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## unitconv

Conversion of units of measurement.

## Usage

(require-extension unitconv)

## Documentation

The `unitconv` library is an implementation of unit conversion routines based on the paper by Gordon S. Novak:

Conversion of Units of Measurement. IEEE Trans. on Software Engineering, vol. 21, no. 8 (Aug. 1995), pp. 651-661.

(Available online at http://www.cs.utexas.edu/users/novak/units95.html).

Correctness of unit conversion is established by the technique of dimensional analysis: the source and goal units must have the same dimensions. Following Novak, this extension defines a dimension as an 8-vector of integral powers of the following base quantities:

(define-base-quantity Unity 0) (define-base-quantity Length dimvals[0]) (define-base-quantity Time dimvals[1]) (define-base-quantity Temperature dimvals[2]) (define-base-quantity Mass dimvals[3]) (define-base-quantity Current dimvals[4]) (define-base-quantity Luminosity dimvals[5]) (define-base-quantity Substance dimvals[6]) (define-base-quantity Currency dimvals[7]) (define-base-quantity Information dimvals[8])

The unit conversion routine uses dimension integers to check that the requested unit conversion is legitimate. For example, the conversion from kilograms to meters illegal. Consequently, the dimensionality of each unit must be specified when the unit is declared.

;; Syntax is (define-unit name quantity factor abbreviation ...) ;; define units of length (define-unit meter Length 1.0 m meters) (define-unit inch Length 0.0254 in inches) ;; define units of mass and time (define-unit kilogram Mass 1.0 kg kilograms) (define-unit second Time 1.0 s seconds) ;; define two new derived quantities: acceleration and force (define-quantity Acceleration (/ Length (** Time 2))) (define-quantity Force (* Mass Acceleration)) ;; define a unit of force (define-unit newton Force (/ (* kilogram meter) (* second second)) nt newtons)

Now only conversion between units of the same dimensionality is permitted:

(unit-convert meter inch 1) -> 39.3700787401575 (unit-convert meter inch 2 3 4) -> (78.740157480315 118.110236220472 157.48031496063) (unit-convert meter kilogram 1) Error: (unitconv) unit-convert : given units are of different dimensions: source= #(unit meter (m meters) [Length] 1.0) ; dest= #(unit kilogram (kg kilograms) [Mass] 1.0)

### Procedures and Macros

*[procedure]*

`unit-convert:: SRC * DEST * [VAL1 ...] -> (FACTOR1 ... )`

Converts the given numeric values expressed in unit `SRC` to their equivalents in unit `DEST`.

Arguments `SRC, DEST` are records of type `unit`. See the definitions below for information about the units that are defined by this extension, as well as for information about creating new units.

*[procedure]*

`unit-equal?:: UNIT1 * UNIT2 -> BOOL`

Returns true if the two units have the same dimension and factor, false otherwise.

*[syntax]*

`(define-quantity name expr)`

Defines a derivative quantity `NAME`.

`EXPR` is an S-expression with the following syntax:

quantity-expr ::= base-quantity | derived-quantity | (* quantity-expr quantity-expr) | (* quantity-expr integer) | (/ quantity-expr quantity-expr) | (/ quantity-expr integer) | (** quantity-expr integer)

where

`base-quantity`- one of the predefined base quantities
`derived-quantity`- a quantity created by
`define-quantity` `**`- exponentiation operator

*[syntax]*

`(define-unit name dims factor . abbrevs)`

Defines a variable `NAME` that holds a unit definition of a unit with the given dimension and factor.

`DIMS` can be either one of the base quantities (see next section) or a derivative quantity created by `define-quantity`.

*[syntax]*

`(define-prefix-unit unit prefix . abbrevs)`

Defines a variable whose name is the concatenated `PREFIX` and `UNIT` and that holds a unit definition of the given unit and prefix.

