What Every Programmer Should Know About Floating Point Arithmetic

📄 Project Abstract

Almost every computer language has floating point data types and allows basic arithmetic operations, such as addition, multiplication, division and remainder, to operate on objects of this type. Unfortunately, the execution of these operations will generally give an approximate answer rather than an exact answer as a result of the different formats of representing numbers (integers, floats and doubles). For instance, the expression (a*b)* c = a*(b*c) is true in standard arithmetic but not usually true in floating point arithmetic. A typical computer program can involve millions of arithmetic operations each of which may have a small error. Therefore, the errors that can be negligible in each arithmetic operation can be devastating when accumulated over a long calculation. The aim of this project is to illustrate the consequences of the above observation on computer arithmetic and also the effects of this on the design and implementation of software. A second aim is to build an online i...