Module type Timing_wheel_intf.Timing_wheel

module type Timing_wheel = sig .. end

module Time: Timing_wheel_intf.Timing_wheel_time 
type 'a t 
type 'a timing_wheel = 'a t 
type 'a t_now = 'a t 
<:sexp_of< _ t_now >> displays only now t, not all the alarms.
module Interval_num: Timing_wheel_intf.Interval_num 
module Alarm: sig .. end
include Invariant.S1
module Level_bits: sig .. end
module Config: sig .. end
val create : config:Config.t ->
start:Time.t -> 'a t
create ~config ~start creates a new timing wheel with current time start.

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.

val alarm_precision : 'a t -> Time.Span.t
Accessors
val now : 'a t -> Time.t
val start : 'a t -> Time.t
val is_empty : 'a t -> bool
One can think of a timing wheel as a set of alarms. Here are various container functions along those lines.
val length : 'a t -> int
val iter : 'a t ->
f:('a Alarm.t -> unit) -> unit
val interval_num : 'a t ->
Time.t -> Timing_wheel_intf.Interval_num.t
interval_num t time returns the number of the interval that time is in, where 0 is the interval that starts at start. interval_num raises if time is too far in the past or future to represent.

now_interval_num t equals interval_num t (now t).

val now_interval_num : 'a t -> Timing_wheel_intf.Interval_num.t
val interval_num_start : 'a t ->
Timing_wheel_intf.Interval_num.t -> Time.t
interval_num_start t n is the start of the n'th interval in t, i.e.:

        start t + n * alarm_precision t
      

interval_start t time is the start of the half-open interval containing time, i.e.:

        interval_num_start t (interval_num t time)
      

interval_start raises in the same cases that interval_num does.

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

val fire_past_alarms : 'a t ->
handle_fired:('a Alarm.t -> unit) -> unit
fire_past_alarms t ~handle_fired fires and removes all alarms a in t with Time.( <= ) (Alarm.at t a) (now t), applying handle_fired to each such a.

fire_past_alarms visits all alarms in interval now_interval_num, to check their Alarm.at.

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

val alarm_upper_bound : 'a t -> Time.t
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.
val add : 'a t ->
at:Time.t -> 'a -> 'a Alarm.t
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 interval_num t at < now_interval_num t || at >= alarm_upper_bound t.

add_at_interval_num t ~at a is equivalent to add t ~at:(interval_num_start t at) a.

val add_at_interval_num : 'a t ->
at:Timing_wheel_intf.Interval_num.t ->
'a -> 'a Alarm.t
val mem : 'a t ->
'a Alarm.t -> bool
val remove : 'a t ->
'a Alarm.t -> unit
remove t alarm removes alarm from t. remove raises if not (mem t alarm).
val reschedule : 'a t ->
'a Alarm.t -> at:Time.t -> unit
reschedule t alarm ~at mutates alarm so that it will fire at at, i.e. so that Alarm.at t alarm = at. reschedule raises if not (mem t alarm) or if at is an invalid time for t, in the same situations that add raises.

reschedule_at_interval_num t alarm ~at is equivalent to:

        reschedule t alarm ~at:(interval_num_start t at)
      

val reschedule_at_interval_num : 'a t ->
'a Alarm.t ->
at:Timing_wheel_intf.Interval_num.t -> unit
val clear : 'a t -> unit
clear t removes all alarms from t.
val next_alarm_fires_at : 'a t -> Time.t option
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.

Implementation details

The rest of this interface is not intended to be used with Timing_wheel, but is a separate data structure used to implement Timing_wheel, and may find use elsewhere.

module Priority_queue: sig .. end
Timing wheel is implemented as a priority queue in which the keys are non-negative integers corresponding to the intervals of time.
val sexp_of_t : ('a -> Sexplib.Sexp.t) ->
'a t -> Sexplib.Sexp.t
val sexp_of_t_now : ('a -> Sexplib.Sexp.t) ->
'a t_now -> Sexplib.Sexp.t
<:sexp_of< _ t_now >> displays only now t, not all the alarms.

null () returns an alarm t such that not (mem timing_wheel t) for all timing_wheels.

All Alarm functions will raise if not (Timing_wheel.mem timing_wheel t).

The timing-wheel implementation uses an array of "levels", where level i is an array of length 2^b_i, where the b_i are the "level bits" specified via Level_bits.create_exn [b_0, b_1; ...].

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.

max_num_bits is how many bits in a key the timing wheel can use, i.e. 61. We subtract 3 for the bits in the word that we won't use:



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.

          default = [11; 10; 10; 10; 10; 10]
        

This default uses 61 bits, i.e. max_num_bits, and less than 10k words of memory.

num_bits t is the sum of the b_i in t.

create raises if alarm_precision <= 0.

accessors

default is create ().

durations t returns the durations of the levels in t

create ~config ~start creates a new timing wheel with current time start.

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.

Accessors

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

interval_num t time returns the number of the interval that time is in, where 0 is the interval that starts at start. interval_num raises if time is too far in the past or future to represent.

now_interval_num t equals interval_num t (now t).

interval_num_start t n is the start of the n'th interval in t, i.e.:

        start t + n * alarm_precision t
      

interval_start t time is the start of the half-open interval containing time, i.e.:

        interval_num_start t (interval_num t time)
      

interval_start raises in the same cases that interval_num does.

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 t 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.

fire_past_alarms t ~handle_fired fires and removes all alarms a in t with Time.( <= ) (Alarm.at t a) (now t), applying handle_fired to each such a.

fire_past_alarms visits all alarms in interval now_interval_num, to check their Alarm.at.

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 interval_num t at < now_interval_num t || at >= alarm_upper_bound t.

add_at_interval_num t ~at a is equivalent to add t ~at:(interval_num_start t at) a.

remove t alarm removes alarm from t. remove raises if not (mem t alarm).

reschedule t alarm ~at mutates alarm so that it will fire at at, i.e. so that Alarm.at t alarm = at. reschedule raises if not (mem t alarm) or if at is an invalid time for t, in the same situations that add raises.

reschedule_at_interval_num t alarm ~at is equivalent to:

        reschedule t alarm ~at:(interval_num_start t at)
      


clear t removes all alarms from 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.

Implementation details

The rest of this interface is not intended to be used with Timing_wheel, but is a separate data structure used to implement Timing_wheel, and may find use elsewhere.

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 () creates a new empty timing wheel, t, with length t = 0 and min_allowed_key t = 0.

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

is_empty t is length t = 0

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 <= Key.max_representable.

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 (Key.max_representable, 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 <= Key.max_representable.

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.

change_key t elt ~key changes the key of elt to key. change_key raises if not (mem t elt) || key < min_allowed_key t || key > max_allowed_key t.

clear t removes all elts from t.

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 > Key.max_representable.

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.