# Patent

## Title
Constructing a logical, regular axis topology from an irregular topology

## Abstract

Constructing a logical regular topology from an irregular topology including, for each axial dimension and recursively, for each compute node in a subcommunicator until returning to a first node: adding to a logical line of the axial dimension a neighbor specified in a nearest neighbor list; calling the added compute node; determining, by the called node, whether any neighbor in the node's nearest neighbor list is available to add to the logical line; if a neighbor in the called compute node's nearest neighbor list is available to add to the logical line, adding, by the called compute node to the logical line, any neighbor in the called compute node's nearest neighbor list for the axial dimension not already added to the logical line; and, if no neighbor in the called compute node's nearest neighbor list is available to add to the logical line, returning to the calling compute node.

## Background
CROSS-REFERENCE TO RELATED APPLICATION
This application is a continuation application of and claims priority from U.S. patent application Ser. No. 13/309,022, filed on Dec. 1, 2011.


STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
This invention was made with Government support under Contract No. B554331 awarded by the Department of Energy. The Government has certain rights in this invention.


BACKGROUND OF THE INVENTION
1. Field of the Invention
The field of the invention is data processing, or, more specifically, methods, apparatus, and products for constructing a logical, regular axis topology from an irregular topology of a subcommunicator's compute nodes in a parallel computer.
2. Description of Related Art
The development of the EDVAC computer system of 1948 is often cited as the beginning of the computer era. Since that time, computer systems have evolved into extremely complicated devices. Today's computers are much more sophisticated than early systems such as the EDVAC. Computer systems typically include a combination of hardware and software components, application programs, operating systems, processors, buses, memory, input/output devices, and so on. As advances in semiconductor processing and computer architecture push the performance of the computer higher and higher, more sophisticated computer software has evolved to take advantage of the higher performance of the hardware, resulting in computer systems today that are much more powerful than just a few years ago.
Parallel computing is an area of computer technology that has experienced advances. Parallel computing is the simultaneous execution of the same task (split up and specially adapted) on multiple processors in order to obtain results faster. Parallel computing is based on the fact that the process of solving a problem usually can be divided into smaller tasks, which may be carried out simultaneously with some coordination.
Parallel computers execute parallel algorithms. A parallel algorithm can be split up to be executed a piece at a time on many different processing devices, and then put back together again at the end to get a data processing result. Some algorithms are easy to divide up into pieces. Splitting up the job of checking all of the numbers from one to a hundred thousand to see which are primes could be done, for example, by assigning a subset of the numbers to each available processor, and then putting the list of positive results back together. In this specification, the multiple processing devices that execute the individual pieces of a parallel program are referred to as ‘compute nodes.’ A parallel computer is composed of compute nodes and other processing nodes as well, including, for example, input/output (‘I/O’) nodes, and service nodes.
Parallel algorithms are valuable because it is faster to perform some kinds of large computing tasks via a parallel algorithm than it is via a serial (non-parallel) algorithm, because of the way modern processors work. It is far more difficult to construct a computer with a single fast processor than one with many slow processors with the same throughput. There are also certain theoretical limits to the potential speed of serial processors. On the other hand, every parallel algorithm has a serial part and so parallel algorithms have a saturation point. After that point adding more processors does not yield any more throughput but only increases the overhead and cost.
Parallel algorithms are designed also to optimize one more resource the data communications requirements among the nodes of a parallel computer. There are two ways parallel processors communicate, shared memory or message passing. Shared memory processing needs additional locking for the data and imposes the overhead of additional processor and bus cycles and also serializes some portion of the algorithm.
Message passing processing uses high-speed data communications networks and message buffers, but this communication adds transfer overhead on the data communications networks as well as additional memory need for message buffers and latency in the data communications among nodes. Designs of parallel computers use specially designed data communications links so that the communication overhead will be small but it is the parallel algorithm that decides the volume of the traffic.
Many data communications network architectures are used for message passing among nodes in parallel computers. Compute nodes may be organized in a network as a ‘torus’ or ‘mesh,’ for example. Also, compute nodes may be organized in a network as a tree. A torus network connects the nodes in a three-dimensional mesh with wrap around links. Every node is connected to its six neighbors through this torus network, and each node is addressed by its x,y,z coordinate in the mesh. In such a manner, a torus network lends itself to point to point operations. In a tree network, the nodes typically are connected into a binary tree: each node has a parent, and two children (although some nodes may only have zero children or one child, depending on the hardware configuration). Although a tree network typically is inefficient in point to point communication, a tree network does provide high bandwidth and low latency for certain collective operations, message passing operations where all compute nodes participate simultaneously, such as, for example, an allgather operation. In computers that use a torus and a tree network, the two networks typically are implemented independently of one another, with separate routing circuits, separate physical links, and separate message buffers.
SUMMARY OF THE INVENTION
Methods, apparatus, and products for of constructing a logical, regular axis topology from an irregular topology of a subcommunicator's compute nodes in a parallel computer, are disclosed in this specification. The subcommunicator includes a subset of a communicators' compute nodes and the communicator's compute nodes are organized into a regular topology with a number of axial dimensions. The subcommunicator's topology is an irregular topology within the communicator's regular topology. Constructing a logical, regular axis topology from the irregular topology of the subcommunicator is carried out by, for each axial dimension: recursively, for each compute node in the subcommunicator beginning with a first compute node and ending upon a return to the first compute node: adding, by the compute node, to a logical line of the axial dimension a neighbor for the axial dimension specified in a nearest neighbor list of the compute node, the compute node's nearest neighbor list comprising a list of the compute node's nearest neighbors in the subcommunicator for each axial dimension; calling the added compute node; determining, by the called compute node, whether any neighbor in the called compute node's nearest neighbor list is available to add to the logical line; if a neighbor in the called compute node's nearest neighbor list is available to add to the logical line, adding, by the called compute node to the logical line, any neighbor in the called compute node's nearest neighbor list for the axial dimension not already added to the logical line; and if no neighbor in the called compute node's nearest neighbor list is available to add to the logical line, returning to the calling compute node.
The foregoing and other objects, features and advantages of the invention will be apparent from the following more particular descriptions of exemplary embodiments of the invention as illustrated in the accompanying drawings wherein like reference numbers generally represent like parts of exemplary embodiments of the invention.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 illustrates an exemplary system for constructing a logical, regular axis topology from an irregular topology of a subcommunicator's compute nodes in a parallel computer according to embodiments of the present invention.
FIG. 2 sets forth a block diagram of an example compute node useful in a parallel computer capable of constructing a logical, regular axis topology from an irregular topology of a subcommunicator's compute nodes according to embodiments of the present invention.
FIG. 3A sets forth a block diagram of an example Point-To-Point Adapter useful in systems for constructing a logical, regular axis topology from an irregular topology of a subcommunicator's compute nodes in a parallel computer according to embodiments of the present invention.
FIG. 3B sets forth a block diagram of an example Global Combining Network Adapter useful in systems for constructing a logical, regular axis topology from an irregular topology of a subcommunicator's compute nodes in a parallel computer according to embodiments of the present invention.
FIG. 4 sets forth a line drawing illustrating an example data communications network optimized for point-to-point operations useful in systems capable of constructing a logical, regular axis topology from an irregular topology of a subcommunicator's compute nodes in a parallel computer according to embodiments of the present invention.
FIG. 5 sets forth a line drawing illustrating an example global combining network useful in systems capable of constructing a logical, regular axis topology from an irregular topology of a subcommunicator's compute nodes in a parallel computer according to embodiments of the present invention.
FIG. 6 sets forth a flow chart illustrating an example method for constructing a logical, regular axis topology from an irregular topology of a subcommunicator's compute nodes in a parallel computer according to embodiments of the present invention.
FIG. 7A sets forth a line drawing illustrating an example communicator with a regular topology and subcommunicator with an irregular topology from which a logical, regular axis topology may be constructed according to embodiments of the present invention.
FIG. 7B sets forth a line drawing illustrating another example communicator with a regular topology and subcommunicator with an irregular topology from which a logical, regular axis topology may be constructed according to embodiments of the present invention.



DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS
Exemplary methods, apparatus, and products for constructing a logical, regular axis topology from an irregular topology of a subcommunicator's compute nodes in a parallel computer in accordance with the present invention are described with reference to the accompanying drawings, beginning with FIG. 1. FIG. 1 illustrates an exemplary system for constructing a logical, regular axis topology from an irregular topology of a subcommunicator's compute nodes in a parallel computer according to embodiments of the present invention. The system of FIG. 1 includes a parallel computer (100), non-volatile memory for the computer in the form of a data storage device (118), an output device for the computer in the form of a printer (120), and an input/output device for the computer in the form of a computer terminal (122).
The parallel computer (100) in the example of FIG. 1 includes a plurality of compute nodes (102). The compute nodes (102) are coupled for data communications by several independent data communications networks including a high speed Ethernet network (174), a Joint Test Action Group (‘JTAG’) network (104), a global combining network (106) which is optimized for collective operations using a binary tree network topology, and a point-to-point network (108), which is optimized for point-to-point operations using a torus network topology. The global combining network (106) is a data communications network that includes data communications links connected to the compute nodes (102) so as to organize the compute nodes (102) as a binary tree. Each data communications network is implemented with data communications links among the compute nodes (102). The data communications links provide data communications for parallel operations among the compute nodes (102) of the parallel computer (100).
The compute nodes (102) of the parallel computer (100) are organized into at least one operational group (132) of compute nodes for collective parallel operations on the parallel computer (100). Each operational group (132) of compute nodes is the set of compute nodes upon which a collective parallel operation executes. Each compute node in the operational group (132) is assigned a unique rank that identifies the particular compute node in the operational group (132). Collective operations are implemented with data communications among the compute nodes of an operational group. Collective operations are those functions that involve all the compute nodes of an operational group (132). A collective operation is an operation, a message-passing computer program instruction that is executed simultaneously, that is, at approximately the same time, by all the compute nodes in an operational group (132) of compute nodes. Such an operational group (132) may include all the compute nodes (102) in a parallel computer (100) or a subset all the compute nodes (102). Collective operations are often built around point-to-point operations. A collective operation requires that all processes on all compute nodes within an operational group call the same collective operation with matching arguments. A ‘broadcast’ is an example of a collective operation for moving data among compute nodes of an operational group. A ‘reduce’ operation is an example of a collective operation that executes arithmetic or logical functions on data distributed among the compute nodes of an operational group (132). An operational group (132) may be implemented as, for example, an MPI ‘communicator.’
‘MPI’ refers to ‘Message Passing Interface,’ a prior art parallel communications library, a module of computer program instructions for data communications on parallel computers. Examples of prior-art parallel communications libraries that may be improved for use in systems configured according to embodiments of the present invention include MPI and the ‘Parallel Virtual Machine’ (‘PVM’) library. PVM was developed by the University of Tennessee, The Oak Ridge National Laboratory and Emory University. MPI is promulgated by the MPI Forum, an open group with representatives from many organizations that define and maintain the MPI standard. MPI at the time of this writing is a de facto standard for communication among compute nodes running a parallel program on a distributed memory parallel computer. This specification sometimes uses MPI terminology for ease of explanation, although the use of MPI as such is not a requirement or limitation of the present invention.
Some collective operations have a single originating or receiving process running on a particular compute node in an operational group (132). For example, in a ‘broadcast’ collective operation, the process on the compute node that distributes the data to all the other compute nodes is an originating process. In a ‘gather’ operation, for example, the process on the compute node that received all the data from the other compute nodes is a receiving process. The compute node on which such an originating or receiving process runs is referred to as a logical root.
Most collective operations are variations or combinations of four basic operations: broadcast, gather, scatter, and reduce. The interfaces for these collective operations are defined in the MPI standards promulgated by the MPI Forum. Algorithms for executing collective operations, however, are not defined in the MPI standards. In a broadcast operation, all processes specify the same root process, whose buffer contents will be sent. Processes other than the root specify receive buffers. After the operation, all buffers contain the message from the root process.
A scatter operation, like the broadcast operation, is also a one-to-many collective operation. In a scatter operation, the logical root divides data on the root into segments and distributes a different segment to each compute node in the operational group (132). In scatter operation, all processes typically specify the same receive count. The send arguments are only significant to the root process, whose buffer actually contains sendcount * N elements of a given datatype, where N is the number of processes in the given group of compute nodes. The send buffer is divided and dispersed to all processes (including the process on the logical root). Each compute node is assigned a sequential identifier termed a ‘rank.’ After the operation, the root has sent sendcount data elements to each process in increasing rank order. Rank 0 receives the first sendcount data elements from the send buffer. Rank 1 receives the second sendcount data elements from the send buffer, and so on.
A gather operation is a many-to-one collective operation that is a complete reverse of the description of the scatter operation. That is, a gather is a many-to-one collective operation in which elements of a datatype are gathered from the ranked compute nodes into a receive buffer in a root node.
A reduction operation is also a many-to-one collective operation that includes an arithmetic or logical function performed on two data elements. All processes specify the same ‘count’ and the same arithmetic or logical function. After the reduction, all processes have sent count data elements from compute node send buffers to the root process. In a reduction operation, data elements from corresponding send buffer locations are combined pair-wise by arithmetic or logical operations to yield a single corresponding element in the root process' receive buffer. Application specific reduction operations can be defined at runtime. Parallel communications libraries may support predefined operations. MPI, for example, provides the following pre-defined reduction operations:

    
    
        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 exclusive or
        MPI_BXOR bitwise exclusive or
    
    


In addition to compute nodes, the parallel computer (100) includes input/output (‘I/O’) nodes (110, 114) coupled to compute nodes (102) through the global combining network (106). The compute nodes (102) in the parallel computer (100) may be partitioned into processing sets such that each compute node in a processing set is connected for data communications to the same I/O node. Each processing set, therefore, is composed of one I/O node and a subset of compute nodes (102). The ratio between the number of compute nodes to the number of I/O nodes in the entire system typically depends on the hardware configuration for the parallel computer (102). For example, in some configurations, each processing set may be composed of eight compute nodes and one I/O node. In some other configurations, each processing set may be composed of sixty-four compute nodes and one I/O node. Such example are for explanation only, however, and not for limitation. Each I/O node provides I/O services between compute nodes (102) of its processing set and a set of I/O devices. In the example of FIG. 1, the I/O nodes (110, 114) are connected for data communications I/O devices (118, 120, 122) through local area network (‘LAN’) (130) implemented using high-speed Ethernet.
The parallel computer (100) of FIG. 1 also includes a service node (116) coupled to the compute nodes through one of the networks (104). Service node (116) provides services common to pluralities of compute nodes, administering the configuration of compute nodes, loading programs into the compute nodes, starting program execution on the compute nodes, retrieving results of program operations on the compute nodes, and so on. Service node (116) runs a service application (124) and communicates with users (128) through a service application interface (126) that runs on computer terminal (122).
The parallel computer (100) of FIG. 1 operates generally for constructing a logical, regular axis topology from an irregular topology of a subcommunicator's compute nodes in a parallel computer in accordance with embodiments of the present invention. A communicator is an example of an operational group, a set of compute nodes configured for data communications and collective operations. A subcommunicator is a subset of the communicator. A communicator is generally established in a regular data communications topology—a mesh, grid, or torus for example. A regular topology is one in which no gaps exist between nodes. Generally, a regular topology is axial, meaning that the topology is defined among one or more axes, such as an X axis, Y axis, and Z axis. An example of a communicator having a regular topology is depicted in FIG. 7A. In that example, the communicator includes 30 nodes in a regular, axial grid pattern.
An irregular topology is a topology in which gaps exist between nodes in the same axis. Consider as an example, the communicator in FIG. 7A. The nodes in the communicator of FIG. 7A that are coupled by links represent nodes of a subcommunicator. As can be seen in FIG. 7A, the subcommunicator is an irregular topology. Node 2 for example, is separated from node 4, both of which are in the same axis. In fact, in FIG. 7A, three distinct groups of nodes form the subcommunicator.
Some data communications optimizations often rely on an underlying regular axial topology to be performed. A deposit bit optimization, for example, generally enables fast communication along one axis of a set of compute nodes. The deposit bit optimization enables a communications adapter of a first node to receive a message and forward the message to the next node in the same axis immediately, even before copying the message to local memory for a process executing on the first compute node. The communication adapter of each compute node in the same axis, can carry out exactly the same steps such that a single message may be broadcast down a single axis very quickly. When the compute nodes on that axis, however, include one or more data communication gaps, the bit deposit optimization fails.
To that end, parallel computer (100) of FIG. 1 operates generally for constructing a logical, regular axis topology from an irregular topology of a subcommunicator's compute nodes in accordance with embodiments of the present invention. The term ‘logical’ here refers to a topology that is not a physical topology. Constructing such a logical topology may be thought of as being carried out in various phases, one phase for each axial dimension of the regular axis topology. During each phase, the following steps are carried out recursively, for each compute node in the subcommunicator beginning with a first compute node and ending upon a return to the first compute node: adding, by the compute node (102), to a logical line of the axial dimension a neighbor for the axial dimension specified in a nearest neighbor list of the compute node. The compute node's nearest neighbor list is a list of the compute node's nearest neighbors in the subcommunicator for each axial dimension. A nearest neighbor to a particular node is a compute node coupled to the particular node directly, with no intervening nodes. That is a nearest neighbor is a point-to-point neighbor.
Once the compute node adds the nearest neighbor to the logical line in the axial dimension, the compute node calls the added compute node and the called compute node determines whether any neighbor in the called compute node's nearest neighbor list is available to add to the logical line. That is, the called compute node determines whether another neighbor exists and whether than neighbor has already been added to the logical line for that axial dimension.
If a neighbor in the called compute node's nearest neighbor list is available to add to the logical line, the called compute node adds, to the logical line, any neighbor in the called compute node's nearest neighbor list for the axial dimension not already added to the logical line. If, no neighbor in the called compute node's nearest neighbor list is available to add to the logical line, the called compute node returns to the calling compute node. From there, the calling compute node either adds an another neighbor to the line if any neighbors are available to add, or all available neighbors have been added and the calling compute node ends the phase for the axial dimension.
