Subject: Re: [boost] Is there interest in Computable Calculus?
From: Matt Calabrese (rivorus_at_[hidden])
Date: 2016-01-13 00:56:25
On Jan 12, 2016 18:40, "Damian Vicino" <damian.vicino_at_[hidden]> wrote:
> Iâm interested in developing basic support of âreal numbersâ for
computable calculus applications.
> In computable calculus, reals have infinite precision ( certain
restrictions may apply).
> The usual approach is representing numbers as functions producing digits.
> An arithmetic operation produces a new function using the functions in
the operands and some simple expression manipulations.
> When a number needs to be evaluated (e.g., for comparisons where
expression rules are unknown), enough digits for reaching an answer are
generated using the functions. For example, 3.14 < pi requires generating 3
digits to answer âtrueâ.
> The algorithms for arithmetic operations and evaluation are well known,
and multiple implementations were developed (mostly in the 90s).
> However, I couldnât find an open source implementation and had to come up
with my own for working in a project during the last 2 years.
> My preferred reference for the required algorithms is the book: Aberth,
Oliver. Computable Calculus. Academic Press, 2001.
> In particular, my initial scope would be the 4 arithmetic operations (+,
-, *, /), and the comparison operators (<, =) for reals.
> Someone is interested in such a library in boost?
Yes! I really want this.
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