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Module Timing_wheel_intf.S.Priority_queue

module Priority_queue: sig .. end
At the heart of a timing wheel is a priority queue in which the keys are non-negative integers corresponding to the intervals of time. The priority queue is unlike a typical priority queue in that rather than having a "delete min" operation, it has a nondecreasing minimum allowed key, which corresponds to the current time, and an increase_min_allowed_key operation, which implements advance_clock. increase_min_allowed_key as a side effect removes all elements from the timing wheel whose key is smaller than the new minimum, which implements firing the alarms whose time has expired.

Adding elements to and removing elements from a timing wheel takes constant time, unlike a heap-based priority queue which takes log(N), where N is the number of elements in the heap. increase_min_allowed_key takes time proportional to the amount of increase in the min-allowed key, as compared to log(N) for a heap. It is these performance differences that motivate the existence of timing wheels and make them a good choice for maintaing a set of alarms. With a timing wheel, one can support any number of alarms paying constant overhead per alarm, while paying a small constant overhead per unit of time passed.

As the minimum allowed key increases, the timing wheel does a lazy radix sort of the element keys, with level 0 handling the least significant b_0 bits in a key, and each subsequent level i handling the next most significant b_i bits. The levels hold increasingly larger ranges of keys, where the union of all the levels can hold any key from min_allowed_key t to max_allowed_key t. When a key is added to the timing wheel, it is added at the lowest possible level that can store the key. As the minimum allowed key increases, timing-wheel elements move down levels until they reach level 0, and then are eventually removed.

type 'a t 
type 'a priority_queue = 'a t 
module Elt: sig .. end
include Invariant.S1
val create : ?level_bits:Timing_wheel_intf.S.Level_bits.t ->
       dummy:'a -> unit -> 'a t
create ?level_bits ~dummy () creates a new empty timing wheel, t, with length t = 0 and min_allowed_key t = 0.

dummy is a dummy value that will never be returned by any operation, but that allows the implementation to be more efficient.

val length : 'a t -> int
length t returns the number of elements in the timing wheel.
val is_empty : 'a t -> bool
is_empty t is length t = 0
val max_representable_key : int
To avoid issues with arithmetic overflow, the implementation restricts keys to being between 0 and max_representable_key, where: 

          max_representable_key = 1 lsl Level_bits.max_num_bits - 1

This is different from max_allowed_key t, which gives the maximum key that can currently be stored in t. The maximum allowed key is never larger than the maximum representable key, but may be smaller.

val min_allowed_key : 'a t -> int
min_allowed_key t is the minimum key that can be stored in t. This only indicates the possibility; there need not be an element elt in t with Elt.key elt = min_allowed_key t. This is not the same as the "min_key" operation in a typical priority queue.

min_allowed_key t can increase over time, via calls to increase_min_allowed_key. It is guaranteed that min_allowed_key t <= max_representable_key.

val max_allowed_key : 'a t -> int
max_allowed_key t is the maximum allowed key that can be stored in t. As min_allowed_key increases, so does max_allowed_key; however it is not the case that max_allowed_key t - min_allowed_key t is a constant. It is guaranteed that max_allowed_key t >= min (max_representable_key, min_allowed_key t + 2^B - 1, where B is the sum of the b_i in level_bits. It is also guaranteed that max_allowed_key t <= max_representable_key.
val min_elt : 'a t ->
       'a Elt.t option
min_elt t returns an element in t that has the minimum key, if t is nonempty. min_elt takes time proportional to the size of the timing-wheel data structure in the worst case. It is implemented via a linear search.

min_key t returns the key of min_elt t, if any.

val min_key : 'a t -> int option
val add : 'a t ->
       key:int -> 'a -> 'a Elt.t
add t ~key value adds a new value to t and returns an element that can later be supplied to remove the element from t. add raises if key < min_allowed_key t || key > max_allowed_key t.
val remove : 'a t ->
       'a Elt.t -> unit
remove t elt removes elt from t. It is an error if elt is not currently in t, and this error may or may not be detected.
val increase_min_allowed_key : 'a t ->
       key:int ->
       handle_removed:('a Elt.t -> unit) -> unit
increase_min_allowed_key t ~key ~handle_removed increases the minimum allowed key in t to key, and removes all elements with keys less than key, applying handle_removed to each element that is removed. If key <= min_allowed_key t, then increase_min_allowed_key does nothing. Otherwise, if increase_min_allowed_key returns successfully, min_allowed_key t = key.

increase_min_allowed_key raises if key > max_representable_key.

increase_min_allowed_key takes time proportional to key - min_allowed_key t, although possibly less time.

Behavior is unspecified if handle_removed accesses t in any way other than Elt functions.

val iter : 'a t ->
       f:('a Elt.t -> unit) -> unit
val sexp_of_t : ('a -> Sexplib.Sexp.t) ->
       'a t -> Sexplib.Sexp.t

An Elt.t represents an element that was added to a timing wheel.

create ?level_bits ~dummy () creates a new empty timing wheel, t, with length t = 0 and min_allowed_key t = 0.

dummy is a dummy value that will never be returned by any operation, but that allows the implementation to be more efficient.

length t returns the number of elements in the timing wheel.

is_empty t is length t = 0

To avoid issues with arithmetic overflow, the implementation restricts keys to being between 0 and max_representable_key, where: 

          max_representable_key = 1 lsl Level_bits.max_num_bits - 1

This is different from max_allowed_key t, which gives the maximum key that can currently be stored in t. The maximum allowed key is never larger than the maximum representable key, but may be smaller.

min_allowed_key t is the minimum key that can be stored in t. This only indicates the possibility; there need not be an element elt in t with Elt.key elt = min_allowed_key t. This is not the same as the "min_key" operation in a typical priority queue.

min_allowed_key t can increase over time, via calls to increase_min_allowed_key. It is guaranteed that min_allowed_key t <= max_representable_key.

max_allowed_key t is the maximum allowed key that can be stored in t. As min_allowed_key increases, so does max_allowed_key; however it is not the case that max_allowed_key t - min_allowed_key t is a constant. It is guaranteed that max_allowed_key t >= min (max_representable_key, min_allowed_key t + 2^B - 1, where B is the sum of the b_i in level_bits. It is also guaranteed that max_allowed_key t <= max_representable_key.

min_elt t returns an element in t that has the minimum key, if t is nonempty. min_elt takes time proportional to the size of the timing-wheel data structure in the worst case. It is implemented via a linear search.

min_key t returns the key of min_elt t, if any.

add t ~key value adds a new value to t and returns an element that can later be supplied to remove the element from t. add raises if key < min_allowed_key t || key > max_allowed_key t.

remove t elt removes elt from t. It is an error if elt is not currently in t, and this error may or may not be detected.

increase_min_allowed_key t ~key ~handle_removed increases the minimum allowed key in t to key, and removes all elements with keys less than key, applying handle_removed to each element that is removed. If key <= min_allowed_key t, then increase_min_allowed_key does nothing. Otherwise, if increase_min_allowed_key returns successfully, min_allowed_key t = key.

increase_min_allowed_key raises if key > max_representable_key.

increase_min_allowed_key takes time proportional to key - min_allowed_key t, although possibly less time.

Behavior is unspecified if handle_removed accesses t in any way other than Elt functions.