# parallel_reduce Template Function¶

## Summary¶

Computes reduction over a range.

## Syntax¶

template<typename Range, typename Value, typename Func, typename Reduction>
Value parallel_reduce( const Range& range, const Value& identity,
const Func& func, const Reduction& reduction,

template<typename Range, typename Body>
void parallel_reduce( const Range& range, Body& body


where the optional partitioner declares any of the partitioners as shown in column 1 of the Partitioners table in the Partitioners section.

## Description¶

The parallel_reduce template has two forms. The functional form is designed to be easy to use in conjunction with lambda expressions. The imperative form is designed to minimize copying of data.

The functional form parallel_reduce(range, identity, func, reduction) performs a parallel reduction by applying func to subranges in range and reducing the results using binary operator reduction. It returns the result of the reduction. Parameter func and reduction can be lambda expressions. The table below summarizes the type requirements on the types of identity, func, and reduction.

Requirements for Func and Reduction: Pseudo-Signature, Semantics

Value identity

Left identity element for Func::operator().

Value Func::operator()(const Range& range, const Value& x) const

Accumulate result for subrange, starting with initial value x.

Value Reduction::operator()(const Value& x, const Value& y) const

Combine results x and y.

The imperative form parallel_reduce(range,body) performs parallel reduction of body over each value in range. Type Range must model the Range concept. The body must model the requirements shown in the table below.

Requirements for parallel_reduce Body: Pseudo-Signature, Semantics

Body::Body( Body&, split )

Splitting constructor. Must be able to run concurrently with operator() and method join.

Body::~Body()

Destructor.

void Body::operator()(const Range& range)

Accumulate result for subrange.

void Body::join( Body& rhs )

Join results. The result in rhs should be merged into the result of this.

A parallel_reduce recursively splits the range into subranges to the point such that is_divisible() is false for each subrange. A parallel_reduce uses the splitting constructor to make one or more copies of the body for each thread. It may copy a body while the body’s operator() or method join runs concurrently. You are responsible for ensuring the safety of such concurrency. In typical usage, the safety requires no extra effort.

When worker threads are available, parallel_reduce invokes the splitting constructor for the body. For each such split of the body, it invokes method join in order to merge the results from the bodies. Define join to update this to represent the accumulated result for this and rhs. The reduction operation should be associative, but does not have to be commutative. For a noncommutative operation op, “left.join(right)” should update left to be the result of left op right.

A body is split only if the range is split, but the converse is not necessarily so. The figure below diagrams a sample execution of parallel_reduce. The root represents the original body b0 being applied to the half-open interval [0,20). The range is recursively split at each level into two subranges. The grain size for the example is 5, which yields four leaf ranges. The slash marks (/) denote where copies (b1 and b2) of the body were created by the body splitting constructor. Bodies b0 and b1 each evaluate one leaf. Body b2 evaluates leaf [10,15) and [15,20), in that order. On the way back up the tree, parallel_reduce invokes b0.join(b1) and b0.join(b2) to merge the results of the leaves.

Execution of parallel_reduce over blocked_range<int>(0,20,5)

The figure above shows only one possible execution. Other valid executions include splitting b2 into b2 and b3, or doing no splitting at all. With no splitting, b0 evaluates each leaf in left to right order, with no calls to join. A given body always evaluates one or more subranges in left to right order. For example, in the figure above, body b2 is guaranteed to evaluate [10,15) before [15,20). You may rely on the left to right property for a given instance of a body. However, you must neither rely on a particular choice of body splitting nor on the subranges processed by a given body object being consecutive. parallel_reduce makes the choice of body splitting nondeterministically.

Example where Body b0 processes non-consecutive subranges.

The subranges evaluated by a given body are not consecutive if there is an intervening join. The joined information represents processing of a gap between evaluated subranges. The figure above shows such an example. The body b0 performs the following sequence of operations:

• b0( [0,5) )

• b0.join()( b1 ) where b1 has already processed [5,10)

• b0( [10,15) )

• b0( [15,20) )

In other words, body b0 gathers information about all the leaf subranges in left to right order, either by directly processing each leaf, or by a join operation on a body that gathered information about one or more leaves in a similar way. When no worker threads are available, parallel_reduce executes sequentially from left to right in the same sense as for parallel_for. Sequential execution never invokes the splitting constructor or method join.

All overloads can be passed a task_group_context object so that the algorithm’s tasks are executed in this group. By default the algorithm is executed in a bound group of its own.

Complexity

If the range and body take O(1) space, and the range splits into nearly equal pieces, then the space complexity is O(P×log(N)), where N is the size of the range and P is the number of threads.

## Example (Imperative Form)¶

The following code sums the values in an array.

#include "tbb/parallel_reduce.h"
#include "tbb/blocked_range.h"

using namespace tbb;

struct Sum {
float value;
Sum() : value(0) {}
Sum( Sum& s, split ) {value = 0;}
void operator()( const blocked_range<float*>& r ) {
float temp = value;
for( float* a=r.begin(); a!=r.end(); ++a ) {
temp += *a;
}
value = temp;
}
void join( Sum& rhs ) {value += rhs.value;}
};

float ParallelSum( float array[], size_t n ) {
Sum total;
parallel_reduce( blocked_range<float*>( array, array+n ),
total );
}


The example generalizes to reduction for any associative operation op as follows:

• Replace occurrences of 0 with the identity element for op

• Replace occurrences of += with op= or its logical equivalent.

• Change the name Sum to something more appropriate for op.

The operation may be noncommutative. For example, op could be matrix multiplication.

## Example with Lambda Expressions¶

The following is analogous to the previous example, but written using lambda expressions and the functional form of parallel_reduce.

#include "tbb/parallel_reduce.h"
#include "tbb/blocked_range.h"

using namespace tbb;

float ParallelSum( float array[], size_t n ) {
return parallel_reduce(
blocked_range<float*>( array, array+n ),
0.f,
[](const blocked_range<float*>& r, float init)->float {
for( float* a=r.begin(); a!=r.end(); ++a )
init += *a;
return init;
},
[]( float x, float y )->float {
return x+y;
}
);
}


STL generalized numeric operations and functions objects can be used to write the example more compactly as follows:

#include <numeric>
#include <functional>
#include "tbb/parallel_reduce.h"
#include "tbb/blocked_range.h"

using namespace tbb;

float ParallelSum( float array[], size_t n ) {
return parallel_reduce(
blocked_range<float*>( array, array+n ),
0.f,
[](const blocked_range<float*>& r, float value)->float {
return std::accumulate(r.begin(),r.end(),value);
},
std::plus<float>()
);
}