C++ Floating Point Examples

Introduction

• Integer Numbers
• Fixed Point Numbers
• Floating Point Numbers
• Floating Point Standard - IEEE-754
• Floating point types in C++

Parsing

• Use case of parsing
• Influence of encoding on std::stof
• Influence of encoding on std::sstream
• Use of std::from_chars
• Parsing benchmarks

Representation

• Floating type literals
• 32 bit floating point binary layout
• Meaningful digits estimation
• Closest representable neighbours

Rounding

• IEEE 754 Standard Rounding Modes
• C++ Standard Round Style
• Floating Point Environment
• Global Rounding Style

Comparison

• Special values
• Operator ==
• Comparison Approaches

Arithmetic

• Operations defined by IEEE 754
• Exceptional conditions
• Not Guaranteed Associativity
• Loss of Significance
• Catastrophic cancellation
• Multiprecision libraries
• Arithmetic benchmarks

Computation

• Siegfried Rump Example
• Summation Example
• Convergence Stability

Compilation

• Value Safety
• Optimizations Affecting Value Safety
• Full Compliance to IEEE 754
• Default Compliance to IEEE 754
• Relaxed Compliance to IEEE 754
• Fast Math
• CPU

References

• CppCon 2015: John Farrier “Demystifying Floating Point"
• An Introduction To Floating Point Math - Martin Hořeňovský - NDC TechTown 2022
• Floating point computations today and in the future - Boguslaw Cyganek - Meeting C++ 2022
• A refresher on the floating-point computations and the standard library. - Boguslaw Cyganek
• Random ASCII – tech blog of Bruce Dawson
• University of Cambridge: Floating-Point Computation
• Onboarding floating-point