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
- 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 = 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(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
