58 CHAPTER 3 Power Estimation in FPGAs 3.5 A COMPLETE ANALYTICAL FPGA POWER MODEL UNDER SPATIAL CORRELATION Hassan et al proposed a complete analytical power model for FPGAs that accounts for spatial correlation between the circuit signals [90]. In this section, the details of this power model will be presented. 3.5.1 Spatial Correlation and Signal Probability Calculations The signal probability can be computed at the output of each logic block through simple probabilistic calculations to evaluate the probability of the output of the logic block being high. In all the available probabilistic power mod- els for FPGAs, the inputs to any specific logic block are assumed independent, the spatial independence assump- tion. This assumption is made to simplify the probability calculation. However, the spatial independence assump- tion reduces the accuracy of any analytical power model by overestimating the signal probabilities, as will be explained later. As an example, for the small circuit shown in Fig. 3.1, assuming that the probability of A = 1 is 0.5, dynamic power estimators operating under the spatial indepen- dence assumption will calculate the probability of B being high as P(B = 1) = P(A = 1) × P(A = 1) = 0.5 × 0.5 = 0.25, (3.16) thus resulting in a transition probability of 0.375 (2×0.25× 0.75), according to Eq. (3.6). However, by clear inspection of Fig. 3.1, this circuit suffers from a reconvergent path. A B FIGURE 3.1 A circuit that exhibits spatial correlation through reconvergent paths.