References:

• https://mpitutorial.com/tutorials/mpi-reduce-and-allreduce/

Reduce (MPI_Reduce):

Reduce is a classic concept from functional programming. Data reduction involves reducing a set of numbers into a smaller set of numbers via a function. For example, let’s say we have a list of numbers { 1,2,3,4,5 }. Reducing this list of numbers with the sum function would produce sum({ 1,2,3,4,5 }) = 15. Similarly, the multiplication reduction would yield multiply({ 1,2,3,4,5 }) = 120.

Following the concept, this function allows the programmer to reduce data from multiple processes grouped by a communicator.

Function prototype:

int MPI_Reduce(
	const void *sendbuf, //Address of the data to be reduced
	void *recvbuf, //Reduced result(s) receiver address
	int count, //Quantity of elements from **each process**
	MPI_Datatype datatype, //Type of data
	MPI_Op op, //Operation to reduce data
	int root, //Rank of the process that receives reduced data
	MPI_Comm comm //Communicator
);

The count parameter determines how many elements will be reduced from each process (it is possible to reduce several data at once), the sending and receiving buffers must have a length equal to count, to work properly.

The receive buffer can be null for processes that will only send data.

MPI_Op is an enum for operations to be applied, you can see all of them here: https://learn.microsoft.com/en-us/message-passing-interface/mpi-op-enumeration. But what the most used operations do is listed below:

• MPI_MAX - Returns the maximum element.
• MPI_MIN - Returns the minimum element.
• MPI_SUM - Sums the elements.
• MPI_PROD - Multiplies all elements.
• MPI_LAND - Performs a logical and across the elements.
• MPI_LOR - Performs a logical or across the elements.
• MPI_BAND - Performs a bitwise and across the bits of the elements.
• MPI_BOR - Performs a bitwise or across the bits of the elements.
• MPI_MAXLOC - Returns the maximum value and the rank of the process that owns it.
• MPI_MINLOC - Returns the minimum value and the rank of the process that owns it.