seg The seg module contains the code for the user-defined type, SEG, representing laboratory measurements as floating point intervals. 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) 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. 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 RANGE (\.\.)(\.)? PLUMIN \'\+\-\' integer [+-]?[0-9]+ real [+-]?[0-9]+\.[0-9]+ FLOAT ({integer}|{real})([eE]{integer})? EXTENSION [<>~] 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(+-)0.35'+-'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: postgres=> 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. .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 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. The access method for SEG is a GiST index (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 a > d and false otherwise [a, b] &< [c, d] Overlaps or is left of This might be better read as "does not extend to right of". It is true when b <= d. [a, b] &> [c, d] Overlaps or is right of This might be better read as "does not extend to left of". It is true when a >= c. [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] Overlaps The segments [a, b] and [c, d] overlap. [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 (Before PostgreSQL 8.2, the containment operators @> and <@ were respectively called @ and ~. These names are still available, but are deprecated and will eventually be retired. Notice that the old names are reversed from the convention formerly followed by the core geometric datatypes!) 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) My thanks are primarily to Prof. Joe Hellerstein () for elucidating the gist of the GiST (). 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