Arbitrary-precision arithmetic

Arbitrary-precision arithmetic refers to a mathematical computation method that allows for greater accuracy in computer algebra systems, such as Mathematica. It overcomes the limitations of numeric systems that work with floating point numbers by providing exact arithmetic for integers and rationals, as well as arbitrary precision arithmetic for real numbers.From: Electromagnetics for Electrical Machines [2019], An elementary algorithm to evaluate trigonometric functions to high precision [2018], The Handbook of Software for Engineers and Scientists [2018]

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Published in Paul W. Ross, The Handbook of Software for Engineers and Scientists, 2018

Roque Waldir L.

One of the main features of the computer algebra systems is their exact arithmetic for integers and rationals and arbitrary precision arithmetic for reals, in contrast to numeric systems, which work with floating point numbers.

An elementary algorithm to evaluate trigonometric functions to high precision

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Published in International Journal of Mathematical Education in Science and Technology, 2018

B. Tomas Johansson

Iterations are suitable for a computer to perform. We can with ease do thousands of iterations; however, halving an angle many times, it will be rounded to zero on most standard calculators and computers. This can be overcome with what is known as arbitrary-precision arithmetic. Before discussing this, in the next section, we briefly investigate the error in the above approximation for cos θ.

Arbitrary-precision arithmetic

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An elementary algorithm to evaluate trigonometric functions to high precision