Abstract: A batched Cholesky decomposition method, system, and non-transitory computer readable medium for a Graphics Processing Unit (GPU) including at least a first problem and a second problem, include mirroring a second problem matrix of the second problem to a first problem matrix of the first problem, combining the first problem matrix and the mirrored second problem matrix into a single problem matrix, and allocating data read to a thread and to the first problem and the second problem, respectively.

Abstract: Methods for sorting a data set. Data items each having a first portion and a second portion is stored. The first and second portions are stored separately and each has a separate set of keys. The first portion has a pointer indicating the second portion. At least some of the first set of keys for each data item is stored in a local memory of a first processor. At least one data stripe set is defined with one stripe within each bucket. An in-place partial bucket radix sort is performed on data items within one data stripe set with a first processor using an initial key. Incorrectly sorted data items are grouped into respective incorrect data item groups within each bucket. A radix sort is then performed using the initial radix on the incorrect data item groups. A first level sorted output is produced.

Abstract: Methods and systems for memory-based computing include combining multiple operations into a single lookup table and combining multiple memory-based operation requests into a single read request. Operation result values are read from a multi-operation lookup table that includes result values for a first operation above a diagonal of the lookup table and includes result values for a second operation below the diagonal. Numerical inputs are used as column and row addresses in the lookup table and the requested operation determines which input corresponds to the column address and which input corresponds to the row address. Multiple operations are combined into a single request by combining respective members from each operation into respective inputs an reading an operation result value from a lookup table to produce a combined result output. The combined result output is separated into a plurality of individual result outputs corresponding to the plurality of requests.

Abstract: Access is obtained to a truth table having a plurality of rows, each including a plurality of input bits and a plurality of output bits. At least some rows include don't-care inputs. At least some of the rows are clustered into a plurality of multi-row clusters. At least some of the multi-row clusters are assigned to ternary content-addressable memory modules of a prefabricated programmable memory array. Instructions for interconnecting the ternary content-addressable memory modules with a plurality of input pins of the prefabricated programmable memory array and a plurality of output pins of the prefabricated programmable memory array are specified in a data structure, in order to implement the truth table.

Abstract: Systems and methods for sorting a data set. A data storage is divided into a plurality of buckets that is each associated with a respective key value. A plurality of stripes is identified in each bucket. At least one data stripe set is defined that has one stripe within each respective bucket. An in-place partial bucket radix sort is performed on data items contained within one data stripe set with a first processor using an initial radix. Incorrectly sorted data items are then grouped in each bucket into a respective incorrect data item group within each bucket. A radix sort is then performed using the initial radix on the items within the respective incorrect data item group. A first level sorted output is produced.

Abstract: Systems and methods for sorting a data set. Data items each having a first portion and a second portion is stored. The first and second portions are stored separately and each has a separate set of keys. The first portion has a pointer indicating the second portion. At least some of the first set of keys for each data item is stored in a local memory of a first processor. At least one data stripe set is defined with one stripe within each bucket. An in-place partial bucket radix sort is performed on data items within one data stripe set with a first processor using an initial key. Incorrectly sorted data items are grouped into respective incorrect data item groups within each bucket. A radix sort is then performed using the initial radix on the incorrect data item groups. A first level sorted output is produced.

Abstract: Techniques for transforming input operands to reduce overhead for implementing addition operations in hardware are provided. In one aspect, a method for transforming input operands of an adder includes the steps of: receiving a bit array of the input operands; replacing a duplicate signal (e.g., a signal that occurs twice) for a given bit k in the bit array with a single signal at bit k+1; reducing a number of occurrences of the signal on adjacent bits of the input operand, wherein by way of the replacing and reducing a transformed bit array is formed; and providing the transformed bit array to the adder.

Abstract: Methods and systems for memory-based computing include combining multiple operations into a single lookup table and combining multiple memory-based operation requests into a single read request. Operation result values are read from a multi-operation lookup table that includes result values for a first operation above a diagonal of the lookup table and includes result values for a second operation below the diagonal. Numerical inputs are used as column and row addresses in the lookup table and the requested operation determines which input corresponds to the column address and which input corresponds to the row address. Multiple operations are combined into a single request by combining respective members from each operation into respective inputs an reading an operation result value from a lookup table to produce a combined result output. The combined result output is separated into a plurality of individual result outputs corresponding to the plurality of requests.

Abstract: Mechanisms are provided for performing a matrix operation. A processor of a data processing system is configured to perform cluster-based matrix reordering of an input matrix. An input matrix, which comprises nodes associated with elements of the matrix, is received. The nodes are clustered into clusters based on numbers of connections with other nodes within and between the clusters, and the clusters are ordered by minimizing a total length of cross cluster connections between nodes of the clusters, to thereby generate a reordered matrix. A lookup table is generated identifying new locations of nodes of the input matrix, in the reordered matrix. A matrix operation is then performed based on the reordered matrix and the lookup table.

Abstract: Systems and methods for sorting a data set stored on an external device. A plurality of smaller radix sizes are determined, based on a first radix size and performance characteristics of an external data storage device, whose sizes add up to a first radix size for an in-place radix sort. The smaller radix sizes reduce a total time to perform the in-place radix sort. Each level of a multiple level in-place radix sort is performed with the smaller radix sizes. Each level of the sort includes dividing the data set into N buckets; dividing the buffer into N buckets; and iteratively loading a respective segment in each bucket of the data set into a respective bucket of the buffer, performing an in-place radix sort on the data in the buffer, and returning sorted buffer data to the data set on the external storage device.