### Predefined Quantities

#### Base Quantities

`Unity`(dimensionless)`Length``Time``Temperature``Mass``Current``Luminosity``Substance``Currency``Information`

#### Derived Quantities

**Geometry**`Area``(** Length 2)``Volume``(** Length 3)`**Mechanics**`Velocity``(/ Length Time)``Acceleration``(/ Length (** Time 2))``Force``(* Mass Acceleration)``Pressure``(/ Force Area)``Energy``(* Force Length)``Power``(/ Energy Time)`**Electricity**`Charge``(* Current Time)``Potential``(/ Energy Charge)``Capacitance``(/ Charge Potential)``Resistance``(/ Potential Current)``Conductance``(/ Current Potential)``Inductance``(/ (* Potential Time) Current)`**Chemistry**`Concentration``(/ Substance Volume)``Density``(/ Mass Volume)`**Optics**`Luminance``(/ Luminosity Area)`**Other**`Frequency``(/ Unity Time)``Rate``(/ Information Time)`

### Predefined Units

SI Unit Prefixes |
|||

Name |
Quantity |
Factor | |

yocto |
Unity |
1e-24 |
{{}} |

zepto |
Unity |
1e-21 |
{{}} |

atto |
Unity |
1e-18 |
{{}} |

femto |
Unity |
1e-15 |
{{}} |

pico |
Unity |
1e-12 |
{{}} |

nano |
Unity |
1e-09 |
{{}} |

micro |
Unity |
1e-06 |
{{}} |

milli |
Unity |
0.001 |
{{}} |

centi |
Unity |
0.01 |
{{}} |

deci |
Unity |
0.1 |
{{}} |

deca |
Unity |
10.0 |
{{}} |

hecto |
Unity |
100.0 |
{{}} |

kilo |
Unity |
1000.0 |
{{}} |

mega |
Unity |
1000000.0 |
{{}} |

giga |
Unity |
1000000000.0 |
{{}} |

tera |
Unity |
1000000000000.0 |
{{}} |

peta |
Unity |
1e+15 |
{{}} |

exa |
Unity |
1e+18 |
{{}} |

zetta |
Unity |
1e+21 |
{{}} |

yotta |
Unity |
1e+24 |
{{}} |

IEC Standard Prefixes |
|||

kibi |
Unity |
1024 |
{{}} |

mebi |
Unity |
1048576 |
{{}} |

gibi |
Unity |
1073741824.0 |
{{}} |

tebi |
Unity |
1099511627776.0 |
{{}} |

pebi |
Unity |
1.12589990684262e+15 |
{{}} |

exbi |
Unity |
1.15292150460685e+18 |
{{}} |

zebi |
Unity |
1.18059162071741e+21 |
{{}} |

yobi |
Unity |
1.20892581961463e+24 |
{{}} |

Time Multiples |
|||

twelve |
Unity |
12 |
{{}} |

sixty |
Unity |
60 |
{{}} |

Angles |
|||

radian |
Unity |
1.0 |
(rad radians) |

degree |
Unity |
(/ pi 180) |
(deg degrees) |

Units of Length |
|||

meter |
Length |
1.0 |
(m meters) |

inch |
Length |
0.0254 |
(in inches) |

foot |
Length |
0.3048 |
(ft feet) |

angstrom |
Length |
1e-10 |
(ang angstroms) |

parsec |
Length |
3.083e+16 |
(parsecs) |

Units of Area and Volume |
|||

square-meter |
Area |
(* meter meter) |
(m^2 m2 meter-squared meters-squared square-meters) |

square-inch |
Area |
(* inch inch) |
(in^2 inch-squared inches-squared square-inches) |

square-micron |
Area |
(* micrometer micrometer) |
(um^2 micrometer-squared micrometers-squared micron-squared microns-squared square-microns) |

square-millimeter |
Area |
(* millimeter millimeter) |
(mm^2 millimeter-squared millimeters-squared square-millimeters) |

cubic-meter |
Volume |
(* meter (* meter meter)) |
(m^3 meter-cubed meters-cubed cubic-meters) |

liter |
Volume |
(* 0.001 cubic-meter) |
(L litre liters) |

Units of Mass |
|||

kilogram |
Mass |
1.0 |
(kg kilograms) |

gram |
Mass |
0.001 |
(g grams) |

pound |
Mass |
(* gram 453.59237) |
(lb pounds) |

slug |
Mass |
(* pound 32.17405) |
(slugs) |

atomic-mass-unit |
Mass |
1.6605402e-27 |
(amu atomic-mass-units) |

Units of Time |
|||

second |
Time |
1.0 |
(s seconds) |

hour |
Time |
(* sixty (* sixty second)) |
(h hrs hours) |

Units of Acceleration |
|||

meters-per-second-squared |
Acceleration |
(/ meter (* second second)) |
(m/s2 m/s^2 m/sec2 m/sec^2) |

