Taskflow Algorithms » Task-parallel Pipeline | Taskflow QuickStart

# Taskflow Algorithms » Task-parallel Pipeline

Taskflow provides a task-parallel pipeline programming framework for you to implement a pipeline algorithm. Pipeline parallelism refers to a parallel execution of multiple data tokens through a linear chain of pipes or stages. Each stage processes the data token sent from the previous stage, applies the given callable to that data token, and then sends the result to the next stage. Multiple data tokens can be processed simultaneously across different stages.

## Include the Header

You need to include the header file, `taskflow/algorithm/pipeline.hpp`, for implementing task-parallel pipeline algorithms.

    #include <taskflow/algorithm/pipeline.hpp>

## Understand the Pipeline Scheduling Framework

A tf::Pipeline object is a composable graph to create a pipeline scheduling framework through a module task in a taskflow (see Composable Tasking). Unlike the conventional pipeline programming frameworks (e.g., Intel TBB Parallel Pipeline), 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 an efficient pipeline scheduling framework.

The figure above gives an example of our pipeline scheduling framework. The framework consists of three pipes (serial-parallel-serial stages) and four lines (maximum parallelism), where each line processes at most one data token. A pipeline of three pipes and four lines will propagate each data token through a sequential chain of three pipes and can simultaneously process up to four data tokens at the four lines. Each edge represents a task dependency. For example, the edge from `pipe-0` to `pipe-1` in line `0` represents the task dependency between the first and the second pipes in the first line; the edge from `pipe-0` in line `0` to `pipe-0` in line `1` represents the task dependency between two adjacent lines when processing two data tokens at the same pipe. Each pipe can be either a serial type or a parallel type, where a serial pipe processes data tokens sequentially and a parallel pipe processes different data tokens simultaneously.

#### Attention

Due to the nature of pipeline, Taskflow requires the first pipe to be a serial type. The pipeline scheduling algorithm operates in a circular fashion with a factor of line count.

## Create a Task-parallel Pipeline Module Task

Taskflow leverages modern C++ and template techniques to strike a balance between the expressiveness and generality in designing the pipeline programming model. In general, there are three steps to create a task-parallel pipeline application:

1. Define the pipeline structure (e.g., pipe type, pipe callable, stopping rule, line count)
2. Define the data storage and layout, if needed for the application
3. Define the pipeline taskflow graph using composition

The following code creates a pipeline scheduling framework using the example from the previous section. The framework schedules a total of five scheduling tokens labeled from 0 to 4. The first pipe stores the token identifier in a custom data storage, `buffer`, and each of the rest pipes adds one to the input data from the result of the previous pipe and stores the result into the corresponding line entry in the buffer.

     1: tf::Taskflow taskflow;
     2: tf::Executor executor;
     3:
     4: // maximum parallelism - each line processes one token at a time
     5: const size_t num_lines = 4;
     6:
     7: // custom data storage
     8: std::array<int, num_lines> buffer;
     9:
    10: // the pipeline consists of three pipes (serial-parallel-serial)
    11: // and up to four concurrent scheduling tokens
    12: tf::Pipeline pl(num_lines,
    13:   tf::Pipe{tf::PipeType::SERIAL, [&buffer](tf::Pipeflow& pf) {
    14:     // generate only 5 scheduling tokens
    15:     if(pf.token() == 5) {
    16:       pf.stop();
    17:     }
    18:     // save the result of this pipe into the buffer
    19:     else {
    20:       printf("pipe 0: input token = %zu\n", pf.token());
    21:       buffer[pf.line()] = pf.token();
    22:     }
    23:   }},
    24:
    25:   tf::Pipe{tf::PipeType::PARALLEL, [&buffer](tf::Pipeflow& pf) {
    26:     printf(
    27:       "pipe 1: input buffer[%zu] = %d\n",
    28:       pf.line(), buffer[pf.line()]
    29:     );
    30:     // propagate the previous result to this pipe by adding one
    31:     buffer[pf.line()] = buffer[pf.line()] + 1;
    32:   }},
    33:
    34:   tf::Pipe{tf::PipeType::SERIAL, [&buffer](tf::Pipeflow& pf) {
    35:     printf(
    36:       "pipe 2: input buffer[%zu] = %d\n",
    37:       pf.line(), buffer[pf.line()]
    38:     );
    39:     // propagate the previous result to this pipe by adding one
    40:     buffer[pf.line()] = buffer[pf.line()] + 1;
    41:   }}
    42: );
    43:
    44: // build the pipeline graph using composition
    45: tf::Task pipeline = taskflow.composed_of(pl).name("pipeline");
    46:
    47: // execute the taskflow
    48: executor.run(taskflow).wait();

