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NAME
MPI_Reduce - Reduces values on all processes within a group.
SYNTAX
C Syntax
#include <mpi.h>
int MPI_Reduce(void *sendbuf, void *recvbuf, int count,
MPI_Datatype datatype, MPI_Op op, int root, MPI_Comm comm)
Fortran Syntax
INCLUDE 'mpif.h'
MPI_REDUCE(SENDBUF, RECVBUF, COUNT, DATATYPE, OP, ROOT, COMM,
IERROR)
<type> SENDBUF(*), RECVBUF(*)
INTEGER COUNT, DATATYPE, OP, ROOT, COMM, IERROR
C++ Syntax
#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
INPUT PARAMETERS
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).
OUTPUT PARAMETERS
recvbuf Address of receive buffer (choice, significant only at root).
IERROR Fortran only: Error status (integer).
DESCRIPTION
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 user-
defined operation. The global reduction functions come in several flavors: a reduce that returns the
result of the reduction at one node, an all-reduce that returns this result at all nodes, and a scan
(parallel prefix) operation. In addition, a reduce-scatter 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 element-wise on each entry of the sequence. For example, if the operation is
MPI_MAX and the send buffer contains two elements that are floating-point numbers (count = 2 and datatype
= MPI_FLOAT), then recvbuf(1) = global max (sendbuf(1)) and recvbuf(2) = global max(sendbuf(2)).
USE OF IN-PLACE OPTION
When the communicator is an intracommunicator, you can perform a reduce operation in-place (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 in-place option converts the receive buffer into a send-and-receive buffer, a Fortran binding
that includes INTENT must mark these as INOUT, not OUT.
WHEN COMMUNICATOR IS AN INTER-COMMUNICATOR
When the communicator is an inter-communicator, 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.
PREDEFINED REDUCE OPERATIONS
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 user-defined 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). User-defined 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, "User-Defined 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 bit-wise and
MPI_LOR logical or
MPI_BOR bit-wise or
MPI_LXOR logical xor
MPI_BXOR bit-wise 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
Floating-point: 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,
floating-point
MPI_SUM, MPI_PROD C integer, Fortran integer,
floating-point, 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
MINLOC AND MAXLOC
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 = min(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(n-1), n-1), 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 mixed-type nature of such
arguments is a problem in Fortran. The problem is circumvented, for Fortran, by having the MPI-provided
type consist of a pair of the same type as value, and coercing the index to this type also. In C, the
MPI-provided 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 DOUBLE-PRECISION 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.
NOTES ON COLLECTIVE OPERATIONS
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.
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 ALSO
MPI_Allreduce
MPI_Reduce_scatter
MPI_Scan
MPI_Op_create
MPI_Op_free