# Package uk.me.nxg.unity

package uk.me.nxg.unity
The Unity package provides a parser for unit strings.

This is the unity parser (version 1.1, released 2023 October 22), which is a Java class library to help parse unit specification strings such as `W.mm**-2`. There is also an associated C library, which uses the same grammars. For more details, see the library's home page; and repository.

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.

## Parsing Units

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 are as follows (cf `Syntax` for the list of parsers) :

fits
  See FITS, 3.0 Sect.4.3 (W.D. Pence et al., A&A 524, A42, 2010); v4.0 Sect.4.3 (FITS standards page)); and further comments in the FITS WCS IV paper.
ogip
  OGIP memo OGIP/93-001, 1993
cds
  Standards for Astronomical Catalogues, Version 2.0, section 3.2, 2000
vounits
  IVOA VOUnits Recommendation

See also:

- The IAU style manual, section 5.1 (1989) is by now rather old, but appears to be one of the few existing standards for units, specific to astronomy.
- ISO/IEC 80000 (parts 1–13) describes a variety of units, including the specification of the 'binary' prefixes kibi, mebi, and so on (see ISO/IEC 80000-13 Sect.4, and IEEE standard 1541-2002).
- The VOUnits Recommendation discusses various tradeoffs and conflicting specifications, at some length.

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 `UnitExpr.toString()`.

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 non-recognised and deprecated units. The result of the parse may be checked for conformance with one or other standard using the methods `UnitExpr.allUnitsRecognised()`, `UnitExpr.allUnitsRecommended(uk.me.nxg.unity.Syntax)` and `UnitExpr.allUsageConstraintsSatisfied(uk.me.nxg.unity.Syntax)`. Note that SI prefixes are still noticed for unrecognised units: thus `furlongs/fortnight` will be parsed as femto-urlongs per femto-ortnight. The same is not true of recognised units: a `pixel/s` is a pixel per second, and does not involve a pico-ixel.

### Known units

The various unit syntaxes have different sets of ‘known units’, namely units, and unit abbreviations, which the syntax blesses as recommended, or at least acknowledged. The list of knowns units in the various syntaxes is below.

Much of the unit information, such as unit names and dimensions, is derived from the QUDT unit ontology which (from its self-description) was ‘developed for the NASA Exploration Initiatives Ontology Models (NExIOM) project, a Constellation Program initiative at the AMES Research Center (ARC).’

## Demo

If you want to experiment with the library, you can do so using the jar file:

        % java -jar unity.jar -icds -oogip 'mm2/s'
        mm**2 /s
        % java -jar unity.jar -icds -ofits -v mm/s
        mm s-1
        check: all units recognised?           yes
        check: all units recommended?          yes
        check: all units satisfy constraints?  yes
        % java -jar unity.jar -ifits -ocds -v 'merg/s'
        merg/s
        check: all units recognised?           yes
        check: all units recommended?          no
        check: all units satisfy constraints?  no
        % java -jar unity.jar -icds -ofits -v 'merg/s'
        merg s-1
        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).

## Grammars supported

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.

Note that in each of the grammars here, the empty string is not a valid units string – in particular, it is not taken to indicate a dimensionless quantity. If a particular context wishes to interpret such a string as indicating a dimensionless quantity, or perhaps instead indicating ‘units unknown’, then it should handle that case separately. To obtain what would be the result of such a parse, use the method `UnitExpr.getDimensionlessExpression()`. The VOUnits syntax, though it also deems the empty string to be invalid, recognises the string `"1"` as indicating a dimensionless quantity.

Current limitations:

- Currently ignores some of the odder unit restrictions (such as the OGIP requirement that 'Crab' can have a 'milli' prefix, but no other SI prefixes)

In the grammars below, the common terminals are as follows:

- WHITESPACE: one or more whitespace characters (in the grammars, whitespace is not permitted unless it matches a WHITESPACE terminal)
- STAR, DOT: a star or a dot, generally used to indicate multiplication
- DIVISION: a slash
- STARSTAR, CARET: the former is "**", the latter "^"; both are used to indicate exponentiation
- OPEN_P, CLOSE_P: open and close parentheses
- INTEGER, FLOAT: numbers; the syntax of FLOAT is `[+-]?[1-9][0-9]*\.[0-9]+` so that there are no exponents allowed; the signed integers have a non-optional leading sign, the unsigned don't
- STRING: a sequence of one or more upper- and lower-case ASCII letters, `[a-zA-Z]+`
- LIT10, LIT1: the literal strings "10" and "1"

There are some other terminals used in some grammars. See the VOUnits specification for further details.

