Computers Floating Point System

In order to gauge the results of the design exercise, both in terms of system performance and cost-effectiveness it is necessary to benchmark the MVP-9500 against other machines for which the benchmark figures are available Fortunately Floating Point systems have published details of a benchmark used to compare the AP120B with mini- and mainframe computer systems (6). 

We thank Dale L. Bodian and Brian K. Shoichet for their help. We thank the Computer Graphics Laboratory (supported by National Institutes of Health RR-01081) for use of their facilities for parts of this project. Partial support was received from the National Institutes of Health GM-31497 (IDK) GM-39552 (IDK), GM-07175 (GLS), and GM-29072 to Peter Kollman. The Floating Point Systems 264 array processor was purchased with grant support from National Science Foundation DMB-84-13762 and National Institutes of Health RR-02441. Assistance from the Macromolecular Workbench supported by the Defense Advanced Research Projects Agency under contract N00014-86-K0757 administered by the Office of Naval Research is also appreciated. 

The appearance of numerous new computer vendors, including Floating Point Systems, Convex, Alliant, and Multiflow, meant that support and reliability of the software became a more significant issue. The public domain approach to distribution of the software did not provide a mechanism to ensure the correctness and reliability of versions for different machines, while the increasing variety of users made such validation more important than ever. Distribution through a university did not prove to be a viable mechanism for managing the relationships with the hardware vendors. 

The program storage requirements will depend somewhat on the computer and FORTRAN compiler involved. The execution times can be corrected approximately to those for other computer systems by use of factors based upon bench-mark programs representative of floating point manipulations. For example, execution times on a CDC 6600 would be less by a factor of roughly 4 than those given in the tcible and on a CDC 7600 less by a factor of roughly 24. 

Fig. 4.4. Comparison of the computing effort, expressed in thousands of floating point operations (Aflop), required to factor the Jacobian matrix for a 20-component system (Nc = 20) during a Newton-Raphson iteration. For a technique that carries a nonlinear variable for each chemical component and each mineral in the system (top line), the computing effort increases as the number of minerals increases. For the reduced basis method (bottom line), however, less computing effort is required as the number of minerals increases.

Magnitude is the final limit. It s the culprit in OVERFLOW errors. The operating system stores floating-point numbers in five bytes. What happens when all the bytes fill up The number is a little beyond 10 to the thirty-eighth power, a one followed by 38 zeros the computer cannot count any higher. 

If one has a computer of moderate capability such as a DEC 20/40 which can perform a floating point multiplication in 2.5 microseconds, then such a calculation should take approximately 241,718 seconds or 67 hours. Over the past several years, numerous improvements in the algorithms used in systematic conformational search have been developed (21) leading to a reduction on the order of (M + 1) 2M. A prototype system on a DEC 20/40... 

Time levels of graphics workstation have come into use over the last few years. The low-end systems typically have 2 to 5 MIPS of processor performance, numeric computing performance of 0.25 to 1 MFLOPS, and a drawing performance of 200,000 v/s and 2,000 to 5,000 p/s. Many of these systems were developed around the Motorola 68020 processor with a floating point processor. Since they are created from off-the-shelf components, they are relatively inexpensive ( 10,000 to 30,000). They are adequate when used for small molecule (250 atoms or less) calculations and interactive display. 

Burks, Goldstine, and von Neumann first identified the principal components of the general-purpose computer as the arithmetic, memory, control, and input-output organs, and then proceeded to formulate the structure and essential characteristics of each unit for the IAS machine. Alternatives were considered and the rationale behind the choice selected presented. Adoption of the binary, rather than decimal, number system was justified by its simplicity and speed in elementary arithmetic operations, its applicability to logical instructions, and the inherent binary nature of electronie components. Built-in floating-point hardware was ruled out, for the prototype at least, as a waste of the critical memory resource, and because of the increased complexity of the circuitry consideration was given to software implementation of such a facility. 

The use of classical potentials for simulations of chemical and biochemical systems with molecular d3mamics has been a field of intense research. Currently, it is possible to simulate systems with millions of atoms and millisecond time scales (Schulten et al., 2008 Shaw et al., 2010). With exa-scale computing, i.e., 10 floating point operations per second (FLOPs), on the horizon it is necessary to evaluate the performance of the current potentials. Indeed, longtime biomolecular simulations have revealed some issues already. 

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