Abstract:
A method, apparatus, system, and signal-bearing medium that, in an embodiment, collect previous and current statistics based on previous and current access plans, respectively, and a query. The previous and current statistics are compared in response to an event, and the differences between the previous and current statistics are presented. In various embodiments, the event may be a change to logic in a database management system that performs the query, a degradation in performance of the query, or a user request. In various embodiments, the difference may be a change to the previous access plan that causes performance degradation of the query, such as missing an index. The previous access plan is copied into the current access plan if an estimated processing time for the current access plan is greater than an estimated processing time for the previous access plan. The current access plan is used to perform the query. In this way, in various embodiments, the source of a performance problem may be more easily diagnosed and resolved, and better query performance may be achieved after changes have been made that impact the access plan, for example, changes due to software fixes, new software releases, or new hardware.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
       [0001]     The present application is related to commonly-assigned patent application Ser. No. 10/354,802, to Craig S. Aldrich et al., filed Jan. 30, 2003, entitled “Data Management System that Provides Intelligent Access Plan Caching,” which is herein incorporated by reference. The present application is also related to commonly-assigned patent application Ser. No. 10/860,402, to Paul R. Day et al., filed Jun. 30, 2004, entitled “Apparatus and Method for Autonomically Generating a Query Implementation that Meets a Defined Performance Specification,” which is herein incorporated by reference. 
     
    
     FIELD  
       [0002]     This invention generally relates to computer database management systems and more specifically relates to determining and presenting differences between query statistics for current and previous access plans used by the query.  
       BACKGROUND  
       [0003]     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 sophisticated devices, and computer systems may be found in many different settings. Computer systems typically include a combination of hardware, such as semiconductors and circuit boards, and software, also known as computer programs.  
         [0004]     Fundamentally, computer systems are used for the storage, manipulation, and analysis of data, which may be anything from complicated financial information to simple baking recipes. It is no surprise, then, that the overall value or worth of a computer system depends largely upon how well the computer system stores, manipulates, and analyzes data. One mechanism for managing data is called a database management system (DMS), which may also be called a database system or simply a database.  
         [0005]     Many different types of databases are known, but the most common is usually called a relational database (RDB), which organizes data in tables that have rows, which represent individual entries or records in the database, and columns, which define what is stored in each entry or record. Each table has a unique name within the database and each column has a unique name within the particular table. The database also has an index, which is a data structure that informs the database management system of the location of a certain row in a table given an indexed column value, analogous to a book index informing the reader on which page a given word appears.  
         [0006]     To be useful, the data stored in databases must be capable of being retrieved in an efficient manner. The most common way to retrieve data from a database is through statements called database queries. A query is an expression evaluated by the database management system. Queries may be issued programmatically via applications or via a user interface. As one might imagine, queries range from being very simple to very complex. When the database management system receives a query, the database management system interprets the query and determines what internal steps are necessary to satisfy the query. These internal steps may include an identification of the table or tables specified in the query, the row or rows selected in the query, and other information such as whether to use an existing index, whether to build a temporary index, whether to use a temporary file to execute a sort, and/or the order in which the tables are to be joined together to satisfy the query.  
         [0007]     When taken together, these internal steps are referred to as an execution plan or an access plan. The access plan is typically created by a software component that is often called a query optimizer. The query optimizer may be part of the database management system or separate from but in communication with the database management system. When a query optimizer creates an access plan for a given query, the access plan is often saved by the database management system in the program object, e.g., the application program, that requested the query. The access plan may also be saved in an SQL (Structured Query Language) package or an access plan cache. Then, when the user or program object repeats the query, which is a common occurrence, the database management system can find and reutilize the associated saved access plan instead of undergoing the expensive and time-consuming process of recreating the access plan. Thus, reusing access plans increases the performance of queries when performed by the database management system.  
         [0008]     For complex queries that are frequently executed, users may spend substantial time fine-tuning the access plan, in order to achieve the best possible performance. Once the access plan has been properly tuned, users naturally expect the query to keep performing well in the future. Unfortunately, an access plan that experienced acceptable or even optimal performance when it was initially created may experience significant performance degradation later because of changes that have occurred to the organization of the target database or changes that have occurred in the database management system, e.g., changes due to a new operating system release for the computer system. For example, the database that is the target of the query may have indexes added, changed, or removed (either intentionally or inadvertently), which can dramatically impact the performance of the previously tuned and saved access plan.  
