# parallel_scan¶

[algorithms.parallel_scan]

Function template that computes parallel prefix.

// Defined in header <tbb/parallel_scan.h>

template<typename Range, typename Body>
void parallel_scan( const Range& range, Body& body );
template<typename Range, typename Body>
void parallel_scan( const Range& range, Body& body, /* see-below */ partitioner );

template<typename Range, typename Value, typename Scan, typename Combine>
Value parallel_scan( const Range& range, const Value& identity, const Scan& scan, const Combine& combine );
template<typename Range, typename Value, typename Scan, typename Combine>
Value parallel_scan( const Range& range, const Value& identity, const Scan& scan, const Combine& combine, /* see-below */ partitioner );


A partitioner type may be one of the following entities:

• const auto_partitioner&

• const simple_partitioner&

Requirements:

The function template parallel_scan computes a parallel prefix, also known as parallel scan. This computation is an advanced concept in parallel computing that is sometimes useful in scenarios that appear to have inherently serial dependences.

A mathematical definition of the parallel prefix is as follows. Let × be an associative operation with left-identity element id×. The parallel prefix of × over a sequence z0, z1, …*z*n-1 is a sequence y0, y1, y2, …*y*n-1 where:

• y0 = id× × z0

• yi = yi-1 × zi

For example, if × is addition, the parallel prefix corresponds a running sum. A serial implementation of parallel prefix is:

T temp = id;
for( int i=1; i<=n; ++i ) {
temp = temp + z[i];
y[i] = temp;
}


Parallel prefix performs this in parallel by reassociating the application of × (+ in example) and using two passes. It may invoke × up to twice as many times as the serial prefix algorithm. Even though it does more work, given the right grain size the parallel algorithm can outperform the serial one because it distributes the work across multiple hardware threads.

The function template parallel_scan has two forms. The imperative form parallel_scan(range, body) implements parallel prefix generically.

A summary (look at ParallelScanBody requirements) contains enough information such that for two consecutive subranges r and s:

• If r has no preceding subrange, the scan result for s can be computed from knowing s and the summary for r.

• A summary of r concatenated with s can be computed from the summaries of r and s.

The functional form parallel_scan(range, identity, scan, combine) is designed to use with functors and lambda expressions, hiding some complexities of the imperative form. It uses the same scan functor in both passes, differentiating them via a Boolean parameter, combines summaries with combine functor, and returns the summary computed over the whole range. The identity argument is the left identity element for Scan::operator().

## pre_scan and final_scan Classes¶

The parallel_scan template makes an effort to avoid prescanning where possible. When executed serially parallel_scan processes the subranges without any pre-scans, by processing the subranges from left to right using final scans. That’s why final scans must compute a summary as well as the final scan result. The summary might be needed to process the next subrange if no other thread has pre-scanned it yet.

## Example (Imperative Form)¶

The following code demonstrates how Body could be implemented for parallel_scan to compute the same result as the earlier sequential example.

class Body {
T sum;
T* const y;
const T* const z;
public:
Body( T y_[], const T z_[] ) : sum(id), z(z_), y(y_) {}
T get_sum() const { return sum; }

template<typename Tag>
void operator()( const tbb::blocked_range<int>& r, Tag ) {
T temp = sum;
for( int i=r.begin(); i<r.end(); ++i ) {
temp = temp + z[i];
if( Tag::is_final_scan() )
y[i] = temp;
}
sum = temp;
}
Body( Body& b, tbb::split ) : z(b.z), y(b.y), sum(id) {}
void reverse_join( Body& a ) { sum = a.sum + sum; }
void assign( Body& b ) { sum = b.sum; }
};

T DoParallelScan( T y[], const T z[], int n ) {
Body body(y,z);
tbb::parallel_scan( tbb::blocked_range<int>(0,n), body );
return body.get_sum();
}


The definition of operator() demonstrates typical patterns when using parallel_scan.

• A single template defines both versions. Doing so is not required, but usually saves coding effort, because the two versions are usually similar. The library defines static method is_final_scan() to enable differentiation between the versions.

• The prescan variant computes the × reduction, but does not update y. The prescan is used by parallel_scan to generate look-ahead partial reductions.

• The final scan variant computes the × reduction and updates y.

The operation reverse_join is similar to the operation join used by parallel_reduce, except that the arguments are reversed. That is, this is the right argument of ×. Template function parallel_scan decides if and when to generate parallel work. It is thus crucial that × is associative and that the methods of Body faithfully represent it. Operations such as floating-point addition that are somewhat associative can be used, with the understanding that the results may be rounded differently depending upon the association used by parallel_scan. The reassociation may differ between runs even on the same machine. However, when executed serially, parallel_scan associates identically to the serial form shown at the beginning of this section.

If you change the example to use a simple_partitioner, be sure to provide a grain size. The code below shows the how to do this for the grain size of 1000:

parallel_scan( blocked_range<int>(0,n,1000), total, simple_partitioner() );


## Example with Lambda Expressions¶

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

T DoParallelScan( T y[], const T z[], int n ) {
return tbb::parallel_scan(
tbb::blocked_range<int>(0,n),
id,
[](const tbb::blocked_range<int>& r, T sum, bool is_final_scan)->T {
T temp = sum;
for( int i=r.begin(); i<r.end(); ++i ) {
temp = temp + z[i];
if( is_final_scan )
y[i] = temp;
}
return temp;
},
[]( T left, T right ) {
return left + right;
}
);
}