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This avoids a major problem with ripple adders caused by the fact that the carry signal must propagate along the entire length of the chain of internal adders, causing longer delays in the electrical signals and thus reducing the clock rates of a circuit or possibly increasing power consumption A carry select adder gets around this through a common hardware trick of speculative execution It divides the inputs into blocks and adds each block twice, once assuming the carry is low and once assuming it is high The result is then selected after the circuit, when the carry for the block has been computed Listing 12-16 shows the specification of the essence of the hardware layout of a carry select adder using the techniques we ve developed so far The specification uses the slicing syntax for arrays described in 4 Listing 12-16.

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2. Define an object view. Next, we define an object view with a query that represents the object-oriented view we have in mind. 3. Define the instead of triggers. In this step, we write instead of triggers on the view to support required DML statements such as insert, update, and delete that work directly on the object view. This step is required only if we want to insert, delete, and update directly on the object view. The alternative is to do these operations directly on the underlying tables. As you ll see shortly, the instead of triggers can be quite complex, and the resulting DMLs on the object view can result in very poor performance. Hence I recommend that you avoid creating these triggers and instead use object views only to perform selects on them. We ll look at each of the preceding steps in the following sections. We will demonstrate the use of object views by creating an object view on top of the relational tables, components_rel and parts_rel, that we created in the earlier section Relational Tables Based Approach. We assume that our relational schema consisting of the tables components_rel and parts_rel has the following data to begin with: benchmark@ORA10G> select * from components_rel; COMPONENT_ID -----------1 2 COMPONENT_NAME -------------component1 component2

The architectures presented here are by no means exhaustive of the choices available to you when inventing your own technical infrastructure. We ve put forth these to demonstrate some of the various ways the pieces and parts of these services can be put together. The chapters that follow present detailed examinations of each of the disparate services available. Mapping these solutions to the nonfunctional requirements that are specific to your application and enterprise will yield a solution that may be similar, but most likely not identical, to those we ve presented here.

A Carry Select Adder Modeled Using Propositional Logic let mux a b c = ((~~~a ==> b) &&& (a ==> c)) let carrySelectAdder totalSize maxBlockSize (x:bitvec) (y:bitvec) (sumLo:bitvec) (sumHi:bitvec) (carryLo:bitvec) (carryHi:bitvec) (sum:bitvec) (carry:bitvec) = Blocks [ for i in 0.maxBlockSize.totalSize-1 -> let sz = min (totalSize-i) maxBlockSize let j = i+sz-1 let carryLo = Arrayappend [| False |] carryLo[i+1.j+1] let adderLo = rippleAdder sz x[i.j] y[i.j] sumLo[i.j] carryLo let carryHi = Arrayappend [| True |] carryHi[i+1.j+1] let adderHi = rippleAdder sz x[i.j] y[i.j] sumHi[i.j] carryHi let carrySelect = (carry[j+1] === mux carry[i] carryLo[sz] carryHi[sz]) let sumSelect = Blocks [for k in i.j -> sum[k] === mux carry[i] sumLo[k] sumHi[k]] adderLo &&& adderHi &&& carrySelect &&& sumSelect ].

benchmark@ORA10G> select * from parts_rel; COMPONENT_ID PART_ID PART_NAME PART_DESC ------------ ------- ---------- -------------------1 1 part11 part 11 desc 1 2 part12 part 12 desc 2 3 part21 part 21 desc 2 4 part22 part 22 desc Now, let s look at each of the previous three steps involved in creating an object view on top of the tables components_rel and parts_rel.

You can now check that a carrySelectAdder is equivalent to a rippleAdder. Here s the overall verification condition: let checkAdders n k = let x = (vec n "x") let y = (vec n "y") let sumA = (vec n "sumA") let sumB = (vec n "sumB") let sumLo = (vec n "sumLo") let sumHi = (vec n "sumHi") let carryA = (vec (n+1) "carryA") let carryB = (vec (n+1) "carryB") let carryLo = (vec (n+1) "carryLo") let carryHi = (vec (n+1) "carryHi") let adder1 = carrySelectAdder n k x y sumLo sumHi carryLo let adder2 = rippleAdder n x y sumB carryB (adder1 &&& adder2 &&& (carryA.[0] === carryB.[0]) ==> (vecEq sumA sumB &&& bitEq carryA.[n] carryB.[n]))