One problem that arises in computation involving large numbers is precision. In certain situations, the result might be represented by the standard data type, but arithmetic precision might be compromised when dealing with large numbers in the course to the result. Binomial coefficients are an example that suffer from this torment. In the present paper, we review numerical methods to compute the binomial coefficients: Pascal’s recursive method; prime factorization to cancel out terms; gamma function approximation; and a simplified iterative method that avoids loss in precision. Acknowledging that the binomial coefficients might be obtained by a successive convolution of a simple discrete rectangular function, we propose a different approach based on the discrete Fourier transform and another based on its fast implementation. We analyze and compare performance and precision of all of them. The proposed methods overcome the previous ones when computing all coefficients for a given level n, attaining better precision for large values of n.

在涉及大量数字的计算中出现的一个问题是精度。在某些情况下，结果可能由标准数据类型表示，但是在处理结果过程中的大量数字时，算术精度可能会受到影响。二项式系数就是遭受这种折磨的一个例子。在本文中，我们回顾了计算二项式系数的数值方法：Pascal递归方法；素因分解以取消条款；伽马函数近似；以及避免精度损失的简化迭代方法。认识到二项式系数可以通过简单的离散矩形函数的连续卷积获得，我们提出了一种基于离散傅里叶变换的方法，另一种基于其快速实现的方法。我们分析并比较它们的性能和精度。在计算给定级别的所有系数时，所提出的方法克服了先前的方法n，对于较大的n值，可以获得更高的精度。