Constructing a logical, regular axis topology from an irregular topology of a subcommunicator's compute nodes according to embodiments of the present invention is generally implemented on a parallel computer that includes a plurality of compute nodes organized for collective operations through at least one data communications network. In fact, such computers may include thousands of such compute nodes. Each compute node is in turn itself a kind of computer composed of one or more computer processing cores, its own computer memory, and its own input/output adapters. For further explanation, therefore, FIG. 2 sets forth a block diagram of an example compute node (102) useful in a parallel computer capable of constructing a logical, regular axis topology from an irregular topology of a subcommunicator's compute nodes according to embodiments of the present invention. The compute node (102) of FIG. 2 includes a plurality of processing cores (165) as well as RAM (156). The processing cores (165) of FIG. 2 may be configured on one or more integrated circuit dies. Processing cores (165) are connected to RAM (156) through a high-speed memory bus (155) and through a bus adapter (194) and an extension bus (168) to other components of the compute node. Stored in RAM (156) is an application program (159), a module of computer program instructions that carries out parallel, user-level data processing using parallel algorithms.
Also stored RAM (156) is a parallel communications library (161), a library of computer program instructions that carry out parallel communications among compute nodes, including point-to-point operations as well as collective operations. A library of parallel communications routines may be developed from scratch for use in systems according to embodiments of the present invention, using a traditional programming language such as the C programming language, and using traditional programming methods to write parallel communications routines that send and receive data among nodes on two independent data communications networks. Alternatively, existing prior art libraries may be improved to operate according to embodiments of the present invention. Examples of prior-art parallel communications libraries include the ‘Message Passing Interface’ (‘MPI’) library and the ‘Parallel Virtual Machine’ (‘PVM’) library.
The compute node (102) of FIG. 2 operates generally for constructing a logical, regular axis topology (228) from an irregular topology of a subcommunicator's compute nodes in a parallel computer in accordance with embodiments of the present invention. The parallel communications library (161) may be configured to construct such a logical topology (228), by carrying out the following steps for each axial dimension of the regular axis topology: recursively, for each compute node (102) in the subcommunicator beginning with a first compute node and ending upon a return to the first compute node: adding, by the compute node (102), to a logical line (232) of the axial dimension a neighbor for the axial dimension specified in a nearest neighbor list (230) of the compute node (102). The compute node's nearest neighbor list (102) is a list of the compute node's nearest neighbors in the subcommunicator for each axial dimension. Consider, for example, the point to network (108) in the example of FIG. 2. The compute node (102) in this example has six nearest neighbors, but not all six need be nearest neighbors in the subcommunicator.
Once the compute node (102) adds the nearest neighbor to the logical line (230) in the axial dimension, the compute node (102) calls the added compute node and the called compute node determines whether any neighbor in the called compute node's nearest neighbor list is available to add to the logical line. If a neighbor in the called compute node's nearest neighbor list is available to add to the logical line, the called compute node adds, to the logical line, any neighbor in the called compute node's nearest neighbor list for the axial dimension not already added to the logical line. If, no neighbor in the called compute node's nearest neighbor list is available to add to the logical line, the called compute node returns to the calling compute node. From there, the calling compute node either adds another neighbor to the line if any neighbors are available to add, or all available neighbors have been added and the calling compute node ends the phase for the axial dimension.
Also stored in RAM (156) is an operating system (162), a module of computer program instructions and routines for an application program's access to other resources of the compute node. It is typical for an application program and parallel communications library in a compute node of a parallel computer to run a single thread of execution with no user login and no security issues because the thread is entitled to complete access to all resources of the node. The quantity and complexity of tasks to be performed by an operating system on a compute node in a parallel computer therefore are smaller and less complex than those of an operating system on a serial computer with many threads running simultaneously. In addition, there is no video I/O on the compute node (102) of FIG. 2, another factor that decreases the demands on the operating system. The operating system (162) may therefore be quite lightweight by comparison with operating systems of general purpose computers, a pared down version as it were, or an operating system developed specifically for operations on a particular parallel computer. Operating systems that may usefully be improved, simplified, for use in a compute node include UNIXTM, LinuxTM, Windows XPTM, AIXTM, IBM's i5/OSTM, and others as will occur to those of skill in the art.
The example compute node (102) of FIG. 2 includes several communications adapters (172, 176, 180, 188) for implementing data communications with other nodes of a parallel computer. Such data communications may be carried out serially through RS-232 connections, through external buses such as USB, through data communications networks such as IP networks, and in other ways as will occur to those of skill in the art. Communications adapters implement the hardware level of data communications through which one computer sends data communications to another computer, directly or through a network. Examples of communications adapters useful in apparatus useful for constructing a logical, regular axis topology from an irregular topology of a subcommunicator's compute nodes in a parallel computer include modems for wired communications, Ethernet (IEEE 802.3) adapters for wired network communications, and 802.11b adapters for wireless network communications.
The data communications adapters in the example of FIG. 2 include a Gigabit Ethernet adapter (172) that couples example compute node (102) for data communications to a Gigabit Ethernet (174). Gigabit Ethernet is a network transmission standard, defined in the IEEE 802.3 standard, that provides a data rate of 1 billion bits per second (one gigabit). Gigabit Ethernet is a variant of Ethernet that operates over multimode fiber optic cable, single mode fiber optic cable, or unshielded twisted pair.
