Weak Memory Models with Matching Axiomatic and Operational Definitions

TL;DR

This paper demonstrates that atomic memory models simplify the creation of matching axiomatic and operational definitions, enabling more confident processor design while maintaining high performance.

Contribution

It introduces a parametrized approach to defining atomic memory models that facilitates proofs of equivalence and supports confident processor architecture development.

Findings

Atomic models enable easier axiomatic and operational definitions.

Operational and axiomatic models are shown to be equivalent.

Proposed models retain most performance benefits of non-atomic models.

Abstract

Memory consistency models are notorious for being difficult to define precisely, to reason about, and to verify. More than a decade of effort has gone into nailing down the definitions of the ARM and IBM Power memory models, and yet there still remain aspects of those models which (perhaps surprisingly) remain unresolved to this day. In response to these complexities, there has been somewhat of a recent trend in the (general-purpose) architecture community to limit new memory models to being (multicopy) atomic: where store values can be read by the issuing processor before being advertised to other processors. TSO is the most notable example, used in the past by IBM 370 and SPARC-TSO, and currently used in x86. Recently (in March 2017) ARM has also switched to a multicopy atomic memory model, and the new RISC-V ISA and recent academic proposals such as WMM are pushing to do the same. In this paper, we show that when memory models are atomic, it becomes much easier to produce axiomatic definitions, operational definitions, and proofs of equivalence than doing the same under non-atomic models. The increased ease with which these definitions can be produced in turn allows architects to build processors much more confidently, and yet the relaxed nature of the models we propose still allows most or all of the performance of non-atomic models to be retained. In fact, in this paper, we show that atomic memory models can be defined in a way that is parametrized by basic instruction and fence orderings. Our operational vs. axiomatic equivalence proofs, which are likewise parameterized, show that the operational model is sound with respect to the axioms and that the operational model is complete: that it can show any behavior permitted by axiomatic model.