Patent Application
20200125326
The present invention generally relates to computing systems, and more specifically, to sort accelerators configured to sort data records of a computer processor.
Computing systems are widely used to process and sort data records stored in a database. A variety of sorting algorithms have been developed to reduce sorting time for improving the processing performance of the computing system. Once such sorting algorithm is referred to as tournament tree sort.
In general, a tournament tree sort is a binary-tree based selection and replacement sort algorithm. Tournament tree sort algorithms allow sorting of keys associated with a data record in a continuous streaming fashion. Incoming keys are entered into the leaf nodes and the keys exit, in sorted order, from the tree's root node. For a set of input records that are initially populated into the leaf nodes, pair-wise comparisons are performed at each tree level until a winning record emerges at the tree root. After the initial round of comparisons and populations, each non-leaf node holds exactly one input key, except the winning key which is sent out of the tree. During a continuous sort, after a winner is removed from the tree, a new input record is inserted at the previous winner's leaf node and is compared (and swapped, if needed) with exactly one non-leaf node at each level, until the tree root is reached and the new winner is determined.
According to a non-limiting embodiment, a computer processor comprises a memory unit configured to store key values to be loaded into a partial tournament sort, and a processor cache configured to obtain tree data from the memory unit indicating the key values. The computer processor further includes a hardware merge sort accelerator in communication with the memory unit and the processor cache. The merge sort accelerator is configured to generate a tournament tree based on the key values stored only in the memory and processor cache and to perform a partial tournament sort to store a first portion of tournament results in the processor cache.
According to another non-limiting embodiment, a computer-implemented method is provided to sort a plurality of data values stored in a hardware computer processor. The method comprises storing, in a memory unit of the computer processor, key values to be loaded into a partial tournament sort, and obtaining, via a processor cache, data from the memory unit indicating the key values. The method further comprises generating, via a hardware merge sort accelerator, a tournament tree based on the key values, and performing, via the merge sort accelerator, a partial tournament sort to store a first portion of tournament results in the processor cache while excluding a second portion of the tournament results from the processor cache.
According to yet another non-limiting embodiment, a computer program product is provided to control an electronic computer processor to sort data. The computer program product comprises a computer readable storage medium having program instructions embodied therewith. The program instructions are executable by the electronic computer processor to perform operations comprising storing, in a memory unit of the computer processor, lists referencing key values to be loaded into a partial tournament sort, and obtaining, via a processor cache, data from the memory unit indicating the key values. The method further includes generating, via a hardware merge sort accelerator, a tournament tree based on the key values, and performing, via the merge sort accelerator, a partial tournament sort to store a first portion of tournament results in the processor cache while excluding a second portion of the tournament results from the processor cache. The key value represents a string of characters divided into a plurality of words or digits of a high-order base (e.g. 2{circumflex over ( )}64). For simplicity, drawings use digits of base 10.
According to still another non-limiting embodiment, a computer system is configured to sort data. The computer system comprises a processor cache and a hardware merge sort accelerator. The processor cache is in signal communication with a separate memory unit installed in the computer system, and is configured to determine a plurality of key values stored in the memory unit. The hardware merge sort accelerator is in signal communication with the memory unit and the processor cache. The merge sort accelerator is configured to generate a tournament tree based on the key values obtained from the processor cache, and to perform multiple partial tournament sorts to determine an overall winning key value among a list of key values participating in the partial tournament sorts. The computer system further comprises a memory unit including memory locations configured to store each overall winning key value. The memory unit is continuously updated in response to storing the overall winning key such that each overall winning key is automatically stored sequentially with respect to one another.
According to yet another non-limiting embodiment, a computer-implemented method is provided to update a computer system with sequentially sorted data. The method comprises determining, via a processor cache, a plurality of key values stored in a memory unit installed on the computer system, and generating, via a hardware merge sort accelerator, a tournament tree based on the key values obtained from the processor cache. The method further comprises determining, via the merge sort accelerator, a plurality of overall winning key value among a list of key values participating in a partial tournament sort. The method further comprises continuously updating the memory unit with the plurality of the overall winning key values that are automatically stored sequentially with respect to one another in response to storing a most recent determined overall winning key value in the memory unit.
