Documentation

Units: A Unit Conversion Program


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1 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.1

Temperature conversions require a special syntax.

See Temperature Conversion Example.

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.

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2 Android port of units

The Android version serves as a front-end to the standard GNU units program which has been recompiled with the Android Native Development Kit. Thus, much of the original functionality of units is maintained.

GNU units was originally written by Adrian Mariano.

The Android port works much like standard units invoked in interactive mode (see below). Enter expressions for your known values in the You have entry box, and target conversion expressions in the You want entry box. Press the Convert button. Conversion and other information (formatted based on flags/options as described below) appear in the editable “Results” box.

Entry history: you can press your device’s Back key in the You have, You want, and Results boxes to cycle back through your entries. Press Back twice in rapid succession to make the “back” function behave as it ordinarily does. You can turn off this functionality viaPreferences if you don’t like it. The application keeps track of your previous 100 entries in each of the entry boxes, and maintains this history even if you leave the application or turn off your phone.

Flags/Options: with some exceptions, many of the original command-line options are available in the Android version. These options can be changed using the Flag/Options settings under the Preferences menu. For simplicity, the Android version sets the --terse option initially by default. You can remove or change this option if it does not suit you.

Autocompletion: you can turn on autocompletion with the Autocomplete threshold preferences item. Select the number of characters entered that will trigger a drop-down list of recognized units of measures and functions beginning with those characters. Autocompletion is off by default.

You can also enter search xxx (where xxx is some string of characters) in the You have box to search for units of measures and functions. For example, to search for units of measure that contain the string “amp”, enter search amp and then press Convert. The Results box will contain:

       abamp           abampere
       abampere        10 A
       amp             ampere
       ampere          A
       amphora         8 congii
       amphorae        amphora
       intamp          intampere
       intampere       0.999835 A
       statamp         statampere
       statampere      10 A cm / s c
       thermalampere   W/K

Share: this menu item allows you to select a sharing application (e.g., email, text message), and copy a units result to that application for transmission. The applications available for sharing results depend on what you have installed on your device.

You can specify custom units files using the -f command-line option (set in Preferences->Flags/Options). You can also edit and/or replace the units.dat file in its default directory (this location may vary based on your platform):

     /mnt/sdcard/Android/data/org.quexotic.gnuunits/files/units.dat

If you use the -f option, you have to specify the full path to where you installed your custom units file. For example, you could install your custom units file on your sdcard (a device’s optional memory card), and then use this file by including the following Preferences->Flags/Options:

     -f /mnt/sdcard/myunits.dat -f ""

(Note the use of the -f "" flag, which loads the default units file in addition to your custom units file – this is almost always what you want to do.) If you edit or use your own custom unit file, you should check it (--check) using a non-Android version of units before use with the Android port. A couple of custom data files are included with the distribution as examples. Using

     -f /mnt/sdcard/gnuunits_med.dat -f ""

you can perform some limited medically-oriented conversions, such as converting between traditional (U.S.) and SI units of measure for various lab values::

           You have:  78 mg/mL glucose
           You want:  mmol/L
           Results:   4.3294849

If you use

     -f /mnt/sdcard/gnuunits_fun.dat -f ""

you get access to some bonus definitions and conversions, for example, “2000 mockingbird = 2 kilomockingbird,” and others:

            You have:  1 paradigm
            You want:
            Results:   Definition: 4 nickels

            You have:  1 unit_of_suspense_in_mystery_novel
            You want:
	    Results:   Definition: 1 whod_unit

            You have:  1 gigolo
            You want:  picolos
            Results:   1e+21 picolos

            You have:  2 megacycles
            You want:  bicycles
            Results:   1e6 bicycles

            You have:  1 megaphone
            You want:  microphones
            Results:   1e12 microphones

            You have:  1 milliHelen_Of_Troy
            You want:
	    Results:   Definition: 1 amount_of_face_that_can_launch_one_ship

(This file also allows use of the proposed hella- SI prefix for values of 10^27. Using this prefix, you can determine that ”1 hellaHelen_Of_Troy” could launch 10^30 ships (“1000 hella ships”).

