バリア同期付き非同期メモリマシンモデル

The Discrete Memory Machine(DMM)とthe Unified Memory Machine(UMM)は，GPUのシェアードメモリとグローバルメモリへのアクセスの本質をとらえた並列計算モデルである．ワープと呼ばれるスレッドの集まりごとに順にラウンドロビンに実行される．しかし，実際のGPUでは任意にワープが選ばれ実行される．本稿では，ワープが任意に実行される非同期DMMと非同期UMMを提案する．そのかわり，synchthreads命令によりバリア同期が行なえるものと仮定する．バリア同期のコストは大きいので，バリア同期の回数を評価し，その回数を最小化するようにアルゴリズムを設計すべきである．本稿では，n個の合計を求める，バリア同期の回数の少ない並列アルゴリズムを示す．The Discrete Memory Machine (DMM) and the Unified Memory Machine (UMM) are theoretical parallel computing models that capture the essence of the shared memory and the global memory of GPUs. It was assumed that warps (i.e. groups of threads) on the DMM and the UMM work synchronously in the round-robin manner. However, warps work asynchronously in the actual GPUs, in the sense that warps may be randomly (or arbitrarily) dispatched for execution. The first contribution of this paper is to introduce an asynchronous version of the DMM and the UMM, in which warps are arbitrarily dispatched. Instead, we assume that threads can execute the "syncthreads" instruction for barrier synchronization. Since the barrier synchronization operation is costly, we should evaluate and minimize the number of barrier synchronization operations performed by parallel algorithms. The second contribution of this paper is to show a parallel algorithm to compute the sum of n numbers in optimal computing time and few barrier synchronization steps.