Additional technical features and benefits are realized through the techniques of the present invention. Embodiments and aspects of the invention are described in detail herein and are considered a part of the claimed subject matter. For a better understanding, refer to the detailed description and to the drawings.
The specifics of the exclusive rights described herein are particularly pointed out and distinctly claimed in the claims at the conclusion of the specification. The foregoing and other features and advantages of the embodiments of the invention are apparent from the following detailed description taken in conjunction with the accompanying drawings in which:
The diagrams depicted herein are illustrative. There can be many variations to the diagram or the operations described therein without departing from the spirit of the invention. For instance, the actions can be performed in a differing order or actions can be added, deleted or modified. Also, the term “coupled” and variations thereof describes having a communications path between two elements and does not imply a direct connection between the elements with no intervening elements/connections between them. All of these variations are considered a part of the specification.
In the accompanying figures and following detailed description of the disclosed embodiments, the various elements illustrated in the figures are provided with two or three digit reference numbers. With minor exceptions, the leftmost digit(s) of each reference number correspond to the figure in which its element is first illustrated.
Various embodiments of the invention are described herein with reference to the related drawings. Alternative embodiments of the invention can be devised without departing from the scope of this invention. Various connections and positional relationships (e.g., over, below, adjacent, etc.) are set forth between elements in the following description and in the drawings. These connections and/or positional relationships, unless specified otherwise, can be direct or indirect, and the present invention is not intended to be limiting in this respect. Accordingly, a coupling of entities can refer to either a direct or an indirect coupling, and a positional relationship between entities can be a direct or indirect positional relationship. Moreover, the various tasks and process steps described herein can be incorporated into a more comprehensive procedure or process having additional steps or functionality not described in detail herein.
The following definitions and abbreviations are to be used for the interpretation of the claims and the specification. As used herein, the terms “comprises,” “comprising,” “includes,” “including,” “has,” “having,” “contains” or “containing,” or any other variation thereof, are intended to cover a non-exclusive inclusion. For example, a composition, a mixture, process, method, article, or apparatus that comprises a list of elements is not necessarily limited to only those elements but can include other elements not expressly listed or inherent to such composition, mixture, process, method, article, or apparatus.
The term “exemplary” is used herein to mean “serving as an example, instance or illustration.” Any embodiment or design described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments or designs. The terms “at least one” and “one or more” may be understood to include any integer number greater than or equal to one, i.e. one, two, three, four, etc. The terms “a plurality” may be understood to include any integer number greater than or equal to two, i.e. two, three, four, five, etc. The term “connection” may include both an indirect “connection” and a direct “connection.”
Additionally, the term “match” refers to a comparison between two keys included in a given tournament sort tree. The term “winner” refers to the key that moves forward to participate in a following “match.” In a “highest-winner” tournament scheme, the higher value key participating in the “match” is deemed the “winner” and moves forward to participate in a match higher up the tree, i.e., in the next “round”. In a “lowest-winner” tournament scheme, however, the lower value key participating in the “match” is deemed the winner and advances to the next “round”, i.e., proceeds to the next higher level of the tree.
For the sake of brevity, conventional techniques related to making and using aspects of the invention may or may not be described in detail herein. In particular, various aspects of computing systems and specific computer programs to implement the various technical features described herein are well known. Accordingly, in the interest of brevity, many conventional implementation details are only mentioned briefly herein or are omitted entirely without providing the well-known system and/or process details.
Turning now to an overview of technologies that are more specifically relevant to aspects of the invention, computing systems include a hardware processor core, which employs a merge sort accelerator. The merge sort accelerator is a hardware component that facilitates various sort algorithms including, for example, a tournament tree sort algorithm. A traditional tournament sort algorithm executes individual “matches” by comparing full keys against one another. The tree itself stores the losers of a prior tournament, when a new element is chosen from a list and enters the tournament, it is compared against existing losers in order to determine whether it is smaller or larger. The winning (smallest) key is stored, the tree list is updated, and the process proceeds to the next level of the tree, i.e., the next “round”, to compare another full key that emerges from the list that the winner was chosen from.