         [0009]     Users may have a very limited awareness of the source of or reason for these changes that have affected the performance of their queries. They may merely know that suddenly their queries are running much slower without any idea of the reason why. Further, the more complicated the query and its associated access plan, the more difficulty users experience when attempting to determine the source of the performance degradation.  
         [0010]     Thus, without a better way to handle changes to databases and operating systems, users will continue to suffer difficulty in diagnosing and solving performance problems related to queries.  
       SUMMARY  
       [0011]     A method, apparatus, system, and signal-bearing medium are provided that in an embodiment collect previous and current statistics based on previous and current access plans, respectively, and a query. The previous and current statistics are compared in response to an event, and the differences between the previous and current statistics are presented. In various embodiments, the statistics may include the name of the query, the library of each file associated with the query, each index that is associated with each used file, the number of records retrieved by the query, the most-frequently used field list for each file, the number of average duplicated values returned by the query, and/or an identification of the best access plan for the query. The statistics may also include the join order of tables associated with the query, join pairs for each join dial, each index that is in use for each dial in the query implementation, and/or the estimated processing time for the associated query. The statistics may also include a field value associated with the query if the field value is skewed from a historical average.  
         [0012]     In various embodiments, the event may be a change to logic in a database management system that performs the query, a degradation in performance of the query, or a user request. In various embodiments, the difference may be a change to the previous access plan that causes performance degradation of the query, such as a change to an index. The previous access plan is copied into the current access plan if an estimated processing time for the current access plan is greater than an estimated processing time for the previous access plan. The current access plan is used to perform the query.  
         [0013]     In this way, in an embodiment, the source of a performance problem may be more easily diagnosed and resolved.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0014]     Various embodiments of the present invention are hereinafter described in conjunction with the appended drawings:  
         [0015]      FIG. 1  depicts a high-level block diagram of an example system for implementing an embodiment of the invention.  
         [0016]      FIG. 2  depicts a flowchart of example processing for a statistics collection engine, according to an embodiment of the invention.  
         [0017]      FIG. 3  depicts a flowchart of example processing for a test engine, according to an embodiment of the invention. 
     
    
     DETAILED DESCRIPTION  
       [0018]     In an embodiment, a statistics collection engine collects previous statistics based on a query and a previous access plan and collects current statistics based on a current access plan and the query. In various embodiments, the statistics may include the name of the query, the library of each file associated with the query, each index that is associated with each used file, the number of records retrieved by the query, the most-frequently used field list for each file, the number of average duplicated values returned by the query, and/or an identification of the best access plan for the query. The statistics may also include the join order of tables associated with the query, join pairs for each join dial, each index that is in use for each dial in the query implementation, and/or the estimated processing time for the associated query. The statistics may also include a field value associated with the query if the field value is skewed from a historical average.  
         [0019]     In response to an event, a test engine compares the previous statistics and the current statistics and presents a difference between them. A user, such as a system administrator or a submitter (human or program) of the query may use the difference to diagnose the source of the problem. In various embodiments, the event may be a change to logic in a database management system that performs the query, a degradation in performance of the query, or a user request. In various embodiments, the difference may be any change between the previous access plan and the current access plan, such as a change that causes performance degradation of the query. An example of such a change is a change (addition, deletion, or modification) to an index. In an embodiment, if performance has degraded from the previous to the current access plan, the source of the problem is likely reflected in the difference between the current and the previous statistics. In this way, by presenting the difference between the current statistics associated with the current access plan and the previous statistics associated with the previous access plan, the source of a performance problem may be more easily diagnosed and resolved.  
         [0020]     Referring to the Drawings, wherein like numbers denote like parts throughout the several views,  FIG. 1  depicts a high-level block diagram representation of a computer system  100  connected to a network  130 , according to an embodiment of the present invention. In an embodiment, the hardware components of the computer system  100  may be implemented by an IBM eServer iSeries computer system. However, those skilled in the art will appreciate that the mechanisms and apparatus of embodiments of the present invention apply equally to any appropriate computing system.  
         [0021]     The major components of the computer system  100  include one or more processors  101 , a main memory  102 , a terminal interface  111 , a storage interface  112 , an I/O (Input/Output) device interface  113 , and communications/network interfaces  114 , all of which are coupled for inter-component communication via a memory bus  103 , an I/O bus  104 , and an I/O bus interface unit  105 .  
