Julien Demouth is a member of the Developer Technology team at NVIDIA where he works on accelerating applications on GPUs. He holds a Ph.D in Computational Geometry from INRIA / Université Nancy 2 in France.
Recently, STAC Research published astonishing performance results for the STAC-A2 benchmarks on an NVIDIA Tesla K80. In short, a single Tesla K80 driven by two CPU cores outperforms all previously audited systems in terms of pure performance and power efficiency.
We obtained these new results after several optimizations of our previously audited code. First of all, a large fraction of the computations are now avoided due to a better factorization of the underlying mathematical process. Secondly, we tuned some of the kernel parameters to take advantage of the larger register file of the Tesla K80. Finally, we were able to significantly reduce the latency in one of the main loops of the benchmark. Let’s take a look at these optimizations. Continue reading →
When I work on the optimization of CUDA kernels, I sometimes see a discrepancy between Achieved andTheoretical Occupancies. The Theoretical Occupancy is the ratio between the number of threads which may run on each multiprocessor (SM) and the maximum number of executable threads per SM (2048 on the Kepler architecture). This value is estimated from the size of the blocks and the amount of resources (registers and shared memory) used by those blocks for a particular GPU and is computed without running the kernel on the GPU. The Achieved Occupancy, on the other hand, is measured from the execution of the kernel (as the number of active warps divided by the number of active cycles compared to the maximum number of executable warps).
Recently, while working on a kernel for a finance benchmark, I could see an Achieved Occupancy of 41.52% whereas the Theoretical Occupancy was 50%. In NVIDIA Nsight Visual Studio Edition, the Instruction per Clock (IPC) showed a lot of load imbalance between the different SMs with respect to the number of executed instructions by the kernel (see the left graph in the figure below).
In finance, an option (or derivative) is the common name for a contract that, under certain conditions, gives a firm the right or obligation to receive or supply certain assets or cash flows. A financial firm uses options to hedge risks when it operates in the markets. It is critical for a firm to be able to accurately price those instruments and understand their dynamics to evaluate its positions, balance its portfolio and limit exposure to potential threats. The calculation of risk and prices for options is a computationally intensive task for which GPUs have a lot to offer. This post describes an efficient implementation of American Option Pricing using Monte Carlo Simulation with a GPU-optimized implementation of the Longstaff Schwarz algorithm.
NVIDIA recently partnered with IBM and STAC to implement the STAC-A2™ benchmark on two NVIDIA Tesla K20X GPUs. It is the first system that was able to calculate the risk and pricing of this particular complex option in less than a second. A system with two Tesla K20X GPUs is up to 6 times faster than a state-of-the-art configuration using only CPUs. Even more interestingly, adding one or two Tesla K20X GPUs to a system offers speedups of slightly more than 5x and 9x, respectively, compared to the same system without GPUs. Continue reading →