dimensional 1.3 → 1.6.2
raw patch · 32 files changed
Files
- CHANGELOG.md +35/−3
- LICENSE +31/−31
- README.md +16/−2
- Setup.lhs +2/−2
- benchmarks/Main.hs +19/−19
- dimensional.cabal +41/−39
- examples/GM.lhs +94/−94
- examples/NewtonianMechanics.hs +37/−0
- examples/ReadmeExample.hs +33/−33
- src/Numeric/Units/Dimensional.hs +781/−780
- src/Numeric/Units/Dimensional/Coercion.hs +35/−35
- src/Numeric/Units/Dimensional/Dimensions.hs +25/−25
- src/Numeric/Units/Dimensional/Dimensions/TermLevel.hs +208/−192
- src/Numeric/Units/Dimensional/Dimensions/TypeLevel.hs +160/−160
- src/Numeric/Units/Dimensional/Dynamic.hs +365/−352
- src/Numeric/Units/Dimensional/FixedPoint.hs +373/−373
- src/Numeric/Units/Dimensional/Float.hs +179/−178
- src/Numeric/Units/Dimensional/Functor.hs +33/−33
- src/Numeric/Units/Dimensional/Internal.hs +274/−266
- src/Numeric/Units/Dimensional/NonSI.hs +938/−904
- src/Numeric/Units/Dimensional/Prelude.hs +52/−52
- src/Numeric/Units/Dimensional/Quantities.hs +436/−435
- src/Numeric/Units/Dimensional/SIUnits.hs +344/−314
- src/Numeric/Units/Dimensional/UnitNames.hs +37/−37
- src/Numeric/Units/Dimensional/UnitNames/InterchangeNames.hs +41/−41
- src/Numeric/Units/Dimensional/UnitNames/Internal.hs +365/−357
- src/Numeric/Units/Dimensional/Variants.hs +98/−94
- tests/DocTests.hs +0/−17
- tests/Numeric/Units/Dimensional/DynamicSpec.hs +157/−157
- tests/Numeric/Units/Dimensional/QuantitiesSpec.hs +137/−137
- tests/Numeric/Units/DimensionalSpec.hs +49/−49
- tests/Spec.hs +4/−4
CHANGELOG.md view
@@ -1,3 +1,35 @@+1.6.2 (2026-01)+---------------++* Support for GHC 9.14;++1.6.1 (2024-10)+---------------++* Fixed an issue where `Control.DeepSeq.Unit`, exported as of version 1.5.1.0, conflicts with `Numeric.Units.Dimensional.Unit` (#228).+* Fixed broken links to the Tau and Pi manifestos (#229).++1.6 (2024-08)+-------------++* Added a package flag `binary`, enabling optional dependency on the `binary` package to provide instances of `Binary`.++1.5 (2022-06)+-------------+* Add Julian `decade` and `millennium` to `NonSI`.+* Rename `deka` prefix to `deca` in accordance with [international spelling](https://www.bipm.org/documents/20126/41483022/SI-Brochure-9.pdf/fcf090b2-04e6-88cc-1149-c3e029ad8232).+* Change `astronomicalUnit` symbol to lowercase (`au`).+* Remove `semigroups` dependency.+* Significant documentation improvements.++Thanks to @konsumlamm for many contributions!+++1.4 (2021-05)+-------------+* Add `calorie` to `NonSI`.+* Remove deprecated `AutoDeriveTypeable` pragmas. This means that `Typable` instances are no provided on GHC prior to 8.2.+ 1.3 (2018-12) ------------- * Breaking: Changed the `Show` instances for `UnitName`, `Unit`, `SQuantity` to use non-breaking spaces@@ -130,7 +162,7 @@ * Added [`tau`][3]. * Added `KinematicViscosity`. -[3]: http://tauday.com/tau-manifesto+[3]: https://tauday.com/tau-manifesto 0.10.1.2 (2011-09)@@ -154,11 +186,11 @@ -------------- See the [announcement][2]. -[2]: http://flygdynamikern.blogspot.se/2011/05/announce-dimensional-010.html+[2]: https://flygdynamikern.blogspot.se/2011/05/announce-dimensional-010.html 0.9 (2011-04) ------------- See the [announcement][1]. -[1]: http://flygdynamikern.blogspot.se/2011/04/announce-dimensional-09.html+[1]: https://flygdynamikern.blogspot.se/2011/04/announce-dimensional-09.html
LICENSE view
@@ -1,31 +1,31 @@-Copyright (c) 2006-2018, Bjorn Buckwalter. -All rights reserved. - -Redistribution and use in source and binary forms, with or without -modification, are permitted provided that the following conditions -are met: - - * Redistributions of source code must retain the above copyright - notice, this list of conditions and the following disclaimer. - - * Redistributions in binary form must reproduce the above - copyright notice, this list of conditions and the following - disclaimer in the documentation and/or other materials provided - with the distribution. - - * Neither the name of the copyright holder(s) nor the names of - contributors may be used to endorse or promote products derived - from this software without specific prior written permission. - -THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS -"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT -LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS -FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE -COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, -INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, -BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; -LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER -CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT -LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN -ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE -POSSIBILITY OF SUCH DAMAGE. +Copyright (c) 2006-2018, Bjorn Buckwalter.+All rights reserved.++Redistribution and use in source and binary forms, with or without+modification, are permitted provided that the following conditions+are met:++ * Redistributions of source code must retain the above copyright+ notice, this list of conditions and the following disclaimer.++ * Redistributions in binary form must reproduce the above+ copyright notice, this list of conditions and the following+ disclaimer in the documentation and/or other materials provided+ with the distribution.++ * Neither the name of the copyright holder(s) nor the names of+ contributors may be used to endorse or promote products derived+ from this software without specific prior written permission.++THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS+FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE+COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,+INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,+BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;+LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT+LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN+ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE+POSSIBILITY OF SUCH DAMAGE.
README.md view
@@ -5,8 +5,7 @@ Data kinds and closed type families provide a flexible, safe, and discoverable implementation that leads to largely self-documenting client code. -[](https://travis-ci.org/bjornbm/dimensional)-[](http://hackage.haskell.org/package/dimensional)+[](https://hackage.haskell.org/package/dimensional) [](https://www.stackage.org/package/dimensional) ## Usage@@ -62,6 +61,21 @@ putStrLn $ "Average speed is: " ++ showIn (mile / hour) averageSpeed putStrLn $ "If we don't want to be explicit about units, the show instance uses the SI basis: " ++ show averageSpeed putStrLn $ "The journey requires " ++ show wholeSeconds ++ " seconds, rounded up to the nearest second."+```++## Package Flags++To provide `Binary` serialization for `Quantity` from the `binary` package, the `binary` flag can be used like so:++```bash+cabal install dimensional -f binary+```++If you use a `cabal.project` file, you can instead add the following clause to activate this package flag:++```txt+package dimensional+ flags: +binary ``` ## Contributing
Setup.lhs view
@@ -1,3 +1,3 @@-#!/usr/bin/env runhaskell -> import Distribution.Simple +#!/usr/bin/env runhaskell+> import Distribution.Simple > main = defaultMain
benchmarks/Main.hs view
@@ -1,19 +1,19 @@-{-# LANGUAGE NoImplicitPrelude #-} - -module Main where - -import Criterion.Main -import Numeric.Units.Dimensional.Prelude -import qualified Prelude as P - -main :: IO () -main = defaultMain [ - bench "RawArithmetic" $ nf rawArithmetic 1000 - , bench "Arithmetic" $ nf arithmetic 1000 - ] - -rawArithmetic :: Int -> [Double] -rawArithmetic n = fmap (P./ 3.7) $ [1.0 .. fromIntegral n] - -arithmetic :: Int -> [Density Double] -arithmetic n = fmap (/ (3.7 *~ cubic meter)) $ [1.0 .. fromIntegral n] *~~ kilo gram +{-# LANGUAGE NoImplicitPrelude #-}++module Main where++import Criterion.Main+import Numeric.Units.Dimensional.Prelude+import qualified Prelude as P++main :: IO ()+main = defaultMain [+ bench "RawArithmetic" $ nf rawArithmetic 1000+ , bench "Arithmetic" $ nf arithmetic 1000+ ]++rawArithmetic :: Int -> [Double]+rawArithmetic n = fmap (P./ 3.7) $ [1.0 .. fromIntegral n]++arithmetic :: Int -> [Density Double]+arithmetic n = fmap (/ (3.7 *~ cubic meter)) $ [1.0 .. fromIntegral n] *~~ kilo gram
dimensional.cabal view
@@ -1,18 +1,25 @@ name: dimensional-version: 1.3+version: 1.6.2 license: BSD3 license-file: LICENSE-copyright: Bjorn Buckwalter 2006-2018+copyright: Bjorn Buckwalter 2006-2024 author: Bjorn Buckwalter maintainer: bjorn@buckwalter.se stability: experimental homepage: https://github.com/bjornbm/dimensional/ bug-reports: https://github.com/bjornbm/dimensional/issues/ category: Math, Physics-synopsis: Statically checked physical dimensions,- using Type Families and Data Kinds.+synopsis: Statically checked physical dimensions cabal-version: >= 1.10-tested-with: GHC == 8.0.1, GHC == 8.0.2, GHC == 8.2.2, GHC == 8.4.4, GHC == 8.6.1+tested-with: GHC == 8.10.7,+ GHC == 9.0.2,+ GHC == 9.2.8,+ GHC == 9.4.8,+ GHC == 9.6.7,+ GHC == 9.8.4,+ GHC == 9.10.3,+ GHC == 9.12.2,+ GHC == 9.14.1 build-type: Simple description:@@ -21,7 +28,7 @@ with physical quantities and units. Information about the physical dimensions of the quantities and units is embedded in their types and the validity of operations is verified by the type checker at compile time.- The boxing and unboxing of numerical values as quantities is done by+ The wrapping and unwrapping of numerical values as quantities is done by multiplication and division with units. The library is designed to, as far as is practical, enforce/encourage best practices of unit usage. @@ -35,44 +42,52 @@ extra-source-files: README.md, CHANGELOG.md, examples/ReadmeExample.hs,- examples/GM.lhs+ examples/GM.lhs,+ examples/NewtonianMechanics.hs +flag binary+ description: Provide instances for use with the binary package.+ default: False+ manual: True+ source-repository head type: git location: https://github.com/bjornbm/dimensional/ library- build-depends: base >= 4.7 && < 5,+ build-depends: base >= 4.9 && < 5, deepseq >= 1.3, exact-pi >= 0.4.1 && < 0.6, ieee754 >= 0.7.6, numtype-dk >= 0.5 && < 1.1,- vector >= 0.10,- semigroups+ vector >= 0.10 hs-source-dirs: src default-language: Haskell2010 default-extensions: NoImplicitPrelude if impl(ghc >= 8.6) default-extensions: NoStarIsType ghc-options: -Wall- exposed-modules: Numeric.Units.Dimensional,- Numeric.Units.Dimensional.Coercion,- Numeric.Units.Dimensional.Dimensions,- Numeric.Units.Dimensional.Dimensions.TermLevel,- Numeric.Units.Dimensional.Dimensions.TypeLevel,- Numeric.Units.Dimensional.Dynamic,- Numeric.Units.Dimensional.FixedPoint,- Numeric.Units.Dimensional.Functor,- Numeric.Units.Dimensional.NonSI,- Numeric.Units.Dimensional.Prelude,- Numeric.Units.Dimensional.Quantities,- Numeric.Units.Dimensional.SIUnits,- Numeric.Units.Dimensional.UnitNames,- Numeric.Units.Dimensional.UnitNames.InterchangeNames,- Numeric.Units.Dimensional.Variants,+ exposed-modules: Numeric.Units.Dimensional+ Numeric.Units.Dimensional.Coercion+ Numeric.Units.Dimensional.Dimensions+ Numeric.Units.Dimensional.Dimensions.TermLevel+ Numeric.Units.Dimensional.Dimensions.TypeLevel+ Numeric.Units.Dimensional.Dynamic+ Numeric.Units.Dimensional.FixedPoint+ Numeric.Units.Dimensional.Functor+ Numeric.Units.Dimensional.NonSI+ Numeric.Units.Dimensional.Prelude+ Numeric.Units.Dimensional.Quantities+ Numeric.Units.Dimensional.SIUnits+ Numeric.Units.Dimensional.UnitNames+ Numeric.Units.Dimensional.UnitNames.InterchangeNames+ Numeric.Units.Dimensional.Variants Numeric.Units.Dimensional.Float- other-modules: Numeric.Units.Dimensional.Internal,+ other-modules: Numeric.Units.Dimensional.Internal Numeric.Units.Dimensional.UnitNames.Internal+ if flag(binary)+ build-depends: binary >= 0.7 && < 1+ cpp-options: -DUSE_BINARY test-suite tests type: exitcode-stdio-1.0@@ -91,19 +106,6 @@ QuickCheck, base build-tool-depends: hspec-discover:hspec-discover == 2.*--test-suite doctests- type: exitcode-stdio-1.0- ghc-options: -threaded- main-is: DocTests.hs- hs-source-dirs: tests- default-language: Haskell2010- build-depends: dimensional,- doctest,- Glob,- QuickCheck,- template-haskell,- base benchmark simple type: exitcode-stdio-1.0
examples/GM.lhs view
@@ -1,94 +1,94 @@- -= GM calculation = - -Several representation can be used to describe a satellite's orbit. Two -of the most popular are the cartesian state vector (position and -velocity vectors) and the keplerian elements. Conversion between the two -representations is fairly straight-forward but requires an assumption -to be made about the universal gravitational constant 'G' and the mass -'M' of the body the satellite is orbiting. In practice they are often -combined into a parameter "mu = GM" where the magnitude of 'mu' is -empirically better known that the magnitudes of 'G' and 'M' individually. - -*The problem:* Given two representations of the same satellite orbit -- one -using the cartesian state vector and using keplerian elements, both at the -same epoch -- determine the value of 'mu' used to convert between the two. -{{{ - -> {-# LANGUAGE NegativeLiterals #-} -> module GM where - -> import Numeric.Units.Dimensional.Prelude -> import qualified Prelude - -}}} -The state vector describing the orbit at epoch. -{{{ - -> x = 4383.9449203752 *~ kilo meter -> y = -41940.917505092 *~ kilo meter -> z = 22.790255916589 *~ kilo meter -> x_dot = 3.0575666627812 *~ (kilo meter / second) -> y_dot = 0.32047068607303 *~ (kilo meter / second) -> z_dot = 0.00084729371755294 *~ (kilo meter / second) - -}}} -From the state vector we calculate the distance from the reference frame center at epoch and the velocity squared at epoch. -{{{ - -> r = sqrt (x ^ pos2 + y ^ pos2 + z ^ pos2) -> v = sqrt (x_dot ^ pos2 + y_dot ^ pos2 + z_dot ^ pos2) - -}}} -The kinetic energy per unit mass at epoch is a function of the velocity. -{{{ - -> e_kin :: EnergyPerUnitMass Double -> e_kin = v ^ pos2 / _2 - -}}} -The only keplerian element we need for this calculation is the semi-major axis. -{{{ - -> semi_major_axis = 42165.221455 *~ kilo meter - -}}} -The expression for 'mu' is obtained by solving the following equation system: - - e_pot = - mu / r, - - e_tot = - mu / 2a, - - e_tot = e_pot + e_kin, - -which gives: - - mu = e_kin / (1 / r - 1 / 2a). - -{{{ - -> mu = e_kin / (_1 / r - _1 / (_2 * semi_major_axis)) - -}}} -Wrap up with a main function showing the value of 'mu' in desired units. -{{{ - -> main = putStrLn $ "The value used for GM was " ++ show mu - -}}} -Loading this module in 'ghci' and running 'main' produces the following output. -{{{ - ___ ___ _ - / _ \ /\ /\/ __(_) - / /_\// /_/ / / | | GHC Interactive, version 6.6.1, for Haskell 98. -/ /_\\/ __ / /___| | http://www.haskell.org/ghc/ -\____/\/ /_/\____/|_| Type :? for help. - -Loading package base ... linking ... done. -[1 of 1] Compiling GM ( GM.lhs, interpreted ) -Ok, modules loaded: GM. -*GM> main -Loading package dimensional-0.5 ... linking ... done. -The value used for GM was 3.986004400008003e14 m^3 s^-2 -*GM> -}}} ++= GM calculation =++Several representation can be used to describe a satellite's orbit. Two+of the most popular are the cartesian state vector (position and+velocity vectors) and the keplerian elements. Conversion between the two+representations is fairly straight-forward but requires an assumption+to be made about the universal gravitational constant 'G' and the mass+'M' of the body the satellite is orbiting. In practice they are often+combined into a parameter "mu = GM" where the magnitude of 'mu' is+empirically better known that the magnitudes of 'G' and 'M' individually.++*The problem:* Given two representations of the same satellite orbit -- one+using the cartesian state vector and using keplerian elements, both at the+same epoch -- determine the value of 'mu' used to convert between the two.+{{{++> {-# LANGUAGE NegativeLiterals #-}+> module GM where++> import Numeric.Units.Dimensional.Prelude+> import qualified Prelude++}}}+The state vector describing the orbit at epoch.+{{{++> x = 4383.9449203752 *~ kilo meter+> y = -41940.917505092 *~ kilo meter+> z = 22.790255916589 *~ kilo meter+> x_dot = 3.0575666627812 *~ (kilo meter / second)+> y_dot = 0.32047068607303 *~ (kilo meter / second)+> z_dot = 0.00084729371755294 *~ (kilo meter / second)++}}}+From the state vector we calculate the distance from the reference frame center at epoch and the velocity squared at epoch.+{{{++> r = sqrt (x ^ pos2 + y ^ pos2 + z ^ pos2)+> v = sqrt (x_dot ^ pos2 + y_dot ^ pos2 + z_dot ^ pos2)++}}}+The kinetic energy per unit mass at epoch is a function of the velocity.+{{{++> e_kin :: EnergyPerUnitMass Double+> e_kin = v ^ pos2 / _2++}}}+The only keplerian element we need for this calculation is the semi-major axis.+{{{++> semi_major_axis = 42165.221455 *~ kilo meter++}}}+The expression for 'mu' is obtained by solving the following equation system:++ e_pot = - mu / r,++ e_tot = - mu / 2a,++ e_tot = e_pot + e_kin,++which gives:++ mu = e_kin / (1 / r - 1 / 2a).++{{{++> mu = e_kin / (_1 / r - _1 / (_2 * semi_major_axis))++}}}+Wrap up with a main function showing the value of 'mu' in desired units.+{{{++> main = putStrLn $ "The value used for GM was " ++ show mu++}}}+Loading this module in 'ghci' and running 'main' produces the following output.+{{{+ ___ ___ _+ / _ \ /\ /\/ __(_)+ / /_\// /_/ / / | | GHC Interactive, version 6.6.1, for Haskell 98.+/ /_\\/ __ / /___| | http://www.haskell.org/ghc/+\____/\/ /_/\____/|_| Type :? for help.++Loading package base ... linking ... done.+[1 of 1] Compiling GM ( GM.lhs, interpreted )+Ok, modules loaded: GM.+*GM> main+Loading package dimensional-0.5 ... linking ... done.+The value used for GM was 3.986004400008003e14 m^3 s^-2+*GM>+}}}
+ examples/NewtonianMechanics.hs view
@@ -0,0 +1,37 @@+{-# LANGUAGE NoImplicitPrelude #-}+module NewtonianMechanics where++import Numeric.Units.Dimensional.Prelude++translationalKineticEnergy :: (Fractional a) => Mass a -> Velocity a -> Energy a+translationalKineticEnergy m v = m * v ^ pos2 / _2++translationalWork :: (Num a) => Force a -> Length a -> Energy a+translationalWork f d = f * d++translationalMomentum :: (Num a) => Mass a -> Velocity a -> Momentum a+translationalMomentum m v = m * v++translationalPower :: (Num a) => Force a -> Velocity a -> Power a+translationalPower f v = f * v++forceFromChangeInMomentum :: (Fractional a) => Momentum a -> Time a -> Force a+forceFromChangeInMomentum dp dt = dp / dt++rotationalKineticEnergy :: (Fractional a) => MomentOfInertia a -> AngularVelocity a -> Energy a+rotationalKineticEnergy i w = i * w ^ pos2 / _2++rotationalWork :: (Num a) => Torque a -> PlaneAngle a -> Energy a+rotationalWork t th = t * th++rotationalMomentum :: (Num a) => MomentOfInertia a -> AngularVelocity a -> AngularMomentum a+rotationalMomentum i w = i * w++rotationalPower :: (Num a) => Torque a -> AngularVelocity a -> Power a+rotationalPower t w = t * w++torque :: (Num a) => Force a -> Length a -> Torque a+torque r f = r * f++torqueFromChangeInMomentum :: (Fractional a) => AngularMomentum a -> Time a -> Torque a+torqueFromChangeInMomentum dL dt = dL / dt
examples/ReadmeExample.hs view
@@ -1,33 +1,33 @@-{-# LANGUAGE NoImplicitPrelude #-} - -module ReadmeExample where - -import Numeric.Units.Dimensional.Prelude -import Numeric.Units.Dimensional.NonSI (mile) - -leg :: Length Double -leg = 1 *~ mile -- *~ combines a raw number and a unit to form a quantity - -speeds :: [Velocity Double] -speeds = [60, 50, 40, 30] *~~ (kilo meter / hour) - -- *~~ does the same thing for a whole Functor at once - -- Parentheses are required around unit expressions that are comingled with *~, /~, *~~, or /~~ operations - -timeOfJourney :: Time Double -timeOfJourney = sum $ fmap (leg /) speeds - -- We can use dimensional versions of ordinary functions like / and sum to combine quantities - -averageSpeed :: Velocity Double -averageSpeed = _4 * leg / timeOfJourney - -- _4 is an alias for the dimensionless number 4 - -wholeSeconds :: Integer -wholeSeconds = ceiling $ timeOfJourney /~ second - -- /~ lets us recover a raw number from a quantity and a unit in which it should be expressed - -main :: IO () -main = do - putStrLn $ "Length of journey is: " ++ showIn minute timeOfJourney - putStrLn $ "Average speed is: " ++ showIn (mile / hour) averageSpeed - putStrLn $ "If we don't want to be explicit about units, the show instance uses the SI basis: " ++ show averageSpeed - putStrLn $ "The journey requires " ++ show wholeSeconds ++ " seconds, rounded up to the nearest second." +{-# LANGUAGE NoImplicitPrelude #-}++module ReadmeExample where++import Numeric.Units.Dimensional.Prelude+import Numeric.Units.Dimensional.NonSI (mile)++leg :: Length Double+leg = 1 *~ mile -- *~ combines a raw number and a unit to form a quantity++speeds :: [Velocity Double]+speeds = [60, 50, 40, 30] *~~ (kilo meter / hour)+ -- *~~ does the same thing for a whole Functor at once+ -- Parentheses are required around unit expressions that are comingled with *~, /~, *~~, or /~~ operations++timeOfJourney :: Time Double+timeOfJourney = sum $ fmap (leg /) speeds+ -- We can use dimensional versions of ordinary functions like / and sum to combine quantities++averageSpeed :: Velocity Double+averageSpeed = _4 * leg / timeOfJourney+ -- _4 is an alias for the dimensionless number 4++wholeSeconds :: Integer+wholeSeconds = ceiling $ timeOfJourney /~ second+ -- /~ lets us recover a raw number from a quantity and a unit in which it should be expressed++main :: IO ()+main = do+ putStrLn $ "Length of journey is: " ++ showIn minute timeOfJourney+ putStrLn $ "Average speed is: " ++ showIn (mile / hour) averageSpeed+ putStrLn $ "If we don't want to be explicit about units, the show instance uses the SI basis: " ++ show averageSpeed+ putStrLn $ "The journey requires " ++ show wholeSeconds ++ " seconds, rounded up to the nearest second."
src/Numeric/Units/Dimensional.hs view
@@ -1,780 +1,781 @@-{-# OPTIONS_HADDOCK show-extensions #-} - -{-# LANGUAGE AutoDeriveTypeable #-} -{-# LANGUAGE ConstraintKinds #-} -{-# LANGUAGE DataKinds #-} -{-# LANGUAGE DeriveDataTypeable #-} -{-# LANGUAGE DeriveGeneric #-} -{-# LANGUAGE FlexibleContexts #-} -{-# LANGUAGE FlexibleInstances #-} -{-# LANGUAGE GeneralizedNewtypeDeriving #-} -{-# LANGUAGE KindSignatures #-} -{-# LANGUAGE PatternGuards #-} -{-# LANGUAGE RankNTypes #-} -{-# LANGUAGE RoleAnnotations #-} -{-# LANGUAGE ScopedTypeVariables #-} -{-# LANGUAGE StandaloneDeriving #-} -{-# LANGUAGE TypeFamilies #-} -{-# LANGUAGE TypeOperators #-} - - -{- | - Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter - License : BSD3 - - Maintainer : bjorn@buckwalter.se - Stability : Stable - Portability: GHC only - -= Summary - -In this module we provide data types for performing arithmetic with -physical quantities and units. Information about the physical -dimensions of the quantities/units is embedded in their types and -the validity of operations is verified by the type checker at compile -time. The boxing and unboxing of numerical values as quantities is -done by multiplication and division of units, of which an incomplete -set is provided. - -We limit ourselves to \"Newtonian\" physics. We do not attempt to -accommodate relativistic physics in which e.g. addition of length -and time would be valid. - -As far as possible and/or practical the conventions and guidelines -of NIST's "Guide for the Use of the International System of Units -(SI)" <#note1 [1]> are followed. Occasionally we will reference specific -sections from the guide and deviations will be explained. - -== Disclaimer - -Merely an engineer, the author doubtlessly uses a language and -notation that makes mathematicians and physicist cringe. He does -not mind constructive criticism (or pull requests). - -The sets of functions and units defined herein are incomplete and -reflect only the author's needs to date. Again, patches are welcome. - -= Usage - -== Preliminaries - -This module requires GHC 8 or later. We utilize Data Kinds, TypeNats, -Closed Type Families, etc. Clients of the module are generally not -required to use these extensions. - -Clients probably will want to use the NegativeLiterals extension. - -== Examples - -We have defined operators and units that allow us to define and -work with physical quantities. A physical quantity is defined by -multiplying a number with a unit (the type signature is optional). - -> v :: Velocity Prelude.Double -> v = 90 *~ (kilo meter / hour) - -It follows naturally that the numerical value of a quantity is -obtained by division by a unit. - -> numval :: Prelude.Double -> numval = v /~ (meter / second) - -The notion of a quantity as the product of a numerical value and a -unit is supported by 7.1 "Value and numerical value of a quantity" of -<#note1 [1]>. While the above syntax is fairly natural it is unfortunate that -it must violate a number of the guidelines in <#note1 [1]>, in particular 9.3 -"Spelling unit names with prefixes", 9.4 "Spelling unit names obtained -by multiplication", 9.5 "Spelling unit names obtained by division". - -As a more elaborate example of how to use the module we define a -function for calculating the escape velocity of a celestial body -<#note2 [2]>. - -> escapeVelocity :: (Floating a) => Mass a -> Length a -> Velocity a -> escapeVelocity m r = sqrt (two * g * m / r) -> where -> two = 2 *~ one -> g = 6.6720e-11 *~ (newton * meter ^ pos2 / kilo gram ^ pos2) - -For completeness we should also show an example of the error messages -we will get from GHC when performing invalid arithmetic. In the -best case GHC will be able to use the type synonyms we have defined -in its error messages. - -> let x = 1 *~ meter + 1 *~ second -> -> Couldn't match type 'Numeric.NumType.DK.Integers.Zero -> with 'Numeric.NumType.DK.Integers.Pos1 -> Expected type: Unit 'Metric DLength a -> Actual type: Unit 'Metric DTime a -> In the second argument of `(*~)', namely `second' -> In the second argument of `(+)', namely `1 *~ second' - -In other cases the error messages aren't very friendly. - -> let x = 1 *~ meter / (1 *~ second) + 1 *~ kilo gram -> -> Couldn't match type 'Numeric.NumType.DK.Integers.Zero -> with 'Numeric.NumType.DK.Integers.Neg1 -> Expected type: Quantity DMass a -> Actual type: Dimensional -> ('DQuantity V.* 'DQuantity) (DLength / DTime) a -> In the first argument of `(+)', namely `1 *~ meter / (1 *~ second)' -> In the expression: 1 *~ meter / (1 *~ second) + 1 *~ kilo gram -> In an equation for `x': -> x = 1 *~ meter / (1 *~ second) + 1 *~ kilo gram - -It is the author's experience that the usefulness of the compiler -error messages is more often than not limited to pinpointing the -location of errors. - -= Notes - -== Future work - -While there is an insane amount of units in use around the world -it is reasonable to provide those in relatively widespread use. Units outside -of SI will most likely be added on an as-needed basis. - -Additional physics models could be implemented. See <#note3 [3]> for ideas. - -== Related work - -Henning Thielemann numeric prelude has a physical units library, -however, checking of dimensions is dynamic rather than static. -Aaron Denney has created a toy example of statically checked -physical dimensions covering only length and time. HaskellWiki -has pointers <#note4 [4]> to these. - -Also see Samuel Hoffstaetter's blog post <#note5 [5]> which uses techniques -similar to this library. - -Libraries with similar functionality exist for other programming -languages and may serve as inspiration. The author has found the -Java library JScience <#note6 [6]> and the Fortress programming language <#note7 [7]> -particularly noteworthy. - -== References - -1. #note1# http://physics.nist.gov/Pubs/SP811/ -2. #note2# http://en.wikipedia.org/wiki/Escape_velocity -3. #note3# http://jscience.org/api/org/jscience/physics/models/package-summary.html -4. #note4# http://www.haskell.org/haskellwiki/Physical_units -5. #note5# http://liftm.wordpress.com/2007/06/03/scientificdimension-type-arithmetic-and-physical-units-in-haskell/ -6. #note6# http://jscience.org/ -7. #note7# http://research.sun.com/projects/plrg/fortress.pdf - --} - -module Numeric.Units.Dimensional - ( - -- * Types - -- $types - Dimensional, - Unit, Quantity, - Metricality(..), - -- * Physical Dimensions - -- $dimensions - Dimension (Dim), - -- ** Dimension Arithmetic - -- $dimension-arithmetic - type (*), type (/), type (^), NRoot, Sqrt, Cbrt, Recip, - -- ** Term Level Representation of Dimensions - -- $dimension-terms - Dimension' (Dim'), HasDimension(..), KnownDimension, - -- * Dimensional Arithmetic - (*~), (/~), - (^), (^/), (**), (*), (/), (+), (-), - negate, abs, signum, recip, nroot, sqrt, cbrt, - -- ** Transcendental Functions - exp, log, logBase, sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, asinh, acosh, atanh, atan2, log1p, expm1, log1pexp, log1mexp, - -- ** Operations on Collections - -- $collections - (*~~), (/~~), sum, mean, product, dimensionlessLength, nFromTo, - -- * Dimension Synonyms - -- $dimension-synonyms - DOne, DLength, DMass, DTime, DElectricCurrent, DThermodynamicTemperature, DAmountOfSubstance, DLuminousIntensity, - -- * Quantity Synonyms - -- $quantity-synonyms - Dimensionless, Length, Mass, Time, ElectricCurrent, ThermodynamicTemperature, AmountOfSubstance, LuminousIntensity, - -- * Constants - -- $constants - _0, _1, _2, _3, _4, _5, _6, _7, _8, _9, pi, tau, - -- * Constructing Units - siUnit, one, mkUnitR, mkUnitQ, mkUnitZ, - -- * Unit Metadata - name, exactValue, weaken, strengthen, exactify, - -- * Pretty Printing - showIn, - -- * On 'Functor', and Conversion Between Number Representations - -- $functor - KnownVariant(dmap), changeRep, changeRepApproximate, - -- * Lenses - -- $lenses - asLens - ) - where - -import Prelude - ( Eq(..), Num, Fractional, Floating, Real, RealFloat, Functor, fmap - , (.), flip, (++), fromIntegral, fromInteger, fromRational, error, max, succ - , Int, Integer, Integral, ($), uncurry, realToFrac, otherwise - ) -import qualified Prelude -import Numeric.NumType.DK.Integers - ( pos2, pos3 - , KnownTypeInt, toNum - ) -import Data.Data -import Data.ExactPi -import Data.Foldable (Foldable(foldr, length)) -import Data.Maybe -import Data.Ratio -import qualified Numeric -import Numeric.Units.Dimensional.Dimensions -import Numeric.Units.Dimensional.Internal -import Numeric.Units.Dimensional.UnitNames hiding ((*), (/), (^), weaken, strengthen, product) -import qualified Numeric.Units.Dimensional.UnitNames.Internal as Name -import Numeric.Units.Dimensional.Variants hiding (type (*), type (/)) -import qualified Numeric.Units.Dimensional.Variants as V - --- $setup --- >>> :set -XFlexibleInstances --- >>> :set -XNoImplicitPrelude --- >>> import Test.QuickCheck.Arbitrary --- >>> import Numeric.Units.Dimensional.Prelude --- >>> import Numeric.Units.Dimensional.Float --- >>> import Numeric.Units.Dimensional.NonSI --- >>> instance Arbitrary a => Arbitrary (Quantity d a) where arbitrary = fmap Quantity arbitrary - -{- -We will reuse the operators and function names from the Prelude. -To prevent unpleasant surprises we give operators the same fixity -as the Prelude. --} - -infixr 8 ^, ^/, ** -infixl 7 *, / -infixl 6 +, - - - -{- $types -Our primary objective is to define a data type that can be used to -represent (while still differentiating between) units and quantities. -There are two reasons for consolidating units and quantities in one -data type. The first being to allow code reuse as they are largely -subject to the same operations. The second being that it allows -reuse of operators (and functions) between the two without resorting -to occasionally cumbersome type classes. - -The relationship between (the value of) a 'Quantity', its numerical -value and its 'Unit' is described in 7.1 "Value and numerical value -of a quantity" of <#note1 [1]>. In short a 'Quantity' is the product of a -number and a 'Unit'. We define the '*~' operator as a convenient -way to declare quantities as such a product. - --} - --- | Extracts the 'UnitName' of a 'Unit'. -name :: Unit m d a -> UnitName m -name (Unit n _ _) = n - --- | Extracts the exact value of a 'Unit', expressed in terms of the SI coherent derived unit (see 'siUnit') of the same 'Dimension'. --- --- Note that the actual value may in some cases be approximate, for example if the unit is defined by experiment. -exactValue :: Unit m d a -> ExactPi -exactValue (Unit _ e _) = e - --- | Discards potentially unwanted type level information about a 'Unit'. -weaken :: Unit m d a -> Unit 'NonMetric d a -weaken (Unit n e v) = Unit (Name.weaken n) e v - --- | Attempts to convert a 'Unit' which may or may not be 'Metric' to one --- which is certainly 'Metric'. -strengthen :: Unit m d a -> Maybe (Unit 'Metric d a) -strengthen (Unit n e v) | Just n' <- Name.strengthen n = Just $ Unit n' e v - | otherwise = Nothing - --- | Forms the exact version of a 'Unit'. -exactify :: Unit m d a -> Unit m d ExactPi -exactify (Unit n e _) = Unit n e e - --- | Forms a 'Quantity' by multipliying a number and a unit. -(*~) :: (Num a) => a -> Unit m d a -> Quantity d a -x *~ (Unit _ _ y) = Quantity (x Prelude.* y) - --- | Divides a 'Quantity' by a 'Unit' of the same physical dimension, obtaining the --- numerical value of the quantity expressed in that unit. -(/~) :: Fractional a => Quantity d a -> Unit m d a -> a -(Quantity x) /~ (Unit _ _ y) = (x Prelude./ y) - -{- -We give '*~' and '/~' the same fixity as '*' and '/' defined below. -Note that this necessitates the use of parenthesis when composing -units using '*' and '/', e.g. "1 *~ (meter / second)". --} - -infixl 7 *~, /~ - -{- $dimensions -The phantom type variable d encompasses the physical dimension of -a 'Dimensional'. As detailed in <#note5 [5]> there are seven base dimensions, -which can be combined in integer powers to a given physical dimension. -We represent physical dimensions as the powers of the seven base -dimensions that make up the given dimension. The powers are represented -using NumTypes. For convenience we collect all seven base dimensions -in a data kind 'Dimension'. - -We could have chosen to provide type variables for the seven base -dimensions in 'Dimensional' instead of creating a new data kind -'Dimension'. However, that would have made any type signatures involving -'Dimensional' very cumbersome. By encompassing the physical dimension -in a single type variable we can "hide" the cumbersome type arithmetic -behind convenient type classes as will be seen later. - --} - -{- $dimension-synonyms -Using our 'Dimension' data kind we define some type synonyms for convenience. -We start with the base dimensions, others can be found in "Numeric.Units.Dimensional.Quantities". - --} - -{- $quantity-synonyms -Using the above type synonyms we can define type synonyms for -quantities of particular physical dimensions. - -Again we limit ourselves to the base dimensions, others can be found in "Numeric.Units.Dimensional.Quantities". - --} - -type Dimensionless = Quantity DOne -type Length = Quantity DLength -type Mass = Quantity DMass -type Time = Quantity DTime -type ElectricCurrent = Quantity DElectricCurrent -type ThermodynamicTemperature = Quantity DThermodynamicTemperature -type AmountOfSubstance = Quantity DAmountOfSubstance -type LuminousIntensity = Quantity DLuminousIntensity - -{- $dimension-arithmetic -When performing arithmetic on units and quantities the arithmetics -must be applied to both the numerical values of the Dimensionals -but also to their physical dimensions. The type level arithmetic -on physical dimensions is governed by closed type families expressed -as type operators. - -We could provide the 'Mul' and 'Div' classes with full functional -dependencies but that would be of limited utility as there is no -limited use for "backwards" type inference. Efforts are underway to -develop a type-checker plugin that does enable these scenarios, e.g. -for linear algebra. - --} - -{- -= Arithmetic on units and quantities = - -Thanks to the arithmetic on physical dimensions having been sorted -out separately a lot of the arithmetic on Dimensionals is straight -forward. In particular the type signatures are much simplified. - -Multiplication, division and powers apply to both units and quantities. --} - --- | Multiplies two 'Quantity's or two 'Unit's. --- --- The intimidating type signature captures the similarity between these operations --- and ensures that composite 'Unit's are 'NonMetric'. -(*) :: (KnownVariant v1, KnownVariant v2, KnownVariant (v1 V.* v2), Num a) => Dimensional v1 d1 a -> Dimensional v2 d2 a -> Dimensional (v1 V.* v2) (d1 * d2) a -(*) = liftD2 (Prelude.*) (Prelude.*) (Name.*) - --- | Divides one 'Quantity' by another or one 'Unit' by another. --- --- The intimidating type signature captures the similarity between these operations --- and ensures that composite 'Unit's are 'NotPrefixable'. -(/) :: (KnownVariant v1, KnownVariant v2, KnownVariant (v1 V./ v2), Fractional a) => Dimensional v1 d1 a -> Dimensional v2 d2 a -> Dimensional (v1 V./ v2) (d1 / d2) a -(/) = liftD2 (Prelude./) (Prelude./) (Name./) - --- | Forms the reciprocal of a 'Quantity', which has the reciprocal dimension. --- --- >>> recip $ 47 *~ hertz --- 2.127659574468085e-2 s -recip :: (Fractional a) => Quantity d a -> Quantity (Recip d) a -recip = liftQ Prelude.recip - --- | Raises a 'Quantity' or 'Unit' to an integer power. --- --- Because the power chosen impacts the 'Dimension' of the result, it is necessary to supply a type-level representation --- of the exponent in the form of a 'Proxy' to some 'TypeInt'. Convenience values 'pos1', 'pos2', 'neg1', ... --- are supplied by the "Numeric.NumType.DK.Integers" module. The most commonly used ones are --- also reexported by "Numeric.Units.Dimensional.Prelude". --- --- The intimidating type signature captures the similarity between these operations --- and ensures that composite 'Unit's are 'NotPrefixable'. -(^) :: (Fractional a, KnownTypeInt i, KnownVariant v, KnownVariant (Weaken v)) - => Dimensional v d1 a -> Proxy i -> Dimensional (Weaken v) (d1 ^ i) a -x ^ n = let n' = (toNum n) :: Int - in liftD (Prelude.^^ n') (Prelude.^^ n') (Name.^ n') x - -{- -A special case is that dimensionless quantities are not restricted -to integer exponents. This is accommodated by the '**' operator -defined later. - - -= Quantity operations = - -Some additional operations obviously only make sense for quantities. -Of these, negation, addition and subtraction are particularly simple -as they are done in a single physical dimension. --} - --- | Negates the value of a 'Quantity'. -negate :: Num a => Quantity d a -> Quantity d a -negate = liftQ Prelude.negate - --- | Adds two 'Quantity's. -(+) :: Num a => Quantity d a -> Quantity d a -> Quantity d a -(+) = liftQ2 (Prelude.+) - --- | Subtracts one 'Quantity' from another. -(-) :: Num a => Quantity d a -> Quantity d a -> Quantity d a -(-) = liftQ2 (Prelude.-) - --- | Takes the absolute value of a 'Quantity'. -abs :: Num a => Quantity d a -> Quantity d a -abs = liftQ Prelude.abs - --- | Takes the sign of a 'Quantity'. The functions 'abs' and 'signum' --- satisy the law that: --- --- > abs x * signum x == x --- --- The sign is either @negate _1@ (negative), @_0@ (zero), --- or @_1@ (positive). -signum :: Num a => Quantity d a -> Dimensionless a -signum = liftQ Prelude.signum - -{- -Roots of arbitrary (integral) degree. Appears to occasionally be useful -for units as well as quantities. --} - --- | Computes the nth root of a 'Quantity' using 'Prelude.**'. --- --- The 'NRoot' type family will prevent application of this operator where the result would have a fractional dimension or where n is zero. --- --- Because the root chosen impacts the 'Dimension' of the result, it is necessary to supply a type-level representation --- of the root in the form of a 'Proxy' to some 'TypeInt'. Convenience values 'pos1', 'pos2', 'neg1', ... --- are supplied by the "Numeric.NumType.DK.Integers" module. The most commonly used ones are --- also reexported by "Numeric.Units.Dimensional.Prelude". --- --- n must not be zero. Negative roots are defined such that @nroot (Proxy :: Proxy (Negate n)) x == nroot (Proxy :: Proxy n) (recip x)@. --- --- Also available in operator form, see '^/'. -nroot :: (KnownTypeInt n, Floating a) - => Proxy n -> Quantity d a -> Quantity (NRoot d n) a -nroot n = let n' = 1 Prelude./ toNum n - in liftQ (Prelude.** n') - -{- -We provide short-hands for the square and cube roots. --} - --- | Computes the square root of a 'Quantity' using 'Prelude.**'. --- --- The 'NRoot' type family will prevent application where the supplied quantity does not have a square dimension. --- --- prop> (x :: Area Double) >= _0 ==> sqrt x == nroot pos2 x -sqrt :: Floating a => Quantity d a -> Quantity (Sqrt d) a -sqrt = nroot pos2 - --- | Computes the cube root of a 'Quantity' using 'Prelude.**'. --- --- The 'NRoot' type family will prevent application where the supplied quantity does not have a cubic dimension. --- --- prop> (x :: Volume Double) >= _0 ==> cbrt x == nroot pos3 x -cbrt :: Floating a => Quantity d a -> Quantity (Cbrt d) a -cbrt = nroot pos3 - -{- -We also provide an operator alternative to nroot for those that -prefer such. --} - --- | Computes the nth root of a 'Quantity' using 'Prelude.**'. --- --- The 'NRoot' type family will prevent application of this operator where the result would have a fractional dimension or where n is zero. --- --- Because the root chosen impacts the 'Dimension' of the result, it is necessary to supply a type-level representation --- of the root in the form of a 'Proxy' to some 'TypeInt'. Convenience values 'pos1', 'pos2', 'neg1', ... --- are supplied by the "Numeric.NumType.DK.Integers" module. The most commonly used ones are --- also reexported by "Numeric.Units.Dimensional.Prelude". --- --- Also available in prefix form, see 'nroot'. -(^/) :: (KnownTypeInt n, Floating a) - => Quantity d a -> Proxy n -> Quantity (NRoot d n) a -(^/) = flip nroot - -{- $collections -Here we define operators and functions to make working with homogenuous -lists of dimensionals more convenient. - -We define two convenience operators for applying units to all -elements of a functor (e.g. a list). --} - --- | Applies '*~' to all values in a functor. -(*~~) :: (Functor f, Num a) => f a -> Unit m d a -> f (Quantity d a) -xs *~~ u = fmap (*~ u) xs - --- | Applies '/~' to all values in a functor. -(/~~) :: forall f m d a.