Implement username availability checker

Outlined here: https://github.com/vector-im/riot-web/issues/3605#issuecomment-298679388

```HTTP
GET /_matrix/.../register/available
{
    "username": "desiredlocalpart123"
}
```

If available, the response looks like
```HTTP
HTTP/1.1 200 OK
{
    "available": true
}
```

Otherwise,
```HTTP
HTTP/1.1 429
{
    "errcode": "M_LIMIT_EXCEEDED",
    "error": "Too Many Requests",
    "retry_after_ms": 2000
}
```
or
```HTTP
HTTP/1.1 400
{
    "errcode": "M_USER_IN_USE",
    "error": "User ID already taken."
}

```
or
```HTTP
HTTP/1.1 400
{
    "errcode": "M_INVALID_USERNAME",
    "error": "Some reason for username being invalid"
}
```

synapse/rest/client/v2_alpha/register.py

@@ -31,6 +31,7 @@ import logging
 import hmac
 from hashlib import sha1
 from synapse.util.async import run_on_reactor
+from synapse.util.ratelimitutils import FederationRateLimiter
 
 
 # We ought to be using hmac.compare_digest() but on older pythons it doesn't
@@ -115,6 +116,40 @@ class MsisdnRegisterRequestTokenRestServlet(RestServlet):
         defer.returnValue((200, ret))
 
 
+class UsernameAvailabilityRestServlet(RestServlet):
+    PATTERNS = client_v2_patterns("/register/available")
+
+    def __init__(self, hs):
+        """
+        Args:
+            hs (synapse.server.HomeServer): server
+        """
+        super(UsernameAvailabilityRestServlet, self).__init__()
+        self.hs = hs
+        self.registration_handler = hs.get_handlers().registration_handler
+        self.ratelimiter = FederationRateLimiter(
+            hs.get_clock(),
+            window_size=2000, # Time window of 2s
+            sleep_limit=1, # Artificially delay requests if rate > sleep_limit/window_size
+            sleep_msec=1000, # Amount of artificial delay to apply
+            reject_limit=1, # Error with 429 if more than reject_limit requests are queued
+            concurrent_requests=1, # Allow 1 request at a time
+        )
+
+    @defer.inlineCallbacks
+    def on_GET(self, request):
+        ip = self.hs.get_ip_from_request(request)
+        with self.ratelimiter.ratelimit(ip) as wait_deferred:
+            yield wait_deferred
+
+            body = parse_json_object_from_request(request)
+            assert_params_in_request(body, ['username'])
+
+            yield self.registration_handler.check_username(body['username'])
+
+            defer.returnValue((200, {"available": True}))
+
+
 class RegisterRestServlet(RestServlet):
     PATTERNS = client_v2_patterns("/register$")
 
@@ -555,4 +590,5 @@ class RegisterRestServlet(RestServlet):
 def register_servlets(hs, http_server):
     EmailRegisterRequestTokenRestServlet(hs).register(http_server)
     MsisdnRegisterRequestTokenRestServlet(hs).register(http_server)
+    UsernameAvailabilityRestServlet(hs).register(http_server)
     RegisterRestServlet(hs).register(http_server)