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MPI_Reduce  Reduces values on all processes within a group.
#include <mpi.h>
int MPI_Reduce(void *sendbuf, void *recvbuf, int count,
MPI_Datatype datatype, MPI_Op op, int root, MPI_Comm comm)
INCLUDE ’mpif.h’
MPI_REDUCE(SENDBUF, RECVBUF, COUNT, DATATYPE, OP, ROOT, COMM,
IERROR)
<type> SENDBUF(*), RECVBUF(*)
INTEGER COUNT, DATATYPE, OP, ROOT, COMM, IERROR
#include <mpi.h>
void MPI::Intracomm::Reduce(const void* sendbuf, void* recvbuf,
int count, const MPI::Datatype& datatype, const MPI::Op& op,
int root) const
 sendbuf
 Address of send buffer (choice).
 count
 Number of
elements in send buffer (integer).
 datatype
 Data type of elements of send
buffer (handle).
 op
 Reduce operation (handle).
 root
 Rank of root process
(integer).
 comm
 Communicator (handle).
 recvbuf
 Address
of receive buffer (choice, significant only at root).
 IERROR
 Fortran only:
Error status (integer).
The global reduce functions (MPI_Reduce,
MPI_Op_create, MPI_Op_free, MPI_Allreduce, MPI_Reduce_scatter, MPI_Scan)
perform a global reduce operation (such as sum, max, logical AND, etc.)
across all the members of a group. The reduction operation can be either
one of a predefined list of operations, or a userdefined operation. The
global reduction functions come in several flavors: a reduce that returns
the result of the reduction at one node, an allreduce that returns this
result at all nodes, and a scan (parallel prefix) operation. In addition,
a reducescatter operation combines the functionality of a reduce and a
scatter operation.
MPI_Reduce combines the elements provided in the input
buffer of each process in the group, using the operation op, and returns
the combined value in the output buffer of the process with rank root. The
input buffer is defined by the arguments sendbuf, count, and datatype;
the output buffer is defined by the arguments recvbuf, count, and datatype;
both have the same number of elements, with the same type. The routine is
called by all group members using the same arguments for count, datatype,
op, root, and comm. Thus, all processes provide input buffers and output
buffers of the same length, with elements of the same type. Each process
can provide one element, or a sequence of elements, in which case the combine
operation is executed elementwise on each entry of the sequence. For example,
if the operation is MPI_MAX and the send buffer contains two elements that
are floatingpoint numbers (count = 2 and datatype = MPI_FLOAT), then recvbuf(1)
= global max (sendbuf(1)) and recvbuf(2) = global max(sendbuf(2)).
When the communicator is an intracommunicator, you can
perform a reduce operation inplace (the output buffer is used as the input
buffer). Use the variable MPI_IN_PLACE as the value of the root process
sendbuf. In this case, the input data is taken at the root from the receive
buffer, where it will be replaced by the output data.
Note that MPI_IN_PLACE
is a special kind of value; it has the same restrictions on its use as
MPI_BOTTOM.
Because the inplace option converts the receive buffer into
a sendandreceive buffer, a Fortran binding that includes INTENT must mark
these as INOUT, not OUT.
When
the communicator is an intercommunicator, the root process in the first
group combines data from all the processes in the second group and then
performs the op operation. The first group defines the root process. That
process uses MPI_ROOT as the value of its root argument. The remaining
processes use MPI_PROC_NULL as the value of their root argument. All processes
in the second group use the rank of that root process in the first group
as the value of their root argument. Only the send buffer arguments are
significant in the second group, and only the receive buffer arguments
are significant in the root process of the first group.
The set of predefined operations provided by MPI is listed below
(Predefined Reduce Operations). That section also enumerates the datatypes
each operation can be applied to. In addition, users may define their own
operations that can be overloaded to operate on several datatypes, either
basic or derived. This is further explained in the description of the userdefined
operations (see the man pages for MPI_Op_create and MPI_Op_free).
The operation
op is always assumed to be associative. All predefined operations are also
assumed to be commutative. Users may define operations that are assumed
to be associative, but not commutative. The ‘‘canonical’’ evaluation order of
a reduction is determined by the ranks of the processes in the group. However,
the implementation can take advantage of associativity, or associativity
and commutativity, in order to change the order of evaluation. This may
change the result of the reduction for operations that are not strictly
associative and commutative, such as floating point addition.
Predefined
operators work only with the MPI types listed below (Predefined Reduce
Operations, and the section MINLOC and MAXLOC, below). Userdefined operators
may operate on general, derived datatypes. In this case, each argument that
the reduce operation is applied to is one element described by such a datatype,
which may contain several basic values. This is further explained in Section
4.9.4 of the MPI Standard, "UserDefined Operations."