### The FITS grammar

    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;

### The OGIP grammar

    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;

### The CDS grammar

This is quite similar to the OGIP grammar, but with more restrictions.

The `CDSFLOAT` terminal is a string matching the regular expression `[0-9]+\.[0-9]+x10[-+][0-9]+` (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 VOUnits grammar

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\.[0-9]+([eE][+-]?[0-9]+)?` or `[1-9][0-9]*(\.[0-9]+)?([eE][+-]?[0-9]+)?` (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
            | LIT1
            ;

    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  function_operand CLOSE_P ;
    function_operand: complete_expression
            | scalefactor complete_expression ;

    scalefactor: LIT10 power numeric_power
            | LIT10
            | LIT1
            | VOUFLOAT
            ;

    division: DIVISION;

    term: unit
            | unit power numeric_power
            ;

    unit: STRING
            | QUOTED_STRING
            | STRING QUOTED_STRING
            | PERCENT
            ;

    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;

### The lists of known units

Below are the lists of known units, taken from Pence et al, the OGIP specification, and the CDS specification. In the columns below, a `1` indicates that the unit is permitted, `s` indicates that SI prefixes are allowed, `b` that IEC binary prefixes are allowed, `d` that the unit is deprecated in some way, and `p` that the symbol is the preferred one in this syntax (where there is more than one symbol that maps to this unit). The CDS standard doesn’t indicate which units may or may not take SI prefixes: in the table below, we generally follow the FITS prescription, except where the CDS specification positively suggests otherwise. Where there are two possible abbreviations for a unit in a syntax, (eg FITS allows ‘pixel’ and ‘pix’), we prefer the one marked with a ‘p’.

