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Pi — Unleashed

Author: Jörg Arndt; Christoph Haenel
Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2001.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Additional Physical Format: Printed edition:
Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jörg Arndt; Christoph Haenel
ISBN: 9783642567353 3642567355
OCLC Number: 1086525797
Description: 1 online resource (XII, 270 p. 1 illus.) online resource.
Contents: 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.
Responsibility: by Jörg Arndt, Christoph Haenel.

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