An approach to the application of shift-and-add algorithms on engineering and industrial processes

Different kinds of algorithms can be chosen so as to compute elementary functions. Among all of them, it is worthwhile mentioning the shift-and-add algorithms due to the fact that they have been specifically designed to be very simple and to save computer resources. In fact, almost the only operations usually involved with these methods are additions and shifts, which can be easily and efficiently performed by a digital processor. Shift-and-add algorithms allow fairly good precision with low cost iterations. The most famous algorithm belonging to this type is CORDIC. CORDIC has the capability of approximating a wide variety of functions with only the help of a slight change in their iterations. In this paper, we will analyze the requirements of some engineering and industrial problems in terms of type of operands and functions to approximate. Then, we will propose the application of shift-and-add algorithms based on CORDIC to these problems. We will make a comparison between the different methods applied in terms of the precision of the results and the number of iterations required.

Drought and grazing combined: Contrasting shifts in plant interactions at species pair and community level

The combined effects of drought stress and grazing pressure on shaping plant–plant interactions are still poorly understood, while this combination is common in arid ecosystems. In this study we assessed the relative effect of grazing pressure and slope aspect (drought stress) on vegetation cover and soil functioning in semi-arid Mediterranean grassland–shrublands in southeastern Spain. Moreover, we linked these two stress factors to plant co-occurrence patterns at species-pair and community levels, by performing C-score analyses. Vegetation cover and soil functioning decreased with higher grazing pressure and more south-facing (drier) slopes. At the community level, plants at south-facing slopes were negatively associated at no grazing but positively associated at low grazing pressure and randomly associated at high grazing pressure. At north-facing slopes, grazing did not result in a shift in the direction of the association. In contrast, analysis of pairwise species co-occurrence patterns showed that the dominant species Stipa tenacissima and Anthyllis cytisoides shifted from excluding each other to co-occurring with increasing grazing pressure at north-facing slopes. Our findings highlight that for improved understanding of plant interactions along stress gradients, interactions between species pairs and interactions at the community level should be assessed, as these may reveal contrasting results.