Let us consider the ordering of real numbers in postgres. As you can see
from
the results below it has clearly returned the correct results.
select( 1.0000000000000000 = 1.0000000000000002 ); => f select( 1.0000000000000000 < 1.0000000000000002 ); => t
select(1.0000000000000000 > 1.0000000000000002 ); => f
Imagine the situation however where postgres returned the following
values to
simple numerical inequalities. In such a case postgresql would be clearly
defective and unfit for purpose.
select( 1.000000 = 1.000001 ); => f select( 1.000000 < 1.000001 ); => f select( 1.000000 > 1.000001 ); => f
If such a situation is unacceptable for the real number line, then in
what way
can it be acceptable for the real number plain.
select( point(1.00000,0) <> point(1.00001,0) ); => f select( point(1.00000,0) << point(1.00001,0) ); => f select(
point(1.00000,0) >> point(1.00001,0) ); => f select( point(1.00000,0) <-> point(1.00001,0) ); => 1.00000000000655e-05
We have two points with a finite separation in the x axis. Postgres
thinks they
are not the same point, nor one left of the other, nor to the right. This is
clearly a both a physical and logical impossibility.
The cause of this is the ill conceived FP* macros. They seem represent a
solution to a problem that simply does not exist.
The first effect of these macros is to reduce the accuracy of all geometric
comparisons from double precision, to less than single precision. The
following
program correctly prints the correct answer. Whereas as we have seen above,
postgres falls in a heap.
int main() { float f = 1.00000; float g = 1.00001; if( f==g ) { printf( "f=g\n" ); } if( f<g ) { printf(
"f<g\n"); } if( f>g ) { printf( "f>g\n" ); } return 0; }
The second effect is to take operations that would of worked correctly
even in
single precision, and to cause them to produce nonsensical result. For
example
points that can be both inside and outside a polygon at the same time.
Simple analysis of the postgres source code shows that the only places
where the
FPzero, FPeq, FPne, FPlt, FPle FPgt and FPge macros are defined and used
are in
the src/backend/utils/adt/geo_ops.c and src/include/utils/geo_decls.h files.
What is the justification for these macros? Why do they only affect
geometric
calculations, and not all numeric calculations? Why should these macro's
not be
abandoned?
Does anyone any any objections to me:
1) removing these macros, or at least disabling EPSILON by default.
2) adding in the obviously missing operators (ie: box @> point)
