Asserting Values in Range

Introduction

With the advent of digital computation, one of the first applications of programs was to solve problems within the scientific computing field. Scientific computing focuses on operations with real numbers. Unfortunately, perfectly representing any arbitrary real number within a machine architecture is impossible. As a result, numerous real number representation schemes have been proposed and implemented to ensure such representations are as accurate as possible.

Floating-point numbers are a data type that represents real numbers in machine architecture. Understanding the detailed mechanics of floating-point numbers is not necessary for unit testing. However, it is vital to understand the potential pitfalls when dealing with floating-point numbers, so that when one of our floating-point assertions doesn’t pass, we will know how to correct it.

The non-precise nature of floating-point types

The floating-point numeric types all represent real numbers. Real numbers are those that assume any value along a continuous number line. Real numbers can equal a value from negative to positive infinity and may equal an infinitely small or large whole part as well as an infinitely small or large fraction. Examples include the following:

$1$

$5.5$

$42$

$6.787676410059283745$

$7.25$

$\sqrt{2}$ ...