         [0022]     The computer system  100  contains one or more general-purpose programmable central processing units (CPUs)  101 A,  101 B,  101 C, and  101 D, herein generically referred to as the processor  101 . In an embodiment, the computer system  100  contains multiple processors typical of a relatively large system; however, in another embodiment the computer system  100  may alternatively be a single CPU system. Each processor  101  executes instructions stored in the main memory  102  and may include one or more levels of on-board cache.  
         [0023]     The main memory  102  is a random-access semiconductor memory for storing data and programs. In another embodiment, the main memory  102  represents the entire virtual memory of the computer system  100 , and may also include the virtual memory of other computer systems coupled to the computer system  100  or connected via the network  130 . The main memory  102  is conceptually a single monolithic entity, but in other embodiments the main memory  102  is a more complex arrangement, such as a hierarchy of caches and other memory devices. For example, memory may exist in multiple levels of caches, and these caches may be further divided by function, so that one cache holds instructions while another holds non-instruction data, which is used by the processor or processors. Memory may be further distributed and associated with different CPUs or sets of CPUs, as is known in any of various so-called non-uniform memory access (NUMA) computer architectures.  
         [0024]     The memory  102  includes a database management system  154 , a test engine  156 , a current access plan  158 , a saved access plan  160 , current statistics  162 , saved statistics  163 , a query optimizer  164 , an application  166 , and a statistics collection engine  168 . Although the database management system  154 , the test engine  156 , the current access plan  158 , the saved access plan  160 , the current statistics  162 , the saved statistics  163 , the query optimizer  164 , the application  166 , and the statistics collection engine  168  are illustrated as being contained within the memory  102  in the computer system  100 , in other embodiments some or all of them may be on different computer systems and may be accessed remotely, e.g., via the network  130 . The computer system  100  may use virtual addressing mechanisms that allow the programs of the computer system  100  to behave as if they only have access to a large, single storage entity instead of access to multiple, smaller storage entities. Thus, while the database management system  154 , the test engine  156 , the current access plan  158 , the saved access plan  160 , the current statistics  162 , the saved statistics  163 , the query optimizer  164 , the application  166 , and the statistics collection engine  168  are illustrated as being contained within the main memory  102 , these elements are not necessarily all completely contained in the same storage device at the same time.  
         [0025]     Further, although the database management system  154 , the test engine  156 , the current access plan  158 , the saved access plan  160 , the current statistics  162 , the saved statistics  163 , the query optimizer  164 , the application  166 , and the statistics collection engine  168  are illustrated as being separate entities, in other embodiments some of them, or portions of some of them, may be packaged together. For example, in various embodiments some or all of the database management system  154 , the test engine  156 , the query optimizer  164 , and the statistics collection engine  168  may be packaged together. As a further example, in various embodiments the current access plan  158  and the saved access plan  160  may be packaged with the application  166 .  
         [0026]     The database management system  154  includes data, e.g., organized in rows and columns, indexes used to access the data, and logic that performs a query against the data using the current access plan  158 . The query optimizer  164  creates the current access plan  158 , which in various embodiments may include an identification of the table or tables in the database management system  154  specified in the query, the row or rows selected in the query, and other information such as whether to use an existing index, whether to build a temporary index, whether to use a temporary file to execute a sort, and/or the order in which the tables are to be joined together to satisfy the query. The saved access plan  160  is a saved version of an access plan, which the database management system  154  used to execute the query the previous time the query was performed.  
         [0027]     The application  166  sends queries to the database management system  154 . The statistics collection engine  168  collects data regarding the query and the current access plan  158  and saves the data to the current statistics  162 . The statistics collection engine  168  is further described below with reference to  FIG. 2 .  
         [0028]     In various embodiments, the current statistics  162  may include the name of the query, the library of each file associated with the query, each index that is associated with each used file, regardless of whether the index is chosen in the query implementation, the number of records retrieved by the query, the most-frequently used field list for each file, the number of average duplicated values returned by the query, and/or an identification of the best access plan for the associated query. The current statistics  162  may also include the join order of tables associated with the query, join pairs for each join dial, each index that is in use for each dial in the query implementation, and/or the estimated processing time for the associated query. The saved statistics  163  are a previous version of the current statistics  162  and are associated with the saved access plan  160 .  
