I've been programming a long time, and the programs I see, when they run out of memory, attempt to clean up and exit, i.e. fail gracefully. I can't remember the last time I saw one actually attempt to recover and continue operating normally.
So much processing relies on being able to successfully allocate memory, especially in garbage collected languages, it seems that out of memory errors should be classified as non-recoverable. (Non-recoverable errors include things like stack overflows.)
What is the compelling argument for making it a recoverable error?
OutOfMemoryError exception. Usually, this error is thrown when there is insufficient space to allocate an object in the Java heap. In this case, The garbage collector cannot make space available to accommodate a new object, and the heap cannot be expanded further.
A recoverable error is an error that does not cause a system failure, but may cause data loss. For example, a user may receive a prompt about an overflow error occurring, but the computer or electronic device continues to operate.
Out of memory (OOM) is an often undesired state of computer operation where no additional memory can be allocated for use by programs or the operating system.
It really depends on what you're building.
It's not entirely unreasonable for a webserver to fail one request/response pair but then keep on going for further requests. You'd have to be sure that the single failure didn't have detrimental effects on the global state, however - that would be the tricky bit. Given that a failure causes an exception in most managed environments (e.g. .NET and Java) I suspect that if the exception is handled in "user code" it would be recoverable for future requests - e.g. if one request tried to allocate 10GB of memory and failed, that shouldn't harm the rest of the system. If the system runs out of memory while trying to hand off the request to the user code, however - that kind of thing could be nastier.
In a library, you want to efficiently copy a file. When you do that, you'll usually find that copying using a small number of big chunks is much more effective than copying a lot of smaller ones (say, it's faster to copy a 15MB file by copying 15 1MB chunks than copying 15'000 1K chunks).
But the code works with any chunk size. So while it may be faster with 1MB chunks, if you design for a system where a lot of files are copied, it may be wise to catch OutOfMemoryError and reduce the chunk size until you succeed.
Another place is a cache for Object stored in a database. You want to keep as many objects in the cache as possible but you don't want to interfere with the rest of the application. Since these objects can be recreated, it's a smart way to conserve memory to attach the cache to an out of memory handler to drop entries until the rest of the app has enough room to breathe, again.
Lastly, for image manipulation, you want to load as much of the image into memory as possible. Again, an OOM-handler allows you to implement that without knowing in advance how much memory the user or OS will grant your code.
[EDIT] Note that I work under the assumption here that you've given the application a fixed amount of memory and this amount is smaller than the total available memory excluding swap space. If you can allocate so much memory that part of it has to be swapped out, several of my comments don't make sense anymore.
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