4. GRAPE and GRAPE-DR

We describe the architecture and performance of GRAPE-DR (Greatly Reduced Array of Processor Elements with Data Reduction). It operates as an accelerator attached to general-purpose PCs or x86-based servers. The processor chip of a GRAPE-DR board have 512 cores operating at the clock frequency of 400 MHz. The peak speed of a processor chip is 410 Gflops (single precision) or 205 Gflops (double precision). A GRAPE-DR board consists of four GRAPE-DR chips, each with its own local memory of 256 MB. Thus, a GRAPE-DR board has the theoretical peak speed of 1.64 SP and 0.82 DP Tflops. Its power consumption is around 200 W. The application area of GRAPE-DR covers particle-based simulations such as astrophysical many-body simulations and molecular-dynamics simulations, quantum chemistry calculations, various applications which requires dense matrix operations, and many other compute-intensive applications. The architecture of GRAPE-DR is in many ways similar to those of modern GPUs, since the evolutionary tracks are rather similar. GPUs have evolved from specialized hardwired logic for specific operations to a more general-purpose computing engine, in order to meet the perform complex shading and other operations. The predecessor of GRAPE-DR is GRAPE (GRAvity PipE), which is a specialized pipeline processor for gravitational \(N\)-body simulations. We have changed the architecture to extend the range of applications. There are two main differences between GRAPE-DR and GPGPU. One is the transistor and power efficiency. With 90 nm technology and 400M transistors, we have integrated 512 processor cores and achieved the speed of 400 Gflops at 400 MHz clock and 50 W. A Fermi processor from NVIDIA integrates 448 processors with 3B transistors and achieved the speed of 1.03 Tflops at 1.15 GHz and 247 W. Thus, Fermi achieved 2.5 times higher speed compared to GRAPE-DR, with 2.9 times higher clock, 8 times more transistors, and 5 times more power consumption. The other is the external memory bandwidth. GPUs typically have the memory bandwidth of around 100 GB/s, while our GRAPE-DR card, with 4 chips, have only 16 GB/s. Thus, the range of application is somewhat limited, but for suitable applications, the performance and performance per watt of GRAPE-DR is quite good. The single-card performance of HPL benchmark is 480 Gflops for matrix size of t 48 k, and for 81 cards 37 Tflops.