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000807317 08204 $$a004.01/51$$223
000807317 1001_ $$aBeebe, Nelson H. F.,$$eauthor.
000807317 24514 $$aThe mathematical-function computation handbook :$$bprogramming using the MathCW portable software library /$$cNelson H.F. Beebe.
000807317 264_1 $$aCham :$$bSpringer,$$c[2017]
000807317 300__ $$a1 online resource.
000807317 336__ $$atext$$btxt$$2rdacontent
000807317 337__ $$acomputer$$bc$$2rdamedia
000807317 338__ $$aonline resource$$bcr$$2rdacarrier
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000807317 5050_ $$aDedication; Preface; Acknowledgements; The Unix family; Trademarks, copyrights, and property ownership; To show code, or not; To cite references, or not; The MathCWWeb site; Contents; List of figures; List of tables; Quick start; 1 Introduction; 1.1 Programming conventions; 1.2 Naming conventions; 1.3 Library contributions and coverage; 1.4 Summary; 2 Iterative solutions and other tools; 2.1 Polynomials and Taylor series; 2.2 First-order Taylor series approximation; 2.3 Second-order Taylor series approximation; 2.4 Another second-order Taylor series approximation
000807317 5058_ $$a2.5 Convergence of second-order methods2.6 Taylor series for elementary functions; 2.7 Continued fractions; 2.8 Summation of continued fractions; 2.9 Asymptotic expansions; 2.10 Series inversion; 2.11 Summary; 3 Polynomial approximations; 3.1 Computation of odd series; 3.2 Computation of even series; 3.3 Computation of general series; 3.4 Limitations of Cody/Waite polynomials; 3.5 Polynomial fits with Maple; 3.6 Polynomial fits with Mathematica; 3.7 Exact polynomial coefficients; 3.8 Cody/Waite rational polynomials; 3.9 Chebyshev polynomial economization; 3.10 Evaluating Chebyshev polynomials
000807317 5058_ $$a3.11 Error compensation in Chebyshev fits3.12 Improving Chebyshev fits; 3.13 Chebyshev fits in rational form; 3.14 Chebyshev fits with Mathematica; 3.15 Chebyshev fits for function representation; 3.16 Extending the library; 3.17 Summary and further reading; 4 Implementation issues; 4.1 Error magnification; 4.2 Machine representation and machine epsilon; 4.3 IEEE 754 arithmetic; 4.4 Evaluation order in C; 4.5 The volatile type qualifier; 4.6 Rounding in floating-point arithmetic; 4.7 Signed zero; 4.7.1 Detecting the sign of zero; 4.7.2 Signed-zero constants; 4.7.3 Arc tangent and signed zero
000807317 5058_ $$a4.8 Floating-point zero divide4.9 Floating-point overflow; 4.10 Integer overflow; 4.10.1 Preventing integer overflow; 4.10.1.1 Safe integer absolute value; 4.10.1.2 Safe integer addition; 4.10.1.3 Safe integer division; 4.10.1.4 Safe integer multiplication; 4.10.1.5 Safe integer negation; 4.10.1.6 Safe integer remainder; 4.10.1.7 Safe integer subtraction; 4.10.1.8 Safe integer operations: a retrospective; 4.11 Floating-point underflow; 4.12 Subnormal numbers; 4.13 Floating-point inexact operation; 4.14 Floating-point invalid operation; 4.15 Remarks on NaN tests
000807317 5058_ $$a4.16 Ulps-units in the last place4.17 Fused multiply-add; 4.18 Fused multiply-add and polynomials; 4.19 Significance loss; 4.20 Error handling and reporting; 4.21 Interpreting error codes; 4.22 C99 changes to error reporting; 4.23 Error reporting with threads; 4.24 Comments on error reporting; 4.26 Extended data types on Hewlett-Packard HP-UX IA-64; 4.27 Extensions for decimal arithmetic; 4.28 Further reading; 4.29 Summary; 5 The floating-point environment; 5.1 IEEE 754 and programming languages; 5.2 IEEE 754 and the mathcw library; 5.3 Exceptions and traps
000807317 506__ $$aAccess limited to authorized users.
000807317 520__ $$aAll major computer programming languages--as well as the disciplines of science and engineering more broadly--require computation of elementary and special functions of mathematics. The MathCW Software Library emphasizes portability, precisely because the code needs to capable of use on a wide variety of platforms. This highly comprehensive handbook provides a substantial advance in such computation, extending the function coverage of major programming languages well beyond their international standards, including full support for decimal floating-point arithmetic. Written with clarity and focusing on the C language, the work pays extensive attention to little-understood aspects of floating-point and integer arithmetic, and to software portability, as well as to important historical architectures. It extends support to a future 256-bit, floating-point format offering 70 decimal digits of precision. Select Topics and Features: references an exceptionally useful, author-maintained MathCW website, containing source code for the book's software, compiled libraries for numerous systems, pre-built C compilers, and other related materials offers a unique approach to covering mathematical-function computation using decimal arithmetic provides extremely versatile appendices for interfaces to numerous other languages:  Ada, C#, C++, Fortran, Java, and Pascal presupposes only basic familiarity with computer programming in a common language, as well as early level algebra supplies a library that readily adapts for existing scripting languages, with minimal effort supports both binary and decimal arithmetic, in up to 10 different floating-point formats covers a significant portion (with highly accurate implementations) of the U.S National Institute of Standards and Technology's 10-year project to codify mathematical functions This highly practical text/reference is an invaluable tool for advanced undergraduates, recording many lessons of the intermingled history of computer hardware and software, numerical algorithms, and mathematics. In addition, professional numerical analysts and others will find the handbook of real interest and utility because it builds on research by the mathematical software community over the last four decades.
000807317 650_0 $$aComputer science$$xMathematics.
000807317 650_0 $$aFunctions$$xComputer programs.
000807317 650_0 $$aComputer programming.
000807317 77608 $$iPrint version:$$z3319641093$$z9783319641096$$w(OCoLC)992783805
000807317 852__ $$bebk
000807317 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-64110-2$$zOnline Access$$91397441.1
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