Sort, bubble

For the number of atoms involved, usually 25-40, the straight selection sort was noticeably faster than the tree selection sorts discussed by Knuth. (] ) The optimum sorting procedure in this case is very much an open question. The numbers of the ligands in each row were sorted by the bubble sort (17) because these numbers are usually in order before canonicaliza-tion, since they are usually in the same order in the reactant molecule at hand as they are in the already canonicalized product molecule connection table. The most efficient sort for an almost sorted list is the bubble sort. 

ACS Symposium Series American Chemical Society Washington, DC, 1977. 

Susseguth, E.H., J. Chem. Doc., 36 (1965). A more rapid procedure using a connection table with much information about each atom, is to be found in the appendix of reference 10. 

International Union of Pure and Applied Chemistry, Nomenclature of Organic Chemistry , Sections A, B C, Third Ed., Butterworths, London, 1971. 

The Wiswesser Line-Formula Chemical Notation , McGraw-Hill, New York, 1968. 

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First of all we need a predicate to sort the members of a list. A simple way to do this is to select to adjacent elements from the list and check whether they are in sequence. If they are not, then they are interchanged before reinserting them into the result list (this is the well knowm bubble sort algorithm). 

Sort calibration pairs, lowest to highest (bubble sort). 

Sorting programs written in BASIC are generally acceptably fast for short lists. One method for sorting is the Shell sort, which is actually quite efficient, certainly far better than a bubble sort, for instance. Nevertheless, there are better sorts. 

Table 4.4 Characteristics for the PODER program transformation to the bubble sort 45...

Table 5.2 Percentage of number of error from fault injection results for PODER fault tolerant technique in miniMIPS mnning the bubble sort 66...

In order to evaluate the Variables techniques, four algorithms were used a 6 x 6 matrix multiplication, a bubble sort, a tiny encryption, and a run length algorithms. We used the HPCT tool to automatically harden each apphcation according to the Variables transformation. 

Tables 4.3 and 4.4 show the original and modified program s execution time, code size, and data size for the matrix multiplication and bubble sort algorithms, respectively. They present results for the original unhardened program, as well as the version hardened with PODER and hardened with PODER combined with the Inverted Branches and Variables software-based techniques (Combined Techniques).

As one can see, PODER s execution time varies fi om 1.33, when applied to the matrix mirltiplicatiorr, to 1.61, when applied to the bubble sort, times the origirral ittrhardetred program code. One can notice that these values vary according to the mtmber of BBs in the apphcation. 

In order to evaluate HETA, two case-study applications based on a 6 x 6 matrix multiplication algorithm and a bubble sort classification algorithm were chosen to be hardened. 

As one can see in Table 5.3, from the total amorrrrt of faults injected, around 20 % affected the system arrd cairsed an error in the firral result. When protected by the OCFCM techniqrres, 100% of the faults were detected. In order to confirm these results, we injected another 140,000 faults in the PC (which is the most sensitive area of the microprocessor with respect to control flow errors) of the bubble sort application, due to its low execution time and got 100% fault detection. These results mean that the studied hardening approach was able to fully protect the microprocessor system, by detecting every transient fault injected in the case-study appUcatiorrs. Aside from these results, an average of 1 % faults with no errors per application was detected. 

To prove the effectiveness of the proposed technique, we injected another 100,000 faults in the PC for the bubble sort application. It represents aronnd 21 times the total number of clock cycles that the microprocessor takes to run the application. The result was still 100% fault detection. 

Figure 5 The data-path generated automatically for the bubble-sort...

Figure 5 shows the data-path generated automatically for a bubble-sort example [15]. The top window shows the detailed micro-scheduling of control step 25. According to the corresponding FU description, each operation is split into a set of transfers related by precedence constraints (lines in the the top window). In this case, the READ ram operation needs two micro-cycles for execution. The micro-scheduling of this control step resulted in two micro-cycles (basic clock cycles). 

Figure 6 Evaluation file for bubble-sort data-path.

A bubble sort example, and six code fragment examples. References BhaskerSO... 

The process graph model, scheduling, and a bubble sort example. 

T The Bubble Sort / void bubble(char item, int count) ... 

Implementing the bubble sort algorithm in VHDL 2" Using a RAM for Internal 70 bit register... 

Logic Synthesis Steps / read -f db bubble sort r1l.db compile... 

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