Debrief:

- Lines 4-5 define the structure of the pipeline scheduling framework
- Line 8 defines the data storage as an one-dimensional array of `num_lines` integers
- Line 12 defines the number of lines in the pipeline
- Lines 13-23 define the first serial pipe, which will stop the pipeline scheduling at the fifth token
- Lines 25-32 define the second parallel pipe
- Lines 34-41 define the third serial pipe
- Line 45 defines the pipeline taskflow graph using composition
- Line 48 executes the taskflow

Taskflow leverages Interact with the Runtime and Composable Tasking to implement the pipeline scheduling framework. The taskflow graph of this pipeline example is shown as follows, where 1) one condition task is used to decide which runtime task to run and 2) four runtime tasks are used to schedule tokens at four parallel lines, respectively.

In this example, we customize the data storage, `buffer`, as an one-dimensional array of 4 integers, since the pipeline structure defines only four parallel lines. Each entry of `buffer` stores stores the data being processed in the corresponding line. For example, `buffer[1]` stores the processed data at line `1`. The following figure shows the data layout of `buffer`.

#### Attention

In practice, you may need to add padding to the data type of the buffer or align it with the cacheline size to avoid false sharing. If the data type varies at different pipes, you can use std::variant to store the data types in a uniform storage.

For each scheduling token, you can use tf::Pipeflow::line() to get its line identifier and tf::Pipeflow::pipe() to get its pipe identifier. For example, if a scheduling token is at the third pipe of the forth line, tf::Pipeflow::line() will return `3` and tf::Pipeflow::pipe() will return `2` (index starts from 0). To stop the execution of the pipeline, you need to call tf::Pipeflow::stop() at the first pipe. Once the stop signal has been triggered, the pipeline will stop scheduling any new tokens after the callable. As we can see from this example, tf::Pipeline gives you the full control to customize your application data on top of a pipeline scheduling framework.

#### Attention

1. Calling tf::Pipeflow::stop() not at the first pipe has no effect on the pipeline scheduling.
2. In most cases, std::thread::hardware_concurrency is a good number for line count.

Our pipeline algorithm schedules tokens in a circular manner, with a factor of `num_lines`. That is, token `t` will be processed at line `t % num_lines`. The following snippet shows one of the possible outputs of this pipeline program:

    pipe 0: input token = 0
    pipe 1: input buffer[0] = 0
    pipe 2: input buffer[0] = 1
    pipe 0: input token = 1
    pipe 1: input buffer[1] = 1
    pipe 2: input buffer[1] = 2
    pipe 0: input token = 2
    pipe 1: input buffer[2] = 2
    pipe 2: input buffer[2] = 3
    pipe 0: input token = 3
    pipe 1: input buffer[3] = 3
    pipe 2: input buffer[3] = 4
    pipe 0: input token = 4
    pipe 1: input buffer[0] = 4
    pipe 2: input buffer[0] = 5

There are a total of five tokens running through three pipes. Each pipes prints its input data value, except the first pipe that prints its token identifier. Since the second pipe is a parallel pipe, the output can interleave.

