Flops, definition

Figure 2-49 A variable used before its definition is inferred as a flip-flop.

Many banded systems are symmetric positive definite and/or diagonally dominant. In those cases, pivoting is unnecessary, and the band structure can be fully exploited one-half of the flops used can be further saved if A has Choleski s factorization. 

PLDL factorization of an n x n symmetric matrix A (where P is a permutation matrix) can be computed, say, by Aasen s algorithm, using about /6 (rather than n /3) flops and 0 n ) comparisons for pivoting, even if A is not positive definite and has no Choleski s factorization. 

The most common and definitely the best way of achieving this is to attach an external asynchronous or synchronous reset signal to each and every storage element in the circuit. When an external initialization signal is specified, the compiler will select an appropriate component from the library (if the elements are inferred). For example, if a flip flop is required to be initialized to V, the selected element will possess an input for a preset signal. A variety of designs based on this form of initialization are given in the examples in this chapter. 

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