⚠️ Warning: This is a draft ⚠️

This means it might contain formatting issues, incorrect code, conceptual problems, or other severe issues.

If you want to help to improve and eventually enable this page, please fork RosettaGit's repository and open a merge request on GitHub.

In [[object-oriented programming]] an object is active when its state depends on clock. Usually an active object encapsulates a [[task]] that updates the object's state. To the outer world the object looks like a normal object with methods that can be called from outside. Implementation of such methods must have a certain synchronization mechanism with the encapsulated task in order to prevent object's state corruption.

A typical instance of an active object is an animation widget. The widget state changes with the time, while as an object it has all properties of a normal widget.

Implement an active integrator object. The object has an input and output. The input can be set using the method ''Input''. The input is a function of time. The output can be queried using the method ''Output''. The object integrates its input over the time and the result becomes the object's output. So if the input is ''K''(''t'') and the output is ''S'', the object state ''S'' is changed to ''S'' + (''K''(''t''1) + ''K''(''t''0)) * (''t''1 - ''t''0) / 2, i.e. it integrates ''K'' using the trapeze method. Initially ''K'' is constant 0 and ''S'' is 0.

In order to test the object:

wait 0.5s

Verify that now the object's output is approximately 0 (the sine has the period of 2s). The accuracy of the result will depend on the [[OS]] scheduler time slicing and the accuracy of the clock.

{{omit from|VBScript}}

procedure Test_Integrator is
type Func is access function (T : Time) return Float;

function Zero (T : Time) return Float is
begin
return 0.0;
end Zero;

Epoch : constant Time := Clock;

function Sine (T : Time) return Float is
begin
return Sin (Pi * Float (T - Epoch));
end Sine;

entry Input  (Value : Func);
entry Output (Value : out Float);
entry Shut_Down;
end Integrator;

K  : Func  := Zero'Access;
S  : Float := 0.0;
F0 : Float := 0.0;
F1 : Float;
T0 : Time  := Clock;
T1 : Time;
begin
loop
select
accept Input (Value : Func) do
K := Value;
end Input;
or accept Output (Value : out Float) do
Value := S;
end Output;
or accept Shut_Down;
exit;
else
T1 := Clock;
F1 := K (T1);
S  := S + 0.5 * (F1 + F0) * Float (T1 - T0);
T0 := T1;
F0 := F1;
end select;
end loop;
end Integrator;

I : Integrator;
S : Float;
begin
I.Input (Sine'Access);
delay 2.0;
I.Input (Zero'Access);
delay 0.5;
I.Output (S);
Put_Line ("Integrated" & Float'Image (S) & "s");
I.Shut_Down;
end Test_Integrator;

Sample output:

Integrated-5.34100E-05s

BBC BASIC

{{works with|BBC BASIC for Windows}}

INSTALL @lib\$+"CLASSLIB"
INSTALL @lib\$+"TIMERLIB"
INSTALL @lib\$+"NOWAIT"

REM Integrator class:
DIM integ{f\$, t#, v#, tid%, @init, @@exit, input, output, tick}
PROC_class(integ{})

REM Methods:
DEF integ.@init integ.f\$ = "0" : integ.tid% = FN_ontimer(10, PROC(integ.tick), 1) : ENDPROC
DEF integ.@@exit PROC_killtimer(integ.tid%) : ENDPROC
DEF integ.input (f\$) integ.f\$ = f\$ : ENDPROC
DEF integ.output = integ.v#
DEF integ.tick integ.t# += 0.01 : integ.v# += EVAL(integ.f\$) : ENDPROC

REM Test:
PROC_new(myinteg{}, integ{})
PROC(myinteg.input) ("SIN(2*PI*0.5*myinteg.t#)")
PROCwait(200)
PROC(myinteg.input) ("0")
PROCwait(50)
PRINT "Final value = " FN(myinteg.output)

Output:

Final value = -1.43349462E-6

C

#include <stdio.h>
#include <stdlib.h>
#include <unistd.h>
#include <math.h>
#include <sys/time.h>

/* no need to lock the object: at worst the readout would be 1 tick off,
which is no worse than integrator's inate inaccuracy */
typedef struct {
double (*func)(double);
struct timeval start;
double v, last_v, last_t;
} integ_t, *integ;

void update(integ x)
{
struct timeval tv;
double t, v, (*f)(double);

f = x->func;
gettimeofday(&tv, 0);
t = ((tv.tv_sec - x->start.tv_sec) * 1000000
+ tv.tv_usec - x->start.tv_usec) * 1e-6;
v = f ? f(t) : 0;
x->v += (x->last_v + v) * (t - x->last_t) / 2;
x->last_t = t;
}

void* tick(void *a)
{
integ x = a;
while (1) {
usleep(100000); /* update every .1 sec */
update(x);
}
}

void set_input(integ x, double (*func)(double))
{
update(x);
x->func = func;
x->last_t = 0;
x->last_v = func ? func(0) : 0;
}

integ new_integ(double (*func)(double))
{
integ x = malloc(sizeof(integ_t));
x->v = x->last_v = 0;
x->func = 0;
gettimeofday(&x->start, 0);
set_input(x, func);
return x;
}

double sine(double t) { return sin(4 * atan2(1, 1) * t); }

int main()
{
integ x = new_integ(sine);
sleep(2);
set_input(x, 0);
usleep(500000);
printf("%g\n", x->v);

return 0;
}

output

-9.99348e-05

C#

{{works with|C# 6}}

using System;

using static System.Diagnostics.Stopwatch;
using static System.Math;

class ActiveObject
{
static double timeScale = 1.0 / Frequency;

Func<double, double> func;
double integral;
double value;
long timestamp0, timestamp;

public ActiveObject(Func<double, double> input)
{
timestamp0 = timestamp = GetTimestamp();
func = input;
value = func(0);
}

public void ChangeInput(Func<double, double> input)
{
{
func = input;
}
}

public double Value
{
get
{
{
return integral;
}
}
}

{
while (true)
{
var newTime = GetTimestamp();
double newValue;

{
newValue = func((newTime - timestamp0) * timeScale);
integral += (newValue + value) * (newTime - timestamp) * timeScale / 2;
}

timestamp = newTime;
value = newValue;
}
}
}

class Program
{
static Func<double, double> Sine(double frequency) =>
t => Sin(2 * PI * frequency * t);

static void Main(string[] args)
{
var ao = new ActiveObject(Sine(0.5));
Sleep(TimeSpan.FromSeconds(2));
ao.ChangeInput(t => 0);
Sleep(TimeSpan.FromSeconds(0.5));
Console.WriteLine(ao.Value);
}
}

Output:

8.62230019255E-5

C++

{{works with|C++14|}}

#include <atomic>
#include <chrono>
#include <cmath>
#include <iostream>
#include <mutex>

using namespace std::chrono_literals;

class Integrator
{
public:
using clock_type = std::chrono::high_resolution_clock;
using dur_t      = std::chrono::duration<double>;
using func_t     = double(*)(double);

explicit Integrator(func_t f = nullptr);
~Integrator();
void input(func_t new_input);
double output() { return integrate(); }

private:
std::atomic_flag continue_;
std::mutex       mutex;

func_t                       func;
double                       state = 0;
//Improves precision by reducing sin result error on large values
clock_type::time_point const beginning = clock_type::now();
clock_type::time_point       t_prev = beginning;

void do_work();
double integrate();
};

Integrator::Integrator(func_t f) : func(f)
{
continue_.test_and_set();
}

Integrator::~Integrator()
{
continue_.clear();
worker.join();
}

void Integrator::input(func_t new_input)
{
integrate();
std::lock_guard<std::mutex> lock(mutex);
func = new_input;
}

void Integrator::do_work()
{
while(continue_.test_and_set()) {
integrate();
}
}

double Integrator::integrate()
{
std::lock_guard<std::mutex> lock(mutex);
auto now = clock_type::now();
dur_t start = t_prev - beginning;
dur_t fin   =    now - beginning;
if(func)
state += (func(start.count()) + func(fin.count())) * (fin - start).count() / 2;
t_prev = now;
return state;
}

double sine(double time)
{
constexpr double PI = 3.1415926535897932;
return std::sin(2 * PI * 0.5 * time);
}

int main()
{
Integrator foo(sine);
foo.input(nullptr);
std::cout << foo.output();
}

output

1.23136e-011

Clojure

(ns active-object

(defn input [integrator k]
(send integrator assoc :k k))

(defn output [integrator]
(:s @integrator))

