论文标题
关于使用Infinity计算机架构来设置动态精确浮点算术
On the use of the Infinity Computer architecture to set up a dynamic precision floating-point arithmetic
论文作者
论文摘要
我们通过利用Infinity计算机提供的框架来设计可变精度的浮点算术。这是一个实现Infinity Arithmetic System的计算平台，它是一个位置数字系统，可以处理由Radix Grossone的正和负有限幂象征的无限和无限量。 Infinity计算机提供的计算功能使我们能够在计算过程中动态更改表示形式和浮点操作的准确性。当适当地实施时，在解决条件不足的问题时，这种可能性尤其有利。实际上，与标准的多精确算术相比，此处仅在需要时才提高准确性，因此不会影响太大的整体计算工作。还提供了有关非线性方程解的说明性示例。
We devise a variable precision floating-point arithmetic by exploiting the framework provided by the Infinity Computer. This is a computational platform implementing the Infinity Arithmetic system, a positional numeral system which can handle both infinite and infinitesimal quantities symbolized by the positive and negative finite powers of the radix grossone. The computational features offered by the Infinity Computer allows us to dynamically change the accuracy of representation and floating-point operations during the flow of a computation. When suitably implemented, this possibility turns out to be particularly advantageous when solving ill-conditioned problems. In fact, compared with a standard multi-precision arithmetic, here the accuracy is improved only when needed, thus not affecting that much the overall computational effort. An illustrative example about the solution of a nonlinear equation is also presented.
