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UNITS(1)							      UNITS(1)

NAME
       units - unit conversion program

OVERVIEW OF `UNITS'
       The  `units' program converts quantities expressed in various scales to
       their equivalents in other scales.  The `units' program can handle mul‐
       tiplicative  scale  changes  as	well  as nonlinear conversions such as
       Fahrenheit to Celsius.  Temperature conversions require a special  syn‐
       tax.  See the examples below.

       The units are defined in an external data file.	You can use the exten‐
       sive data file that comes with this program, or you  can	 provide  your
       own data file to suit your needs.

       You  can	 use the program interactively with prompts, or you can use it
       from the command line.

INTERACTING WITH `UNITS'
       To invoke units for interactive use, type `units' at your shell prompt.
       The program will print something like this:

	   2131 units, 53 prefixes, 24 nonlinear units

	   You have:

       At  the	`You  have:'  prompt, type the quantity and units that you are
       converting from.	 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 to.   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
       Readline support, for more information about readline.

       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

	       * 32.808399
	       / 0.03048

       which tells you that 10 meters equals about 32.8 feet.  The second num‐
       ber  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.

       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.

       If you try to convert grains to pounds, you will see the following:

	   You have: grains
	   You want: pounds
		   * 0.00014285714
		   / 7000

       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   confus‐
       ing, try using the `--verbose' option:

	   You have: grain
	   You want: aeginamina
		   grain = 0.00010416667 aeginamina
		   grain = (1 / 9600) aeginamina

       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:

	   You have: 6 ohms
	   You want: siemens
		   reciprocal conversion
		   * 0.16666667
		   / 6

       Reciprocal conversion can be suppressed by using the `--strict' option.
       As usual, use the `--verbose' option to get more comprehensible output:

	   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

       If you enter incompatible unit types, the `units' program will print  a
       message	indicating that the units are not conformable and it will dis‐
       play the reduced form for each unit:

	   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

       If you only want to find the reduced form or definition of a unit, sim‐
       ply press return at the `You want:' prompt.  Here is an example:

	   You have: jansky
	   You want:
		   Definition: fluxunit = 1e-26 W/m^2 Hz = 1e-26 kg / s^2

       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  combina‐
       tion  of watts, meters, and hertz.  The fully reduced (and in this case
       somewhat more cryptic) form appears on the far right.

       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	 angu‐
       lar  velocity.	This conversion can only be performed if the radian is
       dimensionless.

	   You have: (14 ft lbf) (12 radians/sec)
	   You want: watts
		   * 227.77742
		   / 0.0043902509

       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.

       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 con‐
       formable with the unit that you	entered	 at  the  `You	have:'	prompt
       above.  Note that conformable unit combinations will not appear on this
       list.

       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 histori‐
       cal information about the unit.

       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.

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.

       If you type

	   units '2 liters' 'quarts'

       then `units' will print

	       * 2.1133764
	       / 0.47317647

       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.

       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.

       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.

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 sec‐
       ond highest precedence.	The `**' operator is provided as  an  alterna‐
       tive exponent operator.

	   You have: cm^3
	   You want: gallons
		   * 0.00026417205
		   / 3785.4118

	   You have: arabicfoot * arabictradepound * force
	   You want: ft lbf
		   * 0.7296
		   / 1.370614

       Multiplication  of units can be specified by using spaces, or an aster‐
       isk (`*').  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'.

	   You have: furlongs per fortnight
	   You want: m/s
		   * 0.00016630986
		   / 6012.8727

       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.

       By default, multiplication using the star (`*') now has the same prece‐
       dence 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.

       Multiplication  using  a	 space or using the hyphen has a higher prece‐
       dence 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.

       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'.

	   You have: 1|2 inch
	   You want: cm
		   * 1.27
		   / 0.78740157

       Parentheses can be used for grouping as desired.

	   You have: (1/2) kg / (kg/meter)
	   You want: league
		   * 0.00010356166
		   / 9656.0833

       Prefixes	 are defined separately from base units.  In order to get cen‐
       timeters, 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'..

       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:

	   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

       And  the	 second example shows how the dollar sign in the units conver‐
       sion can precede the five.  Be careful:	`units'	 will  interpret  `$5'
       with no space as equivalent to dollars^5.

       Outside	of  the SI system, it is often desirable to add values of dif‐
       ferent units together.  You may also wish to use `units' as a  calcula‐
       tor  that  keeps track of units.	 Sums of conformable units are written
       with the `+' character.