(defn tick [integrator t1]
(send integrator
(fn [{:keys [k s t0] :as m}]
(assoc m :s (+ s (/ (* (+ (k t1) (k t0)) (- t1 t0)) 2.0)) :t0 t1))))

(defn start-timer [integrator interval]
(let [timer (Timer. true)
start (System/currentTimeMillis)]
(.scheduleAtFixedRate timer
(run [] (tick integrator (double (/ (- (System/currentTimeMillis) start) 1000)))))
(long 0)
(long interval))
#(.cancel timer)))

(defn test-integrator []
(let [integrator (agent {:k (constantly 0.0) :s 0.0 :t0 0.0})
stop-timer (start-timer integrator 10)]
(input integrator #(Math/sin (* 2.0 Math/PI 0.5 %)))
(input integrator (constantly 0.0))
(println (output integrator))
(stop-timer)))

user> (test-integrator)
1.414065859052494E-5

D

{{trans|Java}}

import std.datetime;
import std.math;
import std.stdio;

void main() {
auto func = (double t) => sin(cast(double) PI * t);
Integrator integrator = new Integrator(func);

integrator.setFunc(t => 0.0);

integrator.stop();
writeln(integrator.getOutput());
}

/**
* Integrates input function K over time
* S + (t1 - t0) * (K(t1) + K(t0)) / 2
*/
public class Integrator {
public alias Function = double function (double);

private SysTime start;
private shared bool running;

private Function func;
private shared double t0;
private shared double v0;
private shared double sum = 0.0;

public this(Function func) {
this.start = Clock.currTime();
setFunc(func);
integrate();
}).start();
}

public void setFunc(Function func) {
this.func = func;
v0 = func(0.0);
t0 = 0.0;
}

public double getOutput() {
return sum;
}

public void stop() {
running = false;
}

private void integrate() {
running = true;
while (running) {
update();
}
}

private void update() {
import core.atomic;

Duration t1 = (Clock.currTime() - start);
double v1 = func(t1.total!"msecs");
double rect = (t1.total!"msecs" - t0) * (v0 + v1) / 2;
atomicOp!"+="(this.sum, rect);
t0 = t1.total!"msecs";
v0 = v1;
}
}

{{out}}

-3.07837e-13

E

def makeIntegrator() {
var value := 0.0
var input := fn { 0.0 }

var input1 := input()
var t1 := timer.now()

def update() {
def t2 := timer.now()
def input2 :float64 := input()
def dt := (t2 - t1) / 1000

value += (input1 + input2) * dt / 2

t1 := t2
input1 := input2
}

update <- ()
}

def integrator {
to input(new) :void  { input := new }
to output() :float64 { return value }
to shutdown()        { task := fn {} }
}
return integrator
}

def test() {
def result

def pi := (-1.0).acos()
def freq := pi / 1000

def base := timer.now()
def i := makeIntegrator()

i.input(fn { (freq * timer.now()).sin() })
timer.whenPast(base + 2000, fn {
i.input(fn {0})
})
timer.whenPast(base + 2500, fn {
bind result := i.output()
i.shutdown()
})
return result
}

EchoLisp

We use the functions (at ..) : scheduling, (wait ...), and (every ...) ot the timer.lib. The accuracy will be function of the browser's functions setTimeout and setInterval ...

(require 'timer)

;; returns an 'object' : (&lamdba; message [values])
;; messages : input, output, sample, inspect
(define (make-active)
(let [
(t0 #f) (dt 0)
(t  0) (Kt 0) ; K(t)
(S  0) (K  0)]
(lambda (message . args)
(case message
((output) (// S 2))
((input ) (set! K (car args))  (set! t0 #f))
((inspect) (printf " Active obj : t0 %v t %v S %v "  t0 t Kt (// S 2 )))
((sample)
(when (procedure? K)
;; recved new K : init
(unless t0
(set! t0  (first args))
(set! t 0)
(set! Kt (K 0)))

;; integrate K(t) every time 'sample message is received
(set! dt (- (first args) t t0)) ;; compute once K(t)
(set! S (+ S (* dt Kt)))
(set! t (+ t dt))
(set! Kt (K t))
(set! S (+ S (* dt Kt)))))

{{Out}}

(define (experiment)
(define (K t) (sin (*  PI t )))
(define A (make-active))
(define (stop)  (A 'input 0))
(define (sample t) (A 'sample (// t 1000)))
(define (result) (writeln 'result (A 'output)))

(at 2.5 'seconds 'result)
(every 10 'sample) ;; integrate every 10 ms

(A 'input K)
(wait 2000 'stop))

(experiment) →
3/7/2015 20:34:18 : result
result     0.0002266920372221955
(experiment)  →
3/7/2015 20:34:28 : result
result     0.00026510586971023164

Erlang

I could not see what time to use between each integration so it is the argument to task().

-module( active_object ).
-export( [delete/1, input/2, new/0, output/1, task/1] ).
-compile({no_auto_import,[time/0]}).

delete( Object ) ->
Object ! stop.

input( Object, Fun ) ->
Object ! {input, Fun}.

new( ) ->
K = fun zero/1,
S = 0,
T0 = seconds_with_decimals(),
erlang:spawn( fun() -> loop(K, S, T0) end ).

output( Object ) ->
Object ! {output, erlang:self()},
{output, Object, Output} -> Output
end.

Object = new(),
{ok, _Ref} = timer:send_interval( Integrate_millisec, Object, integrate ),
io:fwrite( "New ~p~n", [output(Object)] ),
input( Object, fun sine/1 ),
timer:sleep( 2000 ),
io:fwrite( "Sine ~p~n", [output(Object)] ),
input( Object, fun zero/1 ),
timer:sleep( 500 ),
io:fwrite( "Approx ~p~n", [output(Object)] ),
delete( Object ).

loop( Fun, Sum, T0 ) ->
integrate ->
T1 = seconds_with_decimals(),
New_sum = trapeze( Sum, Fun, T0, T1 ),
loop( Fun, New_sum, T1 );
stop ->
ok;
{input, New_fun} ->
loop( New_fun, Sum, T0 );
{output, Pid} ->
Pid ! {output, erlang:self(), Sum},
loop( Fun, Sum, T0 )
end.

sine( T ) ->
math:sin( 2 * math:pi() * 0.5 * T ).

seconds_with_decimals() ->
{Megaseconds, Seconds, Microseconds} = os:timestamp(),
(Megaseconds * 1000000) + Seconds + (Microseconds / 1000000).

trapeze( Sum, Fun, T0, T1 ) ->
Sum + (Fun(T1) + Fun(T0)) * (T1 - T0) / 2.

zero( _ ) -> 0.

Factor

Working with dynamic quotations requires the stack effect to be known in advance. The apply-stack-effect serves this purpose.

USING: accessors alarms calendar combinators kernel locals math
math.constants math.functions prettyprint system threads ;
IN: rosettacode.active

TUPLE: active-object alarm function state previous-time ;

: apply-stack-effect ( quot -- quot' )
[ call( x -- x ) ] curry ; inline

: nano-to-seconds ( -- seconds ) nano-count 9 10^ / ;

: object-times ( active-object -- t1 t2 )
[ previous-time>> ]
[ nano-to-seconds [ >>previous-time drop ] keep ] bi ;
:: adding-function ( t1 t2 active-object -- function )
t2 t1 active-object function>> apply-stack-effect bi@ +
t2 t1 - * 2 / [ + ] curry ;
: integrate ( active-object -- )
[ object-times ]
[ swap apply-stack-effect change-state drop ] tri ;

: <active-object> ( -- object )
active-object new
0 >>state
nano-to-seconds >>previous-time
[ drop 0 ] >>function
dup [ integrate ] curry 1 nanoseconds every >>alarm ;
: destroy ( active-object -- ) alarm>> cancel-alarm ;

: input ( object quot -- object ) >>function ;
: output ( object -- val ) state>> ;

: active-test ( -- )
<active-object>
[ 2 pi 0.5 * * * sin ] input
2 seconds sleep
[ drop 0 ] input
0.5 seconds sleep
[ output . ] [ destroy ] bi ;
MAIN: active-test
-5.294207647335787e-05

FBSL

The Dynamic Assembler and Dynamic C JIT compilers integrated in FBSL v3.5 handle multithreading perfectly well. However, pure FBSL infrastructure has never been designed especially to support own multithreading nor can it handle long long integers natively. Yet a number of tasks with careful design and planning are quite feasible in pure FBSL too:

