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NAME

       MPI_Scan, MPI_Iscan - Computes an inclusive scan (partial reduction)

SYNTAX

C Syntax

       #include <mpi.h>
       int MPI_Scan(const void *sendbuf, void *recvbuf, int count,
                    MPI_Datatype datatype, MPI_Op op, MPI_Comm comm)

       int MPI_Iscan(const void *sendbuf, void *recvbuf, int count,
                     MPI_Datatype datatype, MPI_Op op, MPI_Comm comm,
                     MPI_Request *request)

Fortran Syntax

       USE MPI
       ! or the older form: INCLUDE 'mpif.h'
       MPI_SCAN(SENDBUF, RECVBUF, COUNT, DATATYPE, OP, COMM, IERROR)
            <type>    SENDBUF(*), RECVBUF(*)
            INTEGER   COUNT, DATATYPE, OP, COMM, IERROR

       MPI_ISCAN(SENDBUF, RECVBUF, COUNT, DATATYPE, OP, COMM, REQUEST, IERROR)
            <type>    SENDBUF(*), RECVBUF(*)
            INTEGER   COUNT, DATATYPE, OP, COMM, REQUEST, IERROR

Fortran 2008 Syntax

       USE  mpi_f08  MPI_Scan(sendbuf,  recvbuf, count, datatype, op, comm, ierror)      TYPE(*),
       DIMENSION(..), INTENT(IN) :: sendbuf      TYPE(*), DIMENSION(..) :: recvbuf       INTEGER,
       INTENT(IN)  ::  count       TYPE(MPI_Datatype),  INTENT(IN) :: datatype      TYPE(MPI_Op),
       INTENT(IN)  ::  op       TYPE(MPI_Comm),  INTENT(IN)  ::  comm        INTEGER,   OPTIONAL,
       INTENT(OUT) :: ierror

       MPI_Iscan(sendbuf,  recvbuf,  count,  datatype,  op,  comm, request, ierror)      TYPE(*),
       DIMENSION(..),  INTENT(IN),   ASYNCHRONOUS   ::   sendbuf        TYPE(*),   DIMENSION(..),
       ASYNCHRONOUS   ::  recvbuf       INTEGER,  INTENT(IN)  ::  count       TYPE(MPI_Datatype),
       INTENT(IN) :: datatype      TYPE(MPI_Op), INTENT(IN) :: op      TYPE(MPI_Comm), INTENT(IN)
       :: comm      TYPE(MPI_Request), INTENT(OUT) :: request      INTEGER, OPTIONAL, INTENT(OUT)
       :: ierror

C++ Syntax

       #include <mpi.h>
       void MPI::Intracomm::Scan(const void* sendbuf, void* recvbuf,
            int count, const MPI::Datatype& datatype,
            const MPI::Op& op) const

INPUT PARAMETERS

       sendbuf   Send buffer (choice).

       count     Number of elements in input buffer (integer).

       datatype  Data type of elements of input buffer (handle).

       op        Operation (handle).

       comm      Communicator (handle).

OUTPUT PARAMETERS

       recvbuf   Receive buffer (choice).

       request   Request (handle, non-blocking only).

       IERROR    Fortran only: Error status (integer).

DESCRIPTION

       MPI_Scan is used to perform an inclusive prefix reduction on data distributed  across  the
       calling  processes.  The operation returns, in the recvbuf of the process with rank i, the
       reduction (calculated according to the function op) of  the  values  in  the  sendbufs  of
       processes  with  ranks  0,  ...,  i  (inclusive).  The type of operations supported, their
       semantics, and the constraints on send and receive buffers are as for MPI_Reduce.

