Mutually-exclusive branch

Common factoring is the extraction of common subexpressions in mutually-exclusive branches of an i f statement or a case statement. Here is an example. 

The expression fi+C is computed in mutually-exclusive branches of an if statement. However, instead of the synthesis tool generating two adders, it is useful to factor out the expression and place it before the if statement. This is shown next. 

In the next step we calculate the maximum for the mutual exclusive branches and this results in table 4. The now calculated number of components is the estimate for the total number of components of each type, i.e. the necessary components required for each possible branch. 

Two operations opl and op2 are disjoint in time if one of the two following conditions holds (1) opl is serialized with respect to op2 in the graph, such that opl can execute only if opl has completed execution or vice versa, and (2) opl and opl each belong to different mutually exclusive branches of a conditional. The two cases are illustrated in Figure 7.1. Since the conditional branching structure cannot be arbitrarily altered without changing the external behavior of the model, we resolve resource conflicts by serializing operations. 

Mutual exclusivity. In branching from one node to its descendants, we should ensure that none of the subsets overlap with one another otherwise we could potentially explore the same solution subsets in multiple branches of the tree. Formally, if X is the original solution space and x, is the ith subset, then... 

So far, we have never observed, by n.m.r. spectroscopy, oligosaccharides or glycopeptides bearing Fuc and NeuAc both linked to the same N-acetyllactosamine branch this is in agreement with the biosynthetic principle of mutual exclusion existing in transferring (1— 3)-1 inked a-fucosyl and (2— 6)-linked a-sialyl groups to the same N-acetyl lactosamine branch, as formulated by Hill and coworkers.88... 

What if the designer knows that all case item values are mutually exclusive In such a case, a decoder can be synthesized for a case statement control (the case expression is checked for all possible values of the case item values in parallel) instead of the priority logic (which could potentially be nested deep depending on the number of branches in the case statement). 

An example of the use of an analytical methods selection expert which was developed with the KDS3 system is shown in Table 1. In this example the user is attempting to select a method for the determination of total sediment aluminum concentration according to the requirements of the Water Quality Branch of Environment Canada in Ottawa. From the main menu, aluminum, Al, is selected as the analyte of interest. The presentation of a set of values in a menu is a useful technique in the KDS3 shell when mutually exclusive options are to be selected. The KDS3 shell then prompts the user with a series of questions that can be answered with Y(yes), N(no), or (don t know or don t care), based on the conditions set up by the developer. 

Type 2 branches are formed by the transfer of arabinose to form a-L-arabinofuranosyl groups, attached to C-3 of xylosyl residues. UDPAra is presumed to be the arabinosyl donor. Since xylosyl residues that are substituted at C-2 and C-3 are not found, even though gymnospersms and monocytyledons contain both types of branch, there is likely to be a mutual exclusion between the two transferases, analogous to those found with glycoproteins (see Chapter 4). 

We finally review scheduling methods which put more emphasis on conditional branching. The main idea of these algorithms is to schedule mutually exclusive operations to allow sharing of hardware, and possibly a faster schedule for some paths in the control flow graph. 

Maps operations onto functional units, and minimizes the total execution time of expressions using associativity and commutativity. Shares functional units among mutually exclusive conditional branches, inserting multiplexors as necessary. 

Sharing functional units between mutually exclusive conditional branches. 

Some systems consider mutual exclusiveness of some operations in conditional branches[12, 17, 11]. However, most of them search the sharing pairs among operations in each c-step after usual scheduling. Therefore, they cannot produce optimal control for each path, and cannot attain resource sharing globally. 

The value of variable x is not used in all branches. In this description, operations in statement(l) need not be executed when the condition is cl c2. This fact is expressed by extended CVs. Then, basic CV of operations in (1) is [1,1,1], while the extended CV is [1,0, ](=[ ,0,0](2) or [0,0,1](3)). The 0 component shows the conditions that operations need not be carried out cT c2. Therefore, the statement (1) and (3) are mutually exclusive, and add operations in (1) and in (2) can share one adder. In this way, operations which are not mutually exclusive in behavioral description are sometimes mutually exclusive. Such implicit mutual exclusiveness, which does not appear explicitly in the behavioral description, can be considered by extended CVs. 

In Figure 2, the lower vectors next to operation nodes are extended CVs. The examples of implicit mutual exclusiveness are nodes ria and nj. Node ria is not a branch node which should be always executed in behavioral description, but the extended CV for ria is [1,0,1] and not [ij. 

Most of conventional scheduling algorithms do not exploit this kind of possibilities. Actual CV is introduced to enable such scheduling. Namely, operations in different branches are mutually exclusive after the conditionals are resolved and are not mutually exclusive until conditionals are resolved. Such dynamic mutual exclusiveness can be handled by ACVs. The value of ACVs are changed whether conditionals are resolved or not. 

This section discusses the way how to f exploit parallelism among different conditional branches. Operations in different branches are not mutually exclusive and they cannot share hardware. Therefore, the CVLS scheduling algorithm first exploits alternation within a branch, and then exploits parallelism among branches. 

There are sometimes multiple parallel conditional branches in a branch like the following description (a) in figure 7. Operations in branch (cl) and branch (c2) are not mutually exclusive. In this case, the basic CVs for these operation can t be determined by the former definition. Therefore, such kind of branch is converted into multiple basic branches, in which operations can have its basic CVs. The converted description is the description (b) in figure . These two descriptions produce the same outputs. The (b) description can be scheduled by the multiple branches scheduling. More complicated case can be handled in the same way. Such transformation is processed by the tCFG optimizer before generating CDFG. 

An important consideration in scheduling is the effect of control flow in a behavioral description. As shown in Figure 8, if-then-else and case statements imply an exclusive fork-join control block in the CDFG. Operations in the different branches of a block are mutually exclusive if they are scheduled within the control block s boundary. When similar operations in different branches are scheduled into the same c-step, a single FU is required since the operations will never execute concurrently. 

By using the branch labels it is possible for the scheduling algorithm to assign several operations within the same clock cycle to the same component. For operations which are mutual exclusive the maximum of the required components within each branch is sufficient for all branches. This is taken into account by the following algorithm. 

The algorithm starts with the evaluation table given in table 1. Beginning with the main branch Ml, all operations with this label are added to the operations in all direct sub branches. With nested sub branches this is done recursively until the innermost sub branch is reached. Table 2 shows the result produced by this algorithm for our example. (Ml is the main branch, M2 and M3 are mutual exclusive.)... 

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