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Section: Software

Affine clock calculus

Participants : Loïc Besnard, Thierry Gautier.

The affine clock calculus [43] is an extension of the boolean clock calculus based on free boolean conditions. The affine relations allow to express that successive values of some signal are provided at specific micro-instants between any two successive macro-instants in a regular manner. To express affine relations, three predefined processes have been introduced.

affine_sample={integer $ \varphi$ , d} (? x ! y ) , with $ \varphi$$ \ge$0 and d>0 , defines a signal y as an undersampling of an other one x. A value of y is available each dth value of x, and the occurrence of the first value of y is given by the phases ($ \varphi$ + 1 ). For $ \varphi$ = 3 and n = 4 , the process is illustrated on figure 8 .

Figure 8. Example: y := affine_sample{3,4} (x)
IMG/sample

affine_clock_relation={integer n, $ \varphi$ , d} (? x, y) defines the fact that the clock of the input signals x and y are in affine relation with n, $ \varphi$, d as parameters. To implement this process, a clock (I) greater than the clock of x and y is built such that the clock of x is synchronized with the clock of affine_sample { max(0, -$ \varphi$ ), n }(I), and the clock of y is synchronized with the clock of affine_sample { max(0, $ \varphi$ ), d }(I). For n = 5 , $ \varphi$ = 4 and d = 7 , the process is illustrated on figure 9 .

Figure 9. Example: clock_affine{5,4,7}(x,y)
IMG/clkaff

affine_unsample={integer n, $ \varphi$ } (? x, z ! y) with n>0 and $ \varphi$$ \ge$0 , defines the signal y, synchronized with the signal z, as an oversampling from the input signal x; the input signal z is used to fix the values of y when x is absent. For n = 3 , $ \varphi$ = 1 , the process is illustrated on figure 10 .

Figure 10. Example: y := clock_unsample{3,1}(x, z)
IMG/unsample

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