Pi — Unleashed [electronic resource] /

1. The State of Pi Art -- 2. How Random is ?? -- 2.1Probabilities -- 2.2 Is ? normal? -- 2.3 So is ? not normal? -- 2.4 The 163 phenomenon -- 2.5 Other statistical results -- 2.6 The Intuitionists and ? -- 2.7 Representation of continued fractions -- 3. Shortcuts to ? -- 3.1Obscurer approaches to ? -- 3.2 Small is beautiful -- 3.3 Squeezing ? through a sieve -- 3.4 ? and chance (Monte Carlo methods) -- 3.5 Memorabilia -- 3.6 Bit for bit -- 3.7 Refinements -- 3.8 The ? room in Paris -- 4. Approximations for ?and Continued Fractions -- 4.1Rational approximations -- 4.2 Other approximations -- 4.3 Youthful approximations -- 4.4 On continued fractions -- 5. Arcus Tangens -- 5.1 John Machin's arctan formula -- 5.2 Other arctan formulae -- 6. Spigot Algorithms -- 6.1 The spigot algorithm in detail -- 6.2 Sequence of operations -- 6.3 A faster variant -- 6.4 Spigot algorithm for e -- 7.Gauss and ? -- 7.1 The ? AGM formula -- 7.2 The Gauss AGM algorithm -- 7.3 Schönhage variant -- 7.4 History of a formula -- 8. Ramanujan and ? -- 8.1 Ramanujan's series -- 8.2 Ramanujan's unusual biography -- 8.3 Impulses -- 9. The Borweins and ? -- 10. The BBP Algorithm -- 10.1Binary modulo exponentiation -- 10.2 A C program on the BBP series -- 10.3 Refinements -- 11. Arithmetic -- 11.1Multiplication -- 11.2 Karatsuba multiplication -- 11.3 FFT multiplication -- 11.4 Division -- 11.5 Square root -- 11.6 nth root -- 11.7 Series calculation -- 12. Miscellaneous -- 12.1 A ? quiz -- 12.2 Let numbers speak -- 12.3 A proof that ? = 2 -- 12.4 The big change -- 12.5 Almost but not quite -- 12.6 Why always more? -- 12.7 ? and hyperspheres -- 12.8 Viète × Wallis = Osler -- 12.9 Squaring the circle with holes -- 12.10 An (in)finite funnel -- 13.The History of ? -- 13.1 Antiquity -- 13.2 Polygons -- 13.3 Infinite expressions -- 13.4 High-performance algorithms -- 13.5 The hunt for single ? digits -- Table: History of ? in the pre-computer era -- Table: History of ? in the computer era -- Table: History of digit extraction records -- 14. Historical Notes -- 14.1 The earliest squaring the circle in history? -- 14.2 A ? law -- 14.3 The Bieberbach story -- 15.The Future: ?Calculations on the Internet -- 15.1 The binsplit algorithm -- 15.2 The ? project on the Internet -- 16. ?Formula Collection -- 17. Tables -- 17.1 Selected constants to 100 places (base 10) -- 17.2 Digits 0 to 2,500 of ? (base 10) -- 17.3 Digits 2,501 to 5,000 of ? (base 10) -- 17.4 Digits 0 to 2,500 of ? (base 16) -- 17.5 Digits 2,501 to 5,000 of ? (base 16) -- 17.6 Continued fraction elements 0 to 1,000 of ? -- 17.7 Continued fraction elements 1,001 to 2,000 of ? -- A. Documentation for the hfloat Library -- A.1 What hfloat is (good for) -- A.2 Compiling the library -- A.3 Functions of the hfloat library -- A.4 Using hfloats in your own code -- A.5 Computations with extreme precision -- A.6 Precision and radix -- A.7 Compiling & running the ?-example-code -- A.8 Structure of hfloat -- A.9 Organisation of the files -- A. 10 Distribution policy & no warranty.

Bibliographic Details

Main Authors:	Arndt, Jörg. author., Haenel, Christoph. author., SpringerLink (Online service)
Format:	Texto biblioteca
Language:	eng
Published:	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2001
Subjects:	Computer science., Algorithms., Computer science, Number theory., Computer Science., Algorithm Analysis and Problem Complexity., Symbolic and Algebraic Manipulation., Math Applications in Computer Science., Number Theory.,
Online Access:	http://dx.doi.org/10.1007/978-3-642-56735-3
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