Flop-cost

A newer measure of an algorithm s theoretical performance is its Mop-Cost which is defined exactly as the Flop-cost except that Memory Operations (Mops) are counted instead of Floating-Point Operations (Flops). A Mop is a load from, or a store to, fast memory. There are sound theoretical reasons why Mops should be a better indicator of practical performance than Flops, especially on recent computers employing vector or RISC architectures, and this has been discussed in detail by Frisch et al. [62] to cut a long story short, the Mops measure is useful because, on modern computers and in contrast to older ones, memory traffic generally presents a tighter bottleneck than floating-point arithmetic. 

The two versions achieve the same results but the second will run faster on many computers. Both versions have Flop-costs of 3N but their Mop-costs are different, 7N and 6N, respectively. This is because, in the second version, A(I) does not need to be loaded from fast memory since, having just been produced, it will already reside in a register. This example is certainly a very simplistic one but it serves to illustrate the principle of Mop reduction. 

It is clear from (41) that the computational effort to construct the desired class of (ablcd) integrals will rise with the fourth power of K. In fact, it is easily shown [66] that the total Flop-cost of forming the class can always be expressed as... 

Table I Flop-cost parameters for generating integral classes ...

Both HS and LRL proposed that the OS RR be used only to generate [mOlOO] b (mOIOO)(°) and that (74) then be used to form [mOInO] from these. It seems probable from the estimates made by both groups (they disagree somewhat) of the Flop-cost of this new algorithm that it constitutes a marginal improvement over the HGP algorithm. 

How much will the pilot cost, and how does that compare to the cost of launching an innovation that flops ... 

Even the latest ASCI (Advanced Strategic Computing Initiative) computer developed by the U.S. Department of Defense, costing 200 million, occupying 21,000 square feet, and mnning at 30 X 1012 flops, would take an hour to solve this problem. 

The last factor in (75), which scales it according to the angular momentum (a + b) of the shell-pair, is termed the principal scaling and is included only if the MD-PRISM is used. For reasons which will become clearer below, its presence reduces the Flop- and Mop-costs of the algorithm. 

Call MkCost to compute PRISM step-costs in Flops and Mops... 

If the new technology (i.e., the electrie vehiele) is aeeepted by the public, the factory will increase production, and the cost of the investment in the fixed plant will be spread over a great many cars. If the electric vehicle is a flop in the market, the investment costs will be spread over many fewer cars, and per unit costs will be higher. The number of cars produced doesn t affect the aggregate spending on facilities but it does affect the amount of spending per car. 

The Chebyshev filtering in Step 3 costs 0(s N/p) flops. The discretized Hamiltonian is sparse and each matrix-vector product on one processor costs 0 N/p) flops. Step 3 requires m s matrix-vector products, at a total cost of 0(s m N/ p) where the degree w of the polynomial is small (typically between 8 and 20). 

The ortho-normalization in Step 4 costs 0(s N/p) flops. There are additional communication costs because of the global reductions. 

Due to the quite costly Step 2 ( 15n flops), this algorithm is essentially designed for moderate size chemistry up to n 100 species, say. In the above form, the algorithm has been used for all three subsequent examples. For the user prescribed accuracy we always set TOL = 10 . ... 

The algorithm for Gaussian elimination contains three nested loops that each run over all or part of the set of indices 1, 2, A/. Therefore, the total number of FLOPs is proportional to (the exact number, 2N /3 is computed in the supplemental material). If we increase TV by a factor of 10, the amount of work required increases by a factor of 10 = 1000. We see here the major problem with Gaussian elimination it can become very costly for large systems ... 

PS-SFC appears to be a complementary technique to preparative HPLC. Actually, it can be presented as one of the multiple alternatives to HPLC that aims at reducing the cost and solvent consumption while maintaining the efficiency of separation Simulated Moving Bed, Flip-Flop, Back-Flush, PS-SFC, Multi-Dimensional Chromatography, etc. On this basis, the potential applications of PS-SFC can be evaluat-... 

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