(Functor f, Fractional a) => f (Quantity d a) -> Unit m d a -> f a -xs /~~ u = fmap (/~ u) xs - -infixl 7 *~~, /~~ - --- | The sum of all elements in a foldable structure. --- --- >>> sum ([] :: [Mass Double]) --- 0.0 kg --- --- >>> sum [12.4 *~ meter, 1 *~ foot] --- 12.7048 m -sum :: (Num a, Foldable f) => f (Quantity d a) -> Quantity d a -sum = foldr (+) _0 - --- | The product of all elements in a foldable structure. --- --- >>> product ([] :: [Dimensionless Double]) --- 1.0 --- --- >>> product [pi, _4, 0.36 *~ one] --- 4.523893421169302 -product :: (Num a, Foldable f) => f (Dimensionless a) -> Dimensionless a -product = foldr (*) _1 - --- | The arithmetic mean of all elements in a foldable structure. --- --- >>> mean [pi, _7] --- 5.070796326794897 -mean :: (Fractional a, Foldable f) => f (Quantity d a) -> Quantity d a -mean = uncurry (/) . foldr accumulate (_0, _0) - where - accumulate val (accum, count) = (accum + val, count + _1) - --- | The length of the foldable data structure as a 'Dimensionless'. --- This can be useful for purposes of e.g. calculating averages. --- --- >>> dimensionlessLength ["foo", "bar"] --- 2 -dimensionlessLength :: (Num a, Foldable f) => f b -> Dimensionless a -dimensionlessLength x = (fromIntegral $ length x) *~ one - --- | Returns a list of quantities between given bounds. --- --- prop> n <= 0 ==> nFromTo (x :: Mass Double) (y :: Mass Double) n == [x, y] --- --- prop> (x :: Length Double) <= (y :: Length Double) ==> all (\z -> x <= z && z <= y) (nFromTo x y n) --- --- >>> nFromTo _0 _3 2 --- [0.0,1.0,2.0,3.0] --- --- >>> nFromTo _1 _0 7 --- [1.0,0.875,0.75,0.625,0.5,0.375,0.25,0.125,0.0] --- --- >>> nFromTo _0 _1 (-5) --- [0.0,1.0] -nFromTo :: (Fractional a, Integral b) => Quantity d a -- ^ The initial value. - -> Quantity d a -- ^ The final value. - -> b -- ^ The number of intermediate values. If less than one, no intermediate values will result. - -> [Quantity d a] -nFromTo xi xf n = fmap f [0..n'] ++ [xf] - where - n' = max 0 n - f i = xi + realToFrac (i % succ n') *~ one * (xf - xi) - -{- -We continue by defining elementary functions on 'Dimensionless' -that may be obviously useful. --} - -exp, log, sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, asinh, acosh, atanh, log1p, expm1, log1pexp, log1mexp - :: Floating a => Dimensionless a -> Dimensionless a -exp = fmap Prelude.exp -log = fmap Prelude.log -sin = fmap Prelude.sin -cos = fmap Prelude.cos -tan = fmap Prelude.tan -asin = fmap Prelude.asin -acos = fmap Prelude.acos -atan = fmap Prelude.atan -sinh = fmap Prelude.sinh -cosh = fmap Prelude.cosh -tanh = fmap Prelude.tanh -asinh = fmap Prelude.asinh -acosh = fmap Prelude.acosh -atanh = fmap Prelude.atanh -log1p = fmap Numeric.log1p -expm1 = fmap Numeric.expm1 -log1pexp = fmap Numeric.log1pexp -log1mexp = fmap Numeric.log1mexp - --- | Raises a dimensionless quantity to a dimensionless power. -(**) :: Floating a => Dimensionless a -> Dimensionless a -> Dimensionless a -(**) = liftQ2 (Prelude.**) - --- | Takes the logarithm of the second argument in the base of the first. --- --- >>> logBase _2 _8 --- 3.0 -logBase :: Floating a => Dimensionless a -> Dimensionless a -> Dimensionless a -logBase = liftQ2 Prelude.logBase - --- | The standard two argument arctangent function. --- Since it interprets its two arguments in comparison with one another, the input may have any dimension. --- --- >>> atan2 _0 _1 --- 0.0 --- --- >>> atan2 _1 _0 --- 1.5707963267948966 --- --- >>> atan2 _0 (negate _1) --- 3.141592653589793 --- --- >>> atan2 (negate _1) _0 --- -1.5707963267948966 -atan2 :: (RealFloat a) => Quantity d a -> Quantity d a -> Dimensionless a -atan2 = liftQ2 Prelude.atan2 - -{- -The only unit we will define in this module is 'one'. --} - --- | The unit 'one' has dimension 'DOne' and is the base unit of dimensionless values. --- --- As detailed in 7.10 "Values of quantities expressed simply as numbers: --- the unit one, symbol 1" of <#note1 [1]> the unit one generally does not --- appear in expressions. However, for us it is necessary to use 'one' --- as we would any other unit to perform the "boxing" of dimensionless values. -one :: Num a => Unit 'NonMetric DOne a -one = Unit nOne 1 1 - -{- $constants -For convenience we define some constants for small integer values -that often show up in formulae. We also throw in 'pi' and 'tau' for -good measure. - --} - --- | The constant for zero is polymorphic, allowing it to express zero 'Length' or --- 'Numeric.Units.Dimensional.Quantities.Capacitance' or 'Numeric.Units.Dimensional.Quantities.Velocity' etc, --- in addition to the 'Dimensionless' value zero. -_0 :: Num a => Quantity d a -_0 = Quantity 0 - -_1, _2, _3, _4, _5, _6, _7, _8, _9 :: (Num a) => Dimensionless a -_1 = 1 *~ one -_2 = 2 *~ one -_3 = 3 *~ one -_4 = 4 *~ one -_5 = 5 *~ one -_6 = 6 *~ one -_7 = 7 *~ one -_8 = 8 *~ one -_9 = 9 *~ one - -pi :: Floating a => Dimensionless a -pi = Prelude.pi *~ one - --- | Twice 'pi'. --- --- For background on 'tau' see http://tauday.com/tau-manifesto (but also --- feel free to review http://www.thepimanifesto.com). -tau :: Floating a => Dimensionless a -tau = _2 * pi - -{- $functor -We intentionally decline to provide a 'Functor' instance for 'Dimensional' because its use breaks the -abstraction of physical dimensions. - -If you feel your work requires this instance, it is provided as an orphan in "Numeric.Units.Dimensional.Functor". - --} - --- | Convenient conversion between numerical types while retaining dimensional information. --- --- >>> let x = (37 :: Rational) *~ poundMass --- >>> changeRep x :: Mass Double --- 16.78291769 kg -changeRep :: (KnownVariant v, Real a, Fractional b) => Dimensional v d a -> Dimensional v d b -changeRep = dmap realToFrac - --- | Convenient conversion from exactly represented values while retaining dimensional information. -changeRepApproximate :: (KnownVariant v, Floating b) => Dimensional v d ExactPi -> Dimensional v d b -changeRepApproximate = dmap approximateValue - -{- $lenses -These functions are compatible with the lens library. - --} - --- | Converts a 'Unit' into a lens from 'Quantity's to values. -asLens :: (Fractional a) => Unit m d a - -> (forall f.Functor f => (a -> f a) - -> Quantity d a - -> f (Quantity d a)) -asLens u f q = fmap (\v' -> v' *~ u) (f (q /~ u)) - -{- $dimension-terms -To facilitate parsing and pretty-printing functions that may wish to operate on term-level representations of dimension, -we provide a means for converting from type-level dimensions to term-level dimensions. - --} - --- | Forms a new atomic 'Unit' by specifying its 'UnitName' and its definition as a multiple of another 'Unit'. --- --- Use this variant when the scale factor of the resulting unit is irrational or 'Approximate'. See 'mkUnitQ' for when it is rational --- and 'mkUnitZ' for when it is an integer. --- --- Note that supplying zero as a definining quantity is invalid, as the library relies --- upon units forming a group under multiplication. --- --- Supplying negative defining quantities is allowed and handled gracefully, but is discouraged --- on the grounds that it may be unexpected by other readers. -mkUnitR :: Floating a => UnitName m -> ExactPi -> Unit m1 d a -> Unit m d a -mkUnitR n s (Unit _ e _) | isExactZero s = error "Supplying zero as a conversion factor is not valid." - | otherwise = Unit n e' x' - where - e' = s Prelude.* e - x' = approximateValue e' - --- | Forms a new atomic 'Unit' by specifying its 'UnitName' and its definition as a multiple of another 'Unit'. --- --- Use this variant when the scale factor of the resulting unit is rational. See 'mkUnitZ' for when it is an integer --- and 'mkUnitR' for the general case. --- --- For more information see 'mkUnitR'. -mkUnitQ :: Fractional a => UnitName m -> Rational -> Unit m1 d a -> Unit m d a -mkUnitQ n s (Unit _ e x) | s == 0 = error "Supplying zero as a conversion factor is not valid." - | Just x'' <- toExactRational e' = Unit n e' (fromRational x'') - | otherwise = Unit n e' x' - where - e' = fromRational s Prelude.* e - x' = fromRational s Prelude.* x - --- | Forms a new atomic 'Unit' by specifying its 'UnitName' and its definition as a multiple of another 'Unit'. --- --- Use this variant when the scale factor of the resulting unit is an integer. See 'mkUnitQ' for when it is rational --- and 'mkUnitR' for the general case. --- --- For more information see 'mkUnitR'. -mkUnitZ :: Num a => UnitName m -> Integer -> Unit m1 d a -> Unit m d a -mkUnitZ n s (Unit _ e x) | s == 0 = error "Supplying zero as a conversion factor is not valid." - | Just x'' <- toExactInteger e' = Unit n e' (fromInteger x'') - | otherwise = Unit n e' x' - where - e' = fromInteger s Prelude.* e - x' = fromInteger s Prelude.* x +{-# OPTIONS_HADDOCK show-extensions #-}++{-# LANGUAGE ConstraintKinds #-}+{-# LANGUAGE DataKinds #-}+{-# LANGUAGE DeriveDataTypeable #-}+{-# LANGUAGE DeriveGeneric #-}+{-# LANGUAGE FlexibleContexts #-}+{-# LANGUAGE FlexibleInstances #-}+{-# LANGUAGE GeneralizedNewtypeDeriving #-}+{-# LANGUAGE KindSignatures #-}+{-# LANGUAGE PatternGuards #-}+{-# LANGUAGE RankNTypes #-}+{-# LANGUAGE RoleAnnotations #-}+{-# LANGUAGE ScopedTypeVariables #-}+{-# LANGUAGE StandaloneDeriving #-}+{-# LANGUAGE TypeFamilies #-}+{-# LANGUAGE TypeOperators #-}+++{- |+ Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter+ License : BSD3++ Maintainer : bjorn@buckwalter.se+ Stability : Stable+ Portability: GHC only++= Summary++In this module we provide data types for performing arithmetic with+physical quantities and units. Information about the physical+dimensions of the quantities/units is embedded in their types and+the validity of operations is verified by the type checker at compile+time. The wrapping and unwrapping of numerical values as quantities is+done by multiplication and division of units, of which an incomplete+set is provided.++We limit ourselves to \"Newtonian\" physics. We do not attempt to+accommodate relativistic physics in which e.g. addition of length+and time would be valid.++As far as possible and/or practical the conventions and guidelines+of NIST's "Guide for the Use of the International System of Units+(SI)" <#note1 [1]> are followed. Occasionally we will reference specific+sections from the guide and deviations will be explained.++== Disclaimer++Merely an engineer, the author doubtlessly uses a language and+notation that makes mathematicians and physicists cringe. He does+not mind constructive criticism (or pull requests).++The sets of functions and units defined herein are incomplete and+reflect only the author's needs to date. Again, patches are welcome.++= Usage++== Preliminaries++This module requires GHC 8 or later. We utilize Data Kinds, TypeNats,+Closed Type Families, etc. Clients of the module are generally not+required to use these extensions.++Clients probably will want to use the @NegativeLiterals@ extension though.++== Examples++We have defined operators and units that allow us to define and+work with physical quantities. A physical quantity is defined by+multiplying a number with a unit (the type signature is optional).++> v :: Velocity Double+> v = 90 *~ (kilo meter / hour)++It follows naturally that the numerical value of a quantity is+obtained by division by a unit.++> numval :: Double+> numval = v /~ (meter / second)++The notion of a quantity as the product of a numerical value and a+unit is supported by 7.1 "Value and numerical value of a quantity" of+<#note1 [1]>. While the above syntax is fairly natural, it is unfortunate that+it must violate a number of the guidelines in <#note1 [1]>, in particular 9.3+"Spelling unit names with prefixes", 9.4 "Spelling unit names obtained+by multiplication", 9.5 "Spelling unit names obtained by division".++As a more elaborate example of how to use the module, we define a+function for calculating the escape velocity of a celestial body+<#note2 [2]>.++> escapeVelocity :: (Floating a) => Mass a -> Length a -> Velocity a+> escapeVelocity m r = sqrt (two * g * m / r)+> where+> two = 2 *~ one+> g = 6.6720e-11 *~ (newton * meter ^ pos2 / kilo gram ^ pos2)++For completeness, we should also show an example of the error messages+we will get from GHC when performing invalid arithmetic. In the+best case, GHC will be able to use the type synonyms we have defined+in its error messages.++> let x = 1 *~ meter + 1 *~ second+>+> Couldn't match type 'Numeric.NumType.DK.Integers.Zero+> with 'Numeric.NumType.DK.Integers.Pos1+> Expected type: Unit 'Metric DLength a+> Actual type: Unit 'Metric DTime a+> In the second argument of `(*~)', namely `second'+> In the second argument of `(+)', namely `1 *~ second'++In other cases, the error messages aren't very friendly.++> let x = 1 *~ meter / (1 *~ second) + 1 *~ kilo gram+>+> Couldn't match type 'Numeric.NumType.DK.Integers.Zero+> with 'Numeric.NumType.DK.Integers.Neg1+> Expected type: Quantity DMass a+> Actual type: Dimensional+> ('DQuantity V.* 'DQuantity) (DLength / DTime) a+> In the first argument of `(+)', namely `1 *~ meter / (1 *~ second)'+> In the expression: 1 *~ meter / (1 *~ second) + 1 *~ kilo gram+> In an equation for `x':+> x = 1 *~ meter / (1 *~ second) + 1 *~ kilo gram++It is the author's experience that the usefulness of the compiler+error messages is more often than not limited to pinpointing the+location of errors.++= Notes++== Future work++While there is an insane amount of units in use around the world+it is reasonable to provide those in relatively widespread use. Units outside+of SI will most likely be added on an as-needed basis.++Additional physics models could be implemented. See <#note3 [3]> for ideas.++== Related work++Henning Thielemann's numeric prelude has a physical units library,+however, checking of dimensions is dynamic rather than static.+Aaron Denney has created a toy example of statically checked+physical dimensions covering only length and time. HaskellWiki+has pointers <#note4 [4]> to these.++Also see Samuel Hoffstaetter's blog post <#note5 [5]> which uses techniques+similar to this library.++Libraries with similar functionality exist for other programming+languages and may serve as inspiration. The author has found the+Java library JScience <#note6 [6]> and the Fortress programming language <#note7 [7]>+particularly noteworthy.++== References++1. #note1# https://www.nist.gov/pml/special-publication-811+2. #note2# https://en.wikipedia.org/wiki/Escape_velocity+3. #note3# https://web.archive.org/web/20080905151927/http://jscience.org/api/org/jscience/physics/models/package-summary.html+4. #note4# https://wiki.haskell.org/Physical_units+5. #note5# https://liftm.wordpress.com/2007/06/03/scientificdimension-type-arithmetic-and-physical-units-in-haskell/+6. #note6# http://jscience.org/+6. #note6# https://github.com/stokito/fortress-lang++-}++module Numeric.Units.Dimensional+ (+ -- * Types+ -- $types+ Dimensional,+ Unit, Quantity,+ Metricality(..),+ -- * Physical Dimensions+ -- $dimensions+ Dimension (Dim),+ -- ** Dimension Arithmetic+ -- $dimension-arithmetic+ type (*), type (/), type (^), NRoot, Sqrt, Cbrt, Recip,+ -- ** Term Level Representation of Dimensions+ -- $dimension-terms+ Dimension' (Dim'), HasDimension(..), KnownDimension,+ -- * Dimensional Arithmetic+ (*~), (/~),+ (^), (^/), (**), (*), (/), (+), (-),+ negate, abs, signum, recip, nroot, sqrt, cbrt,+ -- ** Transcendental Functions+ exp, log, logBase, sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, asinh, acosh, atanh, atan2, log1p, expm1, log1pexp, log1mexp,+ -- ** Operations on Collections+ -- $collections+ (*~~), (/~~), sum, mean, product, dimensionlessLength, nFromTo,+ -- * Dimension Synonyms+ -- $dimension-synonyms+ DOne, DLength, DMass, DTime, DElectricCurrent, DThermodynamicTemperature, DAmountOfSubstance, DLuminousIntensity,+ -- * Quantity Synonyms+ -- $quantity-synonyms+ Dimensionless, Length, Mass, Time, ElectricCurrent, ThermodynamicTemperature, AmountOfSubstance, LuminousIntensity,+ -- * Constants+ -- $constants+ _0, _1, _2, _3, _4, _5, _6, _7, _8, _9, pi, tau,+ -- * Constructing Units+ siUnit, one, mkUnitR, mkUnitQ, mkUnitZ,+ -- * Unit Metadata+ name, exactValue, weaken, strengthen, exactify,+ -- * Pretty Printing+ showIn,+ -- * On 'Functor', and Conversion Between Number Representations+ -- $functor+ KnownVariant(dmap), changeRep, changeRepApproximate,+ -- * Lenses+ -- $lenses+ asLens+ )+ where++import Prelude+ ( Eq(..), Num, Fractional, Floating, Real, RealFloat, Functor, fmap+ , (.), flip, (++), fromIntegral, fromInteger, fromRational, error, max, succ+ , Int, Integer, Integral, ($), uncurry, realToFrac, otherwise+ )+import qualified Prelude+import Numeric.NumType.DK.Integers+ ( pos2, pos3+ , KnownTypeInt, toNum+ )+import Data.Data+import Data.ExactPi+import Data.Foldable (Foldable(foldr, length))+import Data.Maybe+import Data.Ratio+import qualified Numeric+import Numeric.Units.Dimensional.Dimensions+import Numeric.Units.Dimensional.Internal+import Numeric.Units.Dimensional.UnitNames hiding ((*), (/), (^), weaken, strengthen, product)+import qualified Numeric.Units.Dimensional.UnitNames.Internal as Name+import Numeric.Units.Dimensional.Variants hiding (type (*), type (/))+import qualified Numeric.Units.Dimensional.Variants as V++-- $setup+-- >>> :set -XFlexibleInstances+-- >>> :set -XNoImplicitPrelude+-- >>> :set -fno-warn-orphans+-- >>> :set -fno-warn-type-defaults+-- >>> import Test.QuickCheck.Arbitrary+-- >>> import Numeric.Units.Dimensional.Prelude+-- >>> import Numeric.Units.Dimensional.Float+-- >>> import Numeric.Units.Dimensional.NonSI+-- >>> instance Arbitrary a => Arbitrary (Quantity d a) where arbitrary = fmap Quantity arbitrary++{-+We will reuse the operators and function names from the Prelude.+To prevent unpleasant surprises we give operators the same fixity+as the Prelude.+-}++infixr 8 ^, ^/, **+infixl 7 *, /+infixl 6 +, -+++{- $types+Our primary objective is to define a data type that can be used to+represent (while still differentiating between) units and quantities.+There are two reasons for consolidating units and quantities in one+data type. The first being to allow code reuse as they are largely+subject to the same operations. The second being that it allows+reuse of operators (and functions) between the two without resorting+to occasionally cumbersome type classes.++The relationship between (the value of) a 'Quantity', its numerical+value and its 'Unit' is described in 7.1 "Value and numerical value+of a quantity" of <#note1 [1]>. In short a 'Quantity' is the product of a+number and a 'Unit'. We define the '*~' operator as a convenient+way to declare quantities as such a product.++-}++-- | Extracts the 'UnitName' of a 'Unit'.+name :: Unit m d a -> UnitName m+name (Unit n _ _) = n++-- | Extracts the exact value of a 'Unit', expressed in terms of the SI coherent derived unit (see 'siUnit') of the same 'Dimension'.+--+-- Note that the actual value may in some cases be approximate, for example if the unit is defined by experiment.+exactValue :: Unit m d a -> ExactPi+exactValue (Unit _ e _) = e++-- | Discards potentially unwanted type level information about a 'Unit'.+weaken :: Unit m d a -> Unit 'NonMetric d a+weaken (Unit n e v) = Unit (Name.weaken n) e v++-- | Attempts to convert a 'Unit' which may or may not be 'Metric' to one+-- which is certainly 'Metric'.+strengthen :: Unit m d a -> Maybe (Unit 'Metric d a)+strengthen (Unit n e v) | Just n' <- Name.strengthen n = Just $ Unit n' e v+ | otherwise = Nothing++-- | Forms the exact version of a 'Unit'.+exactify :: Unit m d a -> Unit m d ExactPi+exactify (Unit n e _) = Unit n e e++-- | Forms a 'Quantity' by multipliying a number and a unit.+(*~) :: (Num a) => a -> Unit m d a -> Quantity d a+x *~ (Unit _ _ y) = Quantity (x Prelude.* y)++-- | Divides a 'Quantity' by a 'Unit' of the same physical dimension, obtaining the+-- numerical value of the quantity expressed in that unit.+(/~) :: Fractional a => Quantity d a -> Unit m d a -> a+(Quantity x) /~ (Unit _ _ y) = (x Prelude./ y)++{-+We give '*~' and '/~' the same fixity as '*' and '/' defined below.+Note that this necessitates the use of parenthesis when composing+units using '*' and '/', e.g. "1 *~ (meter / second)".+-}++infixl 7 *~, /~++{- $dimensions+The phantom type variable @d@ encompasses the physical dimension of+a 'Dimensional'. As detailed in <#note5 [5]>, there are seven base dimensions,+which can be combined in integer powers to a given physical dimension.+We represent physical dimensions as the powers of the seven base+dimensions that make up the given dimension. The powers are represented+using NumTypes. For convenience, we collect all seven base dimensions+in a data kind 'Dimension'.++We could have chosen to provide type variables for the seven base+dimensions in 'Dimensional' instead of creating a new data kind+'Dimension'. However, that would have made any type signatures involving+'Dimensional' very cumbersome. By encompassing the physical dimension+in a single type variable we can "hide" the cumbersome type arithmetic+behind convenient type classes as will be seen later.++-}++{- $dimension-synonyms+Using our 'Dimension' data kind we define some type synonyms for convenience.+We start with the base dimensions, others can be found in "Numeric.Units.Dimensional.Quantities".++-}++{- $quantity-synonyms+Using the above type synonyms we can define type synonyms for+quantities of particular physical dimensions.++Again we limit ourselves to the base dimensions, others can be found in "Numeric.Units.Dimensional.Quantities".++-}++type Dimensionless = Quantity DOne+type Length = Quantity DLength+type Mass = Quantity DMass+type Time = Quantity DTime+type ElectricCurrent = Quantity DElectricCurrent+type ThermodynamicTemperature = Quantity DThermodynamicTemperature+type AmountOfSubstance = Quantity DAmountOfSubstance+type LuminousIntensity = Quantity DLuminousIntensity++{- $dimension-arithmetic+When performing arithmetic on units and quantities, the arithmetics+must be applied to both the numerical values of the Dimensionals+but also to their physical dimensions. The type level arithmetic+on physical dimensions is governed by closed type families expressed+as type operators.++We could provide the 'Mul' and 'Div' classes with full functional+dependencies but that would be of limited utility as there is no+limited use for "backwards" type inference. Efforts are underway to+develop a type-checker plugin that does enable these scenarios, e.g.+for linear algebra.++-}++{-+= Arithmetic on units and quantities =++Thanks to the arithmetic on physical dimensions having been sorted+out separately a lot of the arithmetic on Dimensionals is straight+forward. In particular the type signatures are much simplified.++Multiplication, division and powers apply to both units and quantities.+-}++-- | Multiplies two 'Quantity's or two 'Unit's.+--+-- The intimidating type signature captures the similarity between these operations+-- and ensures that composite 'Unit's are 'NonMetric'.+(*) :: (KnownVariant v1, KnownVariant v2, KnownVariant (v1 V.* v2), Num a) => Dimensional v1 d1 a -> Dimensional v2 d2 a -> Dimensional (v1 V.* v2) (d1 * d2) a+(*) = liftD2 (Prelude.*) (Prelude.*) (Name.*)++-- | Divides one 'Quantity' by another or one 'Unit' by another.+--+-- The intimidating type signature captures the similarity between these operations+-- and ensures that composite 'Unit's are 'NonMetric'.+(/) :: (KnownVariant v1, KnownVariant v2, KnownVariant (v1 V./ v2), Fractional a) => Dimensional v1 d1 a -> Dimensional v2 d2 a -> Dimensional (v1 V./ v2) (d1 / d2) a+(/) = liftD2 (Prelude./) (Prelude./) (Name./)++-- | Forms the reciprocal of a 'Quantity', which has the reciprocal dimension.+--+-- >>> recip $ 47 *~ hertz+-- 2.127659574468085e-2 s+recip :: (Fractional a) => Quantity d a -> Quantity (Recip d) a+recip = liftQ Prelude.recip++-- | Raises a 'Quantity' or 'Unit' to an integer power.+--+-- Because the power chosen impacts the 'Dimension' of the result, it is necessary to supply a type-level representation+-- of the exponent in the form of a 'Proxy' to some 'TypeInt'. Convenience values 'pos1', 'pos2', 'neg1', ...+-- are supplied by the "Numeric.NumType.DK.Integers" module. The most commonly used ones are+-- also reexported by "Numeric.Units.Dimensional.Prelude".+--+-- The intimidating type signature captures the similarity between these operations+-- and ensures that composite 'Unit's are 'NonMetric'.+(^) :: (Fractional a, KnownTypeInt i, KnownVariant v, KnownVariant (Weaken v))+ => Dimensional v d1 a -> Proxy i -> Dimensional (Weaken v) (d1 ^ i) a+x ^ n = let n' = (toNum n) :: Int+ in liftD (Prelude.^^ n') (Prelude.^^ n') (Name.^ n') x++{-+A special case is that dimensionless quantities are not restricted+to integer exponents. This is accommodated by the '**' operator+defined later.+++= Quantity operations =++Some additional operations obviously only make sense for quantities.+Of these, negation, addition and subtraction are particularly simple+as they are done in a single physical dimension.+-}++-- | Negates the value of a 'Quantity'.+negate :: Num a => Quantity d a -> Quantity d a+negate = liftQ Prelude.negate++-- | Adds two 'Quantity's.+(+) :: Num a => Quantity d a -> Quantity d a -> Quantity d a+(+) = liftQ2 (Prelude.+)++-- | Subtracts one 'Quantity' from another.+(-) :: Num a => Quantity d a -> Quantity d a -> Quantity d a+(-) = liftQ2 (Prelude.-)++-- | Takes the absolute value of a 'Quantity'.+abs :: Num a => Quantity d a -> Quantity d a+abs = liftQ Prelude.abs++-- | Takes the sign of a 'Quantity'. The functions 'abs' and 'signum'+-- satisy the law that:+--+-- > abs x * signum x == x+--+-- The sign is either @negate _1@ (negative), @_0@ (zero),+-- or @_1@ (positive).+signum :: Num a => Quantity d a -> Dimensionless a+signum = liftQ Prelude.signum++{-+Roots of arbitrary (integral) degree. Appears to occasionally be useful+for units as well as quantities.+-}++-- | Computes the nth root of a 'Quantity' using 'Prelude.**'.+--+-- The 'NRoot' type family will prevent application of this operator where the result would have a fractional dimension or where n is zero.+--+-- Because the root chosen impacts the 'Dimension' of the result, it is necessary to supply a type-level representation+-- of the root in the form of a 'Proxy' to some 'TypeInt'. Convenience values 'pos1', 'pos2', 'neg1', ...+-- are supplied by the "Numeric.NumType.DK.Integers" module. The most commonly used ones are+-- also reexported by "Numeric.Units.Dimensional.Prelude".+--+-- n must not be zero. Negative roots are defined such that @nroot (Proxy :: Proxy (Negate n)) x == nroot (Proxy :: Proxy n) (recip x)@.+--+-- Also available in operator form, see '^/'.+nroot :: (KnownTypeInt n, Floating a)+ => Proxy n -> Quantity d a -> Quantity (NRoot d n) a+nroot n = let n' = 1 Prelude./ toNum n+ in liftQ (Prelude.** n')++{-+We provide short-hands for the square and cube roots.+-}++-- | Computes the square root of a 'Quantity' using 'Prelude.**'.+--+-- The 'NRoot' type family will prevent application where the supplied quantity does not have a square dimension.+--+-- prop> (x :: Area Double) >= _0 ==> sqrt x == nroot pos2 x+sqrt :: Floating a => Quantity d a -> Quantity (Sqrt d) a+sqrt = nroot pos2++-- | Computes the cube root of a 'Quantity' using 'Prelude.**'.+--+-- The 'NRoot' type family will prevent application where the supplied quantity does not have a cubic dimension.+--+-- prop> (x :: Volume Double) >= _0 ==> cbrt x == nroot pos3 x+cbrt :: Floating a => Quantity d a -> Quantity (Cbrt d) a+cbrt = nroot pos3++{-+We also provide an operator alternative to nroot for those that+prefer such.+-}++-- | Computes the nth root of a 'Quantity' using 'Prelude.**'.+--+-- The 'NRoot' type family will prevent application of this operator where the result would have a fractional dimension or where n is zero.+--+-- Because the root chosen impacts the 'Dimension' of the result, it is necessary to supply a type-level representation+-- of the root in the form of a 'Proxy' to some 'TypeInt'. Convenience values 'pos1', 'pos2', 'neg1', ...+-- are supplied by the "Numeric.NumType.DK.Integers" module. The most commonly used ones are+-- also reexported by "Numeric.Units.Dimensional.Prelude".+--+-- Also available in prefix form, see 'nroot'.+(^/) :: (KnownTypeInt n, Floating a)+ => Quantity d a -> Proxy n -> Quantity (NRoot d n) a+(^/) = flip nroot++{- $collections+Here we define operators and functions to make working with homogeneous+lists of dimensionals more convenient.++We define two convenience operators for applying units to all+elements of a functor (e.g. a list).+-}++-- | Applies '*~' to all values in a functor.+(*~~) :: (Functor f, Num a) => f a -> Unit m d a -> f (Quantity d a)+xs *~~ u = fmap (*~ u) xs++-- | Applies '/~' to all values in a functor.+(/~~) :: forall f m d a.(Functor f, Fractional a) => f (Quantity d a) -> Unit m d a -> f a+xs /~~ u = fmap (/~ u) xs++infixl 7 *~~, /~~++-- | The sum of all elements in a foldable structure.+--+-- >>> sum ([] :: [Mass Double])+-- 0.0 kg+--+-- >>> sum [12.4 *~ meter, 1 *~ foot]+-- 12.7048 m+sum :: (Num a, Foldable f) => f (Quantity d a) -> Quantity d a+sum = foldr (+) _0++-- | The product of all elements in a foldable structure.+--+-- >>> product ([] :: [Dimensionless Double])+-- 1.0+--+-- >>> product [pi, _4, 0.36 *~ one]+-- 4.523893421169302+product :: (Num a, Foldable f) => f (Dimensionless a) -> Dimensionless a+product = foldr (*) _1++-- | The arithmetic mean of all elements in a foldable structure.+--+-- >>> mean [pi, _7]+-- 5.070796326794897+mean :: (Fractional a, Foldable f) => f (Quantity d a) -> Quantity d a+mean = uncurry (/) . foldr accumulate (_0, _0)+ where+ accumulate val (accum, count) = (accum + val, count + _1)++-- | The length of the foldable data structure as a 'Dimensionless'.+-- This can be useful for purposes of e.g. calculating averages.+--+-- >>> dimensionlessLength ["foo", "bar"]+-- 2+dimensionlessLength :: (Num a, Foldable f) => f b -> Dimensionless a+dimensionlessLength x = (fromIntegral $ length x) *~ one++-- | Returns a list of quantities between given bounds.+--+-- prop> n <= 0 ==> nFromTo (x :: Mass Double) (y :: Mass Double) n == [x, y]+--+-- prop> (x :: Length Double) <= (y :: Length Double) ==> all (\z -> x <= z && z <= y) (nFromTo x y n)+--+-- >>> nFromTo _0 _3 2+-- [0.0,1.0,2.0,3.0]+--+-- >>> nFromTo _1 _0 7+-- [1.0,0.875,0.75,0.625,0.5,0.375,0.25,0.125,0.0]+--+-- >>> nFromTo _0 _1 (-5)+-- [0.0,1.0]+nFromTo :: (Fractional a, Integral b) => Quantity d a -- ^ The initial value.+ -> Quantity d a -- ^ The final value.+ -> b -- ^ The number of intermediate values. If less than one, no intermediate values will result.+ -> [Quantity d a]+nFromTo xi xf n = fmap f [0..n'] ++ [xf]+ where+ n' = max 0 n+ f i = xi + realToFrac (i % succ n') *~ one * (xf - xi)++{-+We continue by defining elementary functions on 'Dimensionless'+that may be obviously useful.+-}++exp, log, sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, asinh, acosh, atanh, log1p, expm1, log1pexp, log1mexp+ :: Floating a => Dimensionless a -> Dimensionless a+exp = fmap Prelude.exp+log = fmap Prelude.log+sin = fmap Prelude.sin+cos = fmap Prelude.cos+tan = fmap Prelude.tan+asin = fmap Prelude.asin+acos = fmap Prelude.acos+atan = fmap Prelude.atan+sinh = fmap Prelude.sinh+cosh = fmap Prelude.cosh+tanh = fmap Prelude.tanh+asinh = fmap Prelude.asinh+acosh = fmap Prelude.acosh+atanh = fmap Prelude.atanh+log1p = fmap Numeric.log1p+expm1 = fmap Numeric.expm1+log1pexp = fmap Numeric.log1pexp+log1mexp = fmap Numeric.log1mexp++-- | Raises a dimensionless quantity to a dimensionless power.+(**) :: Floating a => Dimensionless a -> Dimensionless a -> Dimensionless a+(**) = liftQ2 (Prelude.**)++-- | Takes the logarithm of the second argument in the base of the first.+--+-- >>> logBase _2 _8+-- 3.0+logBase :: Floating a => Dimensionless a -> Dimensionless a -> Dimensionless a+logBase = liftQ2 Prelude.logBase++-- | The standard two argument arctangent function.+-- Since it interprets its two arguments in comparison with one another, the input may have any dimension.+--+-- >>> atan2 _0 _1+-- 0.0+--+-- >>> atan2 _1 _0+-- 1.5707963267948966+--+-- >>> atan2 _0 (negate _1)+-- 3.141592653589793+--+-- >>> atan2 (negate _1) _0+-- -1.5707963267948966+atan2 :: (RealFloat a) => Quantity d a -> Quantity d a -> Dimensionless a+atan2 = liftQ2 Prelude.atan2++{-+The only unit we will define in this module is 'one'.+-}++-- | The unit 'one' has dimension 'DOne' and is the base unit of dimensionless values.+--+-- As detailed in 7.10 "Values of quantities expressed simply as numbers:+-- the unit one, symbol 1" of <#note1 [1]>, the unit one generally does not+-- appear in expressions. However, for us it is necessary to use 'one'+-- as we would any other unit to perform the "wrapping" of dimensionless values.+one :: Num a => Unit 'NonMetric DOne a+one = Unit nOne 1 1++{- $constants+For convenience we define some constants for small integer values+that often show up in formulae. We also throw in 'pi' and 'tau' for+good measure.++-}++-- | The constant for zero is polymorphic, allowing it to express zero 'Length' or+-- 'Numeric.Units.Dimensional.Quantities.Capacitance' or 'Numeric.Units.Dimensional.Quantities.Velocity' etc,+-- in addition to the 'Dimensionless' value zero.+_0 :: Num a => Quantity d a+_0 = Quantity 0++_1, _2, _3, _4, _5, _6, _7, _8, _9 :: (Num a) => Dimensionless a+_1 = 1 *~ one+_2 = 2 *~ one+_3 = 3 *~ one+_4 = 4 *~ one+_5 = 5 *~ one+_6 = 6 *~ one+_7 = 7 *~ one+_8 = 8 *~ one+_9 = 9 *~ one++pi :: Floating a => Dimensionless a+pi = Prelude.pi *~ one++-- | Twice 'pi'.+--+-- For background on 'tau' see https://tauday.com/tau-manifesto (but also+-- feel free to review https://web.archive.org/web/20200926221249/http://www.thepimanifesto.com/).+tau :: Floating a => Dimensionless a+tau = _2 * pi++{- $functor+We intentionally decline to provide a 'Functor' instance for 'Dimensional' because its use breaks the+abstraction of physical dimensions.++If you feel your work requires this instance, it is provided as an orphan in "Numeric.Units.Dimensional.Functor".++-}++-- | Convenient conversion between numerical types while retaining dimensional information.+--+-- >>> let x = (37 :: Rational) *~ poundMass+-- >>> changeRep x :: Mass Double+-- 16.78291769 kg+changeRep :: (KnownVariant v, Real a, Fractional b) => Dimensional v d a -> Dimensional v d b+changeRep = dmap realToFrac++-- | Convenient conversion from exactly represented values while retaining dimensional information.+changeRepApproximate :: (KnownVariant v, Floating b) => Dimensional v d ExactPi -> Dimensional v d b+changeRepApproximate = dmap approximateValue++{- $lenses+These functions are compatible with the lens library.++-}++-- | Converts a 'Unit' into a lens from 'Quantity's to values.+asLens :: (Fractional a) => Unit m d a+ -> (forall f.Functor f => (a -> f a)+ -> Quantity d a+ -> f (Quantity d a))+asLens u f q = fmap (\v' -> v' *~ u) (f (q /~ u))++{- $dimension-terms+To facilitate parsing and pretty-printing functions that may wish to operate on term-level representations of dimension,+we provide a means for converting from type-level dimensions to term-level dimensions.++-}++-- | Forms a new atomic 'Unit' by specifying its 'UnitName' and its definition as a multiple of another 'Unit'.+--+-- Use this variant when the scale factor of the resulting unit is irrational or 'Approximate'. See 'mkUnitQ' for when it is rational+-- and 'mkUnitZ' for when it is an integer.+--+-- Note that supplying zero as a definining quantity is invalid, as the library relies+-- upon units forming a group under multiplication.+--+-- Supplying negative defining quantities is allowed and handled gracefully, but is discouraged+-- on the grounds that it may be unexpected by other readers.+mkUnitR :: Floating a => UnitName m -> ExactPi -> Unit m1 d a -> Unit m d a+mkUnitR n s (Unit _ e _) | isExactZero s = error "Supplying zero as a conversion factor is not valid."+ | otherwise = Unit n e' x'+ where+ e' = s Prelude.* e+ x' = approximateValue e'++-- | Forms a new atomic 'Unit' by specifying its 'UnitName' and its definition as a multiple of another 'Unit'.+--+-- Use this variant when the scale factor of the resulting unit is rational. See 'mkUnitZ' for when it is an integer+-- and 'mkUnitR' for the general case.+--+-- For more information see 'mkUnitR'.+mkUnitQ :: Fractional a => UnitName m -> Rational -> Unit m1 d a -> Unit m d a+mkUnitQ n s (Unit _ e x) | s == 0 = error "Supplying zero as a conversion factor is not valid."+ | Just x'' <- toExactRational e' = Unit n e' (fromRational x'')+ | otherwise = Unit n e' x'+ where+ e' = fromRational s Prelude.* e+ x' = fromRational s Prelude.* x++-- | Forms a new atomic 'Unit' by specifying its 'UnitName' and its definition as a multiple of another 'Unit'.+--+-- Use this variant when the scale factor of the resulting unit is an integer. See 'mkUnitQ' for when it is rational+-- and 'mkUnitR' for the general case.+--+-- For more information see 'mkUnitR'.+mkUnitZ :: Num a => UnitName m -> Integer -> Unit m1 d a -> Unit m d a+mkUnitZ n s (Unit _ e x) | s == 0 = error "Supplying zero as a conversion factor is not valid."+ | Just x'' <- toExactInteger e' = Unit n e' (fromInteger x'')+ | otherwise = Unit n e' x'+ where+ e' = fromInteger s Prelude.* e+ x' = fromInteger s Prelude.* x
src/Numeric/Units/Dimensional/Coercion.hs view
@@ -1,35 +1,35 @@-{- | - Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter - License : BSD3 - - Maintainer : bjorn@buckwalter.se - Stability : Experimental - Portability: GHC only? - -Re-exports the raw 'Quantity' constructor from the Numeric.Units.Dimensional.Internal module, along with 'Data.Coerce.coerce', -for convenience in converting between raw representations and dimensional values. - -Note that use of these constructs requires the user to verify the dimensional safety of the conversion, -because the coercion doesn't explicitly mention the unit of the representation. Note also that the -'Quantity' constructor constructs a 'Numeric.Units.Dimensional.SQuantity' which may have a scale factor -other than 'Data.ExactPi.TypeLevel.One'. - -Note that the haddock documentation doesn't mention the 'Quantity' constructor because it is a part of the -'Dimensional' associated data family, but it is exported by this module. - --} - -module Numeric.Units.Dimensional.Coercion -( - coerce, Dimensional(Quantity), unQuantity -) -where - -import Data.Coerce (coerce) -import Numeric.Units.Dimensional.Internal (SQuantity, Dimensional(Quantity)) - --- | Unwraps a possibly-scaled `SQuantity`, yielding its underlying representation. --- --- This is a type-restricted version of `coerce`. -unQuantity :: SQuantity s d a -> a -unQuantity = coerce +{- |+ Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter+ License : BSD3++ Maintainer : bjorn@buckwalter.se+ Stability : Experimental+ Portability: GHC only?++Re-exports the raw 'Quantity' constructor from the Numeric.Units.Dimensional.Internal module, along with 'Data.Coerce.coerce',+for convenience in converting between raw representations and dimensional values.++Note that use of these constructs requires the user to verify the dimensional safety of the conversion,+because the coercion doesn't explicitly mention the unit of the representation. Note also that the+'Quantity' constructor constructs a 'Numeric.Units.Dimensional.SQuantity' which may have a scale factor+other than 'Data.ExactPi.TypeLevel.One'.++Note that the haddock documentation doesn't mention the 'Quantity' constructor because it is a part of the+'Dimensional' associated data family, but it is exported by this module.++-}++module Numeric.Units.Dimensional.Coercion+(+ coerce, Dimensional(Quantity), unQuantity+)+where++import Data.Coerce (coerce)+import Numeric.Units.Dimensional.Internal (SQuantity, Dimensional(Quantity))++-- | Unwraps a possibly-scaled `SQuantity`, yielding its underlying representation.+--+-- This is a type-restricted version of `coerce`.+unQuantity :: SQuantity s d a -> a+unQuantity = coerce
src/Numeric/Units/Dimensional/Dimensions.hs view
@@ -1,25 +1,25 @@-{- | - Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter - License : BSD3 - - Maintainer : bjorn@buckwalter.se - Stability : Stable - Portability: GHC only - -Provides both term-level and type-level representations for physical dimensions in -a single import for convenience. - -Presuming that users intend to work primarily with type level dimensions, this module hides -arithmetic operators over term level dimensions and aliases for the base term-level dimensions -to avoid namespace pollution. These features are available directly from -"Numeric.Units.Dimensional.Dimensions.TermLevel" if desired. --} -module Numeric.Units.Dimensional.Dimensions -( - module Numeric.Units.Dimensional.Dimensions.TermLevel, - module Numeric.Units.Dimensional.Dimensions.TypeLevel -) -where - -import Numeric.Units.Dimensional.Dimensions.TermLevel hiding ((*), (/), (^), recip, nroot, sqrt, cbrt, dLength, dMass, dTime, dElectricCurrent, dThermodynamicTemperature, dAmountOfSubstance, dLuminousIntensity) -import Numeric.Units.Dimensional.Dimensions.TypeLevel +{- |+ Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter+ License : BSD3++ Maintainer : bjorn@buckwalter.se+ Stability : Stable+ Portability: GHC only++Provides both term-level and type-level representations for physical dimensions in+a single import for convenience.++Presuming that users intend to work primarily with type level dimensions, this module hides+arithmetic operators over term level dimensions and aliases for the base term-level dimensions+to avoid namespace pollution. These features are available directly from+"Numeric.Units.Dimensional.Dimensions.TermLevel" if desired.+-}+module Numeric.Units.Dimensional.Dimensions+(+ module Numeric.Units.Dimensional.Dimensions.TermLevel,+ module Numeric.Units.Dimensional.Dimensions.TypeLevel+)+where++import Numeric.Units.Dimensional.Dimensions.TermLevel hiding ((*), (/), (^), recip, nroot, sqrt, cbrt, dLength, dMass, dTime, dElectricCurrent, dThermodynamicTemperature, dAmountOfSubstance, dLuminousIntensity)+import Numeric.Units.Dimensional.Dimensions.TypeLevel