#APPTYPE CONSOLE

#INCLUDE <Include\Windows.inc>

DIM Entity AS NEW Integrator(): Sleep(2000) ' respawn and do the job

Entity.Relax(): Sleep(500) ' get some rest

PRINT ">>> ", Entity.Yield(): DELETE Entity ' report and die

PAUSE

' ------------- End Program Code -------------

#DEFINE SpawnMutex CreateMutex(NULL, FALSE, "mutex")
#DEFINE LockMutex WaitForSingleObject(mutex, INFINITE)
#DEFINE UnlockMutex ReleaseMutex(mutex)
#DEFINE KillMutex CloseHandle(mutex)

CLASS Integrator

PRIVATE:

TYPE LARGE_INTEGER
lowPart AS INTEGER
highPart AS INTEGER
END TYPE

DIM dfreq AS DOUBLE, dlast AS DOUBLE, dnow AS DOUBLE, llint AS LARGE_INTEGER
DIM dret0 AS DOUBLE, dret1 AS DOUBLE, mutex AS INTEGER, sum AS DOUBLE, thread AS INTEGER

' --------------------------------------------
SUB INITIALIZE()
mutex = SpawnMutex
QueryPerformanceFrequency(@llint)
dfreq = LargeInt2Double(llint)
QueryPerformanceCounter(@llint)
dlast = LargeInt2Double(llint) / dfreq
END SUB
SUB TERMINATE()
' nothing special
END SUB
' --------------------------------------------

SUB Sampler()
DO
LockMutex
Sleep(5)
QueryPerformanceCounter(@llint)
dnow = LargeInt2Double(llint) / dfreq
sum = sum + (dret1 + dret0) * (dnow - dlast) / 2
dlast = dnow
UnlockMutex
LOOP
END SUB

FUNCTION LargeInt2Double(obj AS VARIANT) AS DOUBLE
STATIC ret
ret = obj.highPart
IF obj.highPart < 0 THEN ret = ret + (2 ^ 32)
ret = ret * 2 ^ 32
ret = ret + obj.lowPart
IF obj.lowPart < 0 THEN ret = ret + (2 ^ 32)
RETURN ret
END FUNCTION

PUBLIC:

METHOD Relax()
LockMutex
UnlockMutex
END METHOD

METHOD Yield() AS DOUBLE
LockMutex
Yield = sum
UnlockMutex
KillMutex
END METHOD

END CLASS

FUNCTION Idle(BYVAL t AS DOUBLE) AS DOUBLE
RETURN 0.0
END FUNCTION

FUNCTION Task(BYVAL t AS DOUBLE) AS DOUBLE
RETURN SIN(2 * PI * 0.5 * t)
END FUNCTION

'''Typical console output:''' >>> -0.000769965989580346 Press any key to continue...

open System

// current time in seconds
let now() = float( DateTime.Now.Ticks / 10000L ) / 1000.0

type Integrator( intervalMs ) as x =
let mutable k = fun _ -> 0.0  // function to integrate
let mutable s = 0.0           // current value
let mutable t0 = now()        // last time s was updated
let mutable running = true    // still running?

do x.ScheduleNextUpdate()

member x.Input(f) = k <- f

member x.Output() = s

member x.Stop() = running <- false

member private x.Update() =
let t1 = now()
s <- s + (k t0 + k t1) * (t1 - t0) / 2.0
t0 <- t1
x.ScheduleNextUpdate()

member private x.ScheduleNextUpdate() =
if running then
async { do! Async.Sleep( intervalMs )
x.Update()
}
|> Async.Start

let i = new Integrator(10)

i.Input( fun t -> Math.Sin (2.0 * Math.PI * 0.5 * t) )

i.Input( fun _ -> 0.0 )

printfn "%f" (i.Output())
i.Stop()

Go

Using time.Tick to sample K at a constant frequency. Three goroutines are involved, main, aif, and tk. Aif controls access to the accumulator s and the integration function K. Tk and main must talk to aif through channels to access s and K.

package main

import (
"fmt"
"math"
"time"
)

// type for input function, k.
// input is duration since an arbitrary start time t0.
type tFunc func(time.Duration) float64

// active integrator object.  state variables are not here, but in
// function aif, started as a goroutine in the constructor.
type aio struct {
iCh chan tFunc        // channel for setting input function
oCh chan chan float64 // channel for requesting output
}

// constructor
func newAio() *aio {
var a aio
a.iCh = make(chan tFunc)
a.oCh = make(chan chan float64)
go aif(&a)
return &a
}

// input method required by task description.  in practice, this method is
// unnecessary; you would just put that single channel send statement in
// your code wherever you wanted to set the input function.
func (a aio) input(f tFunc) {
a.iCh <- f
}

// output method required by task description.  in practice, this method too
// would not likely be best.  instead any client interested in the value would
// likely make a return channel sCh once, and then reuse it as needed.
func (a aio) output() float64 {
sCh := make(chan float64)
a.oCh <- sCh
return <-sCh
}

// integration function that returns constant 0
func zeroFunc(time.Duration) float64 { return 0 }

// goroutine serializes access to integrated function k and state variable s
func aif(a *aio) {
var k tFunc = zeroFunc // integration function
s := 0.                // "object state" initialized to 0
t0 := time.Now()       // initial time
k0 := k(0)             // initial sample value
t1 := t0               // t1, k1 used for trapezoid formula
k1 := k0

tk := time.Tick(10 * time.Millisecond) // 10 ms -> 100 Hz
for {
select {
case t2 := <-tk: // timer tick event
k2 := k(t2.Sub(t0))                        // new sample value
s += (k1 + k2) * .5 * t2.Sub(t1).Seconds() // trapezoid formula
t1, k1 = t2, k2                            // save time and value
case k = <-a.iCh: // input method event: function change
case sCh := <-a.oCh: // output method event: sample object state
sCh <- s
}
}
}

func main() {
a := newAio()                           // create object
a.input(func(t time.Duration) float64 { // 1. set input to sin function
return math.Sin(t.Seconds() * math.Pi)
})
time.Sleep(2 * time.Second) // 2. sleep 2 sec
a.input(zeroFunc)           // 3. set input to zero function
time.Sleep(time.Second / 2) // 4. sleep .5 sec
fmt.Println(a.output())     // output should be near zero
}

Output:

2.4517135756807704e-05

Groovy

{{trans|Java}}

/**
* Integrates input function K over time
* S + (t1 - t0) * (K(t1) + K(t0)) / 2
*/
class Integrator {
interface Function {
double apply(double timeSinceStartInSeconds)
}

private final long start
private volatile boolean running

private Function func
private double t0
private double v0
private double sum

Integrator(Function func) {
this.start = System.nanoTime()
setFunc(func)
}

void setFunc(Function func) {
this.func = func
def temp = func.apply(0.0.toDouble())
v0 = temp
t0 = 0.0.doubleValue()
}

double getOutput() {
return sum
}

void stop() {
running = false
}

private void integrate() {
running = true
while (running) {
try {
update()
} catch (InterruptedException ignored) {
return
}
}
}

private void update() {
double t1 = (System.nanoTime() - start) / 1.0e9
double v1 = func.apply(t1)
double rect = (t1 - t0) * (v0 + v1) / 2.0
this.sum += rect
t0 = t1
v0 = v1
}

static void main(String[] args) {
Integrator integrator = new Integrator({ t -> Math.sin(Math.PI * t) })

integrator.setFunc({ t -> 0.0.toDouble() })

integrator.stop()
System.out.println(integrator.getOutput())
}
}

{{out}}

0.0039642136156300455

module Integrator (
newIntegrator, input, output, stop,
Time, timeInterval
) where
import Control.Concurrent.MVar (MVar, newMVar, modifyMVar_, modifyMVar, readMVar)
import Control.Exception (evaluate)
import Data.Time (UTCTime)
import Data.Time.Clock (getCurrentTime, diffUTCTime)

main = do let f = 0.5 {- Hz -}
t0 <- getCurrentTime
i <- newIntegrator
input i (\t -> sin(2*pi * f * timeInterval t0 t)) -- task step 1
input i (const 0)                                 -- task step 3
result <- output i
stop i
print result

---- Implementation ------------------------------------------------------

-- Utilities for working with the time type
type Time = UTCTime
type Func a = Time -> a
timeInterval t0 t1 = realToFrac \$ diffUTCTime t1 t0

-- Type signatures of the module's interface
newIntegrator :: Fractional a => IO (Integrator a) -- Create an integrator
input  :: Integrator a -> Func a -> IO ()          -- Set the input function
output :: Integrator a           -> IO a           -- Get the current value
stop   :: Integrator a           -> IO ()          -- Stop integration, don't waste CPU