## Connect Pipeline with Other Tasks

You can connect the pipeline module task with other tasks to create a taskflow application that embeds one or multiple pipeline algorithms. We describe three common examples below:

- Example 1: Iterate a Pipeline
- Example 2: Concatenate Two Pipelines
- Example 3: Define Multiple Parallel Pipelines

### Example 1: Iterate a Pipeline

This example emulates a data streaming application that iteratively runs a stream of data through a pipeline using conditional tasking. The taskflow graph consists of one pipeline module task and one condition task. The pipeline module task processes a stream of data. The condition task decides the availability of data and reruns the pipeline when the next stream of data becomes available.

     1: tf::Taskflow taskflow;
     2: tf::Executor executor;
     3:
     4: const size_t num_lines = 4;  // maximum parallelism of the pipeline
     5:
     6: int i = 0, N = 0;
     7: // custom data storage
     8: std::array<int, num_lines> buffer;
     9:
    10: // the pipeline consists of three pipes (serial-parallel-serial)
    11: // and up to four concurrent scheduling tokens
    12: tf::Pipeline pl(num_lines,
    13:   tf::Pipe{tf::PipeType::SERIAL, [&i, &buffer](tf::Pipeflow& pf) {
    14:     // only 5 scheduling tokens are processed
    15:     if(i++ == 5) {
    16:       pf.stop();
    17:     }
    18:     // save the result of this pipe into the buffer
    19:     else {
    20:       printf("stage 0: input token = %zu\n", pf.token());
    21:       buffer[pf.line()] = pf.token();
    22:     }
    23:   }},
    24:
    25:   tf::Pipe{tf::PipeType::PARALLEL, [&buffer](tf::Pipeflow& pf) {
    26:     printf(
    27:       "stage 1: input buffer[%zu] = %d\n",
    28:       pf.line(), buffer[pf.line()]
    29:     );
    30:     // propagate the previous result to this pipe by adding one
    31:     buffer[pf.line()] = buffer[pf.line()] + 1;
    32:   }},
    33:
    34:   tf::Pipe{tf::PipeType::SERIAL, [&buffer](tf::Pipeflow& pf) {
    35:     printf(
    36:       "stage 2: input buffer[%zu] = %d\n",
    37:       pf.line(), buffer[pf.line()]
    38:     );
    39:     // propagate the previous result to this pipe by adding one
    40:     buffer[pf.line()] = buffer[pf.line()] + 1;
    41:   }}
    42: );
    43:
    44: tf::Task conditional = taskflow.emplace([&N, &i](){
    45:   i = 0;
    46:   if (++N < 2) {
    47:     std::cout << "Rerun the pipeline\n";
    48:     return 0;
    49:   }
    50:   else {
    51:     return 1;
    52:   }
    53: }).name("conditional");
    54:
    55: // build the pipeline graph using composition
    56: tf::Task pipeline = taskflow.composed_of(pl)
    57:                             .name("pipeline");
    58: tf::Task initial  = taskflow.emplace([](){ std::cout << "initial\n";  })
    59:                             .name("initial");
    60: tf::Task stop     = taskflow.emplace([](){ std::cout << "stop\n"; })
    61:                             .name("stop");
    62:
    63: // specify the graph dependency
    64: initial.precede(pipeline);
    65: pipeline.precede(conditional);
    66: conditional.precede(pipeline, stop);
    67:
    68: // execute the taskflow
    69: executor.run(taskflow).wait();

Debrief:

- Lines 4-5 define the structure of the pipeline scheduling framework
- Line 8 defines the data storage as an one-dimensional array (`num_lines` integers)
- Line 12 defines the number of lines in the pipeline
- Lines 13-23 define the first serial pipe, which will stop the pipeline scheduling when `i` is `5`
- Lines 25-32 define the second parallel pipe
- Lines 34-41 define the third serial pipe
- Lines 44-53 define a condition task which returns 0 when `N` is less than `2`, otherwise returns `1`
- Line 45 resets variable `i`
- Lines 56-57 define the pipeline graph using composition
- Lines 58-61 define two static tasks
- Line 64-66 define the task dependency
- Line 69 executes the taskflow

The taskflow graph of this pipeline example is illustrated as follows:

