This directory contains the code for the user-defined type,
SEG, representing laboratory measurements as floating point
intervals. 

RATIONALE
=========

The geometry of measurements is usually more complex than that of a
point in a numeric continuum. A measurement is usually a segment of
that continuum with somewhat fuzzy limits. The measurements come out
as intervals because of uncertainty and randomness, as well as because
the value being measured may naturally be an interval indicating some
condition, such as the temperature range of stability of a protein.

Using just common sense, it appears more convenient to store such data
as intervals, rather than pairs of numbers. In practice, it even turns
out more efficient in most applications.

Further along the line of common sense, the fuzziness of the limits
suggests that the use of traditional numeric data types leads to a
certain loss of information. Consider this: your instrument reads
6.50, and you input this reading into the database. What do you get
when you fetch it? Watch:

test=> select 6.50 as "pH";
 pH
---
6.5
(1 row)

In the world of measurements, 6.50 is not the same as 6.5. It may
sometimes be critically different. The experimenters usually write
down (and publish) the digits they trust. 6.50 is actually a fuzzy
interval contained within a bigger and even fuzzier interval, 6.5,
with their center points being (probably) the only common feature they
share. We definitely do not want such different data items to appear the
same.

Conclusion? It is nice to have a special data type that can record the
limits of an interval with arbitrarily variable precision. Variable in
a sense that each data element records its own precision.

Check this out:

test=> select '6.25 .. 6.50'::seg as "pH";
          pH
------------
6.25 .. 6.50
(1 row)


FILES
=====

Makefile		building instructions for the shared library

README.seg		the file you are now reading

seg.c			the implementation of this data type in c

seg.sql.in		SQL code needed to register this type with postgres
			(transformed to seg.sql by make)

segdata.h		the data structure used to store the segments

segparse.y		the grammar file for the parser (used by seg_in() in seg.c)
 
segscan.l		scanner rules (used by seg_yyparse() in segparse.y)

seg-validate.pl		a simple input validation script. It is probably a 
			little stricter than the type itself: for example, 
			it rejects '22 ' because of the trailing space. Use 
			as a filter to discard bad values from a single column;
			redirect to /dev/null to see the offending input

sort-segments.pl	a script to sort the tables having a SEG type column


INSTALLATION
============

To install the type, run

	make
	make install

The user running "make install" may need root access; depending on how you
configured the PostgreSQL installation paths.

This only installs the type implementation and documentation.  To make the
type available in any particular database, do

	psql -d databasename < seg.sql

If you install the type in the template1 database, all subsequently created
databases will inherit it.

To test the new type, after "make install" do

	make installcheck

If it fails, examine the file regression.diffs to find out the reason (the
test code is a direct adaptation of the regression tests from the main
source tree).


SYNTAX
======

The external representation of an interval is formed using one or two
floating point numbers joined by the range operator ('..' or '...'). 
Optional certainty indicators (<, > and ~) are ignored by the internal 
logics, but are retained in the data.

Grammar
-------

rule 1    seg -> boundary PLUMIN deviation
rule 2    seg -> boundary RANGE boundary
rule 3    seg -> boundary RANGE
rule 4    seg -> RANGE boundary
rule 5    seg -> boundary
rule 6    boundary -> FLOAT
rule 7    boundary -> EXTENSION FLOAT
rule 8    deviation -> FLOAT

Tokens
------

RANGE        (\.\.)(\.)?
PLUMIN       \'\+\-\'
integer      [+-]?[0-9]+
real         [+-]?[0-9]+\.[0-9]+
FLOAT        ({integer}|{real})([eE]{integer})?
EXTENSION    [<>~]


Examples of valid SEG representations:
--------------------------------------

Any number	(rules 5,6) -- creates a zero-length segment (a point,
		if you will)

~5.0		(rules 5,7) -- creates a zero-length segment AND records 
		'~' in the data. This notation reads 'approximately 5.0', 
		but its meaning is not recognized by the code. It is ignored 
		until you get the value back. View it is a short-hand comment.

<5.0		(rules 5,7) -- creates a point at 5.0; '<' is ignored but 
		is preserved as a comment

>5.0		(rules 5,7) -- creates a point at 5.0; '>' is ignored but
		is preserved as a comment

5(+-)0.3
5'+-'0.3	(rules 1,8) -- creates an interval '4.7..5.3'. As of this 
		writing (02/09/2000), this mechanism isn't completely accurate 
		in determining the number of significant digits for the 
		boundaries. For example, it adds an extra digit to the lower
		boundary if the resulting interval includes a power of ten:

		template1=> select '10(+-)1'::seg as seg;
		      seg
		---------
		9.0 .. 11 -- should be: 9 .. 11

		Also, the (+-) notation is not preserved: 'a(+-)b' will 
		always be returned as '(a-b) .. (a+b)'. The purpose of this 
		notation is to allow input from certain data sources without 
		conversion.

