CoDaS-HEP2023:

Floating-point Arithmetic is not Real

Outline

• Real numbers
• Holes in the Value Range
• Floating-point Number Systems
• The IEEE Standard 754
• Limits of Floating-point Arithmetics
• Floating-point Guidelines
• Approximate Math

Goals

• Basic understanding of computer representation of numbers
• Basic understanding of floating point arithmetic
• Consequences of floating point arithmetic for scientific computing
• Basic understanding about fast math