The following snippet shows one of the possible outputs:

    initial
    stage 0: input token = 0
    stage 1: input buffer[0] = 0
    stage 2: input buffer[0] = 1
    stage 0: input token = 1
    stage 1: input buffer[1] = 1
    stage 2: input buffer[1] = 2
    stage 0: input token = 2
    stage 1: input buffer[2] = 2
    stage 2: input buffer[2] = 3
    stage 0: input token = 3
    stage 1: input buffer[3] = 3
    stage 2: input buffer[3] = 4
    stage 0: input token = 4
    stage 1: input buffer[0] = 4
    stage 2: input buffer[0] = 5
    Rerun the pipeline
    stage 0: input token = 5
    stage 1: input buffer[1] = 5
    stage 2: input buffer[1] = 6
    stage 0: input token = 6
    stage 1: input buffer[2] = 6
    stage 2: input buffer[2] = 7
    stage 0: input token = 7
    stage 1: input buffer[3] = 7
    stage 2: input buffer[3] = 8
    stage 0: input token = 8
    stage 1: input buffer[0] = 8
    stage 2: input buffer[0] = 9
    stage 0: input token = 9
    stage 1: input buffer[1] = 9
    stage 2: input buffer[1] = 10
    stop

The pipeline runs twice as controlled by the condition task `conditional`. The starting token in the second run of the pipeline is `5` rather than `0` because the pipeline keeps a stateful number of tokens. The last token is `9`, which means the pipeline processes in total `10` scheduling tokens. The first five tokens (token `0` to `4`) are processed in the first run, and the remaining five tokens (token `5` to `9`) are processed in the second run. In the condition task, we use `N` as a decision-making counter to process the next stream of data.

### Example 2: Concatenate Two Pipelines

This example demonstrates two concatenated pipelines where a sequence of data tokens run synchronously from one pipeline to another pipeline. The first pipeline task precedes the second pipeline task.

     1: tf::Taskflow taskflow("pipeline");
     2: tf::Executor executor;
     3:
     4: // define the maximum parallelism of the pipeline
     5: const size_t num_lines = 4;
     6:
     7: // custom data storage
     8: std::array<int, num_lines> buffer_1;
     9: std::array<int, num_lines> buffer_2;
    10:
    11: // the pipeline_1 consists of three pipes (serial-parallel-serial)
    12: // and up to four concurrent scheduling tokens
    13: tf::Pipeline pl_1(num_lines,
    14:   tf::Pipe{tf::PipeType::SERIAL, [&buffer_1](tf::Pipeflow& pf) mutable{
    15:     // generate only 4 scheduling tokens
    16:     if(pf.token() == 4) {
    17:       pf.stop();
    18:     }
    19:     // save the result of this pipe into the buffer
    20:     else {
    21:       printf("pipeline 1, pipe 0: input token = %zu\n", pf.token());
    22:       buffer_1[pf.line()] = pf.token();
    23:     }
    24:   }},
    25:
    26:   tf::Pipe{tf::PipeType::PARALLEL, [&buffer_1](tf::Pipeflow& pf) {
    27:     printf(
    28:       "pipeline 1, pipe 1: input buffer_1[%zu] = %d\n",
    29:       pf.line(), buffer_1[pf.line()]
    30:     );
    31:     // propagate the previous result to this pipe by adding one
    32:     buffer_1[pf.line()] = buffer_1[pf.line()] + 1;
    33:   }},
    34:
    35:   tf::Pipe{tf::PipeType::SERIAL, [&buffer_1](tf::Pipeflow& pf) {
    36:     printf(
    37:       "pipeline 1, pipe 2: input buffer_1[%zu] = %d\n",
    38:       pf.line(), buffer_1[pf.line()]
    39:     );
    40:     // propagate the previous result to this pipe by adding one
    41:     buffer_1[pf.line()] = buffer_1[pf.line()] + 1;
    42:   }}
    43: );
    44:
    45: // the pipeline_2 consists of three pipes (serial-parallel-serial)
    46: // and up to four concurrent scheduling tokens
    47: tf::Pipeline pl_2(num_lines,
    48:   tf::Pipe{tf::PipeType::SERIAL,
    49:   [&buffer_2, &buffer_1](tf::Pipeflow& pf) mutable{
    50:     // generate only 4 scheduling tokens
    51:     if(pf.token() == 4) {
    52:       pf.stop();
    53:     }
    54:     // save the result of this pipe into the buffer
    55:     else {
    56:       printf("pipeline 2, pipe 0: input value = %d\n", buffer_1[pf.line()]);
    57:       buffer_2[pf.line()] = buffer_1[pf.line()];
    58:     }
    59:   }},
    60:
    61:   tf::Pipe{tf::PipeType::PARALLEL, [&buffer_2](tf::Pipeflow& pf) {
    62:     printf(
    63:       "pipeline 2, pipe 1: input buffer_2[%zu] = %d\n",
    64:       pf.line(), buffer_2[pf.line()]
    65:     );
    66:     // propagate the previous result to this pipe by adding 1
    67:     buffer_2[pf.line()] = buffer_2[pf.line()] + 1;
    68:   }},
    69:
    70:   tf::Pipe{tf::PipeType::SERIAL, [&buffer_2](tf::Pipeflow& pf) {
    71:     printf(
    72:       "pipeline 2, pipe 2: input buffer_2[%zu] = %d\n",
    73:       pf.line(), buffer_2[pf.line()]
    74:     );
    75:     // propagate the previous result to this pipe by adding 1
    76:     buffer_2[pf.line()] = buffer_2[pf.line()] + 1;
    77:   }}
    78: );
    79:
    80: // build the pipeline graph using composition
    81: tf::Task pipeline_1 = taskflow.composed_of(pl_1).name("pipeline_1");
    82: tf::Task pipeline_2 = taskflow.composed_of(pl_2).name("pipeline_2");
    83:
    84: // specify the graph dependency
    85: pipeline_1.precede(pipeline_2);
    86:
    87: // execute the taskflow
    88: executor.run(taskflow).wait();

