🚀 go-pugleaf

On 08 Sep 2001 00:22:14 GMT, u98ejr@ecs.ox.ac.uk (Edward Rosten)
wrote:

> > When checking for possible difficulty with division by zero, if you don't
> > wish to get into trapping overflow and the like, you should check at least
> > for small non-zero numbers.  If all your numerators have absolute value < 4,
> > you could safely do
> > #include <float.h>
> > if(fabs(y)>FLT_MIN)
> >     proceed with division by y
> > else
> >     treat as error
> 
> I'm not trying to be pedantic, I'm genuinely curious, but isn't
> 
> fabs(y) > FLT_MIN
> 
> equivalent to
> 
> f != 0
> 
> Since 0 can be represented exactly and FLT_MIN is the smallest
> possible float greater than zero?

Usually not. Lets take a bread and butter i87 implementation.

According to the C Standard FLT_MIN denotes the smallest _normalized_
float value. Normalized means "full precision", in this case 24
significant mantissa bits evaluating to some

value =	1.xxx xxxx xxxx xxxx xxxx xxxx * 2^n

whiere n is in the range between -126 and +127

In IEEE SINGLE which is usally mapped to a C float FLT_MIN corresponds
to

	1.000 0000 0000 0000 0000 0000 * 2^-126 = 2^-126

This isn't the smallest possible float value >0 because there are
still float values of the form

value =	0.xxx xxxx xxxx xxxx xxxx xxxx * 2^-126

down to

realmin = 0.000 0000 0000 0000 0000 0001 * 2^-126 = 2^-149

which is the "real" denormal float value  with one single bit of
precision. All i87-based float implementation I know support
denormals, i.e. values greater equal 2^-149 and less than 2^-126 =
FLT_MIN as if they were normals.

You may test this on your imlementation

	float f;
	for (f=FLT_MIN;f;f/=2) printf("%f\n",f);

after compiling it with _no_ optimizations.


Regards
Horst
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