         [0029]     The test engine  156  chooses between the current access plan  158  or the saved access plan  160  for the database management system  154  to use when executing a query. The test engine  156  further reports the difference between the current statistics  162  and the saved statistics  163 . The test engine  156  is further described below with reference to  FIG. 3 .  
         [0030]     In an embodiment, the test engine  156  and the statistics collection engine  168  include instructions capable of executing on the processor  101  or statements capable of being interpreted by instructions executing on the processor  101  to perform the functions as further described below with reference to  FIGS. 2 and 3 . In another embodiment, the test engine  156  and the statistics collection engine  168  may be implemented in microcode. In another embodiment, the test engine  156  and the statistics collection engine  168  may be implemented in hardware via logic gates and/or other appropriate hardware techniques.  
         [0031]     The memory bus  103  provides a data communication path for transferring data among the processor  101 , the main memory  102 , and the I/O bus interface unit  105 . The I/O bus interface unit  105  is further coupled to the system I/O bus  104  for transferring data to and from the various I/O units. The I/O bus interface unit  105  communicates with multiple I/O interface units  111 ,  112 ,  113 , and  114 , which are also known as I/O processors (IOPs) or I/O adapters (IOAs), through the system I/O bus  104 . The system I/O bus  104  may be, e.g., an industry standard PCI bus, or any other appropriate bus technology.  
         [0032]     The I/O interface units support communication with a variety of storage and I/O devices. For example, the terminal interface unit  111  supports the attachment of one or more user terminals  121 ,  122 ,  123 , and  124 . The storage interface unit  112  supports the attachment of one or more direct access storage devices (DASD)  125 ,  126 , and  127  (which are typically rotating magnetic disk drive storage devices, although they could alternatively be other devices, including arrays of disk drives configured to appear as a single large storage device to a host). The contents of the main memory  102  may be stored to and retrieved from the direct access storage devices  125 ,  126 , and  127 .  
         [0033]     The I/O and other device interface  113  provides an interface to any of various other input/output devices or devices of other types. Two such devices, the printer  128  and the fax machine  129 , are shown in the exemplary embodiment of  FIG. 1 , but in other embodiment many other such devices may exist, which may be of differing types. The network interface  114  provides one or more communications paths from the computer system  100  to other digital devices and computer systems; such paths may include, e.g., one or more networks  130 .  
         [0034]     Although the memory bus  103  is shown in  FIG. 1  as a relatively simple, single bus structure providing a direct communication path among the processors  101 , the main memory  102 , and the I/O bus interface  105 , in fact the memory bus  103  may comprise multiple different buses or communication paths, which may be arranged in any of various forms, such as point-to-point links in hierarchical, star or web configurations, multiple hierarchical buses, parallel and redundant paths, or any other appropriate type of configuration. Furthermore, while the I/O bus interface  105  and the  110  bus  104  are shown as single respective units, the computer system  100  may in fact contain multiple I/O bus interface units  105  and/or multiple I/O buses  104 . While multiple I/O interface units are shown, which separate the system I/O bus  104  from various communications paths running to the various I/O devices, in other embodiments some or all of the I/O devices are connected directly to one or more system I/O buses.  
         [0035]     The computer system  100  depicted in  FIG. 1  has multiple attached terminals  121 ,  122 ,  123 , and  124 , such as might be typical of a multi-user “mainframe” computer system. Typically, in such a case the actual number of attached devices is greater than those shown in  FIG. 1 , although the present invention is not limited to systems of any particular size. The computer system  100  may alternatively be a single-user system, typically containing only a single user display and keyboard input, or might be a server or similar device which has little or no direct user interface, but receives requests from other computer systems (clients). In other embodiments, the computer system  100  may be implemented as a personal computer, portable computer, laptop or notebook computer, PDA (Personal Digital Assistant), tablet computer, pocket computer, telephone, pager, automobile, teleconferencing system, appliance, or any other appropriate type of electronic device.  
         [0036]     The network  130  may be any suitable network or combination of networks and may support any appropriate protocol suitable for communication of data and/or code to/from the computer system  100 . In various embodiments, the network  130  may represent a storage device or a combination of storage devices, either connected directly or indirectly to the computer system  100 . In an embodiment, the network  130  may support Infiniband. In another embodiment, the network  130  may support wireless communications. In another embodiment, the network  130  may support hard-wired communications, such as a telephone line or cable. In another embodiment, the network  130  may support the Ethernet IEEE (Institute of Electrical and Electronics Engineers) 802.3x specification. In another embodiment, the network  130  may be the Internet and may support IP (Internet Protocol).  
