On Apr 21, 1:31 am, Rae Westwood <(E-Mail Removed)>

wrote:

> On Fri, 20 Apr 2007 19:52:01 +0000, JDT wrote:

> > It seems that using floats as the first tupelo for an STL map (shown

> > below) can cause problems but I don't remember what the problems were.

> > Is it common practice to use a structure like below? I would appreciate

> > if you can share your experience using such a structure. Thanks.

> > std::map<float, int> m;

> I'd be interested in authoritative and intelligent input on this as well.

> My understanding is that for a type to be a key for a map, it only need be

> (sortable)..iow: it overloads the relational operators so that two values

> of the same type can be compared.
The term used by the standard is that there must be a comparison

function which "induces a strict weak ordering on the values".

The standard then specifies what it means by a strict weak

ordering:

The term strict refers to the requirement of an irreflexive

relation (!comp (x, x) for all x), and the term weak to

requirements that are not as strong as those for a total

ordering, but stronger than those for a partial ordering. If

we define equiv(a, b) as !comp (a, b) && !comp (b, a), then

the requirements are that comp and equiv both be transitive

relations:

-- comp (a, b) && comp (b, c) implies comp (a, c)

-- equiv(a, b) && equiv(b, c) implies equiv(a, c)

[Note: Under these conditions, it can be shown that

. equiv is an equivalence relation

. comp induces a well-defined relation on the

equivalence classes determined by equiv

. The induced relation is a strict total ordering.

-- end note ]

> As to how you generate your keys...well, that could pose a problem since

> ieee floating point numbers are approximations of actual floating point

> values.
Not really. Floating point numbers are exact

representations of floating point numbers. In many

applications, floating point numbers are used to model real

numbers; the approximation there is not very exact (and many

of the rules of real arithmetic do not hold).

> float n=2.0f

> is it stored internally as 2.0 or 1.9999999997?
Neither. It's stored internally as 0x40000000. Required by

the IEEE standard. As it happens, this value represents the

real number 2.0 exactly---you picked a very bad example

.

The problem is, of course, that floating point can only

represent a very small subset of the real numbers, and a

non-contiguous subset at that. (int can only represent a

very small subset of the integers, but it is a contiguous

subset.) And that while precisely defined by IEEE, floating

point arithmetic doesn't follow some of the expected

rules---addition is not associative, for example---and

often doesn't give the same results as the same operation

in real arithmetic. And of course, the fact that we enter

floating point constants in the form of decimal numbers, and

that the values we "see" often aren't present in the set of

values representable in floating point.

> A way around this would be to (box) the float key into its own class and

> make your relational operators be inexact comparitors.
See above. I suspect that most naïve inexact comparitors

would fail to define a strick weak ordering.

> btw: I HAVE actually found uses for maps that have floating point keys. I

> use them when doing histograms of numerical data.
Just guessing, but in such cases, you would define

equivalences classes over ranges of floating point values,

no? Something along the lines of:

struct FPCmp

{

bool operator()( double a, double b ) const

{

return floor( 100.0 * a ) < floor( 100.0 * b ) ;

}

} ;

(In such cases, I'd probably use a canonic representation of

each equivalence class as the key, i.e. floor(100.0 *

value), in the above example.)

--

James Kanze (Gabi Software) email:

(E-Mail Removed)
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