'Natural' normally means 'positive integer' in mathematics. It is therefore strange to implement it on signed integer types. 'Integer' is probably a better choice.
This adds the following methods to ints and uints:
- div
- modulo
- div_mod
- quot_rem
- gcd
- lcm
- divisible_by
- is_even
- is_odd
I have not implemented Natural for BigInt and BigUInt because they're a little over my head.
The current protocol is very comparable to Python, where `.__iter__()` returns an iterator object which implements `.__next__()` and throws `StopIteration` on completion. `Option` is much cleaner than using a exceptions as a flow control hack though. It requires that the container is frozen so there's no worry about invalidating them.
Advantages over internal iterators, which are functions that are passed closures and directly implement the iteration protocol:
* Iteration is stateful, so you can interleave iteration over arbitrary containers. That's needed to implement algorithms like zip, merge, set union, set intersection, set difference and symmetric difference. I already used this internally in the `TreeMap` and `TreeSet` implementations, but regions and traits weren't solid enough to make it generic yet.
* They provide a universal, generic interface. The same trait is used for a forward/reverse iterator, an iterator over a range, etc. Internal iterators end up resulting in a trait for each possible way you could iterate.
* They can be composed with adaptors like `ZipIterator`, which also implement the same trait themselves.
The disadvantage is that they're a pain to write without support from the compiler for compiling something like `yield` to a state machine. :)
This can coexist alongside internal iterators since both can use the current `for` protocol. It's easier to write an internal iterator, but external ones are far more powerful/useful so they should probably be provided whenever possible by the standard library.
## Current issues
#5801 is somewhat annoying since explicit type hints are required.
I just wanted to get the essentials working well, so I haven't put much thought into making the naming concise (free functions vs. static `new` methods, etc.).
Making an `Iterable` trait seems like it will have to be a long-term goal, requiring type system extensions. At least without resorting to objects which would probably be unacceptably slow.
This restores the trait that was lost in 216e85fadf. It will eventually be broken up into a more fine-grained trait hierarchy in the future once a design can be agreed upon.
Kills some warnings, and implements str::each_char_reverse so that it actually iterates. The test case wasn't detecting a failure, since the loop body was never executed.
This is an implementation of a map and set for integer keys. It's an ordered container (by byte order, which is sorted order for integers and byte strings when done in the right direction) with O(1) worst-case lookup, removal and insertion. There's no rebalancing or rehashing so it's actually O(1) without amortizing any costs.
The fanout can be adjusted in multiples of 2 from 2-ary through 256-ary, but it's hardcoded at 16-ary because there isn't a way to expose that in the type system yet. To keep things simple, it also only allows `uint` keys, but later I'll expand it to all the built-in integer types and byte arrays.
There's quite a bit of room for performance improvement, along with the boost that will come with dropping the headers on `Owned` `~` and getting rid of the overhead from the stack switches to the allocator. It currently does suffix compression for a single node and then splits into two n-ary trie nodes, which could be replaced with an array for at least 4-8 suffixes before splitting it. There's also the option of doing path compression, which may be a good or a bad idea and depends a lot on the data stored.
I want to share the test suite with the other maps so that's why I haven't duplicated all of the existing integer key tests in this file. I'll send in another pull request to deal with that.
Current benchmark numbers against the other map types:
TreeMap:
Sequential integers:
insert: 0.798295
search: 0.188931
remove: 0.435923
Random integers:
insert: 1.557661
search: 0.758325
remove: 1.720527
LinearMap:
Sequential integers:
insert: 0.272338
search: 0.141179
remove: 0.190273
Random integers:
insert: 0.293588
search: 0.162677
remove: 0.206142
TrieMap:
Sequential integers:
insert: 0.0901
search: 0.012223
remove: 0.084139
Random integers:
insert: 0.392719
search: 0.261632
remove: 0.470401
@graydon is using an earlier version of this for the garbage collection implementation, so that's why I added this to libcore. I left out the `next` and `prev` methods *for now* because I just wanted the essentials first.
