Yafeng Yin, Lei Zhou, Hong Man 07/21/2010 CUDA Library and Demo Yafeng Yin, Lei Zhou, Hong Man 07/21/2010

Outline Basic CUDA computation library GPULib, CUBLAS, CUFFT Advanced CUDA computation library CULA /MAGMA , VSIPL CUDA FIR Demo(UMD) Discuss and future work

Basic lib - GPULib GPULib provides a library of mathematical functions addition, subtraction, multiplication, and division, as well as unary functions, including sin(), cos(), gamma(), and exp(), interpolation, array reshaping, array slicing, and reduction operations

Basic lib - CUBLAS BLAS-- Basic Linear Algebra Subprograms CUBLAS Provide a set of functions for basic vector and matrix operations, such as matrix‐vector copy, sort, dot product, Euclidean norm etc Real data Level 1 (vector-vector O(N) ) Level 2 (matrix-vector O(N2) ) Level 3 (matrix-matrix O(N3) ) Complex data Level 1

CUBLAS-Level 2 function cublasSgbmv() y = alpha * op(A) * x + beta * y cublasSgemv() cublasSger() A = alpha * x * yT + A cublasSsbmv() y = alpha * A * x + beta * y , cublasSspmv() y = alpha * A * x + beta * y cublasSspr() A = alpha * x * xT + A cublasSspr2() A = alpha * x * yT + alpha * y * xT + A , cublasSsymv() cublasSsyr() cublasSsyr2() cublasStbmv() x = op(A) * x cublasStbsv() op(A) * x = b , output x

Basic lib - CUFFT CUFFT is the CUDA FFT library Provides a simple interface for computing parallel FFT on an NVIDIA GPU Allows users to leverage the floating-point power and parallelism of the GPU without having to develop a GPU-based FFT implementation cufftPlan1d() ,cufftPlan2d() ,cufftPlan3d() Creates a 1D,2D or 3D FFT plan configuration for a specified signal size

Advanced lib – CULA and MAGMA CULA: GPU Accelerated Linear Algebra provide LAPACK (Linear Algebra PACKage) function on CUDA GPUs MAGMA: Matrix Algebra on GPU and Multicore Architectures develop a dense linear algebra library similar to LAPACK but for heterogeneous/hybrid architectures and "Multicore+GPU" systems

Advanced lib -CULA function Linear Equation Routines Solves a general system of linear equations AX=B. Orthogonal Factorizations LQ ,RQ factorization Least Squares Routines Symmetric and non- Symmetric Eigenvalue Routines Singular Value Decomposition (SVD) Routines

Advanced lib - MAGMA LAPACK on CUDA GPUs LU, QR, and Cholesky factorizations in both real and complex arithmetic (single and double) Linear solvers based on LU, QR, and Cholesky in real arithmetic (single and double) Mixed-precision iterative refinement solvers based on LU, QR, and Cholesky in real arithmetic Reduction to upper Hessenberg form in real arithmetic (single and double) MAGMA BLAS in real arithmetic (single and double),

Advanced lib -VSIPL VSIPL: Vector Image Signal Processing Library Generalized matrix product Fast FIR filtering Correlation Fast Fourier Transform QR decomposition Random number generation    Elementwise arithmetic, logical, and comparison operators, linear algebra procedures

CUDA library Summary Basic vector or matrix computation GPULib, CUBLAS, CUFFT vector or matrix: addition, subtraction, multiplication, and division sin(), cos(), sort, dot product, Libraries can be used for Signal Processing CULA /MAGMA , VSIPL LU, QR, and Cholesky factorizations SVD decompostion

CUDA Demo (FIR) GPU: NVIDIA GeForce 8600 GT CPU: Intel Duo CPU 2.33G Software: Visual Studio 2005

CUDA Demo (FIR) Output NO GPU Run Memory Time(msec) Total Time CPU +GPU CPU Only 1000 0.312121 0.166641 0.482184 0.391251 10000 0.667264 0.284254 0.955568 4.646471 100000 4.210870 1.489784 5.704915 43.831200 1000000 39.460812 5.597150 45.062572 421.615448 10000000 391.816345 48.080204 439.901794 4310.153320

CUDA Demo (FIR)

Discuss and future work how to connect CUDA to the SSP re-hosting demo how to change the sequential executed codes in signal processing system to CUDA codes how to transfer the XML codes to CUDA codes to generate the CUDA input.

Reference CUDA Zone http://www.nvidia.com/object/cuda_home_new.html http://en.wikipedia.org/wiki/CUDA