Re: [9fans] circular fonctions: precision?

[tlaronde@polynum.com]

On Sun, Oct 02, 2011 at 10:52:27AM -0700, Bakul Shah wrote:
> On Sun, 02 Oct 2011 18:38:00 +0200 tlaronde@polynum.com  wrote:
> > Hello,
> > 
> > Is there some documentation about the precision of the circular (i.e
> > trigonometric) fonctions, depending on the (plan9) implementation and
> > the hardware?
> 
> Do you mean precision (number of significant bits) or accuracy
> (closeness to true value)? For a double the precision is 52
> bits, for a float 23.

Sorry, I meant accuracy.

> 
> > To my limited knowledge, an OS is integer based, so the floating
> > point support is mainly "user space" and is, despite IEEE754 and due to
> > the interaction between hardware, software, and programmer, really
> > floating, but is there a range given for the association of OS/hardware
> > telling that say sin(r) or asin(s) is accurate, at worst, at some 
> > epsilon near?
> 
> It depends on the algorithm used, not on the OS. The C
> standard leaves accuracy upto the implementation. If you care,
> you can compare the result of a C function with what bc(1)
> computes for the same function (by using a suitably large
> scale).

Here, I mean by "OS" not the kernel, but the whole soft-system, i.e.
here the implementation of libc and the direct use of sin(3) etc.

It seems you've answered my badly formulated question: if I want
to know exactly what I use, I must rely on some defined library
linked against my software that implements directly the fonctions.
(Testing against bc(1) is probably worth for having an idea; but
the problem is that 1) the results depend on the system/implementation;
2) there may be singularities and testing the whole range with a
small granularity is probably not an option.)

I sometimes wonder if the more common 64bits will not someday see
CAD or related software go back to scaled integer arithmetic à la
Intergraph dgn, where 64bits is enough for the range of coordinates
and precision used...

Thanks for the answer.
-- 
        Thierry Laronde <tlaronde +AT+ polynum +dot+ com>
                      http://www.kergis.com/
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