A method includes receiving, by a processing device, an unsorted set of numbers to be sorted, sorting a first subset of the unsorted set of numbers and a second subset of the unsorted set of numbers using a first sorting technique to obtain a first sorted subset and a second sorted subset of numbers, and merging and sorting the first sorted subset and the second sorted subset of numbers using a second sorting technique to obtain a first sorted set of numbers.

A method includes receiving, by a processing device, an unsorted set of numbers to be sorted, sorting a first subset of the unsorted set of numbers and a second subset of the unsorted set of numbers using a first sorting technique to obtain a first sorted subset and a second sorted subset of numbers, and merging and sorting the first sorted subset and the second sorted subset of numbers using a second sorting technique to obtain a first sorted set of numbers.

The present application relates to a device for selecting top values from a set of raw values, comprising: an output queue, a loop queue, a top value storage module and a control module. The control module is configured to, at a higher priority, merge the intermediate sequence stored in the loop queue with the at most N top values stored in a storage area of the top value storage module, and sort the merged values to generate a merged sequence, until a predetermined number of storage areas in the top value storage module are traversed; wherein the control module is further configured to, when there is no intermediate sequence being stored in the loop queue, merge the output sequence with the at most N top values stored in a storage area of the top value storage module, and sort the merged values to generate a merged sequence; wherein the control module is further configured to provide a first subsequence in the merged sequence which is closer to a top most value of the merged sequence to the top value storage module to update the top value storage module, and provide a second subsequence in the merged sequence which is farther away from the top most value of the merged sequence to the loop queue to generate or update the intermediate sequence.

The present application relates to a device for selecting top values from a set of raw values, comprising: an output queue, a loop queue, a top value storage module and a control module. The control module is configured to, at a higher priority, merge the intermediate sequence stored in the loop queue with the at most N top values stored in a storage area of the top value storage module, and sort the merged values to generate a merged sequence, until a predetermined number of storage areas in the top value storage module are traversed; wherein the control module is further configured to, when there is no intermediate sequence being stored in the loop queue, merge the output sequence with the at most N top values stored in a storage area of the top value storage module, and sort the merged values to generate a merged sequence; wherein the control module is further configured to provide a first subsequence in the merged sequence which is closer to a top most value of the merged sequence to the top value storage module to update the top value storage module, and provide a second subsequence in the merged sequence which is farther away from the top most value of the merged sequence to the loop queue to generate or update the intermediate sequence.

Methods and systems for software analysis include determining a similarity score for an ordered input set and at least one ordered cluster set that represents a distance between the ordered input set and the at least one ordered cluster set. It is determined that he ordered input is similar to a first cluster of the at least one ordered cluster set, based on the similarity score. The ordered input set is merged to the first cluster of the at least one cluster set to generate a merged set that preserves an ordering of the ordered input set and the first cluster. Software analysis is performed using the merged set.

Methods and systems for software analysis include determining a similarity score for an ordered input set and at least one ordered cluster set that represents a distance between the ordered input set and the at least one ordered cluster set. It is determined that he ordered input is similar to a first cluster of the at least one ordered cluster set, based on the similarity score. The ordered input set is merged to the first cluster of the at least one cluster set to generate a merged set that preserves an ordering of the ordered input set and the first cluster. Software analysis is performed using the merged set.

Various aspects of the subject technology relate to methods, systems, and machine-readable media for generating histograms according to a set-theoretic approach. The method includes receiving a command to generate at least one histogram from selected data, the selected data comprising a plurality of column groups. The method also includes identifying a superset from the plurality of column groups. The method also includes materializing, in a memory, a superset multi-column group for the superset. The method also includes identifying at least one subset of the superset from the plurality of column groups, the at least one subset comprising at least one column group. The method also includes processing the at least one subset of the superset to form a grouped resultset. The method also includes generating the at least one histogram for the grouped resultset of the at least one subset of the superset.

Various aspects of the subject technology relate to methods, systems, and machine-readable media for generating histograms according to a set-theoretic approach. The method includes receiving a command to generate at least one histogram from selected data, the selected data comprising a plurality of column groups. The method also includes identifying a superset from the plurality of column groups. The method also includes materializing, in a memory, a superset multi-column group for the superset. The method also includes identifying at least one subset of the superset from the plurality of column groups, the at least one subset comprising at least one column group. The method also includes processing the at least one subset of the superset to form a grouped resultset. The method also includes generating the at least one histogram for the grouped resultset of the at least one subset of the superset.

A system and methods for designing single-stage hardware sorting blocks, and further using the single-stage hardware sorting blocks to reduce the number of stages in multistage sorting processes, or to define multiway merge sorting networks.

A system and methods for designing single-stage hardware sorting blocks, and further using the single-stage hardware sorting blocks to reduce the number of stages in multistage sorting processes, or to define multiway merge sorting networks.