units.man

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.\"Copyright (C) 1996, 1997, 1999, 2000, 2001, 2002, 2004, 2005, 2007 Free Software Foundation, Inc
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.TH UNITS 1   "25 Sep 2007"
.SH NAME
units - unit conversion program
.SH OVERVIEW OF `UNITS'
The `units' program converts quantities expressed in various scales
to their equivalents in other scales.  The `units' program can
handle multiplicative scale changes as well as nonlinear
conversions such as Fahrenheit to 
Celsius.
Temperature conversions require a special
syntax.  
See the examples below.  
.PP
The units are defined in an external data file.  You can use the
extensive data file that comes with this program, or you can 
provide your own data file to suit your needs.  
.PP
You can use the program interactively 
with prompts, or you can use it
from the command line.  
.PP
.SH INTERACTING WITH `UNITS'
To invoke units for interactive use, type `units' at your shell
prompt.  The program will print something like this:
.PP
.nf
    2131 units, 53 prefixes, 24 nonlinear units
    
    You have:
.fi
.PP
At the `You have:' prompt, type the quantity and units that
you are converting \fIfrom\fR.  For example, if you want to convert ten
meters to feet, type `10 meters'.  Next, `units' will print
`You want:'.  You should type the type of units you want to convert
\fIto\fR.  To convert to feet, you would type `feet'.  Note that if
the readline library was compiled in then the tab key can be used to
complete unit names.  See \fIReadline support\fR, for more information
about readline.  
.PP
The answer will be displayed in two ways.  The first line of output,
which is marked with a `*' to indicate multiplication, 
gives the result of the conversion you have asked for.  The second line
of output, which is marked with a `/' to indicate division, gives
the inverse of the conversion factor.  If you convert 10 meters to feet,
`units' will print
.PP
.nf
        * 32.808399
        / 0.03048
.fi
.PP
which tells you that 10 meters equals about 32.8 feet.  
The second number gives the conversion in the opposite direction. 
In this case, it tells you that 1 foot is equal to about  
0.03 dekameters since the dekameter is 10 meters.  
It also tells you that 1/32.8 is about .03.    
.PP
The `units' program prints the inverse because sometimes it is a
more convenient number.  In the example above, for example, the inverse
value is an exact conversion: a foot is exactly .03048 dekameters.  
But the number given the other direction is inexact.  
.PP
If you try to convert grains to pounds, you will see the following:
.PP
.nf
    You have: grains
    You want: pounds
            * 0.00014285714
            / 7000
.fi
.PP
From the second line of the output you can immediately see that a grain
is equal to a seven thousandth of a pound.  This is not so obvious from
the first line of the output. 
If you find  the output format  confusing, try using the
`--verbose' option:
.PP
.nf
    You have: grain
    You want: aeginamina
            grain = 0.00010416667 aeginamina
            grain = (1 / 9600) aeginamina
.fi
.PP
If you request a conversion between units which measure reciprocal
dimensions, then `units' will display the conversion results with an extra
note indicating that reciprocal conversion has been done:
.PP
.nf
    You have: 6 ohms
    You want: siemens
            reciprocal conversion
            * 0.16666667
            / 6
.fi
.PP
Reciprocal conversion can be suppressed by using the `--strict' option.
As usual, use  
the `--verbose' option to get more comprehensible output:
.PP
.nf
    You have: tex
    You want: typp
            reciprocal conversion
            1 / tex = 496.05465 typp
            1 / tex = (1 / 0.0020159069) typp

    You have: 20 mph
    You want: sec/mile
            reciprocal conversion
            1 / 20 mph = 180 sec/mile
            1 / 20 mph = (1 / 0.0055555556) sec/mile
.fi
.PP
If you enter incompatible unit types, the `units' program will
print a message indicating that the units are not conformable and
it will display the reduced form for each unit:
.PP
.nf
    You have: ergs/hour
    You want: fathoms kg^2 / day 
    conformability error
            2.7777778e-11 kg m^2 / sec^3
            2.1166667e-05 kg^2 m / sec
.fi
.PP
If you only want to find the reduced form or definition of a unit,
simply press return at the `You want:' prompt.  Here is an example:
.PP
.nf
    You have: jansky
    You want: 
            Definition: fluxunit = 1e-26 W/m^2 Hz = 1e-26 kg / s^2
.fi
.PP
The output from `units' indicates that the jansky is defined to be
equal to a fluxunit which in turn is defined to be a certain combination
of watts, meters, and hertz.  The fully reduced (and in this case
somewhat more cryptic) form appears on the far right.  