EXAMPLE

       This example uses a user-defined operation to produce a segmented scan. A  segmented  scan
       takes,  as  input, a set of values and a set of logicals, where the logicals delineate the
       various segments of the scan. For example,

       values     v1      v2      v3      v4      v5      v6      v7      v8
       logicals   0       0       1       1       1       0       0       1
       result     v1    v1+v2     v3    v3+v4  v3+v4+v5   v6    v6+v7     v8

       The result for rank j is thus the sum v(i) + ... + v(j), where i is the lowest  rank  such
       that  for  all  ranks  n, i <= n <= j, logical(n) = logical(j). The operator that produces
       this effect is

             [ u ]     [ v ]     [ w ]
             [   ]  o  [   ]  =  [   ]
             [ i ]     [ j ]     [ j ]

       where

                   ( u + v if i  = j
             w  =  (
                   ( v     if i != j

       Note that this is a noncommutative operator. C code that implements it is given below.

            typedef struct {
                 double val;
                 int log;
            } SegScanPair;

            /*
             * the user-defined function
             */
            void segScan(SegScanPair *in, SegScanPair *inout, int *len,
                 MPI_Datatype *dptr)
            {
                 int i;
                 SegScanPair c;

                 for (i = 0; i < *len; ++i) {
                      if (in->log == inout->log)
                           c.val = in->val + inout->val;
                      else
                           c.val = inout->val;

                      c.log = inout->log;
                      *inout = c;
                      in++;
                      inout++;
                 }
            }

       Note that the inout argument to the user-defined function corresponds  to  the  right-hand
       operand  of  the operator. When using this operator, we must be careful to specify that it
       is noncommutative, as in the following:

            int            i, base;
            SeqScanPair    a, answer;
            MPI_Op         myOp;
            MPI_Datatype   type[2] = {MPI_DOUBLE, MPI_INT};
            MPI_Aint       disp[2];
            int            blocklen[2] = {1, 1};
            MPI_Datatype   sspair;

            /*
             * explain to MPI how type SegScanPair is defined
             */
            MPI_Get_address(a, disp);
            MPI_Get_address(a.log, disp + 1);
            base = disp[0];
            for (i = 0; i < 2; ++i)
                 disp[i] -= base;
            MPI_Type_struct(2, blocklen, disp, type, &sspair);
            MPI_Type_commit(&sspair);

            /*
             * create the segmented-scan user-op
             * noncommutative - set commute (arg 2) to 0
             */
            MPI_Op_create((MPI_User_function *)segScan, 0, &myOp);
            ...
            MPI_Scan(a, answer, 1, sspair, myOp, comm);

USE OF IN-PLACE OPTION

       When the communicator is an intracommunicator, you can perform  a  scanning  operation  in
       place  (the  output buffer is used as the input buffer).  Use the variable MPI_IN_PLACE as
       the value of the sendbuf argument.  The input data is taken from the  receive  buffer  and
       replaced by the output data.

NOTES ON COLLECTIVE OPERATIONS

       The  reduction functions of type MPI_Op do not return an error value.  As a result, if the
       functions detect an error, all they can do is either call MPI_Abort or silently  skip  the
       problem. Thus, if the error handler is changed from MPI_ERRORS_ARE_FATAL to something else
       (e.g., MPI_ERRORS_RETURN), then no error may be indicated.

       The reason for this is the performance problems in ensuring that all  collective  routines
       return the same error value.

ERRORS

       Almost all MPI routines return an error value; C routines as the value of the function and
       Fortran routines in the last argument. C++ functions do not return errors. If the  default
       error  handler  is  set  to  MPI::ERRORS_THROW_EXCEPTIONS, then on error the C++ exception
       mechanism will be used to throw an MPI::Exception object.

       Before the error value is returned, the current MPI error handler is called.  By  default,
       this  error  handler aborts the MPI job, except for I/O function errors. The error handler
       may   be   changed   with   MPI_Comm_set_errhandler;   the   predefined   error    handler
       MPI_ERRORS_RETURN may be used to cause error values to be returned. Note that MPI does not
       guarantee that an MPI program can continue past an error.

       See the MPI man page for a full list of MPI error codes.

SEE ALSO

       MPI_Exscan
       MPI_Op_create
       MPI_Reduce