This presentation delves into the fascinating and sometimes aggravating world of numerical data types, exploring the evolution, strengths, and weaknesses of decimal, fixed point, floating point, and shared exponent formats over the past 70 years.

Moving through various Eras, from the early computing era, where arithmetic operations were often emulated using cumbersome decimal arithmetic, to the widespread adoption of floating-point representations in modern computing. Starting with decimal data types, we will examine their suitability for financial and commercial applications where precision and exactness are paramount. Next, we will discuss fixed-point data types and their application in real-time systems and embedded devices where computational resources are limited. A significant portion of the presentation will be dedicated to floating-point data types, including the IEEE 754 standard and its evolution. We will investigate the trade-offs between range, precision, and performance, as well as the challenges of accurately representing real numbers in a finite digital format.

Recent developments in floating-point formats, such as the IEEE 754-2019 standard, Google's Brain Float 16, NVIDIA's 19 bit TensorFloat 32, and the 18 flavors of 8 bit floating point, will also be covered. Additionally, we will explore the concept of shared exponent data types, including block float and posits which have gained popularity in recent years. We will analyze the potential benefits and drawbacks of these formats, including their impact on numerical computations and their suitability for specific applications. Throughout the presentation, we will draw on real-world examples, benchmarks, and use cases to illustrate the practical implications of choosing the right data type for a particular task. By the end of this talk, it is the hope of the speaker that attendees will gain a deeper understanding of the history, trade-offs, and best practices for working with non integer data types, enabling them to make informed decisions in their own projects and applications.