Heterogeneous Computing in Economics: A Simplified Approach

Abstract

This paper shows the potential of heterogeneous computing in solving dynamic equilibrium models in economics. We illustrate the power and simplicity of C++ Accelerated Massive Parallelism (C++ AMP) recently introduced by Microsoft. Starting from the same exercise as Aldrich et al. (J Econ Dyn Control 35:386–393, 2011) we document a speed gain together with a simplified programming style that naturally enables parallelization.

Appendix: The C++ AMP Programming Style

To show the similarities and differences between the standard C++, ISO (2011) and C++ AMP we provide as an example the code to obtain a vector containing the element-by-element squares of the numbers in a given input vector (a sum of the elements of the output vector would give the sum of squares, often useful in econometrics applications). Let’s take vector $Vector = \{1, 2, 3, 4, 5\}$ and calculate the corresponding squares vector $Squares = \{1, 4, 9, 16, 25\}$. Listing 3 reports the C++ and the C++ AMP code. We define three vectors: hostVector is the input vector, while hostSquares_usingCPU and hostSquares_usingGPU are the output vectors (both stored in the host’s memory), obtained using the host (CPU) and the device (GPU), respectively. Functions hostSquares and deviceSquares perform squaring on the host and the device, respectively. Finally the results are compared.

Note that from the point of view of the client code (here: function main), the interface (and, consequently, the use) of hostSquares is identical to that of deviceSquares. This illustrates the fact that C++ AMP can be used to incrementally introduce parallelism to an existing C++ code base—whenever necessary and without breaking changes.

The only differences are in the internal implementation details of both functions—while hostSquares uses standard C++ constructs, deviceSquares uses parallel constructs from the concurrency namespace (made available via the inclusion of the amp.h header).

Note that data-parallel applications are an especially good fit for GPU computing. In terms of Flynn’s taxonomy, Flynn (1972), this can be related to Single Instruction, Multiple Data (SIMD)—or, more precisely, a more general category thereof—SPMD (single program, multiple data). In terms of our example, the single program (here: multiply the values in the input vector by themselves, storing thus obtained squared values in the output vector) is applied to multiple data (elements of the input vector), where the lack of data dependence (between the distinct elements of the input vector) allows to spread the work onto multiple threads.