-- Data structures
data Integrator a = Integrator (MVar (IntState a)) -- MVar is a thread-safe mutable cell
deriving Eq
data IntState a = IntState { func  :: Func a,      -- The current function
run   :: Bool,        -- Whether to keep going
value :: a,           -- The current accumulated value
time  :: Time }       -- The time of the previous update

newIntegrator = do
now <- getCurrentTime
state <- newMVar \$ IntState { func  = const 0,
run   = True,
value = 0,
time  = now }
return (Integrator state)           --   and the client interface object.

input  (Integrator stv) f = modifyMVar_ stv (\st -> return st { func = f })
output (Integrator stv)   = fmap value \$ readMVar stv
stop   (Integrator stv)   = modifyMVar_ stv (\st -> return st { run = False })
-- modifyMVar_ takes an MVar and replaces its contents according to the provided function.
-- a { b = c } is record-update syntax: "the record a, except with field b changed to c"

intThread :: Fractional a => MVar (IntState a) -> IO ()
intThread stv = whileM \$ modifyMVar stv updateAndCheckRun
-- modifyMVar is like modifyMVar_ but the function returns a tuple of the new value
-- and an arbitrary extra value, which in this case ends up telling whileM whether
-- to keep looping.
where updateAndCheckRun st = do
now <- getCurrentTime
let value' = integrate (func st) (value st) (time st) now
evaluate value'                             -- avoid undesired laziness
return (st { value = value', time  = now }, -- updated state
run st)                             -- whether to continue

integrate :: Fractional a => Func a -> a -> Time -> Time -> a
integrate f value t0 t1 = value + (f t0 + f t1)/2 * dt
where dt = timeInterval t0 t1

-- Execute 'action' until it returns false.
whileM action = do b <- action; if b then whileM action else return ()

J

Implementation:

coclass 'activeobject'
require'dates'

create=:setinput NB. constructor

T=:3 :0
if. nc<'T0' do. T0=:tsrep 6!:0'' end.
0.001*(tsrep 6!:0'')-T0
)

F=:G=:0:
Zero=:0

setinput=:3 :0
zero=. getoutput''
'`F ignore'=: y,_:`''
G=: F f.d._1
Zero=: zero-G T ''
getoutput''
)

getoutput=:3 :0
Zero+G T''
)

cocurrent 'testrig'

delay=: 6!:3

object=: conew 'activeobject'
setinput__object 1&o.@o.`''
smoutput (T__object,getoutput__object) ''

delay 2

smoutput (T__object,getoutput__object) ''
setinput__object 0:`''
smoutput (T__object,getoutput__object) ''

delay 0.5

smoutput (T__object,getoutput__object) ''

0.001 0
2.002 4.71237e_6
2.004 1.25663e_5
2.504 1.25663e_5

First column is time relative to start of processing, second column is object's output at that time.

Java

/**
* Integrates input function K over time
* S + (t1 - t0) * (K(t1) + K(t0)) / 2
*/
public class Integrator {

public interface Function {
double apply(double timeSinceStartInSeconds);
}

private final long start;
private volatile boolean running;

private Function func;
private double t0;
private double v0;
private double sum;

public Integrator(Function func) {
this.start = System.nanoTime();
setFunc(func);
}

public void setFunc(Function func) {
this.func = func;
v0 = func.apply(0.0);
t0 = 0;
}

public double getOutput() {
return sum;
}

public void stop() {
running = false;
}

private void integrate() {
running = true;
while (running) {
try {
update();
} catch (InterruptedException e) {
return;
}
}
}

private void update() {
double t1 = (System.nanoTime() - start) / 1.0e9;
double v1 = func.apply(t1);
double rect = (t1 - t0) * (v0 + v1) / 2;
this.sum += rect;
t0 = t1;
v0 = v1;
}

public static void main(String[] args) throws InterruptedException {
Integrator integrator = new Integrator(t -> Math.sin(Math.PI * t));

integrator.setFunc(t -> 0.0);

integrator.stop();
System.out.println(integrator.getOutput());
}
}

Output:

4.783602720556498E-13

JavaScript

{{trans|E}}

function Integrator(sampleIntervalMS) {
var inputF = function () { return 0.0 };
var sum = 0.0;

var t1 = new Date().getTime();
var input1 = inputF(t1 / 1000);

function update() {
var t2 = new Date().getTime();
var input2 = inputF(t2 / 1000);
var dt = (t2 - t1) / 1000;

sum += (input1 + input2) * dt / 2;

t1 = t2;
input1 = input2;
}

var updater = setInterval(update, sampleIntervalMS);

return ({
input: function (newF) { inputF = newF },
output: function () { return sum },
shutdown: function () { clearInterval(updater) },
});
}

Test program as a HTML fragment:

<span id="a">Test running...</span> <code id="b">-</code></p>

<script type="text/javascript">
var f = 0.5;

var i = new Integrator(1);
var displayer = setInterval(function () { document.getElementById("b").firstChild.data = i.output() }, 100)

setTimeout(function () {
i.input(function (t) { return Math.sin(2*Math.PI*f*t) }); // test step 1
setTimeout(function () { // test step 2
i.input(function (t) { return 0 }); // test step 3
setTimeout(function () { // test step 3
i.shutdown();
clearInterval(displayer);
document.getElementById("a").firstChild.data = "Done, should be about 0: "
}, 500);
}, 2000);
}, 1)
</script>

Julia

{{works with|Julia|0.6}} Julia has inheritance of data structures and first-class types, but structures do not have methods. Instead, methods are functions with multiple dispatch based on argument type.

mutable struct Integrator
func::Function
runningsum::Float64
dt::Float64
running::Bool
function Integrator(f::Function, dt::Float64)
this = new()
this.func = f
this.runningsum = 0.0
this.dt = dt
this.running = false
return this
end
end

function run(integ::Integrator, lastval::Float64 = 0.0)
lasttime = time()
while integ.running
sleep(integ.dt)
newtime = time()
measuredinterval = newtime - lasttime
newval = integ.func(measuredinterval)
integ.runningsum += (lastval + newval) * measuredinterval / 2.0
lasttime = newtime
lastval = newval
end
end

start!(integ::Integrator) = (integ.running = true; @async run(integ))
stop!(integ) = (integ.running = false)
f1(t) = sin(2π * t)
f2(t) = 0.0

it = Integrator(f1, 0.00001)
start!(it)
sleep(2.0)
it.func = f2
sleep(0.5)
v2 = it.runningsum
println("After 2.5 seconds, integrator value was \$v2")

Kotlin

{{trans|Java}} Athough this is a faithful translation of the Java entry, on my machine the output of the latter is typically an order of magnitude smaller than this version. I have no idea why.

// version 1.2.0

import kotlin.math.*

typealias Function = (Double) -> Double

/**
* Integrates input function K over time
* S + (t1 - t0) * (K(t1) + K(t0)) / 2
*/
class Integrator {
private val start: Long
private @Volatile var running = false
private lateinit var func: Function
private var t0 = 0.0
private var v0 = 0.0
private var sum = 0.0

constructor(func: Function) {
start = System.nanoTime()
setFunc(func)
}

fun setFunc(func: Function) {
this.func = func
v0 = func(0.0)
t0 = 0.0
}

fun getOutput() = sum

fun stop() {
running = false
}

private fun integrate() {
running = true
while (running) {
try {
update()
}
catch(e: InterruptedException) {
return
}
}
}

private fun update() {
val t1 = (System.nanoTime() - start) / 1.0e9
val v1 = func(t1)
val rect = (t1 - t0) * (v0 + v1) / 2.0
sum  += rect
t0 = t1
v0 = v1
}
}

fun main(args: Array<String>) {
val integrator = Integrator( { sin(PI * it) } )

integrator.setFunc( { 0.0 } )

integrator.stop()
println(integrator.getOutput())
}

Sample output:

2.884266305153741E-4

Lingo

Parent script "Integrator":

property _sum
property _func
property _timeLast
property _valueLast
property _ms0
property _updateTimer

on new (me, func)
if voidP(func) then func = "0.0"
me._sum = 0.0
-- update frequency: 100/sec (arbitrary)
me._updateTimer = timeout().new("update", 10, #_update, me)
me.input(func)
return me
end

on stop (me)
me._updateTimer.period = 0 -- deactivates timer
end

-- func is a term (as string) that might contain "t" and is evaluated at runtime
on input (me, func)
me._func = func
me._ms0 = _system.milliseconds
me._timeLast = 0.0
t = 0.0
me._valueLast = value(me._func)
end

on output (me)
return me._sum
end

on _update (me)
now = _system.milliseconds - me._ms0
t = now/1000.0
val = value(me._func)
me._sum = me._sum + (me._valueLast+val)*(t - me._timeLast)/2
me._timeLast = t
me._valueLast = val
end

