Amazon

Mixed Precision Block QR Implementation on GPU

Amazon Lab126 is an American research and development and computer hardware company owned by Amazon.com. It was founded in 2004 by Gregg Zehr, previously Vice President of Hardware Engineering at Palm, and is based in Sunnyvale, California. QR factorization is extremely powerful way to factorize a matrix into orthogoal matrix Q and upper triangle matrix R. One powerful use of it is in solving non linear systems. The drawback of this algorithm is compute complexity and thereby making it difficult to use for real time applications like robotics. This student team attempted to implement a fast version of this algorithm called mixed precision QR. In this implementation all matrix multiplication are performed in half precision and remaining operations like norm calculation and scalar calculations in single precision. Implementation used the GPU's half precision data type for the matrix multiplications and single precision for remaining operations. This student team worked to create mixed precision implementation of Tiled QR algorithms in Cpp running on x86 and mixed precision implementation of above on CUDA running on Nvidia GPU. This student team also sought to establish performance and accuracy results of the above mentioned implementations.