src/Numeric/Units/Dimensional/Dimensions/TermLevel.hs view
@@ -1,192 +1,208 @@-{-# OPTIONS_HADDOCK not-home, show-extensions #-} - -{-# LANGUAGE BangPatterns #-} -{-# LANGUAGE DefaultSignatures #-} -{-# LANGUAGE DeriveDataTypeable #-} -{-# LANGUAGE DeriveGeneric #-} - -{- | - Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter - License : BSD3 - - Maintainer : bjorn@buckwalter.se - Stability : Stable - Portability: GHC only - -This module defines physical dimensions expressed in terms of -the SI base dimensions, including arithmetic. - --} -module Numeric.Units.Dimensional.Dimensions.TermLevel -( - -- * Type - Dimension'(..), - -- * Access to Dimension of Dimensional Values - HasDimension(..), HasDynamicDimension(..), DynamicDimension(..), - -- * Dimension Arithmetic - (*), (/), (^), recip, nroot, sqrt, cbrt, - -- * Synonyms for Base Dimensions - dOne, - dLength, dMass, dTime, dElectricCurrent, dThermodynamicTemperature, dAmountOfSubstance, dLuminousIntensity, - -- * Deconstruction - asList, - -- * Examining Dynamic Dimensions - matchDimensions, isCompatibleWith, hasSomeDimension -) -where - -import Control.DeepSeq -import Data.Data -import Data.Semigroup (Semigroup(..)) -import Data.Monoid (Monoid(..)) -import GHC.Generics -import Prelude (id, all, fst, snd, fmap, otherwise, divMod, ($), (+), (-), (.), (&&), Int, Show, Eq(..), Ord(..), Maybe(..), Bool(..)) -import qualified Prelude as P - --- $setup --- >>> import Prelude (negate) --- >>> import Control.Applicative --- >>> import Test.QuickCheck.Arbitrary --- >>> instance Arbitrary Dimension' where arbitrary = Dim' <$> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary - --- | A physical dimension, encoded as 7 integers, representing a factorization of the dimension into the --- 7 SI base dimensions. By convention they are stored in the same order as --- in the 'Numeric.Units.Dimensional.Dimensions.TypeLevel.Dimension' data kind. -data Dimension' = Dim' !Int !Int !Int !Int !Int !Int !Int - deriving (Show, Eq, Ord, Data, Generic, Typeable) - -instance NFData Dimension' where - rnf !_ = () -- The Dimension' constructor is already fully strict. - -instance Semigroup Dimension' where - (<>) = (*) - --- | The monoid of dimensions under multiplication. -instance Monoid Dimension' where - mempty = dOne - mappend = (Data.Semigroup.<>) - --- | The dimension of a dynamic value, which may not have any dimension at all. -data DynamicDimension = NoDimension -- ^ The value has no valid dimension. - | SomeDimension Dimension' -- ^ The value has the given dimension. - | AnyDimension -- ^ The value may be interpreted as having any dimension. - deriving (Eq, Ord, Show, Data, Generic, Typeable) - -instance NFData DynamicDimension where - --- | Dimensional values, or those that are only possibly dimensional, inhabit this class, --- which allows access to a term-level representation of their dimension. -class HasDynamicDimension a where - -- | Gets the 'DynamicDimension of a dynamic dimensional value, which may be 'NoDimension' if it does not represent - -- a dimensional value of any 'Dimension'. - -- - -- A default implementation is available for types that are also in the `HasDimension` typeclass. - dynamicDimension :: a -> DynamicDimension - default dynamicDimension :: (HasDimension a) => a -> DynamicDimension - dynamicDimension = SomeDimension . dimension - --- | Dimensional values inhabit this class, which allows access to a term-level representation of their dimension. -class HasDynamicDimension a => HasDimension a where - -- | Obtains a term-level representation of a value's dimension. - dimension :: a -> Dimension' - -instance HasDynamicDimension DynamicDimension where - dynamicDimension = id - -instance HasDynamicDimension Dimension' where - -instance HasDimension Dimension' where - dimension = id - --- | Combines two 'DynamicDimension's, determining the 'DynamicDimension' of a quantity that must --- match both inputs. --- --- This is the lattice meet operation for 'DynamicDimension'. -matchDimensions :: DynamicDimension -> DynamicDimension -> DynamicDimension -matchDimensions AnyDimension AnyDimension = AnyDimension -matchDimensions d@(SomeDimension _) AnyDimension = d -matchDimensions AnyDimension d@(SomeDimension _) = d -matchDimensions (SomeDimension d1) (SomeDimension d2) | d1 == d2 = SomeDimension d1 -matchDimensions _ _ = NoDimension - --- | Determines if a value that has a 'DynamicDimension' is compatible with a specified 'Dimension''. -isCompatibleWith :: (HasDynamicDimension a) => a -> Dimension' -> Bool -isCompatibleWith = f . dynamicDimension - where - f AnyDimension _ = True - f (SomeDimension d1) d2 | d1 == d2 = True - f _ _ = False - --- | Determines if a value that has a 'DynamicDimension' in fact has any valid dimension at all. -hasSomeDimension :: (HasDynamicDimension a) => a -> Bool -hasSomeDimension = (/= NoDimension) . dynamicDimension - --- | The dimension of dimensionless values. -dOne :: Dimension' -dOne = Dim' 0 0 0 0 0 0 0 - -dLength, dMass, dTime, dElectricCurrent, dThermodynamicTemperature, dAmountOfSubstance, dLuminousIntensity :: Dimension' -dLength = Dim' 1 0 0 0 0 0 0 -dMass = Dim' 0 1 0 0 0 0 0 -dTime = Dim' 0 0 1 0 0 0 0 -dElectricCurrent = Dim' 0 0 0 1 0 0 0 -dThermodynamicTemperature = Dim' 0 0 0 0 1 0 0 -dAmountOfSubstance = Dim' 0 0 0 0 0 1 0 -dLuminousIntensity = Dim' 0 0 0 0 0 0 1 - -{- -We will reuse the operators and function names from the Prelude. -To prevent unpleasant surprises we give operators the same fixity -as the Prelude. --} - -infixr 8 ^ -infixl 7 *, / - --- | Forms the product of two dimensions. -(*) :: Dimension' -> Dimension' -> Dimension' -(Dim' l m t i th n j) * (Dim' l' m' t' i' th' n' j') = Dim' (l + l') (m + m') (t + t') (i + i') (th + th') (n + n') (j + j') - --- | Forms the quotient of two dimensions. -(/) :: Dimension' -> Dimension' -> Dimension' -(Dim' l m t i th n j) / (Dim' l' m' t' i' th' n' j') = Dim' (l - l') (m - m') (t - t') (i - i') (th - th') (n - n') (j - j') - --- | Raises a dimension to an integer power. -(^) :: Dimension' -> Int -> Dimension' -(Dim' l m t i th n j) ^ x = Dim' (x P.* l) (x P.* m) (x P.* t) (x P.* i) (x P.* th) (x P.* n) (x P.* j) - --- | Forms the reciprocal of a dimension. -recip :: Dimension' -> Dimension' -recip = (dOne /) - --- | Takes the nth root of a dimension, if it exists. --- --- n must not be zero. --- --- prop> nroot (negate n) d == nroot n (recip d) -nroot :: Int -> Dimension' -> Maybe Dimension' -nroot n d | n /= 0 && all ((== 0) . snd) ds = fromList . fmap fst $ ds - | otherwise = Nothing - where - ds = fmap (`divMod` n) . asList $ d - --- | Takes the square root of a dimension, if it exists. --- --- prop> sqrt d == nroot 2 d -sqrt :: Dimension' -> Maybe Dimension' -sqrt = nroot 2 - --- | Takes the cube root of a dimension, if it exists. --- --- prop> cbrt d == nroot 3 d -cbrt :: Dimension' -> Maybe Dimension' -cbrt = nroot 3 - --- | Converts a dimension to a list of 7 integers, representing the exponent associated with each --- of the 7 SI base dimensions in the standard order. -asList :: Dimension' -> [Int] -asList (Dim' l m t i th n j) = [l, m, t, i, th, n, j] - -fromList :: [Int] -> Maybe Dimension' -fromList [l, m, t, i, th, n, j] = Just $ Dim' l m t i th n j -fromList _ = Nothing +{-# OPTIONS_HADDOCK not-home, show-extensions #-}++{-# LANGUAGE BangPatterns #-}+{-# LANGUAGE CPP #-}+{-# LANGUAGE DefaultSignatures #-}+{-# LANGUAGE DeriveDataTypeable #-}+{-# LANGUAGE DeriveGeneric #-}++{- |+ Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter+ License : BSD3++ Maintainer : bjorn@buckwalter.se+ Stability : Stable+ Portability: GHC only++This module defines physical dimensions expressed in terms of+the SI base dimensions, including arithmetic.++-}+module Numeric.Units.Dimensional.Dimensions.TermLevel+(+ -- * Type+ Dimension'(..),+ -- * Access to Dimension of Dimensional Values+ HasDimension(..), HasDynamicDimension(..), DynamicDimension(..),+ -- * Dimension Arithmetic+ (*), (/), (^), recip, nroot, sqrt, cbrt,+ -- * Synonyms for Base Dimensions+ dOne,+ dLength, dMass, dTime, dElectricCurrent, dThermodynamicTemperature, dAmountOfSubstance, dLuminousIntensity,+ -- * Deconstruction+ asList,+ -- * Examining Dynamic Dimensions+ matchDimensions, isCompatibleWith, hasSomeDimension+)+where++import Control.DeepSeq (NFData(..))+#if USE_BINARY+import qualified Data.Binary+#endif+import Data.Data+import Data.Semigroup (Semigroup(..))+import Data.Monoid (Monoid(..))+import GHC.Generics+import Prelude (id, all, fst, snd, fmap, otherwise, divMod, ($), (+), (-), (.), (&&), Int, Show, Eq(..), Ord(..), Maybe(..), Bool(..))+import qualified Prelude as P++-- $setup+-- >>> :set -fno-warn-orphans+-- >>> import Prelude (negate)+-- >>> import Control.Applicative+-- >>> import Test.QuickCheck.Arbitrary+-- >>> instance Arbitrary Dimension' where arbitrary = Dim' <$> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary++-- | A physical dimension, encoded as 7 integers, representing a factorization of the dimension into the+-- 7 SI base dimensions. By convention they are stored in the same order as+-- in the 'Numeric.Units.Dimensional.Dimensions.TypeLevel.Dimension' data kind.+data Dimension' = Dim' !Int !Int !Int !Int !Int !Int !Int+ deriving (Show, Eq, Ord, Data, Generic, Typeable)++instance NFData Dimension' where+ rnf !_ = () -- The Dimension' constructor is already fully strict.++instance Semigroup Dimension' where+ (<>) = (*)++-- | The monoid of dimensions under multiplication.+instance Monoid Dimension' where+ mempty = dOne+ mappend = (<>)++#if USE_BINARY+instance Data.Binary.Binary Dimension'+#endif++-- | The dimension of a dynamic value, which may not have any dimension at all.+data DynamicDimension = NoDimension -- ^ The value has no valid dimension.+ | SomeDimension Dimension' -- ^ The value has the given dimension.+ | AnyDimension -- ^ The value may be interpreted as having any dimension.+ deriving (Eq, Ord, Show, Data, Generic, Typeable)++instance NFData DynamicDimension where++#if USE_BINARY+instance Data.Binary.Binary DynamicDimension+#endif++-- | Dimensional values, or those that are only possibly dimensional, inhabit this class,+-- which allows access to a term-level representation of their dimension.+class HasDynamicDimension a where+ -- | Gets the 'DynamicDimension' of a dynamic dimensional value, which may be 'NoDimension' if it does not represent+ -- a dimensional value of any 'Dimension'.+ --+ -- A default implementation is available for types that are also in the `HasDimension` typeclass.+ dynamicDimension :: a -> DynamicDimension+ default dynamicDimension :: (HasDimension a) => a -> DynamicDimension+ dynamicDimension = SomeDimension . dimension++-- | Dimensional values inhabit this class, which allows access to a term-level representation of their dimension.+class HasDynamicDimension a => HasDimension a where+ -- | Obtains a term-level representation of a value's dimension.+ dimension :: a -> Dimension'++instance HasDynamicDimension DynamicDimension where+ dynamicDimension = id++instance HasDynamicDimension Dimension' where++instance HasDimension Dimension' where+ dimension = id++-- | Combines two 'DynamicDimension's, determining the 'DynamicDimension' of a quantity that must+-- match both inputs.+--+-- This is the lattice meet operation for 'DynamicDimension'.+matchDimensions :: DynamicDimension -> DynamicDimension -> DynamicDimension+matchDimensions AnyDimension AnyDimension = AnyDimension+matchDimensions d@(SomeDimension _) AnyDimension = d+matchDimensions AnyDimension d@(SomeDimension _) = d+matchDimensions (SomeDimension d1) (SomeDimension d2) | d1 == d2 = SomeDimension d1+matchDimensions _ _ = NoDimension++-- | Determines if a value that has a 'DynamicDimension' is compatible with a specified 'Dimension''.+isCompatibleWith :: (HasDynamicDimension a) => a -> Dimension' -> Bool+isCompatibleWith = f . dynamicDimension+ where+ f AnyDimension _ = True+ f (SomeDimension d1) d2 | d1 == d2 = True+ f _ _ = False++-- | Determines if a value that has a 'DynamicDimension' in fact has any valid dimension at all.+hasSomeDimension :: (HasDynamicDimension a) => a -> Bool+hasSomeDimension = (/= NoDimension) . dynamicDimension++-- | The dimension of dimensionless values.+dOne :: Dimension'+dOne = Dim' 0 0 0 0 0 0 0++dLength, dMass, dTime, dElectricCurrent, dThermodynamicTemperature, dAmountOfSubstance, dLuminousIntensity :: Dimension'+dLength = Dim' 1 0 0 0 0 0 0+dMass = Dim' 0 1 0 0 0 0 0+dTime = Dim' 0 0 1 0 0 0 0+dElectricCurrent = Dim' 0 0 0 1 0 0 0+dThermodynamicTemperature = Dim' 0 0 0 0 1 0 0+dAmountOfSubstance = Dim' 0 0 0 0 0 1 0+dLuminousIntensity = Dim' 0 0 0 0 0 0 1++{-+We will reuse the operators and function names from the Prelude.+To prevent unpleasant surprises we give operators the same fixity+as the Prelude.+-}++infixr 8 ^+infixl 7 *, /++-- | Forms the product of two dimensions.+(*) :: Dimension' -> Dimension' -> Dimension'+(Dim' l m t i th n j) * (Dim' l' m' t' i' th' n' j') = Dim' (l + l') (m + m') (t + t') (i + i') (th + th') (n + n') (j + j')++-- | Forms the quotient of two dimensions.+(/) :: Dimension' -> Dimension' -> Dimension'+(Dim' l m t i th n j) / (Dim' l' m' t' i' th' n' j') = Dim' (l - l') (m - m') (t - t') (i - i') (th - th') (n - n') (j - j')++-- | Raises a dimension to an integer power.+(^) :: Dimension' -> Int -> Dimension'+(Dim' l m t i th n j) ^ x = Dim' (x P.* l) (x P.* m) (x P.* t) (x P.* i) (x P.* th) (x P.* n) (x P.* j)++-- | Forms the reciprocal of a dimension.+recip :: Dimension' -> Dimension'+recip = (dOne /)++-- | Takes the nth root of a dimension, if it exists.+--+-- n must not be zero.+--+-- prop> nroot (negate n) d == nroot n (recip d)+nroot :: Int -> Dimension' -> Maybe Dimension'+nroot n d | n /= 0 && all ((== 0) . snd) ds = fromList . fmap fst $ ds+ | otherwise = Nothing+ where+ ds = fmap (`divMod` n) . asList $ d++-- | Takes the square root of a dimension, if it exists.+--+-- prop> sqrt d == nroot 2 d+sqrt :: Dimension' -> Maybe Dimension'+sqrt = nroot 2++-- | Takes the cube root of a dimension, if it exists.+--+-- prop> cbrt d == nroot 3 d+cbrt :: Dimension' -> Maybe Dimension'+cbrt = nroot 3++-- | Converts a dimension to a list of 7 integers, representing the exponent associated with each+-- of the 7 SI base dimensions in the standard order.+asList :: Dimension' -> [Int]+asList (Dim' l m t i th n j) = [l, m, t, i, th, n, j]++-- | Converts a list of integers, representing the exponent associated with each+-- of the 7 SI base dimensions in the standard order, to a dimension.+-- Returns 'Nothing' if the list doesn't contain exactly 7 elements.+fromList :: [Int] -> Maybe Dimension'+fromList [l, m, t, i, th, n, j] = Just $ Dim' l m t i th n j+fromList _ = Nothing
src/Numeric/Units/Dimensional/Dimensions/TypeLevel.hs view
@@ -1,160 +1,160 @@-{-# OPTIONS_HADDOCK not-home, show-extensions #-} - -{-# LANGUAGE ConstraintKinds #-} -{-# LANGUAGE DataKinds #-} -{-# LANGUAGE FlexibleContexts #-} -{-# LANGUAGE FlexibleInstances #-} -{-# LANGUAGE KindSignatures #-} -{-# LANGUAGE ScopedTypeVariables #-} -{-# LANGUAGE TypeFamilies #-} -{-# LANGUAGE TypeOperators #-} - -{- | - Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter - License : BSD3 - - Maintainer : bjorn@buckwalter.se - Stability : Stable - Portability: GHC only - -This module defines type-level physical dimensions expressed in terms of -the SI base dimensions using 'Numeric.NumType.DK.NumType' for type-level integers. - -Type-level arithmetic, synonyms for the base dimensions, and conversion to the term-level are included. --} -module Numeric.Units.Dimensional.Dimensions.TypeLevel -( - -- * Kind of Type-Level Dimensions - type Dimension(..), - -- * Dimension Arithmetic - type (*), type (/), type (^), type Recip, type NRoot, type Sqrt, type Cbrt, - -- * Synonyms for Base Dimensions - DOne, - DLength, DMass, DTime, DElectricCurrent, DThermodynamicTemperature, DAmountOfSubstance, DLuminousIntensity, - -- * Conversion to Term Level - type KnownDimension -) -where - -import Data.Proxy -import Numeric.NumType.DK.Integers - ( TypeInt (Zero, Pos1, Pos2, Pos3), type (+), type (-) - , KnownTypeInt, toNum - ) -import qualified Numeric.NumType.DK.Integers as N -import Numeric.Units.Dimensional.Dimensions.TermLevel - --- | Represents a physical dimension in the basis of the 7 SI base dimensions, --- where the respective dimensions are represented by type variables --- using the following convention: --- --- * l: Length --- * m: Mass --- * t: Time --- * i: Electric current --- * th: Thermodynamic temperature --- * n: Amount of substance --- * j: Luminous intensity --- --- For the equivalent term-level representation, see 'Dimension'' -data Dimension = Dim TypeInt TypeInt TypeInt TypeInt TypeInt TypeInt TypeInt - --- | The type-level dimension of dimensionless values. -type DOne = 'Dim 'Zero 'Zero 'Zero 'Zero 'Zero 'Zero 'Zero -type DLength = 'Dim 'Pos1 'Zero 'Zero 'Zero 'Zero 'Zero 'Zero -type DMass = 'Dim 'Zero 'Pos1 'Zero 'Zero 'Zero 'Zero 'Zero -type DTime = 'Dim 'Zero 'Zero 'Pos1 'Zero 'Zero 'Zero 'Zero -type DElectricCurrent = 'Dim 'Zero 'Zero 'Zero 'Pos1 'Zero 'Zero 'Zero -type DThermodynamicTemperature = 'Dim 'Zero 'Zero 'Zero 'Zero 'Pos1 'Zero 'Zero -type DAmountOfSubstance = 'Dim 'Zero 'Zero 'Zero 'Zero 'Zero 'Pos1 'Zero -type DLuminousIntensity = 'Dim 'Zero 'Zero 'Zero 'Zero 'Zero 'Zero 'Pos1 - -{- -We will reuse the operators and function names from the Prelude. -To prevent unpleasant surprises we give operators the same fixity -as the Prelude. --} - -infixr 8 ^ -infixl 7 *, / - --- | Multiplication of dimensions corresponds to adding of the base --- dimensions' exponents. -type family (a::Dimension) * (b::Dimension) where - DOne * d = d - d * DOne = d - ('Dim l m t i th n j) * ('Dim l' m' t' i' th' n' j') - = 'Dim (l + l') (m + m') (t + t') (i + i') (th + th') (n + n') (j + j') - --- | Division of dimensions corresponds to subtraction of the base --- dimensions' exponents. -type family (a::Dimension) / (d::Dimension) where - d / DOne = d - d / d = DOne - ('Dim l m t i th n j) / ('Dim l' m' t' i' th' n' j') - = 'Dim (l - l') (m - m') (t - t') (i - i') (th - th') (n - n') (j - j') - --- | The reciprocal of a dimension is defined as the result of dividing 'DOne' by it, --- or of negating each of the base dimensions' exponents. -type Recip (d :: Dimension) = DOne / d - --- | Powers of dimensions corresponds to multiplication of the base --- dimensions' exponents by the exponent. --- --- We limit ourselves to integer powers of Dimensionals as fractional --- powers make little physical sense. -type family (d::Dimension) ^ (x::TypeInt) where - DOne ^ x = DOne - d ^ 'Zero = DOne - d ^ 'Pos1 = d - ('Dim l m t i th n j) ^ x - = 'Dim (l N.* x) (m N.* x) (t N.* x) (i N.* x) (th N.* x) (n N.* x) (j N.* x) - --- | Roots of dimensions corresponds to division of the base dimensions' --- exponents by the order of the root. -type family NRoot (d::Dimension) (x::TypeInt) where - NRoot DOne x = DOne - NRoot d 'Pos1 = d - NRoot ('Dim l m t i th n j) x - = 'Dim (l N./ x) (m N./ x) (t N./ x) (i N./ x) (th N./ x) (n N./ x) (j N./ x) - --- | Square root is a special case of 'NRoot' with order 2. -type Sqrt d = NRoot d 'Pos2 - --- | Cube root is a special case of 'NRoot' with order 3. -type Cbrt d = NRoot d 'Pos3 - --- | A KnownDimension is one for which we can construct a term-level representation. --- Each validly constructed type of kind 'Dimension' has a 'KnownDimension' instance. --- --- While 'KnownDimension' is a constraint synonym, the presence of @'KnownDimension' d@ in --- a context allows use of @'dimension' :: 'Proxy' d -> 'Dimension''@. -type KnownDimension (d :: Dimension) = HasDimension (Proxy d) - -instance ( KnownTypeInt l - , KnownTypeInt m - , KnownTypeInt t - , KnownTypeInt i - , KnownTypeInt th - , KnownTypeInt n - , KnownTypeInt j - ) => HasDynamicDimension (Proxy ('Dim l m t i th n j)) - where - -instance ( KnownTypeInt l - , KnownTypeInt m - , KnownTypeInt t - , KnownTypeInt i - , KnownTypeInt th - , KnownTypeInt n - , KnownTypeInt j - ) => HasDimension (Proxy ('Dim l m t i th n j)) - where - dimension _ = Dim' - (toNum (Proxy :: Proxy l)) - (toNum (Proxy :: Proxy m)) - (toNum (Proxy :: Proxy t)) - (toNum (Proxy :: Proxy i)) - (toNum (Proxy :: Proxy th)) - (toNum (Proxy :: Proxy n)) - (toNum (Proxy :: Proxy j)) +{-# OPTIONS_HADDOCK not-home, show-extensions #-}++{-# LANGUAGE ConstraintKinds #-}+{-# LANGUAGE DataKinds #-}+{-# LANGUAGE FlexibleContexts #-}+{-# LANGUAGE FlexibleInstances #-}+{-# LANGUAGE KindSignatures #-}+{-# LANGUAGE ScopedTypeVariables #-}+{-# LANGUAGE TypeFamilies #-}+{-# LANGUAGE TypeOperators #-}++{- |+ Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter+ License : BSD3++ Maintainer : bjorn@buckwalter.se+ Stability : Stable+ Portability: GHC only++This module defines type-level physical dimensions expressed in terms of+the SI base dimensions using 'Numeric.NumType.DK.NumType' for type-level integers.++Type-level arithmetic, synonyms for the base dimensions, and conversion to the term-level are included.+-}+module Numeric.Units.Dimensional.Dimensions.TypeLevel+(+ -- * Kind of Type-Level Dimensions+ type Dimension(..),+ -- * Dimension Arithmetic+ type (*), type (/), type (^), type Recip, type NRoot, type Sqrt, type Cbrt,+ -- * Synonyms for Base Dimensions+ DOne,+ DLength, DMass, DTime, DElectricCurrent, DThermodynamicTemperature, DAmountOfSubstance, DLuminousIntensity,+ -- * Conversion to Term Level+ type KnownDimension+)+where++import Data.Proxy+import Numeric.NumType.DK.Integers+ ( TypeInt (Zero, Pos1, Pos2, Pos3), type (+), type (-)+ , KnownTypeInt, toNum+ )+import qualified Numeric.NumType.DK.Integers as N+import Numeric.Units.Dimensional.Dimensions.TermLevel++-- | Represents a physical dimension in the basis of the 7 SI base dimensions,+-- where the respective dimensions are represented by type variables+-- using the following convention:+--+-- * l: Length+-- * m: Mass+-- * t: Time+-- * i: Electric current+-- * th: Thermodynamic temperature+-- * n: Amount of substance+-- * j: Luminous intensity+--+-- For the equivalent term-level representation, see 'Dimension''+data Dimension = Dim TypeInt TypeInt TypeInt TypeInt TypeInt TypeInt TypeInt++-- | The type-level dimension of dimensionless values.+type DOne = 'Dim 'Zero 'Zero 'Zero 'Zero 'Zero 'Zero 'Zero+type DLength = 'Dim 'Pos1 'Zero 'Zero 'Zero 'Zero 'Zero 'Zero+type DMass = 'Dim 'Zero 'Pos1 'Zero 'Zero 'Zero 'Zero 'Zero+type DTime = 'Dim 'Zero 'Zero 'Pos1 'Zero 'Zero 'Zero 'Zero+type DElectricCurrent = 'Dim 'Zero 'Zero 'Zero 'Pos1 'Zero 'Zero 'Zero+type DThermodynamicTemperature = 'Dim 'Zero 'Zero 'Zero 'Zero 'Pos1 'Zero 'Zero+type DAmountOfSubstance = 'Dim 'Zero 'Zero 'Zero 'Zero 'Zero 'Pos1 'Zero+type DLuminousIntensity = 'Dim 'Zero 'Zero 'Zero 'Zero 'Zero 'Zero 'Pos1++{-+We will reuse the operators and function names from the Prelude.+To prevent unpleasant surprises we give operators the same fixity+as the Prelude.+-}++infixr 8 ^+infixl 7 *, /++-- | Multiplication of dimensions corresponds to addition of the base+-- dimensions' exponents.+type family (a :: Dimension) * (b :: Dimension) where+ DOne * d = d+ d * DOne = d+ ('Dim l m t i th n j) * ('Dim l' m' t' i' th' n' j')+ = 'Dim (l + l') (m + m') (t + t') (i + i') (th + th') (n + n') (j + j')++-- | Division of dimensions corresponds to subtraction of the base+-- dimensions' exponents.+type family (a :: Dimension) / (d :: Dimension) where+ d / DOne = d+ d / d = DOne+ ('Dim l m t i th n j) / ('Dim l' m' t' i' th' n' j')+ = 'Dim (l - l') (m - m') (t - t') (i - i') (th - th') (n - n') (j - j')++-- | The reciprocal of a dimension is defined as the result of dividing 'DOne' by it,+-- or of negating each of the base dimensions' exponents.+type Recip (d :: Dimension) = DOne / d++-- | Powers of dimensions correspond to multiplication of the base+-- dimensions' exponents by the exponent.+--+-- We limit ourselves to integer powers of Dimensionals as fractional+-- powers make little physical sense.+type family (d :: Dimension) ^ (x :: TypeInt) where+ DOne ^ x = DOne+ d ^ 'Zero = DOne+ d ^ 'Pos1 = d+ ('Dim l m t i th n j) ^ x+ = 'Dim (l N.* x) (m N.* x) (t N.* x) (i N.* x) (th N.* x) (n N.* x) (j N.* x)++-- | Roots of dimensions correspond to division of the base dimensions'+-- exponents by the order of the root.+type family NRoot (d :: Dimension) (x :: TypeInt) where+ NRoot DOne x = DOne+ NRoot d 'Pos1 = d+ NRoot ('Dim l m t i th n j) x+ = 'Dim (l N./ x) (m N./ x) (t N./ x) (i N./ x) (th N./ x) (n N./ x) (j N./ x)++-- | Square root is a special case of 'NRoot' with order 2.+type Sqrt d = NRoot d 'Pos2++-- | Cube root is a special case of 'NRoot' with order 3.+type Cbrt d = NRoot d 'Pos3++-- | A KnownDimension is one for which we can construct a term-level representation.+-- Each validly constructed type of kind 'Dimension' has a 'KnownDimension' instance.+--+-- While 'KnownDimension' is a constraint synonym, the presence of @'KnownDimension' d@ in+-- a context allows use of @'dimension' :: 'Proxy' d -> 'Dimension''@.+type KnownDimension (d :: Dimension) = HasDimension (Proxy d)++instance ( KnownTypeInt l+ , KnownTypeInt m+ , KnownTypeInt t+ , KnownTypeInt i+ , KnownTypeInt th+ , KnownTypeInt n+ , KnownTypeInt j+ ) => HasDynamicDimension (Proxy ('Dim l m t i th n j))+ where++instance ( KnownTypeInt l+ , KnownTypeInt m+ , KnownTypeInt t+ , KnownTypeInt i+ , KnownTypeInt th+ , KnownTypeInt n+ , KnownTypeInt j+ ) => HasDimension (Proxy ('Dim l m t i th n j))+ where+ dimension _ = Dim'+ (toNum (Proxy :: Proxy l))+ (toNum (Proxy :: Proxy m))+ (toNum (Proxy :: Proxy t))+ (toNum (Proxy :: Proxy i))+ (toNum (Proxy :: Proxy th))+ (toNum (Proxy :: Proxy n))+ (toNum (Proxy :: Proxy j))
src/Numeric/Units/Dimensional/Dynamic.hs view
@@ -1,352 +1,365 @@-{- | - Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter - License : BSD3 - - Maintainer : bjorn@buckwalter.se - Stability : Stable - Portability: GHC only? - -Defines types for manipulation of units and quantities without phantom types for their dimensions. --} - -{-# LANGUAGE DataKinds #-} -{-# LANGUAGE DeriveDataTypeable #-} -{-# LANGUAGE DeriveGeneric #-} -{-# LANGUAGE FlexibleContexts #-} -{-# LANGUAGE FlexibleInstances #-} -{-# LANGUAGE KindSignatures #-} -{-# LANGUAGE ScopedTypeVariables #-} - -module Numeric.Units.Dimensional.Dynamic -( - -- * Dynamic Quantities - AnyQuantity -, DynQuantity -, Demotable -, Promotable -, HasDynamicDimension(..), DynamicDimension(..) -, promoteQuantity, demoteQuantity -, (*~), (/~), invalidQuantity, polydimensionalZero - -- * Dynamic Units -, AnyUnit -, demoteUnit, promoteUnit, demoteUnit' -, siUnit, anyUnitName - -- ** Arithmetic on Dynamic Units -, (*), (/), (^), recip, applyPrefix -) where - -import Control.DeepSeq -import Control.Monad -import Data.Data -import Data.ExactPi -import Data.Kind -import Data.Semigroup (Semigroup(..)) -import Data.Monoid (Monoid(..)) -import GHC.Generics -import Prelude (Eq(..), Num, Fractional, Floating, Show(..), Bool(..), Maybe(..), (.), ($), (++), (&&), id, otherwise, error) -import qualified Prelude as P -import Numeric.Units.Dimensional hiding ((*~), (/~), (*), (/), (^), recip, nroot, siUnit) -import qualified Numeric.Units.Dimensional as Dim -import Numeric.Units.Dimensional.Coercion -import Numeric.Units.Dimensional.UnitNames (UnitName, baseUnitName) -import qualified Numeric.Units.Dimensional.UnitNames.InterchangeNames as I -import qualified Numeric.Units.Dimensional.UnitNames as N -import Numeric.Units.Dimensional.Dimensions.TermLevel (HasDynamicDimension(..), DynamicDimension(..), matchDimensions, isCompatibleWith) -import qualified Numeric.Units.Dimensional.Dimensions.TermLevel as D - --- | The class of types that can be used to model 'Quantity's that are certain to have a value with --- some dimension. -class Demotable (q :: Type -> Type) where - demotableOut :: q a -> AnyQuantity a - --- | The class of types that can be used to model 'Quantity's whose 'Dimension's are --- only known dynamically. -class Promotable (q :: Type -> Type) where - promotableIn :: AnyQuantity a -> q a - promotableOut :: q a -> DynQuantity a - --- | Forgets information about a 'Quantity' or 'AnyQuantity', yielding an 'AnyQuantity' or a 'DynQuantity'. -demoteQuantity :: (Demotable q, Promotable d) => q a -> d a -demoteQuantity = promotableIn . demotableOut - --- | Converts a dynamic quantity such as an 'AnyQuantity' or a 'DynQuantity' into a --- 'Quantity', or to 'Nothing' if the dynamic quantity cannot be represented in the --- narrower result type. -promoteQuantity :: forall a d q.(Promotable q, KnownDimension d) => q a -> Maybe (Quantity d a) -promoteQuantity = promoteQ . promotableOut - where - dim' = dimension (Proxy :: Proxy d) - promoteQ (DynQuantity d v) | d `isCompatibleWith` dim' = Just . Quantity $ v - | otherwise = Nothing - -instance (KnownDimension d) => Demotable (Quantity d) where - demotableOut q@(Quantity x) = AnyQuantity (dimension q) x - --- | A 'Quantity' whose 'Dimension' is only known dynamically. -data AnyQuantity a = AnyQuantity !Dimension' !a - deriving (Eq, Data, Generic, Generic1, Typeable) - -instance (Show a) => Show (AnyQuantity a) where - show (AnyQuantity d a) | d == D.dOne = show a - | otherwise = show a ++ " " ++ (show . baseUnitName $ d) - -instance HasDynamicDimension (AnyQuantity a) where - -instance HasDimension (AnyQuantity a) where - dimension (AnyQuantity d _) = d - -instance NFData a => NFData (AnyQuantity a) -- instance is derived from Generic instance - -instance Promotable AnyQuantity where - promotableIn = id - promotableOut (AnyQuantity d a) = DynQuantity (SomeDimension d) a - -instance Demotable AnyQuantity where - demotableOut = id - --- | 'AnyQuantity's form a 'Semigroup' under multiplication, but not under addition because --- they may not be added together if their dimensions do not match. -instance Num a => Semigroup (AnyQuantity a) where - (AnyQuantity d1 a1) <> (AnyQuantity d2 a2) = AnyQuantity (d1 D.* d2) (a1 P.* a2) - --- | 'AnyQuantity's form a 'Monoid' under multiplication, but not under addition because --- they may not be added together if their dimensions do not match. -instance Num a => Monoid (AnyQuantity a) where - mempty = demoteQuantity (1 Dim.*~ one) - mappend = (Data.Semigroup.<>) - --- | Possibly a 'Quantity' whose 'Dimension' is only known dynamically. --- --- By modeling the absence of a value, this type differs from 'AnyQuantity' in that it may --- not be a 'Quantity' of any 'Dimension' whatsoever, but in exchange it gains instances --- for the common numeric classes. It's therefore useful for manipulating, and not merely storing, --- quantities of unknown dimension. --- --- This type also contains a 'polydimensionalZero', representing zero value of any dimension. --- --- Note that the 'Eq' instance for 'DynQuantity' equates all representations of an invalid value, --- and also does not equate polydimensional zero with zero of any specific dimension. -data DynQuantity a = DynQuantity !DynamicDimension a -- we can't have strictness annotation on a as it is sometimes undefined - deriving (Data, Generic, Generic1, Typeable) - -instance Eq a => Eq (DynQuantity a) where - (DynQuantity NoDimension _) == (DynQuantity NoDimension _) = True -- all invalid quantities are equal - (DynQuantity NoDimension _) == _ = False -- invalid quanties are not equal to any other quantity - _ == (DynQuantity NoDimension _) = False - (DynQuantity d1 v1) == (DynQuantity d2 v2) = d1 == d2 && v1 == v2 - -instance NFData a => NFData (DynQuantity a) -- instance is derived from Generic instance - -instance Show a => Show (DynQuantity a) where - show (DynQuantity NoDimension _) = "invalidQuantity" - show (DynQuantity AnyDimension v) = show v - show (DynQuantity (SomeDimension d) v) = show $ AnyQuantity d v - -instance Promotable DynQuantity where - promotableIn (AnyQuantity d a) = DynQuantity (SomeDimension d) a - promotableOut = id - -instance HasDynamicDimension (DynQuantity a) where - dynamicDimension (DynQuantity d _) = d - -instance Num a => Num (DynQuantity a) where - x + y = liftDQ2 matchDimensions (P.+) x y - x - y = liftDQ2 matchDimensions (P.-) x y - x * y = liftDQ2 (valid2 (D.*)) (P.*) x y - negate = liftDQ id P.negate - abs = liftDQ id P.abs - signum = liftDQ (constant D.dOne) P.signum - fromInteger = demoteQuantity . (Dim.*~ one) . P.fromInteger - -instance Fractional a => Fractional (DynQuantity a) where - x / y = liftDQ2 (valid2 (D./)) (P./) x y - recip = liftDQ (valid D.recip) P.recip - fromRational = demoteQuantity . (Dim.*~ one) . P.fromRational - -instance Floating a => Floating (DynQuantity a) where - pi = demoteQuantity pi - exp = liftDimensionless P.exp - log = liftDimensionless P.log - sqrt = liftDQ (whenValid $ D.nroot 2) P.sqrt - (**) = liftDQ2 (matchDimensions3 $ SomeDimension D.dOne) (P.**) - logBase = liftDQ2 (matchDimensions3 $ SomeDimension D.dOne) P.logBase - sin = liftDimensionless P.sin - cos = liftDimensionless P.cos - tan = liftDimensionless P.tan - asin = liftDimensionless P.asin - acos = liftDimensionless P.acos - atan = liftDimensionless P.atan - sinh = liftDimensionless P.sinh - cosh = liftDimensionless P.cosh - tanh = liftDimensionless P.tanh - asinh = liftDimensionless P.asinh - acosh = liftDimensionless P.acosh - atanh = liftDimensionless P.atanh - --- | 'DynQuantity's form a 'Semigroup' under multiplication, but not under addition because --- they may not be added together if their dimensions do not match. -instance Num a => Semigroup (DynQuantity a) where - (<>) = (P.*) - --- | 'DynQuantity's form a 'Monoid' under multiplication, but not under addition because --- they may not be added together if their dimensions do not match. -instance Num a => Monoid (DynQuantity a) where - mempty = demoteQuantity (1 Dim.*~ one) - mappend = (Data.Semigroup.<>) - --- | A 'DynQuantity' which does not correspond to a value of any dimension. -invalidQuantity :: DynQuantity a -invalidQuantity = DynQuantity NoDimension $ error "Attempt to evaluate the value of an invalid quantity." - --- | A 'DynQuantity' which corresponds to zero value of any dimension. --- --- When combined through arithmetic with other 'DynQuantity's, inference is performed. For example, --- adding a length to polydimensional zero produces that length. Adding two polydimensional zeros produces another. --- Taking the sine of a polydimensional zero interprets it as a dimensionless zero and produces a dimensionless result. --- --- Note that division by 'polydimensionalZero' produces a polydimensional result, which may be an error or some representation --- of infinity, as determined by the underlying arithmetic type. This behavior was chosen for consistency with the behavior of division --- by zero 'DynQuantity's of a specific dimension. -polydimensionalZero :: (Num a) => DynQuantity a -polydimensionalZero = DynQuantity AnyDimension 0 - --- Lifts a function which is only valid on dimensionless quantities into a function on DynQuantitys. -liftDimensionless :: (a -> a) -> DynQuantity a -> DynQuantity a -liftDimensionless = liftDQ (matchDimensions $ SomeDimension D.dOne) - --- Lifts a function on values into a function on DynQuantitys. -liftDQ :: (DynamicDimension -> DynamicDimension) -- ^ How the function operates on dimensions. - -> (a -> a) -- ^ How the function operates on values. - -> DynQuantity a -> DynQuantity a -liftDQ fd fv (DynQuantity d v) = case fd d of - NoDimension -> invalidQuantity - d' -> DynQuantity d' $ fv v - --- Lifts a function on values into a function on DynQuantitys. --- --- This works by treating polydimensional zeros as dimensionless zeros. If that is not the desired behavior, --- handle polydimensional zeros first and then call this function. -liftDQ2 :: (DynamicDimension -> DynamicDimension -> DynamicDimension) - -> (a -> a -> a) - -> DynQuantity a -> DynQuantity a -> DynQuantity a -liftDQ2 fd fv (DynQuantity d1 v1) (DynQuantity d2 v2) = case fd d1 d2 of - NoDimension -> invalidQuantity - d' -> DynQuantity d' $ fv v1 v2 - --- Transforms a dynamic dimension in a way which is always valid -valid :: (Dimension' -> Dimension') -> DynamicDimension -> DynamicDimension -valid _ AnyDimension = AnyDimension -valid f (SomeDimension d) = SomeDimension (f d) -valid _ NoDimension = NoDimension - -whenValid :: (Dimension' -> Maybe Dimension') -> DynamicDimension -> DynamicDimension -whenValid _ AnyDimension = AnyDimension -whenValid f (SomeDimension d) | Just d' <- f d = SomeDimension d' -whenValid _ _ = NoDimension - -constant :: Dimension' -> DynamicDimension -> DynamicDimension -constant d AnyDimension = SomeDimension d -constant d (SomeDimension _) = SomeDimension d -constant _ _ = NoDimension - --- Transforms two dynamic dimensions in a way which is always valid -valid2 :: (Dimension' -> Dimension' -> Dimension') -> DynamicDimension -> DynamicDimension -> DynamicDimension -valid2 _ AnyDimension (SomeDimension _) = AnyDimension -valid2 _ (SomeDimension _) AnyDimension = AnyDimension -valid2 _ AnyDimension AnyDimension = AnyDimension -valid2 f (SomeDimension d1) (SomeDimension d2) = SomeDimension (f d1 d2) -valid2 _ _ _ = NoDimension - -matchDimensions3 :: DynamicDimension -> DynamicDimension -> DynamicDimension -> DynamicDimension -matchDimensions3 x y z = matchDimensions x (matchDimensions y z) - --- | A 'Unit' whose 'Dimension' is only known dynamically. -data AnyUnit = AnyUnit Dimension' (UnitName 'NonMetric) ExactPi - deriving (Generic, Typeable) - -instance Show AnyUnit where - show (AnyUnit _ n e) = show n ++ " =def= " ++ show e ++ " of the SI base unit" - -instance HasDynamicDimension AnyUnit where - -instance HasDimension AnyUnit where - dimension (AnyUnit d _ _) = d - -instance I.HasInterchangeName AnyUnit where - interchangeName (AnyUnit _ n _) = I.interchangeName n - --- | 'AnyUnit's form a 'Semigroup' under multiplication. -instance Semigroup AnyUnit where - (<>) = (Numeric.Units.Dimensional.Dynamic.*) - --- | 'AnyUnit's form a 'Monoid' under multiplication. -instance Monoid AnyUnit where - mempty = demoteUnit' one - mappend = (Data.Semigroup.<>) - -anyUnitName :: AnyUnit -> UnitName 'NonMetric -anyUnitName (AnyUnit _ n _) = n - --- | The dynamic SI coherent unit of a given dimension. -siUnit :: Dimension' -> AnyUnit -siUnit d = AnyUnit d (baseUnitName d) 1 - --- | Converts a 'Unit' of statically known 'Dimension' into an 'AnyUnit'. -demoteUnit :: forall m d a.(KnownDimension d) => Unit m d a -> AnyUnit -demoteUnit u = AnyUnit dim (name $ weaken u) (exactValue u) - where - dim = dimension (Proxy :: Proxy d) - --- | Converts a 'Unit' of statically known 'Dimension' into an 'AnyUnit'. --- --- This is the same as the more general 'demoteUnit' but is useful in certain circumstances to avoid --- needlessly introducing an ambiguous type variable. -demoteUnit' :: (KnownDimension d) => Unit m d ExactPi -> AnyUnit -demoteUnit' = demoteUnit - --- | Converts an 'AnyUnit' into a 'Unit' of statically known 'Dimension', or 'Nothing' if the dimension does not match. --- --- The result is represented in 'ExactPi', conversion to other representations is possible using 'changeRepApproximate'. --- --- The result is always tagged as 'NonMetric', conversion to a 'Metric' unit can be attempted using 'strengthen'. -promoteUnit :: forall d.(KnownDimension d) => AnyUnit -> Maybe (Unit 'NonMetric d ExactPi) -promoteUnit (AnyUnit dim n e) | dim == dim' = Just $ mkUnitR n e Dim.siUnit - | otherwise = Nothing - where - dim' = dimension (Proxy :: Proxy d) - --- | Forms the reciprocal of a dynamic unit. -recip :: AnyUnit -> AnyUnit -recip (AnyUnit d n e) = AnyUnit (D.recip d) (N.nOne N./ n) (P.recip e) - --- | Forms the product of two dynamic units. -(*) :: AnyUnit -> AnyUnit -> AnyUnit -(AnyUnit d1 n1 e1) * (AnyUnit d2 n2 e2) = AnyUnit (d1 D.* d2) (n1 N.* n2) (e1 P.* e2) - --- | Forms the quotient of two dynamic units. -(/) :: AnyUnit -> AnyUnit -> AnyUnit -(AnyUnit d1 n1 e1) / (AnyUnit d2 n2 e2) = AnyUnit (d1 D./ d2) (n1 N./ n2) (e1 P./ e2) - --- | Raises a dynamic unit to an integer power. -(^) :: (P.Integral a) => AnyUnit -> a -> AnyUnit -(AnyUnit d n e) ^ x = AnyUnit (d D.^ P.fromIntegral x) (n N.^ P.fromIntegral x) (e P.^^ x) - --- | Applies a prefix to a dynamic unit. --- Returns 'Nothing' if the 'Unit' was 'NonMetric' and thus could not accept a prefix. -applyPrefix :: N.Prefix -> AnyUnit -> Maybe AnyUnit -applyPrefix p (AnyUnit d n e) = do - n' <- N.strengthen n - let n'' = N.applyPrefix p n' - let e' = (P.fromRational $ N.scaleFactor p) P.* e - return $ AnyUnit d n'' e' - --- | Forms a dynamic quantity by multipliying a number and a dynamic unit. -(*~) :: (Floating a, Promotable q) => a -> AnyUnit -> q a -x *~ (AnyUnit d _ e) = promotableIn $ AnyQuantity d (x P.* approximateValue e) - --- | Divides a dynamic quantity by a dynamic unit, obtaining the numerical value of the quantity --- expressed in that unit if they are of the same physical dimension, or 'Nothing' otherwise. -(/~) :: (Floating a, Promotable q) => q a -> AnyUnit -> Maybe a -x /~ (AnyUnit d _ e) = case promotableOut x of - DynQuantity d' x' | d' `isCompatibleWith` d -> Just $ x' P./ approximateValue e - | otherwise -> Nothing +{- |+ Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter+ License : BSD3++ Maintainer : bjorn@buckwalter.se+ Stability : Stable+ Portability: GHC only?++Defines types for manipulation of units and quantities without phantom types for their dimensions.+-}++{-# LANGUAGE CPP #-}+{-# LANGUAGE DataKinds #-}+{-# LANGUAGE DeriveDataTypeable #-}+{-# LANGUAGE DeriveGeneric #-}+{-# LANGUAGE FlexibleContexts #-}+{-# LANGUAGE FlexibleInstances #-}+{-# LANGUAGE KindSignatures #-}+{-# LANGUAGE ScopedTypeVariables #-}++module Numeric.Units.Dimensional.Dynamic+(+ -- * Dynamic Quantities+ AnyQuantity+, DynQuantity+, Demotable+, Promotable+, HasDynamicDimension(..), DynamicDimension(..)