.PP
Some named units are treated as dimensionless in some situations.
These include the radian and steradian.  These units will be treated
as equal to 1 in units conversions.  Power is equal to torque times
angular velocity.  This conversion can only be performed if the radian
is dimensionless.  
.PP
.nf
    You have: (14 ft lbf) (12 radians/sec)
    You want: watts
            * 227.77742
            / 0.0043902509
.fi
.PP
Note that named dimensionaless units are not treated as dimensionless
in other contexts.  They cannot be used as exponents 
so for example, `meter^radian' is not allowed.  
.PP
If you want a list of options you can type `?' at the 
`You want:' prompt.  The program will display a list of named
units which are conformable with the unit that you entered at
the `You have:' prompt above.  Note that conformable unit
combinations will not appear on this list.  
.PP
Typing `help' at either prompt displays a short help message. 
You can also type `help' followed by a unit name.  This will
invoke a pager on the units data base at the point where that unit
is defined.  You can read the definition and comments that may
give more details or historical information about the unit. 
.PP
Typing `search text' will display a list of all of the units whose
names contain `text' as a substring along with their definitions.
This may help in the case where you aren't sure of the right unit
name.
.PP
.SH USING `UNITS' NON-INTERACTIVELY
The `units' program can perform units conversions non-interactively
from the command line.  To do this, type the command, type the
original units expression, and type the new units you want. 
You will probably need to protect the units expressions from
interpretation by the shell using single quote characters. 
.PP
If you type
.PP
.nf
    units '2 liters' 'quarts'
.fi
.PP
then `units' will print
.PP
.nf
        * 2.1133764
        / 0.47317647
.fi
.PP
and then exit.
The output tells you that 2 liters is about 2.1 quarts, or alternatively that
a quart is about 0.47 times 2 liters.  
.PP
If the conversion is successful, then `units' will return success (0)
to the calling environment.  If `units' is given non-conformable
units to convert, it will print a message giving the reduced form of
each unit and it will return failure (nonzero) to the calling environment. 
.PP
When `units' is invoked with only one argument, it will print out
the definition of the specified unit.  It will return failure if the
unit is not defined and success if the unit is defined.
.PP
.SH UNIT EXPRESSIONS
In order to enter more complicated units or fractions, 
you will need to use operations such as powers, products and division.  
Powers of units can be specified using the `^' character as shown in
the following example, or by simple concatenation: `cm3' is equivalent to 
`cm^3'.
If the exponent is more than one digit, the `^' is required.  An
exponent like `2^3^2' is evaluated right to left.  The `^'
operator has the second highest precedence.  The `**' operator is
provided as an alternative exponent operator.  
.PP
.nf
    You have: cm^3
    You want: gallons
            * 0.00026417205
            / 3785.4118

    You have: arabicfoot * arabictradepound * force
    You want: ft lbf  
            * 0.7296
            / 1.370614
.fi
.PP
Multiplication of units can be specified by using spaces, or an asterisk
(`*').  If `units' is invoked with the `--product'
option then the hyphen (`-') also acts as a multiplication
operator.  Division of units is indicated 
by the slash (`/') or by `per'.  
.PP
.nf
    You have: furlongs per fortnight
    You want: m/s  
            * 0.00016630986
            / 6012.8727
.fi
.PP
Historically, multiplication in units was assigned a higher precedence
than division.  This disagrees with the usual precedence rules which
give multiplication and division equal precedence, and it has been a
source of confusion for people who think of units as a calculator.
