| Taskflow: A General-purpose Task-parallel Programming System

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Parallel Reduction

Taskflow provides template functions for constructing tasks to perform parallel reduction over a range of items.

# Include the Header

You need to include the header file, `taskflow/algorithm/reduce.hpp`, for creating a parallel-reduction task.

#include <taskflow/algorithm/reduce.hpp>

# Create a Parallel-Reduction Task

The task created by tf::Taskflow::reduce(B first, E last, T& result, O bop, P part) performs parallel reduction over the range `[first, last)` using the binary operator `bop` and stores the reduced result in `result`. It represents the parallel execution of the following loop:

for(auto itr = first; itr != last; itr++) {
result = bop(result, *itr);
}

At runtime, the reduction task partitions the range among workers, each computing a partial result, and then combines those partial results into `result` using `bop`. The initial value of `result` participates in the reduction — it is combined with the partial results as if it were an additional element. `result` is captured by reference inside the task; it is the user's responsibility to ensure it remains alive during execution.

int sum = 100;
std::vector<int> vec = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
tf::Task task = taskflow.reduce(vec.begin(), vec.end(), sum,
[](int l, int r) { return l + r; }
);
executor.run(taskflow).wait();
assert(sum == 155); // 100 + (1+2+...+10)
tf::Task
class to create a task handle over a taskflow node
Definition task.hpp:569

The order in which `bop` is applied to pairs of elements is unspecified. Elements of the range may be grouped and rearranged in arbitrary order, as illustrated below for a sum-reduction over eight elements:

The result and argument types of `bop` must be consistent with the element type.

## Capture Iterators by Reference

You can pass iterators by reference using std::ref to marshal parameter updates between dependent tasks. This is useful when the range is not known at task-graph construction time but is initialized by an upstream task.

int sum = 100;
std::vector<int> vec;
std::vector<int>::iterator first, last;
tf::Task init = taskflow.emplace([&]() {
vec = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
first = vec.begin();
last = vec.end();
});
tf::Task task = taskflow.reduce(
std::ref(first), std::ref(last), sum,
[](int l, int r) { return l + r; }
);
// wrong! first and last are captured by copy at construction time
// tf::Task task = taskflow.reduce(first, last, sum,
// [](int l, int r) { return l + r; }
// );
init.precede(task);
executor.run(taskflow).wait();
assert(sum == 155);
tf::Task::precede
Task & precede(Ts &&... tasks)
adds precedence links from this to other tasks
Definition task.hpp:1258

When `init` finishes, `first` and `last` point to the initialized data range of `vec`, and the reduction task performs parallel reduction over the 10 elements.

# Create a Parallel-Transform-Reduction Task

It is common to transform each element into a new type and then reduce over the transformed values. The task created by tf::Taskflow::transform_reduce(B first, E last, T& result, BOP bop, UOP uop, P part) applies the unary operator `uop` to each element and then performs parallel reduction over `result` and the transformed values using `bop`. It represents the parallel execution of the following loop:

for(auto itr = first; itr != last; itr++) {
result = bop(result, uop(*itr));
}

The example below transforms each digit character in a string to an integer and then sums them in parallel:

std::string str = "12345678";
int sum = 0;
tf::Task task = taskflow.transform_reduce(str.begin(), str.end(), sum,
[](int a, int b) { return a + b; }, // binary reduction operator
[](char c) -> int { return c - '0'; } // unary transformation operator
);
executor.run(taskflow).wait();
assert(sum == 36); // 1+2+3+4+5+6+7+8

The order in which `bop` is applied to the transformed elements is unspecified. It is possible that `bop` will receive r-value arguments from both sides (e.g., `bop(uop(*itr1), uop(*itr2))`) due to transformed temporaries. When data passing is expensive, define the result type `T` to be move-constructible.

## Capture Iterators by Reference

As with tf::Taskflow::reduce, iterators can be passed by reference using std::ref so that an upstream task can set up the range before the parallel-transform-reduction runs.

std::string str;
std::string::iterator first, last;
int sum = 0;
tf::Task init = taskflow.emplace([&]() {
str = "12345678";
first = str.begin();
last = str.end();
});
tf::Task task = taskflow.transform_reduce(
std::ref(first), std::ref(last), sum,
[](int a, int b) { return a + b; },
[](char c) -> int { return c - '0'; }
);
// wrong! first and last are captured by copy at construction time
// tf::Task task = taskflow.transform_reduce(first, last, sum, bop, uop);
init.precede(task);
executor.run(taskflow).wait();
assert(sum == 36);

# Create a Parallel-Reduce-by-Index Task

Unlike tf::Taskflow::reduce, which gives each worker a single element at a time, tf::Taskflow::reduce_by_index gives each worker a contiguous subrange of the index space. This allows the local reduction to be written as an explicit loop over the subrange, enabling optimisations such as SIMD vectorisation, custom accumulator types, or data initialisation interleaved with reduction. The method, tf::Taskflow::reduce_by_index, represents the parallel execution of the following two-phase loop:

// phase 1: each worker computes a partial result over its subrange
T partial = lop(subrange, std::nullopt); // first subrange: no prior total
T partial = lop(subrange, running_total); // subsequent subranges: accumulate
// phase 2: combine all partial results into the final result
result = gop(result, partial1);
result = gop(result, partial2);
// ...