In some movie script:

global gIntegrator

-- entry point
on startMovie
gIntegrator = script("Integrator").new("sin(PI * t)")
timeout().new("timer", 2000, #step1)
end

on step1 (_, timer)
gIntegrator.input("0.0")
timer.timeoutHandler = #step2
timer.period = 500
end

on step2 (_, timer)
gIntegrator.stop()
put gIntegrator.output()
timer.forget()
end

{{out}}

-- 0.0004

Mathematica

Block[{start = SessionTime[], K, t0 = 0, t1, kt0, S = 0},
K[t_] = Sin[2 Pi f t] /. f -> 0.5; kt0 = K[t0];
While[True, t1 = SessionTime[] - start;
S += (kt0 + (kt0 = K[t1])) (t1 - t0)/2; t0 = t1;
If[t1 > 2, K[t_] = 0; If[t1 > 2.5, Break[]]]]; S]

1.1309*10^-6

Curiously, this value never changes; it is always exactly the same (at 1.1309E-6). Note that closer answers could be achieved by using Mathematica's better interpolation methods, but it would require collecting the data (in a list), which would have a speed penalty large enough to negate the improved estimation.

ooRexx

Not totally certain this is a correct implementation since the value coming out is not close to zero. It does show all of the basics of multithreading and object synchronization though.

integrater = .integrater~new(.routines~sine)   -- start the integrater function
call syssleep 2
integrater~input = .routines~zero              -- update the integrater function
call syssleep .5

say integrater~output
integrater~stop          -- terminate the updater thread

::class integrater
::method init
expose stopped start v last_v last_t k
use strict arg k
stopped = .false
start = .datetime~new   -- initial time stamp
v = 0
last_v = 0
last_t = 0
self~input = k
self~start

-- spin off a new thread and start updating.  Note, this method is unguarded
-- to allow other threads to make calls
::method start unguarded
expose stopped

reply  -- this spins this method invocation off onto a new thread

do while \stopped
call sysSleep .1
self~update    -- perform the update operation
end

-- turn off the thread.  Since this is unguarded,
-- it can be called any time, any where
::method stop unguarded
expose stopped
stopped = .true

-- perform the update.  Since this is a guarded method, the object
-- start is protected.
::method update
expose start v last_v t last_t k

numeric digits 20   -- give a lot of precision

current = .datetime~new
t = (current - start)~microseconds
new_v = k~call(t)    -- call the input function
v += (last_v + new_v) * (t - last_t) / 2
last_t = t
last_v = new_v
say new value is v

-- a write-only attribute setter (this is GUARDED)
::attribute input SET
expose k last_t last_v
self~update          -- update current values
use strict arg k  -- update the call function to the provided value
last_t = 0
last_v = k~call(0)  -- and update to the zero value

-- the output function...returns current calculated value
::attribute output GET
expose v
return v

::routine zero
return 0

::routine sine
use arg t
return rxcalcsin(rxcalcpi() * t)

::requires rxmath library

OxygenBasic

Built from scratch. The ringmaster orchestrates all the active-objects, keeping a list of each individual and its method call.

With a high precision timer the result is around -.0002

double MainTime

'
### =========

class RingMaster
'
### =========

'
indexbase 1
sys List 'limit of 512 objects per ringmaster
sys max,acts
'
method Register(sys meth,obj) as sys
sys i
for i=1 to max step 2
if list[i]=0 then exit for 'vacant slot
next
if i>=max then max+=2
List[i]<=meth,obj
return i 'token for deregistration etc
end method
'
method Deregister(sys *i)
if i then List[i]<=0,0 : i=0
end method
'
method Clear()
max=0
end method
'
method Act() 'called by the timer
sys i,q
for i=1 to max step 2
q=List[i]
if q then
call q List[i+1] 'anon object
end if
next
acts++
end method
'
end class

'
### ===========

class ActiveObject
'
### ===========

'
double     s,freq,t1,t2,v1,v2
sys        nfun,acts,RingToken
RingMaster *Master
'
method fun0() as double
end method
'
method fun1() as double
return sin(2*pi()*freq*MainTime)
end method
'
method func() as double
select case nfun
case 0 : return fun0()
case 1 : return fun1()
end select
'error?
end method
'
method TimeBasedDuties()
t1=t2
v1=v2
t2=MainTime
v2=func
acts++
end method
'
method RegisterWith(RingMaster*r)
@Master=@r
if @Master then
RingToken=Master.register @TimeBasedDuties,@this
end if
end method
'
method Deregister()
if @Master then
Master.Deregister RingToken 'this is set to null
end if
end method
'
method Output() as double
return s
end method
'
method Input(double fr=0,fun=0)
if fr then freq=fr
nfun=fun
end method

method ClearIntegral()
s=0
end method
'
end class

'SETUP TIMING SYSTEM
'
### =============

extern library "kernel32.dll"
declare Sleep(sys milliseconds)
end extern
'
QueryPerformanceFrequency freq
double tscale=1/freq
double t1,t2
QueryPerformanceCounter scount

macro PrecisionTime(time)
QueryPerformanceCounter tcount
time=(tcount-scount)*tscale
end macro

'====
'TEST
'====

double       integral
double       tevent1,tevent2
RingMaster   Rudolpho
ActiveObject A
'
A.RegisterWith Rudolpho
'
'SET EVENT TIMES
'
### =========

tEvent1=2.0 'seconds
tEvent2=2.5 'seconds
'
PrecisionTime t1 'mark initial time
MainTime=t1
'
'
'EVENT LOOP
'
### ====

'
do
PrecisionTime t2
MainTime=t2
if t2-t1>=0.020 'seconds interval
Rudolpho.Act 'service all active objects
t1=t2
end if
'
if tEvent1>=0 and MainTime>=tEvent1
A.input (fun=0) 'switch to null function (0)
tEvent1=-1      'disable this event from happening again
end if
if MainTime>=tEvent2
integral=A.output()
exit do 'end of session
end if
'
sleep 5 'hand control to OS for a while
end do

print str(integral,4)

Rudolpho.clear

Oz

declare
fun {Const X}
fun {\$ _} X end
end

fun {Now}
{Int.toFloat {Property.get 'time.total'}} / 1000.0
end

class Integrator from Time.repeat
attr
k:{Const 0.0}
s:0.0
t1 k_t1
t2 k_t2

meth init(SampleIntervalMS)
t1 := {Now}
k_t1 := {@k @t1}
{self setRepAll(action:Update
delay:SampleIntervalMS)}
{self go}
end
end

meth input(K)
k := K
end

meth output(\$)
@s
end

meth Update
t2 := {Now}
k_t2 := {@k @t2}
s := @s + (@k_t1 + @k_t2) * (@t2 - @t1) / 2.0
t1 := @t2
k_t1 := @k_t2
end
end

Pi = 3.14159265
F = 0.5

I = {New Integrator init(10)}
in
{I input(fun {\$ T}
{Sin 2.0 * Pi * F * T}
end)}

{Delay 2000} %% ms

{I input({Const 0.0})}

{Delay 500} %% ms

{Show {I output(\$)}}
{I stop}

Perl

#!/usr/bin/perl

use strict;
use 5.10.0;

package Integrator;

sub new {
my \$cls = shift;
my \$obj = bless {	t	=> 0,
sum	=> 0,
ref \$cls ? %\$cls : (),
stop	=> 0,
tid	=> 0,
func	=> shift,
}, ref \$cls || \$cls;

share(\$obj->{sum});
share(\$obj->{stop});

\$obj->{tid} = async {
my \$upd = 0.1; # update every 0.1 second
while (!\$obj->{stop}) {
{
my \$f = \$obj->{func};
my \$t = \$obj->{t};

\$obj->{sum} += (\$f->(\$t) + \$f->(\$t + \$upd))* \$upd/ 2;
\$obj->{t} += \$upd;
}
select(undef, undef, undef, \$upd);
}
#	say "stopping \$obj";
};
\$obj
}

sub output { shift->{sum} }

sub delete {
my \$obj = shift;
\$obj->{stop} = 1;
\$obj->{tid}->join;
}

sub setinput {
# This is surprisingly difficult because of the perl sharing model.
# Func refs can't be shared, thus can't be replaced by another thread.
# Have to create a whole new object... there must be a better way.
my \$obj = shift;
\$obj->delete;
\$obj->new(shift);
}

package main;

my \$x = Integrator->new(sub { sin(atan2(1, 1) * 8 * .5 * shift) });

sleep(2);
say "sin after 2 seconds: ", \$x->output;

