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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 -> BOOLReturns 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
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