namespace tf {

/** @page ConditionalTasking Conditional Tasking

Parallel workloads often require making control-flow decisions across dependent tasks.
%Taskflow supports a very efficient interface of conditional tasking
for users to implement general control flow such as dynamic flow, cycles and conditionals 
that are otherwise difficult to do with existing frameworks.

@tableofcontents

@section CreateAConditionTask Create a Condition Task

A condition task evaluates a set of instructions and returns an integer index 
of the next successor task to execute. 
The index is defined with respect to the order of its successor construction.
The following example creates an if-else block using a single condition task.

@code{.cpp}
 1: tf::Taskflow taskflow;
 2:
 3: auto [init, cond, yes, no] = taskflow.emplace(
 4:  [] () { },
 5:  [] () { return 0; },
 6:  [] () { std::cout << "yes\n"; },
 7:  [] () { std::cout << "no\n"; }
 8: );
 9:
10: cond.succeed(init)
11:     .precede(yes, no);  // executes yes if cond returns 0
12:                         // executes no  if cond returns 1
@endcode

@dotfile images/conditional-tasking-if-else.dot

Line 5 creates a condition task @c cond and line 11 creates two dependencies 
from @c cond to two other tasks, @c yes and @c no.
With this order, when @c cond returns 0, the execution moves on to task @c yes.
When @c cond returns 1, the execution moves on to task @c no.

@attention
It is your responsibility to ensure the return of a condition task goes to
a correct successor task. If the return falls beyond the range of the successors,
the executor will not schedule any tasks.

Condition task can go cyclic to describe @em iterative control flow.
The example below implements a simple yet commonly used feedback loop through
a condition task (line 7-10) that returns
a random binary value.
If the return value from @c cond is @c 0, it loops back to itself, 
or otherwise to @c stop. 

@code{.cpp}
 1: tf::Taskflow taskflow;
 2: 
 3: tf::Task init = taskflow.emplace([](){}).name("init");
 4: tf::Task stop = taskflow.emplace([](){}).name("stop");
 5:
 6: // creates a condition task that returns 0 or 1
 7: tf::Task cond = taskflow.emplace([](){
 8:   std::cout << "flipping a coin\n";
 9:   return std::rand() % 2;
10: }).name("cond");
11:
12: // creates a feedback loop {0: cond, 1: stop}
13: init.precede(cond);
14: cond.precede(cond, stop);  // returns 0 to 'cond' or 1 to 'stop'
15:
16: executor.run(taskflow).wait();
@endcode

<!-- @image html images/conditional-tasking-1.svg width=45% -->
@dotfile images/conditional-tasking-1.dot

A taskflow of complex control flow often just takes a few lines of code 
to implement, and different control flow blocks may run in parallel.
The code below creates another taskflow with three condition tasks.

@code{.cpp}
tf::Taskflow taskflow;

tf::Task A = taskflow.emplace([](){}).name("A");
tf::Task B = taskflow.emplace([](){}).name("B");
tf::Task C = taskflow.emplace([](){}).name("C");
tf::Task D = taskflow.emplace([](){}).name("D");
tf::Task E = taskflow.emplace([](){}).name("E");
tf::Task F = taskflow.emplace([](){}).name("F");
tf::Task G = taskflow.emplace([](){}).name("G");
tf::Task H = taskflow.emplace([](){}).name("H");
tf::Task I = taskflow.emplace([](){}).name("I");
tf::Task K = taskflow.emplace([](){}).name("K");
tf::Task L = taskflow.emplace([](){}).name("L");
tf::Task M = taskflow.emplace([](){}).name("M");
tf::Task cond_1 = taskflow.emplace([](){ return std::rand()%2; }).name("cond_1");
tf::Task cond_2 = taskflow.emplace([](){ return std::rand()%2; }).name("cond_2");
tf::Task cond_3 = taskflow.emplace([](){ return std::rand()%2; }).name("cond_3");

A.precede(B, F);
B.precede(C);
C.precede(D);
D.precede(cond_1);
E.precede(K);
F.precede(cond_2);
H.precede(I);
I.precede(cond_3);
L.precede(M);

cond_1.precede(B, E);       // return 0 to 'B' or 1 to 'E'
cond_2.precede(G, H);       // return 0 to 'G' or 1 to 'H'
cond_3.precede(cond_3, L);  // return 0 to 'cond_3' or 1 to 'L'

taskflow.dump(std::cout);
@endcode

The above code creates three condition tasks:
(1) a condition task @c cond_1 that loops back 
to @c B on returning @c 0, or proceeds to @c E on returning @c 1,
(2) a condition task @c cond_2 that goes to @c G on returning @c 0,
or @c H on returning @c 1,
(3) a condition task @c cond_3 that loops back to itself on returning @c 0, 
or proceeds to @c L on returning @c 1

<!-- @image html images/conditional-tasking-2.svg width=100% -->
@dotfile images/conditional-tasking-2.dot

You can use condition tasks to create cycles as long as the graph does not introduce task race during execution. However, cycles are not allowed in non-condition tasks.