The data communications adapters in the example of FIG. 2 include a JTAG Slave circuit (176) that couples example compute node (102) for data communications to a JTAG Master circuit (178). JTAG is the usual name used for the IEEE 1149.1 standard entitled Standard Test Access Port and Boundary-Scan Architecture for test access ports used for testing printed circuit boards using boundary scan. JTAG is so widely adapted that, at this time, boundary scan is more or less synonymous with JTAG. JTAG is used not only for printed circuit boards, but also for conducting boundary scans of integrated circuits, and is also useful as a mechanism for debugging embedded systems, providing a convenient alternative access point into the system. The example compute node of FIG. 2 may be all three of these: It typically includes one or more integrated circuits installed on a printed circuit board and may be implemented as an embedded system having its own processing core, its own memory, and its own I/O capability. JTAG boundary scans through JTAG Slave (176) may efficiently configure processing core registers and memory in compute node (102) for use in dynamically reassigning a connected node to a block of compute nodes useful in systems for constructing a logical, regular axis topology from an irregular topology of a subcommunicator's compute nodes in a parallel computer to embodiments of the present invention.
The data communications adapters in the example of FIG. 2 include a Point-To-Point Network Adapter (180) that couples example compute node (102) for data communications to a network (108) that is optimal for point-to-point message passing operations such as, for example, a network configured as a three-dimensional torus or mesh. The Point-To-Point Adapter (180) provides data communications in six directions on three communications axes, x, y, and z, through six bidirectional links: +x (181), −x (182), +y (183), −y (184), +z (185), and −z (186).
The data communications adapters in the example of FIG. 2 include a Global Combining Network Adapter (188) that couples example compute node (102) for data communications to a global combining network (106) that is optimal for collective message passing operations such as, for example, a network configured as a binary tree. The Global Combining Network Adapter (188) provides data communications through three bidirectional links for each global combining network (106) that the Global Combining Network Adapter (188) supports. In the example of FIG. 2, the Global Combining Network Adapter (188) provides data communications through three bidirectional links for global combining network (106): two to children nodes (190) and one to a parent node (192).
The example compute node (102) includes multiple arithmetic logic units (‘ALUs’). Each processing core (165) includes an ALU (166), and a separate ALU (170) is dedicated to the exclusive use of the Global Combining Network Adapter (188) for use in performing the arithmetic and logical functions of reduction operations, including an allreduce operation. Computer program instructions of a reduction routine in a parallel communications library (161) may latch an instruction for an arithmetic or logical function into an instruction register (169). When the arithmetic or logical function of a reduction operation is a ‘sum’ or a ‘logical OR,’ for example, the collective operations adapter (188) may execute the arithmetic or logical operation by use of the ALU (166) in the processing core (165) or, typically much faster, by use of the dedicated ALU (170) using data provided by the nodes (190, 192) on the global combining network (106) and data provided by processing cores (165) on the compute node (102).
Often when performing arithmetic operations in the global combining network adapter (188), however, the global combining network adapter (188) only serves to combine data received from the children nodes (190) and pass the result up the network (106) to the parent node (192). Similarly, the global combining network adapter (188) may only serve to transmit data received from the parent node (192) and pass the data down the network (106) to the children nodes (190). That is, none of the processing cores (165) on the compute node (102) contribute data that alters the output of ALU (170), which is then passed up or down the global combining network (106). Because the ALU (170) typically does not output any data onto the network (106) until the ALU (170) receives input from one of the processing cores (165), a processing core (165) may inject the identity element into the dedicated ALU (170) for the particular arithmetic operation being perform in the ALU (170) in order to prevent alteration of the output of the ALU (170). Injecting the identity element into the ALU, however, often consumes numerous processing cycles. To further enhance performance in such cases, the example compute node (102) includes dedicated hardware (171) for injecting identity elements into the ALU (170) to reduce the amount of processing core resources required to prevent alteration of the ALU output. The dedicated hardware (171) injects an identity element that corresponds to the particular arithmetic operation performed by the ALU. For example, when the global combining network adapter (188) performs a bitwise OR on the data received from the children nodes (190), dedicated hardware (171) may inject zeros into the ALU (170) to improve performance throughout the global combining network (106).
For further explanation, FIG. 3A sets forth a block diagram of an example Point-To-Point Adapter (180) useful in systems for constructing a logical, regular axis topology from an irregular topology of a subcommunicator's compute nodes in a parallel computer according to embodiments of the present invention. The Point-To-Point Adapter (180) is designed for use in a data communications network optimized for point-to-point operations, a network that organizes compute nodes in a three-dimensional torus or mesh. The Point-To-Point Adapter (180) in the example of FIG. 3A provides data communication along an x-axis through four unidirectional data communications links, to and from the next node in the −x direction (182) and to and from the next node in the +x direction (181). The Point-To-Point Adapter (180) of FIG. 3A also provides data communication along a y-axis through four unidirectional data communications links, to and from the next node in the −y direction (184) and to and from the next node in the +y direction (183). The Point-To-Point Adapter (180) of FIG. 3A also provides data communication along a z-axis through four unidirectional data communications links, to and from the next node in the −z direction (186) and to and from the next node in the +z direction (185).