+, promoteQuantity, demoteQuantity+, (*~), (/~), invalidQuantity, polydimensionalZero+ -- * Dynamic Units+, AnyUnit+, demoteUnit, promoteUnit, demoteUnit'+, siUnit, anyUnitName+ -- ** Arithmetic on Dynamic Units+, (*), (/), (^), recip, applyPrefix+) where++import Control.DeepSeq (NFData)+import Control.Monad+#if USE_BINARY+import qualified Data.Binary+#endif+import Data.Data+import Data.ExactPi+import Data.Kind+import Data.Semigroup (Semigroup(..))+import Data.Monoid (Monoid(..))+import GHC.Generics+import Prelude (Eq(..), Num, Fractional, Floating, Show(..), Bool(..), Maybe(..), (.), ($), (++), (&&), id, otherwise, error)+import qualified Prelude as P+import Numeric.Units.Dimensional hiding ((*~), (/~), (*), (/), (^), recip, nroot, siUnit)+import qualified Numeric.Units.Dimensional as Dim+import Numeric.Units.Dimensional.Coercion+import Numeric.Units.Dimensional.UnitNames (UnitName, baseUnitName)+import qualified Numeric.Units.Dimensional.UnitNames.InterchangeNames as I+import qualified Numeric.Units.Dimensional.UnitNames as N+import Numeric.Units.Dimensional.Dimensions.TermLevel (HasDynamicDimension(..), DynamicDimension(..), matchDimensions, isCompatibleWith)+import qualified Numeric.Units.Dimensional.Dimensions.TermLevel as D++-- | The class of types that can be used to model 'Quantity's that are certain to have a value with+-- some dimension.+class Demotable (q :: Type -> Type) where+ demotableOut :: q a -> AnyQuantity a++-- | The class of types that can be used to model 'Quantity's whose 'Dimension's are+-- only known dynamically.+class Promotable (q :: Type -> Type) where+ promotableIn :: AnyQuantity a -> q a+ promotableOut :: q a -> DynQuantity a++-- | Forgets information about a 'Quantity' or 'AnyQuantity', yielding an 'AnyQuantity' or a 'DynQuantity'.+demoteQuantity :: (Demotable q, Promotable d) => q a -> d a+demoteQuantity = promotableIn . demotableOut++-- | Converts a dynamic quantity such as an 'AnyQuantity' or a 'DynQuantity' into a+-- 'Quantity', or to 'Nothing' if the dynamic quantity cannot be represented in the+-- narrower result type.+promoteQuantity :: forall a d q.(Promotable q, KnownDimension d) => q a -> Maybe (Quantity d a)+promoteQuantity = promoteQ . promotableOut+ where+ dim' = dimension (Proxy :: Proxy d)+ promoteQ (DynQuantity d v) | d `isCompatibleWith` dim' = Just . Quantity $ v+ | otherwise = Nothing++instance (KnownDimension d) => Demotable (Quantity d) where+ demotableOut q@(Quantity x) = AnyQuantity (dimension q) x++-- | A 'Quantity' whose 'Dimension' is only known dynamically.+data AnyQuantity a = AnyQuantity !Dimension' !a+ deriving (Eq, Data, Generic, Generic1, Typeable)++instance (Show a) => Show (AnyQuantity a) where+ show (AnyQuantity d a) | d == D.dOne = show a+ | otherwise = show a ++ " " ++ (show . baseUnitName $ d)++instance HasDynamicDimension (AnyQuantity a) where++instance HasDimension (AnyQuantity a) where+ dimension (AnyQuantity d _) = d++instance NFData a => NFData (AnyQuantity a) -- instance is derived from Generic instance++instance Promotable AnyQuantity where+ promotableIn = id+ promotableOut (AnyQuantity d a) = DynQuantity (SomeDimension d) a++instance Demotable AnyQuantity where+ demotableOut = id++-- | 'AnyQuantity's form a 'Semigroup' under multiplication, but not under addition because+-- they may not be added together if their dimensions do not match.+instance Num a => Semigroup (AnyQuantity a) where+ (AnyQuantity d1 a1) <> (AnyQuantity d2 a2) = AnyQuantity (d1 D.* d2) (a1 P.* a2)++-- | 'AnyQuantity's form a 'Monoid' under multiplication, but not under addition because+-- they may not be added together if their dimensions do not match.+instance Num a => Monoid (AnyQuantity a) where+ mempty = demoteQuantity (1 Dim.*~ one)+ mappend = (<>)++#if USE_BINARY+instance (Data.Binary.Binary a) => Data.Binary.Binary (AnyQuantity a)+#endif++-- | Possibly a 'Quantity' whose 'Dimension' is only known dynamically.+--+-- By modeling the absence of a value, this type differs from 'AnyQuantity' in that it may+-- not be a 'Quantity' of any 'Dimension' whatsoever, but in exchange it gains instances+-- for the common numeric classes. It's therefore useful for manipulating, and not merely storing,+-- quantities of unknown dimension.+--+-- This type also contains a 'polydimensionalZero', representing zero value of any dimension.+--+-- Note that the 'Eq' instance for 'DynQuantity' equates all representations of an invalid value,+-- and also does not equate polydimensional zero with zero of any specific dimension.+data DynQuantity a = DynQuantity !DynamicDimension a -- we can't have strictness annotation on a as it is sometimes undefined+ deriving (Data, Generic, Generic1, Typeable)++instance Eq a => Eq (DynQuantity a) where+ (DynQuantity NoDimension _) == (DynQuantity NoDimension _) = True -- all invalid quantities are equal+ (DynQuantity NoDimension _) == _ = False -- invalid quanties are not equal to any other quantity+ _ == (DynQuantity NoDimension _) = False+ (DynQuantity d1 v1) == (DynQuantity d2 v2) = d1 == d2 && v1 == v2++instance NFData a => NFData (DynQuantity a) -- instance is derived from Generic instance++instance Show a => Show (DynQuantity a) where+ show (DynQuantity NoDimension _) = "invalidQuantity"+ show (DynQuantity AnyDimension v) = show v+ show (DynQuantity (SomeDimension d) v) = show $ AnyQuantity d v++instance Promotable DynQuantity where+ promotableIn (AnyQuantity d a) = DynQuantity (SomeDimension d) a+ promotableOut = id++instance HasDynamicDimension (DynQuantity a) where+ dynamicDimension (DynQuantity d _) = d++instance Num a => Num (DynQuantity a) where+ x + y = liftDQ2 matchDimensions (P.+) x y+ x - y = liftDQ2 matchDimensions (P.-) x y+ x * y = liftDQ2 (valid2 (D.*)) (P.*) x y+ negate = liftDQ id P.negate+ abs = liftDQ id P.abs+ signum = liftDQ (constant D.dOne) P.signum+ fromInteger = demoteQuantity . (Dim.*~ one) . P.fromInteger++instance Fractional a => Fractional (DynQuantity a) where+ x / y = liftDQ2 (valid2 (D./)) (P./) x y+ recip = liftDQ (valid D.recip) P.recip+ fromRational = demoteQuantity . (Dim.*~ one) . P.fromRational++instance Floating a => Floating (DynQuantity a) where+ pi = demoteQuantity pi+ exp = liftDimensionless P.exp+ log = liftDimensionless P.log+ sqrt = liftDQ (whenValid $ D.nroot 2) P.sqrt+ (**) = liftDQ2 (matchDimensions3 $ SomeDimension D.dOne) (P.**)+ logBase = liftDQ2 (matchDimensions3 $ SomeDimension D.dOne) P.logBase+ sin = liftDimensionless P.sin+ cos = liftDimensionless P.cos+ tan = liftDimensionless P.tan+ asin = liftDimensionless P.asin+ acos = liftDimensionless P.acos+ atan = liftDimensionless P.atan+ sinh = liftDimensionless P.sinh+ cosh = liftDimensionless P.cosh+ tanh = liftDimensionless P.tanh+ asinh = liftDimensionless P.asinh+ acosh = liftDimensionless P.acosh+ atanh = liftDimensionless P.atanh++-- | 'DynQuantity's form a 'Semigroup' under multiplication, but not under addition because+-- they may not be added together if their dimensions do not match.+instance Num a => Semigroup (DynQuantity a) where+ (<>) = (P.*)++-- | 'DynQuantity's form a 'Monoid' under multiplication, but not under addition because+-- they may not be added together if their dimensions do not match.+instance Num a => Monoid (DynQuantity a) where+ mempty = demoteQuantity (1 Dim.*~ one)+ mappend = (<>)++#if USE_BINARY+instance (Data.Binary.Binary a) => Data.Binary.Binary (DynQuantity a)+#endif++-- | A 'DynQuantity' which does not correspond to a value of any dimension.+invalidQuantity :: DynQuantity a+invalidQuantity = DynQuantity NoDimension $ error "Attempt to evaluate the value of an invalid quantity."++-- | A 'DynQuantity' which corresponds to zero value of any dimension.+--+-- When combined through arithmetic with other 'DynQuantity's, inference is performed. For example,+-- adding a length to polydimensional zero produces that length. Adding two polydimensional zeros produces another.+-- Taking the sine of a polydimensional zero interprets it as a dimensionless zero and produces a dimensionless result.+--+-- Note that division by 'polydimensionalZero' produces a polydimensional result, which may be an error or some representation+-- of infinity, as determined by the underlying arithmetic type. This behavior was chosen for consistency with the behavior of division+-- by zero 'DynQuantity's of a specific dimension.+polydimensionalZero :: (Num a) => DynQuantity a+polydimensionalZero = DynQuantity AnyDimension 0++-- | Lifts a function which is only valid on dimensionless quantities into a function on 'DynQuantity's.+liftDimensionless :: (a -> a) -> DynQuantity a -> DynQuantity a+liftDimensionless = liftDQ (matchDimensions $ SomeDimension D.dOne)++-- | Lifts a function on values into a function on 'DynQuantity's.+liftDQ :: (DynamicDimension -> DynamicDimension) -- ^ How the function operates on dimensions.+ -> (a -> a) -- ^ How the function operates on values.+ -> DynQuantity a -> DynQuantity a+liftDQ fd fv (DynQuantity d v) = case fd d of+ NoDimension -> invalidQuantity+ d' -> DynQuantity d' $ fv v++-- | Lifts a function on values into a function on 'DynQuantity's.+--+-- This works by treating polydimensional zeros as dimensionless zeros. If that is not the desired behavior,+-- handle polydimensional zeros first and then call this function.+liftDQ2 :: (DynamicDimension -> DynamicDimension -> DynamicDimension)+ -> (a -> a -> a)+ -> DynQuantity a -> DynQuantity a -> DynQuantity a+liftDQ2 fd fv (DynQuantity d1 v1) (DynQuantity d2 v2) = case fd d1 d2 of+ NoDimension -> invalidQuantity+ d' -> DynQuantity d' $ fv v1 v2++-- | Transforms a dynamic dimension in a way which is always valid.+valid :: (Dimension' -> Dimension') -> DynamicDimension -> DynamicDimension+valid _ AnyDimension = AnyDimension+valid f (SomeDimension d) = SomeDimension (f d)+valid _ NoDimension = NoDimension++whenValid :: (Dimension' -> Maybe Dimension') -> DynamicDimension -> DynamicDimension+whenValid _ AnyDimension = AnyDimension+whenValid f (SomeDimension d) | Just d' <- f d = SomeDimension d'+whenValid _ _ = NoDimension++constant :: Dimension' -> DynamicDimension -> DynamicDimension+constant d AnyDimension = SomeDimension d+constant d (SomeDimension _) = SomeDimension d+constant _ _ = NoDimension++-- | Transforms two dynamic dimensions in a way which is always valid.+valid2 :: (Dimension' -> Dimension' -> Dimension') -> DynamicDimension -> DynamicDimension -> DynamicDimension+valid2 _ AnyDimension (SomeDimension _) = AnyDimension+valid2 _ (SomeDimension _) AnyDimension = AnyDimension+valid2 _ AnyDimension AnyDimension = AnyDimension+valid2 f (SomeDimension d1) (SomeDimension d2) = SomeDimension (f d1 d2)+valid2 _ _ _ = NoDimension++matchDimensions3 :: DynamicDimension -> DynamicDimension -> DynamicDimension -> DynamicDimension+matchDimensions3 x y z = matchDimensions x (matchDimensions y z)++-- | A 'Unit' whose 'Dimension' is only known dynamically.+data AnyUnit = AnyUnit Dimension' (UnitName 'NonMetric) ExactPi+ deriving (Generic, Typeable)++instance Show AnyUnit where+ show (AnyUnit _ n e) = show n ++ " =def= " ++ show e ++ " of the SI base unit"++instance HasDynamicDimension AnyUnit where++instance HasDimension AnyUnit where+ dimension (AnyUnit d _ _) = d++instance I.HasInterchangeName AnyUnit where+ interchangeName (AnyUnit _ n _) = I.interchangeName n++-- | 'AnyUnit's form a 'Semigroup' under multiplication.+instance Semigroup AnyUnit where+ (<>) = (Numeric.Units.Dimensional.Dynamic.*)++-- | 'AnyUnit's form a 'Monoid' under multiplication.+instance Monoid AnyUnit where+ mempty = demoteUnit' one+ mappend = (<>)++-- | Extracts the 'UnitName' of an 'AnyUnit'.+anyUnitName :: AnyUnit -> UnitName 'NonMetric+anyUnitName (AnyUnit _ n _) = n++-- | The dynamic SI coherent unit of a given dimension.+siUnit :: Dimension' -> AnyUnit+siUnit d = AnyUnit d (baseUnitName d) 1++-- | Converts a 'Unit' of statically known 'Dimension' into an 'AnyUnit'.+demoteUnit :: forall m d a.(KnownDimension d) => Unit m d a -> AnyUnit+demoteUnit u = AnyUnit dim (name $ weaken u) (exactValue u)+ where+ dim = dimension (Proxy :: Proxy d)++-- | Converts a 'Unit' of statically known 'Dimension' into an 'AnyUnit'.+--+-- This is the same as the more general 'demoteUnit' but is useful in certain circumstances to avoid+-- needlessly introducing an ambiguous type variable.+demoteUnit' :: (KnownDimension d) => Unit m d ExactPi -> AnyUnit+demoteUnit' = demoteUnit++-- | Converts an 'AnyUnit' into a 'Unit' of statically known 'Dimension', or 'Nothing' if the dimension does not match.+--+-- The result is represented in 'ExactPi', conversion to other representations is possible using 'changeRepApproximate'.+--+-- The result is always tagged as 'NonMetric', conversion to a 'Metric' unit can be attempted using 'strengthen'.+promoteUnit :: forall d.(KnownDimension d) => AnyUnit -> Maybe (Unit 'NonMetric d ExactPi)+promoteUnit (AnyUnit dim n e) | dim == dim' = Just $ mkUnitR n e Dim.siUnit+ | otherwise = Nothing+ where+ dim' = dimension (Proxy :: Proxy d)++-- | Forms the reciprocal of a dynamic unit.+recip :: AnyUnit -> AnyUnit+recip (AnyUnit d n e) = AnyUnit (D.recip d) (N.nOne N./ n) (P.recip e)++-- | Forms the product of two dynamic units.+(*) :: AnyUnit -> AnyUnit -> AnyUnit+(AnyUnit d1 n1 e1) * (AnyUnit d2 n2 e2) = AnyUnit (d1 D.* d2) (n1 N.* n2) (e1 P.* e2)++-- | Forms the quotient of two dynamic units.+(/) :: AnyUnit -> AnyUnit -> AnyUnit+(AnyUnit d1 n1 e1) / (AnyUnit d2 n2 e2) = AnyUnit (d1 D./ d2) (n1 N./ n2) (e1 P./ e2)++-- | Raises a dynamic unit to an integer power.+(^) :: (P.Integral a) => AnyUnit -> a -> AnyUnit+(AnyUnit d n e) ^ x = AnyUnit (d D.^ P.fromIntegral x) (n N.^ P.fromIntegral x) (e P.^^ x)++-- | Applies a prefix to a dynamic unit.+-- Returns 'Nothing' if the 'Unit' was 'NonMetric' and thus could not accept a prefix.+applyPrefix :: N.Prefix -> AnyUnit -> Maybe AnyUnit+applyPrefix p (AnyUnit d n e) = do+ n' <- N.strengthen n+ let n'' = N.applyPrefix p n'+ let e' = (P.fromRational $ N.scaleFactor p) P.* e+ return $ AnyUnit d n'' e'++-- | Forms a dynamic quantity by multipliying a number and a dynamic unit.+(*~) :: (Floating a, Promotable q) => a -> AnyUnit -> q a+x *~ (AnyUnit d _ e) = promotableIn $ AnyQuantity d (x P.* approximateValue e)++-- | Divides a dynamic quantity by a dynamic unit, obtaining the numerical value of the quantity+-- expressed in that unit if they are of the same physical dimension, or 'Nothing' otherwise.+(/~) :: (Floating a, Promotable q) => q a -> AnyUnit -> Maybe a+x /~ (AnyUnit d _ e) = case promotableOut x of+ DynQuantity d' x' | d' `isCompatibleWith` d -> Just $ x' P./ approximateValue e+ | otherwise -> Nothing
src/Numeric/Units/Dimensional/FixedPoint.hs view
@@ -1,373 +1,373 @@-{-# LANGUAGE ConstraintKinds #-} -{-# LANGUAGE DataKinds #-} -{-# LANGUAGE FlexibleContexts #-} -{-# LANGUAGE GADTs #-} -{-# LANGUAGE RankNTypes #-} -{-# LANGUAGE ScopedTypeVariables #-} -{-# LANGUAGE TypeOperators #-} - -{- | - Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter - License : BSD3 - - Maintainer : bjorn@buckwalter.se - Stability : Experimental - Portability: GHC only? - -Defines types for manipulation of quantities with fixed point representations. --} -module Numeric.Units.Dimensional.FixedPoint -( - -- * Types - -- $types - Dimensional, - Unit, Quantity, SQuantity, - Metricality(..), - -- * Physical Dimensions - Dimension (Dim), - -- ** Dimension Arithmetic - type (*), type (/), type (^), NRoot, Recip, - -- ** Term Level Representation of Dimensions - Dimension' (Dim'), HasDimension(..), KnownDimension, - -- * Dimensional Arithmetic - (*~), (/~), - (*), (/), (+), (-), - negate, abs, - -- ** Transcendental Functions - -- *** Via 'Double' - expD, logD, sinD, cosD, tanD, asinD, acosD, atanD, sinhD, coshD, tanhD, asinhD, acoshD, atanhD, atan2D, - -- *** Via arbitary 'Floating' type - expVia, logVia, sinVia, cosVia, tanVia, asinVia, acosVia, atanVia, sinhVia, coshVia, tanhVia, asinhVia, acoshVia, atanhVia, atan2Via, - -- ** Operations on Collections - (*~~), (/~~), sum, mean, -- dimensionlessLength, nFromTo, - -- ** Conversion Between Representations - rescale, rescaleFinite, rescaleD, rescaleVia, KnownVariant(dmap), changeRep, changeRepRound, changeRepApproximate, - -- * Dimension Synonyms - DOne, DLength, DMass, DTime, DElectricCurrent, DThermodynamicTemperature, DAmountOfSubstance, DLuminousIntensity, - -- * Quantity Synonyms - Dimensionless, Length, Mass, Time, ElectricCurrent, ThermodynamicTemperature, AmountOfSubstance, LuminousIntensity, - -- * Constants - _0, epsilon, - -- $possibly-imprecise-constants - _1, _2, _3, _4, _5, _6, _7, _8, _9, pi, tau, - -- * Constructing Units - siUnit, one, mkUnitR, mkUnitQ, mkUnitZ, - -- * Unit Metadata - name, exactValue, weaken, strengthen, exactify, - -- * Commonly Used Type Synonyms - -- $synonyms - type Q, type QScale, type Angle8, type Angle16, type Angle32 -) -where - -import Data.Bits -import Data.ExactPi -import qualified Data.ExactPi.TypeLevel as E -import Data.Int -import Data.Proxy -import qualified Data.Foldable as F -import Data.Ratio -import qualified GHC.TypeLits as N -import Numeric.Units.Dimensional.Coercion -import Numeric.Units.Dimensional.Internal -import Numeric.Units.Dimensional.Prelude hiding ((*~), (/~), (+), (-), recip, negate, abs, (*~~), (/~~), sum, mean, _0, _1, _2, _3, _4, _5, _6, _7, _8, _9, pi, tau, changeRep) -import Numeric.Units.Dimensional.Variants hiding (type (*), type (/)) -import qualified Numeric.Units.Dimensional.UnitNames as Name -import qualified Prelude as P - -{- $types - -We provide access to the same 'Dimensional', 'Unit', and 'Quantity' types as are exposed by "Numeric.Units.Dimensional", but additionally -offer the 'SQuantity' type to represent scaled quantities. Fixed-point quantities are quantities backed by integers, it is frequently -necessary to scale those integers into a range appropriate for the physical problem at hand. - --} - -{- - -Arithmetic Operators and Functions - -We will reuse the operators and function names from the Prelude. -To prevent unpleasant surprises we give operators the same fixity -as the Prelude. - --} - ---infixr 8 ^, ^/, ** -infixl 6 +, - - --- | Adds two possibly scaled 'SQuantity's, preserving any scale factor. --- --- Use in conjunction with 'changeRepRound' to combine quantities with differing scale factors. -(+) :: (Num a) => SQuantity s d a -> SQuantity s d a -> SQuantity s d a -(+) = liftQ2 (P.+) - --- | Subtracts one possibly scaled 'SQuantity' from another, preserving any scale factor. --- --- Use in conjunction with 'changeRepRound' to combine quantities with differing scale factors. -(-) :: (Num a) => SQuantity s d a -> SQuantity s d a -> SQuantity s d a -(-) = liftQ2 (P.-) - --- | Takes the absolute value of a possibly scaled 'SQuantity', preserving any scale factor. -abs :: (Num a) => SQuantity s d a -> SQuantity s d a -abs = liftQ (P.abs) - --- | Negates the value of a possibly scaled 'SQuantity', preserving any scale factor. -negate :: (Num a) => SQuantity s d a -> SQuantity s d a -negate = liftQ (P.negate) - -infixl 7 *~~, /~~ - --- | Applies '*~' to all values in a functor. -(*~~) :: (Functor f, RealFrac a, Integral b, E.MinCtxt s a) => f a -> Unit m d a -> f (SQuantity s d b) -xs *~~ u = fmap (*~ u) xs - --- | Applies '/~' to all values in a functor. -(/~~) :: (Functor f, Real a, Fractional b, E.MinCtxt s b) => f (SQuantity s d a) -> Unit m d b -> f b -xs /~~ u = fmap (/~ u) xs - --- | The sum of all elements in a list. -sum :: (Num a, F.Foldable f) => f (SQuantity s d a) -> SQuantity s d a -sum = F.foldr (+) _0 - --- | The arithmetic mean of all elements in a list. -mean :: (Fractional a, F.Foldable f) => f (SQuantity s d a) -> SQuantity s d a -mean = reduce . F.foldr accumulate (_0, 0 :: Int) - where - reduce (s, n) = dmap (P./ fromIntegral n) s - accumulate val (accum, count) = (accum + val, count P.+ 1) - -expD, logD, sinD, cosD, tanD, asinD, acosD, atanD, sinhD, coshD, tanhD, asinhD, acoshD, atanhD - :: (Integral a, Integral b, E.MinCtxt s1 Double, E.MinCtxt s2 Double) => SQuantity s1 DOne a -> SQuantity s2 DOne b -expD = expVia (Proxy :: Proxy P.Double) -logD = logVia (Proxy :: Proxy P.Double) -sinD = sinVia (Proxy :: Proxy P.Double) -cosD = cosVia (Proxy :: Proxy P.Double) -tanD = tanVia (Proxy :: Proxy P.Double) -asinD = asinVia (Proxy :: Proxy P.Double) -acosD = acosVia (Proxy :: Proxy P.Double) -atanD = atanVia (Proxy :: Proxy P.Double) -sinhD = sinhVia (Proxy :: Proxy P.Double) -coshD = coshVia (Proxy :: Proxy P.Double) -tanhD = tanhVia (Proxy :: Proxy P.Double) -asinhD = asinhVia (Proxy :: Proxy P.Double) -acoshD = acoshVia (Proxy :: Proxy P.Double) -atanhD = atanhVia (Proxy :: Proxy P.Double) - --- | The standard two argument arctangent function. --- Since it interprets its two arguments in comparison with one another, the input may have any dimension. -atan2D :: (Integral a, Integral b, E.MinCtxt s1 Double, E.MinCtxt s2 Double, E.MinCtxt s3 Double) => SQuantity s1 DOne a -> SQuantity s2 DOne a -> SQuantity s3 DOne b -atan2D = atan2Via (Proxy :: Proxy P.Double) - -expVia, logVia, sinVia, cosVia, tanVia, asinVia, acosVia, atanVia, sinhVia, coshVia, tanhVia, asinhVia, acoshVia, atanhVia - :: (Integral a, RealFrac b, Floating b, Integral c, E.MinCtxt s1 b, E.MinCtxt s2 b) => Proxy b -> SQuantity s1 DOne a -> SQuantity s2 DOne c -expVia = liftDimensionlessVia P.exp -logVia = liftDimensionlessVia P.log -sinVia = liftDimensionlessPeriodicVia (2 P.* P.pi) P.sin -cosVia = liftDimensionlessPeriodicVia (2 P.* P.pi) P.cos -tanVia = liftDimensionlessPeriodicVia P.pi P.tan -asinVia = liftDimensionlessVia P.asin -acosVia = liftDimensionlessVia P.acos -atanVia = liftDimensionlessVia P.atan -sinhVia = liftDimensionlessPeriodicVia (2 P.* P.pi) P.sinh -coshVia = liftDimensionlessPeriodicVia (2 P.* P.pi) P.cosh -tanhVia = liftDimensionlessPeriodicVia P.pi P.tanh -asinhVia = liftDimensionlessVia P.asinh -acoshVia = liftDimensionlessVia P.acosh -atanhVia = liftDimensionlessVia P.atanh - --- | The standard two argument arctangent function. --- Since it interprets its two arguments in comparison with one another, the input may have any dimension. -atan2Via :: forall s1 s2 s3 a b c d.(Integral a, RealFloat b, Integral c, E.MinCtxt s1 b, E.MinCtxt s2 b, E.MinCtxt s3 b, KnownDimension d) => Proxy b -> SQuantity s1 d a -> SQuantity s2 d a -> SQuantity s3 DOne c -atan2Via _ y x = (*~ siUnit) $ (P.atan2 :: b -> b -> b) (y /~ siUnit) (x /~ siUnit) - --- | Lift a function on dimensionless values of a specified intermediate type to operate on possibly scaled dimensionless. -liftDimensionlessVia :: forall s1 s2 a b c.(Real a, RealFrac b, Integral c, E.MinCtxt s1 b, E.MinCtxt s2 b) => (b -> b) -> Proxy b -> SQuantity s1 DOne a -> SQuantity s2 DOne c -liftDimensionlessVia f _ = (*~ siUnit) . (f :: b -> b) . (/~ siUnit) - --- | Lift a periodic function on dimensionless values of a specified intermediate type to operate on possibly scaled dimensionless. --- --- If the scale factor of the input type is an exact integer divisor of the function's period, the argument --- will be clamped via an integer `mod` operation prior to applying the function to avoid errors introduced by a floating point modulus. -liftDimensionlessPeriodicVia :: forall s1 s2 a b c.(Integral a, RealFrac b, Floating b, Integral c, E.MinCtxt s1 b, E.MinCtxt s2 b) => ExactPi -> (forall d.Floating d => d -> d) -> Proxy b -> SQuantity s1 DOne a -> SQuantity s2 DOne c -liftDimensionlessPeriodicVia p f proxy | Just p'' <- p', p'' /= 0 = (liftDimensionlessVia f proxy) . dmap (`mod` p'') - | otherwise = liftDimensionlessVia f proxy - where - p' :: Maybe a - p' = fmap fromInteger . toExactInteger . P.recip . (P./ p) . E.exactPiVal $ (Proxy :: Proxy s1) - -{- -We give '*~' and '/~' the same fixity as '*' and '/' defined below. -Note that this necessitates the use of parenthesis when composing -units using '*' and '/', e.g. "1 *~ (meter / second)". --} - -infixl 7 *~, /~ - --- | Forms a possibly scaled 'SQuantity' by multipliying a number and a unit. -(*~) :: forall s m d a b.(RealFrac a, Integral b, E.MinCtxt s a) => a -> Unit m d a -> SQuantity s d b -x *~ (Unit _ _ y) = Quantity . round $ (x P.* y P./ s) - where - s = E.injMin (Proxy :: Proxy s) - --- | Divides a possibly scaled 'SQuantity' by a 'Unit' of the same physical dimension, obtaining the --- numerical value of the quantity expressed in that unit. -(/~) :: forall s m d a b.(Real a, Fractional b, E.MinCtxt s b) => SQuantity s d a -> Unit m d b -> b -(Quantity x) /~ (Unit _ _ y) = ((realToFrac x) P.* s P./ y) - where - s = E.injMin (Proxy :: Proxy s) - -{- - -Rescaling Operations - --} - --- | Rescales a fixed point quantity, accomodating changes both in its scale factor and its representation type. --- --- Note that this uses an arbitrary precision representation of 'pi', which may be quite slow. -rescale :: forall a b d s1 s2.(Integral a, Integral b, E.KnownExactPi s1, E.KnownExactPi s2) => SQuantity s1 d a -> SQuantity s2 d b -rescale | Just s' <- toExactInteger s = viaInteger (P.* s') - | Just s' <- toExactInteger (P.recip s) = viaInteger (`P.quot` s') - | Just q <- toExactRational s = viaInteger $ timesRational q - | otherwise = viaInteger $ \x -> fixedPoint (fmap (($ x) . timesRational) (rationalApproximations s)) - where - s = (s1' P./ s2') - s1' = E.exactPiVal (Proxy :: Proxy s1) - s2' = E.exactPiVal (Proxy :: Proxy s2) - timesRational :: Rational -> Integer -> Integer - timesRational q = (`P.quot` denominator q) . (P.* numerator q) - --- | Rescales a fixed point quantity, accomodating changes both in its scale factor and its representation type. --- --- Expected to outperform `rescale` when a `FiniteBits` context is available for the source and destination representation types. -rescaleFinite :: (Integral a, FiniteBits a, Integral b, FiniteBits b, E.KnownExactPi s1, E.KnownExactPi s2) => SQuantity s1 d a -> SQuantity s2 d b -rescaleFinite = rescale -- It should be possible to do this more quickly, since we have a priori knowledge of how well we need to approximate the result - --- | Approximately rescales a fixed point quantity, accomodating changes both in its scale factor and its representation type. --- --- Uses approximate arithmetic by way of an intermediate `Floating` type, to which a proxy must be supplied. -rescaleVia :: forall a b c d s1 s2.(Integral a, RealFrac b, Floating b, Integral c, E.KnownExactPi s1, E.KnownExactPi s2) => Proxy b -> SQuantity s1 d a -> SQuantity s2 d c -rescaleVia _ = viaIntermediate (P.* s) - where - s = approximateValue (s1' P./ s2') :: b - s1' = E.exactPiVal $ (Proxy :: Proxy s1) - s2' = E.exactPiVal $ (Proxy :: Proxy s2) - --- | Approximately rescales a fixed point quantity, accomodating changes both in its scale factor and its representation type. --- --- Uses approximate arithmetic by way of an intermediate `Double` representation. -rescaleD :: (Integral a, Integral b, E.KnownExactPi s1, E.KnownExactPi s2) => SQuantity s1 d a -> SQuantity s2 d b -rescaleD = rescaleVia (Proxy :: Proxy Double) - --- Note that this does not respect scaling factors at all. -viaInteger :: (Integral a, Integral b) => (P.Integer -> P.Integer) -> SQuantity s1 d a -> SQuantity s2 d b -viaInteger f = Quantity . fromInteger . f . fromIntegral . unQuantity - --- Note that this does not respect scaling factors at all. -viaIntermediate :: (Integral a, RealFrac b, Integral c) => (b -> b) -> SQuantity s1 d a -> SQuantity s2 d c -viaIntermediate f = Quantity . round . f . fromIntegral . unQuantity - -fixedPoint :: (Eq a) => [a] -> a -fixedPoint [] = error "Fixed point of empty list." -fixedPoint [x] = x -fixedPoint (x1:x2:xs) | x1 == x2 = x1 - | otherwise = fixedPoint (x2:xs) - -{- - -Changes of Representation - --} - --- | Convenient conversion between numerical types while retaining dimensional information. -changeRep :: forall v1 v2 d a b. - (KnownVariant v1, KnownVariant v2, - CompatibleVariants v1 v2, - E.MinCtxt (ScaleFactor v1 E./ ScaleFactor v2) b, - Real a, Fractional b) - => Dimensional v1 d a -> Dimensional v2 d b -changeRep = liftD (P.* s) ((P.* s') . realToFrac) Name.weaken - where - p :: Proxy (ScaleFactor v1 E./ ScaleFactor v2) - p = Proxy - s = E.exactPiVal p - s' = E.injMin p - --- | Convenient conversion to types with `Integral` representations using `round`. -changeRepRound :: forall v1 v2 d a b. - (KnownVariant v1, KnownVariant v2, - CompatibleVariants v1 v2, - E.MinCtxt (ScaleFactor v1 E./ ScaleFactor v2) a, - RealFrac a, Integral b) - => Dimensional v1 d a -> Dimensional v2 d b -changeRepRound = liftD (P.* s) (round . (P.* s')) Name.weaken - where - p :: Proxy (ScaleFactor v1 E./ ScaleFactor v2) - p = Proxy - s = E.exactPiVal p - s' = E.injMin p - -{- - -Useful Constant Values - --} - -{- $possibly-imprecise-constants - -Note that, other than '_0' and 'epsilon', these constants may not be exactly representable with certain scale factors. - --} - --- | The constant for zero is polymorphic, allowing --- it to express zero 'Length' or 'Capacitance' or 'Velocity' etc, in addition --- to the 'Dimensionless' value zero. -_0 :: Num a => SQuantity s d a -_0 = Quantity 0 - -_1, _2, _3, _4, _5, _6, _7, _8, _9 :: (Integral a, E.KnownExactPi s) => SQuantity s DOne a -_1 = rescale (epsilon :: SQuantity E.One DOne Integer) -_2 = rescale (epsilon :: SQuantity (E.ExactNatural 2) DOne Integer) -_3 = rescale (epsilon :: SQuantity (E.ExactNatural 3) DOne Integer) -_4 = rescale (epsilon :: SQuantity (E.ExactNatural 4) DOne Integer) -_5 = rescale (epsilon :: SQuantity (E.ExactNatural 5) DOne Integer) -_6 = rescale (epsilon :: SQuantity (E.ExactNatural 6) DOne Integer) -_7 = rescale (epsilon :: SQuantity (E.ExactNatural 7) DOne Integer) -_8 = rescale (epsilon :: SQuantity (E.ExactNatural 8) DOne Integer) -_9 = rescale (epsilon :: SQuantity (E.ExactNatural 9) DOne Integer) - -pi :: (Integral a, E.KnownExactPi s) => SQuantity s DOne a -pi = rescale (epsilon :: SQuantity E.Pi DOne Integer) - --- | Twice 'pi'. --- --- For background on 'tau' see http://tauday.com/tau-manifesto (but also --- feel free to review http://www.thepimanifesto.com). -tau :: (Integral a, E.KnownExactPi s) => SQuantity s DOne a -tau = rescale (epsilon :: SQuantity (E.ExactNatural 2 E.* E.Pi) DOne Integer) - --- | The least positive representable value in a given fixed-point scaled quantity type. -epsilon :: (Integral a) => SQuantity s d a -epsilon = Quantity 1 - -{- $synonyms - -These type synonyms for commonly used fixed-point types are provided for convenience. - --} - --- | A binary scale factor. -type QScale n = (E.One E./ (E.ExactNatural (2 N.^ n))) - --- | A dimensionless number with `n` fractional bits, using a representation of type `a`. -type Q n a = SQuantity (QScale n) DOne a - --- | A single-turn angle represented as a signed 8-bit integer. -type Angle8 = SQuantity (E.Pi E.* (QScale 7)) DPlaneAngle Int8 - --- | A single-turn angle represented as a signed 16-bit integer. -type Angle16 = SQuantity (E.Pi E.* (QScale 15)) DPlaneAngle Int16 - --- | A single-turn angle represented as a signed 32-bit integer. -type Angle32 = SQuantity (E.Pi E.* (QScale 31)) DPlaneAngle Int32 +{-# LANGUAGE ConstraintKinds #-}+{-# LANGUAGE DataKinds #-}+{-# LANGUAGE FlexibleContexts #-}+{-# LANGUAGE GADTs #-}+{-# LANGUAGE RankNTypes #-}+{-# LANGUAGE ScopedTypeVariables #-}+{-# LANGUAGE TypeOperators #-}++{- |+ Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter+ License : BSD3++ Maintainer : bjorn@buckwalter.se+ Stability : Experimental+ Portability: GHC only?++Defines types for manipulation of quantities with fixed point representations.+-}+module Numeric.Units.Dimensional.FixedPoint+(+ -- * Types+ -- $types+ Dimensional,+ Unit, Quantity, SQuantity,+ Metricality(..),+ -- * Physical Dimensions+ Dimension (Dim),+ -- ** Dimension Arithmetic+ type (*), type (/), type (^), NRoot, Recip,+ -- ** Term Level Representation of Dimensions+ Dimension' (Dim'), HasDimension(..), KnownDimension,+ -- * Dimensional Arithmetic+ (*~), (/~),+ (*), (/), (+), (-),+ negate, abs,+ -- ** Transcendental Functions+ -- *** Via 'Double'+ expD, logD, sinD, cosD, tanD, asinD, acosD, atanD, sinhD, coshD, tanhD, asinhD, acoshD, atanhD, atan2D,+ -- *** Via arbitary 'Floating' type+ expVia, logVia, sinVia, cosVia, tanVia, asinVia, acosVia, atanVia, sinhVia, coshVia, tanhVia, asinhVia, acoshVia, atanhVia, atan2Via,+ -- ** Operations on Collections+ (*~~), (/~~), sum, mean, -- dimensionlessLength, nFromTo,+ -- ** Conversion Between Representations+ rescale, rescaleFinite, rescaleD, rescaleVia, KnownVariant(dmap), changeRep, changeRepRound, changeRepApproximate,+ -- * Dimension Synonyms+ DOne, DLength, DMass, DTime, DElectricCurrent, DThermodynamicTemperature, DAmountOfSubstance, DLuminousIntensity,+ -- * Quantity Synonyms+ Dimensionless, Length, Mass, Time, ElectricCurrent, ThermodynamicTemperature, AmountOfSubstance, LuminousIntensity,+ -- * Constants+ _0, epsilon,+ -- $possibly-imprecise-constants+ _1, _2, _3, _4, _5, _6, _7, _8, _9, pi, tau,+ -- * Constructing Units+ siUnit, one, mkUnitR, mkUnitQ, mkUnitZ,+ -- * Unit Metadata+ name, exactValue, weaken, strengthen, exactify,+ -- * Commonly Used Type Synonyms+ -- $synonyms+ type Q, type QScale, type Angle8, type Angle16, type Angle32+)+where++import Data.Bits+import Data.ExactPi+import qualified Data.ExactPi.TypeLevel as E+import Data.Int+import Data.Proxy+import qualified Data.Foldable as F+import Data.Ratio+import qualified GHC.TypeLits as N+import Numeric.Units.Dimensional.Coercion+import Numeric.Units.Dimensional.Internal+import Numeric.Units.Dimensional.Prelude hiding ((*~), (/~), (+), (-), recip, negate, abs, (*~~), (/~~), sum, mean, _0, _1, _2, _3, _4, _5, _6, _7, _8, _9, pi, tau, changeRep)+import Numeric.Units.Dimensional.Variants hiding (type (*), type (/))+import qualified Numeric.Units.Dimensional.UnitNames as Name+import qualified Prelude as P++{- $types++We provide access to the same 'Dimensional', 'Unit', and 'Quantity' types as are exposed by "Numeric.Units.Dimensional", but additionally+offer the 'SQuantity' type to represent scaled quantities. Fixed-point quantities are quantities backed by integers, it is frequently+necessary to scale those integers into a range appropriate for the physical problem at hand.++-}++{-++Arithmetic Operators and Functions++We will reuse the operators and function names from the Prelude.+To prevent unpleasant surprises we give operators the same fixity+as the Prelude.++-}++--infixr 8 ^, ^/, **+infixl 6 +, -++-- | Adds two possibly scaled 'SQuantity's, preserving any scale factor.+--+-- Use in conjunction with 'changeRepRound' to combine quantities with differing scale factors.+(+) :: (Num a) => SQuantity s d a -> SQuantity s d a -> SQuantity s d a+(+) = liftQ2 (P.+)++-- | Subtracts one possibly scaled 'SQuantity' from another, preserving any scale factor.+--+-- Use in conjunction with 'changeRepRound' to combine quantities with differing scale factors.+(-) :: (Num a) => SQuantity s d a -> SQuantity s d a -> SQuantity s d a+(-) = liftQ2 (P.-)++-- | Takes the absolute value of a possibly scaled 'SQuantity', preserving any scale factor.+abs :: (Num a) => SQuantity s d a -> SQuantity s d a+abs = liftQ (P.abs)++-- | Negates the value of a possibly scaled 'SQuantity', preserving any scale factor.+negate :: (Num a) => SQuantity s d a -> SQuantity s d a+negate = liftQ (P.negate)++infixl 7 *~~, /~~++-- | Applies '*~' to all values in a functor.+(*~~) :: (Functor f, RealFrac a, Integral b, E.MinCtxt s a) => f a -> Unit m d a -> f (SQuantity s d b)+xs *~~ u = fmap (*~ u) xs++-- | Applies '/~' to all values in a functor.+(/~~) :: (Functor f, Real a, Fractional b, E.MinCtxt s b) => f (SQuantity s d a) -> Unit m d b -> f b+xs /~~ u = fmap (/~ u) xs++-- | The sum of all elements in a list.+sum :: (Num a, F.Foldable f) => f (SQuantity s d a) -> SQuantity s d a+sum = F.foldr (+) _0++-- | The arithmetic mean of all elements in a list.+mean :: (Fractional a, F.Foldable f) => f (SQuantity s d a) -> SQuantity s d a+mean = reduce . F.foldr accumulate (_0, 0 :: Int)+ where+ reduce (s, n) = dmap (P./ fromIntegral n) s+ accumulate val (accum, count) = (accum + val, count P.+ 1)++expD, logD, sinD, cosD, tanD, asinD, acosD, atanD, sinhD, coshD, tanhD, asinhD, acoshD, atanhD+ :: (Integral a, Integral b, E.MinCtxt s1 Double, E.MinCtxt s2 Double) => SQuantity s1 DOne a -> SQuantity s2 DOne b+expD = expVia (Proxy :: Proxy P.Double)+logD = logVia (Proxy :: Proxy P.Double)+sinD = sinVia (Proxy :: Proxy P.Double)+cosD = cosVia (Proxy :: Proxy P.Double)+tanD = tanVia (Proxy :: Proxy P.Double)+asinD = asinVia (Proxy :: Proxy P.Double)+acosD = acosVia (Proxy :: Proxy P.Double)+atanD = atanVia (Proxy :: Proxy P.Double)+sinhD = sinhVia (Proxy :: Proxy P.Double)+coshD = coshVia (Proxy :: Proxy P.Double)+tanhD = tanhVia (Proxy :: Proxy P.Double)+asinhD = asinhVia (Proxy :: Proxy P.Double)+acoshD = acoshVia (Proxy :: Proxy P.Double)+atanhD = atanhVia (Proxy :: Proxy P.Double)++-- | The standard two argument arctangent function.+-- Since it interprets its two arguments in comparison with one another, the input may have any dimension.+atan2D :: (Integral a, Integral b, E.MinCtxt s1 Double, E.MinCtxt s2 Double, E.MinCtxt s3 Double) => SQuantity s1 DOne a -> SQuantity s2 DOne a -> SQuantity s3 DOne b+atan2D = atan2Via (Proxy :: Proxy P.Double)++expVia, logVia, sinVia, cosVia, tanVia, asinVia, acosVia, atanVia, sinhVia, coshVia, tanhVia, asinhVia, acoshVia, atanhVia+ :: (Integral a, RealFrac b, Floating b, Integral c, E.MinCtxt s1 b, E.MinCtxt s2 b) => Proxy b -> SQuantity s1 DOne a -> SQuantity s2 DOne c+expVia = liftDimensionlessVia P.exp+logVia = liftDimensionlessVia P.log+sinVia = liftDimensionlessPeriodicVia (2 P.* P.pi) P.sin+cosVia = liftDimensionlessPeriodicVia (2 P.* P.pi) P.cos+tanVia = liftDimensionlessPeriodicVia P.pi P.tan+asinVia = liftDimensionlessVia P.asin+acosVia = liftDimensionlessVia P.acos+atanVia = liftDimensionlessVia P.atan+sinhVia = liftDimensionlessPeriodicVia (2 P.* P.pi) P.sinh+coshVia = liftDimensionlessPeriodicVia (2 P.* P.pi) P.cosh+tanhVia = liftDimensionlessPeriodicVia P.pi P.tanh+asinhVia = liftDimensionlessVia P.asinh+acoshVia = liftDimensionlessVia P.acosh+atanhVia = liftDimensionlessVia P.atanh++-- | The standard two argument arctangent function.+-- Since it interprets its two arguments in comparison with one another, the input may have any dimension.+atan2Via :: forall s1 s2 s3 a b c d.(Integral a, RealFloat b, Integral c, E.MinCtxt s1 b, E.MinCtxt s2 b, E.MinCtxt s3 b, KnownDimension d) => Proxy b -> SQuantity s1 d a -> SQuantity s2 d a -> SQuantity s3 DOne c+atan2Via _ y x = (*~ siUnit) $ (P.atan2 :: b -> b -> b) (y /~ siUnit) (x /~ siUnit)++-- | Lift a function on dimensionless values of a specified intermediate type to operate on possibly scaled dimensionless values.+liftDimensionlessVia :: forall s1 s2 a b c.(Real a, RealFrac b, Integral c, E.MinCtxt s1 b, E.MinCtxt s2 b) => (b -> b) -> Proxy b -> SQuantity s1 DOne a -> SQuantity s2 DOne c+liftDimensionlessVia f _ = (*~ siUnit) . (f :: b -> b) . (/~ siUnit)++-- | Lift a periodic function on dimensionless values of a specified intermediate type to operate on possibly scaled dimensionless values.+--+-- If the scale factor of the input type is an exact integer divisor of the function's period, the argument+-- will be clamped via an integer `mod` operation prior to applying the function to avoid errors introduced by a floating point modulus.+liftDimensionlessPeriodicVia :: forall s1 s2 a b c.(Integral a, RealFrac b, Floating b, Integral c, E.MinCtxt s1 b, E.MinCtxt s2 b) => ExactPi -> (forall d.Floating d => d -> d) -> Proxy b -> SQuantity s1 DOne a -> SQuantity s2 DOne c+liftDimensionlessPeriodicVia p f proxy | Just p'' <- p', p'' /= 0 = (liftDimensionlessVia f proxy) . dmap (`mod` p'')+ | otherwise = liftDimensionlessVia f proxy+ where+ p' :: Maybe a+ p' = fmap fromInteger . toExactInteger . P.recip . (P./ p) . E.exactPiVal $ (Proxy :: Proxy s1)++{-+We give '*~' and '/~' the same fixity as '*' and '/' defined below.+Note that this necessitates the use of parenthesis when composing+units using '*' and '/', e.g. "1 *~ (meter / second)".+-}++infixl 7 *~, /~++-- | Forms a possibly scaled 'SQuantity' by multipliying a number and a unit.+(*~) :: forall s m d a b.(RealFrac a, Integral b, E.MinCtxt s a) => a -> Unit m d a -> SQuantity s d b+x *~ (Unit _ _ y) = Quantity . round $ (x P.* y P./ s)+ where+ s = E.injMin (Proxy :: Proxy s)++-- | Divides a possibly scaled 'SQuantity' by a 'Unit' of the same physical dimension, obtaining the+-- numerical value of the quantity expressed in that unit.+(/~) :: forall s m d a b.(Real a, Fractional b, E.MinCtxt s b) => SQuantity s d a -> Unit m d b -> b+(Quantity x) /~ (Unit _ _ y) = ((realToFrac x) P.* s P./ y)+ where+ s = E.injMin (Proxy :: Proxy s)++{-++Rescaling Operations++-}++-- | Rescales a fixed point quantity, accomodating changes both in its scale factor and its representation type.+--+-- Note that this uses an arbitrary precision representation of 'pi', which may be quite slow.+rescale :: forall a b d s1 s2.(Integral a, Integral b, E.KnownExactPi s1, E.KnownExactPi s2) => SQuantity s1 d a -> SQuantity s2 d b+rescale | Just s' <- toExactInteger s = viaInteger (P.* s')+ | Just s' <- toExactInteger (P.recip s) = viaInteger (`P.quot` s')+ | Just q <- toExactRational s = viaInteger $ timesRational q+ | otherwise = viaInteger $ \x -> fixedPoint (fmap (($ x) . timesRational) (rationalApproximations s))+ where+ s = (s1' P./ s2')+ s1' = E.exactPiVal (Proxy :: Proxy s1)+ s2' = E.exactPiVal (Proxy :: Proxy s2)+ timesRational :: Rational -> Integer -> Integer+ timesRational q = (`P.quot` denominator q) . (P.* numerator q)++-- | Rescales a fixed point quantity, accomodating changes both in its scale factor and its representation type.+--+-- Expected to outperform `rescale` when a `FiniteBits` context is available for the source and destination representation types.+rescaleFinite :: (Integral a, FiniteBits a, Integral b, FiniteBits b, E.KnownExactPi s1, E.KnownExactPi s2) => SQuantity s1 d a -> SQuantity s2 d b+rescaleFinite = rescale -- It should be possible to do this more quickly, since we have a priori knowledge of how well we need to approximate the result++-- | Approximately rescales a fixed point quantity, accomodating changes both in its scale factor and its representation type.+--+-- Uses approximate arithmetic by way of an intermediate `Floating` type, to which a proxy must be supplied.+rescaleVia :: forall a b c d s1 s2.(Integral a, RealFrac b, Floating b, Integral c, E.KnownExactPi s1, E.KnownExactPi s2) => Proxy b -> SQuantity s1 d a -> SQuantity s2 d c+rescaleVia _ = viaIntermediate (P.* s)+ where+ s = approximateValue (s1' P./ s2') :: b+ s1' = E.exactPiVal $ (Proxy :: Proxy s1)+ s2' = E.exactPiVal $ (Proxy :: Proxy s2)++-- | Approximately rescales a fixed point quantity, accomodating changes both in its scale factor and its representation type.+--+-- Uses approximate arithmetic by way of an intermediate `Double` representation.+rescaleD :: (Integral a, Integral b, E.KnownExactPi s1, E.KnownExactPi s2) => SQuantity s1 d a -> SQuantity s2 d b+rescaleD = rescaleVia (Proxy :: Proxy Double)++-- Note that this does not respect scaling factors at all.+viaInteger :: (Integral a, Integral b) => (P.Integer -> P.Integer) -> SQuantity s1 d a -> SQuantity s2 d b+viaInteger f = Quantity . fromInteger . f . fromIntegral . unQuantity++-- Note that this does not respect scaling factors at all.+viaIntermediate :: (Integral a, RealFrac b, Integral c) => (b -> b) -> SQuantity s1 d a -> SQuantity s2 d c+viaIntermediate f = Quantity . round . f . fromIntegral . unQuantity++fixedPoint :: (Eq a) => [a] -> a+fixedPoint [] = error "Fixed point of empty list."+fixedPoint [x] = x+fixedPoint (x1:x2:xs) | x1 == x2 = x1+ | otherwise = fixedPoint (x2:xs)++{-++Changes of Representation++-}++-- | Convenient conversion between numerical types while retaining dimensional information.+changeRep :: forall v1 v2 d a b.+ (KnownVariant v1, KnownVariant v2,+ CompatibleVariants v1 v2,+ E.MinCtxt (ScaleFactor v1 E./ ScaleFactor v2) b,+ Real a, Fractional b)+ => Dimensional v1 d a -> Dimensional v2 d b+changeRep = liftD (P.* s) ((P.* s') . realToFrac) Name.weaken+ where+ p :: Proxy (ScaleFactor v1 E./ ScaleFactor v2)+ p = Proxy+ s = E.exactPiVal p+ s' = E.injMin p++-- | Convenient conversion to types with `Integral` representations using `round`.+changeRepRound :: forall v1 v2 d a b.+ (KnownVariant v1, KnownVariant v2,+ CompatibleVariants v1 v2,+ E.MinCtxt (ScaleFactor v1 E./ ScaleFactor v2) a,+ RealFrac a, Integral b)+ => Dimensional v1 d a -> Dimensional v2 d b+changeRepRound = liftD (P.* s) (round . (P.* s')) Name.weaken+ where+ p :: Proxy (ScaleFactor v1 E./ ScaleFactor v2)+ p = Proxy+ s = E.exactPiVal p+ s' = E.injMin p++{-++Useful Constant Values++-}++{- $possibly-imprecise-constants++Note that, other than '_0' and 'epsilon', these constants may not be exactly representable with certain scale factors.++-}++-- | The constant for zero is polymorphic, allowing+-- it to express zero 'Length' or 'Capacitance' or 'Velocity' etc, in addition+-- to the 'Dimensionless' value zero.+_0 :: Num a => SQuantity s d a+_0 = Quantity 0++_1, _2, _3, _4, _5, _6, _7, _8, _9 :: (Integral a, E.KnownExactPi s) => SQuantity s DOne a+_1 = rescale (epsilon :: SQuantity E.One DOne Integer)+_2 = rescale (epsilon :: SQuantity (E.ExactNatural 2) DOne Integer)+_3 = rescale (epsilon :: SQuantity (E.ExactNatural 3) DOne Integer)+_4 = rescale (epsilon :: SQuantity (E.ExactNatural 4) DOne Integer)+_5 = rescale (epsilon :: SQuantity (E.ExactNatural 5) DOne Integer)+_6 = rescale (epsilon :: SQuantity (E.ExactNatural 6) DOne Integer)+_7 = rescale (epsilon :: SQuantity (E.ExactNatural 7) DOne Integer)+_8 = rescale (epsilon :: SQuantity (E.ExactNatural 8) DOne Integer)+_9 = rescale (epsilon :: SQuantity (E.ExactNatural 9) DOne Integer)++pi :: (Integral a, E.KnownExactPi s) => SQuantity s DOne a+pi = rescale (epsilon :: SQuantity E.Pi DOne Integer)++-- | Twice 'pi'.+--+-- For background on 'tau' see [The Tau Manifesto](https://tauday.com/tau-manifesto) (but also+-- feel free to review [The Pi Manifesto](https://web.archive.org/web/20200926221249/http://www.thepimanifesto.com/)).+tau :: (Integral a, E.KnownExactPi s) => SQuantity s DOne a+tau = rescale (epsilon :: SQuantity (E.ExactNatural 2 E.* E.Pi) DOne Integer)++-- | The smallest positive representable value in a given fixed-point scaled quantity type.+epsilon :: (Integral a) => SQuantity s d a+epsilon = Quantity 1++{- $synonyms++These type synonyms for commonly used fixed-point types are provided for convenience.++-}++-- | A binary scale factor.+type QScale n = (E.One E./ (E.ExactNatural (2 N.^ n)))++-- | A dimensionless number with `n` fractional bits, using a representation of type `a`.+type Q n a = SQuantity (QScale n) DOne a++-- | A single-turn angle represented as a signed 8-bit integer.+type Angle8 = SQuantity (E.Pi E.* (QScale 7)) DPlaneAngle Int8++-- | A single-turn angle represented as a signed 16-bit integer.+type Angle16 = SQuantity (E.Pi E.* (QScale 15)) DPlaneAngle Int16++-- | A single-turn angle represented as a signed 32-bit integer.+type Angle32 = SQuantity (E.Pi E.* (QScale 31)) DPlaneAngle Int32
