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Dedication; 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
2.5 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
3.11 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
4.8 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
4.16 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
2.5 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
3.11 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
4.8 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
4.16 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