Traditional tournament tree sort algorithms require that the conventional merge sort accelerator itself employ large individual buffers to store records associated with a sort tree, along with the data indicating the losers and/or winners of the tournament. In addition, several comparators are employed with the merge sort accelerator to facilitate the pair-wise comparisons of the keys. As the size of the sort tree and/or individual keys increases, however, the available buffer space of the merge sort accelerator decreases and the sort runtime increases. It may also be necessary to increase the number of comparators included in the merge sort accelerator, thereby increasing cost on required processing power.
Turning now to an overview of the aspects of the invention, one or more embodiments of the disclosure address the shortcomings described above by employing a partial tournament sort that partially processes subsets of keys participating in a tournament iteratively. In at least one embodiment, a partial sort can be achieved by performing tournaments on a digit by digit basis. A digit can be of the base 10, but in computer systems will typically be chosen to be a high power of 2 (e.g. 2{circumflex over ( )}64) matching the data bus size of the computer system. The partial sort performs a first tournament that compares a first digit in a first place holder (e.g., the “tens” place holder) of a first key with a second digit located in the first place holder (e.g., the “tens” place holder) of a second key, and then performs a second tournament that compares a second digit located in a second place holder (e.g., the “ones” place holder) of the first key with a second digit located in the second place holder (e.g., the “ones” place holder) of the second key.
When executing conventional tournament sorts, the winner data either must be store/buffered in the accelerator or it must be repeatedly read in order to compare it to the other nodes on the path to the root. The partial tournament sort according to various embodiments described herein (e.g., performing a partial tournament sort on a digit-by-digit basis) requires only a small number of bytes, equivalent to the data bus width of the data cache, be stored in the accelerator to avoid the penalty of repeatedly reading the winner's data. In this manner, the load on the accelerator is reduced thereby improving the performance and speed of the overall computer system.
In addition, the computer system provides a merge sort accelerator that leverages the existing cache of the computing system to execute a partial compare tournament sort. Instead of storing all the keys of the tournament's losers in the memory of the individual accelerator, at least one embodiment stores a portion of the tournament source data (a single digit), e.g., only the winner of a particular match, in the accelerator. When all losers have been compared for a first digit, the winning digit stored in the accelerator and that data can be stored to the output without having to retrieve it from the processor cache again. And even if the winner is ambiguous due to a tie on the prefix of digits processed up to that point the winner data itself is unambiguous due to being equal by definition.
Referring now to
In an exemplary embodiment, in terms of hardware architecture, as shown in
The processor 105 is a computing device for executing hardware instructions or software, particularly that stored in memory 110. The processor 105 can be any custom made or commercially available processor, a central processing unit (CPU), an auxiliary processor among several processors associated with the computer 101, a semiconductor based microprocessor (in the form of a microchip or chip set), a macroprocessor, or generally any device for executing instructions. The processor 105 may include a cache 170, which may be organized as a hierarchy of more cache levels (L1, L2, etc.).
The memory 110 can include any one or combination of volatile memory elements (e.g., random access memory (RAM, such as DRAM, SRAM, SDRAM, etc.)) and nonvolatile memory elements (e.g., ROM, erasable programmable read only memory (EPROM), electronically erasable programmable read only memory (EEPROM), programmable read only memory (PROM), tape, compact disc read only memory (CD-ROM), disk, diskette, cartridge, cassette or the like, etc.). Moreover, the memory 110 may incorporate electronic, magnetic, optical, and/or other types of storage media. Note that the memory 110 can have a distributed architecture, where various components are situated remote from one another but can be accessed by the processor 105.