src/Numeric/Units/Dimensional/Float.hs view
@@ -1,178 +1,179 @@-{- | - Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter - License : BSD3 - - Maintainer : bjorn@buckwalter.se - Stability : Stable - -Defines convenience functions for inspecting and manipulating quantities with 'RealFloat' -floating-point representations. - -The dimensionally-typed versions of functions from Patrick Perry's @ieee754@ package -copy that package's API as closely as possible, by permission. In turn they are based on -the @tango@ math library for the D language. - --} - -{-# LANGUAGE ScopedTypeVariables #-} - -module Numeric.Units.Dimensional.Float -( - -- * Lifted Predicates from 'RealFloat' - isDenormalized, isInfinite, isNaN, isNegativeZero - -- * Convenience Functions -, isFiniteNumber, scaleFloat - -- * Lifted Functions from "Numeric.IEEE" - -- ** Values -, infinity, minNormal, maxFinite, epsilon, nan - -- ** Arithmetic -, predIEEE, succIEEE, bisectIEEE, copySign - -- ** NaN with Payload -, nanWithPayload, nanPayload, F.maxNaNPayload - -- ** Comparisons -, identicalIEEE, minNum, maxNum, minNaN, maxNaN -) -where - -import Control.Applicative -import Data.Word (Word64) -import Prelude (RealFloat) -import qualified Prelude as P -import Numeric.IEEE (IEEE) -import qualified Numeric.IEEE as F -import Numeric.Units.Dimensional.Internal (liftQ, liftQ2) -import Numeric.Units.Dimensional.Prelude hiding (RealFloat(..)) -import Numeric.Units.Dimensional.Coercion - --- $setup --- >>> :set -XExtendedDefaultRules --- >>> :set -XNegativeLiterals - --- | 'True' if the representation of the argument is too small to be represented in normalized format. -isDenormalized :: RealFloat a => Quantity d a -> Bool -isDenormalized = P.isDenormalized . unQuantity - --- | 'True' if the representation of the argument is a number and is not infinite. --- --- >>> isFiniteNumber (_1 / _0) --- False --- --- >>> isFiniteNumber (_0 / _0) --- False --- --- >>> isFiniteNumber (_3 / _2) --- True -isFiniteNumber :: RealFloat a => Quantity d a -> Bool -isFiniteNumber = not . liftA2 (||) isNaN isInfinite - --- | 'True' if the representation of the argument is an IEEE infinity or negative infinity. --- --- >>> isInfinite (_1 / _0) --- True --- --- >>> isInfinite (42 *~ micro farad) --- False -isInfinite :: RealFloat a => Quantity d a -> Bool -isInfinite = P.isInfinite . unQuantity - --- | 'True' if the representation of the argument is an IEEE "not-a-number" (NaN) value. --- --- >>> isNaN _3 --- False --- --- >>> isNaN (_1 / _0) --- False --- --- >>> isNaN (asin _4) --- True -isNaN :: RealFloat a => Quantity d a -> Bool -isNaN = P.isNaN . unQuantity - --- | 'True' if the representation of the argument is an IEEE negative zero. --- --- >>> isNegativeZero _0 --- False --- --- >>> isNegativeZero $ (-1e-200 *~ one) * (1e-200 *~ one) --- True -isNegativeZero :: RealFloat a => Quantity d a -> Bool -isNegativeZero = P.isNegativeZero . unQuantity - --- | Multiplies a floating-point quantity by an integer power of the radix of the representation type. --- --- Use 'P.floatRadix' to determine the radix. --- --- >>> let x = 3 *~ meter --- >>> scaleFloat 3 x --- 24.0 m -scaleFloat :: RealFloat a => Int -> Quantity d a -> Quantity d a -scaleFloat x = Quantity . P.scaleFloat x . unQuantity - --- | An infinite floating-point quantity. -infinity :: IEEE a => Quantity d a -infinity = Quantity F.infinity - --- | The smallest representable positive quantity whose representation is normalized. -minNormal :: IEEE a => Quantity d a -minNormal = Quantity F.minNormal - --- | The largest representable finite floating-point quantity. -maxFinite :: IEEE a => Quantity d a -maxFinite = Quantity F.maxFinite - --- | The smallest positive value @x@ such that @_1 + x@ is representable. -epsilon :: IEEE a => Dimensionless a -epsilon = Quantity F.epsilon - --- | @copySign x y@ returns the quantity @x@ with its sign changed to match that of @y@. -copySign :: IEEE a => Quantity d a -> Quantity d a -> Quantity d a -copySign = liftQ2 F.copySign - --- | Return 'True' if two floating-point quantities are /exactly/ (bitwise) equal. -identicalIEEE :: IEEE a => Quantity d a -> Quantity d a -> Bool -identicalIEEE (Quantity x) (Quantity y) = F.identicalIEEE x y - --- | Return the next largest representable floating-point quantity (@Infinity@ and @NaN@ are unchanged). -succIEEE :: IEEE a => Quantity d a -> Quantity d a -succIEEE = liftQ F.succIEEE - --- | Return the next smallest representable floating-point quantity (@Infinity@ and @NaN@ are unchanged). -predIEEE :: IEEE a => Quantity d a -> Quantity d a -predIEEE = liftQ F.predIEEE - --- | Given two floating-point quantities with the same sign, return the quantity whose representation is halfway --- between their representations on the IEEE number line. If the signs of the values differ or either is @NaN@, --- the value is undefined. -bisectIEEE :: IEEE a => Quantity d a -> Quantity d a -> Quantity d a -bisectIEEE (Quantity x) (Quantity y) = Quantity $ F.bisectIEEE x y - --- | Default @NaN@ quantity. -nan :: IEEE a => Quantity d a -nan = Quantity F.nan - --- | Quiet @NaN@ quantity with a positive integer payload. --- Payload must be less than 'maxNaNPayload' of the representation type. --- --- Beware that while some platforms allow using 0 as a payload, this behavior is not portable. -nanWithPayload :: IEEE a => Word64 -> Quantity d a -nanWithPayload = Quantity . F.nanWithPayload - --- | The payload stored in a @NaN@ quantity. Undefined if the argument is not @NaN@. -nanPayload :: IEEE a => Quantity d a -> Word64 -nanPayload = F.nanPayload . unQuantity - --- | Return the minimum of two quantities; if one value is @NaN@, return the other. Prefer the first if both values are @NaN@. -minNum :: RealFloat a => Quantity d a -> Quantity d a -> Quantity d a -minNum = liftQ2 F.minNum - --- | Return the maximum of two quantities; if one value is @NaN@, return the other. Prefer the first if both values are @NaN@. -maxNum :: RealFloat a => Quantity d a -> Quantity d a -> Quantity d a -maxNum = liftQ2 F.maxNum - --- | Return the minimum of two quantities; if one value is @NaN@, return it. Prefer the first if both values are @NaN@. -minNaN :: RealFloat a => Quantity d a -> Quantity d a -> Quantity d a -minNaN = liftQ2 F.minNaN - --- | Return the maximum of two quantities; if one value is @NaN@, return it. Prefer the first if both values are @NaN@. -maxNaN :: RealFloat a => Quantity d a -> Quantity d a -> Quantity d a -maxNaN = liftQ2 F.maxNaN +{- |+ Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter+ License : BSD3++ Maintainer : bjorn@buckwalter.se+ Stability : Stable++Defines convenience functions for inspecting and manipulating quantities with 'RealFloat'+floating-point representations.++The dimensionally-typed versions of functions from Patrick Perry's [ieee754](https://hackage.haskell.org/package/ieee754) package+copy that packages API as closely as possible, by permission. In turn they are based on+the @tango@ math library for the D language.++-}++{-# LANGUAGE ScopedTypeVariables #-}++module Numeric.Units.Dimensional.Float+(+ -- * Lifted Predicates from 'RealFloat'+ isDenormalized, isInfinite, isNaN, isNegativeZero+ -- * Convenience Functions+, isFiniteNumber, scaleFloat+ -- * Lifted Functions from "Numeric.IEEE"+ -- ** Values+, infinity, minNormal, maxFinite, epsilon, nan+ -- ** Arithmetic+, predIEEE, succIEEE, bisectIEEE, copySign+ -- ** NaN with Payload+, nanWithPayload, nanPayload, F.maxNaNPayload+ -- ** Comparisons+, identicalIEEE, minNum, maxNum, minNaN, maxNaN+)+where++import Control.Applicative+import Data.Word (Word64)+import Prelude (RealFloat)+import qualified Prelude as P+import Numeric.IEEE (IEEE)+import qualified Numeric.IEEE as F+import Numeric.Units.Dimensional.Internal (liftQ, liftQ2)+import Numeric.Units.Dimensional.Prelude hiding (RealFloat(..))+import Numeric.Units.Dimensional.Coercion++-- $setup+-- >>> :set -fno-warn-type-defaults+-- >>> :set -XExtendedDefaultRules+-- >>> :set -XNegativeLiterals++-- | 'True' if the representation of the argument is too small to be represented in normalized format.+isDenormalized :: RealFloat a => Quantity d a -> Bool+isDenormalized = P.isDenormalized . unQuantity++-- | 'True' if the representation of the argument is a number and is not infinite.+--+-- >>> isFiniteNumber (_1 / _0)+-- False+--+-- >>> isFiniteNumber (_0 / _0)+-- False+--+-- >>> isFiniteNumber (_3 / _2)+-- True+isFiniteNumber :: RealFloat a => Quantity d a -> Bool+isFiniteNumber = not . liftA2 (||) isNaN isInfinite++-- | 'True' if the representation of the argument is an IEEE infinity or negative infinity.+--+-- >>> isInfinite (_1 / _0)+-- True+--+-- >>> isInfinite (42 *~ micro farad)+-- False+isInfinite :: RealFloat a => Quantity d a -> Bool+isInfinite = P.isInfinite . unQuantity++-- | 'True' if the representation of the argument is an IEEE "not-a-number" (NaN) value.+--+-- >>> isNaN _3+-- False+--+-- >>> isNaN (_1 / _0)+-- False+--+-- >>> isNaN (asin _4)+-- True+isNaN :: RealFloat a => Quantity d a -> Bool+isNaN = P.isNaN . unQuantity++-- | 'True' if the representation of the argument is an IEEE negative zero.+--+-- >>> isNegativeZero _0+-- False+--+-- >>> isNegativeZero $ (-1e-200 *~ one) * (1e-200 *~ one)+-- True+isNegativeZero :: RealFloat a => Quantity d a -> Bool+isNegativeZero = P.isNegativeZero . unQuantity++-- | Multiplies a floating-point quantity by an integer power of the radix of the representation type.+--+-- Use 'P.floatRadix' to determine the radix.+--+-- >>> let x = 3 *~ meter+-- >>> scaleFloat 3 x+-- 24.0 m+scaleFloat :: RealFloat a => Int -> Quantity d a -> Quantity d a+scaleFloat x = Quantity . P.scaleFloat x . unQuantity++-- | An infinite floating-point quantity.+infinity :: IEEE a => Quantity d a+infinity = Quantity F.infinity++-- | The smallest representable positive quantity whose representation is normalized.+minNormal :: IEEE a => Quantity d a+minNormal = Quantity F.minNormal++-- | The largest representable finite floating-point quantity.+maxFinite :: IEEE a => Quantity d a+maxFinite = Quantity F.maxFinite++-- | The smallest positive value @x@ such that @_1 + x@ is representable.+epsilon :: IEEE a => Dimensionless a+epsilon = Quantity F.epsilon++-- | @copySign x y@ returns the quantity @x@ with its sign changed to match that of @y@.+copySign :: IEEE a => Quantity d a -> Quantity d a -> Quantity d a+copySign = liftQ2 F.copySign++-- | Return 'True' if two floating-point quantities are /exactly/ (bitwise) equal.+identicalIEEE :: IEEE a => Quantity d a -> Quantity d a -> Bool+identicalIEEE (Quantity x) (Quantity y) = F.identicalIEEE x y++-- | Return the next largest representable floating-point quantity (@Infinity@ and @NaN@ are unchanged).+succIEEE :: IEEE a => Quantity d a -> Quantity d a+succIEEE = liftQ F.succIEEE++-- | Return the next smallest representable floating-point quantity (@Infinity@ and @NaN@ are unchanged).+predIEEE :: IEEE a => Quantity d a -> Quantity d a+predIEEE = liftQ F.predIEEE++-- | Given two floating-point quantities with the same sign, return the quantity whose representation is halfway+-- between their representations on the IEEE number line. If the signs of the values differ or either is @NaN@,+-- the value is undefined.+bisectIEEE :: IEEE a => Quantity d a -> Quantity d a -> Quantity d a+bisectIEEE (Quantity x) (Quantity y) = Quantity $ F.bisectIEEE x y++-- | Default @NaN@ quantity.+nan :: IEEE a => Quantity d a+nan = Quantity F.nan++-- | Quiet @NaN@ quantity with a positive integer payload.+-- Payload must be less than 'maxNaNPayload' of the representation type.+--+-- Beware that while some platforms allow using 0 as a payload, this behavior is not portable.+nanWithPayload :: IEEE a => Word64 -> Quantity d a+nanWithPayload = Quantity . F.nanWithPayload++-- | The payload stored in a @NaN@ quantity. Undefined if the argument is not @NaN@.+nanPayload :: IEEE a => Quantity d a -> Word64+nanPayload = F.nanPayload . unQuantity++-- | Return the minimum of two quantities; if one value is @NaN@, return the other. Prefer the first if both values are @NaN@.+minNum :: RealFloat a => Quantity d a -> Quantity d a -> Quantity d a+minNum = liftQ2 F.minNum++-- | Return the maximum of two quantities; if one value is @NaN@, return the other. Prefer the first if both values are @NaN@.+maxNum :: RealFloat a => Quantity d a -> Quantity d a -> Quantity d a+maxNum = liftQ2 F.maxNum++-- | Return the minimum of two quantities; if one value is @NaN@, return it. Prefer the first if both values are @NaN@.+minNaN :: RealFloat a => Quantity d a -> Quantity d a -> Quantity d a+minNaN = liftQ2 F.minNaN++-- | Return the maximum of two quantities; if one value is @NaN@, return it. Prefer the first if both values are @NaN@.+maxNaN :: RealFloat a => Quantity d a -> Quantity d a -> Quantity d a+maxNaN = liftQ2 F.maxNaN
src/Numeric/Units/Dimensional/Functor.hs view
@@ -1,33 +1,33 @@-{-# OPTIONS_GHC -fno-warn-orphans #-} -{-# OPTIONS_HADDOCK show-extensions #-} - -{- | - Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter - License : BSD3 - - Maintainer : bjorn@buckwalter.se - Stability : Stable - Portability: GHC only - -Provides a 'Functor' instance for 'Dimensional'. - -Note that this instance is dubious, because it allows you to break the dimensional abstraction. See 'dmap' for more information. - -Note that, while this instance overlaps with that given for 'Dimensionless', it is confluent with that instance. - -Note that this is an orphan instance. --} -module Numeric.Units.Dimensional.Functor where - -import Numeric.Units.Dimensional -import Prelude - --- | A 'Functor' instance for 'Dimensional'. --- --- Note that this instance is dubious, because it allows you to break the dimensional abstraction. See 'dmap' for more information. --- --- Note that, while this instance overlaps with that given for 'Dimensionless', it is confluent with that instance. --- --- Note that this is an orphan instance. -instance {-# OVERLAPPING #-} (KnownVariant v) => Functor (Dimensional v d) where - fmap = dmap +{-# OPTIONS_GHC -fno-warn-orphans #-}+{-# OPTIONS_HADDOCK show-extensions #-}++{- |+ Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter+ License : BSD3++ Maintainer : bjorn@buckwalter.se+ Stability : Stable+ Portability: GHC only++Provides a 'Functor' instance for 'Dimensional'.++Note that this instance is dubious, because it allows you to break the dimensional abstraction. See 'dmap' for more information.++Note that, while this instance overlaps with that given for 'Dimensionless', it is confluent with that instance.++Note that this is an orphan instance.+-}+module Numeric.Units.Dimensional.Functor where++import Numeric.Units.Dimensional+import Prelude++-- | A 'Functor' instance for 'Dimensional'.+--+-- Note that this instance is dubious, because it allows you to break the dimensional abstraction. See 'dmap' for more information.+--+-- Note that, while this instance overlaps with that given for 'Dimensionless', it is confluent with that instance.+--+-- Note that this is an orphan instance.+instance {-# OVERLAPPING #-} (KnownVariant v) => Functor (Dimensional v d) where+ fmap = dmap
src/Numeric/Units/Dimensional/Internal.hs view
@@ -1,266 +1,274 @@-{-# LANGUAGE CPP #-} -{-# LANGUAGE DataKinds #-} -{-# LANGUAGE DeriveDataTypeable #-} -{-# LANGUAGE DeriveGeneric #-} -{-# LANGUAGE FlexibleContexts #-} -{-# LANGUAGE FlexibleInstances #-} -{-# LANGUAGE GeneralizedNewtypeDeriving #-} -{-# LANGUAGE KindSignatures #-} -{-# LANGUAGE MultiParamTypeClasses #-} -- for Vector instances only -{-# LANGUAGE RankNTypes #-} -{-# LANGUAGE ScopedTypeVariables #-} -{-# LANGUAGE StandaloneDeriving #-} -{-# LANGUAGE TypeFamilies #-} -{-# LANGUAGE TypeOperators #-} -{-# LANGUAGE TypeSynonymInstances #-} - -module Numeric.Units.Dimensional.Internal -( - KnownVariant(..), - Dimensional(..), - type Unit, type Quantity, type SQuantity, - siUnit, showIn, - liftD, liftD2, - liftQ, liftQ2 -) -where - -import Control.Applicative -import Control.DeepSeq -import Data.AEq (AEq) -import Data.Coerce (coerce) -import Data.Data -import Data.Kind -import Data.ExactPi -import Data.Functor.Classes (Eq1(..), Ord1(..)) -import qualified Data.ExactPi.TypeLevel as E -import Data.Monoid (Monoid(..)) -import Data.Semigroup (Semigroup(..)) -import Foreign.Ptr (Ptr, castPtr) -import Foreign.Storable (Storable(..)) -import GHC.Generics -import Numeric.Units.Dimensional.Dimensions -import Numeric.Units.Dimensional.Variants -import Numeric.Units.Dimensional.UnitNames hiding ((*), (/), (^), weaken, strengthen) -import qualified Numeric.Units.Dimensional.UnitNames.Internal as Name -import Numeric.Units.Dimensional.UnitNames.InterchangeNames (HasInterchangeName(..)) -import qualified Data.Vector.Generic.Mutable as M -import qualified Data.Vector.Generic as G -import qualified Data.Vector.Unboxed.Base as U -import Prelude - ( Show, Eq(..), Ord, Bounded(..), Num, Fractional, Functor, Real(..) - , String, Maybe(..), Double - , (.), ($), (++), (+), (/) - , show, otherwise, undefined, error, fmap, realToFrac - ) -import qualified Prelude as P - --- $setup --- >>> :set -XNoImplicitPrelude --- >>> import Numeric.Units.Dimensional.Prelude - --- | A unit of measurement. -type Unit (m :: Metricality) = Dimensional ('DUnit m) - --- | A dimensional quantity. -type Quantity = SQuantity E.One - --- | A dimensional quantity, stored as an 'ExactPi'' multiple of its value in its dimension's SI coherent unit. --- --- The name is an abbreviation for scaled quantity. -type SQuantity s = Dimensional ('DQuantity s) - --- | A KnownVariant is one whose term-level 'Dimensional' values we can represent with an associated data family instance --- and manipulate with certain functions, not all of which are exported from the package. --- --- Each validly constructed type of kind 'Variant' has a 'KnownVariant' instance. -class KnownVariant (v :: Variant) where - -- | A dimensional value, either a 'Quantity' or a 'Unit', parameterized by its 'Dimension' and representation. - data Dimensional v :: Dimension -> Type -> Type - -- | A scale factor by which the numerical value of this dimensional value is implicitly multiplied. - type ScaleFactor v :: E.ExactPi' - extractValue :: Dimensional v d a -> (a, Maybe ExactPi) - extractName :: Dimensional v d a -> Maybe (UnitName 'NonMetric) - injectValue :: Maybe (UnitName 'NonMetric) -> (a, Maybe ExactPi) -> Dimensional v d a - -- | Maps over the underlying representation of a dimensional value. - -- The caller is responsible for ensuring that the supplied function respects the dimensional abstraction. - -- This means that the function must preserve numerical values, or linearly scale them while preserving the origin. - dmap :: (a1 -> a2) -> Dimensional v d a1 -> Dimensional v d a2 - -deriving instance Typeable Dimensional - -instance KnownVariant ('DQuantity s) where - newtype Dimensional ('DQuantity s) d a = Quantity a - deriving (Eq, Ord, AEq, Data, Generic, Generic1, Typeable) - type (ScaleFactor ('DQuantity s)) = s - extractValue (Quantity x) = (x, Nothing) - extractName _ = Nothing - injectValue _ (x, _) = Quantity x - dmap = coerce - -instance (Typeable m) => KnownVariant ('DUnit m) where - data Dimensional ('DUnit m) d a = Unit !(UnitName m) !ExactPi !a - deriving (Generic, Generic1, Typeable) - type (ScaleFactor ('DUnit m)) = E.One - extractValue (Unit _ e x) = (x, Just e) - extractName (Unit n _ _) = Just . Name.weaken $ n - injectValue (Just n) (x, Just e) | Just n' <- relax n = Unit n' e x - | otherwise = error "Shouldn't be reachable. Needed a metric name but got a non-metric one." - injectValue _ _ = error "Shouldn't be reachable. Needed to name a quantity." - dmap f (Unit n e x) = Unit n e (f x) - --- GHC is somewhat unclear about why, but it won't derive this instance, so we give it explicitly. -instance (Bounded a) => Bounded (SQuantity s d a) where - minBound = Quantity minBound - maxBound = Quantity maxBound - -instance Eq1 (SQuantity s d) where - liftEq = coerce - -instance Ord1 (SQuantity s d) where - liftCompare = coerce - -instance HasInterchangeName (Unit m d a) where - interchangeName (Unit n _ _) = interchangeName n - -{- -Since quantities form a monoid under addition, but not under multiplication unless they are dimensionless, -we will define a monoid instance that adds. --} - --- | 'Quantity's of a given 'Dimension' form a 'Semigroup' under addition. -instance (Num a) => Semigroup (SQuantity s d a) where - (<>) = liftQ2 (+) - --- | 'Quantity's of a given 'Dimension' form a 'Monoid' under addition. -instance (Num a) => Monoid (SQuantity s d a) where - mempty = Quantity 0 - mappend = liftQ2 (+) - -{- - -= Dimensionless = - -For dimensionless quantities pretty much any operation is applicable. -We provide this freedom by making 'Dimensionless' an instance of -'Functor'. --} - -instance Functor (SQuantity s DOne) where - fmap = dmap - -instance (KnownDimension d) => HasDynamicDimension (Dimensional v d a) where - -instance (KnownDimension d) => HasDimension (Dimensional v d a) where - dimension _ = dimension (Proxy :: Proxy d) - --- | A polymorphic 'Unit' which can be used in place of the coherent --- SI base unit of any dimension. This allows polymorphic quantity --- creation and destruction without exposing the 'Dimensional' constructor. -siUnit :: forall d a.(KnownDimension d, Num a) => Unit 'NonMetric d a -siUnit = Unit (baseUnitName $ dimension (Proxy :: Proxy d)) 1 1 - -instance NFData a => NFData (Quantity d a) -- instance is derived from Generic instance - -instance Storable a => Storable (SQuantity s d a) where - sizeOf _ = sizeOf (undefined::a) - {-# INLINE sizeOf #-} - alignment _ = alignment (undefined::a) - {-# INLINE alignment #-} - poke ptr = poke (castPtr ptr :: Ptr a) . coerce - {-# INLINE poke #-} - peek ptr = fmap Quantity (peek (castPtr ptr :: Ptr a)) - {-# INLINE peek #-} - -{- -Instances for vectors of quantities. --} -newtype instance U.Vector (SQuantity s d a) = V_Quantity {unVQ :: U.Vector a} -newtype instance U.MVector v (SQuantity s d a) = MV_Quantity {unMVQ :: U.MVector v a} -instance U.Unbox a => U.Unbox (SQuantity s d a) - -instance (M.MVector U.MVector a) => M.MVector U.MVector (SQuantity s d a) where - basicLength = M.basicLength . unMVQ - {-# INLINE basicLength #-} - basicUnsafeSlice m n = MV_Quantity . M.basicUnsafeSlice m n . unMVQ - {-# INLINE basicUnsafeSlice #-} - basicOverlaps u v = M.basicOverlaps (unMVQ u) (unMVQ v) - {-# INLINE basicOverlaps #-} - basicUnsafeNew = fmap MV_Quantity . M.basicUnsafeNew - {-# INLINE basicUnsafeNew #-} - basicUnsafeRead v = fmap Quantity . M.basicUnsafeRead (unMVQ v) - {-# INLINE basicUnsafeRead #-} - basicUnsafeWrite v i = M.basicUnsafeWrite (unMVQ v) i . coerce - {-# INLINE basicUnsafeWrite #-} -#if MIN_VERSION_vector(0,11,0) - basicInitialize = M.basicInitialize . unMVQ - {-# INLINE basicInitialize #-} -#endif - -instance (G.Vector U.Vector a) => G.Vector U.Vector (SQuantity s d a) where - basicUnsafeFreeze = fmap V_Quantity . G.basicUnsafeFreeze . unMVQ - {-# INLINE basicUnsafeFreeze #-} - basicUnsafeThaw = fmap MV_Quantity . G.basicUnsafeThaw . unVQ - {-# INLINE basicUnsafeThaw #-} - basicLength = G.basicLength . unVQ - {-# INLINE basicLength #-} - basicUnsafeSlice m n = V_Quantity . G.basicUnsafeSlice m n . unVQ - {-# INLINE basicUnsafeSlice #-} - basicUnsafeIndexM v = fmap Quantity . G.basicUnsafeIndexM (unVQ v) - {-# INLINE basicUnsafeIndexM #-} - -{- -We will conclude by providing a reasonable 'Show' instance for -quantities. The SI unit of the quantity is inferred -from its dimension. --} --- | Uses non-breaking spaces between the value and the unit, and within the unit name. -instance (KnownDimension d, E.KnownExactPi s, Show a, Real a) => Show (SQuantity s d a) where - show (Quantity x) | isExactOne s' = show x ++ showName n - | otherwise = "Quantity " ++ show x ++ " {- " ++ show q ++ " -}" - where - s' = E.exactPiVal (Proxy :: Proxy s) - s'' = approximateValue s' :: Double - q = Quantity (realToFrac x P.* s'') :: Quantity d Double - (Unit n _ _) = siUnit :: Unit 'NonMetric d a - --- | Shows the value of a 'Quantity' expressed in a specified 'Unit' of the same 'Dimension'. --- --- Uses non-breaking spaces between the value and the unit, and within the unit name. --- --- >>> putStrLn $ showIn watt $ (37 *~ volt) * (4 *~ ampere) --- 148.0 W -showIn :: (Show a, Fractional a) => Unit m d a -> Quantity d a -> String -showIn (Unit n _ y) (Quantity x) = show (x / y) ++ (showName . Name.weaken $ n) - -showName :: UnitName 'NonMetric -> String -showName n | n == nOne = "" - | otherwise = "\xA0" ++ show n - --- | Unit names are shown with non-breaking spaces. -instance (Show a) => Show (Unit m d a) where - show (Unit n e x) = "The unit " ++ show n ++ ", with value " ++ show e ++ " (or " ++ show x ++ ")" - --- Operates on a dimensional value using a unary operation on values, possibly yielding a Unit. -liftD :: (KnownVariant v1, KnownVariant v2) => (ExactPi -> ExactPi) -> (a -> b) -> UnitNameTransformer -> Dimensional v1 d1 a -> Dimensional v2 d2 b -liftD fe f nt x = let (x', e') = extractValue x - n = extractName x - n' = fmap nt n - in injectValue n' (f x', fmap fe e') - --- Operates on a dimensional value using a unary operation on values, yielding a Quantity. -liftQ :: (a -> a) -> SQuantity s1 d1 a -> SQuantity s2 d2 a -liftQ = coerce - --- Combines two dimensional values using a binary operation on values, possibly yielding a Unit. -liftD2 :: (KnownVariant v1, KnownVariant v2, KnownVariant v3) => (ExactPi -> ExactPi -> ExactPi) -> (a -> a -> a) -> UnitNameTransformer2 -> Dimensional v1 d1 a -> Dimensional v2 d2 a -> Dimensional v3 d3 a -liftD2 fe f nt x1 x2 = let (x1', e1') = extractValue x1 - (x2', e2') = extractValue x2 - n1 = extractName x1 - n2 = extractName x2 - n' = liftA2 nt n1 n2 - in injectValue n' (f x1' x2', fe <$> e1' <*> e2') - --- Combines two dimensional values using a binary operation on values, yielding a Quantity. -liftQ2 :: (a -> a -> a) -> SQuantity s1 d1 a -> SQuantity s2 d2 a -> SQuantity s3 d3 a -liftQ2 = coerce +{-# LANGUAGE CPP #-}+{-# LANGUAGE DataKinds #-}+{-# LANGUAGE DeriveDataTypeable #-}+{-# LANGUAGE DeriveGeneric #-}+{-# LANGUAGE FlexibleContexts #-}+{-# LANGUAGE FlexibleInstances #-}+{-# LANGUAGE GeneralizedNewtypeDeriving #-}+{-# LANGUAGE KindSignatures #-}+{-# LANGUAGE MultiParamTypeClasses #-} -- for Vector instances only+{-# LANGUAGE RankNTypes #-}+{-# LANGUAGE ScopedTypeVariables #-}+{-# LANGUAGE StandaloneDeriving #-}+{-# LANGUAGE TypeFamilies #-}+{-# LANGUAGE TypeOperators #-}+{-# LANGUAGE TypeSynonymInstances #-}++module Numeric.Units.Dimensional.Internal+(+ KnownVariant(..),+ Dimensional(..),+ type Unit, type Quantity, type SQuantity,+ siUnit, showIn,+ liftD, liftD2,+ liftQ, liftQ2+)+where++import Control.Applicative+import Control.DeepSeq (NFData)+import Data.AEq (AEq)+#if USE_BINARY+import qualified Data.Binary+#endif+import Data.Coerce (coerce)+import Data.Data+import Data.Kind+import Data.ExactPi+import Data.Functor.Classes (Eq1(..), Ord1(..))+import qualified Data.ExactPi.TypeLevel as E+import Data.Monoid (Monoid(..))+import Data.Semigroup (Semigroup(..))+import Foreign.Ptr (Ptr, castPtr)+import Foreign.Storable (Storable(..))+import GHC.Generics+import Numeric.Units.Dimensional.Dimensions+import Numeric.Units.Dimensional.Variants+import Numeric.Units.Dimensional.UnitNames hiding ((*), (/), (^), weaken, strengthen)+import qualified Numeric.Units.Dimensional.UnitNames.Internal as Name+import Numeric.Units.Dimensional.UnitNames.InterchangeNames (HasInterchangeName(..))+import qualified Data.Vector.Generic.Mutable as M+import qualified Data.Vector.Generic as G+import qualified Data.Vector.Unboxed.Base as U+import Prelude+ ( Show, Eq(..), Ord, Bounded(..), Num, Fractional, Functor, Real(..)+ , String, Maybe(..), Double+ , (.), ($), (++), (+), (/)+ , show, otherwise, undefined, error, fmap, realToFrac+ )+import qualified Prelude as P++-- $setup+-- >>> :set -XNoImplicitPrelude+-- >>> :set -fno-warn-type-defaults+-- >>> import Numeric.Units.Dimensional.Prelude++-- | A unit of measurement.+type Unit (m :: Metricality) = Dimensional ('DUnit m)++-- | A dimensional quantity.+type Quantity = SQuantity E.One++-- | A dimensional quantity, stored as an 'ExactPi'' multiple of its value in its dimension's SI coherent unit.+--+-- The name is an abbreviation for scaled quantity.+type SQuantity s = Dimensional ('DQuantity s)++-- | A KnownVariant is one whose term-level 'Dimensional' values we can represent with an associated data family instance+-- and manipulate with certain functions, not all of which are exported from the package.+--+-- Each validly constructed type of kind 'Variant' has a 'KnownVariant' instance.+class KnownVariant (v :: Variant) where+ -- | A dimensional value, either a 'Quantity' or a 'Unit', parameterized by its 'Dimension' and representation.+ data Dimensional v :: Dimension -> Type -> Type+ -- | A scale factor by which the numerical value of this dimensional value is implicitly multiplied.+ type ScaleFactor v :: E.ExactPi'+ extractValue :: Dimensional v d a -> (a, Maybe ExactPi)+ extractName :: Dimensional v d a -> Maybe (UnitName 'NonMetric)+ injectValue :: Maybe (UnitName 'NonMetric) -> (a, Maybe ExactPi) -> Dimensional v d a+ -- | Maps over the underlying representation of a dimensional value.+ -- The caller is responsible for ensuring that the supplied function respects the dimensional abstraction.+ -- This means that the function must preserve numerical values, or linearly scale them while preserving the origin.+ dmap :: (a1 -> a2) -> Dimensional v d a1 -> Dimensional v d a2++deriving instance Typeable Dimensional++instance KnownVariant ('DQuantity s) where+ newtype Dimensional ('DQuantity s) d a = Quantity a+ deriving (Eq, Ord, AEq, Data, Generic, Generic1, Typeable)+ type (ScaleFactor ('DQuantity s)) = s+ extractValue (Quantity x) = (x, Nothing)+ extractName _ = Nothing+ injectValue _ (x, _) = Quantity x+ dmap = coerce++instance (Typeable m) => KnownVariant ('DUnit m) where+ data Dimensional ('DUnit m) d a = Unit !(UnitName m) !ExactPi !a+ deriving (Generic, Generic1, Typeable)+ type (ScaleFactor ('DUnit m)) = E.One+ extractValue (Unit _ e x) = (x, Just e)+ extractName (Unit n _ _) = Just . Name.weaken $ n+ injectValue (Just n) (x, Just e) | Just n' <- relax n = Unit n' e x+ | otherwise = error "Shouldn't be reachable. Needed a metric name but got a non-metric one."+ injectValue _ _ = error "Shouldn't be reachable. Needed to name a quantity."+ dmap f (Unit n e x) = Unit n e (f x)++-- GHC is somewhat unclear about why, but it won't derive this instance, so we give it explicitly.+instance (Bounded a) => Bounded (SQuantity s d a) where+ minBound = Quantity minBound+ maxBound = Quantity maxBound++instance Eq1 (SQuantity s d) where+ liftEq = coerce++instance Ord1 (SQuantity s d) where+ liftCompare = coerce++instance HasInterchangeName (Unit m d a) where+ interchangeName (Unit n _ _) = interchangeName n++{-+Since quantities form a monoid under addition, but not under multiplication unless they are dimensionless,+we will define a monoid instance that adds.+-}++-- | 'Quantity's of a given 'Dimension' form a 'Semigroup' under addition.+instance (Num a) => Semigroup (SQuantity s d a) where+ (<>) = liftQ2 (+)++-- | 'Quantity's of a given 'Dimension' form a 'Monoid' under addition.+instance (Num a) => Monoid (SQuantity s d a) where+ mempty = Quantity 0+ mappend = (<>)++#if USE_BINARY+deriving instance (Data.Binary.Binary a) => Data.Binary.Binary (SQuantity s d a)+#endif++{-++= Dimensionless =++For dimensionless quantities pretty much any operation is applicable.+We provide this freedom by making 'Dimensionless' an instance of+'Functor'.+-}++instance Functor (SQuantity s DOne) where+ fmap = dmap++instance (KnownDimension d) => HasDynamicDimension (Dimensional v d a) where++instance (KnownDimension d) => HasDimension (Dimensional v d a) where+ dimension _ = dimension (Proxy :: Proxy d)++-- | A polymorphic 'Unit' which can be used in place of the coherent+-- SI base unit of any dimension. This allows polymorphic quantity+-- creation and destruction without exposing the 'Dimensional' constructor.+siUnit :: forall d a.(KnownDimension d, Num a) => Unit 'NonMetric d a+siUnit = Unit (baseUnitName $ dimension (Proxy :: Proxy d)) 1 1++instance NFData a => NFData (Quantity d a) -- instance is derived from Generic instance++instance Storable a => Storable (SQuantity s d a) where+ sizeOf _ = sizeOf (undefined :: a)+ {-# INLINE sizeOf #-}+ alignment _ = alignment (undefined :: a)+ {-# INLINE alignment #-}+ poke ptr = poke (castPtr ptr :: Ptr a) . coerce+ {-# INLINE poke #-}+ peek ptr = fmap Quantity (peek (castPtr ptr :: Ptr a))+ {-# INLINE peek #-}++{-+Instances for vectors of quantities.+-}+newtype instance U.Vector (SQuantity s d a) = V_Quantity {unVQ :: U.Vector a}+newtype instance U.MVector v (SQuantity s d a) = MV_Quantity {unMVQ :: U.MVector v a}+instance U.Unbox a => U.Unbox (SQuantity s d a)++instance (M.MVector U.MVector a) => M.MVector U.MVector (SQuantity s d a) where+ basicLength = M.basicLength . unMVQ+ {-# INLINE basicLength #-}+ basicUnsafeSlice m n = MV_Quantity . M.basicUnsafeSlice m n . unMVQ+ {-# INLINE basicUnsafeSlice #-}+ basicOverlaps u v = M.basicOverlaps (unMVQ u) (unMVQ v)+ {-# INLINE basicOverlaps #-}+ basicUnsafeNew = fmap MV_Quantity . M.basicUnsafeNew+ {-# INLINE basicUnsafeNew #-}+ basicUnsafeRead v = fmap Quantity . M.basicUnsafeRead (unMVQ v)+ {-# INLINE basicUnsafeRead #-}+ basicUnsafeWrite v i = M.basicUnsafeWrite (unMVQ v) i . coerce+ {-# INLINE basicUnsafeWrite #-}+#if MIN_VERSION_vector(0,11,0)+ basicInitialize = M.basicInitialize . unMVQ+ {-# INLINE basicInitialize #-}+#endif++instance (G.Vector U.Vector a) => G.Vector U.Vector (SQuantity s d a) where+ basicUnsafeFreeze = fmap V_Quantity . G.basicUnsafeFreeze . unMVQ+ {-# INLINE basicUnsafeFreeze #-}+ basicUnsafeThaw = fmap MV_Quantity . G.basicUnsafeThaw . unVQ+ {-# INLINE basicUnsafeThaw #-}+ basicLength = G.basicLength . unVQ+ {-# INLINE basicLength #-}+ basicUnsafeSlice m n = V_Quantity . G.basicUnsafeSlice m n . unVQ+ {-# INLINE basicUnsafeSlice #-}+ basicUnsafeIndexM v = fmap Quantity . G.basicUnsafeIndexM (unVQ v)+ {-# INLINE basicUnsafeIndexM #-}++{-+We will conclude by providing a reasonable 'Show' instance for+quantities. The SI unit of the quantity is inferred+from its dimension.+-}+-- | Uses non-breaking spaces between the value and the unit, and within the unit name.+instance (KnownDimension d, E.KnownExactPi s, Show a, Real a) => Show (SQuantity s d a) where+ show (Quantity x) | isExactOne s' = show x ++ showName n+ | otherwise = "Quantity " ++ show x ++ " {- " ++ show q ++ " -}"+ where+ s' = E.exactPiVal (Proxy :: Proxy s)+ s'' = approximateValue s' :: Double+ q = Quantity (realToFrac x P.* s'') :: Quantity d Double+ (Unit n _ _) = siUnit :: Unit 'NonMetric d a++-- | Shows the value of a 'Quantity' expressed in a specified 'Unit' of the same 'Dimension'.+--+-- Uses non-breaking spaces between the value and the unit, and within the unit name.+--+-- >>> putStrLn $ showIn watt $ (37 *~ volt) * (4 *~ ampere)+-- 148.0 W+showIn :: (Show a, Fractional a) => Unit m d a -> Quantity d a -> String+showIn (Unit n _ y) (Quantity x) = show (x / y) ++ (showName . Name.weaken $ n)++showName :: UnitName 'NonMetric -> String+showName n | n == nOne = ""+ | otherwise = "\xA0" ++ show n++-- | Unit names are shown with non-breaking spaces.+instance (Show a) => Show (Unit m d a) where+ show (Unit n e x) = "The unit " ++ show n ++ ", with value " ++ show e ++ " (or " ++ show x ++ ")"++-- Operates on a dimensional value using a unary operation on values, possibly yielding a Unit.+liftD :: (KnownVariant v1, KnownVariant v2) => (ExactPi -> ExactPi) -> (a -> b) -> UnitNameTransformer -> Dimensional v1 d1 a -> Dimensional v2 d2 b+liftD fe f nt x = let (x', e') = extractValue x+ n = extractName x+ n' = fmap nt n+ in injectValue n' (f x', fmap fe e')++-- Operates on a dimensional value using a unary operation on values, yielding a Quantity.+liftQ :: (a -> a) -> SQuantity s1 d1 a -> SQuantity s2 d2 a+liftQ = coerce++-- Combines two dimensional values using a binary operation on values, possibly yielding a Unit.+liftD2 :: (KnownVariant v1, KnownVariant v2, KnownVariant v3) => (ExactPi -> ExactPi -> ExactPi) -> (a -> a -> a) -> UnitNameTransformer2 -> Dimensional v1 d1 a -> Dimensional v2 d2 a -> Dimensional v3 d3 a+liftD2 fe f nt x1 x2 = let (x1', e1') = extractValue x1+ (x2', e2') = extractValue x2+ n1 = extractName x1+ n2 = extractName x2+ n' = liftA2 nt n1 n2+ in injectValue n' (f x1' x2', fe <$> e1' <*> e2')++-- Combines two dimensional values using a binary operation on values, yielding a Quantity.+liftQ2 :: (a -> a -> a) -> SQuantity s1 d1 a -> SQuantity s2 d2 a -> SQuantity s3 d3 a+liftQ2 = coerce
src/Numeric/Units/Dimensional/NonSI.hs view