\$x = \$x->setinput(sub {0});

select(undef, undef, undef, .5);
say "0 after .5 seconds: ", \$x->output;

\$x->delete;

Perl 6

{{works with|Rakudo|2018.12}} There is some jitter in the timer, but it is typically accurate to within a few thousandths of a second.

class Integrator {
has \$.f is rw = sub (\$t) { 0 };
has \$.now is rw;
has \$.value is rw = 0;
has \$.integrator is rw;

method init() {
self.value = &(self.f)(0);
:code({
loop {
my \$t1 = now;
self.value += (&(self.f)(self.now) + &(self.f)(\$t1)) * (\$t1 - self.now) / 2;
self.now = \$t1;
sleep .001;
}
}),
).run
}

method Input (&f-of-t) {
self.f = &f-of-t;
self.now = now;
self.init;
}

method Output { self.value }
}

my \$a = Integrator.new;

\$a.Input( sub (\$t) { sin(2 * π * .5 * \$t) } );

say "Initial value: ", \$a.Output;

sleep 2;

say "After 2 seconds: ", \$a.Output;

\$a.Input( sub (\$t) { 0 } );

sleep .5;

say "f(0): ", \$a.Output;

{{out|Typical output}}

Initial value: 0
After 2 seconds: -0.0005555887464620366
f(0): 0

Phix

Note that in Phix you cannot pass a variable to another procedure and have it "change under your feet".

The copy-on-write semantics mean it would not have any effect, in that the original would be preserved (deemed in phix to be a "very good thing") while the value passed along, a shared reference until it gets modified and a copy made, would most likely simply be discarded, unless explicitly returned and stored, which obviously cannot be done from a separate thread. Instead we pass around an index (dx) as a way of emulating the "pointer references" of other languages.

If anything phix requires more locking that other languages due to the hidden shared reference counts.

Just lock everything, it is not that hard, and you should never need much more than the stuff below.

sequence x = {}
enum TERMINATE, INTERVAL, KFUN, VALUE, T0, K0, ID, ISIZE=\$
integer xlock = init_cs()

function zero(atom /*t*/) return 0 end function
function sine(atom t) return sin(2*PI*0.5*t) end function

procedure update(integer dx)
enter_cs(xlock)
atom t1 = time(),
k1 = call_func(x[dx][KFUN],{t1})
x[dx][VALUE] += (k1 + x[dx][K0]) * (t1 - x[dx][T0]) / 2
x[dx][T0] = t1
x[dx][K0] = k1
leave_cs(xlock)
end procedure

procedure tick(integer dx)
while not x[dx][TERMINATE] do
sleep(x[dx][INTERVAL])
update(dx)
end while
end procedure

function new_integrator(integer rid, atom interval)
x = append(x,repeat(0,ISIZE))
integer dx = length(x)
x[dx][TERMINATE] = false
x[dx][INTERVAL] = interval
x[dx][KFUN] = rid
x[dx][T0] = time()
update(dx)
return dx
end function

procedure set_input(integer dx, rid)
enter_cs(xlock)
x[dx][KFUN] = rid
x[dx][K0] = 0
leave_cs(xlock)
end procedure

function get_output(integer dx)
enter_cs(xlock)
atom v = x[dx][VALUE]
leave_cs(xlock)
return v
end function

procedure stop_integrator(integer dx)
x[dx][TERMINATE] = true
end procedure

puts(1,"")
integer dx = new_integrator(routine_id("sine"),0.01)
sleep(2)
printf(1,"%f\n",get_output(dx))
set_input(dx,routine_id("zero"))
sleep(0.5)
printf(1,"%f\n",get_output(dx))
stop_integrator(dx)

{{out}}

-0.00326521
0.00196980

PicoLisp

(class +Active)
# inp val sum usec

(dm T ()
(unless (assoc -100 *Run)           # Install timer task
(task -100 100                   # Update objects every 0.1 sec
(mapc 'update> *Actives) ) )
(=: inp '((U) 0))                   # Set zero input function
(=: val 0)                          # Initialize last value
(=: sum 0)                          # Initialize sum
(=: usec (usec))                    # and time
(push '*Actives This) )             # Install in notification list

(dm input> (Fun)
(=: inp Fun) )

(dm update> ()
(let (U (usec)  V ((: inp) U))      # Get current time, calculate value
(inc (:: sum)
(*/
(+ V (: val))              # (K(t) + K(t)) *
(- U (: usec))             # (t - t) /
2.0 ) )                    # 2.0
(=: val V)
(=: usec U) ) )

(dm output> ()
(format (: sum) *Scl) )             # Get result

(dm stop> ()
(unless (del This '*Actives)        # Removing the last active object?

(de integrate ()                       # Test it
(let Obj (new '(+Active))           # Create an active object
(input> Obj                      # Set input function
'((U) (sin (*/ pi U 1.0))) )  # to sin(π * t)
(wait 2000)                      # Wait 2 sec
(input> Obj '((U) 0))            # Reset input function
(wait 500)                       # Wait 0.5 sec
(prinl "Output: " (output> Obj)) # Print return value
(stop> Obj) ) )                  # Stop active object

PureBasic

Using the open-source precompiler [http://www.development-lounge.de/viewtopic.php?t=5915 SimpleOOP].

Prototype.d ValueFunction(f.d, t.d)

Class IntegralClass
Time0.i
Mutex.i
S.d
Freq.d
Quit.i
*func.ValueFunction

Protect Method Sampler()
Repeat
Delay(1)
If This\func And This\Mutex
LockMutex(This\Mutex)
This\S + This\func(This\Freq, ElapsedMilliseconds()-This\Time0)
UnlockMutex(This\Mutex)
EndIf
Until This\Quit
EndMethod

BeginPublic
Method Input(*func.ValueFunction)
LockMutex(This\Mutex)
This\func = *func
UnlockMutex(This\Mutex)
EndMethod

Method.d Output()
Protected Result.d
LockMutex(This\Mutex)
Result = This\S
UnlockMutex(This\Mutex)
MethodReturn Result
EndMethod

Method Init(F.d, *f)
This\Freq   = F
This\func   = *f
This\Mutex  = CreateMutex()
This\Time0  = ElapsedMilliseconds()
EndMethod

Method Release()
This\Quit = #True
EndMethod
EndPublic

EndClass

;- Procedures for generating values
Procedure.d n(f.d, t.d)
; Returns nothing
EndProcedure

Procedure.d f(f.d, t.d)
; Returns the function of this task
ProcedureReturn Sin(2*#PI*f*t)
EndProcedure

;- Test Code
*a.IntegralClass = NewObject.IntegralClass(0.5, @n()) ; Create the AO
*a\Input(@f()) ; Start sampling function f()
Delay(2000)    ; Delay 2 sec
*a\Input(@n()) ; Change to sampling 'nothing'
Delay( 500)    ; Wait 1/2 sec
MessageRequester("Info", StrD(*a\Output()))           ; Present the result
*a= FreeObject

Python

Assignment is thread-safe in Python, so no extra locks are needed in this case.

from time import time, sleep

'continuously integrate a function `K`, at each `interval` seconds'
def __init__(self, K=lambda t:0, interval=1e-4):
self.interval  = interval
self.K   = K
self.S   = 0.0
self.__run = True
self.start()

def run(self):
interval = self.interval
start = time()
t0, k0 = 0, self.K(0)
while self.__run:
sleep(interval)
t1 = time() - start
k1 = self.K(t1)
self.S += (k1 + k0)*(t1 - t0)/2.0
t0, k0 = t1, k1

def join(self):
self.__run = False

if __name__ == "__main__":
from math import sin, pi

ai = Integrator(lambda t: sin(pi*t))
sleep(2)
print ai.S
ai.K = lambda t: 0
sleep(0.5)
print ai.S

Racket

#lang racket

(require (only-in racket/gui sleep/yield timer%))

(define active%
(class object%
(super-new)
(init-field k) ; input function
(field [s 0])  ; state
(define t_0 0)

(define/public (input new-k) (set! k new-k))
(define/public (output) s)

(define (callback)
(define t_1 (/ (- (current-inexact-milliseconds) start) 1000))
(set! s (+ s (* (+ (k t_0) (k t_1))
(/ (- t_1 t_0) 2))))
(set! t_0 t_1))

(define start (current-inexact-milliseconds))
(new timer%
[interval 1000]
[notify-callback callback])))