The instructions in memory 110 may include one or more separate programs, each of which comprises an ordered listing of executable instructions for implementing logical functions. In the example of
In an exemplary embodiment, a conventional keyboard 150 and mouse 155 can be coupled to the input/output controller 135. Other output devices such as the I/O devices 140, 145 may include input devices, for example, but not limited to a printer, a scanner, microphone, and the like. Finally, the I/O devices 140, 145 may further include devices that communicate both inputs and outputs, for instance but not limited to, a network interface card (NIC) or modulator/demodulator (for accessing other files, devices, systems, or a network), a radio frequency (RF) or other transceiver, a telephonic interface, a bridge, a router, and the like. The system 100 can further include a display controller 125 coupled to a display 130. In an exemplary embodiment, the system 100 can further include a network interface 160 for coupling to a network 165. The network 165 can be an IP-based network for communication between the computer 101 and any external server, client and the like via a broadband connection. The network 165 transmits and receives data between the computer 101 and external systems. In an exemplary embodiment, network 165 can be a managed IP network administered by a service provider. The network 165 may be implemented in a wireless fashion, e.g., using wireless protocols and technologies, such as Wi-Fi, WiMax, etc. The network 165 can also be a packet-switched network such as a local area network, wide area network, metropolitan area network, Internet network, or other similar type of network environment. The network 165 may be a fixed wireless network, a wireless local area network (LAN), a wireless wide area network (WAN) a personal area network (PAN), a virtual private network (VPN), intranet or other suitable network system and includes equipment for receiving and transmitting signals.
If the computer 101 is a PC, workstation, intelligent device or the like, the instructions in the memory 110 may further include a basic input output system (BIOS) (omitted for simplicity). The BIOS is a set of essential routines that initialize and test hardware at startup, start the OS 111, and support the transfer of data among the storage devices. The BIOS is stored in ROM so that the BIOS can be executed when the computer 101 is activated.
When the computer 101 is in operation, the processor 105 is configured to execute instructions stored within the memory 110, to communicate data to and from the memory 110, and to generally control operations of the computer 101 pursuant to the instructions. In exemplary embodiments, the computer system 100 includes one or more accelerators 180 that are configured to communicate with the processor 105. The accelerator 180 may be a field programmable gate array (FPGA), an application-specific integrated circuit (ASIC), or other suitable device that is configured to perform specific processing tasks. In exemplary embodiments, the computer system 100 may be configured to offload certain processing tasks to an accelerator 180 because the accelerator 180 can perform the processing tasks more efficiently than the processor 105.
A tournament tree algorithm allows continuous sorting of streaming input keys. Tournament trees with N leaf nodes guarantee a minimum sorted run of size N, although much larger sorted runs can usually be achieved, with typical run sizes being 2N. (The definition of a run is prior art and not considered here. Extension of the invention to the support of multiple runs is considered trivial to anyone skilled in the art.) For each new key inserted into the tree, the tournament tree algorithm requires only one comparison at each of the log(N) levels of the tree, since the comparisons are made along a known path to the root. This characteristic allows the entire tree to be served with a single comparator, with a throughput of 1 key per log(N) cycles.
In general, the implementation of a tournament tree sort includes multiple levels from the beginning to the end of a sorting run, sometimes referred to as a sorting “pass”. During an initial setup phase, an initial set of keys are first input into the tournament tree, which populates the leaf nodes of the tournament tree. The keys can be inserted serially and all comparisons (i.e., matches) performed during the tournament can be made using a single comparator, evaluating the comparisons for all the levels of the tournament tree.
A second phase, referred to as the evaluation phase, includes evaluating the remaining levels of the tournament tree and performing sorting after the leaf nodes are fully populated. In a conventional tournament tree sort, the evaluation phase can add to the cost of sorting the tournament tree after the last key from the initial set of keys is inserted. For example, it can take approximately four thousand comparisons to fully evaluate a sixteen thousand node conventional tournament tree once the keys are populated. Since all the keys are available at this time and since the comparisons are being done across one level of the tree at a time, this process can be easily pipelined, with one comparison being performed every cycle (provided that whole key pair can be compared ever cycle, leading to large buffers).
A third phase includes a continuous sorting phase. During the continuous sorting phase, incoming new keys are inserted into the leaf node of the previous winner and proceed up the tree (i.e., to the next level) following the path of the previous winner. At each level, the value of the new key is compared with the value at the internal node and either the current winner is kept or the key is swapped at that node. In exemplary embodiments, each new key that is inserted results in the next sorted key being emitted from the tree.
A fourth phase includes a flush phase, which occurs when no more keys to be sorted are added to the tree. The flush phase may include inserting dummy keys, which are guaranteed to be the smallest/largest possible key, into the tree and flushing the remaining valid keys. Since the dummy keys are the smallest/largest possible key, they always lose in the comparisons and thus do not emerge as winners until all the remaining valid keys have been flushed from the tree. At this point, all the valid keys have been sorted and the sort operation is complete. The invention focuses mostly on improving the continuous sorting phase, buts techniques can be applied to the setup/evaluation/flush phases as well.
