One option is to use the `@cached_function`

decorator which saves the result of already computed values:

```
sage: @cached_function
....: def fib(n):
....: print('computation performed')
....: if n == 0 or n == 1:
....: return 1
....: else:
....: return fib(n-1) + fib(n-2)
....:
sage: fib(5)
computation performed
computation performed
computation performed
computation performed
computation performed
computation performed
8
sage: fib(5) # no computation is performed
8
```

Internally, results are saved in a dictionary where keys are of the form `(*args,**kwds`

):

```
sage: fib.cache
{((1,), ()): 1, ((0,), ()): 1, ((2,), ()): 2, ((3,), ()): 3, ((4,), ()): 5, ((5,), ()): 8}
```

See the documentation of

```
sage: cached_function?
```

Then, you can save the `fib`

function locally:

```
sage: save(fib, 'fib')
sage: ls fib*
fib.sobj
```

Then, in the same or in another Sage session, you can reload that function and its previous cache is still there:

```
sage: gib = load('fib.sobj')
sage: gib.cache
{((1,), ()): 1, ((0,), ()): 1, ((2,), ()): 2, ((3,), ()): 3, ((4,), ()): 5, ((5,), ()): 8}
sage: gib(5)
8
```

Which means that the default behavior is to include the cache in the pickle (documentation says one should write `@cached_function(do_pickle=True)`

which does not seem necessary). Behind the scene, `save`

is using `dumps`

to create the file `fib.sobj`

which contains binary code looking something like :

```
sage: dumps(fib)
b'x\x9cm\x8c\xbb\x12@0\x10\x00\xe39&\x7f\xa2\xc9W\xa8\x15*\xddM\x9c\xe0\x06\xc7M\xe8u~\xdb\xab\xd5\xed\x16\xbbG\x88\xde\xf6\xce\xcc\xe4\xd1\xa0\xc5\xc1u;\xa3\x86\x17[xd\xa3\x85a\xe7\x95p\x9c\x9c\x16UgJ)\x80\xd9\x12\x03HPG\xb7v\xd4\xc8\xff\xa9\\\xbe\x92\xb8/\x087-Q^I|JRIj.\xbe\xa8)\xf2'
```

which can also be loaded:

```
sage: hib = loads(dumps(fib))
sage: hib.cache
{((1,), ()): 1, ((0,), ()): 1, ((2,), ()): 2, ((3,), ()): 3, ((4,), ()): 5, ((5,), ()): 8}
```

If the cache becomes very heavy in memory, then saving and loading the function will take long time. I think I already heard of a decorator that query automatically a file if result is already computed or saves automatically to the file (or database) if it is a new computation, but I can't remember what/where I saw that, whether it was a ticket or just a discussion. I am sure people involved in LMFDB project (which computes stuff on the fly if not already in a database) have an idea about that.