关键词: 浮点运算, 精度优化, 强化学习, 经验库, 相似度匹配

Abstract: With the rapid development of numerical computing,precision optimization of floating-point programs has become a key issue in improving computational reliability.While traditional approaches,such as mixed-precision optimization,approximate rounding error correction,error detection and repair,and expression optimization rewriting,have achieved some progress,they still face limitations such as a large search space,low optimization efficiency,and reliance on expert experience.To address these issues,this paper proposes a reinforcement learning-based adaptive optimization method for floating-point expressions and implements an expression optimization tool,ExprRL.By combining reinforcement learning with a dynamic precision optimization experience library,ExprRL achieves efficient and adaptive precision optimization.ExprRL uses a Tree-LSTM model to compute embedding vectors of the symbolic,structural,and semantic features of expressions.It then uses cosine similarity to retrieve and match optimization strategies in the experience library to accelerate the optimization process.If a match fails,a reinforcement learning module is initiated,modeling the expression optimization problem as a Markov decision process.A Q-learning algorithm is used to explore the optimal rewriting action sequence and dynamically updates it to the experience library.Experiment selects 31 expressions from the FPBench standard dataset as the test set.Experimental results show that after ExprRL optimization,the average ulp error is reduced by 41.42%,and the maximum ulp error is reduced by 46.92%,which is better than traditional precision optimization tools Herbie and exprAuto.

Key words: Floating-point arithmetic, Precision optimization, Reinforcement learning, Experience repository, Similarity matching