Unbounded Spigot Algorithms for the Digits of π
نویسنده
چکیده
Rabinowitz and Wagon (in American Mathematical Monthly 102(3):195–203, 1995) present a spigot algorithm for computing the digits of π. A spigot algorithm yields its outputs incrementally, and does not reuse them after producing them. Their algorithm is inherently bounded ; it requires a commitment in advance to the number of digits to be computed, and in fact might still produce an incorrect last few digits. We propose some streaming algorithms based on the same and some other characterizations of π, with the same incremental characteristics but without requiring the prior bound.
منابع مشابه
Unbounded Spigot Algorithms for the Digits of Pi
Rabinowitz and Wagon call their algorithm a spigot algorithm, because it yields digits incrementally and does not reuse digits after they have been computed. The digits drip out one by one, as if from a leaky tap. In contrast, most algorithms for computing the digits of π execute inscrutably, delivering no output until the whole computation is completed. However, the Rabinowitz–Wagon algorithm ...
متن کاملPi Fractions for Generating Uniformly Distributed Sampling Points in Global Search and Optimization Algorithms
π Fractions are used to create deterministic uniformly distributed pseudorandom decision space sample points for a global search and optimization algorithm. These fractions appear to be uniformly distributed on [0,1] and can be used in any stochastic algorithm rendering it effectively deterministic without compromising its ability to explore the decision space. π Fractions are generated using t...
متن کاملDistant decimals of $\pi$
We describe how to compute very far decimals of π and how to provide formal guarantees that the decimals we compute are correct. In particular, we report on an experiment where 1 million decimals of π and the billionth hexadecimal (without the preceding ones) have been computed in a formally verified way. Three methods have been studied, the first one relying on a spigot formula to obtain at a ...
متن کاملExploration in π Calculation Using Various Methods Implemented in Python
The mathematical constant π, found ubiquitously in many applications, has been a subject of interest for mathematicians ever since the beginning of recorded history. In order to seek out better understanding of its nature, calculation of the its decimal digits has been a perennial favored activity of many mathematicians throughout history. The length of digit of π capable of being obtained has ...
متن کاملParallel Computation of π Using High Precision Arithmetics
During the last decades estimating π has become a competition and a benchmarking tool. Many different algorithms have been developed and with the advent of high performance architectures it is possible to calculate very large number of π decimal digits. Within the scope of the Parallel Algorithms lecture a parallel library for high precision arithmetics will be introduced and its performance on...
متن کامل