The local operator `lop` is invoked once per subrange assigned to a worker. Its second argument is a `std::optional<T>` carrying the running total accumulated by that worker so far:

- `std::nullopt` on the first subrange processed by a worker — the worker should initialise its accumulator from scratch.
- A value on subsequent subranges — the worker should continue accumulating from the provided running total.

The global operator `gop` combines the per-worker partial results and the initial value of `result` into the final answer.

The example below performs a sum-reduction over a large array, initialising each element inside the local reducer:

std::vector<double> data(100000);
double res = 1.0;
taskflow.reduce_by_index(
tf::IndexRange<size_t>(0, data.size(), 1),
res,
// local reducer: called once per subrange per worker
[&](tf::IndexRange<size_t> subrange, std::optional<double> running_total) {
double partial = running_total ? *running_total : 0.0;
for(size_t i = subrange.begin(); i < subrange.end(); i += subrange.step_size()) {
data[i] = 1.0;
partial += data[i];
}
return partial;
},
// global reducer: combines partial results into res
std::plus<double>()
);
executor.run(taskflow).wait();
assert(res == 100001.0); // 1.0 (initial) + 100000 * 1.0
tf::IndexRanges
class to create an N-dimensional index range of integral indices
Definition iterator.hpp:188

The global reducer combines all partial results with the initial value of `res` (here `1.0`), so the final answer is `1.0` + `100000.0` = `100001.0`.

## Capture IndexRange by Reference

You can pass the index range by reference using std::ref so that an upstream task can set the bounds before the parallel-reduce-by-index runs.

std::vector<double> data;
double res = 0.0;
tf::IndexRange<size_t> range(0, 0, 1); // placeholder — filled by init
tf::Task init = taskflow.emplace([&]() {
data.assign(100000, 1.0);
range.begin(0).end(data.size()).step_size(1);
});
tf::Task task = taskflow.reduce_by_index(
std::ref(range),
res,
[&](tf::IndexRange<size_t> subrange, std::optional<double> running_total) {
double partial = running_total ? *running_total : 0.0;
for(size_t i = subrange.begin(); i < subrange.end(); i += subrange.step_size()) {
partial += data[i];
}
return partial;
},
std::plus<double>()
);
// wrong! range is captured by copy at construction time
// tf::Task task = taskflow.reduce_by_index(range, res, lop, gop);
init.precede(task);
executor.run(taskflow).wait();
assert(res == 100000.0);
tf::IndexRanges::end
T end() const
queries the ending index of the range (only available when N == 1)
Definition iterator.hpp:358
tf::IndexRanges::begin
T begin() const
queries the starting index of the range (only available when N == 1)
Definition iterator.hpp:346
tf::IndexRanges::step_size
T step_size() const
queries the step size of the range (only available when N == 1)
Definition iterator.hpp:370

# Configure a Partitioner

A partitioner controls how the iteration space is divided among workers. Taskflow provides four partitioners, each suited to different workload characteristics:

- tf::StaticPartitioner divides the range into equal-sized chunks ahead of execution and assigns them to workers in order. It has the lowest scheduling overhead and delivers the best performance when every element costs roughly the same amount of work to reduce.
- tf::DynamicPartitioner distributes fixed-sized chunks to workers on demand as they become available. It adapts well to workloads where reduction cost varies per element, at the expense of slightly higher coordination overhead.
- tf::GuidedPartitioner distributes chunks whose size decreases adaptively as work is consumed — large chunks early to reduce overhead, smaller chunks late to balance the tail. This is the default partitioner and delivers stable, near-optimal performance across a wide range of workloads.
- tf::RandomPartitioner distributes chunks of randomly sampled sizes, which can help avoid systematic load imbalances caused by data-dependent cost patterns.

The following example creates two parallel-reduction tasks using different partitioners:

int sum1 = 100, sum2 = 100;
std::vector<int> vec = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
tf::StaticPartitioner static_partitioner(0); // chunk size auto-determined
tf::GuidedPartitioner guided_partitioner(0); // minimum chunk size auto-determined
// parallel-reduction with static partitioner
taskflow.reduce(vec.begin(), vec.end(), sum1,
[](int l, int r) { return l + r; },
static_partitioner
);
// parallel-reduction with guided partitioner
taskflow.reduce(vec.begin(), vec.end(), sum2,
[](int l, int r) { return l + r; },
guided_partitioner
);
tf::GuidedPartitioner
class to create a guided partitioner for scheduling parallel algorithms
Definition partitioner.hpp:417
tf::StaticPartitioner
class to construct a static partitioner for scheduling parallel algorithms
Definition partitioner.hpp:262

As a rule of thumb, prefer tf::StaticPartitioner when every element costs the same to reduce (e.g., summation over a plain array) and tf::GuidedPartitioner for irregular workloads (e.g., reductions whose cost depends on the element value). tf::DynamicPartitioner is a good choice when chunks must be kept small and strictly equal in size.

Note
  By default, parallel-reduction tasks use tf::DefaultPartitioner (currently tf::GuidedPartitioner) if no partitioner is specified.