Re: [9fans] circular fonctions: precision?

[tlaronde@polynum.com]

On Sun, Oct 02, 2011 at 12:06:18PM -0700, Bakul Shah wrote:
>
> > I sometimes wonder if the more common 64bits will not someday see
> > CAD or related software go back to scaled integer arithmetic =E0 la
> > Intergraph dgn, where 64bits is enough for the range of coordinates
> > and precision used...
>
> double precision seems enough for most things. ieee754-2008
> has quad precision... Symbolic math package Macsyma (& Maxima)
> has had bigfloats (arbitray precision floating point) for
> decades.  Supposedly some Common Lisp implementation have
> those as well.  Mechanical CAD packages would probably get
> more benefit from symbolic math capabilities than just scaled
> integers (keep everything in formulas until when you
> absolutely need numerical results!).

To resort to algebra (infinite precision by symbol combinations) is,
indeed, a general rule. For symbolic math capabilities, I have wandered
around the concept for geometrical description (like METAFONT/MetaPost,
where there is this distinction that is mostly blurred in programming
languages---except for basic conditionnals--- : the distinction between
an assignation and an equation).

But to come back to programming, when calculus is the crux, the more
common/known even new! programming languages are not great tools, and
"portability" i.e. proved accuracy of the implementation for a wide
range of hardware/software is fuzzy. And it's amazing to see how one can
rapidly face errors even with very basic computations. And even with
integer arithmetic, not much help is guaranteed by languages.
--
        Thierry Laronde <tlaronde +AT+ polynum +dot+ com>
                      http://www.kergis.com/
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