@@ -1,904 +1,938 @@-{-# LANGUAGE DataKinds #-} -{-# LANGUAGE NumDecimals #-} - -{- | - Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter - License : BSD3 - - Maintainer : bjorn@buckwalter.se - Stability : Stable - Portability: GHC only - -= Summary - -This module defines units that are not part of the SI, with the -exception of those defined in the "Numeric.Units.Dimensional.SIUnits" module (units outside -of the SI accepted for use with the SI). - -Any chapters, sections or tables referenced are from <#note1 [1]> unless -otherwise specified. - -== Neper, bel, shannon and the like - -The units of section 5.1.2 are purposefully (but not permanently) -omitted. In fact the logarithmic units (see section 8.7) are -problematic and it is not clear how to implement them. Perhaps with -a conversion function similar to for degrees Celsius. - -= References - -1. #note1# http://physics.nist.gov/Pubs/SP811/ -2. #note2# http://www.iau.org/science/publications/proceedings_rules/units/ -3. #note3# http://en.m.wikipedia.org/wiki/Pressure -4. #note4# http://en.m.wikipedia.org/wiki/Torr - --} - -module Numeric.Units.Dimensional.NonSI -( - -- * Units Defined By Experiment - -- $values-obtained-experimentally - electronVolt, unifiedAtomicMassUnit, dalton, - -- * Dimensionless Units - percent, - -- * Standard Gravity - gee, - -- * Inch-pound Units - -- $inch-pound-units - poundMass, ounce, poundForce, horsepower, btu, shortTon, - nauticalMile, knot, - revolution, solid, - slug, psi, - teaspoon, - -- ** International Foot - foot, inch, mil, yard, mile, acre, - -- ** US Survey Foot - usSurveyFoot, usSurveyInch, usSurveyMil, usSurveyYard, usSurveyMile, usSurveyAcre, - -- * Years - -- $year - year, century, - -- * Pressure Units - -- $pressure-units - bar, atmosphere, technicalAtmosphere, mmHg, inHg, inHg_UCUM, inHg_NIST, torr, - -- * Radiation Units - rad, - -- * Kinematic Viscosity - stokes, - -- * Temperature - -- $temperature - degreeFahrenheit, degreeRankine, - -- * Imperial Volumes - -- $imperial-volumes - imperialGallon, imperialQuart, imperialPint, imperialCup, imperialGill, imperialFluidOunce, - -- * US Customary Volumes - -- $us-customary-volumes - usGallon, usQuart, usPint, usCup, usGill, usFluidOunce, - -- * Atomic-Scale Units - angstrom, - -- * Units from the Centimeter-Gram-Second Electrostatic System of Units - gauss -) -where - -import Numeric.Units.Dimensional.Prelude -import Numeric.Units.Dimensional.UnitNames.Internal (ucumMetric, ucum, dimensionalAtom) -import qualified Prelude - --- $setup --- >>> import Data.ExactPi --- >>> import Data.Function (on) --- >>> import Numeric.Units.Dimensional.Coercion --- >>> default (Double) --- >>> :{ --- >>> let infix 4 === --- >>> (===) = areExactlyEqual `on` unQuantity :: Quantity d ExactPi -> Quantity d ExactPi -> Bool --- >>> :} - -{- $values-obtained-experimentally - -From Table 7, units accepted for use with the SI whose values in SI units are -obtained experimentally. - -When <#note1 [1]> was published the electron volt had a standard combined -uncertainity of 0.00000049e-19 J and the unified atomic mass unit -had a combined uncertainty of 0.0000010e-27 kg. - --} - -electronVolt :: Floating a => Unit 'Metric DEnergy a -electronVolt = mkUnitR (ucumMetric "eV" "eV" "electron volt") 1.60217733e-19 $ joule - -unifiedAtomicMassUnit :: Floating a => Unit 'Metric DMass a -unifiedAtomicMassUnit = mkUnitR (ucumMetric "u" "u" "atomic mass unit") 1.6605402e-27 $ kilo gram - -dalton :: Floating a => Unit 'Metric DMass a -dalton = mkUnitR (ucumMetric "u" "Da" "Dalton") 1 $ unifiedAtomicMassUnit - --- | One percent is one hundrendth. --- --- The dimensionless number 0.01 , represented by the symbol %, is commonly used as a dimensionless unit. --- --- See section 7.10.2 of the <#note1 [1]> for further information. --- --- >>> 1 *~ percent --- 1.0e-2 -percent :: (Fractional a) => Unit 'NonMetric DOne a -percent = mkUnitQ (ucum "%" "%" "percent") (1 Prelude./ 100) one - --- | One gee is the standard value of the acceleration due to gravity at the --- Earth's surface, as standardized by CIPM. --- --- Note that local values of acceleration due to gravity will differ from the --- standard gravity. --- --- See <https://en.wikipedia.org/wiki/Standard_gravity here> for further information. --- --- >>> 1 *~ gee --- 9.80665 m s^-2 --- --- >>> 1 *~ gee :: Acceleration Rational --- 196133 % 20000 m s^-2 -gee :: Fractional a => Unit 'Metric DAcceleration a -gee = mkUnitQ (ucumMetric "[g]" "g" "gee") 9.80665 $ meter / second ^ pos2 - -{- $inch-pound-units -Some US customary (that is, inch-pound) units. --} - --- | One international foot is one third of an international 'yard'. --- --- See <https://en.wikipedia.org/wiki/Foot_%28unit%29#International_foot here> for further information. --- --- >>> 1 *~ foot --- 0.3048 m --- --- prop> 3 *~ foot === 1 *~ yard --- --- >>> 1 *~ foot :: Length Rational --- 381 % 1250 m -foot :: Fractional a => Unit 'NonMetric DLength a -foot = mkUnitQ (ucum "[ft_i]" "ft" "foot") (1 Prelude./ 3) $ yard - --- | One inch is one twelth of a 'foot'. --- --- This inch is based on the international 'foot'. --- --- See <https://en.wikipedia.org/wiki/Inch#Modern_standardisation here> for further information. --- --- >>> 1 *~ inch --- 2.54e-2 m --- --- prop> 12 *~ inch === 1 *~ foot --- --- >>> 1 *~ inch :: Length Rational --- 127 % 5000 m -inch :: Fractional a => Unit 'NonMetric DLength a -inch = mkUnitQ (ucum "[in_i]" "in" "inch") (1 Prelude./ 12) $ foot - --- | One mil is one thousandth of an 'inch'. --- --- This mil is based on the international 'inch'. --- --- See <https://en.wikipedia.org/wiki/Thousandth_of_an_inch here> for further information. --- --- >>> 1 *~ mil --- 2.54e-5 m --- --- prop> 1000 *~ mil === 1 *~ inch --- --- >>> 1 *~ mil :: Length Rational --- 127 % 5000000 m -mil :: Fractional a => Unit 'NonMetric DLength a -mil = mkUnitQ (ucum "[mil_i]" "mil" "mil") 0.001 $ inch - --- | One yard, as defined by international agreement in 1959, is precisely --- 0.9144 'meter'. --- --- See <https://en.wikipedia.org/wiki/Yard here> for further information. --- --- >>> 1 *~ yard --- 0.9144 m --- --- >>> 1 *~ yard :: Length Rational --- 1143 % 1250 m -yard :: (Fractional a) => Unit 'NonMetric DLength a -yard = mkUnitQ (ucum "[yd_i]" "yd" "yard") 0.9144 $ meter - --- | One mile is 5 280 feet. --- --- This mile is based on the international 'foot'. --- --- See <https://en.wikipedia.org/wiki/Mile#International_mile here> for further information. --- --- >>> 1 *~ mile --- 1609.344 m --- --- prop> 1 *~ mile === 5280 *~ foot --- --- >>> 1 *~ mile :: Length Rational --- 201168 % 125 m -mile :: (Fractional a) => Unit 'NonMetric DLength a -mile = mkUnitQ (ucum "[mi_i]" "mi" "mile") 5280 $ foot - --- | One acre is 43 560 square feet. --- --- This acre is based on the international 'foot'. For the acre based on the US Survey Foot, --- see 'usSurveyAcre'. While both acres are in use, the difference between them is of little consequence --- for most applications in which either is used. --- --- See <https://en.wikipedia.org/wiki/Acre#Differences_between_international_and_US_survey_acres here> for further information. --- --- >>> 1 *~ acre --- 4046.8564224 m^2 --- --- prop> 1 *~ acre === 43560 *~ foot ^ pos2 --- --- >>> 1 *~ acre :: Area Rational --- 316160658 % 78125 m^2 -acre :: (Fractional a) => Unit 'NonMetric DArea a -acre = mkUnitQ (dimensionalAtom "[acr_i]" "ac" "acre") 43560 $ square foot - --- | One US survey foot is 1200/3937 'meter'. --- --- For the international foot, see 'foot'. Note that this is not the foot in routine use --- in the United States. --- --- See <https://en.wikipedia.org/wiki/Foot_%28unit%29#US_survey_foot here> for further information. --- --- >>> 1 *~ usSurveyFoot --- 0.3048006096012192 m --- --- >>> 1 *~ usSurveyFoot :: Length Rational --- 1200 % 3937 m -usSurveyFoot :: Fractional a => Unit 'NonMetric DLength a -usSurveyFoot = mkUnitQ (ucum "[ft_us]" "ft" "foot") (1200 Prelude./ 3937) $ meter - --- | One inch is one twelth of a foot. --- --- This inch is based on the 'usSurveyFoot'. For the inch based on the international foot, --- see 'inch'. Note that this is not the inch in routine use in the United States. --- --- See <https://en.wikipedia.org/wiki/Inch here> for further information. --- --- >>> 1 *~ usSurveyInch --- 2.54000508001016e-2 m --- --- prop> 12 *~ usSurveyInch === 1 *~ usSurveyFoot --- --- >>> 1 *~ usSurveyInch :: Length Rational --- 100 % 3937 m -usSurveyInch :: Fractional a => Unit 'NonMetric DLength a -usSurveyInch = mkUnitQ (ucum "[in_us]" "in" "inch") (1 Prelude./ 12) $ usSurveyFoot - --- | One mil is one thousandth of an inch. --- --- This mil is based on the 'usSurveyInch'. For the mil based on the international inch, --- see 'mil'. Note that this is not the mil in routine use in the United States. --- --- See <https://en.wikipedia.org/wiki/Thousandth_of_an_inch here> for further information. --- --- >>> 1 *~ usSurveyMil --- 2.54000508001016e-5 m --- --- prop> 1000 *~ usSurveyMil === 1 *~ usSurveyInch --- --- >>> 1 *~ usSurveyMil :: Length Rational --- 1 % 39370 m -usSurveyMil :: Fractional a => Unit 'NonMetric DLength a -usSurveyMil = mkUnitQ (ucum "[mil_us]" "mil" "mil") 0.001 $ usSurveyInch - --- | One yard is three feet. --- --- This yard is based on the 'usSurveyFoot'. For the international yard, --- see 'yard'. Note that this is not the yard in routine use in the United States. --- --- See <https://en.wikipedia.org/wiki/Yard here> for further information. --- --- >>> 1 *~ usSurveyYard --- 0.9144018288036576 m --- --- prop> 1 *~ usSurveyYard === 3 *~ usSurveyFoot --- --- >>> 1 *~ usSurveyYard :: Length Rational --- 3600 % 3937 m -usSurveyYard :: (Fractional a) => Unit 'NonMetric DLength a -usSurveyYard = mkUnitQ (ucum "[yd_us]" "yd" "yard") 3 $ usSurveyFoot - --- | One US survey mile is 5 280 US survey feet. --- --- This mile is based on the 'usSurveyFoot'. For the mile based on the international foot, --- see 'mile'. Note that this is not the mile in routine use in the United States. --- --- See <https://en.wikipedia.org/wiki/Mile#US_survey_mile here> for further information. --- --- >>> 1 *~ usSurveyMile --- 1609.3472186944373 m --- --- prop> 1 *~ usSurveyMile === 5280 *~ usSurveyFoot --- --- >>> 1 *~ usSurveyMile :: Length Rational --- 6336000 % 3937 m -usSurveyMile :: (Fractional a) => Unit 'NonMetric DLength a -usSurveyMile = mkUnitQ (ucum "[mi_us]" "mi" "mile") 5280 $ usSurveyFoot - --- | One acre is 43 560 square feet. --- --- This acre is based on the 'usSurveyFoot'. For the acre based on the international foot, --- see 'acre'. While both acres are in use, the difference between them is of little consequence --- for most applications in which either is used. This is the only acre defined by the UCUM. --- --- See <https://en.wikipedia.org/wiki/Acre#Differences_between_international_and_US_survey_acres here> for further information. --- --- >>> 1 *~ usSurveyAcre --- 4046.872609874252 m^2 --- --- prop> 1 *~ usSurveyAcre === 43560 *~ usSurveyFoot ^ pos2 --- --- >>> 1 *~ usSurveyAcre :: Area Rational --- 62726400000 % 15499969 m^2 -usSurveyAcre :: (Fractional a) => Unit 'NonMetric DArea a -usSurveyAcre = mkUnitQ (ucum "[acr_us]" "ac" "acre") 43560 $ square usSurveyFoot - --- | One avoirdupois pound is a mass, exactly defined in terms of the kilogram by the international --- yard and pound agreement of 1959. --- --- See <https://en.wikipedia.org/wiki/Avoirdupois#Internationalization here> for further information. --- --- >>> 1 *~ poundMass --- 0.45359237 kg --- --- >>> 1 *~ poundMass :: Mass Rational --- 45359237 % 100000000 kg -poundMass :: Fractional a => Unit 'NonMetric DMass a -poundMass = mkUnitQ (ucum "[lb_av]" "lb" "pound") 0.45359237 $ kilo gram - --- | One avoirdupois ounce is one sixteenth of a 'poundMass'. --- --- See <https://en.wikipedia.org/wiki/Ounce#International_avoirdupois_ounce here> for further information. --- --- >>> 1 *~ ounce --- 2.8349523125e-2 kg --- --- prop> 16 *~ ounce === 1 *~ poundMass --- --- >>> 1 *~ ounce :: Mass Rational --- 45359237 % 1600000000 kg -ounce :: Fractional a => Unit 'NonMetric DMass a -ounce = mkUnitQ (ucum "[oz_av]" "oz" "ounce") (1 Prelude./ 16) $ poundMass - --- | One short ton is two thousand 'poundMass'. --- --- See <https://en.wikipedia.org/wiki/Short_ton#United_States here> for further information. --- --- >>> 1 *~ shortTon --- 907.18474 kg --- --- >>> 1 *~ shortTon :: Mass Rational --- 45359237 % 50000 kg -shortTon :: Fractional a => Unit 'NonMetric DMass a -shortTon = mkUnitQ (ucum "[ston_av]" "ton" "short ton") 2000 $ poundMass - --- | The pound-force is equal to the gravitational force exerted on a mass --- of one avoirdupois pound on the surface of Earth. --- --- This definition is based on standard gravity (the 'gee') and the --- international avoirdupois 'poundMass'. --- --- See <https://en.wikipedia.org/wiki/Pound_%28force%29 here> for further information. --- --- >>> 1 *~ poundForce --- 4.4482216152605 m kg s^-2 --- --- prop> 1 *~ poundForce === 1 *~ poundMass * (1 *~ gee) --- --- >>> 1 *~ poundForce :: Force Rational --- 8896443230521 % 2000000000000 m kg s^-2 -poundForce :: Fractional a => Unit 'NonMetric DForce a -poundForce = mkUnitQ (ucum "[lbf_av]" "lbf" "pound force") 1 $ poundMass * gee - --- | One mechanical horsepower is by definition the power necessary --- to apply a force of 550 'poundForce' through a distance of one 'foot' --- per 'second'. --- --- See <https://en.wikipedia.org/wiki/Horsepower#Mechanical_horsepower here> for further information. --- --- >>> 1 *~ horsepower --- 745.6998715822702 m^2 kg s^-3 --- --- prop> 1 *~ horsepower === 550 *~ poundForce * (1 *~ foot) / (1 *~ second) --- --- >>> 1 *~ horsepower :: Power Rational --- 37284993579113511 % 50000000000000 m^2 kg s^-3 -horsepower :: Fractional a => Unit 'NonMetric DPower a -horsepower = mkUnitQ (ucum "[HP]" "hp" "horsepower") 550 $ foot * poundForce / second - --- | The slug is a unit of mass associated with Imperial units and United States customary units. --- It is a mass that accelerates by 1 foot per second per second when a force of one pound is exerted on it. --- --- This definition is based on standard gravity (the 'gee'), the international 'foot', and the international avoirdupois 'poundMass'. --- --- See <https://en.wikipedia.org/wiki/Slug_%28mass%29 here> for further information. --- --- >>> 1 *~ slug --- 14.593902937206364 kg --- --- >>> 1 *~ slug :: Mass Rational --- 8896443230521 % 609600000000 kg -slug :: Fractional a => Unit 'NonMetric DMass a -slug = mkUnitQ (dimensionalAtom "slug" "slug" "slug") 1 $ poundForce * (second^pos2) / foot - --- | One psi is a pressure of one 'poundForce' per 'square' 'inch' of area. --- --- See <https://en.wikipedia.org/wiki/Pounds_per_square_inch here> for further information. --- --- >>> 1 *~ psi --- 6894.757293168362 m^-1 kg s^-2 --- --- >>> 1 *~ psi :: Pressure Rational --- 8896443230521 % 1290320000 m^-1 kg s^-2 -psi :: Fractional a => Unit 'NonMetric DPressure a -psi = mkUnitQ (ucum "[psi]" "psi" "pound per square inch") 1 $ poundForce / inch ^ pos2 - --- | One nautical mile is a unit of length, set by international agreement as being exactly 1 852 meters. --- --- Historically, it was defined as the distance spanned by one minute of arc along a meridian of the Earth. --- --- See <https://en.wikipedia.org/wiki/Nautical_mile here> for further information. --- --- >>> 1 *~ nauticalMile --- 1852.0 m --- --- >>> 1 *~ nauticalMile :: Length Rational --- 1852 % 1 m -nauticalMile :: (Num a) => Unit 'NonMetric DLength a -nauticalMile = mkUnitZ (ucum "[nmi_i]" "NM" "nautical mile") 1852 $ meter - --- | One knot is a velocity equal to one 'nauticalMile' per 'hour'. --- --- See <https://en.wikipedia.org/wiki/Knot_%28unit%29 here> for further information. --- --- >>> 1 *~ knot --- 0.5144444444444445 m s^-1 --- --- >>> 1 *~ knot :: Velocity Rational --- 463 % 900 m s^-1 -knot :: (Fractional a) => Unit 'NonMetric DVelocity a -knot = mkUnitQ (ucum "[kt_i]" "kt" "knot") 1 $ nauticalMile / hour - --- | One revolution is an angle equal to 2 pi radians; a full circle. --- --- See <https://en.wikipedia.org/wiki/Turn_%28geometry%29 here> for further information. --- --- >>> 1 *~ revolution --- 6.283185307179586 --- --- prop> 1 *~ revolution === _2 * pi * (1 *~ radian) --- --- prop> 1 *~ revolution === 360 *~ degree -revolution :: (Floating a) => Unit 'NonMetric DOne a -revolution = mkUnitR (dimensionalAtom "rev" "rev" "revolution") (2 Prelude.* Prelude.pi) $ radian - -solid :: (Floating a) => Unit 'NonMetric DOne a -solid = mkUnitR (dimensionalAtom "solid" "solid" "solid") (4 Prelude.* Prelude.pi) $ steradian - -teaspoon :: (Fractional a) => Unit 'NonMetric DVolume a -teaspoon = mkUnitQ (ucum "[tsp_m]" "tsp" "teaspoon") 5 $ milli liter - --- | One btu is is the 'QuantityOfHeat' required to raise the temperature --- of 1 avoirdupois 'poundMass' of liquid water by 1 'degreeFahrenheit' at a constant pressure of one 'atmosphere'. --- --- Because this value must be determined experimentally and varies with temperature, several standardized --- values of the btu have arisen. This is the value based on the International Steam Table calorie, --- defined by the Fifth International Conference on the Properties of Steam. --- --- See <https://en.wikipedia.org/wiki/British_thermal_unit#Definitions here> for further information. --- --- >>> 1 *~ btu --- 1055.05585262 m^2 kg s^-2 --- --- >>> 1 *~ btu :: Energy Rational --- 52752792631 % 50000000 m^2 kg s^-2 -btu :: Fractional a => Unit 'NonMetric DEnergy a -btu = mkUnitQ (ucum "[Btu_IT]" "btu" "British thermal unit") 1055.05585262 $ joule - - -{- $year - -The IAU recommends <#note2 [2]> that: - - Although there are several different kinds of year (as there are - several kinds of day), it is best to regard a year as a julian - year of 365.25 days (31.5576 Ms) unless otherwise specified. - --} - --- | One mean Julian year is a unit of measurement of time defined as exactly 365.25 days of 86 400 'second's each. --- --- See <https://en.wikipedia.org/wiki/Julian_year_%28astronomy%29 here> for further information. --- --- >>> 1 *~ year --- 3.15576e7 s --- --- >>> 1 *~ year :: Time Rational --- 31557600 % 1 s -year :: Num a => Unit 'NonMetric DTime a -year = mkUnitZ (ucum "a_j" "a" "mean Julian year") 31557600 $ second - --- | One mean Julian century is one hundred mean Julian 'year's. --- --- >>> 1 *~ century --- 3.15576e9 s --- --- >>> 1 *~ century :: Time Rational --- 3155760000 % 1 s -century :: Num a => Unit 'NonMetric DTime a -century = mkUnitZ (dimensionalAtom "c_j" "cen" "mean Julian century") 100 $ year - -{- $pressure-units -It seems that nearly every area of application has its own customary unit for measuring pressure. -We include some of the common ones here. 'psi' was defined earlier. --} - --- | The bar is exactly 100 000 'Numeric.Units.Dimensional.SIUnits.pascal'. --- --- From Wikipedia: --- --- It is about equal to the atmospheric pressure on Earth at sea level. --- --- >>> 1 *~ bar --- 100000.0 m^-1 kg s^-2 --- --- >>> 1 *~ bar :: Pressure Rational --- 100000 % 1 m^-1 kg s^-2 -bar :: (Num a) => Unit 'Metric DPressure a -bar = mkUnitZ (ucumMetric "bar" "bar" "bar") 1e5 $ pascal - --- | The "standard atmosphere". --- --- From Wikipedia <#note3 [3]>: --- --- The standard atmosphere (atm) is an established constant. It is --- approximately equal to typical air pressure at earth mean sea --- level. --- --- >>> 1 *~ atmosphere --- 101325.0 m^-1 kg s^-2 --- --- >>> 1 *~ atmosphere :: Pressure Rational --- 101325 % 1 m^-1 kg s^-2 -atmosphere :: (Num a) => Unit 'NonMetric DPressure a -atmosphere = mkUnitZ (ucum "atm" "atm" "standard atmosphere") 101325 $ pascal - --- | The "technical atmosphere" --- --- From Wikipedia: --- --- A technical atmosphere (symbol: at) is a non-SI unit of pressure equal --- to one kilogram-force per square centimeter. --- --- >>> 1 *~ technicalAtmosphere --- 98066.5 m^-1 kg s^-2 --- --- >>> 1 *~ technicalAtmosphere :: Pressure Rational --- 196133 % 2 m^-1 kg s^-2 -technicalAtmosphere :: (Fractional a) => Unit 'NonMetric DPressure a -technicalAtmosphere = mkUnitQ (ucum "att" "at" "technical atmosphere") 1 $ kilo gram * gee * centi meter ^ neg2 - --- | The conventional value for the pressure exerted by a 1 mm high column of mercury. --- --- Per Wikipedia <#note4 [4]>, one mmHg (millimeter of mercury) is defined as: --- --- The pressure exerted at the base of a column of fluid exactly 1 mm high, --- when the density of the fluid is exactly 13.5951 g/cm^3, at a place --- where the acceleration of gravity is exactly 9.80665 m/s^2. --- --- The chosen fluid density approximately corresponds to that of mercury --- at 0 deg. Under most conditions, 1 mmHg is approximately equal to 1 'torr'. --- --- >>> 1 *~ mmHg --- 133.322 m^-1 kg s^-2 --- --- >>> 1 *~ mmHg :: Pressure Rational --- 66661 % 500 m^-1 kg s^-2 -mmHg :: (Fractional a) => Unit 'NonMetric DPressure a -mmHg = milli mHg - -mHg :: (Fractional a) => Unit 'Metric DPressure a -mHg = mkUnitQ (ucumMetric "m[Hg]" "m Hg" "meter of mercury") 133.3220 $ kilo pascal - --- | The conventional value for the pressure exerted by a 1 inch high column of mercury. --- --- Column inches of mercury are also used to measure pressure, especially in --- meteorological or aeronautical contexts in the United States. --- --- This is the value defined by UCUM. For the value defined by NIST, see 'inHg_NIST'. --- --- >>> 1 *~ inHg --- 3386.3788 m^-1 kg s^-2 --- --- >>> 1 *~ inHg :: Pressure Rational --- 8465947 % 2500 m^-1 kg s^-2 -inHg :: (Fractional a) => Unit 'NonMetric DPressure a -inHg = inHg_UCUM - --- | The conventional value for the pressure exerted by a 1 inch high column of mercury. --- --- Column inches of mercury are also used to measure pressure, especially in --- meteorological or aeronautical contexts in the United States. --- --- This is the value defined by UCUM. For the value defined by NIST, see 'inHg_NIST'. --- --- >>> 1 *~ inHg_UCUM --- 3386.3788 m^-1 kg s^-2 --- --- >>> 1 *~ inHg_UCUM :: Pressure Rational --- 8465947 % 2500 m^-1 kg s^-2 -inHg_UCUM :: (Fractional a) => Unit 'NonMetric DPressure a -inHg_UCUM = mkUnitQ (ucum "[in_i'Hg]" "in Hg" "inch of mercury") 1 $ mHg * inch / meter - --- | The conventional value for the pressure exerted by a 1 inch high column of mercury. --- --- Column inches of mercury are also used to measure pressure, especially in --- meteorological or aeronautical contexts in the United States. --- --- This is the value defined by NIST. For the value defined by UCUM, see 'inHg_UCUM'. --- --- >>> 1 *~ inHg_NIST --- 3386.389 m^-1 kg s^-2 --- --- >>> 1 *~ inHg_NIST :: Pressure Rational --- 3386389 % 1000 m^-1 kg s^-2 -inHg_NIST :: (Fractional a) => Unit 'NonMetric DPressure a -inHg_NIST = mkUnitQ (dimensionalAtom "[in_i'Hg_NIST]" "in Hg" "inch of mercury") 3.386389e3 $ pascal - --- | One torr (symbol: Torr) is defined as 1/760 'atmosphere', which is approximately equal to 1 'mmHg'. --- --- See <https://en.wikipedia.org/wiki/Torr here> for further information. --- --- >>> 1 *~ torr --- 133.32236842105263 m^-1 kg s^-2 --- --- >>> 1 *~ torr :: Pressure Rational --- 20265 % 152 m^-1 kg s^-2 -torr :: (Fractional a) => Unit 'NonMetric DPressure a -torr = mkUnitQ (dimensionalAtom "Torr" "Torr" "Torr") (1 Prelude./ 760) $ atmosphere - --- | The rad is a deprecated unit of 'AbsorbedDose', defined as --- 0.01 'gray'. --- --- See <https://en.wikipedia.org/wiki/Rad_%28unit%29 here> for further information. --- --- >>> 1 *~ rad --- 1.0e-2 m^2 s^-2 --- --- >>> 1 *~ rad :: AbsorbedDose Rational --- 1 % 100 m^2 s^-2 -rad :: (Fractional a) => Unit 'Metric DAbsorbedDose a -rad = mkUnitQ (ucumMetric "RAD" "RAD" "RAD") 1 $ centi gray - --- | One Stokes is a unit of 'KinematicViscosity' equal to @1 cm^2 / s@. --- --- See <https://en.wikipedia.org/wiki/Viscosity#Kinematic_viscosity_.CE.BD here> for further information. --- --- >>> 1 *~ stokes --- 1.0e-4 m^2 s^-1 --- --- >>> 1 *~ stokes :: KinematicViscosity Rational --- 1 % 10000 m^2 s^-1 -stokes :: (Fractional a) => Unit 'Metric DKinematicViscosity a -stokes = mkUnitQ (ucumMetric "St" "St" "Stokes") 1 $ centi meter ^ pos2 / second - -{- $temperature -These units of temperature are relative. For absolute temperatures, see 'Numeric.Units.Dimensional.SIUnits.fromDegreeCelsiusAbsolute'. --} - --- | One degree Fahrenheit is a unit of relative temperature equal to 5/9 'kelvin'. --- --- Note that although the Fahrenheit scale is an absolute temperature scale, this unit is a unit of difference within --- that scale and measures relative temperature. --- --- See <https://en.wikipedia.org/wiki/Fahrenheit#Definition_and_conversions here> for further information. --- --- >>> 1 *~ degreeFahrenheit --- 0.5555555555555556 K --- --- >>> 1 *~ degreeFahrenheit :: ThermodynamicTemperature Rational --- 5 % 9 K -degreeFahrenheit :: (Fractional a) => Unit 'NonMetric DThermodynamicTemperature a -degreeFahrenheit = mkUnitQ (ucum "[degF]" "°F" "degree Fahrenheit") (5 Prelude./ 9) $ degreeCelsius - --- | One degree Rankine is a unit of relative temperature equal to 5/9 'kelvin'. --- --- Note that although the Rankine scale is an absolute temperature scale, this unit is a unit of difference within --- that scale and measures relative temperature. --- --- See <https://en.wikipedia.org/wiki/Rankine_scale here> for further information. --- --- >>> 1 *~ degreeRankine --- 0.5555555555555556 K --- --- >>> 1 *~ degreeRankine :: ThermodynamicTemperature Rational --- 5 % 9 K -degreeRankine :: (Fractional a) => Unit 'NonMetric DThermodynamicTemperature a -degreeRankine = mkUnitQ (ucum "[degR]" "°R" "degree Rankine") 1 $ degreeFahrenheit - -{- $imperial-volumes -Per http://en.wikipedia.org/wiki/Imperial_units and http://en.wikipedia.org/wiki/Cup_(unit)#Imperial_cup. --} - --- | One imperial gallon is defined exactly in terms of the 'liter' --- by the Weights and Measures Act 1985. --- --- See <https://en.wikipedia.org/wiki/Imperial_units#Volume here> for further information. --- --- >>> 1 *~ imperialGallon --- 4.54609e-3 m^3 --- --- >>> 1 *~ imperialGallon :: Volume Rational --- 454609 % 100000000 m^3 -imperialGallon :: (Fractional a) => Unit 'NonMetric DVolume a -imperialGallon = mkUnitQ (ucum "[gal_br]" "gal" "gallon") 4.54609 $ liter - --- | One imperial quart is one quarter of an 'imperialGallon'. --- --- See <https://en.wikipedia.org/wiki/Imperial_units#Volume here> for further information. --- --- >>> 1 *~ imperialQuart --- 1.1365225e-3 m^3 --- --- >>> 1 *~ imperialQuart :: Volume Rational --- 454609 % 400000000 m^3 -imperialQuart :: (Fractional a) => Unit 'NonMetric DVolume a -imperialQuart = mkUnitQ (ucum "[qt_br]" "qt" "quart") (1 Prelude./ 4) $ imperialGallon - --- | One imperial pint is one half of an 'imperialQuart'. --- --- See <https://en.wikipedia.org/wiki/Imperial_units#Volume here> for further information. --- --- >>> 1 *~ imperialPint --- 5.6826125e-4 m^3 --- --- >>> 1 *~ imperialPint :: Volume Rational --- 454609 % 800000000 m^3 -imperialPint :: (Fractional a) => Unit 'NonMetric DVolume a -imperialPint = mkUnitQ (ucum "[pt_br]" "pt" "pint") (1 Prelude./ 8) $ imperialGallon - --- | One imperial cup is one half of an 'imperialPint'. --- --- This unit is not in common use and is does not appear in some sources --- describing the imperial fluid volume units. --- --- See <https://en.wikipedia.org/wiki/Cup_%28unit%29#Imperial_cup here> for further information. --- --- >>> 1 *~ imperialCup --- 2.84130625e-4 m^3 --- --- >>> 1 *~ imperialCup :: Volume Rational --- 454609 % 1600000000 m^3 -imperialCup :: (Fractional a) => Unit 'NonMetric DVolume a -imperialCup = mkUnitQ (dimensionalAtom "[cup_br]" "cup" "cup") 0.5 $ imperialPint - --- | One imperial gill is one quarter of an 'imperialPint'. --- --- See <https://en.wikipedia.org/wiki/Imperial_units#Volume here> for further information. --- --- >>> 1 *~ imperialGill --- 1.420653125e-4 m^3 --- --- >>> 1 *~ imperialGill :: Volume Rational --- 454609 % 3200000000 m^3 -imperialGill :: (Fractional a) => Unit 'NonMetric DVolume a -imperialGill = mkUnitQ (ucum "[gil_br]" "gill" "gill") (1 Prelude./ 4) $ imperialPint - --- | One imperial fluid ounce is one twentieth of an 'imperialPint'. --- --- See <https://en.wikipedia.org/wiki/Imperial_units#Volume here> for further information. --- --- >>> 1 *~ imperialFluidOunce --- 2.84130625e-5 m^3 --- --- >>> 1 *~ imperialFluidOunce :: Volume Rational --- 454609 % 16000000000 m^3 -imperialFluidOunce :: (Fractional a) => Unit 'NonMetric DVolume a -imperialFluidOunce = mkUnitQ (ucum "[foz_br]" "fl oz" "fluid ounce") (1 Prelude./ 20) $ imperialPint - -{- $us-customary-volumes -Per http://www.nist.gov/pml/wmd/pubs/upload/2012-hb44-final.pdf page 452 and http://en.wikipedia.org/wiki/United_States_customary_units#Fluid_volume -Note that there exist rarely-used "dry" variants of units with overlapping names. --} - --- | One US liquid gallon is a volume of 231 cubic inches. --- --- See <https://en.wikipedia.org/wiki/Gallon#The_US_liquid_gallon here> for further information. --- --- >>> 1 *~ usGallon --- 3.785411784e-3 m^3 --- --- >>> 1 *~ usGallon :: Volume Rational --- 473176473 % 125000000000 m^3 -usGallon :: (Fractional a) => Unit 'NonMetric DVolume a -usGallon = mkUnitQ (ucum "[gal_us]" "gal" "gallon") 231 $ cubic inch - --- | One US liquid quart is one quarter of a 'usGallon'. --- --- See <https://en.wikipedia.org/wiki/United_States_customary_units#Fluid_volume here> for further information. --- --- >>> 1 *~ usQuart --- 9.46352946e-4 m^3 --- --- >>> 1 *~ usQuart :: Volume Rational --- 473176473 % 500000000000 m^3 -usQuart :: (Fractional a) => Unit 'NonMetric DVolume a -usQuart = mkUnitQ (ucum "[qt_us]" "qt" "quart") (1 Prelude./ 4) $ usGallon - --- | One US liquid pint is one half of a 'usQuart'. --- --- See <https://en.wikipedia.org/wiki/United_States_customary_units#Fluid_volume here> for further information. --- --- >>> 1 *~ usPint --- 4.73176473e-4 m^3 --- --- >>> 1 *~ usPint :: Volume Rational --- 473176473 % 1000000000000 m^3 -usPint :: (Fractional a) => Unit 'NonMetric DVolume a -usPint = mkUnitQ (ucum "[pt_us]" "pt" "pint") (1 Prelude./ 8) $ usGallon - --- | One US liquid cup is one half of a 'usPint'. --- --- See <https://en.wikipedia.org/wiki/United_States_customary_units#Fluid_volume here> for further information. --- --- >>> 1 *~ usCup --- 2.365882365e-4 m^3 --- --- >>> 1 *~ usCup :: Volume Rational --- 473176473 % 2000000000000 m^3 -usCup :: (Fractional a) => Unit 'NonMetric DVolume a -usCup = mkUnitQ (ucum "[cup_us]" "cup" "cup") (1 Prelude./ 2) $ usPint - --- | One US liquid gill is one half of a 'usCup'. --- --- See <https://en.wikipedia.org/wiki/United_States_customary_units#Fluid_volume here> for further information. --- --- >>> 1 *~ usGill --- 1.1829411825e-4 m^3 --- --- >>> 1 *~ usGill :: Volume Rational --- 473176473 % 4000000000000 m^3 -usGill :: (Fractional a) => Unit 'NonMetric DVolume a -usGill = mkUnitQ (ucum "[gil_us]" "gill" "gill") (1 Prelude./ 4) $ usPint - --- | One US fluid ounce is 1/128 'usGallon' or 1/8 'usCup'. --- --- See <https://en.wikipedia.org/wiki/United_States_customary_units#Fluid_volume here> for further information. --- --- >>> 1 *~ usFluidOunce --- 2.95735295625e-5 m^3 --- --- >>> 1 *~ usFluidOunce :: Volume Rational --- 473176473 % 16000000000000 m^3 -usFluidOunce :: (Fractional a) => Unit 'NonMetric DVolume a -usFluidOunce = mkUnitQ (ucum "[foz_us]" "fl oz" "fluid ounce") (1 Prelude./ 16) $ usPint -- sic, does not match factor used in imperial system - --- | One Ångström is 1/10 'nano' 'meter'. --- --- See <https://en.wikipedia.org/wiki/%C3%85ngstr%C3%B6m here> for further information. --- --- >>> 1 *~ angstrom --- 1.0e-10 m --- --- >>> 1 *~ angstrom :: Length Rational --- 1 % 10000000000 m -angstrom :: (Fractional a) => Unit 'NonMetric DLength a -angstrom = mkUnitQ (ucum "Ao" "Å" "Ångström") 0.1 $ nano meter - --- | One Gauss is 1/10000 'tesla'. --- --- See <https://en.wikipedia.org/wiki/Gauss_%28unit%29 here> for further information. --- --- >>> 1 *~ gauss --- 1.0e-4 kg s^-2 A^-1 --- --- >>> 1 *~ gauss :: MagneticFluxDensity Rational --- 1 % 10000 kg s^-2 A^-1 -gauss :: (Fractional a) => Unit 'NonMetric DMagneticFluxDensity a -gauss = mkUnitQ (ucum "G" "G" "Gauss") 1e-4 $ tesla +{-# LANGUAGE DataKinds #-}+{-# LANGUAGE NumDecimals #-}++{- |+ Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter+ License : BSD3++ Maintainer : bjorn@buckwalter.se+ Stability : Stable+ Portability: GHC only++= Summary++This module defines units that are not part of the SI, with the+exception of those defined in the "Numeric.Units.Dimensional.SIUnits" module (units outside+of the SI accepted for use with the SI).++Any chapters, sections or tables referenced are from <#note1 [1]> unless+otherwise specified.++== Neper, bel, shannon and the like++The units of section 5.1.2 are purposefully (but not permanently)+omitted. In fact the logarithmic units (see section 8.7) are+problematic and it is not clear how to implement them. Perhaps with+a conversion function similar to for degrees Celsius.++= References++1. #note1# https://www.nist.gov/pml/special-publication-811+2. #note2# https://www.iau.org/publications/proceedings_rules/units/+3. #note3# https://en.wikipedia.org/wiki/Pressure+4. #note4# https://en.wikipedia.org/wiki/Torr++-}++module Numeric.Units.Dimensional.NonSI+(+ -- * Units Defined By Experiment+ -- $values-obtained-experimentally+ electronVolt, calorie, unifiedAtomicMassUnit, dalton,+ -- * Dimensionless Units+ percent,+ -- * Standard Gravity+ gee,+ -- * Inch-pound Units+ -- $inch-pound-units+ poundMass, ounce, poundForce, horsepower, btu, shortTon,+ nauticalMile, knot,+ revolution, solid,+ slug, psi,+ teaspoon,+ -- ** International Foot+ foot, inch, mil, yard, mile, acre,+ -- ** US Survey Foot+ usSurveyFoot, usSurveyInch, usSurveyMil, usSurveyYard, usSurveyMile, usSurveyAcre,+ -- * Years+ -- $year+ year, decade, century, millennium,+ -- * Pressure Units+ -- $pressure-units+ bar, atmosphere, technicalAtmosphere, mmHg, inHg, inHg_UCUM, inHg_NIST, torr,+ -- * Radiation Units+ rad,+ -- * Kinematic Viscosity+ stokes,+ -- * Temperature+ -- $temperature+ degreeFahrenheit, degreeRankine,+ -- * Imperial Volumes+ -- $imperial-volumes+ imperialGallon, imperialQuart, imperialPint, imperialCup, imperialGill, imperialFluidOunce,+ -- * US Customary Volumes+ -- $us-customary-volumes+ usGallon, usQuart, usPint, usCup, usGill, usFluidOunce,+ -- * Atomic-Scale Units+ angstrom,+ -- * Units from the Centimeter-Gram-Second Electrostatic System of Units+ gauss+)+where++import Numeric.Units.Dimensional.Prelude+import Numeric.Units.Dimensional.UnitNames.Internal (ucumMetric, ucum, dimensionalAtom)+import qualified Prelude++-- $setup+-- >>> :set -fno-warn-type-defaults+-- >>> import Data.ExactPi+-- >>> import Data.Function (on)+-- >>> import Numeric.Units.Dimensional.Coercion+-- >>> default (Double)+-- >>> :{+-- >>> let infix 4 ===+-- >>> (===) = areExactlyEqual `on` unQuantity :: Quantity d ExactPi -> Quantity d ExactPi -> Bool+-- >>> :}++{- $values-obtained-experimentally++From Table 7, units accepted for use with the SI whose values in SI units are+obtained experimentally.++When <#note1 [1]> was published, the electron volt had a standard combined+uncertainity of 0.00000049e-19 J and the unified atomic mass unit+had a combined uncertainty of 0.0000010e-27 kg.++-}++electronVolt :: Floating a => Unit 'Metric DEnergy a+electronVolt = mkUnitR (ucumMetric "eV" "eV" "electron volt") 1.60217733e-19 $ joule++calorie :: Floating a => Unit 'Metric DEnergy a+calorie = mkUnitR (ucumMetric "cal" "cal" "calorie") 4.184 $ joule++unifiedAtomicMassUnit :: Floating a => Unit 'Metric DMass a+unifiedAtomicMassUnit = mkUnitR (ucumMetric "u" "u" "atomic mass unit") 1.6605402e-27 $ kilo gram++dalton :: Floating a => Unit 'Metric DMass a+dalton = mkUnitR (ucumMetric "u" "Da" "Dalton") 1 $ unifiedAtomicMassUnit++-- | One percent is one hundrendth.+--+-- The dimensionless number 0.01, represented by the symbol %, is commonly used as a dimensionless unit.+--+-- See section 7.10.2 of the <#note1 [1]> for further information.+--+-- >>> 1 *~ percent+-- 1.0e-2+percent :: (Fractional a) => Unit 'NonMetric DOne a+percent = mkUnitQ (ucum "%" "%" "percent") (1 Prelude./ 100) one++-- | One gee is the standard value of the acceleration due to gravity at the+-- Earth's surface, as standardized by CIPM.+--+-- Note that local values of acceleration due to gravity will differ from the+-- standard gravity.+--+-- See <https://en.wikipedia.org/wiki/Standard_gravity here> for further information.+--+-- >>> 1 *~ gee+-- 9.80665 m s^-2+--+-- >>> 1 *~ gee :: Acceleration Rational+-- 196133 % 20000 m s^-2+gee :: Fractional a => Unit 'Metric DAcceleration a+gee = mkUnitQ (ucumMetric "[g]" "g" "gee") 9.80665 $ meter / second ^ pos2++{- $inch-pound-units+Some US customary (that is, inch-pound) units.+-}++-- | One international foot is one third of an international 'yard'.+--+-- See <https://en.wikipedia.org/wiki/Foot_%28unit%29#International_foot here> for further information.+--+-- >>> 1 *~ foot+-- 0.3048 m+--+-- prop> 3 *~ foot === 1 *~ yard+--+-- >>> 1 *~ foot :: Length Rational+-- 381 % 1250 m+foot :: Fractional a => Unit 'NonMetric DLength a+foot = mkUnitQ (ucum "[ft_i]" "ft" "foot") (1 Prelude./ 3) $ yard++-- | One inch is one twelth of a 'foot'.+--+-- This inch is based on the international 'foot'.+--+-- See <https://en.wikipedia.org/wiki/Inch#Modern_standardisation here> for further information.+--+-- >>> 1 *~ inch+-- 2.54e-2 m+--+-- prop> 12 *~ inch === 1 *~ foot+--+-- >>> 1 *~ inch :: Length Rational+-- 127 % 5000 m+inch :: Fractional a => Unit 'NonMetric DLength a+inch = mkUnitQ (ucum "[in_i]" "in" "inch") (1 Prelude./ 12) $ foot++-- | One mil is one thousandth of an 'inch'.+--+-- This mil is based on the international 'inch'.+--+-- See <https://en.wikipedia.org/wiki/Thousandth_of_an_inch here> for further information.+--+-- >>> 1 *~ mil+-- 2.54e-5 m+--+-- prop> 1000 *~ mil === 1 *~ inch+--+-- >>> 1 *~ mil :: Length Rational+-- 127 % 5000000 m+mil :: Fractional a => Unit 'NonMetric DLength a+mil = mkUnitQ (ucum "[mil_i]" "mil" "mil") 0.001 $ inch++-- | One yard, as defined by international agreement in 1959, is precisely+-- 0.9144 'meter'.+--+-- See <https://en.wikipedia.org/wiki/Yard here> for further information.+--+-- >>> 1 *~ yard+-- 0.9144 m+--+-- >>> 1 *~ yard :: Length Rational+-- 1143 % 1250 m+yard :: (Fractional a) => Unit 'NonMetric DLength a+yard = mkUnitQ (ucum "[yd_i]" "yd" "yard") 0.9144 $ meter++-- | One mile is 5 280 feet.+--+-- This mile is based on the international 'foot'.+--+-- See <https://en.wikipedia.org/wiki/Mile#International_mile here> for further information.+--+-- >>> 1 *~ mile+-- 1609.344 m+--+-- prop> 1 *~ mile === 5280 *~ foot+--+-- >>> 1 *~ mile :: Length Rational+-- 201168 % 125 m+mile :: (Fractional a) => Unit 'NonMetric DLength a+mile = mkUnitQ (ucum "[mi_i]" "mi" "mile") 5280 $ foot++-- | One acre is 43 560 square feet.+--+-- This acre is based on the international 'foot'. For the acre based on the US Survey Foot,+-- see 'usSurveyAcre'. While both acres are in use, the difference between them is of little consequence+-- for most applications in which either is used.+--+-- See <https://en.wikipedia.org/wiki/Acre#Differences_between_international_and_US_survey_acres here> for further information.+--+-- >>> 1 *~ acre+-- 4046.8564224 m^2+--+-- prop> 1 *~ acre === 43560 *~ foot ^ pos2+--+-- >>> 1 *~ acre :: Area Rational+-- 316160658 % 78125 m^2+acre :: (Fractional a) => Unit 'NonMetric DArea a+acre = mkUnitQ (dimensionalAtom "[acr_i]" "ac" "acre") 43560 $ square foot++-- | One US survey foot is 1200/3937 'meter'.+--+-- For the international foot, see 'foot'. Note that this is not the foot in routine use+-- in the United States.+--+-- See <https://en.wikipedia.org/wiki/Foot_%28unit%29#US_survey_foot here> for further information.+--+-- >>> 1 *~ usSurveyFoot+-- 0.3048006096012192 m+--+-- >>> 1 *~ usSurveyFoot :: Length Rational+-- 1200 % 3937 m+usSurveyFoot :: Fractional a => Unit 'NonMetric DLength a+usSurveyFoot = mkUnitQ (ucum "[ft_us]" "ft" "foot") (1200 Prelude./ 3937) $ meter++-- | One inch is one twelth of a foot.+--+-- This inch is based on the 'usSurveyFoot'. For the inch based on the international foot,+-- see 'inch'. Note that this is not the inch in routine use in the United States.+--+-- See <https://en.wikipedia.org/wiki/Inch here> for further information.+--+-- >>> 1 *~ usSurveyInch+-- 2.54000508001016e-2 m+--+-- prop> 12 *~ usSurveyInch === 1 *~ usSurveyFoot+--+-- >>> 1 *~ usSurveyInch :: Length Rational+-- 100 % 3937 m+usSurveyInch :: Fractional a => Unit 'NonMetric DLength a+usSurveyInch = mkUnitQ (ucum "[in_us]" "in" "inch") (1 Prelude./ 12) $ usSurveyFoot++-- | One mil is one thousandth of an inch.+--+-- This mil is based on the 'usSurveyInch'. For the mil based on the international inch,+-- see 'mil'. Note that this is not the mil in routine use in the United States.+--+-- See <https://en.wikipedia.org/wiki/Thousandth_of_an_inch here> for further information.+--+-- >>> 1 *~ usSurveyMil+-- 2.54000508001016e-5 m+--+-- prop> 1000 *~ usSurveyMil === 1 *~ usSurveyInch+--+-- >>> 1 *~ usSurveyMil :: Length Rational+-- 1 % 39370 m+usSurveyMil :: Fractional a => Unit 'NonMetric DLength a+usSurveyMil = mkUnitQ (ucum "[mil_us]" "mil" "mil") 0.001 $ usSurveyInch++-- | One yard is three feet.+--+-- This yard is based on the 'usSurveyFoot'. For the international yard,+-- see 'yard'. Note that this is not the yard in routine use in the United States.+--+-- See <https://en.wikipedia.org/wiki/Yard here> for further information.+--+-- >>> 1 *~ usSurveyYard+-- 0.9144018288036576 m+--+-- prop> 1 *~ usSurveyYard === 3 *~ usSurveyFoot+--+-- >>> 1 *~ usSurveyYard :: Length Rational+-- 3600 % 3937 m+usSurveyYard :: (Fractional a) => Unit 'NonMetric DLength a+usSurveyYard = mkUnitQ (ucum "[yd_us]" "yd" "yard") 3 $ usSurveyFoot++-- | One US survey mile is 5 280 US survey feet.+--+-- This mile is based on the 'usSurveyFoot'. For the mile based on the international foot,+-- see 'mile'. Note that this is not the mile in routine use in the United States.+--+-- See <https://en.wikipedia.org/wiki/Mile#US_survey_mile here> for further information.