.PP
By default, multiplication using the star (`*') now has the same
precedence as division and hence follows the usual precedence rules.
If units is invoked with the the `--oldstar' option then then the
old behavior is activated and `*' will have the same precedence
as the other multiplication operators described next.
.PP
Multiplication using a space or using the hyphen has a higher
precedence than division and is evaluated left to right.  So @samp{m/s
s/day} is equivalent to `m / s s day' and has dimensions of
length per time cubed.  Similarly, `1/2 meter' refers to a unit
of reciprocal length equivalent to .5/meter, which is probably not
what you would intend if you entered that expression.  
.PP
You can indicate division of numbers with the vertical dash
(`|'), so if you wanted half a meter you could write @samp{1|2
meter}.  This operator has the highest precedence so the square root
of two thirds could be written `2|3^1|2'.
.PP
.nf
    You have: 1|2 inch
    You want: cm
            * 1.27
            / 0.78740157
.fi
.PP
Parentheses can be used for grouping as desired.  
.PP
.nf
    You have: (1/2) kg / (kg/meter)
    You want: league
            * 0.00010356166
            / 9656.0833
.fi
.PP
Prefixes are defined separately from base units.  In order to get
centimeters, the units database defines `centi-' and `c-' as
prefixes.  Prefixes can appear alone with no unit following them.  
An exponent applies only to the immediately preceding unit and its
prefix so that `cm^3' or `centimeter^3' refer to cubic centimeters 
but `centi*meter^3' refers to hundredths of cubic meters.  Only one
prefix is permitted per unit, so `micromicrofarad' will fail, but
`micro*microfarad' will work, as will `micro microfarad'..  
.PP
For `units', numbers are just another kind of unit.  They can
appear as many times as you like and in any order in a unit expression.
For example, to find the volume of a box which is 2 ft by 3 ft by 12 ft
in steres, you could do the following:
.PP
.nf
    You have: 2 ft 3 ft 12 ft
    You want: stere
            * 2.038813
            / 0.49048148
    
    You have: $ 5 / yard
    You want: cents / inch
            * 13.888889
            / 0.072
.fi
.PP
And the second example shows how the dollar sign in the units conversion
can precede the five.  Be careful:  `units' will interpret
`$5' with no space as equivalent to dollars^5.  
.PP
Outside of the SI system, it is often desirable to add values of
different units together.  You may also wish to use `units' as a
calculator that keeps track of units.  Sums of conformable units are written with
the `+' character. 
.PP
.nf
    You have: 2 hours + 23 minutes + 32 seconds
    You want: seconds
            * 8612
            / 0.00011611705
    
    You have: 12 ft + 3 in
    You want: cm
            * 373.38
            / 0.0026782366

    You have: 2 btu + 450 ft lbf
    You want: btu
            * 2.5782804
            / 0.38785542
.fi
.PP
The expressions which are added together must reduce to identical
expressions in primitive units, or an error message will be displayed:
.PP
.nf
    You have: 12 printerspoint + 4 heredium
                                          ^
    Illegal sum of non-conformable units
.fi
.PP
Historically `-' has been used for products of units, which complicates
its iterpretation in `units'.  Because `units' provides
several other ways to obtain unit products, and because `-' is a
subtraction operator in general algebraic expressions, `units'
treats the binary `-' as a subtraction operator by default.  This
behavior can be altered using the `--product' option which
causes `units' to treat the binary `-' operator as a product
operator.  Note that when `-' is a multiplication operator it has
the same precedence as `*', but when `-' is a subtraction operator
it has the lower precedence as the addition operator.  
.PP
When `-' is used as a unary operator it negates its operand.
Regardless of the `units' options, if 
`-' appears after `(' or after
`+' then it will act as a negation operator.  So you can always compute 20
degrees minus 12 minutes by entering `20 degrees + -12 arcmin'.
You must use this construction when you define new units because you
cannot know what options will be in force when your definition is
processed. 