The following predefined
operations are supplied for MPI_Reduce and related functions MPI_Allreduce,
MPI_Reduce_scatter, and MPI_Scan. These operations are invoked by placing
the following in op:
Name Meaning
 
MPI_MAX maximum
MPI_MIN minimum
MPI_SUM sum
MPI_PROD product
MPI_LAND logical and
MPI_BAND bitwise and
MPI_LOR logical or
MPI_BOR bitwise or
MPI_LXOR logical xor
MPI_BXOR bitwise xor
MPI_MAXLOC max value and location
MPI_MINLOC min value and location
The two operations MPI_MINLOC and MPI_MAXLOC are discussed separately below
(MINLOC and MAXLOC). For the other predefined operations, we enumerate below
the allowed combinations of op and datatype arguments. First, define groups
of MPI basic datatypes in the following way:
C integer: MPI_INT, MPI_LONG, MPI_SHORT,
MPI_UNSIGNED_SHORT, MPI_UNSIGNED,
MPI_UNSIGNED_LONG
Fortran integer: MPI_INTEGER
Floatingpoint: MPI_FLOAT, MPI_DOUBLE, MPI_REAL,
MPI_DOUBLE_PRECISION, MPI_LONG_DOUBLE
Logical: MPI_LOGICAL
Complex: MPI_COMPLEX
Byte: MPI_BYTE
Now, the valid datatypes for each option is specified below.
Op Allowed Types
 
MPI_MAX, MPI_MIN C integer, Fortran integer,
floatingpoint
MPI_SUM, MPI_PROD C integer, Fortran integer,
floatingpoint, complex
MPI_LAND, MPI_LOR, C integer, logical
MPI_LXOR
MPI_BAND, MPI_BOR, C integer, Fortran integer, byte
MPI_BXOR
Example 1: A routine that computes the dot product of two vectors that
are distributed across a group of processes and returns the answer at
process zero.
SUBROUTINE PAR_BLAS1(m, a, b, c, comm)
REAL a(m), b(m) ! local slice of array
REAL c ! result (at process zero)
REAL sum
INTEGER m, comm, i, ierr
! local sum
sum = 0.0
DO i = 1, m
sum = sum + a(i)*b(i)
END DO
! global sum
CALL MPI_REDUCE(sum, c, 1, MPI_REAL, MPI_SUM, 0, comm, ierr)
RETURN
Example 2: A routine that computes the product of a vector and an array
that are distributed across a group of processes and returns the answer
at process zero.
SUBROUTINE PAR_BLAS2(m, n, a, b, c, comm)
REAL a(m), b(m,n) ! local slice of array
REAL c(n) ! result
REAL sum(n)
INTEGER n, comm, i, j, ierr
! local sum
DO j= 1, n
sum(j) = 0.0
DO i = 1, m
sum(j) = sum(j) + a(i)*b(i,j)
END DO
END DO
! global sum
CALL MPI_REDUCE(sum, c, n, MPI_REAL, MPI_SUM, 0, comm, ierr)
! return result at process zero (and garbage at the other nodes)
RETURN
The operator MPI_MINLOC is used to compute a global minimum
and also an index attached to the minimum value. MPI_MAXLOC similarly computes
a global maximum and index. One application of these is to compute a global
minimum (maximum) and the rank of the process containing this value.
The operation that defines MPI_MAXLOC is
( u ) ( v ) ( w )
( ) o ( ) = ( )
( i ) ( j ) ( k )
where
w = max(u, v)
and
( i if u > v
(
k = ( min(i, j) if u = v
(
( j if u < v)
MPI_MINLOC is defined similarly:
( u ) ( v ) ( w )
( ) o ( ) = ( )
( i ) ( j ) ( k )
where
w = max(u, v)
and
( i if u < v
(
k = ( min(i, j) if u = v
(
( j if u > v)
Both operations are associative and commutative. Note that if MPI_MAXLOC
is applied to reduce a sequence of pairs (u(0), 0), (u(1), 1), ..., (u(n1),
n1), then the value returned is (u , r), where u= max(i) u(i) and r is
the index of the first global maximum in the sequence. Thus, if each process
supplies a value and its rank within the group, then a reduce operation
with op = MPI_MAXLOC will return the maximum value and the rank of the
first process with that value. Similarly, MPI_MINLOC can be used to return
a minimum and its index. More generally, MPI_MINLOC computes a lexicographic
minimum, where elements are ordered according to the first component of
each pair, and ties are resolved according to the second component.