Debrief:

- Line 8 defines the data storage (`num_lines` integers) for pipeline `pl_1`
- Line 9 defines the data storage (`num_lines` integers) for pipeline `pl_2`
- Lines 14-24 define the first serial pipe in `pl_1`
- Lines 26-33 define the second parallel pipe in `pl_1`
- Lines 35-42 define the third serial pipe in `pl_1`
- Lines 48-59 define the first serial pipe in `pl_2` that takes the results of `pl_1` as inputs
- Lines 61-68 define the second parallel pipe in `pl_2`
- Lines 70-77 define the third serial pipe in `pl_2`
- Lines 81-82 define the pipeline graphs using composition
- Line 85 defines the task dependency
- Line 88 runs the taskflow

The taskflow graph of this pipeline example is illustrated as follows:

The following snippet shows one of the possible outputs:

    pipeline 1, pipe 0: input token = 0
    pipeline 1, pipe 1: input buffer_1[0] = 0
    pipeline 1, pipe 2: input buffer_1[0] = 1
    pipeline 1, pipe 0: input token = 1
    pipeline 1, pipe 1: input buffer_1[1] = 1
    pipeline 1, pipe 2: input buffer_1[1] = 2
    pipeline 1, pipe 0: input token = 2
    pipeline 1, pipe 1: input buffer_1[2] = 2
    pipeline 1, pipe 2: input buffer_1[2] = 3
    pipeline 1, pipe 0: input token = 3
    pipeline 1, pipe 1: input buffer_1[3] = 3
    pipeline 1, pipe 2: input buffer_1[3] = 4
    pipeline 2, pipe 1: input value = 2
    pipeline 2, pipe 2: input buffer_2[0] = 2
    pipeline 2, pipe 3: input buffer_2[0] = 3
    pipeline 2, pipe 1: input value = 3
    pipeline 2, pipe 2: input buffer_2[1] = 3
    pipeline 2, pipe 3: input buffer_2[1] = 4
    pipeline 2, pipe 1: input value = 4
    pipeline 2, pipe 2: input buffer_2[2] = 4
    pipeline 2, pipe 3: input buffer_2[2] = 5
    pipeline 2, pipe 1: input value = 5
    pipeline 2, pipe 2: input buffer_2[3] = 5
    pipeline 2, pipe 3: input buffer_2[3] = 6

The output of pipelines `pl_1` and `pl_2` can be different from run to run because their second pipes are both parallel types. Due to the task dependency between `pipeline_1` and `pipeline_2`, the output of `pl_1` precedes the output of `pl_2`.

