Common wisdom on arithmetic (IEEE)

[Bob Cassels]

The reader should be able to read -0.0, and the printer should print it as -0.0.

(= 0.0 -0.0)
(not (eq 0.0 -0.0))
(eql 0.0 -0.0))

Infinities should just be floating-point values, not symbols. You should pick a way to print them and read them. I hope you’d pick one of the ways that current implementations use, rather than invent a new one. I’d suggest using what we used at Symbolics, but I don’t remember what that was. I would assume it starts with 1e / 1d, -1e / -1d, but I don’t remember what we used after that.



> On Nov 2, 2018, at 4:19 PM, Daniel Herring <dherring at tentpost.com> wrote:
> 
> 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