	   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

       The expressions which are  added	 together  must	 reduce	 to  identical
       expressions in primitive units, or an error message will be displayed:

	   You have: 12 printerspoint + 4 heredium
						 ^
	   Illegal sum of non-conformable units

       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  subtrac‐
       tion operator it has the lower precedence as the addition operator.

       When  `-'  is used as a unary operator it negates its operand.  Regard‐
       less 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.

       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.

       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.

	   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

       The  other  functions on the list require dimensionless arguments.  The
       inverse trigonometric functions return  arguments  with	dimensions  of
       angle.

       If  you	wish  to take roots of units, you may use the `sqrt' or `cube‐
       root' functions.	 These functions require that the  argument  have  the
       appropriate  root.   Higher  roots can  be obtained by using fractional
       exponents:

	   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

       Nonlinear units are represented using functional notation.   They  make
       possible	 nonlinear unit conversions such temperature.  This is differ‐
       ent 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.

	   You have: tempF(45)
	   You want: tempC
		   7.2222222

	   You have: 45 degF
	   You want: degC
		   * 25
		   / 0.04

       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 Nonlinear
       units.  The first conversion shows that if it's 45  degrees  Fahrenheit
       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.

       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.   Alterna‐
       tively,	you  can  use  the  synonyms `g00', `g000', and so on that are
       defined in the units database.

	   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

INVOKING `UNITS'
       You invoke `units' like this:

	   units [OPTIONS] [FROM-UNIT [TO-UNIT]]

       If the FROM-UNIT and TO-UNIT are omitted, then  the  program  will  use
       interactive  prompts  to	 determine  which conversions to perform.  See
       Interactive use.	 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 defini‐
       tion  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 Command line use.

       The  following  options allow you to read in an alternative units file,
       check your units file, or change the output format:

       -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 can‐
	      not be reduced.  Also display some other diagnostics about  sus‐
	      picious definitions in the units data file.  Note that only def‐
	      initions active in the current locale are checked.

       --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 defi‐
	      nition.  Note that only definitions active in the current locale
	      are checked.

       -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'.

       -f filename, --file filename
	      Instruct	`units'	 to load the units file `filename'.  If `file‐
	      name' 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' envi‐
	      ronment variable.

       -h, --help
	      Print out a summary of the options for `units'.

       -m, --minus
	      Causes `-' to be interpreted as a subtraction operator.  This is
	      usually the default behavior.

       -p, --product
	      Causes  `-'  to be interpreted as a multiplication operator when
	      it has two operands.  It will as a negation operator when it has
	      only  one	 operand: `(-3)'.  Note that by default `-' is treated
	      as a subtraction operator.

       , --oldstar Causes `*' to have the old style  precedence,  higher  than
       the precedence of division so that `1/2*3' will equal `6'.

       ,  --newstar Forces `*' to have the new (default) precedence which fol‐
       lows the usual rules of algebra: the precedence of `*' is the  same  as
       the precedence of `/', so that `1/2*3' will equal `3/2'.

       ,  --compact  Give compact output featuring only the conversion factor.
       This turns off the `--verbose' option.

       -q, --quiet, --silent
	      Suppress prompting of the user for units and the display of sta‐
	      tistics about the number of units loaded.

       -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 conver‐
	      sion,  and will give an error if you attempt to convert hertz to
	      seconds.

       -1, --one-line
	      Give only one line of output (the forward conversion).   Do  not
	      print the reverse conversion.  Note that if a reciprocal conver‐
	      sion is performed	 then  `units'	will  print  still  print  the
	      "reciprocal conversion" line.

       -t, --terse
	      Give  terse  output  when	 converting units.  This option can be
	      used when calling `units' from another program so that the  out‐
	      put  is  easy  to parse.	This option has the combined effect of
	      these options:  `--strict' `--quiet' `--one-line' `--compact'.

       -v, --verbose
	      Give slightly more verbose output when converting	 units.	  When
	      combined	with  the  `-c'	 option	 this gives the same effect as
	      `--check-verbose'.

       -V, --version
	      Print program version number, tell whether the readline  library
	      has  been	 included,  and give the location of the default units
	      data file.

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.

       Many constants of nature are defined, including these:

	      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
       The  database includes atomic masses for all of the elements and numer‐
       ous other constants.  Also included are the densities of various ingre‐
       dients 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.

       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 counter‐
       parts, such as the British Imperial gallon,  are	 prefixed  with	 `br'.
       Currency	 is  prefixed with its country name: `belgiumfranc', `britain‐
       pound'.

       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  interna‐
       tional  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'.