(Many of the conversions in gnuunits_fun.dat are adapted from the “Q Files, a subsidiary of Evil Mad Scientist Laboratories (see http://windell.oskay.net/humor/qqqfiles/quarks1.html), which in turn notes that the original information was taken from “The Bent of Tau Beta Pi, Spring 1988″).

License and warranty:

Be cautious when using this software. Conversion values have not been verified and tested rigorously, and may be outdated or inaccurate.

You can redistribute this software and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program (see end of this document). You can also find the license at

     http://www.gnu.org/licenses/

The documentation that follows is primarily the original units documentation, edited lightly to reflect the Android port.


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3 Interacting with units

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 queries for You want. You should type the type to convert to. To convert to feet, you would type feet.

The answer will be displayed in two ways (note: the Android port sets the –terse option by default. Remove this option if you want more verbose output as indicated in the following examples). 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 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.

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 confusing, 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 display 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, simply 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 combination 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 angular 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 conformable with the unit that you entered at the You have: prompt above. Note that conformable unit combinations will not appear on this list.


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4 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.

         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 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.

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

Multiplication has a higher precedence than division and is evaluated left to right, so 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 (|). 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 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.. 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 conversion 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 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.

         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 subtraction operator it has the lower precedence as the addition operator.

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. 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 cuberoot 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
Temperature Conversion Example

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.

         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 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. 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.

         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

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5 Invoking units

The program uses 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 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 Command line use.

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

-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.
-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.
-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.
–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 statistics 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 conversion, 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 conversion 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 output 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.

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6 Unit definitions

The conversion information is read from a units data file which is called units.dat. 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 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.

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. 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. 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.


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7 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. 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. 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. 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. 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. 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  # A dimensionless 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.


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8 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. 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. 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. 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 correct 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 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. 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 produces 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 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

         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 [ 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

         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 performed:

         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 linear unit is encountered.


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9 Warranty/License

The GNU General Public License is a free, copyleft license for software and other kinds of works. The licenses for most software and other practical works are designed to take away your freedom to share and change the works. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change all versions of a program–to make sure it remains free software for all its users. We, the Free Software Foundation, use the GNU General Public License for most of our software; it applies also to any other work released this way by its authors. You can apply it to your programs, too. When we speak of free software, we are referring to freedom, not price. Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software (and charge for them if you wish), that you receive source code or can get it if you want it, that you can change the software or use pieces of it in new free programs, and that you know you can do these things.

To protect your rights, we need to prevent others from denying you these rights or asking you to surrender the rights. Therefore, you have certain responsibilities if you distribute copies of the software, or if you modify it: responsibilities to respect the freedom of others. For example, if you distribute copies of such a program, whether gratis or for a fee, you must pass on to the recipients the same freedoms that you received. You must make sure that they, too, receive or can get the source code. And you must show them these terms so they know their rights. Developers that use the GNU GPL protect your rights with two steps: (1) assert copyright on the software, and (2) offer you this License giving you legal permission to copy, distribute and/or modify it.

For the developers’ and authors’ protection, the GPL clearly explains that there is no warranty for this free software. For both users’ and authors’ sake, the GPL requires that modified versions be marked as changed, so that their problems will not be attributed erroneously to authors of previous versions. Some devices are designed to deny users access to install or run modified versions of the software inside them, although the manufacturer can do so. This is fundamentally incompatible with the aim of protecting users’ freedom to change the software. The systematic pattern of such abuse occurs in the area of products for individuals to use, which is precisely where it is most unacceptable. Therefore, we have designed this version of the GPL to prohibit the practice for those products. If such problems arise substantially in other domains, we stand ready to extend this provision to those domains in future versions of the GPL, as needed to protect the freedom of users.