@attention
Conditional tasking lets you make in-task control-flow decisions to
enable @em end-to-end parallelism, 
instead of resorting to client-side partition or synchronizing your task graph
at the decision points of control flow.

@section TaskSchedulingPolicy Understand our Task-level Scheduling

In order to understand how an executor schedules condition tasks,
we define two dependency types,
<em>strong dependency</em> and <em>weak dependency</em>.
A strong dependency is a preceding link from a non-condition task to 
another task.
A weak dependency is a preceding link from a condition task to
another task. 
The number of dependents of a task is the sum of strong dependency 
and weak dependency.
The table below lists the strong dependency and
weak dependency numbers of each task in the previous example.

<div align="center">
| task   | strong dependency | weak dependency | dependents |
| :-:    | :-:               | :-:             |            |
| A      | 0                 | 0               | 0          |
| B      | 1                 | 1               | 2          |
| C      | 1                 | 0               | 1          |
| D      | 1                 | 0               | 1          |
| E      | 0                 | 1               | 1          |
| F      | 1                 | 0               | 1          |
| G      | 0                 | 1               | 1          |
| H      | 0                 | 1               | 1          |
| I      | 1                 | 0               | 1          |
| K      | 1                 | 0               | 1          |
| L      | 0                 | 1               | 1          | 
| M      | 1                 | 0               | 1          |
| cond_1 | 1                 | 0               | 1          |
| cond_2 | 1                 | 0               | 1          |
| cond_3 | 1                 | 1               | 2          |
</div>

You can query the number of strong dependents,
the number of weak dependents,
and the number of dependents of a task.

@code{.cpp}
 1: tf::Taskflow taskflow;
 2: 
 3: tf::Task task = taskflow.emplace([](){});
 4: 
 5: // ... add more tasks and preceding links
 6:
 7: std::cout << task.num_dependents() << '\n';
 8: std::cout << task.num_strong_dependents() << '\n'; 
 9: std::cout << task.num_weak_dependents() << '\n';
@endcode

When you submit a task to an executor,
the scheduler starts with tasks of <em>zero dependents</em>
(both zero strong and weak dependencies)
and continues to execute successive tasks whenever 
their <em>strong dependencies</em> are met.
However, the scheduler skips this rule when executing a condition task
and jumps directly to its successors indexed by the return value.

<!-- @image html images/conditional-tasking-rules.svg width=100% -->
@dotfile images/task_level_scheduling.dot

Each task has an @em atomic join counter to keep track of strong dependents
that are met at runtime.
When a task completes,
the join counter is restored to the task's strong dependency number 
in the graph, such that the subsequent execution can reuse the counter again.

@subsection TaskLevelSchedulingExample Example

Let's take a look at an example to understand how task-level scheduling
works. Suppose we have the following taskflow of one condition task @c cond
that forms a loop to itself on returning @c 0 and moves on to @c stop on
returning @c 1:

@dotfile images/conditional-tasking-1.dot

The scheduler starts with @c init task because it has no dependencies 
(both strong and weak dependencies).
Then, the scheduler moves on to the condition task @c cond.
If @c cond returns @c 0, the scheduler enqueues @c cond and runs it again.
If @c cond returns @c 1, the scheduler enqueues @c stop and then moves on.


@section AvoidCommonPitfalls Avoid Common Pitfalls

Condition tasks are handy in creating dynamic and cyclic control flows,
but they are also easy to make mistakes.
It is your responsibility to ensure a taskflow is properly conditioned. 
Top things to avoid include <em>no source tasks</em> to start with 
and <em>task race</em>. 
The figure below shows common pitfalls and their remedies. 

<!-- @image html images/conditional-tasking-pitfalls.svg  width=100% -->
@dotfile images/conditional-tasking-pitfalls.dot

In the @c error1 scenario,
there is no source task for the scheduler to start with,
and the simplest fix is to add a task @c S that has no dependents.
In the @c error2 scenario,
@c D might be scheduled twice by @c E through the strong dependency 
and @c C through the weak dependency (on returning @c 1).
To fix this problem, you can add an auxiliary task @c D-aux to break
the mixed use of strong dependency and weak dependency.
In the risky scenario, task @c X may be raced by @c M and @c P if @c M
returns @c 0 and P returns @c 1.

@attention
It is your responsibility to ensure a written taskflow graph is properly
conditioned.
We suggest that you @ref TaskSchedulingPolicy and infer if task race
exists in the execution of your graph.