       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.

       To  find	 out  what units and prefixes are available, read the standard
       units data file.

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.

       A  unit is specified on a single line by giving its name and an equiva‐
       lence.  Comments start with a `#' character, which can appear  anywhere
       in a line.  The backslash character (`´) acts as a continuation charac‐
       ter 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.

       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 `!' char‐
       acters.	Dimensionless units are indicated by using the string `!dimen‐
       sionless' for the unit definition.

       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 defini‐
       tions, 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.

       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'.

       Here is an example of a short units file that defines some basic units:

	      m	       !		# The meter is a primitive unit
	      sec      !		# The second is a primitive unit
	      rad      !dimensionless	# The second is a primitive unit
	      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

		     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'.

DEFINING NONLINEAR UNITS
       Some units conversions of interest are nonlinear; for example, tempera‐
       ture  conversions  between  the Fahrenheit and Celsius scales cannot be
       done by simply multiplying by conversions factors.

       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	 func‐
       tional definition that provides the same information.

       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 lin‐
       ear units in the data file, so that an eventual conversion to primitive
       units is possible.

       Here is an example nonlinear unit definition:

       tempF(x) [1;K] (x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32

       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  cor‐
       rect  dimensions.   To  facilitate  error checking, you may specify the
       dimensions.

       The definition begins with the unit name followed immediately (with  no
       spaces)	by a `(' character.  In parentheses is the name of the parame‐
       ter.  Next is an optional specification of the units  required  by  the
       functions  in this definition.  In the example above, the `tempF' func‐
       tion requires an input argument conformable with `1'.  For normal  non‐
       linear units definitions the forward function will always take a dimen‐
       sionless 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 pur‐
       pose  of	 the expression in brackets to enable `units' to perform error
       checking on function arguments.

       Next the function  definitions  appear.	 In  the  example  above,  the
       `tempF' function is defined by

	   tempF(x) = (x+(-32)) degF + stdtemp

       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.

       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

	   x(tempF) = (tempF+(-stdtemp))/degF + 32

       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.

       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

	   fahrenheit(x) [1;K] tempF(x); ~tempF(fahrenheit)

       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  pro‐
       duces an area as output, as indicated by the specification in brackets.

	   circlearea(r) [m;m^2] pi r^2 ; sqrt(circlearea/pi)

       Sometimes you may be interested in a piecewise linear unit such as many
       wire gauges.  Piecewise linear units can be defined by specifying  con‐
       versions	 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

	   zincgauge[in] 1 0.002, 10 0.02, 15 0.04, 19 0.06, 23 0.1

       In  this example, `zincgauge' is the name of the piecewise linear unit.
       The definition of such a unit is indicated by the embedded `['  charac‐
       ter.   After  the bracket, you should indicate the units to be attached
       to the numbers in the table.  No spaces can appear before the `]' char‐
       acter,  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
	      zincgauge[in]	    \
		      1	       0.002 \
		      10	0.02 \
		      15	0.04 \
		      19	0.06 \
		      23	0.1

       With the preceeding definition, the following conversion	 can  be  per‐
       formed:

	   You have: zincgauge(10)
	   You want: in
	       * 0.02
	       / 50
	   You have: .01 inch
	   You want: zincgauge
	       5

       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 lin‐
       ear unit is encountered.

LOCALIZATION
       Some units have different values in different locations.	 The localiza‐
       tion 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.

       !locale en_GB
       ton		       brton
       gallon		       brgallon
       !endlocale

       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.

ENVIRONMENT VARIABLES
       The `units' programs uses the following environment variables.

       LOCALE Specifies	 the locale.  The default is `en_US'.  Sections of the
	      units database are specific to certain locales.

       PAGER  Specifies the pager to use for help and for displaying the  con‐
	      formable	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.

       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 environ‐
	      ment variable.

READLINE SUPPORT
       If  the	`readline'  package has been compiled in, then when `units' is
       used interactively, numerous command line editing features  are	avail‐
       able.   To  check  if  your  version  of `units' includes the readline,
       invoke the program with the `--version' option.

       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.

       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:

       You have: metr
       metre		 metriccup	   metrichorsepower  metrictenth
       metretes		 metricfifth	   metricounce	     metricton
       metriccarat	 metricgrain	   metricquart	     metricyarncount
       You have: metr

       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.

FILES
       /usr/share/units.dat - the standard units data file

AUTHOR
       Adrian Mariano (adrian@cam.cornell.edu)

				  25 Sep 2007			      UNITS(1)
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