Finally, every program is threatened constantly by software patents. States should not allow patents to restrict development and use of software on general-purpose computers, but in those that do, we wish to avoid the special danger that patents applied to a free program could make it effectively proprietary. To prevent this, the GPL assures that patents cannot be used to render the program non-free. The precise terms and conditions for copying, distribution and modification follow.

TERMS AND CONDITIONS

0. Definitions.

“This License” refers to version 3 of the GNU General Public License. “Copyright” also means copyright-like laws that apply to other kinds of works, such as semiconductor masks. “The Program” refers to any copyrightable work licensed under this License. Each licensee is addressed as “you”. “Licensees” and “recipients” may be individuals or organizations. To “modify” a work means to copy from or adapt all or part of the work in a fashion requiring copyright permission, other than the making of an exact copy. The resulting work is called a “modified version” of the earlier work or a work “based on” the earlier work. A “covered work” means either the unmodified Program or a work based on the Program. To “propagate” a work means to do anything with it that, without permission, would make you directly or secondarily liable for infringement under applicable copyright law, except executing it on a computer or modifying a private copy. Propagation includes copying, distribution (with or without modification), making available to the public, and in some countries other activities as well. To “convey” a work means any kind of propagation that enables other parties to make or receive copies. Mere interaction with a user through a computer network, with no transfer of a copy, is not conveying. An interactive user interface displays “Appropriate Legal Notices” to the extent that it includes a convenient and prominently visible feature that (1) displays an appropriate copyright notice, and (2) tells the user that there is no warranty for the work (except to the extent that warranties are provided), that licensees may convey the work under this License, and how to view a copy of this License. If the interface presents a list of user commands or options, such as a menu, a prominent item in the list meets this criterion.

1. Source Code.

The “source code” for a work means the preferred form of the work for making modifications to it. “Object code” means any non-source form of a work. A “Standard Interface” means an interface that either is an official standard defined by a recognized standards body, or, in the case of interfaces specified for a particular programming language, one that is widely used among developers working in that language. The “System Libraries” of an executable work include anything, other than the work as a whole, that (a) is included in the normal form of packaging a Major Component, but which is not part of that Major Component, and (b) serves only to enable use of the work with that Major Component, or to implement a Standard Interface for which an implementation is available to the public in source code form. A “Major Component”, in this context, means a major essential component (kernel, window system, and so on) of the specific operating system (if any) on which the executable work runs, or a compiler used to produce the work, or an object code interpreter used to run it. The “Corresponding Source” for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities. However, it does not include the work’s System Libraries, or general-purpose tools or generally available free programs which are used unmodified in performing those activities but which are not part of the work. For example, Corresponding Source includes interface definition files associated with source files for the work, and the source code for shared libraries and dynamically linked subprograms that the work is specifically designed to require, such as by intimate data communication or control flow between those subprograms and other parts of the work. The Corresponding Source need not include anything that users can regenerate automatically from other parts of the Corresponding Source. The Corresponding Source for a work in source code form is that same work.

2. Basic Permissions.

All rights granted under this License are granted for the term of copyright on the Program, and are irrevocable provided the stated conditions are met. This License explicitly affirms your unlimited permission to run the unmodified Program. The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work. This License acknowledges your rights of fair use or other equivalent, as provided by copyright law. You may make, run and propagate covered works that you do not convey, without conditions so long as your license otherwise remains in force. You may convey covered works to others for the sole purpose of having them make modifications exclusively for you, or provide you with facilities for running those works, provided that you comply with the terms of this License in conveying all material for which you do not control copyright. Those thus making or running the covered works for you must do so exclusively on your behalf, under your direction and control, on terms that prohibit them from making any copies of your copyrighted material outside their relationship with you. Conveying under any other circumstances is permitted solely under the conditions stated below. Sublicensing is not allowed; section 10 makes it unnecessary.

