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Concept# Expression (mathematics)

Summary

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Many authors distinguish an expression from a formula, the former denoting a mathematical object, and the latter denoting a statement about mathematical objects. For example, 8x-5 is an expression, while 8x-5 \geq 5x-8 is a formula. However, in modern mathematics, and in particular in computer algebra, formulas are viewed as expressions that can be evaluated to true or false, depending on the values that are given to the variables occurring in the expressions. For example 8x-5 \geq 5x-8 takes the value false if x is given a value less than –1, and the value true otherwise.

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Modern online services are shifting away from monolithic applications to loosely-coupled microservices because of their improved scalability, reliability, programmability and development velocity. Microservices communicating over the datacenter network require data transformation (DT) to convert messages back and forth between their internal formats. This work identifies DT as a bottleneck due to reductions in latency of the surrounding system components, namely application runtimes, protocol stacks, and network hardware. We therefore propose Optimus Prime (OP), a programmable DT accelerator that uses a novel abstraction, an in-memory schema, to represent DT operations. The schema is compatible with today's DT frameworks and enables any compliant accelerator to perform the transformations comprising a request in parallel. Our evaluation shows that OP's DT throughput matches the line rate of today's NICs and has 60x higher throughput compared to software, at a tiny fraction of the CPU's silicon area and power. We also evaluate a set of microservices running on Thrift, and show up to 30% reduction in service latency.

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