+--+-- >>> 1 *~ usSurveyMile+-- 1609.3472186944373 m+--+-- prop> 1 *~ usSurveyMile === 5280 *~ usSurveyFoot+--+-- >>> 1 *~ usSurveyMile :: Length Rational+-- 6336000 % 3937 m+usSurveyMile :: (Fractional a) => Unit 'NonMetric DLength a+usSurveyMile = mkUnitQ (ucum "[mi_us]" "mi" "mile") 5280 $ usSurveyFoot++-- | One acre is 43 560 square feet.+--+-- This acre is based on the 'usSurveyFoot'. For the acre based on the international foot,+-- see 'acre'. While both acres are in use, the difference between them is of little consequence+-- for most applications in which either is used. This is the only acre defined by the UCUM.+--+-- See <https://en.wikipedia.org/wiki/Acre#Differences_between_international_and_US_survey_acres here> for further information.+--+-- >>> 1 *~ usSurveyAcre+-- 4046.872609874252 m^2+--+-- prop> 1 *~ usSurveyAcre === 43560 *~ usSurveyFoot ^ pos2+--+-- >>> 1 *~ usSurveyAcre :: Area Rational+-- 62726400000 % 15499969 m^2+usSurveyAcre :: (Fractional a) => Unit 'NonMetric DArea a+usSurveyAcre = mkUnitQ (ucum "[acr_us]" "ac" "acre") 43560 $ square usSurveyFoot++-- | One avoirdupois pound is a mass, exactly defined in terms of the kilogram by the international+-- yard and pound agreement of 1959.+--+-- See <https://en.wikipedia.org/wiki/Avoirdupois#Internationalization here> for further information.+--+-- >>> 1 *~ poundMass+-- 0.45359237 kg+--+-- >>> 1 *~ poundMass :: Mass Rational+-- 45359237 % 100000000 kg+poundMass :: Fractional a => Unit 'NonMetric DMass a+poundMass = mkUnitQ (ucum "[lb_av]" "lb" "pound") 0.45359237 $ kilo gram++-- | One avoirdupois ounce is one sixteenth of a 'poundMass'.+--+-- See <https://en.wikipedia.org/wiki/Ounce#International_avoirdupois_ounce here> for further information.+--+-- >>> 1 *~ ounce+-- 2.8349523125e-2 kg+--+-- prop> 16 *~ ounce === 1 *~ poundMass+--+-- >>> 1 *~ ounce :: Mass Rational+-- 45359237 % 1600000000 kg+ounce :: Fractional a => Unit 'NonMetric DMass a+ounce = mkUnitQ (ucum "[oz_av]" "oz" "ounce") (1 Prelude./ 16) $ poundMass++-- | One short ton is two thousand 'poundMass'.+--+-- See <https://en.wikipedia.org/wiki/Short_ton#United_States here> for further information.+--+-- >>> 1 *~ shortTon+-- 907.18474 kg+--+-- >>> 1 *~ shortTon :: Mass Rational+-- 45359237 % 50000 kg+shortTon :: Fractional a => Unit 'NonMetric DMass a+shortTon = mkUnitQ (ucum "[ston_av]" "ton" "short ton") 2000 $ poundMass++-- | The pound-force is equal to the gravitational force exerted on a mass+-- of one avoirdupois pound on the surface of Earth.+--+-- This definition is based on standard gravity (the 'gee') and the+-- international avoirdupois 'poundMass'.+--+-- See <https://en.wikipedia.org/wiki/Pound_%28force%29 here> for further information.+--+-- >>> 1 *~ poundForce+-- 4.4482216152605 m kg s^-2+--+-- prop> 1 *~ poundForce === 1 *~ poundMass * (1 *~ gee)+--+-- >>> 1 *~ poundForce :: Force Rational+-- 8896443230521 % 2000000000000 m kg s^-2+poundForce :: Fractional a => Unit 'NonMetric DForce a+poundForce = mkUnitQ (ucum "[lbf_av]" "lbf" "pound force") 1 $ poundMass * gee++-- | One mechanical horsepower is by definition the power necessary+-- to apply a force of 550 'poundForce' through a distance of one 'foot'+-- per 'second'.+--+-- See <https://en.wikipedia.org/wiki/Horsepower#Mechanical_horsepower here> for further information.+--+-- >>> 1 *~ horsepower+-- 745.6998715822702 m^2 kg s^-3+--+-- prop> 1 *~ horsepower === 550 *~ poundForce * (1 *~ foot) / (1 *~ second)+--+-- >>> 1 *~ horsepower :: Power Rational+-- 37284993579113511 % 50000000000000 m^2 kg s^-3+horsepower :: Fractional a => Unit 'NonMetric DPower a+horsepower = mkUnitQ (ucum "[HP]" "hp" "horsepower") 550 $ foot * poundForce / second++-- | The slug is a unit of mass associated with Imperial units and United States customary units.+-- It is a mass that accelerates by 1 foot per second per second when a force of one pound is exerted on it.+--+-- This definition is based on standard gravity (the 'gee'), the international 'foot', and the international avoirdupois 'poundMass'.+--+-- See <https://en.wikipedia.org/wiki/Slug_%28mass%29 here> for further information.+--+-- >>> 1 *~ slug+-- 14.593902937206364 kg+--+-- >>> 1 *~ slug :: Mass Rational+-- 8896443230521 % 609600000000 kg+slug :: Fractional a => Unit 'NonMetric DMass a+slug = mkUnitQ (dimensionalAtom "slug" "slug" "slug") 1 $ poundForce * (second^pos2) / foot++-- | One psi is a pressure of one 'poundForce' per 'square' 'inch' of area.+--+-- See <https://en.wikipedia.org/wiki/Pounds_per_square_inch here> for further information.+--+-- >>> 1 *~ psi+-- 6894.757293168362 m^-1 kg s^-2+--+-- >>> 1 *~ psi :: Pressure Rational+-- 8896443230521 % 1290320000 m^-1 kg s^-2+psi :: Fractional a => Unit 'NonMetric DPressure a+psi = mkUnitQ (ucum "[psi]" "psi" "pound per square inch") 1 $ poundForce / inch ^ pos2++-- | One nautical mile is a unit of length, set by international agreement as being exactly 1 852 meters.+--+-- Historically, it was defined as the distance spanned by one minute of arc along a meridian of the Earth.+--+-- See <https://en.wikipedia.org/wiki/Nautical_mile here> for further information.+--+-- >>> 1 *~ nauticalMile+-- 1852.0 m+--+-- >>> 1 *~ nauticalMile :: Length Rational+-- 1852 % 1 m+nauticalMile :: (Num a) => Unit 'NonMetric DLength a+nauticalMile = mkUnitZ (ucum "[nmi_i]" "NM" "nautical mile") 1852 $ meter++-- | One knot is a velocity equal to one 'nauticalMile' per 'hour'.+--+-- See <https://en.wikipedia.org/wiki/Knot_%28unit%29 here> for further information.+--+-- >>> 1 *~ knot+-- 0.5144444444444445 m s^-1+--+-- >>> 1 *~ knot :: Velocity Rational+-- 463 % 900 m s^-1+knot :: (Fractional a) => Unit 'NonMetric DVelocity a+knot = mkUnitQ (ucum "[kt_i]" "kt" "knot") 1 $ nauticalMile / hour++-- | One revolution is an angle equal to 2*pi radians; a full circle.+--+-- See <https://en.wikipedia.org/wiki/Turn_%28geometry%29 here> for further information.+--+-- >>> 1 *~ revolution+-- 6.283185307179586+--+-- prop> 1 *~ revolution === _2 * pi * (1 *~ radian)+--+-- prop> 1 *~ revolution === 360 *~ degree+revolution :: (Floating a) => Unit 'NonMetric DOne a+revolution = mkUnitR (dimensionalAtom "rev" "rev" "revolution") (2 Prelude.* Prelude.pi) $ radian++solid :: (Floating a) => Unit 'NonMetric DOne a+solid = mkUnitR (dimensionalAtom "solid" "solid" "solid") (4 Prelude.* Prelude.pi) $ steradian++teaspoon :: (Fractional a) => Unit 'NonMetric DVolume a+teaspoon = mkUnitQ (ucum "[tsp_m]" "tsp" "teaspoon") 5 $ milli liter++-- | One btu is is the 'QuantityOfHeat' required to raise the temperature+-- of 1 avoirdupois 'poundMass' of liquid water by 1 'degreeFahrenheit' at a constant pressure of one 'atmosphere'.+--+-- Because this value must be determined experimentally and varies with temperature, several standardized+-- values of the btu have arisen. This is the value based on the International Steam Table calorie,+-- defined by the Fifth International Conference on the Properties of Steam.+--+-- See <https://en.wikipedia.org/wiki/British_thermal_unit#Definitions here> for further information.+--+-- >>> 1 *~ btu+-- 1055.05585262 m^2 kg s^-2+--+-- >>> 1 *~ btu :: Energy Rational+-- 52752792631 % 50000000 m^2 kg s^-2+btu :: Fractional a => Unit 'NonMetric DEnergy a+btu = mkUnitQ (ucum "[Btu_IT]" "btu" "British thermal unit") 1055.05585262 $ joule+++{- $year++The IAU recommends <#note2 [2]> that:++ Although there are several different kinds of year (as there are+ several kinds of day), it is best to regard a year as a Julian+ year of 365.25 days (31557600 s) unless otherwise specified.++-}++-- | One Julian year is a unit of measurement of time defined as exactly 365.25 days of 86 400 'second's each.+--+-- See <https://en.wikipedia.org/wiki/Julian_year_%28astronomy%29 here> for further information.+--+-- prop> 1 *~ year === 365.25 *~ day+--+-- >>> 1 *~ year+-- 3.15576e7 s+--+-- >>> 1 *~ year :: Time Rational+-- 31557600 % 1 s+year :: Num a => Unit 'NonMetric DTime a+year = mkUnitZ (ucum "a_j" "a" "mean Julian year") 31557600 $ second++-- | One Julian decade is ten Julian 'year's.+--+-- prop> 1 *~ decade === 10 *~ year+--+-- >>> 1 *~ decade+-- 3.15576e8 s+--+-- >>> 1 *~ decade :: Time Rational+-- 315576000 % 1 s+decade :: Num a => Unit 'NonMetric DTime a+decade = mkUnitZ (dimensionalAtom "d_j" "dec" "mean Julian decade") 10 $ year++-- | One Julian century is one hundred Julian 'year's, or 35 525 'day's of 86 400 'second's each.+--+-- prop> 1 *~ century === 100 *~ year+--+-- prop> 1 *~ century === 36525 *~ day+--+-- >>> 1 *~ century+-- 3.15576e9 s+--+-- >>> 1 *~ century :: Time Rational+-- 3155760000 % 1 s+century :: Num a => Unit 'NonMetric DTime a+century = mkUnitZ (dimensionalAtom "c_j" "cen" "mean Julian century") 100 $ year++-- | One Julian millennium is one thousand Julian 'year's.+--+-- prop> 1 *~ millennium === 1000 *~ year+--+-- >>> 1 *~ millennium+-- 3.15576e10 s+--+-- >>> 1 *~ millennium :: Time Rational+-- 31557600000 % 1 s+millennium :: Num a => Unit 'NonMetric DTime a+millennium = mkUnitZ (dimensionalAtom "m_j" "mil" "mean Julian millennium") 1000 $ year++{- $pressure-units+It seems that nearly every area of application has its own customary unit for measuring pressure.+We include some of the common ones here. 'psi' was defined earlier.+-}++-- | The bar is exactly 100 000 'Numeric.Units.Dimensional.SIUnits.pascal'.+--+-- From Wikipedia:+--+-- It is about equal to the atmospheric pressure on Earth at sea level.+--+-- >>> 1 *~ bar+-- 100000.0 m^-1 kg s^-2+--+-- >>> 1 *~ bar :: Pressure Rational+-- 100000 % 1 m^-1 kg s^-2+bar :: (Num a) => Unit 'Metric DPressure a+bar = mkUnitZ (ucumMetric "bar" "bar" "bar") 1e5 $ pascal++-- | The "standard atmosphere".+--+-- From Wikipedia <#note3 [3]>:+--+-- The standard atmosphere (atm) is an established constant. It is+-- approximately equal to typical air pressure at earth mean sea+-- level.+--+-- >>> 1 *~ atmosphere+-- 101325.0 m^-1 kg s^-2+--+-- >>> 1 *~ atmosphere :: Pressure Rational+-- 101325 % 1 m^-1 kg s^-2+atmosphere :: (Num a) => Unit 'NonMetric DPressure a+atmosphere = mkUnitZ (ucum "atm" "atm" "standard atmosphere") 101325 $ pascal++-- | The "technical atmosphere"+--+-- From Wikipedia:+--+-- A technical atmosphere (symbol: at) is a non-SI unit of pressure equal+-- to one kilogram-force per square centimeter.+--+-- >>> 1 *~ technicalAtmosphere+-- 98066.5 m^-1 kg s^-2+--+-- >>> 1 *~ technicalAtmosphere :: Pressure Rational+-- 196133 % 2 m^-1 kg s^-2+technicalAtmosphere :: (Fractional a) => Unit 'NonMetric DPressure a+technicalAtmosphere = mkUnitQ (ucum "att" "at" "technical atmosphere") 1 $ kilo gram * gee * centi meter ^ neg2++-- | The conventional value for the pressure exerted by a 1 mm high column of mercury.+--+-- Per Wikipedia <#note4 [4]>, one mmHg (millimeter of mercury) is defined as:+--+-- The pressure exerted at the base of a column of fluid exactly 1 mm high,+-- when the density of the fluid is exactly 13.5951 g/cm^3, at a place+-- where the acceleration of gravity is exactly 9.80665 m/s^2.+--+-- The chosen fluid density approximately corresponds to that of mercury+-- at 0 deg. Under most conditions, 1 mmHg is approximately equal to 1 'torr'.+--+-- >>> 1 *~ mmHg+-- 133.322 m^-1 kg s^-2+--+-- >>> 1 *~ mmHg :: Pressure Rational+-- 66661 % 500 m^-1 kg s^-2+mmHg :: (Fractional a) => Unit 'NonMetric DPressure a+mmHg = milli mHg++mHg :: (Fractional a) => Unit 'Metric DPressure a+mHg = mkUnitQ (ucumMetric "m[Hg]" "m Hg" "meter of mercury") 133.3220 $ kilo pascal++-- | The conventional value for the pressure exerted by a 1 inch high column of mercury.+--+-- Column inches of mercury are also used to measure pressure, especially in+-- meteorological or aeronautical contexts in the United States.+--+-- This is the value defined by UCUM. For the value defined by NIST, see 'inHg_NIST'.+--+-- >>> 1 *~ inHg+-- 3386.3788 m^-1 kg s^-2+--+-- >>> 1 *~ inHg :: Pressure Rational+-- 8465947 % 2500 m^-1 kg s^-2+inHg :: (Fractional a) => Unit 'NonMetric DPressure a+inHg = inHg_UCUM++-- | The conventional value for the pressure exerted by a 1 inch high column of mercury.+--+-- Column inches of mercury are also used to measure pressure, especially in+-- meteorological or aeronautical contexts in the United States.+--+-- This is the value defined by UCUM. For the value defined by NIST, see 'inHg_NIST'.+--+-- >>> 1 *~ inHg_UCUM+-- 3386.3788 m^-1 kg s^-2+--+-- >>> 1 *~ inHg_UCUM :: Pressure Rational+-- 8465947 % 2500 m^-1 kg s^-2+inHg_UCUM :: (Fractional a) => Unit 'NonMetric DPressure a+inHg_UCUM = mkUnitQ (ucum "[in_i'Hg]" "in Hg" "inch of mercury") 1 $ mHg * inch / meter++-- | The conventional value for the pressure exerted by a 1 inch high column of mercury.+--+-- Column inches of mercury are also used to measure pressure, especially in+-- meteorological or aeronautical contexts in the United States.+--+-- This is the value defined by NIST. For the value defined by UCUM, see 'inHg_UCUM'.+--+-- >>> 1 *~ inHg_NIST+-- 3386.389 m^-1 kg s^-2+--+-- >>> 1 *~ inHg_NIST :: Pressure Rational+-- 3386389 % 1000 m^-1 kg s^-2+inHg_NIST :: (Fractional a) => Unit 'NonMetric DPressure a+inHg_NIST = mkUnitQ (dimensionalAtom "[in_i'Hg_NIST]" "in Hg" "inch of mercury") 3.386389e3 $ pascal++-- | One torr (symbol: Torr) is defined as 1/760 'atmosphere', which is approximately equal to 1 'mmHg'.+--+-- See <https://en.wikipedia.org/wiki/Torr here> for further information.+--+-- >>> 1 *~ torr+-- 133.32236842105263 m^-1 kg s^-2+--+-- >>> 1 *~ torr :: Pressure Rational+-- 20265 % 152 m^-1 kg s^-2+torr :: (Fractional a) => Unit 'NonMetric DPressure a+torr = mkUnitQ (dimensionalAtom "Torr" "Torr" "Torr") (1 Prelude./ 760) $ atmosphere++-- | The rad is a deprecated unit of 'AbsorbedDose', defined as+-- 0.01 'gray'.+--+-- See <https://en.wikipedia.org/wiki/Rad_%28unit%29 here> for further information.+--+-- >>> 1 *~ rad+-- 1.0e-2 m^2 s^-2+--+-- >>> 1 *~ rad :: AbsorbedDose Rational+-- 1 % 100 m^2 s^-2+rad :: (Fractional a) => Unit 'Metric DAbsorbedDose a+rad = mkUnitQ (ucumMetric "RAD" "RAD" "RAD") 1 $ centi gray++-- | One Stokes is a unit of 'KinematicViscosity' equal to @1 cm^2 / s@.+--+-- See <https://en.wikipedia.org/wiki/Viscosity#Kinematic_viscosity_.CE.BD here> for further information.+--+-- >>> 1 *~ stokes+-- 1.0e-4 m^2 s^-1+--+-- >>> 1 *~ stokes :: KinematicViscosity Rational+-- 1 % 10000 m^2 s^-1+stokes :: (Fractional a) => Unit 'Metric DKinematicViscosity a+stokes = mkUnitQ (ucumMetric "St" "St" "Stokes") 1 $ centi meter ^ pos2 / second++{- $temperature+These units of temperature are relative. For absolute temperatures, see 'Numeric.Units.Dimensional.SIUnits.fromDegreeCelsiusAbsolute'.+-}++-- | One degree Fahrenheit is a unit of relative temperature equal to 5/9 'kelvin'.+--+-- Note that although the Fahrenheit scale is an absolute temperature scale, this unit is a unit of difference within+-- that scale and measures relative temperature.+--+-- See <https://en.wikipedia.org/wiki/Fahrenheit#Definition_and_conversions here> for further information.+--+-- >>> 1 *~ degreeFahrenheit+-- 0.5555555555555556 K+--+-- >>> 1 *~ degreeFahrenheit :: ThermodynamicTemperature Rational+-- 5 % 9 K+degreeFahrenheit :: (Fractional a) => Unit 'NonMetric DThermodynamicTemperature a+degreeFahrenheit = mkUnitQ (ucum "[degF]" "°F" "degree Fahrenheit") (5 Prelude./ 9) $ degreeCelsius++-- | One degree Rankine is a unit of relative temperature equal to 5/9 'kelvin'.+--+-- Note that although the Rankine scale is an absolute temperature scale, this unit is a unit of difference within+-- that scale and measures relative temperature.+--+-- See <https://en.wikipedia.org/wiki/Rankine_scale here> for further information.+--+-- >>> 1 *~ degreeRankine+-- 0.5555555555555556 K+--+-- >>> 1 *~ degreeRankine :: ThermodynamicTemperature Rational+-- 5 % 9 K+degreeRankine :: (Fractional a) => Unit 'NonMetric DThermodynamicTemperature a+degreeRankine = mkUnitQ (ucum "[degR]" "°R" "degree Rankine") 1 $ degreeFahrenheit++{- $imperial-volumes+Per https://en.wikipedia.org/wiki/Imperial_units and https://en.wikipedia.org/wiki/Cup_(unit)#Imperial_cup.+-}++-- | One imperial gallon is defined exactly in terms of the 'liter'+-- by the Weights and Measures Act 1985.+--+-- See <https://en.wikipedia.org/wiki/Imperial_units#Volume here> for further information.+--+-- >>> 1 *~ imperialGallon+-- 4.54609e-3 m^3+--+-- >>> 1 *~ imperialGallon :: Volume Rational+-- 454609 % 100000000 m^3+imperialGallon :: (Fractional a) => Unit 'NonMetric DVolume a+imperialGallon = mkUnitQ (ucum "[gal_br]" "gal" "gallon") 4.54609 $ liter++-- | One imperial quart is one quarter of an 'imperialGallon'.+--+-- See <https://en.wikipedia.org/wiki/Imperial_units#Volume here> for further information.+--+-- >>> 1 *~ imperialQuart+-- 1.1365225e-3 m^3+--+-- >>> 1 *~ imperialQuart :: Volume Rational+-- 454609 % 400000000 m^3+imperialQuart :: (Fractional a) => Unit 'NonMetric DVolume a+imperialQuart = mkUnitQ (ucum "[qt_br]" "qt" "quart") (1 Prelude./ 4) $ imperialGallon++-- | One imperial pint is one half of an 'imperialQuart'.+--+-- See <https://en.wikipedia.org/wiki/Imperial_units#Volume here> for further information.+--+-- >>> 1 *~ imperialPint+-- 5.6826125e-4 m^3+--+-- >>> 1 *~ imperialPint :: Volume Rational+-- 454609 % 800000000 m^3+imperialPint :: (Fractional a) => Unit 'NonMetric DVolume a+imperialPint = mkUnitQ (ucum "[pt_br]" "pt" "pint") (1 Prelude./ 8) $ imperialGallon++-- | One imperial cup is one half of an 'imperialPint'.+--+-- This unit is not in common use and is does not appear in some sources+-- describing the imperial fluid volume units.+--+-- See <https://en.wikipedia.org/wiki/Cup_%28unit%29#Imperial_cup here> for further information.+--+-- >>> 1 *~ imperialCup+-- 2.84130625e-4 m^3+--+-- >>> 1 *~ imperialCup :: Volume Rational+-- 454609 % 1600000000 m^3+imperialCup :: (Fractional a) => Unit 'NonMetric DVolume a+imperialCup = mkUnitQ (dimensionalAtom "[cup_br]" "cup" "cup") 0.5 $ imperialPint++-- | One imperial gill is one quarter of an 'imperialPint'.+--+-- See <https://en.wikipedia.org/wiki/Imperial_units#Volume here> for further information.+--+-- >>> 1 *~ imperialGill+-- 1.420653125e-4 m^3+--+-- >>> 1 *~ imperialGill :: Volume Rational+-- 454609 % 3200000000 m^3+imperialGill :: (Fractional a) => Unit 'NonMetric DVolume a+imperialGill = mkUnitQ (ucum "[gil_br]" "gill" "gill") (1 Prelude./ 4) $ imperialPint++-- | One imperial fluid ounce is one twentieth of an 'imperialPint'.+--+-- See <https://en.wikipedia.org/wiki/Imperial_units#Volume here> for further information.+--+-- >>> 1 *~ imperialFluidOunce+-- 2.84130625e-5 m^3+--+-- >>> 1 *~ imperialFluidOunce :: Volume Rational+-- 454609 % 16000000000 m^3+imperialFluidOunce :: (Fractional a) => Unit 'NonMetric DVolume a+imperialFluidOunce = mkUnitQ (ucum "[foz_br]" "fl oz" "fluid ounce") (1 Prelude./ 20) $ imperialPint++{- $us-customary-volumes+Per https://www.nist.gov/system/files/documents/2017/05/09/2012-hb44-final.pdf page 452 and https://en.wikipedia.org/wiki/United_States_customary_units#Fluid_volume+Note that there exist rarely-used "dry" variants of units with overlapping names.+-}++-- | One US liquid gallon is a volume of 231 cubic inches.+--+-- See <https://en.wikipedia.org/wiki/Gallon#The_US_liquid_gallon here> for further information.+--+-- >>> 1 *~ usGallon+-- 3.785411784e-3 m^3+--+-- >>> 1 *~ usGallon :: Volume Rational+-- 473176473 % 125000000000 m^3+usGallon :: (Fractional a) => Unit 'NonMetric DVolume a+usGallon = mkUnitQ (ucum "[gal_us]" "gal" "gallon") 231 $ cubic inch++-- | One US liquid quart is one quarter of a 'usGallon'.+--+-- See <https://en.wikipedia.org/wiki/United_States_customary_units#Fluid_volume here> for further information.+--+-- >>> 1 *~ usQuart+-- 9.46352946e-4 m^3+--+-- >>> 1 *~ usQuart :: Volume Rational+-- 473176473 % 500000000000 m^3+usQuart :: (Fractional a) => Unit 'NonMetric DVolume a+usQuart = mkUnitQ (ucum "[qt_us]" "qt" "quart") (1 Prelude./ 4) $ usGallon++-- | One US liquid pint is one half of a 'usQuart'.+--+-- See <https://en.wikipedia.org/wiki/United_States_customary_units#Fluid_volume here> for further information.+--+-- >>> 1 *~ usPint+-- 4.73176473e-4 m^3+--+-- >>> 1 *~ usPint :: Volume Rational+-- 473176473 % 1000000000000 m^3+usPint :: (Fractional a) => Unit 'NonMetric DVolume a+usPint = mkUnitQ (ucum "[pt_us]" "pt" "pint") (1 Prelude./ 8) $ usGallon++-- | One US liquid cup is one half of a 'usPint'.+--+-- See <https://en.wikipedia.org/wiki/United_States_customary_units#Fluid_volume here> for further information.+--+-- >>> 1 *~ usCup+-- 2.365882365e-4 m^3+--+-- >>> 1 *~ usCup :: Volume Rational+-- 473176473 % 2000000000000 m^3+usCup :: (Fractional a) => Unit 'NonMetric DVolume a+usCup = mkUnitQ (ucum "[cup_us]" "cup" "cup") (1 Prelude./ 2) $ usPint++-- | One US liquid gill is one half of a 'usCup'.+--+-- See <https://en.wikipedia.org/wiki/United_States_customary_units#Fluid_volume here> for further information.+--+-- >>> 1 *~ usGill+-- 1.1829411825e-4 m^3+--+-- >>> 1 *~ usGill :: Volume Rational+-- 473176473 % 4000000000000 m^3+usGill :: (Fractional a) => Unit 'NonMetric DVolume a+usGill = mkUnitQ (ucum "[gil_us]" "gill" "gill") (1 Prelude./ 4) $ usPint++-- | One US fluid ounce is 1/128 'usGallon' or 1/8 'usCup'.+--+-- See <https://en.wikipedia.org/wiki/United_States_customary_units#Fluid_volume here> for further information.+--+-- >>> 1 *~ usFluidOunce+-- 2.95735295625e-5 m^3+--+-- >>> 1 *~ usFluidOunce :: Volume Rational+-- 473176473 % 16000000000000 m^3+usFluidOunce :: (Fractional a) => Unit 'NonMetric DVolume a+usFluidOunce = mkUnitQ (ucum "[foz_us]" "fl oz" "fluid ounce") (1 Prelude./ 16) $ usPint -- sic, does not match factor used in imperial system++-- | One Ångström is 1/10 'nano' 'meter'.+--+-- See <https://en.wikipedia.org/wiki/%C3%85ngstr%C3%B6m here> for further information.+--+-- >>> 1 *~ angstrom+-- 1.0e-10 m+--+-- >>> 1 *~ angstrom :: Length Rational+-- 1 % 10000000000 m+angstrom :: (Fractional a) => Unit 'NonMetric DLength a+angstrom = mkUnitQ (ucum "Ao" "Å" "Ångström") 0.1 $ nano meter++-- | One Gauss is 1/10000 'tesla'.+--+-- See <https://en.wikipedia.org/wiki/Gauss_%28unit%29 here> for further information.+--+-- >>> 1 *~ gauss+-- 1.0e-4 kg s^-2 A^-1+--+-- >>> 1 *~ gauss :: MagneticFluxDensity Rational+-- 1 % 10000 kg s^-2 A^-1+gauss :: (Fractional a) => Unit 'NonMetric DMagneticFluxDensity a+gauss = mkUnitQ (ucum "G" "G" "Gauss") 1e-4 $ tesla
src/Numeric/Units/Dimensional/Prelude.hs view
@@ -1,52 +1,52 @@-{- | - Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter - License : BSD3 - - Maintainer : bjorn@buckwalter.se - Stability : Stable - Portability: GHC only - -= Summary - -This module supplies a convenient set of imports for working with the dimensional package, including aliases for common 'Quantity's and 'Dimension's, -and a comprehensive set of SI units and units accepted for use with the SI. - -It re-exports the "Prelude", hiding arithmetic functions whose names collide with the dimensionally-typed versions supplied by this package. - --} -module Numeric.Units.Dimensional.Prelude - ( module Numeric.Units.Dimensional - , module Numeric.Units.Dimensional.Quantities - , module Numeric.Units.Dimensional.SIUnits - , module Numeric.NumType.DK.Integers - , module Control.Category - , module Data.Foldable - , module Prelude - ) where - -import Numeric.Units.Dimensional hiding - ( dmap - ) - -import Numeric.Units.Dimensional.Quantities - -import Numeric.Units.Dimensional.SIUnits - -import Numeric.NumType.DK.Integers - ( neg5, neg4, neg3, neg2, neg1, zero, pos1, pos2, pos3, pos4, pos5 - ) -- Used in exponents. - -import Control.Category - ( Category(..) ) - -import Data.Foldable - ( minimum, maximum ) - -import Prelude hiding - ( (+), (-), (*), (/), (^), (**) - , abs, signum, negate, recip, pi, exp, log, logBase, sqrt - , sin, cos, tan, asin, acos, atan, atan2 - , sinh, cosh, tanh, asinh, acosh, atanh - , sum, product, minimum, maximum - , id, (.) - ) -- Hide definitions overridden by 'Numeric.Dimensional'. +{- |+ Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter+ License : BSD3++ Maintainer : bjorn@buckwalter.se+ Stability : Stable+ Portability: GHC only++= Summary++This module supplies a convenient set of imports for working with the dimensional package, including aliases for common 'Quantity's and 'Dimension's,+and a comprehensive set of SI units and units accepted for use with the SI.++It re-exports the "Prelude", hiding arithmetic functions whose names collide with the dimensionally-typed versions supplied by this package.++-}+module Numeric.Units.Dimensional.Prelude+ ( module Numeric.Units.Dimensional+ , module Numeric.Units.Dimensional.Quantities+ , module Numeric.Units.Dimensional.SIUnits+ , module Numeric.NumType.DK.Integers+ , module Control.Category+ , module Data.Foldable+ , module Prelude+ ) where++import Numeric.Units.Dimensional hiding+ ( dmap+ )++import Numeric.Units.Dimensional.Quantities++import Numeric.Units.Dimensional.SIUnits++import Numeric.NumType.DK.Integers+ ( neg5, neg4, neg3, neg2, neg1, zero, pos1, pos2, pos3, pos4, pos5+ ) -- Used in exponents.++import Control.Category+ ( Category(..) )++import Data.Foldable+ ( minimum, maximum )++import Prelude hiding+ ( (+), (-), (*), (/), (^), (**)+ , abs, signum, negate, recip, pi, exp, log, logBase, sqrt+ , sin, cos, tan, asin, acos, atan, atan2+ , sinh, cosh, tanh, asinh, acosh, atanh+ , sum, product, minimum, maximum+ , id, (.)+ ) -- Hide definitions overridden by 'Numeric.Dimensional'.
src/Numeric/Units/Dimensional/Quantities.hs view
@@ -1,435 +1,436 @@-{-# OPTIONS_HADDOCK show-extensions #-} - -{-# LANGUAGE DataKinds #-} - -{- | - Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter - License : BSD3 - - Maintainer : bjorn@buckwalter.se - Stability : Stable - Portability: GHC only - -= Summary - -This module defines type synonyms for common dimensionalities and -the associated quantity types. Additional dimensionalities and -quantity types will be added on an as-needed basis. - -The definitions in this module are grouped so that a type synonym -for the dimensionality is defined first in terms of base dimension -exponents. Then a type synonym for the corresponding quantity type -is defined. If there are several quantity types with the same -dimensionality type synonyms are provided for each quantity type. - -= References - -1. #note1# http://physics.nist.gov/Pubs/SP811/ - --} - -module Numeric.Units.Dimensional.Quantities -( - -- * Quantities from the NIST Guide - -- $nist-guide - Area, Volume, Velocity, Acceleration, WaveNumber, MassDensity, Density, SpecificVolume, CurrentDensity, - MagneticFieldStrength, AmountOfSubstanceConcentration, Concentration, Luminance, - -- $table3 - PlaneAngle, SolidAngle, Frequency, Force, Pressure, Stress, Energy, Work, QuantityOfHeat, Power, RadiantFlux, - ElectricCharge, QuantityOfElectricity, ElectricPotential, PotentialDifference, ElectromotiveForce, - Capacitance, ElectricResistance, ElectricConductance, MagneticFlux, MagneticFluxDensity, - Inductance, LuminousFlux, Illuminance, CelsiusTemperature, - Activity, AbsorbedDose, SpecificEnergy, Kerma, DoseEquivalent, AmbientDoseEquivalent, DirectionalDoseEquivalent, PersonalDoseEquivalent, EquivalentDose, CatalyticActivity, - -- $table4 - AngularVelocity, AngularAcceleration, DynamicViscosity, MomentOfForce, SurfaceTension, HeatFluxDensity, - Irradiance, RadiantIntensity, Radiance, HeatCapacity, Entropy, SpecificHeatCapacity, SpecificEntropy, - ThermalConductivity, EnergyDensity, ElectricFieldStrength, ElectricChargeDensity, ElectricFluxDensity, Permittivity, Permeability, - MolarEnergy, MolarEntropy, MolarHeatCapacity, Exposure, AbsorbedDoseRate, - -- * Quantities not from the NIST Guide - -- $not-nist-guide - Impulse, Momentum, MassFlow, VolumeFlow, GravitationalParameter, KinematicViscosity, FirstMassMoment, MomentOfInertia, AngularMomentum, - ThermalResistivity, ThermalConductance, ThermalResistance, HeatTransferCoefficient, ThermalAdmittance, ThermalInsulance, - Jerk, Angle, Thrust, Torque, EnergyPerUnitMass, - -- * Powers of Unit Lengths - -- $powers-of-length-units - square, cubic, - -- * Dimension Aliases - -- $dimension-aliases - DArea, DVolume, DVelocity, DAcceleration, DWaveNumber, DMassDensity, DDensity, DSpecificVolume, DCurrentDensity, - DMagneticFieldStrength, DAmountOfSubstanceConcentration, DConcentration, DLuminance, - DPlaneAngle, DSolidAngle, DFrequency, DForce, DPressure, DStress, DEnergy, DWork, DQuantityOfHeat, DPower, DRadiantFlux, - DElectricCharge, DQuantityOfElectricity, DElectricPotential, DPotentialDifference, DElectromotiveForce, - DCapacitance, DElectricResistance, DElectricConductance, DMagneticFlux, DMagneticFluxDensity, - DInductance, DLuminousFlux, DIlluminance, DCelsiusTemperature, - DActivity, DAbsorbedDose, DSpecificEnergy, DKerma, DDoseEquivalent, DAmbientDoseEquivalent, DDirectionalDoseEquivalent, DPersonalDoseEquivalent, DEquivalentDose, DCatalyticActivity, - DAngularVelocity, DAngularAcceleration, DDynamicViscosity, DMomentOfForce, DSurfaceTension, DHeatFluxDensity, - DIrradiance, DRadiantIntensity, DRadiance, DHeatCapacity, DEntropy, DSpecificHeatCapacity, DSpecificEntropy, - DThermalConductivity, DEnergyDensity, DElectricFieldStrength, DElectricChargeDensity, DElectricFluxDensity, DPermittivity, DPermeability, - DMolarEnergy, DMolarEntropy, DMolarHeatCapacity, DExposure, DAbsorbedDoseRate, - DImpulse, DMomentum, DMassFlow, DVolumeFlow, DGravitationalParameter, DKinematicViscosity, DFirstMassMoment, DMomentOfInertia, DAngularMomentum, - DThermalResistivity, DThermalConductance, DThermalResistance, DHeatTransferCoefficient, DThermalAdmittance, DThermalInsulance, - DJerk, DAngle, DThrust, DTorque, DEnergyPerUnitMass -) -where - -import Numeric.Units.Dimensional - ( Dimension (Dim), Quantity, Dimensionless - , DOne, DLuminousIntensity, DThermodynamicTemperature - , Unit, DLength, (^) -- Used only for 'square' and 'cubic'. - , Metricality(..) - ) -import Numeric.NumType.DK.Integers - ( TypeInt (Neg3, Neg2, Neg1, Zero, Pos1, Pos2, Pos3, Pos4) - , pos2, pos3 -- Used only for 'square' and 'cubic'. - ) -import Prelude (Fractional) -import Data.Typeable - -{- $nist-guide -The following quantities are all from the NIST publication "Guide -for the Use of the International System of Units (SI)" <#note1 [1]>. Any -chapters, sections or tables referenced are from <#note1 [1]> unless otherwise -specified. - -For lack of better organization we provide definitions grouped by -table in <#note1 [1]>. - -== Table 2 - -"Examples of SI derived units expressed in terms of SI base units." - --} - -{- $dimension-aliases -For each 'Quantity' alias supplied above, we also supply a corresponding 'Dimension' alias. - -These dimension aliases may be convenient for supplying type signatures for 'Unit's or for other type-level dimensional programming. --} - -type DArea = 'Dim 'Pos2 'Zero 'Zero 'Zero 'Zero 'Zero 'Zero -type Area = Quantity DArea - -type DVolume = 'Dim 'Pos3 'Zero 'Zero 'Zero 'Zero 'Zero 'Zero -type Volume = Quantity DVolume - -type DVelocity = 'Dim 'Pos1 'Zero 'Neg1 'Zero 'Zero 'Zero 'Zero -type Velocity = Quantity DVelocity - -type DAcceleration = 'Dim 'Pos1 'Zero 'Neg2 'Zero 'Zero 'Zero 'Zero -type Acceleration = Quantity DAcceleration - -type DWaveNumber = 'Dim 'Neg1 'Zero 'Zero 'Zero 'Zero 'Zero 'Zero -type WaveNumber = Quantity DWaveNumber - -type DMassDensity = 'Dim 'Neg3 'Pos1 'Zero 'Zero 'Zero 'Zero 'Zero -type DDensity = DMassDensity -type MassDensity = Quantity DMassDensity -type Density = MassDensity -- Short name. - -type DSpecificVolume = 'Dim 'Pos3 'Neg1 'Zero 'Zero 'Zero 'Zero 'Zero -type SpecificVolume = Quantity DSpecificVolume - -type DCurrentDensity = 'Dim 'Neg2 'Zero 'Zero 'Pos1 'Zero 'Zero 'Zero -type CurrentDensity = Quantity DCurrentDensity - -type DMagneticFieldStrength = 'Dim 'Neg1 'Zero 'Zero 'Pos1 'Zero 'Zero 'Zero -type MagneticFieldStrength = Quantity DMagneticFieldStrength - -type DAmountOfSubstanceConcentration = 'Dim 'Neg3 'Zero 'Zero 'Zero 'Zero 'Pos1 'Zero -type DConcentration = DAmountOfSubstanceConcentration -type AmountOfSubstanceConcentration = Quantity DAmountOfSubstanceConcentration -type Concentration = AmountOfSubstanceConcentration -- Short name. - -type DLuminance = 'Dim 'Neg2 'Zero 'Zero 'Zero 'Zero 'Zero 'Pos1 -type Luminance = Quantity DLuminance - - -{- $table3 -== Table 3 - -SI coherent derived units with special names and symbols. - --} - -type DPlaneAngle = DOne -type PlaneAngle = Dimensionless - -type DSolidAngle = DOne -type SolidAngle = Dimensionless - -type DFrequency = 'Dim 'Zero 'Zero 'Neg1 'Zero 'Zero 'Zero 'Zero -type Frequency = Quantity DFrequency - -type DForce = 'Dim 'Pos1 'Pos1 'Neg2 'Zero 'Zero 'Zero 'Zero -type Force = Quantity DForce - -type DPressure = 'Dim 'Neg1 'Pos1 'Neg2 'Zero 'Zero 'Zero 'Zero -type DStress = DPressure -type Pressure = Quantity DPressure -type Stress = Quantity DStress - -type DEnergy = 'Dim 'Pos2 'Pos1 'Neg2 'Zero 'Zero 'Zero 'Zero -type DWork = DEnergy -type DQuantityOfHeat = DEnergy -type Energy = Quantity DEnergy -type Work = Quantity DWork -type QuantityOfHeat = Quantity DQuantityOfHeat - -type DPower = 'Dim 'Pos2 'Pos1 'Neg3 'Zero 'Zero 'Zero 'Zero -type DRadiantFlux = DPower -type Power = Quantity DPower -type RadiantFlux = Quantity DRadiantFlux - -type DElectricCharge = 'Dim 'Zero 'Zero 'Pos1 'Pos1 'Zero 'Zero 'Zero -type DQuantityOfElectricity = DElectricCharge -type ElectricCharge = Quantity DElectricCharge -type QuantityOfElectricity = Quantity DQuantityOfElectricity - -type DElectricPotential = 'Dim 'Pos2 'Pos1 'Neg3 'Neg1 'Zero 'Zero 'Zero -type DPotentialDifference = DElectricPotential -type DElectromotiveForce = DElectricPotential -type ElectricPotential = Quantity DElectricPotential -type PotentialDifference = Quantity DPotentialDifference -type ElectromotiveForce = Quantity DElectromotiveForce - -type DCapacitance = 'Dim 'Neg2 'Neg1 'Pos4 'Pos2 'Zero 'Zero 'Zero -type Capacitance = Quantity DCapacitance - -type DElectricResistance = 'Dim 'Pos2 'Pos1 'Neg3 'Neg2 'Zero 'Zero 'Zero -type ElectricResistance = Quantity DElectricResistance - -type DElectricConductance = 'Dim 'Neg2 'Neg1 'Pos3 'Pos2 'Zero 'Zero 'Zero -type ElectricConductance = Quantity DElectricConductance - -type DMagneticFlux = 'Dim 'Pos2 'Pos1 'Neg2 'Neg1 'Zero 'Zero 'Zero -type MagneticFlux = Quantity DMagneticFlux - -type DMagneticFluxDensity = 'Dim 'Zero 'Pos1 'Neg2 'Neg1 'Zero 'Zero 'Zero -type MagneticFluxDensity = Quantity DMagneticFluxDensity - -type DInductance = 'Dim 'Pos2 'Pos1 'Neg2 'Neg2 'Zero 'Zero 'Zero -type Inductance = Quantity DInductance - -type DLuminousFlux = DLuminousIntensity -type LuminousFlux = Quantity DLuminousFlux - -type DIlluminance = 'Dim 'Neg2 'Zero 'Zero 'Zero 'Zero 'Zero 'Pos1 -type Illuminance = Quantity DIlluminance - -type DCelsiusTemperature = DThermodynamicTemperature -type CelsiusTemperature = Quantity DCelsiusTemperature - -type DActivity = DFrequency -- Activity of a radionuclide. -type Activity = Quantity DActivity - -type DAbsorbedDose = 'Dim 'Pos2 'Zero 'Neg2 'Zero 'Zero 'Zero 'Zero -type DSpecificEnergy = DAbsorbedDose -type DKerma = DAbsorbedDose -type AbsorbedDose = Quantity DAbsorbedDose -type SpecificEnergy = Quantity DSpecificEnergy -- Specific energy imparted. -type Kerma = Quantity DKerma - -type DDoseEquivalent = DAbsorbedDose -type DAmbientDoseEquivalent = DDoseEquivalent -type DDirectionalDoseEquivalent = DDoseEquivalent -type DPersonalDoseEquivalent = DDoseEquivalent -type DEquivalentDose = DDoseEquivalent -type DoseEquivalent = Quantity DDoseEquivalent -type AmbientDoseEquivalent = DoseEquivalent -type DirectionalDoseEquivalent = DoseEquivalent -type PersonalDoseEquivalent = DoseEquivalent -type EquivalentDose = DoseEquivalent - -type DCatalyticActivity = 'Dim 'Zero 'Zero 'Neg1 'Zero 'Zero 'Pos1 'Zero -type CatalyticActivity = Quantity DCatalyticActivity - -{- $table4 -== Table 4 - -"Examples of SI coherent derived units expressed with the aid of SI derived -units having special names and symbols." - -We use the same grouping as for table 2. - --} - -type DAngularVelocity = DFrequency -type AngularVelocity = Quantity DAngularVelocity - -type DAngularAcceleration = 'Dim 'Zero 'Zero 'Neg2 'Zero 'Zero 'Zero 'Zero -type AngularAcceleration = Quantity DAngularAcceleration - -type DDynamicViscosity = 'Dim 'Neg1 'Pos1 'Neg1 'Zero 'Zero 'Zero 'Zero -type DynamicViscosity = Quantity DDynamicViscosity - -type DMomentOfForce = DEnergy -type MomentOfForce = Quantity DMomentOfForce - -type DSurfaceTension = 'Dim 'Zero 'Pos1 'Neg2 'Zero 'Zero 'Zero 'Zero -type SurfaceTension = Quantity DSurfaceTension - -type DHeatFluxDensity = 'Dim 'Zero 'Pos1 'Neg3 'Zero 'Zero 'Zero 'Zero -type DIrradiance = DHeatFluxDensity -type HeatFluxDensity = Quantity DHeatFluxDensity -type Irradiance = Quantity DIrradiance - -type DRadiantIntensity = DPower -type RadiantIntensity = Quantity DRadiantIntensity - -type DRadiance = DIrradiance -type Radiance = Quantity DRadiance - -type DHeatCapacity = 'Dim 'Pos2 'Pos1 'Neg2 'Zero 'Neg1 'Zero 'Zero -type DEntropy = DHeatCapacity -type HeatCapacity = Quantity DHeatCapacity -type Entropy = Quantity DEntropy - -type DSpecificHeatCapacity = 'Dim 'Pos2 'Zero 'Neg2 'Zero 'Neg1 'Zero 'Zero -type DSpecificEntropy = DSpecificHeatCapacity -type SpecificHeatCapacity = Quantity DSpecificHeatCapacity -type SpecificEntropy = Quantity DSpecificEntropy - -{- - -Specific energy was already defined in table 3. - --} - -type DThermalConductivity = 'Dim 'Pos1 'Pos1 'Neg3 'Zero 'Neg1 'Zero 'Zero -type ThermalConductivity = Quantity DThermalConductivity - -type DEnergyDensity = DPressure -type EnergyDensity = Quantity DEnergyDensity - -type DElectricFieldStrength = 'Dim 'Pos1 'Pos1 'Neg3 'Neg1 'Zero 'Zero 'Zero -type ElectricFieldStrength = Quantity DElectricFieldStrength - -type DElectricChargeDensity = 'Dim 'Neg3 'Zero 'Pos1 'Pos1 'Zero 'Zero 'Zero -type ElectricChargeDensity = Quantity DElectricChargeDensity - -type DElectricFluxDensity = 'Dim 'Neg2 'Zero 'Pos1 'Pos1 'Zero 'Zero 'Zero -type ElectricFluxDensity = Quantity DElectricFluxDensity - -type DPermittivity = 'Dim 'Neg3 'Neg1 'Pos4 'Pos2 'Zero 'Zero 'Zero -type Permittivity = Quantity DPermittivity - -type DPermeability = 'Dim 'Pos1 'Pos1 'Neg2 'Neg2 'Zero 'Zero 'Zero -type Permeability = Quantity DPermeability - -type DMolarEnergy = 'Dim 'Pos2 'Pos1 'Neg2 'Zero 'Zero 'Neg1 'Zero -type MolarEnergy = Quantity DMolarEnergy - -type DMolarEntropy = 'Dim 'Pos2 'Pos1 'Neg2 'Zero 'Neg1 'Neg1 'Zero -type DMolarHeatCapacity = DMolarEntropy -type MolarEntropy = Quantity DMolarEntropy -type MolarHeatCapacity = Quantity DMolarHeatCapacity - -type DExposure = 'Dim 'Zero 'Neg1 'Pos1 'Pos1 'Zero 'Zero 'Zero -type Exposure = Quantity DExposure -- Exposure to x and gamma rays. - -type DAbsorbedDoseRate = 'Dim 'Pos2 'Zero 'Neg3 'Zero 'Zero 'Zero 'Zero -type AbsorbedDoseRate = Quantity DAbsorbedDoseRate - -{- $not-nist-guide -Here we define additional quantities on an as-needed basis. We also -provide some synonyms that we anticipate will be useful. --} - -type DImpulse = 'Dim 'Pos1 'Pos1 'Neg1 'Zero 'Zero 'Zero 'Zero -type Impulse = Quantity DImpulse - -type DMomentum = DImpulse -type Momentum = Quantity DMomentum - -type DMassFlow = 'Dim 'Zero 'Pos1 'Neg1 'Zero 'Zero 'Zero 'Zero -type MassFlow = Quantity DMassFlow - -type DVolumeFlow = 'Dim 'Pos3 'Zero 'Neg1 'Zero 'Zero 'Zero 'Zero -type VolumeFlow = Quantity DVolumeFlow - -type DGravitationalParameter = 'Dim 'Pos3 'Zero 'Neg2 'Zero 'Zero 'Zero 'Zero -type GravitationalParameter = Quantity DGravitationalParameter - -type DKinematicViscosity = 'Dim 'Pos2 'Zero 'Neg1 'Zero 'Zero 'Zero 'Zero -type KinematicViscosity = Quantity DKinematicViscosity - -type DFirstMassMoment = 'Dim 'Pos1 'Pos1 'Zero 'Zero 'Zero 'Zero 'Zero -type FirstMassMoment = Quantity DFirstMassMoment - -type DMomentOfInertia = 'Dim 'Pos2 'Pos1 'Zero 'Zero 'Zero 'Zero 'Zero -type MomentOfInertia = Quantity DMomentOfInertia - -type DAngularMomentum = 'Dim 'Pos2 'Pos1 'Neg1 'Zero 'Zero 'Zero 'Zero -type AngularMomentum = Quantity DAngularMomentum - -{- - -The reciprocal of thermal conductivity. - --} - -type DThermalResistivity = 'Dim 'Neg1 'Neg1 'Pos3 'Zero 'Pos1 'Zero 'Zero -type ThermalResistivity = Quantity DThermalResistivity - -{- - -Thermal conductance and resistance quantities after http://en.wikipedia.org/wiki/Thermal_conductivity#Definitions. - --} - -type DThermalConductance = 'Dim 'Pos2 'Pos1 'Neg3 'Zero 'Neg1 'Zero 'Zero -type ThermalConductance = Quantity DThermalConductance - -type DThermalResistance = 'Dim 'Neg2 'Neg1 'Pos3 'Zero 'Pos1 'Zero 'Zero -type ThermalResistance = Quantity DThermalResistance - -type DHeatTransferCoefficient = 'Dim 'Zero 'Pos1 'Neg3 'Zero 'Neg1 'Zero 'Zero -type HeatTransferCoefficient = Quantity DHeatTransferCoefficient - -type DThermalAdmittance = DHeatTransferCoefficient -type ThermalAdmittance = HeatTransferCoefficient - -type DThermalInsulance = 'Dim 'Zero 'Neg1 'Pos3 'Zero 'Pos1 'Zero 'Zero -type ThermalInsulance = Quantity DThermalInsulance - -type DJerk = 'Dim 'Pos1 'Zero 'Neg3 'Zero 'Zero 'Zero 'Zero -type Jerk = Quantity DJerk - -type Angle = PlaneAngle -- Abbreviation -type DAngle = DPlaneAngle -- Abbreviation - -type Thrust = Force -type DThrust = DForce - -type Torque = MomentOfForce -type DTorque = DMomentOfForce - -type EnergyPerUnitMass = SpecificEnergy -type DEnergyPerUnitMass = DSpecificEnergy - -{- $powers-of-length-units -It is permissible to express powers of length units by prefixing -'square' and 'cubic' (see section 9.6 "Spelling unit names raised -to powers" of <#note1 [1]>). - -These definitions may seem slightly out of place but these is no -obvious place where they should be. Here they are at least close -to the definitions of 'DArea' and 'DVolume'. --} - --- $setup --- >>> import Numeric.Units.Dimensional.Prelude - --- | Constructs a unit of area from a unit of length, taking the area of a square whose sides are that length. --- --- >>> 64 *~ square meter == (8 *~ meter) ^ pos2 --- True -square :: (Fractional a, Typeable m) => Unit m DLength a -> Unit 'NonMetric DArea a -square x = x ^ pos2 - --- | Constructs a unit of volume from a unit of length, taking the volume of a cube whose sides are that length. --- --- >>> 64 *~ cubic meter == (4 *~ meter) ^ pos3 --- True -cubic :: (Fractional a, Typeable m) => Unit m DLength a -> Unit 'NonMetric DVolume a -cubic x = x ^ pos3 +{-# OPTIONS_HADDOCK show-extensions #-}++{-# LANGUAGE DataKinds #-}++{- |+ Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter+ License : BSD3++ Maintainer : bjorn@buckwalter.se+ Stability : Stable+ Portability: GHC only++= Summary++This module defines type synonyms for common dimensionalities and+the associated quantity types. Additional dimensionalities and+quantity types will be added on an as-needed basis.