3. Protecting Users’ Legal Rights From Anti-Circumvention Law.

No covered work shall be deemed part of an effective technological measure under any applicable law fulfilling obligations under article 11 of the WIPO copyright treaty adopted on 20 December 1996, or similar laws prohibiting or restricting circumvention of such measures. When you convey a covered work, you waive any legal power to forbid circumvention of technological measures to the extent such circumvention is effected by exercising rights under this License with respect to the covered work, and you disclaim any intention to limit operation or modification of the work as a means of enforcing, against the work’s users, your or third parties’ legal rights to forbid circumvention of technological measures.

4. Conveying Verbatim Copies.

You may convey verbatim copies of the Program’s source code as you receive it, in any medium, provided that you conspicuously and appropriately publish on each copy an appropriate copyright notice; keep intact all notices stating that this License and any non-permissive terms added in accord with section 7 apply to the code; keep intact all notices of the absence of any warranty; and give all recipients a copy of this License along with the Program. You may charge any price or no price for each copy that you convey, and you may offer support or warranty protection for a fee.

5. Conveying Modified Source Versions.

You may convey a work based on the Program, or the modifications to produce it from the Program, in the form of source code under the terms of section 4, provided that you also meet all of these conditions:

  • a) The work must carry prominent notices stating that you modified it, and giving a relevant date.
  • b) The work must carry prominent notices stating that it is released under this License and any conditions added under section 7. This requirement modifies the requirement in section 4 to “keep intact all notices”.
  • c) You must license the entire work, as a whole, under this License to anyone who comes into possession of a copy. This License will therefore apply, along with any applicable section 7 additional terms, to the whole of the work, and all its parts, regardless of how they are packaged. This License gives no permission to license the work in any other way, but it does not invalidate such permission if you have separately received it.
  • d) If the work has interactive user interfaces, each must display Appropriate Legal Notices; however, if the Program has interactive interfaces that do not display Appropriate Legal Notices, your work need not make them do so.

A compilation of a covered work with other separate and independent works, which are not by their nature extensions of the covered work, and which are not combined with it such as to form a larger program, in or on a volume of a storage or distribution medium, is called an “aggregate” if the compilation and its resulting copyright are not used to limit the access or legal rights of the compilation’s users beyond what the individual works permit. Inclusion of a covered work in an aggregate does not cause this License to apply to the other parts of the aggregate.

6. Conveying Non-Source Forms.

You may convey a covered work in object code form under the terms of sections 4 and 5, provided that you also convey the machine-readable Corresponding Source under the terms of this License, in one of these ways:

  • a) Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by the Corresponding Source fixed on a durable physical medium customarily used for software interchange.
  • b) Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by a written offer, valid for at least three years and valid for as long as you offer spare parts or customer support for that product model, to give anyone who possesses the object code either (1) a copy of the Corresponding Source for all the software in the product that is covered by this License, on a durable physical medium customarily used for software interchange, for a price no more than your reasonable cost of physically performing this conveying of source, or (2) access to copy the Corresponding Source from a network server at no charge.
  • c) Convey individual copies of the object code with a copy of the written offer to provide the Corresponding Source. This alternative is allowed only occasionally and noncommercially, and only if you received the object code with such an offer, in accord with subsection 6b.
  • d) Convey the object code by offering access from a designated place (gratis or for a charge), and offer equivalent access to the Corresponding Source in the same way through the same place at no further charge. You need not require recipients to copy the Corresponding Source along with the object code. If the place to copy the object code is a network server, the Corresponding Source may be on a different server (operated by you or a third party) that supports equivalent copying facilities, provided you maintain clear directions next to the object code saying where to find the Corresponding Source. Regardless of what server hosts the Corresponding Source, you remain obligated to ensure that it is available for as long as needed to satisfy these requirements.
  • e) Convey the object code using peer-to-peer transmission, provided you inform other peers where the object code and Corresponding Source of the work are being offered to the general public at no charge under subsection 6d.