Units of Frequency |
|||

hertz |
Frequency |
1.0 |
(hz) |

Units of Force |
|||

newton |
Force |
(/ (* kilogram meter) (* second second)) |
(nt newtons) |

pound-force |
Force |
(/ (* slug foot) (* second second)) |
(lbf) |

Units of Power |
|||

watt |
Power |
(/ (* kilogram meter meter) (* second second second)) |
(W watts) |

horsepower |
Power |
(* 550 (/ (* foot pound-force) second)) |
(hp) |

Units of Energy |
|||

joule |
Energy |
(* newton meter) |
(J joules) |

electron-volt |
Energy |
(* 1.60217733e-19 joule) |
(ev electron-volts) |

kilowatt-hour |
Energy |
(* kilo (* watt hour)) |
(kwh kilowatt-hours) |

calorie |
Energy |
(* 4.184 joule) |
(cal calories) |

erg |
Energy |
(* 1e-07 joule) |
(ergs) |

british-thermal-unit |
Energy |
(* 1055.056 joule) |
(btu btus) |

Units of Current |
|||

ampere |
Current |
1.0 |
(A amp amps amperes) |

Units of Electric Charge |
|||

coulomb |
Charge |
(* ampere second) |
(C coulombs) |

Units of Electric Potential |
|||

volt |
Potential |
(/ (* kilogram meter meter) (* ampere second second second)) |
(V volts) |

Units of Resistance |
|||

ohm |
Resistance |
(/ volt ampere) |
(ohms) |

Units of Capacitance |
|||

farad |
Capacitance |
(/ coulomb volt) |
(F farads) |

Units of Conductance |
|||

siemens |
Conductance |
(/ ampere volt) |
(S mho) |

Units of Inductance |
|||

henry |
Inductance |
(/ (* meter meter kilogram) (* ampere ampere second second)) |
(H) |

Units of Substance |
|||

mole |
Substance |
1.0 |
(mol moles) |

Units of density |
|||

rho |
Density |
(/ kilogram cubic-meter) |
{{}} |

Units of concentration |
|||

molarity |
Concentration |
(/ mole liter) |
(M mol/L) |

parts-per-million |
Concentration |
(/ milligram kilogram) |
(ppm) |

Units of temperature |
|||

degK |
Temperature |
1.0 |
(K) |

Units of information |
|||

bit |
Information |
1 |
(b bits shannon shannons Sh) |

byte |
Information |
8 |
(B bytes) |

nat |
Information |
1.44269504088896 |
(nats nit nits nepit nepits) |

ban |
Information |
3.32192809488736 |
(bans hartley hartleys Hart Harts dit dits) |

Units of information rate |
|||

bits-per-second |
Rate |
(/ bit second) |
(bps) |

bytes-per-second |
Rate |
(/ byte second) |
(Bps) |

### Arithmetic Operations with Units

The `with-units` library contains procedures for arithmetic operations on quantities with units. A quantity with unit information is created by procedure `val-with-units`:

(use unitconv with-units) (val-with-units 10 m) -> #(10 #(unit meter (m meters) [Length] 1.0))

The following operations are available for operations on quantities with units:

`u:value`- Returns the value of the given quantity.
`u:units`- Returns the unit of the given quantity.
`u:equal?`- Returns true if the units of the given quantities are equal, false otherwise.
`u:zero?``u:=``u:negate``u:invert``u:+ u:- u:* u:/``u:sqrt``u:sin``u:cos``u:expt`

## About this egg

### Author

### Version history

- 2.1
- Documentation converted to wiki format
- 2.0
- Added unit arithmetic (with-units)
- 1.8
- Exporting all prefixed units; added info on information units [Joshua Griffith]
- 1.7
- Exporting the Rate quantity
- 1.6
- Exporting the IEC standard prefixes
- 1.5
- Ported to Chicken 4
- 1.4
- The predefined quantities have been put into unit-definitions.scm
- 1.3
- Bug fix in unit-convert
- 1.2
- Changed unit-convert to return a single numeric value given a single conversion argument
- 1.1
- Added information units [patch by Joshua Griffith]
- 1.0
- Initial release

### License

Copyright 2007-2010 Ivan Raikov and the Okinawa Institute of Science and Technology 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. A full copy of the GPL license can be found at <http://www.gnu.org/licenses/>.