public async Task CalculateAsync(double param1, double param2)
// CalculateSync is synchronous and cpu-intensive (<10s)
await Task.Run(() => this.CalculateSync(param1, param2))).ConfigureAwait(false);
Is there any performance benefit in using Task.Run in an async Web API Controller for cpu-bound operations?
Zero. None. In fact, you're hindering performance by spawning a new thread. Within the context of a web application, spawning a thread is not the same thing as running in the "background". This is due to the nature of a web request. When there's an incoming request, a thread is taken from the pool to service the request. Using async allows the thread to be returned before the end of the request, if and only if the thread is in a wait-state, i.e. idle. Spawning a thread to do work on, effectively idles the primary thread, allowing it to be returned to the pool, but you've still got an active thread. Returning the original thread to the pool does nothing at that point. Then, when the new thread finishes its work, you've got to request a main thread back from the pool, and finally return the response. The response cannot be returned until all work has completed, so whether you use 1 thread or a hundred, async or sync, the response cannot be returned until everything finishes. Therefore, using additional threads does nothing but add overhead.
Does ConfigureAwait(false) really avoid the creation of an extra thread?
No, or more appropriately, it's not about that.
ConfigureAwait is just an optimization hint, and only determines whether the original context is maintained between thread jumps. Long and short, it has nothing to do with the creation of a thread, and at least in the context of an ASP.NET application, has negligible performance impact either way.