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Less-Numerical Algorithms part 1

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You can stop reading now. You are done with Numerical Recipes, as such. This final chapter is an idiosyncratic collection of “less-numerical recipes” which, for one reason or another, we have decided to include between the covers of an otherwise more-numerically oriented book. | Chapter 20. Less-Numerical Algorithms 20.0 Introduction You can stop reading now. You are done with Numerical Recipes as such. This final chapter is an idiosyncratic collection of less-numerical recipes which for one reason or another we have decided to include between the covers of an otherwise more-numerically oriented book. Authors of computer science texts we ve noticed like to throw in a token numerical subject usually quite a dull one quadrature for example . We find that we are not free of the reverse tendency. Our selection of material is not completely arbitrary. One topic Gray codes was already used in the construction of quasi-random sequences 7.7 and here needs only some additional explication. Two other topics on diagnosing a computer s floating-point parameters and on arbitrary precision arithmetic give additional insight into the machinery behind the casual assumption that computers are useful for doing things with numbers as opposed to bits or characters . The latter of these topics also shows a very different use for Chapter 12 s fast Fourier transform. The three other topics checksums Huffman and arithmetic coding involve different aspects of data coding compression and validation. If you handle a large amount of data numerical data even then a passing familiarity with these subjects might at some point come in handy. In 13.6 for example we already encountered a good use for Huffman coding. But again you don t have to read this chapter. And you should learn about quadrature from Chapters 4 and 16 not from a computer science text 20.1 Diagnosing Machine Parameters A convenient fiction is that a computer s floating-point arithmetic is accurate enough. If you believe this fiction then numerical analysis becomes a very clean subject. Roundoff error disappears from view many finite algorithms become exact only docile truncation error 1.3 stands between you and a perfect calculation. Sounds rather naive doesn t it Yes it is naive. Notwithstanding it is