(1) Transformer CheckpointingCalculatePI { (2) Within(Function CalculatePI){ (3) Statement stmt = getStatement("pi = pi + f(x)"); (4) StartCheckpointing(After, stmt){ (5) CKPSaveReal(pi); (7) CKPFrequencey(5); (8) CKPType(Sequential); (9) } (10) StartInitializating(Before, "do i=1, n"){ (11) CKPReadReal(pi); (13) } (14) } (15) } ALGORITHM 15: The generated

Fortran program with checkpointing code.

For [I.sub.2] factor examines showed that graph of Yang book (fig.6) offer the best answer but none of relative integrals have accordance with

FORTRAN program.

The bivariate statistical method involved log-ratio transformation procedures and a computer

FORTRAN program developed by Weltje (1993) for construction of 90, 95, and 99% confidence regions.

A

FORTRAN program has been developed to numerically compute the Green's tensor for a layer on a half-space with three different bonding conditions between the layer and the half-space.

A

FORTRAN program was used to enumerate completely the makespans of 500 different problems.

Translation is accomplished through a

FORTRAN program that runs on an IBM 4300 series or 308X series mainframe operating under VM or MVS, and is executable from PCs linked to the mainframe.

The "Best First" order adds one program at a time to the training set, starting with the program that achieved the lowest average miss rate in Figures 4 and 5 (e.g., the C program flex and the

Fortran program ora) and ending with the program that had the highest miss rate.

The

Fortran program in file gngrf.f is used to randomly generate the test problems used to test gmis in the computational results presented in Section 4.

Thus, faculty and students set to work on mathematical and working models, as well as on a

FORTRAN program to analyze their work.

"True" supercomputers use the Cray design formula: ECL circuits and dense packaging technology to reduce size, allow the fastest clock; one or more pipelined vector units with each processor provide peak processing for a

Fortran program; and multiple vector processors communicate via a switch to a common, shared memory to handle large workloads and parallel processing.

An alternative to Mathcad in producing nonlinear equations is to write a

FORTRAN program. Hugo estimated that writing and solving the fracture mechanics equations in FORTRAN would have required approximately 500 lines of code.

The

Fortran program, Lsopt, assists the user in employing this design approach by solving for the optimum source impedance, the corresponding load impedance necessary for the conjugate input impedance match, and the resultant transducer gain over all frequencies and user-specified values of [L.sub.s].

It formulates the equations of motion symbolically and then writes a

Fortran program called a simulation code to solve them.

(OpenCL is based on the C programming language.) Currently C, C++ and

Fortran programs can be annotated with OpenACC pragmas, but there is no reason why other languages such as Java can not also benefit from pragma-based annotation.

Many report that their use of NAG Fortran Builder for maintaining standards, debugging and verification of their

Fortran programs is invaluable, even if they also use another compiler."