@section ImplementControlFlowGraphs Implement Control-flow Graphs

@subsection ImplementIfElseControlFlow Implement If-Else Control Flow

You can use conditional tasking to implement if-else control flow.
The following example creates a nested if-else control flow diagram that 
executes three condition tasks to check the range of @c i.

@code{.cpp}
tf::Taskflow taskflow;

int i;

// create three condition tasks for nested control flow
auto initi = taskflow.emplace([&](){ i=3; }); 
auto cond1 = taskflow.emplace([&](){ return i>1 ? 1 : 0; }); 
auto cond2 = taskflow.emplace([&](){ return i>2 ? 1 : 0; }); 
auto cond3 = taskflow.emplace([&](){ return i>3 ? 1 : 0; }); 
auto equl1 = taskflow.emplace([&](){ std::cout << "i=1\n"; }); 
auto equl2 = taskflow.emplace([&](){ std::cout << "i=2\n"; }); 
auto equl3 = taskflow.emplace([&](){ std::cout << "i=3\n"; }); 
auto grtr3 = taskflow.emplace([&](){ std::cout << "i>3\n"; }); 

initi.precede(cond1);
cond1.precede(equl1, cond2);  // goes to cond2 if i>1
cond2.precede(equl2, cond3);  // goes to cond3 if i>2
cond3.precede(equl3, grtr3);  // goes to grtr3 if i>3
@endcode

@dotfile images/conditional-tasking-nested-if-else.dot


@subsection ImplementSwitchControlFlow Implement Switch Control Flow

You can use conditional tasking to implement @em switch control flow.
The following example creates a switch control flow diagram that 
executes one of the three cases at random using four condition tasks.

@code{.cpp}
tf::Taskflow taskflow;

auto [source, swcond, case1, case2, case3, target] = taskflow.emplace(
  [](){ std::cout << "source\n"; },
  [](){ std::cout << "switch\n"; return rand()%3; },
  [](){ std::cout << "case 1\n"; return 0; },
  [](){ std::cout << "case 2\n"; return 0; },
  [](){ std::cout << "case 3\n"; return 0; },
  [](){ std::cout << "target\n"; }
);

source.precede(swcond);
swcond.precede(case1, case2, case3);
target.succeed(case1, case2, case3);
@endcode

@dotfile images/conditional-tasking-switch.dot

Assuming @c swcond returns 1, the program outputs:

@code{.shell-session}
source
switch
case 2
target
@endcode

Keep in mind, both switch and case tasks must be described as condition tasks.
The following implementation is a common mistake in which case tasks
are not described as condition tasks.

@code{.cpp}
// wrong implementation of switch control flow using only one condition task
tf::Taskflow taskflow;

auto [source, swcond, case1, case2, case3, target] = taskflow.emplace(
  [](){ std::cout << "source\n"; },
  [](){ std::cout << "switch\n"; return rand()%3; },
  [](){ std::cout << "case 1\n"; },
  [](){ std::cout << "case 2\n"; },
  [](){ std::cout << "case 3\n"; },
  [](){ std::cout << "target\n"; }  // target has three strong dependencies
);

source.precede(swcond);
swcond.precede(case1, case2, case3);
target.succeed(case1, case2, case3);
@endcode

@dotfile images/conditional-tasking-switch-wrong.dot

In this faulty implementation, task @c target has three strong dependencies
but only one of them will be met.
This is because @c swcond is a condition task,
and only one case task will be executed depending on the return of @c swcond.


@subsection ImplementDoWhileLoopControlFlow Implement Do-While-Loop Control Flow

You can use conditional tasking to implement @em do-while-loop control flow.
The following example creates a do-while-loop control flow diagram that 
repeatedly increments variable @c i five times using one condition task.

@code{.cpp}
tf::Taskflow taskflow;

int i;

auto [init, body, cond, done] = taskflow.emplace(
  [&](){ std::cout << "i=0\n"; i=0; },
  [&](){ std::cout << "i++ => i="; i++; },
  [&](){ std::cout << i << '\n'; return i<5 ? 0 : 1; },
  [&](){ std::cout << "done\n"; }
);  

init.precede(body);
body.precede(cond);
cond.precede(body, done);
@endcode

@dotfile images/conditional-tasking-do-while.dot

The program outputs:

@code{.shell-session}
i=0
i++ => i=1
i++ => i=2
i++ => i=3
i++ => i=4
i++ => i=5
done
@endcode

@subsection ImplementWhileLoopControlFlow Implement While-Loop Control Flow

You can use conditional tasking to implement @em while-loop control flow.
The following example creates a while-loop control flow diagram that 
repeatedly increments variable @c i five times using two condition task.