Unlike a conventional tournament tree sorting scheme, at least one embodiment described herein includes a merge sort accelerator that performs a partial compare tournament sort. The merge sort accelerator can be constructed as an individual hardware processor configured to sort data values (e.g., keys) stored in a separate main hardware processor included in the computer system. With reference to
Turning to
Each match 204a-204g of the first round compares a first digit located in a first place holder (e.g., the “tens” place holder) with a second digit located in the first place holder (e.g., the “tens” place holder) of a second key (the winner of the preceding match of the tournament). The winner (e.g., “4”) of match 204g is deemed the winner of the first round and is stored from the merge sort accelerator 180, and stored in the main memory 110 of the processor.
In some scenarios, a “tie” can occur during a first round, i.e., the same value of each key may be compared in a given match. For example, match 204a is deemed a tie because both keys (e.g., 50 and 53) have the same value, i.e., a matching first digit being “5”. In this scenario, the value of the matching digit (e.g. 5) advances to the next match (i.e., 204e), and the winner of the tied match (204a) is determined in the following pass.
In order to support processing a tournament, digit by digit binary state 207 is retained across partial tournaments for the current selected key 205. The binary state vector 207 includes a “decided state” binary vector and a “loser state” binary vector. Each binary vector includes a value corresponding to the rounds or levels of the tournament tree 200. Thus, a tournament tree 200 including three rounds/matches or three levels to determine a winner will include a binary state vector 207 including a 3-bit “decided state” binary vector and a 3-bit “loser state” binary vector. Still referring to
For instance, during the first round, a tie occurred between 5 (e.g., 50) and 5 (e.g., 53). Thus, no decision occurred in the first round, and the first digit of the 3-bit “decided state” binary vector was set to “0”. In the second round, however, 5 (e.g., 5×) lost to 4 (e.g., 49). Thus, a decision (e.g., a win/loss) occurred in the second round, and the second digit of the binary vector was set to “1”. In the third round, 4 (e.g., 49) was deemed the winner over 5 (e.g., 54). Thus, a decision (e.g., a win/loss) occurred in the third round, and the third digit of the binary vector was set to “1”.
The 3-bit “loser state” binary vector operates to indicate a round in which the currently selected key 205 realizes a loss, if at all. During the first round of the first pass, for instance, the currently selected key 205 (e.g. 50) realized a tie and therefore did not lose. Thus, the first digit of the 3-bit “loser state” binary vector was set to “0”. However, the currently selected key 205 realized a loss in the second round (i.e., 5 was deemed a loser against 4). Therefore, the second digit of the 3-bit “loser state” binary vector was set to “1”. Because currently selected key 205 did not advance to the third round, the third digit of the 3-bit “loser state” binary vector was set to “0”. Accordingly, the 3-bit “loser state” binary vector corresponding to the currently selected key 205 (e.g. 50) following completion of the second pass reads “010”.
Turning now
The binary state vector 207 is also updated to read “111” according to the results of the second pass. For instance, a decision in the first round occurs because now a winner can be determined between key value “50” and key value “53”. That is, “0” is less than “3” such that it is determined that “50” is the winner of “53”. Accordingly, the first digit of the 3-bit “decided state” binary vector was set to “1”. Therefore, the “decided state” vector is updated to read “111”.
Turning to
Referring to the second pass shown in
As can be seen with reference to
For instance, in view of the tournament sort described herein, key “52” would be selected as the next current key 205 (see
Turning now to
The pipelined cache 170 includes a directory access 302 and a cache access 304. The pipelined cache 170 is configured to provide fast access to memory locations that store the data to be sorted (e.g., data keys). The data that is requested at the beginning of the pipeline will not be available until the end of the cache's data access pipeline. In at least one embodiment, the memory addresses to be read are known at least as many cycles ahead of time as there as stages in the cache's pipeline. In the tournament sort described herein, all addresses from a leaf of the tree to its root are known ahead of time making it particularly suitable for the pipelined cache 170.