(define active (new active% [k (λ (t) (sin (* 2 pi 0.5 t)))]))
(sleep/yield 2)
(send active input (λ _ 0))
(sleep/yield 0.5)
(displayln (send active output))

Rust

#![feature(mpsc_select)]

extern crate num;
extern crate schedule_recv;

use num::traits::Zero;
use num::Float;
use schedule_recv::periodic_ms;
use std::f64::consts::PI;
use std::ops::Mul;
use std::sync::mpsc::{self, SendError, Sender};
use std::sync::{Arc, Mutex};
use std::time::Duration;

pub type Actor<S> = Sender<Box<Fn(u32) -> S + Send>>;
pub type ActorResult<S> = Result<(), SendError<Box<Fn(u32) -> S + Send>>>;

/// Rust supports both shared-memory and actor models of concurrency, and the `Integrator` utilizes
/// both.  We use an `Actor` to send the `Integrator` new functions, while we use a `Mutex`
/// (shared-memory concurrency) to hold the result of the integration.
///
/// Note that these are not the only options here--there are many, many ways you can deal with
/// concurrent access.  But when in doubt, a plain old `Mutex` is often a good bet.  For example,
/// this might look like a good situation for a `RwLock`--after all, there's no reason for a read
/// in the main task to block writes.  Unfortunately, unless you have significantly more reads than
/// writes (which is certainly not the case here), a `Mutex` will usually outperform a `RwLock`.
pub struct Integrator<S: 'static, T: Send> {
input: Actor<S>,
output: Arc<Mutex<T>>,
}

/// In Rust, time durations are strongly typed.  This is usually exactly what you want, but for a
/// problem like this--where the integrated value has unusual (unspecified?) units--it can actually
/// be a bit tricky.  Right now, `Duration`s can only be multiplied or divided by `i32`s, so in
/// order to be able to actually do math with them we say that the type parameter `S` (the result
/// of the function being integrated) must yield `T` (the type of the integrated value) when
/// multiplied by `f64`.  We could possibly replace `f64` with a generic as well, but it would make
/// things a bit more complex.
impl<S, T> Integrator<S, T>
where
S: Mul<f64, Output = T> + Float + Zero,
T: 'static + Clone + Send + Float,
{
pub fn new(frequency: u32) -> Integrator<S, T> {
// We create a pipe allowing functions to be sent from tx (the sending end) to input (the
// receiving end).  In order to change the function we are integrating from the task in
// which the Integrator lives, we simply send the function through tx.
let (tx, input) = mpsc::channel();
// The easiest way to do shared-memory concurrency in Rust is to use atomic reference
// counting, or Arc, around a synchronized type (like Mutex<T>).  Arc gives you a guarantee
// that memory will not be freed as long as there is at least one reference to it.
// It is similar to C++'s shared_ptr, but it is guaranteed to be safe and is never
// incremented unless explicitly cloned (by default, it is moved).
let s: Arc<Mutex<T>> = Arc::new(Mutex::new(Zero::zero()));
let integrator = Integrator {
input: tx,
// Here is the aforementioned clone.  We have to do it before s enters the closure,
// because once that happens it is moved into the closure (and later, the new task) and
// becomes inaccessible to the outside world.
output: Arc::clone(&s),
};
// The frequency is how often we want to "tick" as we update our integrated total.  In
// Rust, timers can yield Receivers that are periodically notified with an empty
// message (where the period is the frequency).  This is useful because it lets us wait
// on either a tick or another type of message (in this case, a request to change the
// function we are integrating).
let periodic = periodic_ms(frequency);
let mut t = 0;
let mut k: Box<Fn(u32) -> S + Send> = Box::new(|_| Zero::zero());
let mut k_0: S = Zero::zero();
loop {
// Here's the selection we talked about above.  Note that we are careful to call
// the *non*-failing function, recv(), here.  The reason we do this is because
// recv() will return Err when the sending end of a channel is dropped.  While
// this is unlikely to happen for the timer (so again, you could argue for failure
// there), it's normal behavior for the sending end of input to be dropped, since
// it just happens when the Integrator falls out of scope.  So we handle it cleanly
// and break out of the loop, rather than failing.
select! {
res = periodic.recv() => match res {
Ok(_) => {
t += frequency;
let k_1: S = k(t);
// Rust Mutexes are a bit different from Mutexes in many other
// languages, in that the protected data is actually encapsulated by
// the Mutex.  The reason for this is that Rust is actually capable of
// enforcing (via its borrow checker) the invariant that the contents
// of a Mutex may only be read when you have acquired its lock.  This
// is enforced by way of a MutexGuard, the return value of lock(),
// which implements some special traits (Deref and DerefMut) that allow
// access to the inner element "through" the guard.  The element so
// acquired has a lifetime bounded by that of the MutexGuard, the
// MutexGuard can only be acquired by taking a lock, and the only way
// to release the lock is by letting the MutexGuard fall out of scope,
// so it's impossible to access the data incorrectly.  There are some
// additional subtleties around the actual implementation, but that's
// the basic idea.
let mut s = s.lock().unwrap();
*s = *s + (k_1 + k_0) * (f64::from(frequency) / 2.);
k_0 = k_1;
}
Err(_) => break,
},
res = input.recv() => match res {
Ok(k_new) => k = k_new,
Err(_) => break,
}
}
}
});
integrator
}

pub fn input(&self, k: Box<Fn(u32) -> S + Send>) -> ActorResult<S> {
// The meat of the work is done in the other thread, so to set the
// input we just send along the Sender we set earlier...
self.input.send(k)
}

pub fn output(&self) -> T {
// ...and to read the input, we simply acquire a lock on the output Mutex and return a
// copy. Why do we have to copy it?  Because, as mentioned above, Rust won't let us
// retain access to the interior of the Mutex unless we have possession of its lock.  There
// are ways and circumstances in which one can avoid this (e.g. by using atomic types) but
// a copy is a perfectly reasonable solution as well, and a lot easier to reason about :)
*self.output.lock().unwrap()
}
}

/// This function is fairly straightforward.  We create the integrator, set its input function k(t)
/// to 2pi * f * t, and then wait as described in the Rosetta stone problem.
fn integrate() -> f64 {
let object = Integrator::new(10);
object
.input(Box::new(|t: u32| {
let two_seconds_ms = 2 * 1000;
let f = 1. / f64::from(two_seconds_ms);
(2. * PI * f * f64::from(t)).sin()
}))
.expect("Failed to set input");
object.input(Box::new(|_| 0.)).expect("Failed to set input");
object.output()
}

fn main() {
println!("{}", integrate());
}

/// Will fail on a heavily loaded machine
#[test]
#[ignore]
fn solution() {
// We should just be able to call integrate, but can't represent the closure properly due to
// rust-lang/rust issue #17060 if we make frequency or period a variable.
// FIXME(pythonesque): When unboxed closures are fixed, fix integrate() to take two arguments.
let object = Integrator::new(10);
object
.input(Box::new(|t: u32| {
let two_seconds_ms = 2 * 1000;
let f = 1. / (two_seconds_ms / 10) as f64;
(2. * PI * f * t as f64).sin()
}))
.expect("Failed to set input");
object.input(Box::new(|_| 0.)).expect("Failed to set input");
assert_eq!(object.output() as u32, 0)
}

Scala

object ActiveObject {

class Integrator {

import java.util._
import scala.actors.Actor._

case class Pulse(t: Double)
case class Input(k: Double => Double)
case object Output
case object Bye

val timer = new Timer(true)
var k: Double => Double = (_ => 0.0)
var s: Double = 0.0
var t0: Double = 0.0

val handler = actor {
loop {
react {
case Pulse(t1) => s += (k(t1) + k(t0)) * (t1 - t0) / 2.0; t0 = t1
case Input(k) => this.k = k
case Bye => timer.cancel; exit
}
}
}

val start = System.currentTimeMillis
def run { handler ! Pulse((System.currentTimeMillis - start) / 1000.0) }
}, 0, 10) // send Pulse every 10 ms

def input(k: Double => Double) = handler ! Input(k)
def output = handler !? Output
def bye = handler ! Bye
}

def main(args: Array[String]) {
val integrator = new Integrator
integrator.input(t => Math.sin(2.0 * Math.Pi * 0.5 * t))
integrator.input(_ => 0.0)
println(integrator.output)
integrator.bye
}
}

Smalltalk

Object subclass:#Integrator
classVariableNames:''
poolDictionaries:''
category:'Rosetta'

instance methods:

input:aFunctionOfT
input := aFunctionOfT.

startWithTickRate:r
"setup and start sampling"
tickRate := r.
s := 0.
thread := [ self integrateLoop ] fork.

stop
"stop and return the 'final' output"
^ s

integrateLoop
"no need for any locks
- the assignment to s is atomic in Smallalk; its either done or not, when terminated, so who cares"

|tBegin tPrev tNow kPrev kNow deltaT delta|

tBegin := tPrev := Timestamp nowWithMilliseconds.
kPrev := input value:0.