The
reduce operation is defined to operate on arguments that consist of a pair:
value and index. For both Fortran and C, types are provided to describe
the pair. The potentially mixedtype nature of such arguments is a problem
in Fortran. The problem is circumvented, for Fortran, by having the MPIprovided
type consist of a pair of the same type as value, and coercing the index
to this type also. In C, the MPIprovided pair type has distinct types and
the index is an int.
In order to use MPI_MINLOC and MPI_MAXLOC in a reduce
operation, one must provide a datatype argument that represents a pair
(value and index). MPI provides nine such predefined datatypes. The operations
MPI_MAXLOC and MPI_MINLOC can be used with each of the following datatypes:
Fortran:
Name Description
MPI_2REAL pair of REALs
MPI_2DOUBLE_PRECISION pair of DOUBLEPRECISION variables
MPI_2INTEGER pair of INTEGERs
C:
Name Description
MPI_FLOAT_INT float and int
MPI_DOUBLE_INT double and int
MPI_LONG_INT long and int
MPI_2INT pair of ints
MPI_SHORT_INT short and int
MPI_LONG_DOUBLE_INT long double and int
The data type MPI_2REAL is equivalent to:
MPI_TYPE_CONTIGUOUS(2, MPI_REAL, MPI_2REAL)
Similar statements apply for MPI_2INTEGER, MPI_2DOUBLE_PRECISION, and MPI_2INT.
The datatype MPI_FLOAT_INT is as if defined by the following sequence of
instructions.
type[0] = MPI_FLOAT
type[1] = MPI_INT
disp[0] = 0
disp[1] = sizeof(float)
block[0] = 1
block[1] = 1
MPI_TYPE_STRUCT(2, block, disp, type, MPI_FLOAT_INT)
Similar statements apply for MPI_LONG_INT and MPI_DOUBLE_INT.
Example
3: Each process has an array of 30 doubles, in C. For each of the 30 locations,
compute the value and rank of the process containing the largest value.
...
/* each process has an array of 30 double: ain[30]
*/
double ain[30], aout[30];
int ind[30];
struct {
double val;
int rank;
} in[30], out[30];
int i, myrank, root;
MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
for (i=0; i<30; ++i) {
in[i].val = ain[i];
in[i].rank = myrank;
}
MPI_Reduce( in, out, 30, MPI_DOUBLE_INT, MPI_MAXLOC, root, comm
);
/* At this point, the answer resides on process root
*/
if (myrank == root) {
/* read ranks out
*/
for (i=0; i<30; ++i) {
aout[i] = out[i].val;
ind[i] = out[i].rank;
}
}
Example 4: Same example, in Fortran.
...
! each process has an array of 30 double: ain(30)
DOUBLE PRECISION ain(30), aout(30)
INTEGER ind(30);
DOUBLE PRECISION in(2,30), out(2,30)
INTEGER i, myrank, root, ierr;
MPI_COMM_RANK(MPI_COMM_WORLD, myrank);
DO I=1, 30
in(1,i) = ain(i)
in(2,i) = myrank ! myrank is coerced to a double
END DO
MPI_REDUCE( in, out, 30, MPI_2DOUBLE_PRECISION, MPI_MAXLOC, root,
comm, ierr
);
! At this point, the answer resides on process root
IF (myrank .EQ. root) THEN
! read ranks out
DO I= 1, 30
aout(i) = out(1,i)
ind(i) = out(2,i) ! rank is coerced back to an integer
END DO
END IF
Example 5: Each process has a nonempty array of values. Find the minimum
global value, the rank of the process that holds it, and its index on this
process.
#define LEN 1000
float val[LEN]; /* local array of values */
int count; /* local number of values */
int myrank, minrank, minindex;
float minval;
struct {
float value;
int index;
} in, out;
/* local minloc */
in.value = val[0];
in.index = 0;
for (i=1; i < count; i++)
if (in.value > val[i]) {
in.value = val[i];
in.index = i;
}
/* global minloc */
MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
in.index = myrank*LEN + in.index;
MPI_Reduce( in, out, 1, MPI_FLOAT_INT, MPI_MINLOC, root, comm );
/* At this point, the answer resides on process root
*/
if (myrank == root) {
/* read answer out
*/
minval = out.value;
minrank = out.index / LEN;
minindex = out.index % LEN;
All MPI objects (e.g., MPI_Datatype, MPI_Comm) are of type INTEGER in Fortran.
The reduction functions ( 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 you change the error handler from MPI_ERRORS_ARE_FATAL to something
else, for example, 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.
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.
MPI_Allreduce
MPI_Reduce_scatter
MPI_Scan
MPI_Op_create
MPI_Op_free
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