Unity 1.0
Parser for unit strings

The Unity package provides a parser for unit strings.
NOTE: The library should currently be regarded as beta quality: the implementation and interface may change in response to experience and comments.
This is the unity parser (version 1.0), which is a C library to help parse unit specification strings such as W.mm**2
. There is also an associated Java class library which uses the same grammars. For more details, see the library's home page; the source is on bitbucket.
As well as parsing various unit strings, the library can also serialise a parsed expression in various formats, including the four formats that it can parse, a LaTeX version with name latex
(which uses the {siunitx}
package) and a debug
format which lists the parsed unit in an unambiguous, but not otherwise useful, form.
You can parse units using a couple of different syntaxes since, unfortunately, there is no general consensus on which syntax the world should agree on. The ones supported (and their names within this library) are as follows :
See also:
Each of these has an associated writer, which allows you to write a parsed UnitExpression to a string, in a format which should be conformant with the particular syntax's standard. See unity_write_formatted.
In addition, there is a latex writer, which produces a formatted form for the the expression, in a form suitable for inclusion in a LaTeX document, using the siunitx
package. To use the resulting output in a LaTeX document, include the following in the preamble of the file:
\usepackage{siunitx} \DeclareSIQualifier\solar{$\odot$}
You may add any siunitx
options that seem convenient, and you may omit the declaration of \solar
if the units in the document do not include the various solar ones.
The parsing is permissive, to the extent that it permits nonrecognised and deprecated units. The result of the parse may be checked for conformance with one or other standard using the functions unity_check_unit and unity_check_expression. Note that SI prefixes are still noticed for unrecognised units: thus furlongs/fortnight
will be parsed as femtourlongs per femtoortnight. The same is not true of recognised units: a pixel/s
is a pixel per second, and does not involve a picoixel.
If you want to experiment with the library, build the program src/c/unity
(in the distribution):
% ./unity icds oogip 'mm2/s' mm**2 /s % ./unity icds ofits v mm/s mm s1 check: all units recognised? yes check: all units recommended? yes check: all units satisfy constraints? yes % ./unity ifits ocds v 'merg/s' merg/s check: all units recognised? yes check: all units recommended? no check: all units satisfy constraints? no % ./unity icds ofits v 'merg/s' merg s1 check: all units recognised? no check: all units recommended? no check: all units satisfy constraints? yes
In the latter cases, the v
option validates the input string against various constraints. The expression mm/s
is completely valid in all the syntaxes. In the FITS syntax, the erg
is a recognised unit, but it is deprecated; although it is recognised, it is not permitted to have SI prefixes. In the CDS syntax, the erg
is neither recognised nor (a fortiori) recommended; since there are no constraints on it in this syntax, it satisfies all of them (this latter behaviour is admittedly slightly counterintuitive).
The four supported grammars have a fair amount in common, but the differences are nonetheless significant enough that they require separate grammars. Important differences are in the number of solidi they allow in the units specifications, and the symbols they use for products and powers.
Current limitations:
In the grammars below, the common terminals are as follows:
[+]?[19][09]*\\.[09]+
, so that there are no exponents allowed; the signed integers have a nonoptional leading sign, the unsigned don't There are some other terminals used in some grammars. See the VOUnits specification for further details.