[true] whileTrue:[
Delay waitForSeconds: tickRate.
tNow := Timestamp nowWithMilliseconds.
kNow := input value:(tNow millisecondDeltaFrom:tBegin) / 1000.

deltaT := (tNow millisecondDeltaFrom:tPrev) / 1000.
delta := (kPrev + kNow) * deltaT / 2.

s := s + delta.
tPrev := tNow. kPrev := kNow.
].

class methods:

example
#( 0.5 0.1 0.05 0.01 0.005 0.001 0.0005 ) do:[:sampleRate |
|i|

i := Integrator new.
i input:[:t | (2 * Float pi * 0.5 * t) sin].
i startWithTickRate:sampleRate.

Delay waitForSeconds:2.
i input:[:t | 0].
Delay waitForSeconds:0.5.

Transcript
show:'Sample rate: '; showCR:sampleRate;
showCR:(i stop).
].

running:

output:

Sample rate: 0.5
-0.0258202058271805
Sample rate: 0.1
-0.00519217893508676
Sample rate: 0.05
-0.000897807957672559
Sample rate: 0.01
-0.000650159409949159
Sample rate: 0.005
-0.00033633922519125
Sample rate: 0.001
0.000286557714782226
Sample rate: 0.0005
0.000253571129723327

for backward compatibility, the smalltalk used here returns only timestamps with second-precision from "Timestamp now". Therefore, the millisecond-precision variant was used here. An alternative would have been to ask the OS for its ticker, which is more precise.

## SuperCollider

Instead of writing a class, here we just use an environment to encapsulate state.

```SuperCollider

(
envir.use {
~integral = 0;
~time = 0;
~prev = 0;
~running = true;
loop {
~val = ~input.(~time);
~integral = ~integral + (~val + ~prev * ~dt / 2);
~prev = ~val;
~time = ~time + ~dt;
~dt.wait;
}
}
};
)

// run the test
(
fork {
a.set(\dt, 0.0001);
a.set(\input, { |t| sin(2pi * 0.5 * t) });
a.play(quant: 0); // play immediately
2.wait;
a.set(\input, 0);
0.5.wait;
a.stop;
}
)

Swift

// For NSObject, NSTimeInterval and NSThread
import Foundation
// For PI and sin
import Darwin

class ActiveObject:NSObject {

let sampling = 0.1
var K: (t: NSTimeInterval) -> Double
var S: Double
var t0, t1: NSTimeInterval

func integrateK() {
t0 = t1
t1 += sampling
S += (K(t:t1) + K(t: t0)) * (t1 - t0) / 2
}

func updateObject() {
while true {
integrateK()
usleep(100000)
}
}

init(function: (NSTimeInterval) -> Double) {
S = 0
t0 = 0
t1 = 0
K = function
super.init()
}

func Input(function: (NSTimeInterval) -> Double) {
K = function

}

func Output() -> Double {
return S
}

}

// main
func sine(t: NSTimeInterval) -> Double {
let f = 0.5

return sin(2 * M_PI * f * t)
}

var activeObject = ActiveObject(function: sine)

var date = NSDate()

sleep(2)

activeObject.Input({(t: NSTimeInterval) -> Double in return 0.0})

usleep(500000)

println(activeObject.Output())

Sample output:

1.35308431126191e-16

Tcl

This implementation Tcl 8.6 for object support (for the active integrator object) and coroutine support (for the controller task). It could be rewritten to only use 8.5 plus the TclOO library.

package require Tcl 8.6
oo::class create integrator {
variable e sum delay tBase t0 k0 aid
constructor {{interval 1}} {
set delay \$interval
set tBase [clock microseconds]
set t0 0
set e { 0.0 }
set k0 0.0
set sum 0.0
set aid [after \$delay [namespace code {my Step}]]
}
destructor {
after cancel \$aid
}
method input expression {
set e \$expression
}
method output {} {
return \$sum
}
method Eval t {
expr \$e
}
method Step {} {
set aid [after \$delay [namespace code {my Step}]]
set t [expr {([clock microseconds] - \$tBase) / 1e6}]
set k1 [my Eval \$t]
set sum [expr {\$sum + (\$k1 + \$k0) * (\$t - \$t0) / 2.}]
set t0 \$t
set k0 \$k1
}
}

set pi 3.14159265
proc pause {time} {
yield [after [expr {int(\$time * 1000)}] [info coroutine]]
}
coroutine task_ apply [list {} "\$script;set ::done ok"]
vwait done
}
integrator create i
i input {sin(2*\$::pi * 0.5 * \$t)}
pause 2
i input { 0.0 }
pause 0.5
puts [format %.15f [i output]]
}

Sample output: -0.000000168952702

Visual Basic .NET

Since this object is CPU intensive, shutting it down when done is crucial. To facilitate this, the IDisposable pattern was used.

Module Module1

Sub Main()
Using active As New Integrator
active.Operation = Function(t As Double) Math.Sin(2 * Math.PI * 0.5 * t)
Console.WriteLine(active.Value)
active.Operation = Function(t As Double) 0
Console.WriteLine(active.Value)
End Using
End Sub

End Module

Class Integrator
Implements IDisposable

Private m_Operation As Func(Of Double, Double)
Private m_Disposed As Boolean
Private m_SyncRoot As New Object
Private m_Value As Double

Public Sub New()
m_Operation = Function(void) 0.0
t.Start()
End Sub

Private Sub MainLoop()
Dim epoch = Now
Dim t0 = 0.0
Do
SyncLock m_SyncRoot
Dim t1 = (Now - epoch).TotalSeconds
m_Value = m_Value + (Operation(t1) + Operation(t0)) * (t1 - t0) / 2
t0 = t1
End SyncLock
Loop Until m_Disposed
End Sub

Public Property Operation() As Func(Of Double, Double)
Get
SyncLock m_SyncRoot
Return m_Operation
End SyncLock
End Get
Set(ByVal value As Func(Of Double, Double))
SyncLock m_SyncRoot
m_Operation = value
End SyncLock
End Set
End Property

Public ReadOnly Property Value() As Double
Get
SyncLock m_SyncRoot
Return m_Value
End SyncLock
End Get
End Property

Protected Overridable Sub Dispose(ByVal disposing As Boolean)
m_Disposed = True
End Sub

Public Sub Dispose() Implements IDisposable.Dispose
Dispose(True)
GC.SuppressFinalize(Me)
End Sub

End Class

Output: 0.000241446762282308

zkl

{{trans|Python}} Uses cheese ball thread safety: since the integrator runs continuously and I don't want to queue the output, just sample it, strong references are used as they change atomically.

class Integrator{
// continuously integrate a function `K`, at each `interval` seconds'
fcn init(f,interval=1e-4){
var _interval=interval, K=Ref(f), S=Ref(0.0), run=True;
self.launch();  // start me as a thread
}
fcn liftoff{ // entry point for the thread
start:=Time.Clock.timef;  // floating point seconds since Epoch
t0,k0,s:=0,K.value(0),S.value;
while(run){
Atomic.sleep(_interval);
t1,k1:=Time.Clock.timef - start, K.value(t1);
s+=(k1 + k0)*(t1 - t0)/2.0; S.set(s);
t0,k0=t1,k1;
}
}
fcn sample  { S.value  }
fcn setF(f) { K.set(f) }
}
ai:=Integrator(fcn(t){ ((0.0).pi*t).sin() });
Atomic.sleep(2);
ai.sample().println();

ai.setF(fcn{ 0 });
Atomic.sleep(0.5);
ai.sample().println();

{{out}}

4.35857e-09
1.11571e-07

{{omit from|ACL2}} {{omit from|AWK}} {{omit from|gnuplot}} {{omit from|GUISS}} {{omit from|LaTeX}} {{omit from|Locomotive Basic}} {{omit from|Make}} {{omit from|Metafont}} {{omit from|M4}} {{omit from|Maxima}} {{omit from|ML/I}} {{omit from|Octave}} {{omit from|PlainTeX}} {{omit from|TI-89 BASIC}} {{omit from|Retro}} {{omit from|UNIX Shell}} {{omit from|ZX Spectrum Basic}}