There are many natural phenomena that can best be described by the use of infinitesimal and infinite numbers (see e.g. [1,5,13,23]. However, until now, the Non-standard techniques have been applied to theoretical models. In this paper we investigate the possibility to implement such models in numerical simulations. First we define the field of Euclidean numbers which is a particular field of hyperreal numbers. Then, we introduce a set of families of Euclidean numbers, that we have called altogether algorithmic numbers, some of which are inspired by the IEEE 754 standard for floating point numbers. In particular, we suggest three formats which are relevant from the hardware implementation point of view: the Polynomial Algorithmic Numbers, the Bounded Algorithmic Numbers and the Truncated Algorithmic Numbers. In the second part of the paper, we show a few applications of such numbers.

中文翻译：

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非档案数值计算环境中的算法数

通过使用无穷小和无穷数，可以最好地描述许多自然现象（例如，参见[1个，5，13，23]。但是，到目前为止，非标准技术已应用于理论模型。在本文中，我们研究了在数值模拟中实施此类模型的可能性。首先，我们定义欧几里德数的字段，这是超实数的特定字段。然后，我们介绍了一组欧几里德数，我们称它们为算法数，其中一些是受IEEE 754浮点数标准的启发。特别是，从硬件实现的角度来看，我们建议了三种相关的格式：多项式算法数，有界算法数和截断算法数。在本文的第二部分，我们展示了此类数字的一些应用。