continue reading
Posted in computation, proof
Tagged binary, double, efficiency, exponent, increment, proof, repeated, squaring, steps
3 Comments
Efficiency of repeated squaring: proof
My last post proposed a claim: The binary algorithm is the most efficient way to build using only doubling and incrementing steps. That is, any other way to build by doubling and incrementing uses an equal or greater number of … Continue reading
Posted in computation, proof
Tagged binary, double, efficiency, exponent, increment, proof, repeated, squaring, steps
2 Comments
Efficiency of repeated squaring
As you probably realized if you read both, my recent post without words connects directly to my previous post on exponentiation by repeated squaring Each section shows the sequence of operations used by the repeated squaring algorithm to build up … Continue reading
Posted in computation
Tagged binary, double, efficiency, exponent, increment, repeated, squaring, steps
7 Comments
Post without words #22
Posted in arithmetic, computation, number theory, posts without words
Tagged logarithmic, repeated, squaring
8 Comments
Modular exponentiation by repeated squaring
In my last post we saw how to quickly compute powers of the form by repeatedly squaring: ; then ; and so on. This is much more efficient than computing powers by repeated multiplication: for example, we need only three … Continue reading
Posted in computation, number theory
Tagged algorithm, exponentiation, logarithmic, modular, primality, repeated, squaring, test
4 Comments