.PP
The `+' character sometimes appears in exponents like
`3.43e+8'.  This leads to an ambiguity in an expression like
`3e+2 yC'.  The unit `e' is a small unit of charge, so this
can be regarded as equivalent to `(3e+2) yC' or `(3 e)+(2 yC)'.  
This ambiguity is resolved by always interpreting `+' as part
of an exponent if possible.
.PP
Several built in functions are provided: `sin', `cos',
`tan', `ln', `log', `log2', `exp', `acos',
`atan' and `asin'.  The `sin', `cos', and `tan'
functions require either a dimensionless argument or an argument with
dimensions of angle.  
.PP
.nf
    You have: sin(30 degrees)
    You want: 
            Definition: 0.5

    You have: sin(pi/2)
    You want:  
            Definition: 1

    You have: sin(3 kg)
                      ^
    Unit not dimensionless
.fi
.PP
The other functions on the list require dimensionless arguments.  The
inverse trigonometric functions return arguments with dimensions of
angle.
.PP
If you wish to take roots of units, you may use the `sqrt' or
`cuberoot' functions.  These functions require that the argument
have the appropriate root.  Higher roots can  be obtained by using
fractional exponents:
.PP
.nf
    You have: sqrt(acre)
    You want: feet
            * 208.71074
            / 0.0047913202
    
    You have: (400 W/m^2 / stefanboltzmann)^(1/4)
    You have:
            Definition: 289.80882 K
    
    You have: cuberoot(hectare)
                              ^
    Unit not a root
.fi
.PP
Nonlinear units are represented using functional notation.  They make
possible nonlinear unit conversions such temperature.  This is different
from the linear units that convert temperature differences.  Note the
difference below.  The absolute temperature conversions are handled by
units starting with `temp', and you must use functional notation.
The temperature differences are done using units starting with
`deg' and they do not require functional notation.
.PP
.nf
    You have: tempF(45)
    You want: tempC
            7.2222222

    You have: 45 degF
    You want: degC
            * 25
            / 0.04
.fi
.PP
Think of `tempF(x)' not as a function but as a notation which
indicates that `x' should have units of `tempF' attached to
it.  See \fINonlinear units\fR.  The first conversion shows that if it's 45
degrees Fahrehneit outside it's 7.2 degrees Celsius.  The second
conversions indicates that a change of 45 degrees Fahrenheit corresponds
to a change of 25 degrees Celsius.
.PP
Some other examples of nonlinears units are ring size and wire gauge.  
There are numerous different gauges and ring sizes.  See the units
database for more details.  Note that wire gauges
with multiple zeroes are signified using negative numbers where two
zeroes is -1.  Alternatively, you can use the synonyms `g00',
`g000', and so on that are defined in the units database.
.PP
.nf
    You have: wiregauge(11)
    You want: inches
            * 0.090742002
            / 11.020255

    You have: brwiregauge(g00)
    You want: inches
            * 0.348
            / 2.8735632

    You have: 1 mm
    You want: wiregauge
            18.201919
.fi
.PP
.SH INVOKING `UNITS'
You invoke `units' like this:
.PP
.nf
    units [OPTIONS] [FROM-UNIT [TO-UNIT]]
.fi
.PP
If the FROM-UNIT and TO-UNIT are omitted, then the program
will use interactive prompts to determine which conversions to perform.
See \fIInteractive use\fR.
If both FROM-UNIT and TO-UNIT are given, `units' will
print the result of that single conversion and then exit.  
If only FROM-UNIT appears on the command line, `units' will
display the definition of that unit and exit.  
Units specified on the command line will need
to be quoted to protect them from shell interpretation and to group
them into two arguments.  See \fICommand line use\fR.
.PP
The following options allow you to read in an alternative units file,
check your units file, or change the output format:
.PP
.TP
.B -c, --check
Check that all units and prefixes defined in the units data file reduce
to primitive units.  Print a list of all units that
cannot be reduced.  Also display some other diagnostics about 
suspicious definitions in the units data file.  Note that only
definitions active in the current locale are checked.  
