An Iterative Method for Computing π by Argument Reduction of the Tangent Function

In this work, we develop a new iterative method for computing the digits of π by argument reduction of the tangent function. This method combines a modified version of the iterative formula for π with squared convergence that we proposed in a previous work and a leading arctangent term from the Machin-like formula. The computational test we performed shows that algorithmic implementation can provide more than 17 digits of π per increment. Mathematica codes, showing the convergence rate for computing the digits of π, are presented.