For further explanation, FIG. 3B sets forth a block diagram of an example Global Combining Network Adapter (188) useful in systems for constructing a logical, regular axis topology from an irregular topology of a subcommunicator's compute nodes in a parallel computer according to embodiments of the present invention. The Global Combining Network Adapter (188) is designed for use in a network optimized for collective operations, a network that organizes compute nodes of a parallel computer in a binary tree. The Global Combining Network Adapter (188) in the example of FIG. 3B provides data communication to and from children nodes of a global combining network through four unidirectional data communications links (190), and also provides data communication to and from a parent node of the global combining network through two unidirectional data communications links (192).
For further explanation, FIG. 4 sets forth a line drawing illustrating an example data communications network (108) optimized for point-to-point operations useful in systems capable of constructing a logical, regular axis topology from an irregular topology of a subcommunicator's compute nodes in a parallel computer according to embodiments of the present invention. In the example of FIG. 4, dots represent compute nodes (102) of a parallel computer, and the dotted lines between the dots represent data communications links (103) between compute nodes. The data communications links are implemented with point-to-point data communications adapters similar to the one illustrated for example in FIG. 3A, with data communications links on three axis, x, y, and z, and to and fro in six directions +x (181), −x (182), +y (183), −y (184), +z (185), and −z (186). The links and compute nodes are organized by this data communications network optimized for point-to-point operations into a three dimensional mesh (105). The mesh (105) has wrap-around links on each axis that connect the outermost compute nodes in the mesh (105) on opposite sides of the mesh (105). These wrap-around links form a torus (107). Each compute node in the torus has a location in the torus that is uniquely specified by a set of x, y, z coordinates. Readers will note that the wrap-around links in the y and z directions have been omitted for clarity, but are configured in a similar manner to the wrap-around link illustrated in the x direction. For clarity of explanation, the data communications network of FIG. 4 is illustrated with only 27 compute nodes, but readers will recognize that a data communications network optimized for point-to-point operations for use in constructing a logical, regular axis topology from an irregular topology of a subcommunicator's compute nodes in a parallel computer in accordance with embodiments of the present invention may contain only a few compute nodes or may contain thousands of compute nodes. For ease of explanation, the data communications network of FIG. 4 is illustrated with only three dimensions, but readers will recognize that a data communications network optimized for point-to-point operations for use in constructing a logical, regular axis topology from an irregular topology of a subcommunicator's compute nodes in a parallel computer in accordance with embodiments of the present invention may in facet be implemented in two dimensions, four dimensions, five dimensions, and so on. Several supercomputers now use five dimensional mesh or torus networks, including, for example, IBM's Blue Gene QTM.
For further explanation, FIG. 5 sets forth a line drawing illustrating an example global combining network (106) useful in systems capable of constructing a logical, regular axis topology from an irregular topology of a subcommunicator's compute nodes in a parallel computer according to embodiments of the present invention. The example data communications network of FIG. 5 includes data communications links (103) connected to the compute nodes so as to organize the compute nodes as a tree. In the example of FIG. 5, dots represent compute nodes (102) of a parallel computer, and the dotted lines (103) between the dots represent data communications links between compute nodes. The data communications links are implemented with global combining network adapters similar to the one illustrated for example in FIG. 3B, with each node typically providing data communications to and from two children nodes and data communications to and from a parent node, with some exceptions. Nodes in the global combining network (106) may be characterized as a physical root node (202), branch nodes (204), and leaf nodes (206). The physical root (202) has two children but no parent and is so called because the physical root node (202) is the node physically configured at the top of the binary tree. The leaf nodes (206) each has a parent, but leaf nodes have no children. The branch nodes (204) each has both a parent and two children. The links and compute nodes are thereby organized by this data communications network optimized for collective operations into a binary tree (106). For clarity of explanation, the data communications network of FIG. 5 is illustrated with only 31 compute nodes, but readers will recognize that a global combining network (106) optimized for collective operations for use in constructing a logical, regular axis topology from an irregular topology of a subcommunicator's compute nodes in a parallel computer in accordance with embodiments of the present invention may contain only a few compute nodes or may contain thousands of compute nodes.
In the example of FIG. 5, each node in the tree is assigned a unit identifier referred to as a ‘rank’ (250). The rank actually identifies a task or process that is executing a parallel operation according to embodiments of the present invention. Using the rank to identify a node assumes that only one such task is executing on each node. To the extent that more than one participating task executes on a single node, the rank identifies the task as such rather than the node. A rank uniquely identifies a task's location in the tree network for use in both point-to-point and collective operations in the tree network. The ranks in this example are assigned as integers beginning with 0 assigned to the root tasks or root node (202), 1 assigned to the first node in the second layer of the tree, 2 assigned to the second node in the second layer of the tree, 3 assigned to the first node in the third layer of the tree, 4 assigned to the second node in the third layer of the tree, and so on. For ease of illustration, only the ranks of the first three layers of the tree are shown here, but all compute nodes in the tree network are assigned a unique rank.
