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#include <taskflow/algorithm/pipeline.hpp>
template<typename... Ps>
tf::Pipeline class

class to create a pipeline scheduling framework

Template parameters
Ps | pipe types

A pipeline is a composable graph object for users to create a pipeline scheduling framework using a module task in a taskflow. Unlike the conventional pipeline programming frameworks (e.g., Intel TBB), Taskflow's pipeline algorithm does not provide any data abstraction, which often restricts users from optimizing data layouts in their applications, but a flexible framework for users to customize their application data atop our pipeline scheduling. The following code creates a pipeline of four parallel lines to schedule tokens through three serial pipes:

    tf::Taskflow taskflow;
    tf::Executor executor;

    const size_t num_lines = 4;
    const size_t num_pipes = 3;

    // create a custom data buffer
    std::array<std::array<int, num_pipes>, num_lines> buffer;

    // create a pipeline graph of four concurrent lines and three serial pipes
    tf::Pipeline pipeline(num_lines,
      // first pipe must define a serial direction
      tf::Pipe{tf::PipeType::SERIAL, [&buffer](tf::Pipeflow& pf) {
        // generate only 5 scheduling tokens
        if(pf.token() == 5) {
          pf.stop();
        }
        // save the token id into the buffer
        else {
          buffer[pf.line()][pf.pipe()] = pf.token();
        }
      }},
      tf::Pipe{tf::PipeType::SERIAL, [&buffer] (tf::Pipeflow& pf) {
        // propagate the previous result to this pipe by adding one
        buffer[pf.line()][pf.pipe()] = buffer[pf.line()][pf.pipe()-1] + 1;
      }},
      tf::Pipe{tf::PipeType::SERIAL, [&buffer](tf::Pipeflow& pf){
        // propagate the previous result to this pipe by adding one
        buffer[pf.line()][pf.pipe()] = buffer[pf.line()][pf.pipe()-1] + 1;
      }}
    );

    // build the pipeline graph using composition
    tf::Task init = taskflow.emplace([](){ std::cout << "ready\n"; })
                            .name("starting pipeline");
    tf::Task task = taskflow.composed_of(pipeline)
                            .name("pipeline");
    tf::Task stop = taskflow.emplace([](){ std::cout << "stopped\n"; })
                            .name("pipeline stopped");

    // create task dependency
    init.precede(task);
    task.precede(stop);

    // run the pipeline
    executor.run(taskflow).wait();

The above example creates a pipeline graph that schedules five tokens over four parallel lines in a circular fashion, as depicted below:

    o -> o -> o
    |    |    |
    v    v    v
    o -> o -> o
    |    |    |
    v    v    v
    o -> o -> o
    |    |    |
    v    v    v
    o -> o -> o

At each pipe stage, the program propagates the result to the next pipe by adding one to the result stored in a custom data storage, `buffer`. The pipeline scheduler will generate five scheduling tokens and then stop.

Internally, tf::Pipeline uses std::tuple to store the given sequence of pipes. The definition of each pipe can be different, completely decided by the compiler to optimize the object layout. After a pipeline is constructed, it is not possible to change its pipes. If applications need to change these pipes, please use tf::ScalablePipeline.

## Constructors, destructors, conversion operators

Pipeline(size_t num_lines, Ps && ... ps)
  constructs a pipeline object
Pipeline(size_t num_lines, std::tuple<Ps...>&& ps)
  constructs a pipeline object

## Public functions

auto num_lines() const -> size_t noexcept
  queries the number of parallel lines
auto num_pipes() const -> size_t constexpr noexcept
  queries the number of pipes
void reset()
  resets the pipeline
auto num_tokens() const -> size_t noexcept
  queries the number of generated tokens in the pipeline
auto graph() -> Graph&
  obtains the graph object associated with the pipeline construct

## Function documentation

###
template<typename... Ps>
tf::Pipeline<Ps>:: Pipeline(size_t num_lines, Ps && ... ps)

constructs a pipeline object

Parameters
num_lines | the number of parallel lines
ps | a list of pipes

Constructs a pipeline of up to `num_lines` parallel lines to schedule tokens through the given linear chain of pipes. The first pipe must define a serial direction (tf::PipeType::SERIAL) or an exception will be thrown.

###
template<typename... Ps>
tf::Pipeline<Ps>:: Pipeline(size_t num_lines, std::tuple<Ps...>&& ps)

constructs a pipeline object

Parameters
num_lines | the number of parallel lines
ps | a tuple of pipes

Constructs a pipeline of up to `num_lines` parallel lines to schedule tokens through the given linear chain of pipes. The first pipe must define a serial direction (tf::PipeType::SERIAL) or an exception will be thrown.

###
template<typename... Ps>
size_t tf::Pipeline<Ps>:: num_lines() const noexcept

queries the number of parallel lines

The function returns the number of parallel lines given by the user upon the construction of the pipeline. The number of lines represents the maximum parallelism this pipeline can achieve.

###
template<typename... Ps>
size_t tf::Pipeline<Ps>:: num_pipes() const constexpr noexcept

queries the number of pipes

The Function returns the number of pipes given by the user upon the construction of the pipeline.

###
template<typename... Ps>
void tf::Pipeline<Ps>:: reset()

resets the pipeline

Resetting the pipeline to the initial state. After resetting a pipeline, its token identifier will start from zero as if the pipeline was just constructed.

###
template<typename... Ps>
size_t tf::Pipeline<Ps>:: num_tokens() const noexcept

queries the number of generated tokens in the pipeline

The number represents the total scheduling tokens that has been generated by the pipeline so far.

###
template<typename... Ps>
Graph& tf::Pipeline<Ps>:: graph()

obtains the graph object associated with the pipeline construct

This method is primarily used as an opaque data structure for creating a module task of the this pipeline.

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