A separable portion of the object code, whose source code is excluded from the Corresponding Source as a System Library, need not be included in conveying the object code work. A “User Product” is either (1) a “consumer product”, which means any tangible personal property which is normally used for personal, family, or household purposes, or (2) anything designed or sold for incorporation into a dwelling. In determining whether a product is a consumer product, doubtful cases shall be resolved in favor of coverage. For a particular product received by a particular user, “normally used” refers to a typical or common use of that class of product, regardless of the status of the particular user or of the way in which the particular user actually uses, or expects or is expected to use, the product. A product is a consumer product regardless of whether the product has substantial commercial, industrial or non-consumer uses, unless such uses represent the only significant mode of use of the product. “Installation Information” for a User Product means any methods, procedures, authorization keys, or other information required to install and execute modified versions of a covered work in that User Product from a modified version of its Corresponding Source. The information must suffice to ensure that the continued functioning of the modified object code is in no case prevented or interfered with solely because modification has been made. If you convey an object code work under this section in, or with, or specifically for use in, a User Product, and the conveying occurs as part of a transaction in which the right of possession and use of the User Product is transferred to the recipient in perpetuity or for a fixed term (regardless of how the transaction is characterized), the Corresponding Source conveyed under this section must be accompanied by the Installation Information. But this requirement does not apply if neither you nor any third party retains the ability to install modified object code on the User Product (for example, the work has been installed in ROM). The requirement to provide Installation Information does not include a requirement to continue to provide support service, warranty, or updates for a work that has been modified or installed by the recipient, or for the User Product in which it has been modified or installed. Access to a network may be denied when the modification itself materially and adversely affects the operation of the network or violates the rules and protocols for communication across the network. Corresponding Source conveyed, and Installation Information provided, in accord with this section must be in a format that is publicly documented (and with an implementation available to the public in source code form), and must require no special password or key for unpacking, reading or copying.

7. Additional Terms.

“Additional permissions” are terms that supplement the terms of this License by making exceptions from one or more of its conditions. Additional permissions that are applicable to the entire Program shall be treated as though they were included in this License, to the extent that they are valid under applicable law. If additional permissions apply only to part of the Program, that part may be used separately under those permissions, but the entire Program remains governed by this License without regard to the additional permissions. When you convey a copy of a covered work, you may at your option remove any additional permissions from that copy, or from any part of it. (Additional permissions may be written to require their own removal in certain cases when you modify the work.) You may place additional permissions on material, added by you to a covered work, for which you have or can give appropriate copyright permission. Notwithstanding any other provision of this License, for material you add to a covered work, you may (if authorized by the copyright holders of that material) supplement the terms of this License with terms:

  • a) Disclaiming warranty or limiting liability differently from the terms of sections 15 and 16 of this License; or
  • b) Requiring preservation of specified reasonable legal notices or author attributions in that material or in the Appropriate Legal Notices displayed by works containing it; or
  • c) Prohibiting misrepresentation of the origin of that material, or requiring that modified versions of such material be marked in reasonable ways as different from the original version; or
  • d) Limiting the use for publicity purposes of names of licensors or authors of the material; or
  • e) Declining to grant rights under trademark law for use of some trade names, trademarks, or service marks; or
  • f) Requiring indemnification of licensors and authors of that material by anyone who conveys the material (or modified versions of it) with contractual assumptions of liability to the recipient, for any liability that these contractual assumptions directly impose on those licensors and authors.

All other non-permissive additional terms are considered “further restrictions” within the meaning of section 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that term. If a license document contains a further restriction but permits relicensing or conveying under this License, you may add to a covered work material governed by the terms of that license document, provided that the further restriction does not survive such relicensing or conveying. If you add terms to a covered work in accord with this section, you must place, in the relevant source files, a statement of the additional terms that apply to those files, or a notice indicating where to find the applicable terms. Additional terms, permissive or non-permissive, may be stated in the form of a separately written license, or stated as exceptions; the above requirements apply either way.

