Floating-point

The computer storage requirements (floating point machine words) for the Icibeled common storage blocks and, approximately, for the principal computer subroutines are given in Tcible J-1. 

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. 

Basically, two different methods arc commonly used for representing a chemical struchiive in 3D space. Both methods utilize different coordinate systems to describe the spatial arrangement of the atoms of a molecule under con.sidcration. The most common way is to choose a Cartesian coordinate system, i.e., to code the X-, y-, and z-coordinates of each atom, usually as floating point numbers, For each atom the Cartesian coordinates can be listed in a single row. giving consecutively the X-, )> , and z-valnc.s. Figure 2-90 illustrates this method for methane. 

A lustrous metal has the heat capacities as a function of temperature shown in Table 1-4 where the integers are temperatures and the floating point numbers (numbers with decimal points) are heat capacities. Print the curve of Cp vs. T and Cp/T vs. T and determine the entropy of the metal at 298 K assuming no phase changes over the interval [0, 298]. Use as many of the methods described above as feasible. If you do not have a plotting program, draw the curves by hand. Scan a table of standard entropy values and decide what the metal might he. 

The format markers in Eile 4-lb are at intervals of five spaces each. Thus the entire file might be thought of as a 10 x 67 matrix with row 1 containing the integers 6 and 4 in columns 65 and 67 and zeros elsewhere. (In EORTRAN, a blank is read as a zero.) Row 5 has the floating point number 2. in columns 4 and 5. Both the 2 and the. (decimal point) occupy a column. Row 5 column 35 contains the integer 2 and so on. 

A common acronym is MFLOPS, millions of floating-point operations per second. Because most scientific computations are limited by the speed at which floating point operations can be performed, this is a common measure of peak computing speed. Supercomputers of 1991 offered peak speeds of 1000 MFLOPS (1 GFLOP) and higher. 

A pipelined floating-point multiply unit might accomplish a floating-point multiply by performing four independent suboperations, labeled a, b, c, and d, on the operands. The suboperations can be envisioned as the four workers on a four-person assembly line. The floating-point multiply pipeline could accept a new set of operands every clock cycle. The pipeline occupancy of this code fragment would look like... 

On a vector computer having vector registers that hold 64 floating-point numbers, this loop would be processed 64 elements at a time. The first 64 elements of Y would be fetched from memory and stored in a vector register. Each iteration of the loop is independent of the previous iteration, so this loop can be fliUy pipelined, with successive iterations started every clock cycle. Once the pipeline is filled, the result, X, will be produced one element per clock cycle and will be stored in another vector register. The results in the vector register will then be stored back into main memory or used as input to a subsequent vector operation. 

Where available, the SPEC integer (int) rating and the SPEC floating-point (fp) rating are reported separately. 

The norm is useful when doing numerical calculations. If the computer s floating-point precision is 10" , then K = 10 indicates an ill-conditioned matrix. If the floating-point precision is I0" (double precision), then a matrix with K = I0 may be ill-conditioned. Two other measures are useful and are more easily calculated ... 

The new line illustrates an important point about numeric values within Z-matrices. Since they correspond to floating point quantities, they must include a decimal point, as in the value above. This is true even for a value of 0. 

Another obvious advantage that the LG method typically enjoys over floating-point methods is one of programming efficiency. Because LG dynamics are a natural transcription of the kinetic processes taking place on the micro-lattice, the actual program code is generally concise and straightforward, and often amounts to little more than a few dozen lines of FORTRAN. 

Finally, we should mention that the stability of a running program itself is never really an issue for LG simulations, unlike that for floating-point methods for which certain (sometimes unforeseen) conditions can lead to serious software crashes. 

Floating point, 276 Fluorine, ion, electronic correlation energy, 240 London energy, 78 molecules, intramolecular London energies, 78... 

There are two standard schemes for the machine representation of a number, called fixed-point and floating-point. The older electronic machines used only fixed-point. In its most usual form, every number was assumed to satisfy... 

The usual floating-point representation permitted the storage also of an exponent, thus allowing a representation... 

Flehinger, Betty /., 284 Floating-point representation of numbers, 50... 

At best the ST-100 is capable of 100 million floating point operations per second (MFLOPS) however for reasonably large macro-... 

Arc-length continuation, steady states of a model premixed laminar flame, 410 Architecture, between parallel machines, 348 Arithmetic control processor, ST-100, 125 Arithmetic floating point operations,... 

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