Connection Machine Computer Research Articles

Data parallel computers and the Forall statement

The array constructs of Fortran 90 (formerly called Fortran 8x) map naturally onto SIMD architectures, such as that of the Connection Machine computer system, that support a data parallel programming style. The Forall statement, an extension to Fortran 90 allowing for the expression of simultaneous execution of certain do loop bodies, enhances this natural fit. A Fortran 90 compiler for data parallel machines is naturally extended to handle the Forall statement. We describe the data structures and algorithms used to effect this extension and present some examples of source code fragments and the target operations generated for them.

Massively parallel three-dimensional Euler/Navier-Stokes method

A method for solving the three-dimensional Euler and Navier-Stokes equations using the massively parallel Connection Machine computer is described. The program uses a finite-volume, Runge-Kutta time-marching scheme and can accept structured or unstructured grids. The computer program is written entirely in * LISP. Significant computational speedups were obtained over similar codes developed for vector supercomputers.

A quantum Monte Carlo calculation of the ground state energy of the hydrogen molecule

We have calculated the ground state energy of the hydrogen molecule using the quantum Monte Carlo (QMC) method of solving the Schrödinger equation, without the use of the Born–Oppenheimer or any other adiabatic approximations. The wave function sampling was carried out in the full 12-dimensional configuration space of the four particles (two electrons and two protons). Two different methods were employed: the diffusion quantum Monte Carlo (DQMC) method and the Green’s function quantum Monte Carlo (GFQMC) method. This computation is very demanding because the configurations must be evolved on the time scale of the electronic motion, whereas the finite nuclear mass effects are resolved accurately only after equilibration on the much slower time scale of the nuclear motion. Thus, a very large number of iterations is required. The calculations were performed on the CM-2 Connection Machine computer, a massively parallel supercomputer. The enormous speedup afforded by the massive parallelism allowed us to complete the computation in a reasonable amount of time. The total energy from the DQMC calculations is −1.163 97±0.000 05 a.u. A more accurate result was obtained from the GFQMC calculations of −1.164 024±0.000 009 a.u. Expressed as a dissociation energy, the GFQMC result is 36 117.9±2.0 cm−1, including the corrections for relativistic and radiative effects. This result is in close agreement with accurate nonadiabatic-relativistic dissociation energies from variational calculations (corrected for radiative effects) in the range of 36 117.9–36 118.1 cm−1 and with the best experimentally determined dissociation energy of McCormack and Eyler 36 118.1±0.2 cm−1.

Compiling collection-oriented languages onto massively parallel computers

This paper introduces techniques for compiling the nested parallelism of collection-oriented languages onto existing parallel hardware. Programmers of parallel machines encounter nested parallelism whenever they write a routine that performs parallel operations, and then want to call that routine itself in parallel. This occurs naturally in many applications. Most parallel systems, however, do not permit the expression of nested parallelism. This forces the programmer to exploit only one level of parallelism or to implement nested parallelism themselves. Both of these alternatives tend to produce code that is harder to maintain and less modular than code described at a higher level with nested parallel constructs. Not permitting the expression of nested parallelism is analogous to not permitting nested loops in serial languages. This paper describes issues and techniques for taking high-level descriptions of parallelism in the form of operations on nested collections and automatically translating them into flat, single-level parallelism. A compiler that translates a subset of a collection-oriented language, Paralation Lisp, into the instruction set of a flat virtual machine is presented. The instructions of the virtual machine are simple instructions on vectors of atomic values, and can be implemented on a broad class of target architectures, including vector machines, single-instruction parallel machines, and multiple-instruction parallel machines. We have implemented the instructions on the Connection Machine computer (CM-2), a massively parallel, single-instruction computer. As an illustration of the compiler techniques, the paper presents a quicksort example. The example has been tested on the CM-2. The speed of the compiled sort is only a factor of 3 slower than that of the fastest CM-2 sort.

Data optimization: Allocation of arrays to reduce communication on SIMD machines

An optimizing compiler for a data parallel programming language can significantly improve program performance on a massively parallel computing system by incorporating new strategies for allocating array elements to processors. We discuss techniques for automatic layout of arrays in a compiler targeted to SIMD architectures, such as the Connection Machine computer system. Our primary goal is to minimize the cost of moving data among processors. We also attempt to minimize memory usage. Improved array layout may allow more specialized communication operations with lower cost. We discuss the algorithms to effect such improvement and present some typical examples of code fragments that can be improved significantly with respect to memory consumption and by orders of magnitude with respect to execution time.

Computational fluid dynamics on the connection machine

This paper describes a method for solving the three-dimensional Euler and Navier-Stokes equations using the massively parallel Connection Machine computer. The program uses a finite volume Runge-Kutta time marching scheme and can accept structured or unstructured grids. The computer program was written entirely in *Lisp.

Three conformers in a crystal of N-Ac-L-Leu-L-Tyr-OMe.

C18H26N2O5, three independent molecules with different conformations, Mr = 350.4, orthorhombic, P2(1)2(1)2(1), a = 16.077 (10), b = 28.935 (18), c = 12.597 (6) A, V = 5860.0 A3, Z = 12, Dx = 1.191 g cm-3, lambda(Cu K alpha) = 1.54178 A, F(000) = 2256, room temperature, final R = 4.9% for 4596 data with [F omicron] greater than 3 sigma and 5.4% for all 4977 measured data. The three independent molecules have different conformations for the backbones and the side-chains, although each molecule is relatively flat and has an approximate H shape. The backbone in one of the conformations has phi, psi angles near those for a beta-turn. There is extensive intermolecular hydrogen bonding, but there are no intramolecular hydrogen bonds. The 75-atom structure was solved with the aid of the Connection Machine computer, a parallel processor for which the symbolic addition procedure was programmed.

Compiling Fortran 8x array features for the connection machine computer system

The Connection Machine® computer system supports a data parallel programming style, making it a natural target architecture for Fortran 8x array constructs. The Connection Machine Fortran compiler generates VAX code that performs scalar operations and directs the Connection Machine to perform array operations. The Connection Machine virtual processor mechanism supports elemental operations on very large arrays. Most array operators and intrinsic functions map into single instructions or short instruction sequences. Noncontiguous array sections, array-valued subscripts, and parallel constructs such as WHERE and FORALL are also readily accommodated on the Connection Machine. In addition to such customary optimizations as common subexpression elimination, the CM Fortran compiler minimizes data motion for aligning array operations, minimizes transfers between the Connection Machine and the VAX and minimizes context switching for masked computations.