The lists of known units
unit | meaning | FITS | OGIP | CDS | VOUnits
% | qudt:Percent |  |  | 1 | 1
A | qudt:Ampere | 1s | 1s | 1s | 1s
a | unity:JulianYear | 1ps |  | 1s | 1s
adu | unity:ADU | 1 |  |  | 1s
Angstrom | qudt:Angstrom | 1d |  | 1 | 1dp
angstrom | qudt:Angstrom |  | 1 |  | 1d
arcmin | qudt:ArcMinute | 1 | 1 | 1 | 1s
arcsec | qudt:ArcSecond | 1 | 1 | 1s | 1s
AU | qudt:AstronomicalUnit | 1 | 1 | 1 | 1p
au | qudt:AstronomicalUnit |  |  |  | 1
Ba | unity:BesselianYear | 1d |  |  | 1d
barn | qudt:Barn | 1sd | 1 | 1s | 1sd
beam | unity:Beam | 1 |  |  | 1s
bin | unity:DistributionBin | 1 | 1 |  | 1s
bit | qudt:Bit | 1s |  | 1s | 1sb
byte | qudt:Byte | 1s | 1 | 1s | 1sbp
B | qudt:Byte |  |  |  | 1sb
C | qudt:Coulomb | 1s | 1s | 1s | 1s
cd | qudt:Candela | 1s | 1s | 1s | 1s
chan | unity:DetectorChannel | 1 | 1 |  | 1s
count | qudt:Number | 1 | 1 |  | 1sp
Crab | unity:Crab |  | 1s |  |
ct | qudt:Number | 1 |  | 1 | 1s
cy | unity:JulianCentury | 1 |  |  |
d | qudt:Day | 1 | 1 | 1 | 1s
dB | qudt:Decibel |  |  |  | 1
D | qudt:Debye | 1 |  | 1 | 1s
deg | qudt:DegreeAngle | 1 | 1 | 1 | 1s
erg | qudt:Erg | 1d | 1 |  | 1sd
eV | qudt:ElectronVolt | 1s | 1s | 1s | 1s
F | qudt:Farad | 1s | 1s | 1s | 1s
g | qudt:Gram | 1s | 1s | 1s | 1s
G | qudt:Gauss | 1sd | 1 |  | 1sd
H | qudt:Henry | 1s | 1s | 1s | 1s
h | qudt:Hour | 1 | 1 | 1 | 1s
Hz | qudt:Hertz | 1s | 1s | 1s | 1s
J | qudt:Joule | 1s | 1s | 1s | 1s
Jy | unity:Jansky | 1s | 1s | 1s | 1s
K | qudt:Kelvin | 1s | 1s | 1s | 1s
lm | qudt:Lumen | 1s | 1s | 1s | 1s
lx | qudt:Lux | 1s | 1s | 1s | 1s
lyr | qudt:LightYear | 1 | 1 |  | 1s
m | qudt:Meter | 1s | 1s | 1s | 1s
mag | unity:StellarMagnitude | 1s | 1 | 1s | 1s
mas | unity:MilliArcSecond | 1 |  | 1 | 1
min | qudt:MinuteTime | 1 | 1 | 1 | 1s
mol | qudt:Mole | 1s | 1s | 1s | 1s
N | qudt:Newton | 1s | 1s | 1s | 1s
Ohm | qudt:Ohm | 1s |  | 1s | 1s
ohm | qudt:Ohm |  | 1s |  |
Pa | qudt:Pascal | 1s | 1s | 1s | 1s
pc | qudt:Parsec | 1s | 1s | 1s | 1s
ph | unity:Photon | 1 |  |  | 1s
photon | unity:Photon | 1p | 1 |  | 1sp
pix | unity:Pixel | 1 |  | 1 | 1s
pixel | unity:Pixel | 1p | 1 |  | 1sp
R | unity:Rayleigh | 1s |  |  | 1s
rad | qudt:Radian | 1s | 1s | 1s | 1s
Ry | unity:Rydberg | 1 |  | 1s | 1s
s | qudt:SecondTime | 1s | 1s | 1s | 1s
S | qudt:Siemens | 1s | 1s | 1s | 1s
solLum | unity:SolarLuminosity | 1 |  | 1 | 1s
solMass | unity:SolarMass | 1 |  | 1 | 1s
solRad | unity:SolarRadius | 1 |  | 1 | 1s
sr | qudt:Steradian | 1s | 1s | 1s | 1s
T | qudt:Tesla | 1s | 1s | 1s | 1s
ta | qudt:YearTropical | 1d |  |  | 1d
u | qudt:UnifiedAtomicMassUnit | 1 |  |  | 1s
V | qudt:Volt | 1s | 1s | 1s | 1s
voxel | unity:Voxel | 1 | 1 |  | 1s
W | qudt:Watt | 1s | 1s | 1s | 1s
Wb | qudt:Weber | 1s | 1s | 1s | 1s
yr | unity:JulianYear | 1s | 1 | 1sp | 1sp

Class
Description
Dimensions
A dimensions specification is a record of the measurement dimensions of a quantity.
Dimensions.BaseQuantity
The base quantities in the International System of Quantites.
FunctionDefinition
Describes a ‘known’' function.
FunctionDefinitionMap
Provides a mapping from function abbreviations to function definitions.
FunctionOfUnit
Represents a function of a unit, such as `log(m)`.
OneUnit
A single unit.
SimpleBinaryUnit
A unit which has a prefix which is a round power of 1024.
SimpleDecimalUnit
A unit which has a prefix which is a round power of 1000.
SimpleUnit
A single simple unit, such as 'kg'.
Syntax
An enumeration of the allowed syntaxes within the Unity libary.
UnitDefinition
Describes a unit.
UnitDefinitionMap
Provides a mapping from unit abbreviations to unit definitions.
UnitExpr
A parsed unit expression.
UnitParser
A parser for unit strings.
UnitParser.Lexeme
A single lexeme.
UnitParserException
Thrown when an expression cannot be parsed.
UnitRepresentation
A description of the way that a unit is represented in a particular syntax.
UnwritableExpression
Thrown when an expression cannot be written in a particular syntax.
Version
Manage version information