For further explanation, FIG. 6 sets forth a flow chart illustrating an example method of constructing a logical, regular axis topology from an irregular topology of a subcommunicator's compute nodes in a parallel computer according to embodiments of the present invention. The method of FIG. 6 is carried out in a parallel computer in which the subcommunicator includes a subset of a communicator's compute nodes, the communicator's compute nodes are organized into a regular topology that includes a plurality of axial dimensions and the subcommunicator's topology is an irregular topology within the regular topology. In some embodiments the regular topology is a torus network topology that includes N-dimensions, where N is an integer greater than one—a five dimensional torus network topology for example.
The method of FIG. 6 includes establishing (602), by each compute node in the subcommunicator, a nearest neighbor list for each axial dimension of the communicator. Establishing (602), by each compute node in the subcommunicator, a nearest neighbor list for each axial dimension of the communicator may be carried out by establishing an array for each dimension, pinging each nearest neighbor for an identifier, and storing the identifier of each nearest neighbor in the array for the dimension in which the nearest neighbor exists. For a nearest neighbor having an identifier of 7 in the x-dimension, for example, the compute node will store the identifier 7 in the array for the x-dimension.
The method of FIG. 6 includes removing (604), by each compute node of the subcommunicator, from the compute node's nearest neighbor list, any nearest neighbor not included in the subcommunicator. That is, each compute node curates its nearest neighbor list to recite only compute nodes in the subcommunicator.
The method of FIG. 6 includes providing (606), by each compute node of the subcommunicator to all other compute nodes of the subcommunicator, the compute node's nearest neighbor list. Providing (606), by each compute node of the subcommunicator to all other compute nodes of the subcommunicator, the compute node's nearest neighbor list may be carried out by performing, by the compute nodes of the subcommunicator, an ALLGATHER collective operation.
The method of FIG. 6 continues, beginning at a first dimension and beginning with a first compute node, by determining (608) by the compute node whether any nearest neighbors are available to add to a logical line in the dimension. Determining whether a nearest neighbor is available to add to a logical line in the dimension includes determining whether a nearest neighbor exists and whether that nearest neighbor has already been added to the line. If a neighbor is available to add, the method of FIG. 6 continues by adding (610), by the compute node, to a logical line of the axial dimension a neighbor for the axial dimension specified in the nearest neighbor list. The logical line may be represented as a data structure in memory shared amongst the subcommunicator's compute nodes. Adding (610) a node to the logical line may be carried out by storing the added node' identifier in the data structure.
The method of FIG. 6 includes calling (612) the added compute node. Calling (612) the added compute node includes instructing the added to begin logical line construction. The method of FIG. 6 continues by determining (620), by the called compute node, whether any neighbor in the called compute node's nearest neighbor list is available to add to the logical line. If a neighbor in the called compute node's nearest neighbor list is available to add to the logical line, the method of FIG. 6 continues by adding (616), by the called compute node to the logical line, any neighbor in the called compute node's nearest neighbor list for the axial dimension not already added to the logical line. Once the called node adds the neighbor to the logical line, the called node calls (612) the added node and the method continues recursively. If no neighbor in the called compute node's nearest neighbor list is available to add to the logical line, the method of FIG. 6 continues by returning (618) to the calling compute node.
Once returned to the calling compute node, the calling node again determines (608) whether any neighbor is available to add. If so, the process describes above repeats. If not, the method of FIG. 6 continues by determining (620) whether a logical line has been constructed for each axial dimension. If a logical line has not been constructed for each axial dimension, the method of FIG. 6 continues (624) to the next axial dimension and repeats the steps of logical line construction for that dimension. If a logical line has been constructed for each axial dimension, the method of FIG. 6 continues by performing (622) regular topology optimized data communications amongst the compute nodes of the subcommunicator.
For further explanation, FIG. 7A sets forth a line drawing illustrating an example communicator with a regular topology and subcommunicator with an irregular topology from which a logical, regular axis topology may be constructed according to embodiments of the present invention. In the example of FIG. 7A, the communicator includes 30 compute nodes (node 0-node 30) with a regular grid topology in two dimensions—an X and Y dimension. A subcommunicator is formed from the communicator's nodes and is depicted in the example of FIG. 7A as those nodes coupled by links. Nodes 0-3, 4-5, 7-8, 13-14, 18-23, and 26 are part of the subcommunicator. As can be seen from the links, the subcommunicator is an irregular topology—not a grid, mesh, torus, or the like. In this subcommunicator, many data communication optimization techniques may not be performed due to the underlying irregular topology of the subcommunicator.
For further explanation, FIG. 7B sets forth a line drawing illustrating another example communicator with a regular topology and subcommunicator with an irregular topology from which a logical, regular axis topology may be constructed according to embodiments of the present invention. The communicator of FIG. 7A includes many nodes, configured in a regular grid topology with two dimensions.
For clarity of explanation, only a portion of the subcommunicator is depicted. The portion of the subcommunicator includes Nodes 0-2 and Nodes 6-7. This portion represents one single group of subcommunicator nodes in one dimension. While many other groups of subcommunicator nodes may exist in the same or other dimensions within the regular topology of the communicator, only this portion of the subcommunicator is described here for clarity.
To reconstruct the irregular topology of the subcommunicator into a regular, axial topology, each compute node will generate a nearest neighbor list for the X dimension and then remove any neighbors not part of the subcommunicator as follows:

    
    
        node 0 creates a list containing nodes 1 and 7
        node 1 creates a list containing nodes 0 and 2
        node 2 creates a list containing node 1
        node 6 creates a list containing node 7
        node 7 creates a list containing node 0 and 6
    
    


Then, node zero begins carrying out the logical line construction described in FIG. 6 as follows:

    
    
        node 0 adds node 0 and node 1 to the x-dimension logical line;
        node 0 calls node 1;
        node 1 adds node 2 to the line;
        node 1 calls node 2;
        node 2 has no available nodes to add because node 1 is node 2's only neighbor and node 1 has been added to the line;
        node 2 returns to 1;
        node 1 has no available nodes to add, and returns to node 0
        node 0 adds node 7, the only available node not already added to the line;
        node 0 calls 7;
        node 7 adds node 6;
        node 7 calls node 6;
        node 6 has no other nodes to add;
        node 6 returns to node 7 which has no other nodes to add;
        node 7 returns to node 0 which has no other nodes to add;
        having returned to node 0, the beginning node, the line is complete.
    
    


The logical line constructed by the nodes in the x-dimension includes nodes 0, 1, 2, 7, and 6. This logical line may now be utilized by the subcommunicator for efficient communication techniques that rely on axial topology structure for operation.
As will be appreciated by one skilled in the art, aspects of the present invention may be embodied as a system, method or computer program product. Accordingly, aspects of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, micro-code, etc.) or an embodiment combining software and hardware aspects that may all generally be referred to herein as a “circuit,” “module” or “system.” Furthermore, aspects of the present invention may take the form of a computer program product embodied in one or more computer readable medium(s) having computer readable program code embodied thereon.
Any combination of one or more computer readable medium(s) may be utilized. The computer readable medium may be a computer readable transmission medium or a computer readable storage medium. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device.
A computer readable transmission medium may include a propagated data signal with computer readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable transmission medium may be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device.
Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing.
Computer program code for carrying out operations for aspects of the present invention may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C++ or the like and conventional procedural programming languages, such as the “C” programming language or similar programming languages. The program code may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider).
Aspects of the present invention are described above with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer readable medium that can direct a computer, other programmable data processing apparatus, or other devices to function in a particular manner, such that the instructions stored in the computer readable medium produce an article of manufacture including instructions which implement the function/act specified in the flowchart and/or block diagram block or blocks.
The computer program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other devices to cause a series of operational steps to be performed on the computer, other programmable apparatus or other devices to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide processes for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks.
The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
It will be understood from the foregoing description that modifications and changes may be made in various embodiments of the present invention without departing from its true spirit. The descriptions in this specification are for purposes of illustration only and are not to be construed in a limiting sense. The scope of the present invention is limited only by the language of the following claims.

## Claims

1. A method of constructing a logical, regular axis topology from an irregular topology of a subcommunicator's compute nodes in a parallel computer, the subcommunicator comprising a subset of a communicator's compute nodes, the communicator's compute nodes organized into a regular topology comprising a plurality of axial dimensions, the subcommunicator's topology comprising an irregular topology within the regular topology, the method comprising:
for each axial dimension:
recursively, for each compute node in the subcommunicator beginning with a first compute node and ending upon a return to the first compute node:
adding, by the compute node, to a logical line of the axial dimension a neighbor for the axial dimension specified in a nearest neighbor list of the compute node, the compute node's nearest neighbor list comprising a list of the compute node's nearest neighbors in the subcommunicator for each axial dimension;
calling the added compute node;
determining, by the called compute node, whether any neighbor in the called compute node's nearest neighbor list is available to add to the logical line;
if a neighbor in the called compute node's nearest neighbor list is available to add to the logical line, adding, by the called compute node to the logical line, any neighbor in the called compute node's nearest neighbor list for the axial dimension not already added to the logical line; and
if no neighbor in the called compute node's nearest neighbor list is available to add to the logical line, returning to the calling compute node.

2. The method of claim 1, further comprising:
establishing, by each compute node in the subcommunicator, a nearest neighbor list for each axial dimension of the communicator;
removing, by each compute node of the subcommunicator, from the compute node's nearest neighbor list, any nearest neighbor not included in the sub communicator; and
providing, by each compute node of the subcommunicator to all other compute nodes of the subcommunicator, the compute node's nearest neighbor list.

3. The method of claim 2, wherein:
providing, by each compute node of the subcommunicator to all other compute nodes of the subcommunicator, the compute node's nearest neighbor list further comprises performing, by the compute nodes of the subcommunicator, an ALLGATHER collective operation.

4. The method of claim 1, wherein the regular topology of the communicator comprising a torus network topology comprising N-dimensions, wherein N comprises an integer greater than one.

5. The method of claim 1, wherein the regular topology of the communicator comprising a grid network topology comprising N-dimensions, wherein N comprising an integer greater than one.

6. The method of claim 1, further comprising:
upon construction of each logical construction, performing regular topology optimized data communications amongst the compute nodes of the subcommunicator.