We present an auto-tuning framework for FFTs on graphics processors (GPUs). Due to complex design of the memory and compute subsystems on GPUs, the performance of FFT kernels over the range of possible input parameters can vary widely. We generate several variants for each component of the FFT kernel that, for different cases, are likely to perform well. Our auto-tuner composes variants to generate kernels and selects the best ones. We present heuristics to prune the search space and profile only a small fraction of all possible kernels. We compose optimized kernels to improve the performance of larger FFT computations. We implement the system using the NVIDIA CUDA API and compare its performance to the state-of-the-art FFT libraries. On a range of NVIDIA GPUs and input sizes, our auto-tuned FFTs outperform the NVIDIA CUFFT 3.0 library by up to 38x and deliver up to 3x higher performance compared to a manually-tuned FFT.

We present an interactive system for synthesizing high quality, physically based audio on current video game consoles. From a recorded impact sound, we compute a modal model, which we use to synthesize variations of the sound on the fly. We show that for many sounds greater quality is obtained by using the amplitude envelopes of the extracted modes directly rather than fitting the envelopes to the standard exponential decay model. When combined with a residual, the synthesized sounds in most cases are indistinguishable from recorded clips. Compared to using multiple prerecorded clips to obtain variation, our system consumes less of the limited console memory. For sounds that are less amenable to modal synthesis, we introduce a simple filter that generates plausible variations from a single clip. Our system integrates easily with existing audio middleware and have been implemented in the Xbox360 game Crackdown II.

We present an implementation of general FFTs for graphics processing units (GPUs). Unlike most existing GPU FFT implementations, we handle both complex and real data of any size that can fit in a texture. The basic building block for our algorithms is a radix-2 Stockham formulation of the FFT for power-of-two data sizes that avoids expensive bit reversals and exploits the high GPU memory band-width efficiently. We implemented our algorithms using the DirectX9 API, which enables our routines to be used on many of the existing GPUs today. We have performed comparisons against optimized CPU-based and GPU-based FFT libraries (Intel Math Kernel Library and NVIDIA CUFFT, respectively). Our results on a NVIDIA GeForce 8800 GTX GPU indicate a significant performance improvement over the existing libraries for many input cases.

We present novel algorithms for computing discrete Fourier transforms with high performance on GPUs. We present hierarchical, mixed radix FFT algorithms for both power-of-two and non-power-of-two sizes. Our hierarchical FFT algorithms efficiently exploit shared memory on GPUs using a Stockham formulation. We reduce the memory transpose overheads in hierarchical algorithms by combining the transposes into a block-based multi-FFT algorithm. For non-power-of-two sizes, we use a combination of mixed radix FFTs of small primes and Bluestein's algorithm. We use modular arithmetic in Bluestein's algorithm to improve the accuracy. We implemented our algorithms using the NVIDIA CUDA API and compared their performance with NVIDIA's CUFFT library and an optimized CPU-implementation (Intel's MKL) on a high-end quad-core CPU. On an NVIDIA GPU, we obtained performance of up to 300 GFlops, with typical performance improvements of 2–4× over CUFFT and 8–40× improvement over MKL for large sizes.

We present a novel shadow map parameterization to reduce perspective aliasing artifacts for both point and directional light sources. We derive the aliasing error equations for both types of light sources in general position. Using these equations we compute tight bounds on the aliasing error. From these bounds we derive our shadow map parameterization, which is a simple combination of a perspective projection with a logarithmic transformation. We formulate several types of logarithmic perspective shadow maps (LogPSMs) by replacing the parameterization of existing algorithms with our own. We perform an extensive error analysis for both LogPSMs and existing algorithms. This analysis is a major contribution of this paper and is useful for gaining insight into existing techniques. We show that compared with competing algorithms, LogPSMs can produce significantly less aliasing error. Equivalently, for the same error as competing algorithms, LogPSMs can produce significant savings in both storage and bandwidth. We demonstrate the benefit of LogPSMs for several models of varying complexity.

We present new algorithms for performing fast computation of several common database operations on commodity graphics processors. Specifically, we consider operations such as conjunctive selections, aggregations, and semi-linear queries, which are essential computational components of typical database, data warehousing, and data mining applications. While graphics processing units (GPUs) have been designed for fast display of geometric primitives, we utilize the inherent pipelining and parallelism, single instruction and multiple data (SIMD) capabilities, and vector processing functionality of GPUs, for evaluating boolean predicate combinations and semi-linear queries on attributes and executing database operations efficiently. Our algorithms take into account some of the limitations of the programming model of current GPUs and perform no data rearrangements. Our algorithms have been implemented on a programmable GPU (e.g. NVIDIA's GeForce FX 5900) and applied to databases consisting of up to a million records. We have compared their performance with an optimized implementation of CPU-based algorithms. Our experiments indicate that the graphics processor available on commodity computer systems is an effective co-processor for performing database operations.

We present a new algorithm for interactive generation of hard-edged, umbral shadows in complex environments with a moving light source. Our algorithm uses a hybrid approach that combines the image quality of object-precision methods with the efficiencies of image-precision techniques. We present an algorithm for computing a compact potentially visible set (PVS) using levels-of-detail (LODs) and visibility culling. We use the PVSs computed from both the eye and the light in a novel cross-culling algorithm that identifies a reduced set of potential shadow-casters and shadow-receivers. Finally, we use a combination of shadow-polygons and shadow maps to generate shadows. We also present techniques for LOD-selection to minimize possible artifacts arising from the use of LODs. Our algorithm can generate sharp shadow edges and reduces the aliasing in pure shadow map approaches. We have implemented the algorithm on a three-PC system with NVIDIA GeForce 4 cards. We achieve 7--25 frames per second in three complex environments composed of millions of triangles.

We present a technique to perform occlusion culling for hierarchical terrains at run-time. The algorithm is simple to implement and requires minimal pre-processing and additional storage, yet leads to 2-4 times improvement in framerate for views with high degrees of occlusion. Our method is based on the well-known occlusion horizon algorithm. We show how to adapt the algorithm for use with hierarchical terrains. The occlusion horizon is constructed as the terrain is traversed in an approximate front to back ordering. Regions of the terrain are compared to the horizon to determine when they are completely occluded from the viewpoint. Culling these regions leads to significant savings in rendering.