50 .. 		(rule 3) -- everything that is greater than or equal to 50

.. 0		(rule 4) -- everything that is less than or equal to 0

1.5e-2 .. 2E-2 	(rule 2) -- creates an interval (0.015 .. 0.02)

1 ... 2		The same as 1...2, or 1 .. 2, or 1..2 (space is ignored).
		Because of the widespread use of '...' in the data sources,
		I decided to stick to is as a range operator. This, and
		also the fact that the white space around the range operator
		is ignored, creates a parsing conflict with numeric constants 
		starting with a	decimal point.


Examples of invalid SEG input:
------------------------------

.1e7		should be: 0.1e7
.1 .. .2	should be: 0.1 .. 0.2
2.4 E4		should be: 2.4E4

The following, although it is not a syntax error, is disallowed to improve
the sanity of the data:

5 .. 2		should be: 2 .. 5


PRECISION
=========

The segments are stored internally as pairs of 32-bit floating point
numbers. It means that the numbers with more than 7 significant digits
will be truncated.

The numbers with less than or exactly 7 significant digits retain their
original precision. That is, if your query returns 0.00, you will be
sure that the trailing zeroes are not the artifacts of formatting: they
reflect the precision of the original data. The number of leading
zeroes does not affect precision: the value 0.0067 is considered to
have just 2 significant digits.


USAGE
=====

The access method for SEG is a GiST (gist_seg_ops), which is a
generalization of R-tree. GiSTs allow the postgres implementation of
R-tree, originally encoded to support 2-D geometric types such as
boxes and polygons, to be used with any data type whose data domain
can be partitioned using the concepts of containment, intersection and
equality. In other words, everything that can intersect or contain
its own kind can be indexed with a GiST. That includes, among other
things, all geometric data types, regardless of their dimensionality
(see also contrib/cube).

The operators supported by the GiST access method include:


[a, b] << [c, d]	Is left of

	The left operand, [a, b], occurs entirely to the left of the
	right operand, [c, d], on the axis (-inf, inf). It means,
	[a, b] << [c, d] is true if b < c and false otherwise

[a, b] >> [c, d]	Is right of

	[a, b] is occurs entirely to the right of [c, d]. 
	[a, b] >> [c, d] is true if b > c and false otherwise

[a, b] &< [c, d]	Over left

	The segment [a, b] overlaps the segment [c, d] in such a way
	that a <= c <= b and b <= d

[a, b] &> [c, d]	Over right

	The segment [a, b] overlaps the segment [c, d] in such a way
	that a > c and b <= c <= d

[a, b] = [c, d]		Same as

	The segments [a, b] and [c, d] are identical, that is, a == b
	and c == d

[a, b] @ [c, d]		Contains

	The segment [a, b] contains the segment [c, d], that is, 
	a <= c and b >= d

[a, b] @ [c, d]		Contained in

	The segment [a, b] is contained in [c, d], that is, 
	a >= c and b <= d

Although the mnemonics of the following operators is questionable, I
preserved them to maintain visual consistency with other geometric
data types defined in Postgres.

Other operators:

[a, b] < [c, d]		Less than
[a, b] > [c, d]		Greater than

	These operators do not make a lot of sense for any practical
	purpose but sorting. These operators first compare (a) to (c),
	and if these are equal, compare (b) to (d). That accounts for
	reasonably good sorting in most cases, which is useful if
	you want to use ORDER BY with this type

There are a few other potentially useful functions defined in seg.c 
that vanished from the schema because I stopped using them. Some of 
these were meant to support type casting. Let me know if I was wrong: 
I will then add them back to the schema. I would also appreciate 
other ideas that would enhance the type and make it more useful.

For examples of usage, see sql/seg.sql

NOTE: The performance of an R-tree index can largely depend on the
order of input values. It may be very helpful to sort the input table
on the SEG column (see the script sort-segments.pl for an example)


CREDITS
=======

My thanks are primarily to Prof. Joe Hellerstein
(http://db.cs.berkeley.edu/~jmh/) for elucidating the gist of the GiST
(http://gist.cs.berkeley.edu/). I am also grateful to all postgres
developers, present and past, for enabling myself to create my own
world and live undisturbed in it. And I would like to acknowledge my
gratitude to Argonne Lab and to the U.S. Department of Energy for the
years of faithful support of my database research.


------------------------------------------------------------------------
Gene Selkov, Jr.
Computational Scientist
Mathematics and Computer Science Division
Argonne National Laboratory
9700 S Cass Ave.
Building 221
Argonne, IL 60439-4844

selkovjr@mcs.anl.gov

