We develop a very simple compensated scheme for computing very accurate Givens rotations. The approach is significantly more straightforward than the one in \cite{borges2021fast}, and the derivation leads to a very satisfying algorithm whereby a naively computed Givens rotation can be used to construct a correction to itself. It is also seen that this scheme continues to provide high accuracy even when built on a hypoteneuse calculation that is of lesser accuracy.

翻译：我们提出了一种非常简单的补偿方案，用于计算高精度的Givens旋转。该方法比文献\cite{borges2021fast}中的方案更为直接，其推导过程生成了一种令人非常满意的算法：通过直接计算的Givens旋转可构造对其自身的修正。同时发现，即使基于精度较低的斜边计算，该方案仍能保持高精度。