REAL (was: Verified compilers?)

[stefan-lucks@see-the.signature]

On Wed, 14 Mar 2012, Georg Bauhaus wrote:

> Side note: WRT finiteness, language designers have made one
> particular mistake again and again, following a convention,
> by telling programmers about some type called REAL. The set
> of supposed real numbers that programmers have heard about
> before, in math lessons, is not finite [...]
> 
> What the language designers usually mean, though, is some finite
> Fraction_with_Split_Shifting thing, having infinitesimally
> little to do with the reals. Consequence: an infinite supply
> of surprises, cause by the name REAL.

In general, floating point numbers are meant to approximate the real 
numbers (in the mathematical sense). Unfortunately, most programmers have 
been educated just to apply floating point arithmetic in their programs, 
expecting the result to be close enough to the "real result".

Hardly anyone cares enough to analyze how the error grows from operation 
to operation. Hardly anyone even bothers to define how close the result 
should to be -- which depends on the application at hand, of course. 

And, to be honest, that approach works well most of the time. Which is 
precisely the reason why wrong results (= approximations not close enough 
to the real result) come as *surprises* ...


-- 
---- Stefan.Lucks (at) uni-weimar.de, University of Weimar, Germany  ----
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