.PP
.TP
.B --check-verbose
Like the `-check' option, this option prints a list of units that
cannot be reduced.  But to help find unit  definitions that cause
endless loops, 
it lists the units as they are checked.  
If `units' hangs, then the last unit to be printed has a bad
definition.  Note that only
definitions active in the current locale are checked.  
.PP
.TP
.B -o format, --output-format format
Use the specified format for numeric output.  Format is the same
as that for the printf function in the ANSI C standard. 
For example, if you want more precision you might use `-o %.15g'. 
.PP
.TP
.B -f filename, --file filename
Instruct `units' to load the units file `filename'.  
If `filename' is the empty string (`-f "') 
then the default units file will
be loaded.  This enables you to load the default file plus a personal
units file.  Up to 25 units files may be specified on the command line.
This option overrides the `UNITSFILE' environment variable.  
.PP
.TP
.B -h, --help
Print out a summary of the options for `units'.  
.PP
.TP
.B -m, --minus
Causes `-' to be interpreted as a subtraction operator.  This is
usually the default behavior.  
.PP
.TP
.B -p, --product
Causes `-' to be interpreted as a multiplication operator when it
has two operands.  It will act as a negation operator when it has only one
operand: `(-3)'.  Note that by default `-' is treated as a
subtraction operator.
.PP
, --oldstar
Causes `*' to have the old style precedence, higher than the
precedence of division so that `1/2*3' will equal `1/6'.
.PP
, --newstar
Forces `*' to have the new (default) precedence which follows
the usual rules of algebra: the precedence of `*' is the same as
the precedence of `/', so that `1/2*3' will equal `3/2'.
.PP
, --compact
Give compact output featuring only the conversion factor.  This turns
off the `--verbose' option. 
.PP
.TP
.B -q, --quiet, --silent
Suppress prompting of the user for units and the display of statistics
about the number of units loaded.
.PP
.TP
.B -s, --strict
Suppress conversion of units to their reciprocal units.  For 
example, `units' will normally convert hertz to seconds
because these units are reciprocals of each other.  The strict option
requires that units be strictly conformable to perform a conversion, and
will give an error if you attempt to convert hertz to seconds. 
.PP
.TP
.B -1, --one-line
Give only one line of output (the forward conversion).  Do not print
the reverse conversion.  Note that if a reciprocal conversion is
performed then `units' will still print the "reciprocal
conversion" line.
.PP
.TP
.B -t, --terse
Give terse output when converting units.  This option can be used when
calling `units' from another program so that the output is easy to
parse.  This option has the combined
effect of these options:  `--strict' `--quiet' `--one-line'
`--compact'.
.PP
.TP
.B -v, --verbose
Give slightly more verbose output when converting units.  When combined
with the `-c' option this gives the same effect as
`--check-verbose'. 
.PP
.TP
.B -V, --version
Print program version number, tell whether the readline library
has been included, and give the location of the default units
data file. 
.PP
.SH UNIT DEFINITIONS
The conversion information is read from a units data file which 
is called `units.dat' and is probably located in
the `/usr/local/share' directory.  
If you invoke `units' with the `-V' option, it will print
the location of this file. 
The default
file includes definitions for all familiar units, abbreviations and
metric prefixes.  It also includes many obscure or archaic units.  
.PP
Many constants of nature are defined, including these:
.RS
.TS
l l.
pi	ratio of circumference to diameter
c	speed of light
e	charge on an electron
force	acceleration of gravity
mole	Avogadro's number
water	pressure per unit height of water
Hg	pressure per unit height of mercury
au	astronomical unit
k	Boltzman's constant
mu0	permeability of vacuum
epsilon0	permitivity of vacuum
G	gravitational constant
mach	speed of sound
.TE
.RE
The database includes atomic masses for all of the elements and numerous
other constants.  Also included are the densities of various ingredients
used in baking so that `2 cups flour_sifted' can be converted 
to `grams'.  This is not an exhaustive list.  Consult the units
data file to see the complete list, or to see the definitions that are
used.