The sort accelerator 180 includes a tree memory unit 306, a results memory unit 308, and a logic controller 310. The logic controller 310 generates addresses of the tournament, which are then stored in the tree memory unit 306. Previous results from the tournament, (e.g., previous losers and/or winners of a match) can be retrieved from the cache access 304, loaded in the results memory unit 308, and utilized to perform a current match (e.g., comparison between two digits) between a pair of keys included in the tournament tree. Once the match is complete, the results can be again stored to the cache 170, and new results data (e.g., another previous winner) can be loaded in the results memory unit 308 to perform another match. In this manner, the sort accelerator 180 is not required to store all the results of from the tournament, but only the (partial) key data of the winner from the previous level participating in a current match.
Turning now to
The memory array 401 stores the addresses defining the tournament tree used to perform partial compare tournament sort. The first pipeline stage 402a reads the addresses/length and index of the key elements participating the tournament sort tree, and delivers the addresses to the cache 170 to determine the key elements associated with a given address. The second pipeline stage 402b and third additional pipeline stages 402c are provided to match data exchange latency between the accelerator and the (pipelined) cache. Although two additional pipeline stages (e.g., 402b and 402c) are illustrated, the merge sort accelerator pipeline 400 is not limited thereto and can have more or less additional pipeline stages.
The fourth pipeline stage 402d receives the data from the cache 170 and delivers it to a comparator 404. In at least one embodiment, the data received from the cache 170 includes a first DW and a second DW. The first and second DWs can include, for example, a first digit from a first key and a second digit from a second key. The comparator 404 then performs the match by comparing the first digit to the second digit. In a lowest-winner tournament (i.e., loser-based tournament), for example, the lower digit is deemed the winner and is output to the fifth pipeline stage 402e. The comparator 404 also feeds the loser and/or winner back to an update register 406. The update register 406 implements the bits for the lost and decided vectors. The fifth pipeline stage 402e receives the “winner” of the comparison. The winner data is then stored from the merge sort accelerator pipeline 400 and stored it in the memory unit (e.g., memory 110) of the processor (e.g. 105).
Turning now to
At operation 504, a current input list from which to take a next key element (e.g., DW) is obtained. In at least one embodiment, a key element is a DW, referring to a number of the “s byte” word that is processed in each key element. In addition, the winner node (i.e., the index and address of the winner of a previous run) is set to “nil” because no runs have yet been executed. At operation 506, a node (e.g., an integer identifying an entry of the tree array/list) is selected and increased by 1 iteration based on the current input list from which to take the next element (i.e., N+cur>>1). In addition, the current round or tree level (“i”) is set to 1 (i.e., i=1) such that the partial tournament sort begins at round 1 or at the first level of the tournament tree. At operation 508, winner data (e.g., the 8 byte data word that is considered the winner) from a first match is determined. At operation 510, the winner advances to the next level of the tree (i.e., to the next match), and a determination is made as to whether one or more given nodes along the current path has already been decided at operation 512.
When a given node proceeding along a tournament path is not decided, the method proceeds to operation 514 and determines whether the winner is less than the fetch data (i.e., the data fetched for comparisons (and potentially promoting to new winner data). When the winner data is less than the fetch data, the method proceeds to operation 516, and both the lost binary state vector and decided binary state vector are incremented (i.e., set to bit value “1”). Setting the lost binary state vector to “1” indicates that one or more given nodes along the tournament path have lost a match. At operation 518, the current round or tree level “i” is incremented by 1 iteration (i.e., “i=i+1”). Accordingly, the matches between two keys at the next level of the tree are performed.
When, however, a given node proceeding along a tournament path has been decided at operation 512, the method proceeds to operation 550 and a determination is made as to whether the node has lost its match. When the node has not lost its match, the decision binary state vector is set to 1 and the winner data is set as the fetch data at operation 552, and “i” is incremented by 1 iteration (i.e., “i=i+1”) so as to advance to the next round or next tree level at operation 518.
