Table of Content
Introduction, Basic Definitions, and Standards.- Definitions and Basic Notions.- Floating-Point Formats and Environment.- Cleverly Using Floating-Point Arithmetic.- Basic Properties and Algorithms.- The Fused Multiply-Add Instruction.- Enhanced Floating-Point Sums, Dot Products, and Polynomial Values.- Languages and Compilers.- Implementing Floating-Point Operators.- Algorithms for the Five Basic Operations.- Hardware Implementation of Floating-Point Arithmetic.- Software Implementation of Floating-Point Arithmetic.- Elementary Functions.- Evaluating Floating-Point Elementary Functions.- Solving the Table Maker’s Dilemma.- Extensions.- Formalisms for Certifying Floating-Point Algorithms.- Extending the Precision.- Perspectives and Appendix.- Conclusion and Perspectives.- Appendix: Number Theory Tools for Floating-Point Arithmetic.
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