Common wisdom on arithmetic (IEEE)

[Daniel Herring]

Hi Marco,

I would just rely on the IEEE 754 values and define constants for 
convenience.  Negative zero is an artifact of floating-point calculations, 
not a symbol in math.  Don't forget that many values are classified as NaN 
(common exponent, many fractions).

C defines fpclassify() and related predicates to return NaN, infinite, 
zero, subnormal, or normal.

Obligatory reference:  What Every Computer Scientist Should Know About 
Floating-Point Arithmetic by David Goldberg

Rounding error causes loss of life:
http://www-users.math.umn.edu/~arnold/disasters/patriot.html


- Daniel


On Fri, 2 Nov 2018, Antoniotti Marco wrote:

> Dear all
> I am fooling around (again!) with the spec of a math library that I want the students to work on as a project.  Language is Common Lisp.
> 
> Essentially the library is an extended generic math library built on the basis of the many ones floating around.
> 
> Now.  Here comes IEEE. And “infinity"
> 
> Among many implementations there is more or less a consensus about how to “represent” IEEE infinities in CL.
> 
> E.g.
> 
> LW > math:long-float-positive-infinity
> +1D++0 #| +1D++0 is double-float plus-infinity |#
> 
> CCL ? math:long-float-positive-infinity
> 1D++0
> 
> 
> and so on.
> 
> NaN is not as clearly defined.
> 
> LW 45 > math:nan
> 1D+-0 #| 1D+-0 is double-float not-a-number |#
> 
> CCL ? math:nan
> 1D+-0 #| not-a-number |#
> 
> But to get a NaN in SBCL/CMUCL requires a trick.  I use
> 
> (sb-kernel:make-double-float -524288 0)) ; Courtesy of Raymond Toy.
> 
> In any case…  There are two issues that I would like to brainstorm a bit.
> 
> The first one pertains rounding modes.  Give the current state of affairs, it does not seem possible to access them in all the CL implementations.  CMUCL/SBCL give you the necessary hooks, but LW doesn’t.
>  Let’s skip this.
> 
> The second is just a simple question.
> 
> Given that we *do* have (with some acrobatics) access to IEEE infinities, would you add symbolic constants to such library like
> 
> (defconstant +posinf+ ‘+posinf+)
> 
> or would you just rely on the IEEE infinities?
> 
> Generic functions like
> 
> (defgeneric plus (x y) …)
> 
> Will obviously be affected.
> 
> I just want to get a feeling about the overall wisdom of this crowd.
> 
> All the best
> 
> Marco
> 
> 
> 
> --
> Marco Antoniotti
> 
> 
> 
>