[openvrml-develop] Re: Numbers Close together

[Damian M. <da...@er...>]

While there is an inline routine, fpequal(a, b) which tests whether 2
numbers are close together to a floating point tolerance, there are
3 instances where this is not used but maybe should be.

field.cpp
		(1.0 - cosom) > FPTOLERANCE)		Anonymous

vrml97node.cpp
		(dotval+1.0) > FPTOLERANCE)		S.K.Bose
 		(1.0-dotval) > FPTOLERANCE)

which would appear to be saying

		cosom is damn close to +1
+
		dotval is damn close to -1
+
		dotval is damn close to +1

respectively.

If this is the case, then the way this is written will cause some
cases, where what I think they are saying, will not actually happen.

Is this a potential bug or am I being paranoid?

Also, FPTOLERANCE is 1.0e-6 in the main library, but 1.0e-7 in the
OpenGL stuff.  Should they be consistent?

And

	const float FPTOLERANCE(1.0e-6);

	inline fpzero(float a)
	{
		return fabs(b) <= FPTOLERANCE;
	}

will probably kill the optimizer because it will trigger a call to fabs.
If you really want it inline, it will often be faster to do something like

	inline fpzero(float a)
	{
		static float FPTOLERANCE = 1.0e-6;

		return (-FPTOLERANCE <= a && a <= FPTOLERANCE);
	}
or

	inline fpzero(float a)
	{
		static float FPTOLERANCE = 1.0e-6;

		return ((a < 0.0 ? -a : a) <= FPTOLERANCE);
	}

and I hope I got that right.

If you want really optimal and machine portable code of a number within 3
binary digits of the machine precison, you can try

	inline fpzero(float a)
	{
		return 1.0f + a * 0.125 == 1.0f;
	}

but most optimizers kill portability of this by almost always returning
true so we instead do

	inline fpadd1(float a)
	{
		return 1.0f + a * 0.125;
	}

	inline fpzero(float a)
	{
		return fpadd1(a) == 1.0f;
	}

to at least fool g++/gcc.  I've yet to try it on some other compilers.

I hope we all understood this while we are nursing our sore heads from
last night.

Many Thanks - Damian (McGuckin)

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