Turning to operation 520, a determination is made as to whether “i” is less than the depth (d) of the tree (i.e., whether i<d). When “i” is less than “d”, the method returns to operation 510, and the node is incremented by an iteration. When, however, “i” is not less than “d”, the method proceeds to operation 522 (see
At operation 524, a determination is made as to whether the current key element (e.g., DW) is less than the total number of key elements (K) participating in the tournament sort. When DW is less than K, the method returns to operation 506. When, however, DW is not less than K, the method proceeds to operation 526 and the node is incremented (i.e., node=(N+cur_»1). When DW is less than K, the method returns to operation 506. When, however, DW is not less than K, the method increases the address of the list by K*s bytes to now point to the next element of the list at operation 525, before returning to operation 506 and incrementing the node “i” (i.e., node=(N+cur_»1)
At operation 528, the node is incremented (i.e., node =(N+cur_»1)). At operation 530, a determination is made as to whether “i” has lost. When “i” has not lost, “i” is incremented (i.e., i=i+1) at operation 532. When, however, “i” has lost, the method swaps the sorted locations of the current node and the winner node (i.e., the node that defeated “i”) at operation 534, and “i” is incremented (i.e., i=i+1) at operation 532.
Turning to operation 536, a determination is made as to whether “i” is less than the depth (d) of the tree (i.e., whether i<d). When “i” is less than “d”, the method returns to operation 528 and increments the current node (i.e., node=node>>1). When, however, “i” is not less than “d”, the method proceeds to operation 538 to determine where to start next sort (i.e., DW=0″ start with first digit again). In other words, the method determines where begin the sort for the next key/element from our unsorted lists before returning to operation 506.
The present invention may be a system, a method, and/or a computer program product at any possible technical detail level of integration. The computer program product may include a computer readable storage medium (or media) having computer readable program instructions thereon for causing a processor to carry out aspects of the present invention.
The terms “about,” “substantially,” “approximately,” and variations thereof, are intended to include the degree of error associated with measurement of the particular quantity based upon the equipment available at the time of filing the application. For example, “about” can include a range of ±8% or 5%, or 2% of a given value.
The computer readable storage medium can be a tangible device that can retain and store instructions for use by an instruction execution device. The computer readable storage medium may be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. A non-exhaustive list of more specific examples of the computer readable storage medium includes the following: 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), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanically encoded device such as punch-cards or raised structures in a groove having instructions recorded thereon, and any suitable combination of the foregoing. A computer readable storage medium, as used herein, is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiber-optic cable), or electrical signals transmitted through a wire.
Computer readable program instructions described herein can be downloaded to respective computing/processing devices from a computer readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and/or a wireless network. The network may comprise copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and/or edge servers. A network adapter card or network interface in each computing/processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium within the respective computing/processing device.
Computer readable program instructions for carrying out operations of the present invention may be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state-setting data, configuration data for integrated circuitry, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, C++, or the like, and procedural programming languages, such as the “C” programming language or similar programming languages. The computer readable program instructions 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). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate arrays (FPGA), or programmable logic arrays (PLA) may execute the computer readable program instruction by utilizing state information of the computer readable program instructions to personalize the electronic circuitry, in order to perform aspects of the present invention.
Aspects of the present invention are described herein 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 readable program instructions.
These computer readable 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 readable program instructions may also be stored in a computer readable storage medium that can direct a computer, a programmable data processing apparatus, and/or other devices to function in a particular manner, such that the computer readable storage medium having instructions stored therein comprises an article of manufacture including instructions which implement aspects of the function/act specified in the flowchart and/or block diagram block or blocks.
The computer readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process, such that the instructions which execute on the computer, other programmable apparatus, or other device implement 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 instructions, which comprises one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the blocks 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 carry out combinations of special purpose hardware and computer instructions.
The descriptions of the various embodiments of the present invention have been presented for purposes of illustration, but are not intended to be exhaustive or limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terminology used herein was chosen to best explain the principles of the embodiments, the practical application or technical improvement over technologies found in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments described herein.
This application is a continuation of U.S. application Ser. No. 16/118,560, filed Aug. 31, 2018, the contents of which are incorporated by reference herein in its entirety.
| Number | Date | Country | |
|---|---|---|---|
| Parent | 16118560 | Aug 2018 | US |
| Child | 16718419 | US |