input: complete_expression  scalefactor complete_expression  scalefactor WHITESPACE complete_expression  division unit_expression ;
complete_expression: product_of_units  product_of_units division unit_expression ;
product_of_units: unit_expression  product_of_units product unit_expression ;
unit_expression: term // m(2) is m^2, not function application  STRING parenthesized_number  function_application  OPEN_P complete_expression CLOSE_P ;
function_application: STRING OPEN_P complete_expression CLOSE_P ;
scalefactor: LIT10 power numeric_power  LIT10 SIGNED_INTEGER ;
division: DIVISION;
term: unit  unit numeric_power  unit power numeric_power ;
unit: STRING ;
power: CARET  STARSTAR ;
numeric_power: integer  parenthesized_number ;
parenthesized_number: OPEN_P integer CLOSE_P  OPEN_P FLOAT CLOSE_P  OPEN_P integer division UNSIGNED_INTEGER CLOSE_P ;
integer: SIGNED_INTEGER  UNSIGNED_INTEGER;
product: WHITESPACE  STAR  DOT;
input: complete_expression  scalefactor complete_expression  scalefactor WHITESPACE complete_expression ;
complete_expression: product_of_units ;
product_of_units: unit_expression  division unit_expression  product_of_units product unit_expression  product_of_units division unit_expression ;
unit_expression: term  function_application  OPEN_P complete_expression CLOSE_P ;
function_application: STRING OPEN_P complete_expression CLOSE_P ;
scalefactor: LIT10 power numeric_power  LIT10  FLOAT ;
division: DIVISION  WHITESPACE DIVISION  WHITESPACE DIVISION WHITESPACE  DIVISION WHITESPACE;
term: unit  unit power numeric_power ;
unit: STRING ;
power: STARSTAR;
numeric_power: UNSIGNED_INTEGER  FLOAT  parenthesized_number ;
parenthesized_number: OPEN_P integer CLOSE_P  OPEN_P FLOAT CLOSE_P  OPEN_P integer division UNSIGNED_INTEGER CLOSE_P ;
integer: SIGNED_INTEGER  UNSIGNED_INTEGER;
product: WHITESPACE  STAR  WHITESPACE STAR  WHITESPACE STAR WHITESPACE  STAR WHITESPACE;
This is quite similar to the OGIP grammar, but with more restrictions.
The CDSFLOAT
terminal is a string matching the regular expression [09]+\\.[09]+x10[+][09]+
(that is, something resembling 1.5x10+11
). The termainals OPEN_SQ
and CLOSE_SQ
are opening and closing square brackets [...]
.
input: complete_expression  scalefactor complete_expression ;
complete_expression: product_of_units ;
product_of_units: unit_expression  division unit_expression  product_of_units product unit_expression  product_of_units division unit_expression ;
unit_expression: term  function_application  OPEN_P complete_expression CLOSE_P ;
function_application: OPEN_SQ complete_expression CLOSE_SQ ;
scalefactor: LIT10 power numeric_power  LIT10 SIGNED_INTEGER  UNSIGNED_INTEGER  LIT10  CDSFLOAT  FLOAT ;
division: DIVISION;
term: unit  unit numeric_power ;
unit: STRING  PERCENT ;
power: STARSTAR;
numeric_power: integer ;
integer: SIGNED_INTEGER  UNSIGNED_INTEGER;
product: DOT;
The VOUFLOAT
and QUOTED_STRING
features are extensions beyond the other grammars. These aside, this syntax is a strict subset of the FITS and CDS grammars, in the sense that any VOUnit unit string, without these extensions, is a valid FITS and CDS string, too), and it is almost a subset of the OGIP grammar, except that it uses the dot for multiplication rather than star.
The VOUFLOAT
terminal is a string matching either of the regular expressions 0\\.[09]+([eE][+]?[09]+)?
or [19][09]*(\\.[09]+)?([eE][+]?[09]+)?
(that is, something resembling, for example, 0.123
or 1.5e+11
). Also QUOTED_STRING
is a STRING
enclosed in single quotes '...'
.
input: complete_expression  scalefactor complete_expression ;
complete_expression: product_of_units  product_of_units division unit_expression ;
product_of_units: unit_expression  product_of_units product unit_expression ;
unit_expression: term  function_application  OPEN_P complete_expression CLOSE_P ;
function_application: STRING OPEN_P complete_expression CLOSE_P ;
scalefactor: LIT10 power numeric_power  LIT10  VOUFLOAT ;
division: DIVISION;
term: unit  unit power numeric_power ;
unit: STRING  QUOTED_STRING  STRING QUOTED_STRING ;
power: STARSTAR;
numeric_power: integer  parenthesized_number ;
parenthesized_number: OPEN_P integer CLOSE_P  OPEN_P FLOAT CLOSE_P  OPEN_P integer division UNSIGNED_INTEGER CLOSE_P ;
integer: SIGNED_INTEGER  UNSIGNED_INTEGER;
product: DOT;