### Example 3: Define Multiple Parallel Pipelines

This example creates two independent pipelines that run in parallel on different data sets.

     1: tf::Taskflow taskflow("pipeline");
     2: tf::Executor executor;
     3:
     4: // define the maximum parallelism of the pipeline
     5: const size_t num_lines = 4;
     6:
     7: // custom data storage
     8: std::array<int, num_lines> buffer_1;
     9: std::array<int, num_lines> buffer_2;
    10:
    11: // the pipeline_1 consists of three pipes (serial-parallel-serial)
    12: // and up to four concurrent scheduling tokens
    13: tf::Pipeline pl_1(num_lines,
    14:   tf::Pipe{tf::PipeType::SERIAL, [&buffer_1](tf::Pipeflow& pf) mutable{
    15:     // generate only 5 scheduling tokens
    16:     if(pf.token() == 5) {
    17:       pf.stop();
    18:     }
    19:     // save the result of this pipe into the buffer
    20:     else {
    21:       printf("pipeline 1, pipe 0: input token = %zu\n", pf.token());
    22:       buffer_1[pf.line()] = pf.token();
    23:     }
    24:   }},
    25:
    26:   tf::Pipe{tf::PipeType::PARALLEL, [&buffer_1](tf::Pipeflow& pf) {
    27:     printf(
    28:       "pipeline 1, pipe 1: input buffer_1[%zu] = %d\n",
    29:       pf.line(), buffer_1[pf.line()]
    30:     );
    31:     // propagate the previous result to this pipe by adding one
    32:     buffer_1[pf.line()] = buffer_1[pf.line()] + 1;
    33:   }},
    34:
    35:   tf::Pipe{tf::PipeType::SERIAL, [&buffer_1](tf::Pipeflow& pf) {
    36:     printf(
    37:       "pipeline 1, pipe 2: input buffer_1[%zu] = %d\n",
    38:       pf.line(), buffer_1[pf.line()]
    39:     );
    40:     // propagate the previous result to this pipe by adding one
    41:     buffer_1[pf.line()] = buffer_1[pf.line()] + 1;
    42:   }}
    43: );
    44:
    45: // the pipeline_2 consists of three pipes (serial-parallel-serial)
    46: // and up to four concurrent scheduling tokens
    47: tf::Pipeline pl_2(num_lines,
    48:   tf::Pipe{tf::PipeType::SERIAL, [&buffer_2](tf::Pipeflow& pf) mutable{
    49:     // generate only 2 scheduling tokens
    50:     if(pf.token() == 5) {
    51:       pf.stop();
    52:     }
    53:     // save the result of this pipe into the buffer
    54:     else {
    55:       printf("pipeline 2, pipe 0: input token = %zu\n", pf.token());
    56:       buffer_2[pf.line()] = "pipeline";
    57:     }
    58:   }},
    59:
    60:   tf::Pipe{tf::PipeType::PARALLEL, [&buffer_2](tf::Pipeflow& pf) {
    61:     printf(
    62:       "pipeline 2, pipe 1: input buffer_2[%zu] = %d\n",
    63:       pf.line(), buffer_2[pf.line()]
    64:     );
    65:     // propagate the previous result to this pipe by concatenating "_"
    66:     buffer_2[pf.line()] = buffer_2[pf.line()];
    67:   }},
    68:
    69:   tf::Pipe{tf::PipeType::SERIAL, [&buffer_2](tf::Pipeflow& pf) {
    70:     printf(
    71:       "pipeline 2, pipe 2: input buffer_2[%zu] = %d\n",
    72:       pf.line(), buffer_2[pf.line()]
    73:     );
    74:     // propagate the previous result to this pipe by concatenating "2"
    75:     buffer_2[pf.line()] = buffer_2[pf.line()];
    76:   }}
    77: );
    78:
    79: tf::Task pipeline_1 = taskflow.composed_of(pl_1)
    80:                               .name("pipeline_1");
    81: tf::Task pipeline_2 = taskflow.composed_of(pl_2)
    82:                               .name("pipeline_2");
    83: tf::Task initial = taskflow.emplace([](){ std::cout << "initial"; })
    84:                               .name("initial");
    85:
    86: initial.precede(pipeline_1, pipeline_2);
    87:
    88: executor.run(taskflow).wait();

