Xerox Corporation

John R Gilbert

Robert S Schreiber

Siddhartha Chatterjee

Tatiana Shpeisman

John Ogden Lamping

Anurag Mendhekar

William W Pugh, Jr

Fred J Long

Shang-Hua Teng

A data structure, called an ordered sparse accumulator (Ordered SPA), permits sequencing in numeric order by index and dynamic alteration of the nonzero structure of the active column in sparse matrix computations during the sequencing operation.

Ordered sparse accumulator and its use in efficient sparse matrix

To generate computationally efficient computer program code for carrying out computer computations on matrix organized input data, a program first is written in a relatively high-level language which includes programmer specifiable constructs for manipulating matrices and parts thereof; and which permits certain of the constructs to be annotated to specify programmer selected data structures and programmer selected operations on those data structures. This high-level program then is translated into a relatively high-level program into a relatively low-level language using low-level language routines that provide a compilable representation of the program, including all programmer selected data structures and all programmer selected operations on said data structures then the low-level representation of the program is compiled to generate computer executable code for implementing the program, including all programmer selected data structures and all programmer selected operations on said data structures.

Tools for efficient sparse matrix computation

When a data-parallel language like Fortran 90 is compiled for a distributed-memory machine, aggregate data objects (such as arrays) are distributed across the processor memories. The mapping determines the amount of residual communication needed to bring operands of parallel operations into alignment with each other. A common approach is to break the mapping into two stages: first, an alignment that maps all the objects to an abstract template, and then a distribution that maps the template to the processors. This disclosure deals with two facets of the problem of finding alignments that reduce residual communication; namely, alignments that vary in loops, and objects that permit of replicated alignments. It is shown that loop-dependent dynamic alignment is sometimes necessary for optimum performance, and algorithms are provided so that a compiler can determine good dynamic alignments for objects within 'do' loops. Also situations are identified in which replicated alignment is either required by the program itself (via spread operations) or can be used to improve performance. An algorithm based on network flow is proposed for determing which objects to replicate so as to minimize the total amount of broadcast communication in replication.

Method of compilation optimization using an N-dimensional template for

An optimizing compilation process generates executable code which defines the computation and communication actions that are to be taken by each individual processor of a computer having a distributed memory, parallel processor architecture to run a program written in a data-parallel language. To this end, local memory layouts of the one-dimensional and multidimensional arrays that are used in the program are derived from one-level and two-level data mappings consisting of alignment and distribution, so that array elements are laid out in canonical order and local memory space is conserved. Executable code then is generated to produce at program run time, a set of tables for each individual processor for each computation requiring access to a regular section of an array, so that the entries of these tables specify the spacing between successive elements of said regular section resident in the local memory of said processor, and so that all the elements of said regular section can be located in a single pass through local memory using said tables. Further executable code is generated to produce at program run time, another set of tables for each individual processor for each communication action requiring a given processor to transfer array data to another processor, so that the entries of these tables specify the identity of a destination processor to which the array data must be transferred and the location in said destination processor's local memory at which the array data must be stored, and so that all of said array data can be located in a single pass through local memory using these communication tables. And, executable node code is generated for each individual processor that uses the foregoing tables at program run time to perform the necessary computation and communication actions on each individual processor of the parallel computer.

Growing community of inventors

Palo Alto, CA, United States of America

John R Gilbert