@code{.cpp}
tf::Taskflow taskflow;

int i;

auto [init, cond, body, back, done] = taskflow.emplace(
  [&](){ std::cout << "i=0\n"; i=0; },
  [&](){ std::cout << "while i<5\n"; return i < 5 ? 0 : 1; },
  [&](){ std::cout << "i++=" << i++ << '\n'; },
  [&](){ std::cout << "back\n"; return 0; },
  [&](){ std::cout << "done\n"; }
);

init.precede(cond);
cond.precede(body, done);
body.precede(back);
back.precede(cond);
@endcode

@dotfile images/conditional-tasking-while.dot

The program outputs:

@code{.shell-session}
i=0
while i<5
i++=0
back
while i<5
i++=1
back
while i<5
i++=2
back
while i<5
i++=3
back
while i<5
i++=4
back
while i<5
done
@endcode

Notice that, when you implement a while-loop block, you cannot direct 
a dependency from the body task to the loop condition task.
Doing so will introduce a strong dependency between the body task
and the loop condition task, and the loop condition task will never be executed.
The following code shows a common faulty implementation of 
while-loop control flow.

@code{.cpp}
// wrong implementation of while-loop using only one condition task
tf::Taskflow taskflow;

int i;

auto [init, cond, body, done] = taskflow.emplace(
  [&](){ std::cout << "i=0\n"; i=0; },
  [&](){ std::cout << "while i<5\n"; return i < 5 ? 0 : 1; },
  [&](){ std::cout << "i++=" << i++ << '\n'; },
  [&](){ std::cout << "done\n"; }
);

init.precede(cond);
cond.precede(body, done);
body.precede(cond);
@endcode

@dotfile images/conditional-tasking-while-wrong.dot

In the taskflow diagram above,
the scheduler starts with @c init and then decrements the strong dependency of
the loop condition task, <tt>while i<5</tt>. 
After this, there remains one strong dependency, i.e., introduced by
the loop body task, @c i++.
However, task @c i++ will not be executed until the loop condition task returns @c 0,
causing a deadlock.


@section CreateAMultiConditionTask Create a Multi-condition Task

A <i>multi-condition task</i> is a generalized version of conditional tasking.
In some cases, applications need to jump to multiple branches from a parent task.
This can be done by creating a <i>multi-condition task</i> which allows a task
to select one or more successor tasks to execute.
Similar to a condition task, a multi-condition task returns
a vector of integer indices that indicate the successors to execute
when the multi-condition task completes.
The index is defined with respect to the order of successors preceded by
a multi-condition task.
For example, the following code creates a multi-condition task, @c A,
that informs the scheduler to run on its two successors, @c B and @c D.

@code{.cpp}
tf::Executor executor;
tf::Taskflow taskflow;

auto A = taskflow.emplace([&]() -> tf::SmallVector<int> { 
  std::cout << "A\n"; 
  return {0, 2};
}).name("A");
auto B = taskflow.emplace([&](){ std::cout << "B\n"; }).name("B");
auto C = taskflow.emplace([&](){ std::cout << "C\n"; }).name("C");
auto D = taskflow.emplace([&](){ std::cout << "D\n"; }).name("D");

A.precede(B, C, D);

executor.run(taskflow).wait();
@endcode

@dotfile images/multi-condition-task-1.dot

@attention
The return type of a multi-condition task is tf::SmallVector,
which provides C++ vector-style functionalities but comes with small buffer optimization.

One important application of conditional tasking is implementing 
<i>iterative control flow</i>.
You can use multi-condition tasks to create multiple loops that run concurrently.
The following code creates a sequential chain of four loops in which
each loop increments a counter variable ten times.
When the program completes, the value of the counter variable is @c 40.

@code{.cpp}
tf::Executor executor;
tf::Taskflow taskflow;
std::atomic<int> counter{0};

auto loop = [&, c = int(0)]() mutable -> tf::SmallVector<int> {
  counter.fetch_add(1, std::memory_order_relaxed);
  return {++c < 10 ? 0 : 1};
};
auto init = taskflow.emplace([](){}).name("init");
auto A = taskflow.emplace(loop).name("A");
auto B = taskflow.emplace(loop).name("B");
auto C = taskflow.emplace(loop).name("C");
auto D = taskflow.emplace(loop).name("D");

init.precede(A);
A.precede(A, B);
B.precede(B, C);
C.precede(C, D);
D.precede(D);

executor.run(taskflow).wait();  // counter == 40
taskflow.dump(std::cout);

std::cout << "counter == " << counter << '\n';
@endcode

@dotfile images/multi-condition-task-2.dot

@attention
It is your responsibility to ensure the return of a multi-condition task 
goes to a correct successor task.
If a returned index falls outside the successor range of a multi-condition task,
the scheduler will skip that index without doing anything.

*/

}