Abstract: Mechanisms are provided for performing a matrix operation. A processor of a data processing system is configured to perform cluster-based matrix reordering of an input matrix. An input matrix, which comprises nodes associated with elements of the matrix, is received. The nodes are clustered into clusters based on numbers of connections with other nodes within and between the clusters, and the clusters are ordered by minimizing a total length of cross cluster connections between nodes of the clusters, to thereby generate a reordered matrix. A lookup table is generated identifying new locations of nodes of the input matrix, in the reordered matrix. A matrix operation is then performed based on the reordered matrix and the lookup table.

Abstract: Methods and systems for sorting a dataset include partitioning the dataset into 2n partitions, where n is a number of available processors. A first quicksort is performed in parallel across pairs of partitions based on a pivot using a plurality of processors. A second quicksort is performed in parallel on unsorted elements within each partition based on the pivot, where the unsorted elements were left unsorted by the first quicksort. Misplaced elements from a left side of the dataset are swapped with misplaced elements from a right side of the dataset to produce a left dataset that has elements equal to or lower than the pivot and a right dataset that has elements equal to or higher than the pivot.

Abstract: Mechanisms, in a system comprising a host system and at least one accelerator device, for performing a concept analysis operation are provided. The host system extracts a set of one or more concepts from an information source and provides the set of one or more concepts to the accelerator device. The host system also provides at least one matrix representation data structure representing a graph of concepts and relationships between concepts in a corpus. The accelerator device executes the concept analysis operation internal to the accelerator device to generate an output vector identifying concepts in the corpus, identified in the at least one matrix representation data structure, related to the set of one or more concepts extracted from the information source. The accelerator device outputs the output vector to the host system which utilizes the output vector to respond to a request submitted to the host system associated with the information source.

Abstract: Mechanisms are provided for performing a matrix operation. A processor of a data processing system is configured to perform cluster-based matrix reordering of an input matrix. An input matrix, which comprises nodes associated with elements of the matrix, is received. The nodes are clustered into clusters based on numbers of connections with other nodes within and between the clusters, and the clusters are ordered by minimizing a total length of cross cluster connections between nodes of the clusters, to thereby generate a reordered matrix. A lookup table is generated identifying new locations of nodes of the input matrix, in the reordered matrix. A matrix operation is then performed based on the reordered matrix and the lookup table.

Abstract: Methods and systems for memory-based computing include combining multiple operations into a single lookup table and combining multiple memory-based operation requests into a single read request. Operation result values are read from a multi-operation lookup table that includes result values for a first operation above a diagonal of the lookup table and includes result values for a second operation below the diagonal. Numerical inputs are used as column and row addresses in the lookup table and the requested operation determines which input corresponds to the column address and which input corresponds to the row address. Multiple operations are combined into a single request by combining respective members from each operation into respective inputs an reading an operation result value from a lookup table to produce a combined result output. The combined result output is separated into a plurality of individual result outputs corresponding to the plurality of requests.

Abstract: Methods and systems for memory-based computing include combining multiple operations into a single lookup table and combining multiple memory-based operation requests into a single read request. Operation result values are read from a multi-operation lookup table that includes result values for a first operation above a diagonal of the lookup table and includes result values for a second operation below the diagonal. Numerical inputs are used as column and row addresses in the lookup table and the requested operation determines which input corresponds to the column address and which input corresponds to the row address. Multiple operations are combined into a single request by combining respective members from each operation into respective inputs an reading an operation result value from a lookup table to produce a combined result output. The combined result output is separated into a plurality of individual result outputs corresponding to the plurality of requests.

Abstract: Systems for memory-based computing include combining multiple operations into a single lookup table and combining multiple memory-based operation requests into a single read request. Operation result values are read from a multi-operation lookup table that includes result values for a first operation above a diagonal of the lookup table and includes result values for a second operation below the diagonal. Numerical inputs are used as column and row addresses in the lookup table and the requested operation determines which input corresponds to the column address and which input corresponds to the row address. Multiple operations are combined into a single request by combining respective members from each operation into respective inputs an reading an operation result value from a lookup table to produce a combined result output. The combined result output is separated into a plurality of individual result outputs corresponding to the plurality of requests.

Abstract: Methods and systems for memory-based computing include combining multiple operations into a single lookup table and combining multiple memory-based operation requests into a single read request. Operation result values are read from a multi-operation lookup table that includes result values for a first operation above a diagonal of the lookup table and includes result values for a second operation below the diagonal. Numerical inputs are used as column and row addresses in the lookup table and the requested operation determines which input corresponds to the column address and which input corresponds to the row address. Multiple operations are combined into a single request by combining respective members from each operation into respective inputs an reading an operation result value from a lookup table to produce a combined result output. The combined result output is separated into a plurality of individual result outputs corresponding to the plurality of requests.

Abstract: Methods for sorting a data set. Data items each having a first portion and a second portion is stored. The first and second portions are stored separately and each has a separate set of keys. The first portion has a pointer indicating the second portion. At least some of the first set of keys for each data item is stored in a local memory of a first processor. At least one data stripe set is defined with one stripe within each bucket. An in-place partial bucket radix sort is performed on data items within one data stripe set with a first processor using an initial key. Incorrectly sorted data items are grouped into respective incorrect data item groups within each bucket. A radix sort is then performed using the initial radix on the incorrect data item groups. A first level sorted output is produced.

Abstract: Methods for sorting a data set. A data storage is divided into a plurality of buckets that is each associated with a respective key value. A plurality of stripes is identified in each bucket. At least one data stripe set is defined that has one stripe within each respective bucket. An in-place partial bucket radix sort is performed on data items contained within one data stripe set with a first processor using an initial radix. Incorrectly sorted data items are then grouped in each bucket into a respective incorrect data item group within each bucket. A radix sort is then performed using the initial radix on the items within the respective incorrect data item group. A first level sorted output is produced.