Lecture
This lecture introduces the concept of associative operations in parallel programming, explaining the properties of associativity and commutativity. Various examples from mathematics, such as addition, multiplication, and set operations, are used to illustrate these concepts. The lecture also covers the implications of associativity on reduce operations, the difference between commutativity and associativity, and the challenges of preserving associativity when combining operations. Additionally, the lecture explores the limitations of floating-point arithmetic in maintaining associativity and commutativity. Finally, a method to make an operation commutative using a total ordering is presented.