# CUDA Standard Algorithms » Parallel Scan

Taskflow provides standard template methods for scanning a range of items on a CUDA GPU.

## Include the Header

You need to include the header file, `taskflow/cuda/algorithm/scan.hpp`, for using the parallel-scan algorithm.

    #include <taskflow/cuda/algorithm/find.hpp>

## What is a Scan Operation?

A parallel scan task performs the cumulative sum, also known as prefix sum or scan, of the input range and writes the result to the output range. Each element of the output range contains the running total of all earlier elements using the given binary operator for summation.

## Scan a Range of Items

tf::cuda_inclusive_scan computes an inclusive prefix sum operation using the given binary operator over a range of elements specified by `[first, last)`. The term "inclusive" means that the i-th input element is included in the i-th sum. The following code computes the inclusive prefix sum over an input array and stores the result in an output array.

    const size_t N = 1000000;
    int* input  = tf::cuda_malloc_shared<int>(N);  // input  vector
    int* output = tf::cuda_malloc_shared<int>(N);  // output vector

    // initializes the data
    for(size_t i=0; i<N; input[i++] = rand());

    // create an execution policy
    tf::cudaStream stream;
    tf::cudaDefaultExecutionPolicy policy(stream);

    // queries the required buffer size to scan N elements using the given policy
    auto bytes  = policy.scan_bufsz<int>(N);
    auto buffer = tf::cuda_malloc_device<std::byte>(bytes);

    // computes inclusive scan over input and stores the result in output
    tf::cuda_inclusive_scan(policy,
      input, input + N, output, [] __device__ (int a, int b) {return a + b;}, buffer
    );

    // synchronizes and verifies the result
    stream.synchronize();

    for(size_t i=1; i<N; i++) {
      assert(output[i] == output[i-1] + input[i]);
    }

    // delete the device memory
    cudaFree(input);
    cudaFree(output);
    cudaFree(buffer);

The scan algorithm runs asynchronously through the stream specified in the execution policy. You need to synchronize the stream to obtain correct results. Since the GPU scan algorithm may require extra buffer to store the temporary results, you need to provide a buffer of size at least larger or equal to the value returned from `tf::cudaDefaultExecutionPolicy::scan_bufsz`.

#### Attention

You must keep the buffer alive before the scan call completes.

On the other hand, tf::cuda_exclusive_scan computes an exclusive prefix sum operation. The term "exclusive" means that the i-th input element is NOT included in the i-th sum.

    // computes exclusive scan over input and stores the result in output
    tf::cuda_exclusive_scan(policy,
      input, input + N, output, [] __device__ (int a, int b) {return a + b;}, buffer
    );

    // synchronizes the execution and verifies the result
    stream.synchronize();
    for(size_t i=1; i<N; i++) {
      assert(output[i] == output[i-1] + input[i-1]);
    }

## Scan a Range of Transformed Items

tf::cuda_transform_inclusive_scan transforms each item in the range `[first, last)` and computes an inclusive prefix sum over these transformed items. The following code multiplies each item by 10 and then compute the inclusive prefix sum over 1000000 transformed items.

    const size_t N = 1000000;
    int* input  = tf::cuda_malloc_shared<int>(N);  // input  vector
    int* output = tf::cuda_malloc_shared<int>(N);  // output vector

    // initializes the data
    for(size_t i=0; i<N; input[i++] = rand());

    // create an execution policy
    tf::cudaStream stream;
    tf::cudaDefaultExecutionPolicy policy(stream);

    // queries the required buffer size to scan N elements using the given policy
    auto bytes  = policy.scan_bufsz<int>(N);
    auto buffer = tf::cuda_malloc_device<std::byte>(bytes);

    // computes inclusive scan over transformed input and stores the result in output
    tf::cuda_transform_inclusive_scan(policy,
      input, input + N, output,
      [] __device__ (int a, int b) { return a + b; },  // binary scan operator
      [] __device__ (int a) { return a*10; },          // unary transform operator
      buffer
    );

    // wait for the scan to complete
    stream.synchronize();

    // verifies the result
    for(size_t i=1; i<N; i++) {
      assert(output[i] == output[i-1] + input[i] * 10);
    }

    // delete the device memory
    cudaFree(input);
    cudaFree(output);
    cudaFree(buffer);

Similarly, tf::cuda_transform_exclusive_scan performs an exclusive prefix sum over a range of transformed items. The following code computes the exclusive prefix sum over 1000000 transformed items each multipled by 10.

    const size_t N = 1000000;
    int* input  = tf::cuda_malloc_shared<int>(N);  // input  vector
    int* output = tf::cuda_malloc_shared<int>(N);  // output vector

    // initializes the data
    for(size_t i=0; i<N; input[i++] = rand());

    // create an execution policy
    tf::cudaStream stream;
    tf::cudaDefaultExecutionPolicy policy(stream);

    // queries the required buffer size to scan N elements using the given policy
    auto bytes  = policy.scan_bufsz<int>(N);
    auto buffer = tf::cuda_malloc_device<std::byte>(bytes);

    // computes exclusive scan over transformed input and stores the result in output
    tf::cuda_transform_exclusive_scan(policy,
      input, input + N, output,
      [] __device__ (int a, int b) { return a + b; },  // binary scan operator
      [] __device__ (int a) { return a*10; },          // unary transform operator
      buffer
    );

    // wait for the scan to complete
    stream.synchronize();

    // verifies the result
    for(size_t i=1; i<N; i++) {
      assert(output[i] == output[i-1] + input[i-1] * 10);
    }

    // delete the device memory
    cudaFree(input);
    cudaFree(output);
    cudaFree(buffer);

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