.PP
The unit `pound' is a unit of mass.  To get force, multiply by the
force conversion unit `force' or use the shorthand `lbf'.
(Note that `g' is already taken as the standard abbreviation for
the gram.)  The unit `ounce' is also a unit of mass.  The fluid
ounce is `fluidounce' or `floz'.  British capacity units that
differ from their US counterparts, such as the British Imperial gallon,
are prefixed with `br'.  Currency is prefixed with its country
name: `belgiumfranc', `britainpound'.
.PP
The US Survey foot,
yard, and mile can be obtained by using the `US' prefix. 
These units differ slightly from the international length units.  
They were in general use until 1959, and are still used
for geographic surveys.
The acre is officially defined in terms of the US Survey foot.
If you want an acre 
defined according to the international foot, use `intacre'.  The 
difference between these units is 
about 4 parts per million. 
The British also used a slightly different length measure before 1959.  
These can be obtained with the prefix `UK'. 
.PP
When searching for
a unit, if the specified string does not appear exactly as a unit
name, then the `units' program will try to remove a 
trailing `s' or a trailing `es'.  If that fails, `units'
will check for a prefix.  
All of the standard metric prefixes are defined.
.PP
To find out what units and prefixes are available, read the standard
units data file.
.PP
.SH DEFINING NEW UNITS
All of the units and prefixes that `units' can convert are defined
in the units data file.  If you want to add your own units, you can
supply your own file.  You can also add your own units definitions in
the `.units.dat' file in your home directory.  If this file
exists it is read before the units data file.  It will not be read if
any units files are specified on the command line.  
.PP
A unit is specified on a single line by giving its name and an
equivalence.  Comments start with a `#' character, which can appear
anywhere in a line.  The backslash character (`\')
acts as a continuation
character if it appears as the last character on a line, making it
possible to spread definitions out over several lines if desired.
A file can be included by giving the command `!include' followed by
the file's name.  The file will be sought in the same directory as the
parent file unless a full path is given.  
.PP
Unit names must not contain any of the operator characters `+',
`-', `*', `/', `|', `^' or the parentheses.
They cannot begin with a digit or a decimal point (`.'), nor can
they end with a digit (except for zero).  
Be careful to define
new units in terms of old ones so that a reduction leads to the
primitive units, which are marked with `!' characters.  
Dimensionless units are indicated by using the string
`!dimensionless' for the unit definition.  
.PP
When adding new units, be sure to use the `-c' option to check that
the new units reduce properly.  
If you create a loop in the units definitions, then `units' will
hang when invoked with the `-c' options.  You will need to 
use the `--check-verbose' option which prints out each unit as it
checks them.  The program will still hang, but the last unit printed
will be the unit which caused the infinite loop.
.PP
If you define any units which contain
`+' characters, carefully check them because the `-c' option
will not catch non-conformable sums.  Be careful with the `-'
operator as well.  When used as a binary operator, the `-'
character can perform addition or multiplication
depending on the options used to invoke `units'.
To ensure consistent behavior use `-' only as a unary negation
operator when writing units definitions.  To multiply two units leave a
space or use the `*' operator with care, recalling that it has
two possible precedence values and may require parentheses to ensure
consistent behavior.  To compute the difference 
of `foo' and `bar' write `foo+(-bar)' or even `foo+-bar'.
.PP
Here is an example of a short units file that defines some basic
units:  
.RS
.TS
l l l.
m	!	# The meter is a primitive unit
sec	!	# The second is a primitive unit
rad	!dimensionless	# The radian is dimensionless
micro-	1e-6	# Define a prefix
minute	60 sec	# A minute is 60 seconds
hour	60 min	# An hour is 60 minutes
inch	0.0254 m	# Inch defined in terms of meters
ft	12 inches	# The foot defined in terms of inches
mile	5280 ft	# And the mile
.TE
.RS
.PP
A unit which ends with a `-' character is a prefix.  If a prefix
definition contains any `/' characters, be sure they are protected
by parentheses.  If you define `half- 1/2' then `halfmeter'
would be equivalent to `1 / 2 meter'.  