         [0037]     In another embodiment, the network  130  may be a local area network (LAN) or a wide area network (WAN). In another embodiment, the network  130  may be a hotspot service provider network. In another embodiment, the network  130  may be an intranet. In another embodiment, the network  130  may be a GPRS (General Packet Radio Service) network. In another embodiment, the network  130  may be a FRS (Family Radio Service) network. In another embodiment, the network  130  may be any appropriate cellular data network or cell-based radio network technology. In another embodiment, the network  130  may be an IEEE 802.11B wireless network. In still another embodiment, the network  130  may be any suitable network or combination of networks. Although one network  130  is shown, in other embodiments any number (including zero) of networks (of the same or different types) may be present.  
         [0038]     It should be understood that  FIG. 1  is intended to depict the representative major components of the computer system  100  and the network  130  at a high level, that individual components may have greater complexity that represented in  FIG. 1 , that components other than or in addition to those shown in  FIG. 1  may be present, and that the number, type, and configuration of such components may vary. Several particular examples of such additional complexity or additional variations are disclosed herein; it being understood that these are by way of example only and are not necessarily the only such variations.  
         [0039]     The various software components illustrated in  FIG. 1  and implementing various embodiments of the invention may be implemented in a number of manners, including using various computer software applications, routines, components, programs, objects, modules, data structures, etc., referred to hereinafter as “computer programs,” or simply “programs.” The computer programs typically comprise one or more instructions that are resident at various times in various memory and storage devices in the computer system  100 , and that, when read and executed by one or more processors  101  in the computer system  100 , cause the computer system  100  to perform the steps necessary to execute steps or elements comprising the various aspects of an embodiment of the invention.  
         [0040]     Moreover, while embodiments of the invention have and hereinafter will be described in the context of fully-functioning computer systems, the various embodiments of the invention are capable of being distributed as a program product in a variety of forms, and the invention applies equally regardless of the particular type of signal-bearing medium used to actually carry out the distribution. The programs defining the functions of this embodiment may be delivered to the computer system  100  via a variety of signal-bearing media, which include, but are not limited to:  
         [0041]     (1) information permanently stored on a non-rewriteable storage medium, e.g., a read-only memory device attached to or within a computer system, such as a CD-ROM, DVD-R, or DVD+R;  
         [0042]     (2) alterable information stored on a rewriteable storage medium, e.g., a hard disk drive (e.g., the DASD 125, 126, or 127), CD-RW, DVD-RW, DVD+RW, DVD-RAM, or diskette; or  
         [0043]     (3) information conveyed by a communications medium, such as through a computer or a telephone network, e.g., the network  130 , including wireless communications.  
         [0044]     Such signal-bearing media, when carrying machine-readable instructions that direct the functions of the present invention, represent embodiments of the present invention.  
         [0045]     In addition, various programs described hereinafter may be identified based upon the application for which they are implemented in a specific embodiment of the invention. But, any particular program nomenclature that follows is used merely for convenience, and thus embodiments of the invention should not be limited to use solely in any specific application identified and/or implied by such nomenclature.  
         [0046]     The exemplary environments illustrated in  FIG. 1  are not intended to limit the present invention. Indeed, other alternative hardware and/or software environments may be used without departing from the scope of the invention.  
         [0047]      FIG. 2  depicts a flowchart of example processing for the statistics collection engine  168 , according to an embodiment of the invention. Control begins at block  200 . Control then continues to block  205  where the application  166  submits a query to the database management system  154 . Control then continues to block  210  where the database management system  154  invokes the statistics collection engine  168 , which determines whether a field value used by the query is skewed from the average field used historically. For example, in an embodiment, the statistics collection engine  168  determines whether a field value used by the query is different from the historical average by an amount that is greater than a threshold.  
         [0048]     If the determination at block  210  is true, then the field value is skewed from the historical average, so control continues to block  215  where the statistics collection engine  168  saves the field value in the current statistics  162 . Control then continues to block  220  where the statistics collection engine  168  saves performance statistics related to the query and the current access plan  158  into the current statistics  162  and further saves the current access plan  158  into the saved access plan  160 .  
