What if there will some additional operators for float comparement? E.g ==~ <~
>~ etc. Because of floats nature it is very often we have to use constructions like

if (equal(firstVector3, secondVector3))
{
}

or

if (greater_equal(float1, float2))
{
}

Definition of this functions is very simple and as a rule wraps to comparement difference of operants with float.epsilon. But I think it is very annoying to use this method very often, even more usual operators like ==, <= are used rarely then a approximal comparement. Is this necessary, how do u think?

nail wrote:

> What if there will some additional operators for float comparement? E.g ==~ <~ >~ etc.

Defining either of those will potentially break existing code, as ~ is a unary operator.

> Because of floats nature it is very often we have to use
> constructions like
> 
> if (equal(firstVector3, secondVector3))
> {
> }

What's wrong with == ?

> or
> 
> if (greater_equal(float1, float2))
> {
> }

What's wrong with >= ?

Stewart.

"nail" <nail_member@pathlink.com> wrote in message news:ckm51l$2kfr$1@digitaldaemon.com...
> What if there will some additional operators for float comparement? E.g
==~ <~
> >~ etc. Because of floats nature it is very often we have to use
constructions like
>
> if (equal(firstVector3, secondVector3))
> {
> }
>
> or
>
> if (greater_equal(float1, float2))
> {
> }
>
> Definition of this functions is very simple and as a rule wraps to
comparement
> difference of operants with float.epsilon. But I think it is very annoying
to
> use this method very often, even more usual operators like ==, <= are used rarely then a approximal comparement. Is this necessary, how do u think?
>

There are two problems with defining an "approximate equality" operator:
1) precision: what exactly is the tolerance for testing approximate
equality?
2) absolute vs relative: how is the approximate value measured?

For example, 1e-10 and 1e-11 might be considered approximately equal since they are close to zero but if your data is all very small anyway then 1e-10 and 1e-11 might be very far apart for the particular application.

Given these complications I don't think a builtin operator would be sufficient. Measuring against eps is by itself not good enough since eps is meaningful near 1.0 and differences in floating point numbers with maginitutes in the 1000's won't be anywhere close to eps. A user-defined function (or some functions in std.math perhaps) would be good enough.

-Ben

In article <ckm5p7$2lao$1@digitaldaemon.com>, Stewart Gordon says...
>
>nail wrote:
>
>> What if there will some additional operators for float comparement? E.g ==~ <~ >~ etc.
>
>Defining either of those will potentially break existing code, as ~ is a unary operator.

Hm... I forgot about this.

>> Because of floats nature it is very often we have to use constructions like
>> 
>> if (equal(firstVector3, secondVector3))
>> {
>> }
>
>What's wrong with == ?

exp(x) not always equal to exp(x)

>> or
>> 
>> if (greater_equal(float1, float2))
>> {
>> }
>
>What's wrong with >= ?

float x = 5.f / 6.f;
for ( ; x < 100; x += 5.f / 6.f)
;
for ( ; x >= 5.f / 6.f; x -= 5.f / 6.f)
;

if (x != 5.f / 6.f)
assert(0);

Assertion will be thrown

nail wrote:
> In article <ckm5p7$2lao$1@digitaldaemon.com>, Stewart Gordon says...
> 
>> nail wrote:
<snip>
>>> if (equal(firstVector3, secondVector3))
>>> {
>>> }
>> 
>> What's wrong with == ?
> 
> exp(x) not always equal to exp(x)

You mean if exp(x) is NaN?  And that your equal would treat NaN as
equal to NaN?  Or what?

>>> or
>>> 
>>> if (greater_equal(float1, float2))
>>> {
>>> }
>> 
>> What's wrong with >= ?
> 
> float x = 5.f / 6.f;
> for ( ; x < 100; x += 5.f / 6.f)
> ;
> for ( ; x >= 5.f / 6.f; x -= 5.f / 6.f)
> ;
> 
> if (x != 5.f / 6.f)
> assert(0);
> 
> Assertion will be thrown

Actually, compiler error will be thrown.  A ; by itself isn't a statement in D.

But I've no idea what you're talking about.  How would your greater_equal enable x to be not greater than or equal to a certain value, while at the same time being equal to that same value?

Stewart.

In article <cko4tu$1fnf$1@digitaldaemon.com>, Stewart Gordon says...
> (...)
>But I've no idea what you're talking about.  How would your greater_equal enable x to be not greater than or equal to a certain value, while at the same time being equal to that same value?
>
>Stewart.

All apologies if I've misunderstood the question here. :)

It all goes back to what my high-school CS teacher said: "Never directly compare the values of two reals with '=='.  It won't work."

The problem here is with precision: floating-point representations have to convert a nice, neat decimal number into a binary equivalent.  This generates some error in the lowest order bits, and for most purposes is acceptable  to ignore.

But when comparing the result of a calculation against other values, you need to account for this precision error.  This is because the result of your calculation is going to be /close/ to what you'd expect plus or minus that error.  This "fudge factor" is usually called "Epsilon".

So when you want to do this:

float a,b;
if(a == b){ /*...*/ }

You really need to do this:

const float epsilon = 0.000000001; // depends on your application
float a,b;
if( b-epsilon <= a && a <= b+epsilon){ /*...*/ }

.. and so forth. This is better served by a suite of functions for readability's sake:

const float epsilon = 0.000000001; // depends on your application
float equals(float a,float b){ return b-epsilon <= a && a <= b+epsilon; }
float a,b;
if(equals(a,b)){ /*...*/ }

It's not really so complicated or exotic as it would seem.  Anywhere you use floating-point mathematics heavily (3D games, finance, statistics, etc.) you need something like this to keep things sane.

Now, if I were to suggest a feature in D to support this, i'd advocate a simple class that contains the needed operators called 'Epsilon'.

> class Epsilon{
>     float eps;
>     bit eq(float a,float b){
>         return(b-eps <= a && a <= b+eps);
>     }
>     /* other operations like lt, lte, gt, gte, neq, etc go here */
>     this(float eps){ this.eps = eps; return this; }
> }

Combine this with D's 'with' syntax and you get something that's pretty useful.

> void main(){
>       float a,b;
>       a=0;
>       b=0.0000001;
>       with(new Epsilon(0.0000001)){
>           if(eq(a,b)){
>               printf("a is equal to b\n");
>           }
>       }
> }

You could even do the same with a struct which would be even more efficent.

Eric Anderton -- at -- yahoo

pragma wrote:

<snip>
> But when comparing the result of a calculation against other values, you need to
> account for this precision error.  This is because the result of your
> calculation is going to be /close/ to what you'd expect plus or minus that
> error.  This "fudge factor" is usually called "Epsilon".
> 
> So when you want to do this:
> 
> float a,b;
> if(a == b){ /*...*/ }
> 
> You really need to do this:
> 
> const float epsilon = 0.000000001; // depends on your application
> float a,b;
> if( b-epsilon <= a && a <= b+epsilon){ /*...*/ }

I see.  But numerical noise is relative to the order of magnitude of the numbers being dealt with.  So it might make more sense to consider values as correct to significant figures rather than decimal places...?

<snip>
> It's not really so complicated or exotic as it would seem.  Anywhere you use
> floating-point mathematics heavily (3D games, finance, statistics, etc.) you
> need something like this to keep things sane.

Do many financial applications necessitate dealing with units arbitrarily smaller than a penny, cent or whatever?

> Now, if I were to suggest a feature in D to support this, i'd advocate a simple
> class that contains the needed operators called 'Epsilon'.  Combine this with D's 'with' syntax and you get something that's pretty useful.
<snip>

Hmm....

Stewart.