mirror of
https://github.com/vale981/arb
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50 lines
2.4 KiB
ReStructuredText
50 lines
2.4 KiB
ReStructuredText
Feature overview
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===============================================================================
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Ball arithmetic, also known as mid-rad interval arithmetic, is an
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extension of floating-point arithmetic in which an error bound is
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attached to each variable. This allows doing rigorous computations
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over the real numbers, while avoiding the overhead of
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traditional (inf-sup) interval arithmetic at high precision,
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and eliminating much of the need for time-consuming
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and bug-prone manual error analysis associated with
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standard floating-point arithmetic. (See for example [Hoe2009]_.)
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At the moment, Arb contains:
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* A module (fmpr) for correctly rounded arbitrary-precision
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floating-point arithmetic. Arb numbers have a few special features, such
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as arbitrary-size exponents (useful for combinatorics and asymptotics) and
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dynamic allocation (facilitating implementation of hybrid
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integer/floating-point and mixed-precision algorithms).
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* A module (fmprb) for real ball arithmetic, where a ball is
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implemented as a pair of fmpr numbers.
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* Functions for fast high-precision computation of some mathematical constants,
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based on ball arithmetic.
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* A module (fmprb_poly) for polynomials or power series over the real numbers,
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implemented using balls as coefficients, with fast polynomial multiplication.
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* A rudimentary module (fmprb_mat) for matrices over the real numbers,
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implemented using balls as coefficients.
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Planned features include: transcendental functions and more extensive
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polynomial and matrix functionality, as well as support for complex numbers.
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Arb uses `MPIR <http://mpir.org>`_ and `FLINT <http://flintlib.org/>`_
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for the underlying integer arithmetic and other functions.
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The code conventions borrow from FLINT, and the project might get
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merged back into FLINT when the code stabilizes in the future.
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Arb also uses `MPFR <http://mpfr.org/>`_, mainly for testing purposes
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and fallback code.
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The current version of Arb implements most of its floating-point arithmetic
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naively using high-level FLINT types. The speed at low precision is far from
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optimal, and the memory management can sometimes be wasteful. The internals
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will be rewritten in the future to fix the inefficiencies,
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which eventually should make Arb ball arithmetic about as fast as mpz or mpfr arithmetic at any precision.
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**Warning**: as this is an early version, any part of the interface is
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subject to change! Also be aware that there are known and unknown bugs.
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