Most problems that are good targets for parallelization involve doing calculations in tight loops. These places are good for all kinds of performance optimizations, from hoisting conditionals out of them to fine-tuning compiler hints, which we will do here.

Being a dynamic language, Clojure doesn't require type declarations. However, if we know what types we are using, we can get better performance by including type hints in our code. This is helpful for object types, where Clojure can then resolve method calls at compile time, and also for primitive types, where Clojure can generate well-tuned code that doesn't include boxing, or wrapping the primitive type in a heavier Java object. For more information about this, see the documentation about interacting with Java from Clojure for information about type hints and working with Java primitives (http://clojure.org/java_interop). Type hints are expressed as metadata tags for return types and object types. We'll see examples...