Floating-point numbers represent only a subset of real numbers. As such, floating-point arithmetic introduces approximations that can compound and have a significant impact on numerical simulations. We introduce Encapsulated error, a new way to estimate the numerical error of an application and provide a reference implementation, the Shaman library. Our method uses dedicated arithmetic over a type that encapsulates both the result the user would have had with the original computation and an approximation of its numerical error. We thus can measure the number of significant digits of any result or intermediate result in a simulation. We show that this approach, while simple, gives results competitive with state of the art methods. It has a smaller overhead, and it is compatible with parallelism, making it suitable for the study of large scale applications.

浮点数仅表示实数的一个子集。因此，浮点运算引入了可以复合并对数值模拟产生重大影响的近似值。我们引入了封装误差，这是一种估计应用程序数值误差的新方法，并提供了一个参考实现，即 Shaman 库。我们的方法在一种类型上使用专用算法，该类型封装了用户在原始计算中可能得到的结果及其数值误差的近似值。因此，我们可以测量模拟中任何结果或中间结果的有效数字的数量。我们表明，这种方法虽然简单，但提供的结果可与最先进的方法相媲美。它具有更小的开销，并且与并行性兼容，