Debrief:

- Line 8 defines the data storage (`num_lines` integers) for pipeline `pl_1`
- Line 9 defines the data storage (`num_lines` integers) for pipeline `pl_2`
- Lines 14-24 define the first serial pipe in `pl_1`
- Lines 26-33 define the second parallel pipe in `pl_1`
- Lines 35-42 define the third serial pipe in `pl_1`
- Lines 48-58 define the first serial pipe in `pl_2`
- Lines 60-67 define the second parallel pipe in `pl_2`
- Lines 69-76 define the third serial pipe in `pl_2`
- Lines 79-82 define the pipeline graphs using composition
- Lines 83-84 define a static task.
- Line 86 defines the task dependency
- Line 88 runs the taskflow

The taskflow graph of this pipeline example is illustrated as follows:

The following snippet shows one of the possible outputs:

    initial
    pipeline 2, pipe 0: input token = 0
    pipeline 2, pipe 1: input buffer_2[0] = 0
    pipeline 2, pipe 2: input buffer_2[0] = 1
    pipeline 1, pipe 0: input token = 0
    pipeline 1, pipe 1: input buffer_1[0] = 0
    pipeline 1, pipe 2: input buffer_1[0] = 1
    pipeline 1, pipe 0: input token = 1
    pipeline 1, pipe 1: input buffer_1[1] = 1
    pipeline 1, pipe 0: input token = 2
    pipeline 1, pipe 1: input buffer_1[2] = 2
    pipeline 1, pipe 0: input token = 3
    pipeline 1, pipe 1: input buffer_1[3] = 3
    pipeline 1, pipe 0: input token = 4
    pipeline 1, pipe 1: input buffer_1[0] = 4
    pipeline 2, pipe 0: input token = 1
    pipeline 2, pipe 1: input buffer_2[1] = 1
    pipeline 2, pipe 0: input buffer_2[1] = 2
    pipeline 2, pipe 0: input token = 2
    pipeline 2, pipe 1: input buffer_2[2] = 2
    pipeline 2, pipe 2: input buffer_2[2] = 3
    pipeline 2, pipe 0: input token = 3
    pipeline 2, pipe 1: input buffer_2[3] = 3
    pipeline 2, pipe 2: input buffer_2[3] = 4
    pipeline 2, pipe 0: input token = 4
    pipeline 2, pipe 1: input buffer_2[0] = 4
    pipeline 2, pipe 2: input buffer_2[0] = 5
    pipeline 1, pipe 2: input buffer_1[1] = 2
    pipeline 1, pipe 2: input buffer_1[2] = 3
    pipeline 1, pipe 2: input buffer_1[3] = 4
    pipeline 1, pipe 2: input buffer_1[0] = 5

Because pipeline `pl_1` and pipeline `pl_2` are running in parallel, their outputs may interleave.

