As parallel workloads grow in complexity, managing fine-grained data dependencies becomes a critical challenge. Futures offer a promising model for handling these dependencies, particularly in irregular algorithms, but they also come with the restriction of value-immutability. This immutability limits the ability to perform in-place memory updates, a necessity for high-performance linear algebra where memory recycling is paramount. In this paper, we address these limitations by introducing a new construct, await_delete, which extends traditional future semantics to allow safe value reuse once consumers are finished. Building on this extension, we present a novel future-based algorithm for the block-wise inversion of dense, symmetric matrices, motivated by a recent algorithm for finding conservation laws of dynamical systems. We implement our approach in an extended version of Taskflow and evaluate it through strong-scaling experiments. Our results demonstrate that while futures incur significant overhead on smaller problem sizes, they achieve nearly linear scaling on large matrices. We analyze the amortization threshold and show that futures are a viable high-performance tool for large-scale linear algebra.

翻译：随着并行工作负载复杂性的增加，细粒度数据依赖管理成为关键挑战。未来（Futures）为处理这些依赖提供了一种有前景的模型，尤其适用于不规则算法，但其存在值不可变性限制。这一限制阻碍了原地内存更新（高性能线性代数中内存回收的关键需求）。本文通过引入新构造await_delete解决上述限制，该构造扩展了传统未来语义，允许在消费者完成处理后安全复用数值。基于此扩展，我们提出一种基于未来的新型稠密对称矩阵分块求逆算法，其灵感源自近期用于发现动力学系统守恒律的算法。我们在扩展版Taskflow中实现该方法，并通过强扩展实验进行评估。结果表明：未来机制在小规模问题上产生显著开销，但在大规模矩阵处理中可实现近线性扩展。我们分析了摊销阈值，证明未来机制是大规模线性代数中可行的高性能工具。