.PP
.SH DEFINING NONLINEAR UNITS
Some units conversions of interest are nonlinear; for
example, temperature conversions between the Fahrenheit and Celsius
scales cannot be done by simply multiplying by conversions factors.  
.PP
When you give a linear unit definition such as `inch 2.54 cm' you
are providing information that `units' uses to convert values in
inches into primitive units of meters.  For nonlinear units, you give
a functional definition that provides the same information.  
.PP
Nonlinear units are represented using a functional notation.  
It is best to regard this notation not as a function call but 
as a way of adding units to a number, much the same way that
writing a linear unit name after a number adds units to that number.
Internally, nonlinear units are defined by a pair of functions
which convert to and from linear units in the data file, so that 
an eventual conversion to primitive units is possible.  
.PP
Here is an example nonlinear unit definition:
.PP
.nf
tempF(x) [1;K] (x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32
.fi
.PP
A nonlinear unit definition comprises a unit name, a dummy parameter
name, two functions, and two corresponding units.  The functions tell
`units' how to convert to and from the new unit.  In order to 
produce valid results, the arguments of these functions need to have
the correct dimensions.  To facilitate error checking, you may specify
the dimensions. 
.PP
The definition begins with the unit name followed immediately (with no
spaces) by a `(' character.  In parentheses is the name of the
parameter.  Next is an optional specification of the units required by
the functions in this definition.  In the example above, the
`tempF' function requires an input argument conformable with
`1'.  For normal nonlinear units definitions the forward 
function will always take a dimensionless argument.  
The inverse function requires an input argument conformable
with `K'.  In general the inverse function will need units
that match the quantity measured by your nonlinear unit. 
The sole purpose of the expression in brackets to enable
`units' to perform error checking on function arguments.
.PP
Next the function definitions appear.  In the example above, the
`tempF' function is defined by
.PP
.nf
    tempF(x) = (x+(-32)) degF + stdtemp
.fi
.PP
This gives a rule for converting `x' in the units `tempF'
to linear units of absolute temperature, which makes it possible to 
convert from tempF to other units. 
.PP
In order to make conversions to Fahrenheit possible, you must give
a rule for the inverse conversions. The inverse will be `x(tempF)' and
its definition appears after a `;' character.  
In our example, the inverse is
.PP
.nf
    x(tempF) = (tempF+(-stdtemp))/degF + 32
.fi
.PP
This inverse definition takes an absolute temperature as its argument
and converts it to the Fahrenheit temperature.  The inverse can be
omitted by leaving out the `;' character, but then conversions to
the unit will be impossible.  If the inverse is omitted then the
`--check' option will display a warning.  It is up to you to
calculate and enter the correct inverse function to obtain proper
conversions.  The `--check' option tests the inverse at one point
and print an error if it is not valid there, but this is not a guarantee
that your inverse is correct.
.PP
If you wish to make synonyms for nonlinear units, you still need to define
both the forward and inverse functions.  Inverse functions can be
obtained using the `~' operator.  So to create a synonym 
for `tempF' you could write
.PP
.nf
    fahrenheit(x) [1;K] tempF(x); ~tempF(fahrenheit)
.fi
.PP
You may occasionally wish to define a function that operates on units.  
This can be done
using a nonlinear unit definition.  For example, the definition below
provides conversion between radius and the area of a circle.  Note
that this definition requires a length as input and produces an
area as output, as indicated by the specification in brackets. 
.PP
.nf
    circlearea(r) [m;m^2] pi r^2 ; sqrt(circlearea/pi)
.fi
.PP
Sometimes you may be interested in a piecewise linear unit such as 
many wire gauges.  Piecewise linear units can be defined by specifying
conversions to linear units on a list of points.
Conversion at other points will be done by linear interpolation.