## Reset a Pipeline

Our pipeline scheduling framework keeps a stateful number of scheduled tokens at each submitted run. You can reset the pipeline to the initial state using tf::Pipeline::reset(), where the number of scheduled tokens will start from zero in the next run. Borrowed from Example 1: Iterate a Pipeline, the program below resets the pipeline at the second iteration (inside the condition task) so the scheduling token will start from zero in the next run.

    tf::Taskflow taskflow("pipeline");
    tf::Executor executor;

    // define the maximum parallelism of the pipeline
    const size_t num_lines = 4;

    // custom data storage
    std::array<int, num_lines> buffer;

    // the pipeline consists of three pipes (serial-parallel-serial)
    // and up to four concurrent scheduling tokens
    tf::Pipeline pl(num_lines,
      tf::Pipe{tf::PipeType::SERIAL, [&buffer](tf::Pipeflow& pf) mutable{
        // generate only 5 scheduling tokens
        if(pf.token() == 5) {
          pf.stop();
        }
        // save the result of this pipe into the buffer
        else {
          printf("pipe 0: input token = %zu\n", pf.token());
          buffer[pf.line()] = pf.token();
        }
      }},

      tf::Pipe{tf::PipeType::PARALLEL, [&buffer](tf::Pipeflow& pf) {
        printf(
          "pipe 1: input buffer_1[%zu] = %d\n", pf.line(), buffer[pf.line()]
        );
        // propagate the previous result to this pipe by adding one
        buffer[pf.line()] = buffer[pf.line()] + 1;
      }},

      tf::Pipe{tf::PipeType::SERIAL, [&buffer](tf::Pipeflow& pf) {
        printf(
          "pipe 2: input buffer[%zu][%zu] = %d\n", pf.line(), buffer[pf.line()]
        );
        // propagate the previous result to this pipe by adding one
        buffer[pf.line()] = buffer[pf.line()] + 1;
      }}
    );

    tf::Task conditional = taskflow.emplace([&](){
      if (++N < 2) {
        pl.reset();
        std::cout << "Rerun the pipeline\n";
        return 0;
      }
      else {
        return 1;
      }
    }).name("conditional");

    tf::Task pipeline = taskflow.composed_of(pl)
                                .name("pipeline");
    tf::Task initial  = taskflow.emplace([](){ std::cout << "initial"; })
                                .name("initial");
    tf::Task stop     = taskflow.emplace([](){ std::cout << "stop"; })
                                .name("stop");

    initial.precede(pipeline);
    pipeline.precede(conditional);
    conditional.precede(pipeline, stop);

    executor.run(taskflow).wait();

The following snippet shows one of the possible outputs:

    initial
    pipe 0: input token = 0
    pipe 1: input buffer_1[0] = 0
    pipe 2: input buffer_1[0] = 1
    pipe 0: input token = 1
    pipe 1: input buffer_1[1] = 1
    pipe 2: input buffer_1[1] = 2
    pipe 0: input token = 2
    pipe 1: input buffer_1[2] = 2
    pipe 2: input buffer_1[2] = 3
    pipe 0: input token = 3
    pipe 1: input buffer_1[3] = 3
    pipe 2: input buffer_1[3] = 4
    pipe 0: input token = 4
    pipe 1: input buffer_1[0] = 4
    pipe 2: input buffer_1[0] = 5
    Rerun the pipeline
    pipe 0: input token = 0
    pipe 1: input buffer_1[0] = 0
    pipe 2: input buffer_1[0] = 1
    pipe 0: input token = 1
    pipe 1: input buffer_1[1] = 1
    pipe 2: input buffer_1[1] = 2
    pipe 0: input token = 2
    pipe 1: input buffer_1[2] = 2
    pipe 2: input buffer_1[2] = 3
    pipe 0: input token = 3
    pipe 1: input buffer_1[3] = 3
    pipe 2: input buffer_1[3] = 4
    pipe 0: input token = 4
    pipe 1: input buffer_1[0] = 4
    pipe 2: input buffer_1[0] = 5
    stop

The output can be different from run to run, since the second pipe is a parallel type. At the second iteration from the condition task, we reset the pipeline so the token identifier starts from `0` rather than `5`.

## Learn More about Taskflow Pipeline

Visit the following pages to learn more about pipeline:

- Task-parallel Scalable Pipeline
- Data-parallel Pipeline
- Text Processing Pipeline
- Graph Processing Pipeline
- Taskflow Processing Pipeline

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