         [0049]     In various embodiments, the performance statistics include the name of the query, the library of each file associated with the query, each index that is associated with each used file, regardless of whether the index is chosen in the query implementation, the number of records retrieved by the query, the most-frequently used field list for each file, the number of average duplicated values returned by the query, and/or an identification of the best access plan for the associated query. The statistics may also include the join order of tables associated with the query, join pairs for each join dial, each index that is in use for each dial in the query implementation, and/or the estimated processing time for the associated query.  
         [0050]     Control then continues to block  225  where the database management system  154  performs the query using the current access plan  158 . Control then continues to block  299  where the logic of  FIG. 2  returns.  
         [0051]     If the determination at block  210  is false, then the field value is not skewed from the historical average, so control continues from block  210  to block  220 , as previously described above.  
         [0052]      FIG. 3  depicts a flowchart of example processing for the test engine  156 , according to an embodiment of the invention. Control begins at block  300 . Control then continues to block  305  where the computer system  100  is updated with a new version of an operating system, a fix, update, new release, or any other change is applied to the logic of the database management system  154 , performance of the computer system  100  or the database management system  154  has degraded more than a threshold amount, or a user (e.g. a system administrator or the user submitting the query) or the application  166  makes a request to test the current access plan  158 .  
         [0053]     Control then continues to block  310  where the test engine  156  invokes the query optimizer  164  with a request to build or rebuild the current access plan  158  and a request to return the estimated processing time for the current access plan  158 . The test engine  156  further invokes the statistics collection engine  168  with a request to return the current statistics  162  associated with the current access plan  158 .  
         [0054]     Control then continues to block  315  where the test engine  156  compares the estimated processing time for the current access plan  158  to the estimated processing time for the saved access plan  160 . The test engine  156  further compares the current statistics  162  associated with the current access plan  158  to the saved statistics  163  associated with the saved access plan  160 .  
         [0055]     Control then continues to block  320  where the test engine  156  determines whether the current access plan  158  is better than the saved access plan  160  by determining whether the estimated processing time for the current access plan  158  is less than or equal to the estimated processing time for the saved access plan  160 .  
         [0056]     If the determination at block  320  is true, then the estimated processing time for the current access plan  158  is less than or equal to the estimated processing time for the saved access plan  160 , so control continues to block  325  where the test engine  156  instructs the database management system  154  to use the current access plan  158 . Control then continues to block  330  where the test engine  156  saves the current access plan  158  into the saved access plan  160 . Control then continues to block  335  where the test engine  156  saves the current statistics  162  into the saved statistics  163 . Control then continues to block  340  where, in various embodiments, the test engine  156  presents or reports the current statistics  162 , the current statistics  162  and the saved statistics  163 , and/or the difference between the current statistics  162  and the saved statistics  163 . In various embodiments, the test engine  156  makes the presentation via a message, a printer, a user interface, an email, an image, a video, a notification, an audio speaker, via invoking a program or method, or via any other appropriate technique.  
         [0057]     Control then continues to block  399  where the logic of  FIG. 3  returns.  
         [0058]     If the determination at block  320  is false, then the estimated processing time for the current access plan  158  is greater than the estimated processing time for the saved access plan  160 , so control continues to block  345  where the test engine  156  instructs the database management system  154  to use the saved access plan  158  and copies the saved access plan  160  into the current access plan  158 . Control then continues to block  340  where, in various embodiments, the test engine  156  presents or reports the current statistics  162 , the current statistics  162  and the saved statistics  163 , and/or the difference between the current statistics  162  and the saved statistics  163 , as previously described above.  
         [0059]     Control then continues to block  399  where the logic of  FIG. 3  returns.  
         [0060]     In the previous detailed description of exemplary embodiments of the invention, reference was made to the accompanying drawings (where like numbers represent like elements), which form a part hereof, and in which is shown by way of illustration specific exemplary embodiments in which the invention may be practiced. These embodiments were described in sufficient detail to enable those skilled in the art to practice the invention, but other embodiments may be utilized and logical, mechanical, electrical, and other changes may be made without departing from the scope of the present invention. Different instances of the word “embodiment” as used within this specification do not necessarily refer to the same embodiment, but they may. The previous detailed description is, therefore, not to be taken in a limiting sense, and the scope of the present invention is defined only by the appended claims.  
         [0061]     In the previous description, numerous specific details were set forth to provide a thorough understanding of embodiments of the invention. But, the invention may be practiced without these specific details. In other instances, well-known circuits, structures, and techniques have not been shown in detail in order not to obscure the invention.