A partial definition of zinc gauge is
.PP
.nf
    zincgauge[in] 1 0.002, 10 0.02, 15 0.04, 19 0.06, 23 0.1
.fi
.PP
In this example, `zincgauge' is the name of the piecewise linear
unit.  The definition of such a unit is indicated by the
embedded `[' character.  After the bracket, you should indicate the
units to be attached to the numbers in the table.  
No spaces can appear before the
`]' character, so a definition like `foo[kg meters]' is
illegal; instead write `foo[kg*meters]'.  The definition of the
unit consists of a list of pairs optionally separated by commas.  
This list defines a function for converting from the piecewise linear
unit to linear units.  The
first item in each pair is the function argument; the second item is the
value of the function at that argument (in the units specified in brackets).
In this example,
we define `zincgauge' at five points.  For example, we set
`zincgauge(1)' equal to `0.002 in'.  Definitions like this
may be  more readable  if written using  continuation characters as
.RS
.nf
zincgauge[in]         \\
        1        0.002 \\
        10        0.02 \\
        15        0.04 \\
        19        0.06 \\
        23        0.1    
.fi
.RE
.PP
With the preceeding definition, the following conversion can be
performed:
.PP
.nf
    You have: zincgauge(10)
    You want: in
        * 0.02
        / 50
    You have: .01 inch
    You want: zincgauge
        5
.fi
.PP
If you define a piecewise linear unit that is not strictly
monotonic, then the inverse will not be well defined.  If the inverse is
requested for such a unit, `units' will return the smallest
inverse.  The `--check' option will print a warning if a
non-monotonic piecewise linear unit is encountered.  
.PP
.SH LOCALIZATION
Some units have different values in different locations.  The
localization feature accomodates this by allowing the units database to
specify region dependent definitions.   A locale region in the units
database begins with `!locale' followed by the name of the locale.
The leading `!' must appear in the first column of the units
database.  The locale region is terminated by `!endlocale'.  The
following example shows how to define a couple units in a locale.
.PP
.nf
!locale en_GB
ton                     brton
gallon                  brgallon
!endlocale
.fi
.PP
The current locale is specified
by the `LOCALE' environment variable.  Note that the `-c'
option only checks the definitions which are active for the current locale.
.PP
.SH ENVIRONMENT VARIABLES
The `units' programs uses the following environment variables. 
.PP
.TP
.B LOCALE
Specifies the locale.  The default is `en_US'.  Sections of the
units database are specific to certain locales.  
.PP
.TP
.B PAGER
Specifies the pager to use for help and for displaying the conformable
units.  The help function browses the units database and calls
the pager using the `+nn' syntax for specifying a line number.  The
default pager is `more', but `less', `emacs', or
`vi' are possible alternatives.  
.PP
.TP
.B UNITSFILE
Specifies the units database file to use (instead of the default). This
will be overridden by the `-f' option.  Note that you can only
specify a single units database using this environment variable. 
.PP
.SH READLINE SUPPORT
If the `readline' package has been compiled in, then when
`units' is used interactively, numerous command line editing
features are available.  To check if your version of `units'
includes the readline, invoke the program with the `--version'
option.
.PP
For complete information about readline, consult the documentation for
the readline package.  Without any configuration, `units' will
allow editing in the style of emacs.  Of particular use with
`units' are the completion commands.  
.PP
If you type a few characters and then hit `ESC' followed by the
`?' key then `units' will display a list of all the units which
start with the characters typed.  For example, if you type `metr' and
then request completion, you will see something like this:
.PP
.nf
You have: metr
metre             metriccup         metrichorsepower  metrictenth
metretes          metricfifth       metricounce       metricton
metriccarat       metricgrain       metricquart       metricyarncount
You have: metr
.fi
.PP
If there is a unique way to complete a unitname, you can hit the tab key
and `units' will provide the rest of the unit name.  If `units'
beeps, it means that there is no unique completion.  Pressing the tab
key a second time will print the list of all completions.  
.PP
.SH FILES
@DATAFILE@ - the standard units data file
.SH AUTHOR
Adrian Mariano (adrian@cam.cornell.edu)