8. Termination.

You may not propagate or modify a covered work except as expressly provided under this License. Any attempt otherwise to propagate or modify it is void, and will automatically terminate your rights under this License (including any patent licenses granted under the third paragraph of section 11). However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation. Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice. Termination of your rights under this section does not terminate the licenses of parties who have received copies or rights from you under this License. If your rights have been terminated and not permanently reinstated, you do not qualify to receive new licenses for the same material under section 10.

9. Acceptance Not Required for Having Copies.

You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so.

10. Automatic Licensing of Downstream Recipients.

Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License. An “entity transaction” is a transaction transferring control of an organization, or substantially all assets of one, or subdividing an organization, or merging organizations. If propagation of a covered work results from an entity transaction, each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party’s predecessor in interest had or could give under the previous paragraph, plus a right to possession of the Corresponding Source of the work from the predecessor in interest, if the predecessor has it or can get it with reasonable efforts. You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it.

11. Patents.

A “contributor” is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor’s “contributor version”. A contributor’s “essential patent claims” are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, “control” includes the right to grant patent sublicenses in a manner consistent with the requirements of this License. Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contributor’s essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version. In the following three paragraphs, a “patent license” is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To “grant” such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party. If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. “Knowingly relying” means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your recipient’s use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid. If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it. A patent license is “discriminatory” if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007. Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law.

12. No Surrender of Others’ Freedom.

If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program.

13. Use with the GNU Affero General Public License.

Notwithstanding any other provision of this License, you have permission to link or combine any covered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such.

14. Revised Versions of this License.

The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License “or any later version” applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation. If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy’s public statement of acceptance of a version permanently authorizes you to choose that version for the Program. Later license versions may give you additional or different permissions. However, no additional obligations are imposed on any author or copyright holder as a result of your choosing to follow a later version.

15. Disclaimer of Warranty.

THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM “AS IS” WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.

16. Limitation of Liability.

IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.

17. Interpretation of Sections 15 and 16.

If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee. END OF TERMS AND CONDITIONS

How to Apply These Terms to Your New Programs

If you develop a new program, and you want it to be of the greatest possible use to the public, the best way to achieve this is to make it free software which everyone can redistribute and change under these terms. To do so, attach the following notices to the program. It is safest to attach them to the start of each source file to most effectively state the exclusion of warranty; and each file should have at least the “copyright” line and a pointer to where the full notice is found.

    <one line to give the program's name and a brief idea of what it does.>
    Copyright (C) <year>  <name of author>

    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with this program.  If not, see <http://www.gnu.org/licenses/>.

Also add information on how to contact you by electronic and paper mail. If the program does terminal interaction, make it output a short notice like this when it starts in an interactive mode:

    <program>  Copyright (C) <year>  <name of author>
    This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
    This is free software, and you are welcome to redistribute it
    under certain conditions; type `show c' for details.

The hypothetical commands `show w’ and `show c’ should show the appropriate parts of the General Public License. Of course, your program’s commands might be different; for a GUI interface, you would use an “about box”. You should also get your employer (if you work as a programmer) or school, if any, to sign a “copyright disclaimer” for the program, if necessary. For more information on this, and how to apply and follow the GNU GPL, see <http://www.gnu.org/licenses/>. The GNU General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Lesser General Public License instead of this License. But first, please read <http://www.gnu.org/philosophy/why-not-lgpl.html>.


Next: Previous: Warranty/License, Up: Top

Index


 

Footnotes

[1] But Fahrenheit to Celsius is linear, you insist. Not so. A transformation T is linear if T(x+y)=T(x)+T(y) and this fails for T(x)=ax+b. This transformation is affine, but not linear.


Copyright © 2010-2011 Keith Flower, and 2004-2006 Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA Verbatim copying and distribution of this entire article is permitted in any medium, provided this notice is preserved.

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