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Arbitrary precision arithmetic is also used to compute fundamental mathematical constants such as π to millions or more digits and to analyze the properties of the digit strings [8] or more generally to investigate the precise behaviour of functions such as the Riemann zeta function where certain questions are difficult to explore via ...
Routines for Gauss–Kronrod quadrature are provided by the QUADPACK library, the GNU Scientific Library, the NAG Numerical Libraries, R, [2] the C++ library Boost., [3] as well as the Julia package QuadGK.jl [4] (which can compute Gauss–Kronrod formulas to arbitrary precision).
A variant of the spigot approach uses an algorithm which can be used to compute a single arbitrary digit of the transcendental without computing the preceding digits: an example is the Bailey–Borwein–Plouffe formula, a digit extraction algorithm for π which produces base 16 digits. The inevitable truncation of the underlying infinite ...
Programming languages that support arbitrary precision computations, either built-in, or in the standard library of the language: Ada: the upcoming Ada 202x revision adds the Ada.Numerics.Big_Numbers.Big_Integers and Ada.Numerics.Big_Numbers.Big_Reals packages to the standard library, providing arbitrary precision integers and real numbers.
This category presents articles pertaining to the calculation of Pi to arbitrary precision. Pages in category "Pi algorithms" The following 17 pages are in this category, out of 17 total.
In the 1980s, Rump made an example. [ 3 ] [ 4 ] He made a complicated function and tried to obtain its value. Single precision, double precision, extended precision results seemed to be correct, but its plus-minus sign was different from the true value.
PARI/GP performs arbitrary precision calculations (e.g., the significand can be millions of digits long—and billions of digits on 64-bit machines). It can compute factorizations , perform elliptic curve computations and perform algebraic number theory calculations.
The method is based on the individual work of Carl Friedrich Gauss (1777–1855) and Adrien-Marie Legendre (1752–1833) combined with modern algorithms for multiplication and square roots. It repeatedly replaces two numbers by their arithmetic and geometric mean , in order to approximate their arithmetic-geometric mean .