Module type Timing_wheel_intf.S

module type S = sig .. end

type 'a t 

type 'a timing_wheel = 'a t 

module Alarm: sig .. end

include Invariant.S1

module Level_bits: sig .. end

val create : ?level_bits:Level_bits.t ->
       start:Timing_wheel_intf.Time.t ->
       alarm_precision:Timing_wheel_intf.Time.Span.t ->
       dummy:'a -> unit -> 'a t

val alarm_precision : 'a t -> Timing_wheel_intf.Time.Span.t

val now : 'a t -> Timing_wheel_intf.Time.t

val start : 'a t -> Timing_wheel_intf.Time.t

val is_empty : 'a t -> bool

val length : 'a t -> int

val iter : 'a t ->
       f:('a Alarm.t -> unit) -> unit

val interval_start : 'a t ->
       Timing_wheel_intf.Time.t -> Timing_wheel_intf.Time.t

val advance_clock : 'a t ->
       to_:Timing_wheel_intf.Time.t ->
       handle_fired:('a Alarm.t -> unit) -> unit

val alarm_upper_bound : 'a t -> Timing_wheel_intf.Time.t

val add : 'a t ->
       at:Timing_wheel_intf.Time.t -> 'a -> 'a Alarm.t

val remove : 'a t -> 'a Alarm.t -> unit

val next_alarm_fires_at : 'a t -> Timing_wheel_intf.Time.t option

module Priority_queue: sig .. end

val sexp_of_t : ('a -> Sexplib.Sexp.t) -> 'a t -> Sexplib.Sexp.t

A timing wheel can handle approximately 2 ** num_bits t intervals/keys beyond the current minimum time/key, where num_bits t = b_0 + b_1 + ....

One can use a Level_bits.t to trade off run time and space usage of a timing wheel. For a fixed num_bits, as the number of levels increases, the length of the levels decreases and the timing wheel uses less space, but the constant factor for the running time of add and increase_min_allowed_key increases.

In create_exn bits, it is an error if any of the b_i in bits has b_i <= 0, or if the sum of the b_i in bits is greater than max_num_bits.

default returns the default value of level_bits used by Timing_wheel.create and Timing_wheel.Priority_queue.create. It varies based on the machine's word size. Here are the the values and the amount of space used for the level arrays.

| word | bits used | level_bits | space used | |------+-----------+--------------------------+-------------| | 32 | 29 | 10; 10; 9 | < 4k words | | 64 | 61 | 11; 10; 10; 10; 10; 10 | < 10k words |

num_bits t is the sum of the b_i in t.

durations t ~alarm_precision returns the durations of the levels in t, assuming that each interval has duration alarm_precision.

create ~start ~alarm_precision ~dummy () creates a new timing wheel with current time start. The dummy value is a performance optimization; it would be a bug if the timing wheel ever returned the dummy value to client code.

For a fixed level_bits, a smaller (i.e. more precise) alarm_precision decreases the representable range of times/keys and increases the constant factor for advance_clock.

create raises if alarm_precision <= 0.

Accessors

One can think of a timing wheel as a set of alarms. Here are various container functions along those lines.

interval_start t time returns the time at the start of the half-open interval containing time, i.e. the largest time less than or equal to time that is of the form start t + k * alarm_precision t. interval_start raises if time < start t or time is too far in the future to represent.

advance_clock t ~to_ ~handle_fired advances t's clock to to_. It fires and removes all alarms a in t with Time.(<) (Alarm.at a) (interval_start t to_) applying handle_fired to each such a.

If to_ <= now t, then advance_clock does nothing.

advance_clock fails if to_ is too far in the future to represent.

Behavior is unspecified if handle_fired accesses t in any way other than Alarm functions.

alarm_upper_bound t returns the upper bound on an at that can be supplied to add. alarm_upper_bound t is not constant; its value increases as now t increases.

add t ~at a adds a new value a to t and returns an alarm that can later be supplied to remove the alarm from t. add raises if at < now t || at >= alarm_upper_bound t.

remove t alarm removes alarm from t. It is an error to remove an alarm that is not in t.

next_alarm_fires_at t returns the minimum time to which the clock can be advanced such that an alarm will fire, or None if t has no alarms. If next_alarm_fires_at t = Some next, then for the minimum alarm time min that occurs in t, it is guaranteed that: next - alarm_precision t <= min < next.

Timing wheel is implemented as 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.

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.