++The definitions in this module are grouped so that a type synonym+for the dimensionality is defined first in terms of base dimension+exponents. Then a type synonym for the corresponding quantity type+is defined. If there are several quantity types with the same+dimensionality, type synonyms are provided for each quantity type.++= References++1. #note1# https://www.nist.gov/pml/special-publication-811++-}++module Numeric.Units.Dimensional.Quantities+(+ -- * Quantities from the NIST Guide+ -- $nist-guide+ Area, Volume, Velocity, Acceleration, WaveNumber, MassDensity, Density, SpecificVolume, CurrentDensity,+ MagneticFieldStrength, AmountOfSubstanceConcentration, Concentration, Luminance,+ -- $table3+ PlaneAngle, SolidAngle, Frequency, Force, Pressure, Stress, Energy, Work, QuantityOfHeat, Power, RadiantFlux,+ ElectricCharge, QuantityOfElectricity, ElectricPotential, PotentialDifference, ElectromotiveForce,+ Capacitance, ElectricResistance, ElectricConductance, MagneticFlux, MagneticFluxDensity,+ Inductance, LuminousFlux, Illuminance, CelsiusTemperature,+ Activity, AbsorbedDose, SpecificEnergy, Kerma, DoseEquivalent, AmbientDoseEquivalent, DirectionalDoseEquivalent, PersonalDoseEquivalent, EquivalentDose, CatalyticActivity,+ -- $table4+ AngularVelocity, AngularAcceleration, DynamicViscosity, MomentOfForce, SurfaceTension, HeatFluxDensity,+ Irradiance, RadiantIntensity, Radiance, HeatCapacity, Entropy, SpecificHeatCapacity, SpecificEntropy,+ ThermalConductivity, EnergyDensity, ElectricFieldStrength, ElectricChargeDensity, ElectricFluxDensity, Permittivity, Permeability,+ MolarEnergy, MolarEntropy, MolarHeatCapacity, Exposure, AbsorbedDoseRate,+ -- * Quantities not from the NIST Guide+ -- $not-nist-guide+ Impulse, Momentum, MassFlow, VolumeFlow, GravitationalParameter, KinematicViscosity, FirstMassMoment, MomentOfInertia, AngularMomentum,+ ThermalResistivity, ThermalConductance, ThermalResistance, HeatTransferCoefficient, ThermalAdmittance, ThermalInsulance,+ Jerk, Angle, Thrust, Torque, EnergyPerUnitMass,+ -- * Powers of Unit Lengths+ -- $powers-of-length-units+ square, cubic,+ -- * Dimension Aliases+ -- $dimension-aliases+ DArea, DVolume, DVelocity, DAcceleration, DWaveNumber, DMassDensity, DDensity, DSpecificVolume, DCurrentDensity,+ DMagneticFieldStrength, DAmountOfSubstanceConcentration, DConcentration, DLuminance,+ DPlaneAngle, DSolidAngle, DFrequency, DForce, DPressure, DStress, DEnergy, DWork, DQuantityOfHeat, DPower, DRadiantFlux,+ DElectricCharge, DQuantityOfElectricity, DElectricPotential, DPotentialDifference, DElectromotiveForce,+ DCapacitance, DElectricResistance, DElectricConductance, DMagneticFlux, DMagneticFluxDensity,+ DInductance, DLuminousFlux, DIlluminance, DCelsiusTemperature,+ DActivity, DAbsorbedDose, DSpecificEnergy, DKerma, DDoseEquivalent, DAmbientDoseEquivalent, DDirectionalDoseEquivalent, DPersonalDoseEquivalent, DEquivalentDose, DCatalyticActivity,+ DAngularVelocity, DAngularAcceleration, DDynamicViscosity, DMomentOfForce, DSurfaceTension, DHeatFluxDensity,+ DIrradiance, DRadiantIntensity, DRadiance, DHeatCapacity, DEntropy, DSpecificHeatCapacity, DSpecificEntropy,+ DThermalConductivity, DEnergyDensity, DElectricFieldStrength, DElectricChargeDensity, DElectricFluxDensity, DPermittivity, DPermeability,+ DMolarEnergy, DMolarEntropy, DMolarHeatCapacity, DExposure, DAbsorbedDoseRate,+ DImpulse, DMomentum, DMassFlow, DVolumeFlow, DGravitationalParameter, DKinematicViscosity, DFirstMassMoment, DMomentOfInertia, DAngularMomentum,+ DThermalResistivity, DThermalConductance, DThermalResistance, DHeatTransferCoefficient, DThermalAdmittance, DThermalInsulance,+ DJerk, DAngle, DThrust, DTorque, DEnergyPerUnitMass+)+where++import Numeric.Units.Dimensional+ ( Dimension (Dim), Quantity, Dimensionless+ , DOne, DLuminousIntensity, DThermodynamicTemperature+ , Unit, DLength, (^) -- Used only for 'square' and 'cubic'.+ , Metricality(..)+ )+import Numeric.NumType.DK.Integers+ ( TypeInt (Neg3, Neg2, Neg1, Zero, Pos1, Pos2, Pos3, Pos4)+ , pos2, pos3 -- Used only for 'square' and 'cubic'.+ )+import Prelude (Fractional)+import Data.Typeable++{- $nist-guide+The following quantities are all from the NIST publication "Guide+for the Use of the International System of Units (SI)" <#note1 [1]>. Any+chapters, sections or tables referenced are from <#note1 [1]> unless otherwise+specified.++For lack of better organization we provide definitions grouped by+table in <#note1 [1]>.++== Table 2++"Examples of SI derived units expressed in terms of SI base units."++-}++{- $dimension-aliases+For each 'Quantity' alias supplied above, we also supply a corresponding 'Dimension' alias.++These dimension aliases may be convenient for supplying type signatures for 'Unit's or for other type-level dimensional programming.+-}++type DArea = 'Dim 'Pos2 'Zero 'Zero 'Zero 'Zero 'Zero 'Zero+type Area = Quantity DArea++type DVolume = 'Dim 'Pos3 'Zero 'Zero 'Zero 'Zero 'Zero 'Zero+type Volume = Quantity DVolume++type DVelocity = 'Dim 'Pos1 'Zero 'Neg1 'Zero 'Zero 'Zero 'Zero+type Velocity = Quantity DVelocity++type DAcceleration = 'Dim 'Pos1 'Zero 'Neg2 'Zero 'Zero 'Zero 'Zero+type Acceleration = Quantity DAcceleration++type DWaveNumber = 'Dim 'Neg1 'Zero 'Zero 'Zero 'Zero 'Zero 'Zero+type WaveNumber = Quantity DWaveNumber++type DMassDensity = 'Dim 'Neg3 'Pos1 'Zero 'Zero 'Zero 'Zero 'Zero+type DDensity = DMassDensity+type MassDensity = Quantity DMassDensity+type Density = MassDensity -- Short name.++type DSpecificVolume = 'Dim 'Pos3 'Neg1 'Zero 'Zero 'Zero 'Zero 'Zero+type SpecificVolume = Quantity DSpecificVolume++type DCurrentDensity = 'Dim 'Neg2 'Zero 'Zero 'Pos1 'Zero 'Zero 'Zero+type CurrentDensity = Quantity DCurrentDensity++type DMagneticFieldStrength = 'Dim 'Neg1 'Zero 'Zero 'Pos1 'Zero 'Zero 'Zero+type MagneticFieldStrength = Quantity DMagneticFieldStrength++type DAmountOfSubstanceConcentration = 'Dim 'Neg3 'Zero 'Zero 'Zero 'Zero 'Pos1 'Zero+type DConcentration = DAmountOfSubstanceConcentration+type AmountOfSubstanceConcentration = Quantity DAmountOfSubstanceConcentration+type Concentration = AmountOfSubstanceConcentration -- Short name.++type DLuminance = 'Dim 'Neg2 'Zero 'Zero 'Zero 'Zero 'Zero 'Pos1+type Luminance = Quantity DLuminance+++{- $table3+== Table 3++SI coherent derived units with special names and symbols.++-}++type DPlaneAngle = DOne+type PlaneAngle = Dimensionless++type DSolidAngle = DOne+type SolidAngle = Dimensionless++type DFrequency = 'Dim 'Zero 'Zero 'Neg1 'Zero 'Zero 'Zero 'Zero+type Frequency = Quantity DFrequency++type DForce = 'Dim 'Pos1 'Pos1 'Neg2 'Zero 'Zero 'Zero 'Zero+type Force = Quantity DForce++type DPressure = 'Dim 'Neg1 'Pos1 'Neg2 'Zero 'Zero 'Zero 'Zero+type DStress = DPressure+type Pressure = Quantity DPressure+type Stress = Quantity DStress++type DEnergy = 'Dim 'Pos2 'Pos1 'Neg2 'Zero 'Zero 'Zero 'Zero+type DWork = DEnergy+type DQuantityOfHeat = DEnergy+type Energy = Quantity DEnergy+type Work = Quantity DWork+type QuantityOfHeat = Quantity DQuantityOfHeat++type DPower = 'Dim 'Pos2 'Pos1 'Neg3 'Zero 'Zero 'Zero 'Zero+type DRadiantFlux = DPower+type Power = Quantity DPower+type RadiantFlux = Quantity DRadiantFlux++type DElectricCharge = 'Dim 'Zero 'Zero 'Pos1 'Pos1 'Zero 'Zero 'Zero+type DQuantityOfElectricity = DElectricCharge+type ElectricCharge = Quantity DElectricCharge+type QuantityOfElectricity = Quantity DQuantityOfElectricity++type DElectricPotential = 'Dim 'Pos2 'Pos1 'Neg3 'Neg1 'Zero 'Zero 'Zero+type DPotentialDifference = DElectricPotential+type DElectromotiveForce = DElectricPotential+type ElectricPotential = Quantity DElectricPotential+type PotentialDifference = Quantity DPotentialDifference+type ElectromotiveForce = Quantity DElectromotiveForce++type DCapacitance = 'Dim 'Neg2 'Neg1 'Pos4 'Pos2 'Zero 'Zero 'Zero+type Capacitance = Quantity DCapacitance++type DElectricResistance = 'Dim 'Pos2 'Pos1 'Neg3 'Neg2 'Zero 'Zero 'Zero+type ElectricResistance = Quantity DElectricResistance++type DElectricConductance = 'Dim 'Neg2 'Neg1 'Pos3 'Pos2 'Zero 'Zero 'Zero+type ElectricConductance = Quantity DElectricConductance++type DMagneticFlux = 'Dim 'Pos2 'Pos1 'Neg2 'Neg1 'Zero 'Zero 'Zero+type MagneticFlux = Quantity DMagneticFlux++type DMagneticFluxDensity = 'Dim 'Zero 'Pos1 'Neg2 'Neg1 'Zero 'Zero 'Zero+type MagneticFluxDensity = Quantity DMagneticFluxDensity++type DInductance = 'Dim 'Pos2 'Pos1 'Neg2 'Neg2 'Zero 'Zero 'Zero+type Inductance = Quantity DInductance++type DLuminousFlux = DLuminousIntensity+type LuminousFlux = Quantity DLuminousFlux++type DIlluminance = 'Dim 'Neg2 'Zero 'Zero 'Zero 'Zero 'Zero 'Pos1+type Illuminance = Quantity DIlluminance++type DCelsiusTemperature = DThermodynamicTemperature+type CelsiusTemperature = Quantity DCelsiusTemperature++type DActivity = DFrequency -- Activity of a radionuclide.+type Activity = Quantity DActivity++type DAbsorbedDose = 'Dim 'Pos2 'Zero 'Neg2 'Zero 'Zero 'Zero 'Zero+type DSpecificEnergy = DAbsorbedDose+type DKerma = DAbsorbedDose+type AbsorbedDose = Quantity DAbsorbedDose+type SpecificEnergy = Quantity DSpecificEnergy -- Specific energy imparted.+type Kerma = Quantity DKerma++type DDoseEquivalent = DAbsorbedDose+type DAmbientDoseEquivalent = DDoseEquivalent+type DDirectionalDoseEquivalent = DDoseEquivalent+type DPersonalDoseEquivalent = DDoseEquivalent+type DEquivalentDose = DDoseEquivalent+type DoseEquivalent = Quantity DDoseEquivalent+type AmbientDoseEquivalent = DoseEquivalent+type DirectionalDoseEquivalent = DoseEquivalent+type PersonalDoseEquivalent = DoseEquivalent+type EquivalentDose = DoseEquivalent++type DCatalyticActivity = 'Dim 'Zero 'Zero 'Neg1 'Zero 'Zero 'Pos1 'Zero+type CatalyticActivity = Quantity DCatalyticActivity++{- $table4+== Table 4++"Examples of SI coherent derived units expressed with the aid of SI derived+units having special names and symbols."++We use the same grouping as for table 2.++-}++type DAngularVelocity = DFrequency+type AngularVelocity = Quantity DAngularVelocity++type DAngularAcceleration = 'Dim 'Zero 'Zero 'Neg2 'Zero 'Zero 'Zero 'Zero+type AngularAcceleration = Quantity DAngularAcceleration++type DDynamicViscosity = 'Dim 'Neg1 'Pos1 'Neg1 'Zero 'Zero 'Zero 'Zero+type DynamicViscosity = Quantity DDynamicViscosity++type DMomentOfForce = DEnergy+type MomentOfForce = Quantity DMomentOfForce++type DSurfaceTension = 'Dim 'Zero 'Pos1 'Neg2 'Zero 'Zero 'Zero 'Zero+type SurfaceTension = Quantity DSurfaceTension++type DHeatFluxDensity = 'Dim 'Zero 'Pos1 'Neg3 'Zero 'Zero 'Zero 'Zero+type DIrradiance = DHeatFluxDensity+type HeatFluxDensity = Quantity DHeatFluxDensity+type Irradiance = Quantity DIrradiance++type DRadiantIntensity = DPower+type RadiantIntensity = Quantity DRadiantIntensity++type DRadiance = DIrradiance+type Radiance = Quantity DRadiance++type DHeatCapacity = 'Dim 'Pos2 'Pos1 'Neg2 'Zero 'Neg1 'Zero 'Zero+type DEntropy = DHeatCapacity+type HeatCapacity = Quantity DHeatCapacity+type Entropy = Quantity DEntropy++type DSpecificHeatCapacity = 'Dim 'Pos2 'Zero 'Neg2 'Zero 'Neg1 'Zero 'Zero+type DSpecificEntropy = DSpecificHeatCapacity+type SpecificHeatCapacity = Quantity DSpecificHeatCapacity+type SpecificEntropy = Quantity DSpecificEntropy++{-++Specific energy was already defined in table 3.++-}++type DThermalConductivity = 'Dim 'Pos1 'Pos1 'Neg3 'Zero 'Neg1 'Zero 'Zero+type ThermalConductivity = Quantity DThermalConductivity++type DEnergyDensity = DPressure+type EnergyDensity = Quantity DEnergyDensity++type DElectricFieldStrength = 'Dim 'Pos1 'Pos1 'Neg3 'Neg1 'Zero 'Zero 'Zero+type ElectricFieldStrength = Quantity DElectricFieldStrength++type DElectricChargeDensity = 'Dim 'Neg3 'Zero 'Pos1 'Pos1 'Zero 'Zero 'Zero+type ElectricChargeDensity = Quantity DElectricChargeDensity++type DElectricFluxDensity = 'Dim 'Neg2 'Zero 'Pos1 'Pos1 'Zero 'Zero 'Zero+type ElectricFluxDensity = Quantity DElectricFluxDensity++type DPermittivity = 'Dim 'Neg3 'Neg1 'Pos4 'Pos2 'Zero 'Zero 'Zero+type Permittivity = Quantity DPermittivity++type DPermeability = 'Dim 'Pos1 'Pos1 'Neg2 'Neg2 'Zero 'Zero 'Zero+type Permeability = Quantity DPermeability++type DMolarEnergy = 'Dim 'Pos2 'Pos1 'Neg2 'Zero 'Zero 'Neg1 'Zero+type MolarEnergy = Quantity DMolarEnergy++type DMolarEntropy = 'Dim 'Pos2 'Pos1 'Neg2 'Zero 'Neg1 'Neg1 'Zero+type DMolarHeatCapacity = DMolarEntropy+type MolarEntropy = Quantity DMolarEntropy+type MolarHeatCapacity = Quantity DMolarHeatCapacity++type DExposure = 'Dim 'Zero 'Neg1 'Pos1 'Pos1 'Zero 'Zero 'Zero+type Exposure = Quantity DExposure -- Exposure to x and gamma rays.++type DAbsorbedDoseRate = 'Dim 'Pos2 'Zero 'Neg3 'Zero 'Zero 'Zero 'Zero+type AbsorbedDoseRate = Quantity DAbsorbedDoseRate++{- $not-nist-guide+Here we define additional quantities on an as-needed basis. We also+provide some synonyms that we anticipate will be useful.+-}++type DImpulse = 'Dim 'Pos1 'Pos1 'Neg1 'Zero 'Zero 'Zero 'Zero+type Impulse = Quantity DImpulse++type DMomentum = DImpulse+type Momentum = Quantity DMomentum++type DMassFlow = 'Dim 'Zero 'Pos1 'Neg1 'Zero 'Zero 'Zero 'Zero+type MassFlow = Quantity DMassFlow++type DVolumeFlow = 'Dim 'Pos3 'Zero 'Neg1 'Zero 'Zero 'Zero 'Zero+type VolumeFlow = Quantity DVolumeFlow++type DGravitationalParameter = 'Dim 'Pos3 'Zero 'Neg2 'Zero 'Zero 'Zero 'Zero+type GravitationalParameter = Quantity DGravitationalParameter++type DKinematicViscosity = 'Dim 'Pos2 'Zero 'Neg1 'Zero 'Zero 'Zero 'Zero+type KinematicViscosity = Quantity DKinematicViscosity++type DFirstMassMoment = 'Dim 'Pos1 'Pos1 'Zero 'Zero 'Zero 'Zero 'Zero+type FirstMassMoment = Quantity DFirstMassMoment++type DMomentOfInertia = 'Dim 'Pos2 'Pos1 'Zero 'Zero 'Zero 'Zero 'Zero+type MomentOfInertia = Quantity DMomentOfInertia++type DAngularMomentum = 'Dim 'Pos2 'Pos1 'Neg1 'Zero 'Zero 'Zero 'Zero+type AngularMomentum = Quantity DAngularMomentum++{-++The reciprocal of thermal conductivity.++-}++type DThermalResistivity = 'Dim 'Neg1 'Neg1 'Pos3 'Zero 'Pos1 'Zero 'Zero+type ThermalResistivity = Quantity DThermalResistivity++{-++Thermal conductance and resistance quantities after https://en.wikipedia.org/wiki/Thermal_conductivity#Definitions.++-}++type DThermalConductance = 'Dim 'Pos2 'Pos1 'Neg3 'Zero 'Neg1 'Zero 'Zero+type ThermalConductance = Quantity DThermalConductance++type DThermalResistance = 'Dim 'Neg2 'Neg1 'Pos3 'Zero 'Pos1 'Zero 'Zero+type ThermalResistance = Quantity DThermalResistance++type DHeatTransferCoefficient = 'Dim 'Zero 'Pos1 'Neg3 'Zero 'Neg1 'Zero 'Zero+type HeatTransferCoefficient = Quantity DHeatTransferCoefficient++type DThermalAdmittance = DHeatTransferCoefficient+type ThermalAdmittance = HeatTransferCoefficient++type DThermalInsulance = 'Dim 'Zero 'Neg1 'Pos3 'Zero 'Pos1 'Zero 'Zero+type ThermalInsulance = Quantity DThermalInsulance++type DJerk = 'Dim 'Pos1 'Zero 'Neg3 'Zero 'Zero 'Zero 'Zero+type Jerk = Quantity DJerk++type Angle = PlaneAngle -- Abbreviation+type DAngle = DPlaneAngle -- Abbreviation++type Thrust = Force+type DThrust = DForce++type Torque = MomentOfForce+type DTorque = DMomentOfForce++type EnergyPerUnitMass = SpecificEnergy+type DEnergyPerUnitMass = DSpecificEnergy++{- $powers-of-length-units+It is permissible to express powers of length units by prefixing+'square' and 'cubic' (see section 9.6 "Spelling unit names raised+to powers" of <#note1 [1]>).++These definitions may seem slightly out of place but these is no+obvious place where they should be. Here they are at least close+to the definitions of 'DArea' and 'DVolume'.+-}++-- $setup+-- >>> :set -fno-warn-type-defaults+-- >>> import Numeric.Units.Dimensional.Prelude++-- | Constructs a unit of area from a unit of length, taking the area of a square whose sides are that length.+--+-- >>> 64 *~ square meter == (8 *~ meter) ^ pos2+-- True+square :: (Fractional a, Typeable m) => Unit m DLength a -> Unit 'NonMetric DArea a+square x = x ^ pos2++-- | Constructs a unit of volume from a unit of length, taking the volume of a cube whose sides are that length.+--+-- >>> 64 *~ cubic meter == (4 *~ meter) ^ pos3+-- True+cubic :: (Fractional a, Typeable m) => Unit m DLength a -> Unit 'NonMetric DVolume a+cubic x = x ^ pos3
src/Numeric/Units/Dimensional/SIUnits.hs view
@@ -1,314 +1,344 @@-{-# LANGUAGE DataKinds #-} -{-# LANGUAGE RankNTypes #-} - -{- | - Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter - License : BSD3 - - Maintainer : bjorn@buckwalter.se - Stability : Stable - Portability: GHC only - -= Summary - -This module defines the SI prefixes, the SI base units and the SI -derived units. It also defines the units outside of the SI that are -accepted for use with the SI. Any chapters, sections or tables -referenced are from <#note1 [1]> unless otherwise specified. - -= References - -1. #note1# http://physics.nist.gov/Pubs/SP811/ -2. #note2# http://en.wikipedia.org/wiki/Minute_of_arc -3. #note3# http://en.wikipedia.org/wiki/Astronomical_unit - --} - -module Numeric.Units.Dimensional.SIUnits -( - -- * SI Base Units - -- $base-units - metre, meter, gram, second, ampere, kelvin, mole, candela, - -- * SI Derived Units - -- $derived-units - radian, steradian, hertz, newton, pascal, joule, watt, coulomb, volt, farad, ohm, siemens, weber, tesla, henry, lumen, lux, - -- ** Celsius Temperature - -- $celsius - degreeCelsius, fromDegreeCelsiusAbsolute, toDegreeCelsiusAbsolute, - -- ** Units Admitted for Reasons of Safeguarding Human Health - -- $health - becquerel, gray, sievert, katal, - -- * Units Accepted for Use with the SI - -- $accepted-units - minute, hour, day, - hectare, litre, liter, tonne, metricTon, - -- ** Units of Plane Angle - -- $arc-units - degree, arcminute, arcsecond, - -- $arc-units-alternate - degreeOfArc, minuteOfArc, secondOfArc, - -- ** Units Formerly Defined By Experiment - -- $values-obtained-experimentally - astronomicalUnit, - -- * SI Prefixes - -- $multiples - deka, deca, hecto, kilo, mega, giga, tera, peta, exa, zetta, yotta, - -- $submultiples - deci, centi, milli, micro, nano, pico, femto, atto, zepto, yocto, - -- $reified-prefixes - Prefix, applyPrefix, siPrefixes -) -where - -import Data.Ratio -import Numeric.Units.Dimensional -import Numeric.Units.Dimensional.Quantities -import Numeric.Units.Dimensional.UnitNames (Prefix, siPrefixes) -import qualified Numeric.Units.Dimensional.UnitNames as N -import Numeric.Units.Dimensional.UnitNames.Internal (ucum, ucumMetric) -import qualified Numeric.Units.Dimensional.UnitNames.Internal as I -import Numeric.NumType.DK.Integers ( pos3 ) -import Prelude ( Eq(..), ($), Num, Fractional, Floating, otherwise, error) -import qualified Prelude - -{- $multiples -Prefixes are used to form decimal multiples and submultiples of SI -Units as described in section 4.4. We will define the SI prefixes -in terms of the 'prefix' function which applies a scale factor to a -unit. - -By defining SI prefixes as functions applied to a 'Unit' we satisfy -section 6.2.6 "Unacceptability of stand-alone prefixes". - -We define all SI prefixes from Table 5. Multiples first. --} - -applyMultiple :: (Num a) => Prefix -> Unit 'Metric d a -> Unit 'NonMetric d a -applyMultiple p u | denominator x == 1 = mkUnitZ n' (numerator x) u - | otherwise = error "Attempt to apply a submultiple prefix as a multiple." - where - n' = N.applyPrefix p (name u) - x = N.scaleFactor p - -deka, deca, hecto, kilo, mega, giga, tera, peta, exa, zetta, yotta - :: Num a => Unit 'Metric d a -> Unit 'NonMetric d a -deka = applyMultiple I.deka -- International English. -deca = deka -- American English. -hecto = applyMultiple I.hecto -kilo = applyMultiple I.kilo -mega = applyMultiple I.mega -giga = applyMultiple I.giga -tera = applyMultiple I.tera -peta = applyMultiple I.peta -exa = applyMultiple I.exa -zetta = applyMultiple I.zetta -yotta = applyMultiple I.yotta - -{- $submultiples -Then the submultiples. --} - -applyPrefix :: (Fractional a) => Prefix -> Unit 'Metric d a -> Unit 'NonMetric d a -applyPrefix p u = mkUnitQ n' x u - where - n' = N.applyPrefix p (name u) - x = N.scaleFactor p - -deci, centi, milli, micro, nano, pico, femto, atto, zepto, yocto - :: Fractional a => Unit 'Metric d a -> Unit 'NonMetric d a -deci = applyPrefix I.deci -centi = applyPrefix I.centi -milli = applyPrefix I.milli -micro = applyPrefix I.micro -nano = applyPrefix I.nano -pico = applyPrefix I.pico -femto = applyPrefix I.femto -atto = applyPrefix I.atto -zepto = applyPrefix I.zepto -yocto = applyPrefix I.yocto - -{- $reified-prefixes - -We supply an explicit representation of an SI prefix, along with a function to apply one and a -list of all prefixes defined by the SI. - --} - -{- $base-units -These are the base units from section 4.1. To avoid a -myriad of one-letter functions that would doubtlessly cause clashes -and frustration in users' code we spell out all unit names in full, -as we did for prefixes. We also elect to spell the unit names in -singular form, as allowed by section 9.7 "Other spelling conventions". - -We define the SI base units in the order of table 1. --} - -metre, meter :: Num a => Unit 'Metric DLength a -metre = mkUnitZ I.nMeter 1 siUnit -- International English. -meter = metre -- American English. - -{- - -For mass the SI base unit is kilogram. For sensible prefixes we -define gram here (see section 6.2.7 "Prefixes and the kilogram"). -The drawback is that we are forced to use 'Fractional'. - --} - -gram :: Fractional a => Unit 'Metric DMass a -gram = mkUnitQ I.nGram 1e-3 siUnit -second :: Num a => Unit 'Metric DTime a -second = mkUnitZ I.nSecond 1 siUnit -ampere :: Num a => Unit 'Metric DElectricCurrent a -ampere = mkUnitZ I.nAmpere 1 siUnit -kelvin :: Num a => Unit 'Metric DThermodynamicTemperature a -kelvin = mkUnitZ I.nKelvin 1 siUnit -mole :: Num a => Unit 'Metric DAmountOfSubstance a -mole = mkUnitZ I.nMole 1 siUnit -candela :: Num a => Unit 'Metric DLuminousIntensity a -candela = mkUnitZ I.nCandela 1 siUnit - -{- $derived-units -From Table 3, SI derived units with special names and symbols, including the -radian and steradian. --} - -radian :: Num a => Unit 'Metric DPlaneAngle a -radian = mkUnitZ (ucumMetric "rad" "rad" "radian") 1 siUnit -- meter * meter ^ neg1 -steradian :: Num a => Unit 'Metric DSolidAngle a -steradian = mkUnitZ (ucumMetric "sr" "sr" "steradian") 1 siUnit -- meter ^ pos2 * meter ^ neg2 -hertz :: Num a => Unit 'Metric DFrequency a -hertz = mkUnitZ (ucumMetric "Hz" "Hz" "Hertz") 1 $ siUnit -newton :: Num a => Unit 'Metric DForce a -newton = mkUnitZ (ucumMetric "N" "N" "Newton") 1 $ siUnit -pascal :: Num a => Unit 'Metric DPressure a -pascal = mkUnitZ (ucumMetric "Pa" "Pa" "Pascal") 1 $ siUnit -joule :: Num a => Unit 'Metric DEnergy a -joule = mkUnitZ (ucumMetric "J" "J" "Joule") 1 $ siUnit -watt :: Num a => Unit 'Metric DPower a -watt = mkUnitZ (ucumMetric "W" "W" "Watt") 1 $ siUnit -coulomb :: Num a => Unit 'Metric DElectricCharge a -coulomb = mkUnitZ (ucumMetric "C" "C" "Coulomb") 1 $ siUnit -volt :: Num a => Unit 'Metric DElectricPotential a -volt = mkUnitZ (ucumMetric "V" "V" "Volt") 1 $ siUnit -farad :: Num a => Unit 'Metric DCapacitance a -farad = mkUnitZ (ucumMetric "F" "F" "Farad") 1 $ siUnit -ohm :: Num a => Unit 'Metric DElectricResistance a -ohm = mkUnitZ (ucumMetric "Ohm" "Ω" "Ohm") 1 $ siUnit -siemens :: Num a => Unit 'Metric DElectricConductance a -siemens = mkUnitZ (ucumMetric "S" "S" "Siemens") 1 $ siUnit -weber :: Num a => Unit 'Metric DMagneticFlux a -weber = mkUnitZ (ucumMetric "Wb" "Wb" "Weber") 1 $ siUnit -tesla :: Num a => Unit 'Metric DMagneticFluxDensity a -tesla = mkUnitZ (ucumMetric "T" "T" "Tesla") 1 $ siUnit -henry :: Num a => Unit 'Metric DInductance a -henry = mkUnitZ (ucumMetric "H" "H" "Henry") 1 $ siUnit - -{- -We defer the definition of Celcius temperature to another section (would -appear here if we stricly followed table 3). --} - -lumen :: Num a => Unit 'Metric DLuminousFlux a -lumen = mkUnitZ (ucumMetric "lm" "lm" "lumen") 1 $ siUnit -lux :: Num a => Unit 'Metric DIlluminance a -lux = mkUnitZ (ucumMetric "lx" "lx" "lux") 1 $ siUnit - -{- $celsius -A problematic area is units which increase proportionally to the -base SI units but cross zero at a different point. An example would -be degrees Celsius (see section 4.2.1.1). The author feels that it -is appropriate to define a unit for use with relative quantities -(taking only into account the proportionality) and complement the -unit with functions for converting absolute values. - -The function 'fromDegreeCelsiusAbsolute' should be used in lieu of -"*~ degreeCelsius" when working with absolute temperatures. Similarily, -'toDegreeCelsiusAbsolute' should be used in lieu of "/~ degreeCelsius" -when working with absolute temperatures. --} - -degreeCelsius :: Num a => Unit 'Metric DCelsiusTemperature a -degreeCelsius = kelvin - -fromDegreeCelsiusAbsolute :: Floating a => a -> ThermodynamicTemperature a -fromDegreeCelsiusAbsolute x = x *~ degreeCelsius + 273.15 *~ degreeCelsius -toDegreeCelsiusAbsolute :: Floating a => ThermodynamicTemperature a -> a -toDegreeCelsiusAbsolute x = (x - 273.15 *~ degreeCelsius) /~ degreeCelsius - -{- $health - -The last units from Table 3 are SI derived units with special names and symbols admitted for reasons -of safeguarding human health. --} - -becquerel :: Num a => Unit 'Metric DActivity a -becquerel = mkUnitZ (ucumMetric "Bq" "Bq" "Becquerel") 1 $ siUnit -gray :: Num a => Unit 'Metric DAbsorbedDose a -gray = mkUnitZ (ucumMetric "Gy" "Gy" "Gray") 1 $ siUnit -sievert :: Num a => Unit 'Metric DDoseEquivalent a -sievert = mkUnitZ (ucumMetric "Sv" "Sv" "Sievert") 1 $ siUnit -katal :: Num a => Unit 'Metric DCatalyticActivity a -katal = mkUnitZ (ucumMetric "kat" "kat" "katal") 1 $ siUnit - -{- $accepted-units -There are several units that are not strictly part of the SI but -are either permanently or temporarily accepted for use with the SI. -We define the permanently accepted ones in this module. - -From Table 6, Units accepted for use with the SI. - -We start with time which we grant exclusive rights to 'minute' and -'second'. --} -minute, hour, day :: Num a => Unit 'NonMetric DTime a -minute = mkUnitZ (ucum "min" "min" "minute") 60 $ second -hour = mkUnitZ (ucum "h" "h" "hour") 60 $ minute -day = mkUnitZ (ucum "d" "d" "day") 24 $ hour -- Mean solar day. - -{- $arc-units - -Since 'minute' and 'second' are already in use for time we use -'arcminute' and 'arcsecond' <#note2 [2]> for plane angle instead. --} - -degree, arcminute, arcsecond :: Floating a => Unit 'NonMetric DPlaneAngle a -degree = mkUnitR (ucum "deg" "°" "degree") (Prelude.pi Prelude./ 180) $ radian -arcminute = mkUnitR (ucum "'" "'" "arcminute") (Prelude.recip 60) $ degreeOfArc -arcsecond = mkUnitR (ucum "''" "''" "arcsecond") (Prelude.recip 60) $ minuteOfArc - -{- $arc-units-alternate -Alternate (longer) forms of the above. In particular 'degreeOfArc' -can be used if there is a percieved need to disambiguate from e.g. -temperature. --} - -degreeOfArc, minuteOfArc, secondOfArc :: Floating a => Unit 'NonMetric DPlaneAngle a -degreeOfArc = degree -secondOfArc = arcsecond -minuteOfArc = arcminute - -hectare :: Fractional a => Unit 'NonMetric DArea a -hectare = square (hecto meter) - -litre, liter :: Fractional a => Unit 'Metric DVolume a -litre = mkUnitQ (ucumMetric "L" "L" "litre") 1 $ deci meter ^ pos3 -- International English. -liter = litre -- American English. - -tonne, metricTon :: Num a => Unit 'Metric DMass a -tonne = mkUnitZ (ucumMetric "t" "t" "tonne") 1000 $ siUnit -- Name in original SI text. -metricTon = tonne -- American name. - -{- $values-obtained-experimentally -We decline to provide here those units - listed in Table 7 - which, -while accepted for use with the SI, have values which are determined experimentally. -For versioning purposes, those units can be found in "Numeric.Units.Dimensional.NonSI". - -However, in 2012 the IAU redefined the astronomical unit as a conventional -unit of length directly tied to the meter, with a length of exactly -149 597 870 700 m and the official abbreviation of au <#note3 [3]>. We therefore include it here. --} - -astronomicalUnit :: Num a => Unit 'NonMetric DLength a -astronomicalUnit = mkUnitZ (ucum "AU" "AU" "astronomical unit") 149597870700 $ meter +{-# LANGUAGE DataKinds #-}+{-# LANGUAGE RankNTypes #-}++{- |+ Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter+ License : BSD3++ Maintainer : bjorn@buckwalter.se+ Stability : Stable+ Portability: GHC only++= Summary++This module defines the SI prefixes, the SI base units and the SI+derived units. It also defines the units outside of the SI that are+accepted for use with the SI. Any chapters, sections or tables+referenced are from <#note1 [1]> unless otherwise specified.++= References++1. #note1# https://www.nist.gov/pml/special-publication-811+2. #note2# https://en.wikipedia.org/wiki/Minute_of_arc+3. #note3# https://en.wikipedia.org/wiki/Astronomical_unit++-}++module Numeric.Units.Dimensional.SIUnits+(+ -- * SI Base Units+ -- $base-units+ metre, meter, gram, second, ampere, kelvin, mole, candela,+ -- * SI Derived Units+ -- $derived-units+ radian, steradian, hertz, newton, pascal, joule, watt, coulomb, volt, farad, ohm, siemens, weber, tesla, henry, lumen, lux,+ -- ** Celsius Temperature+ -- $celsius+ degreeCelsius, fromDegreeCelsiusAbsolute, toDegreeCelsiusAbsolute,+ -- ** Units Admitted for Reasons of Safeguarding Human Health+ -- $health+ becquerel, gray, sievert, katal,+ -- * Units Accepted for Use with the SI+ -- $accepted-units+ minute, hour, day,+ hectare, litre, liter, tonne, metricTon,+ -- ** Units of Plane Angle+ -- $arc-units+ degree, arcminute, arcsecond,+ -- $arc-units-alternate+ degreeOfArc, minuteOfArc, secondOfArc,+ -- ** Units Formerly Defined By Experiment+ -- $values-obtained-experimentally+ astronomicalUnit,+ -- * SI Prefixes+ -- $multiples+ deka, deca, hecto, kilo, mega, giga, tera, peta, exa, zetta, yotta, ronna, quetta,+ -- $submultiples+ deci, centi, milli, micro, nano, pico, femto, atto, zepto, yocto, ronto, quecto,+ -- $reified-prefixes+ Prefix, applyPrefix, siPrefixes+)+where++import Data.Ratio+import Numeric.Units.Dimensional+import Numeric.Units.Dimensional.Quantities+import Numeric.Units.Dimensional.UnitNames (Prefix, siPrefixes)+import qualified Numeric.Units.Dimensional.UnitNames as N+import Numeric.Units.Dimensional.UnitNames.Internal (ucum, ucumMetric)+import qualified Numeric.Units.Dimensional.UnitNames.Internal as I+import Numeric.NumType.DK.Integers ( pos3 )+import Prelude ( Eq(..), ($), Num, Fractional, Floating, otherwise, error)+import qualified Prelude++{- $multiples+Prefixes are used to form decimal multiples and submultiples of SI+Units as described in section 4.4.++By defining SI prefixes as functions applied to a 'Unit' we satisfy+section 6.2.6 "Unacceptability of stand-alone prefixes".++We define all SI prefixes from Table 5. Multiples first.+-}++applyMultiple :: (Num a) => Prefix -> Unit 'Metric d a -> Unit 'NonMetric d a+applyMultiple p u | denominator x == 1 = mkUnitZ n' (numerator x) u+ | otherwise = error "Attempt to apply a submultiple prefix as a multiple."+ where+ n' = N.applyPrefix p (name u)+ x = N.scaleFactor p++deca, deka, hecto, kilo, mega, giga, tera, peta, exa, zetta, yotta, ronna, quetta+ :: Num a => Unit 'Metric d a -> Unit 'NonMetric d a+-- | The "deca" prefix, denoting a factor of 10.+deca = applyMultiple I.deca -- International English.+-- | An alias for 'deca'.+deka = deca -- American English.+-- | The "hecto" prefix, denoting a factor of 100.+hecto = applyMultiple I.hecto+-- | The "kilo" prefix, denoting a factor of 1000.+kilo = applyMultiple I.kilo+-- | The "mega" prefix, denoting a factor of 10^6.+mega = applyMultiple I.mega+-- | The "giga" prefix, denoting a factor of 10^9.+giga = applyMultiple I.giga+-- | The "tera" prefix, denoting a factor of 10^12.+tera = applyMultiple I.tera+-- | The "peta" prefix, denoting a factor of 10^15.+peta = applyMultiple I.peta+-- | The "exa" prefix, denoting a factor of 10^18.+exa = applyMultiple I.exa+-- | The "zetta" prefix, denoting a factor of 10^21.+zetta = applyMultiple I.zetta+-- | The "yotta" prefix, denoting a factor of 10^24.+yotta = applyMultiple I.yotta+-- | The "ronna" prefix, denoting a factor of 10^27.+ronna = applyMultiple I.ronna+-- | The "quetta" prefix, denoting a factor of 10^30.+quetta = applyMultiple I.quetta+++{- $submultiples+Then the submultiples.+-}++-- | Apply a 'Prefix' to a metric 'Unit'.+applyPrefix :: (Fractional a) => Prefix -> Unit 'Metric d a -> Unit 'NonMetric d a+applyPrefix p u = mkUnitQ n' x u+ where+ n' = N.applyPrefix p (name u)+ x = N.scaleFactor p++deci, centi, milli, micro, nano, pico, femto, atto, zepto, yocto, ronto, quecto+ :: Fractional a => Unit 'Metric d a -> Unit 'NonMetric d a+-- | The "deci" prefix, denoting a factor of 0.1.+deci = applyPrefix I.deci+-- | The "centi" prefix, denoting a factor of 0.01.+centi = applyPrefix I.centi+-- | The "milli" prefix, denoting a factor of 0.001.+milli = applyPrefix I.milli+-- | The "micro" prefix, denoting a factor of 10^-6.+micro = applyPrefix I.micro+-- | The "nano" prefix, denoting a factor of 10^-9.+nano = applyPrefix I.nano+-- | The "pico" prefix, denoting a factor of 10^-12.+pico = applyPrefix I.pico+-- | The "femto" prefix, denoting a factor of 10^-15.+femto = applyPrefix I.femto+-- | The "atto" prefix, denoting a factor of 10^-18.+atto = applyPrefix I.atto+-- | The "zepto" prefix, denoting a factor of 10^-21.+zepto = applyPrefix I.zepto+-- | The "yocto" prefix, denoting a factor of 10^-24.+yocto = applyPrefix I.yocto+-- | The "ronto" prefix, denoting a factor of 10^-27.+ronto = applyPrefix I.ronto+-- | The "quecto" prefix, denoting a factor of 10^-30.+quecto = applyPrefix I.quecto+++{- $reified-prefixes++We supply an explicit representation of an SI prefix, along with a function to apply one and a+list of all prefixes defined by the SI.++-}++{- $base-units+These are the base units from section 4.1. To avoid a+myriad of one-letter functions that would doubtlessly cause clashes+and frustration in users' code, we spell out all unit names in full,+as we did for prefixes. We also elect to spell the unit names in+singular form, as allowed by section 9.7 "Other spelling conventions".++We define the SI base units in the order of table 1.+-}++metre, meter :: Num a => Unit 'Metric DLength a+metre = mkUnitZ I.nMeter 1 siUnit -- International English.+meter = metre -- American English.++{-++For mass the SI base unit is kilogram. For sensible prefixes we+define gram here (see section 6.2.7 "Prefixes and the kilogram").+The drawback is that we are forced to use 'Fractional'.++-}++gram :: Fractional a => Unit 'Metric DMass a+gram = mkUnitQ I.nGram 1e-3 siUnit+second :: Num a => Unit 'Metric DTime a+second = mkUnitZ I.nSecond 1 siUnit+ampere :: Num a => Unit 'Metric DElectricCurrent a+ampere = mkUnitZ I.nAmpere 1 siUnit+kelvin :: Num a => Unit 'Metric DThermodynamicTemperature a+kelvin = mkUnitZ I.nKelvin 1 siUnit+mole :: Num a => Unit 'Metric DAmountOfSubstance a+mole = mkUnitZ I.nMole 1 siUnit+candela :: Num a => Unit 'Metric DLuminousIntensity a+candela = mkUnitZ I.nCandela 1 siUnit++{- $derived-units+From Table 3, SI derived units with special names and symbols, including the+radian and steradian.+-}++radian :: Num a => Unit 'Metric DPlaneAngle a+radian = mkUnitZ (ucumMetric "rad" "rad" "radian") 1 siUnit -- meter * meter ^ neg1+steradian :: Num a => Unit 'Metric DSolidAngle a+steradian = mkUnitZ (ucumMetric "sr" "sr" "steradian") 1 siUnit -- meter ^ pos2 * meter ^ neg2+hertz :: Num a => Unit 'Metric DFrequency a+hertz = mkUnitZ (ucumMetric "Hz" "Hz" "Hertz") 1 $ siUnit+newton :: Num a => Unit 'Metric DForce a+newton = mkUnitZ (ucumMetric "N" "N" "Newton") 1 $ siUnit+pascal :: Num a => Unit 'Metric DPressure a+pascal = mkUnitZ (ucumMetric "Pa" "Pa" "Pascal") 1 $ siUnit+joule :: Num a => Unit 'Metric DEnergy a+joule = mkUnitZ (ucumMetric "J" "J" "Joule") 1 $ siUnit+watt :: Num a => Unit 'Metric DPower a+watt = mkUnitZ (ucumMetric "W" "W" "Watt") 1 $ siUnit+coulomb :: Num a => Unit 'Metric DElectricCharge a+coulomb = mkUnitZ (ucumMetric "C" "C" "Coulomb") 1 $ siUnit+volt :: Num a => Unit 'Metric DElectricPotential a+volt = mkUnitZ (ucumMetric "V" "V" "Volt") 1 $ siUnit+farad :: Num a => Unit 'Metric DCapacitance a+farad = mkUnitZ (ucumMetric "F" "F" "Farad") 1 $ siUnit+ohm :: Num a => Unit 'Metric DElectricResistance a+ohm = mkUnitZ (ucumMetric "Ohm" "Ω" "Ohm") 1 $ siUnit+siemens :: Num a => Unit 'Metric DElectricConductance a+siemens = mkUnitZ (ucumMetric "S" "S" "Siemens") 1 $ siUnit+weber :: Num a => Unit 'Metric DMagneticFlux a+weber = mkUnitZ (ucumMetric "Wb" "Wb" "Weber") 1 $ siUnit+tesla :: Num a => Unit 'Metric DMagneticFluxDensity a+tesla = mkUnitZ (ucumMetric "T" "T" "Tesla") 1 $ siUnit+henry :: Num a => Unit 'Metric DInductance a+henry = mkUnitZ (ucumMetric "H" "H" "Henry") 1 $ siUnit++{-+We defer the definition of Celcius temperature to another section (would+appear here if we stricly followed table 3).+-}++lumen :: Num a => Unit 'Metric DLuminousFlux a+lumen = mkUnitZ (ucumMetric "lm" "lm" "lumen") 1 $ siUnit+lux :: Num a => Unit 'Metric DIlluminance a+lux = mkUnitZ (ucumMetric "lx" "lx" "lux") 1 $ siUnit++{- $celsius+A problematic area is units which increase proportionally to the+base SI units but cross zero at a different point. An example would+be degrees Celsius (see section 4.2.1.1). The author feels that it+is appropriate to define a unit for use with relative quantities+(taking only into account the proportionality) and complement the+unit with functions for converting absolute values.++The function 'fromDegreeCelsiusAbsolute' should be used in lieu of+"*~ degreeCelsius" when working with absolute temperatures. Similarily,+'toDegreeCelsiusAbsolute' should be used in lieu of "/~ degreeCelsius"+when working with absolute temperatures.+-}++degreeCelsius :: Num a => Unit 'Metric DCelsiusTemperature a+degreeCelsius = kelvin++fromDegreeCelsiusAbsolute :: Floating a => a -> ThermodynamicTemperature a+fromDegreeCelsiusAbsolute x = x *~ degreeCelsius + 273.15 *~ degreeCelsius+toDegreeCelsiusAbsolute :: Floating a => ThermodynamicTemperature a -> a+toDegreeCelsiusAbsolute x = (x - 273.15 *~ degreeCelsius) /~ degreeCelsius++{- $health++The last units from Table 3 are SI derived units with special names and symbols admitted for reasons+of safeguarding human health.+-}++becquerel :: Num a => Unit 'Metric DActivity a+becquerel = mkUnitZ (ucumMetric "Bq" "Bq" "Becquerel") 1 $ siUnit+gray :: Num a => Unit 'Metric DAbsorbedDose a+gray = mkUnitZ (ucumMetric "Gy" "Gy" "Gray") 1 $ siUnit+sievert :: Num a => Unit 'Metric DDoseEquivalent a+sievert = mkUnitZ (ucumMetric "Sv" "Sv" "Sievert") 1 $ siUnit+katal :: Num a => Unit 'Metric DCatalyticActivity a+katal = mkUnitZ (ucumMetric "kat" "kat" "katal") 1 $ siUnit++{- $accepted-units+There are several units that are not strictly part of the SI but+are either permanently or temporarily accepted for use with the SI.+We define the permanently accepted ones in this module.++From Table 6, Units accepted for use with the SI.++We start with time which we grant exclusive rights to 'minute' and+'second'.+-}+minute, hour, day :: Num a => Unit 'NonMetric DTime a+minute = mkUnitZ (ucum "min" "min" "minute") 60 $ second+hour = mkUnitZ (ucum "h" "h" "hour") 60 $ minute+day = mkUnitZ (ucum "d" "d" "day") 24 $ hour -- Mean solar day.++{- $arc-units++Since 'minute' and 'second' are already in use for time we use+'arcminute' and 'arcsecond' <#note2 [2]> for plane angle instead.+-}++degree, arcminute, arcsecond :: Floating a => Unit 'NonMetric DPlaneAngle a+degree = mkUnitR (ucum "deg" "°" "degree") (Prelude.pi Prelude./ 180) $ radian+arcminute = mkUnitR (ucum "'" "'" "arcminute") (Prelude.recip 60) $ degreeOfArc+arcsecond = mkUnitR (ucum "''" "''" "arcsecond") (Prelude.recip 60) $ minuteOfArc++{- $arc-units-alternate+Alternate (longer) forms of the above. In particular 'degreeOfArc'+can be used if there is a percieved need to disambiguate from e.g.+temperature.+-}++degreeOfArc, minuteOfArc, secondOfArc :: Floating a => Unit 'NonMetric DPlaneAngle a+degreeOfArc = degree+secondOfArc = arcsecond+minuteOfArc = arcminute++hectare :: Fractional a => Unit 'NonMetric DArea a+hectare = square (hecto meter)++litre, liter :: Fractional a => Unit 'Metric DVolume a+litre = mkUnitQ (ucumMetric "L" "L" "litre") 1 $ deci meter ^ pos3 -- International English.+liter = litre -- American English.++tonne, metricTon :: Num a => Unit 'Metric DMass a+tonne = mkUnitZ (ucumMetric "t" "t" "tonne") 1000 $ siUnit -- Name in original SI text.+metricTon = tonne -- American name.++{- $values-obtained-experimentally+We decline to provide here those units - listed in Table 7 - which,+while accepted for use with the SI, have values which are determined experimentally.+For versioning purposes, those units can be found in "Numeric.Units.Dimensional.NonSI".++However, in 2012 the IAU redefined the astronomical unit as a conventional+unit of length directly tied to the meter, with a length of exactly+149 597 870 700 m and the official abbreviation of au <#note3 [3]>. We therefore include it here.+-}++astronomicalUnit :: Num a => Unit 'NonMetric DLength a+astronomicalUnit = mkUnitZ (ucum "au" "au" "astronomical unit") 149597870700 $ meter
src/Numeric/Units/Dimensional/UnitNames.hs view
@@ -1,37 +1,37 @@-{-# LANGUAGE PatternSynonyms #-} - -{- | - Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter - License : BSD3 - - Maintainer : bjorn@buckwalter.se - Stability : Stable - Portability: GHC only - -This module provides types and functions for manipulating unit names. - -Please note that the details of the name representation may be less stable than the other APIs -provided by this package, as new features using them are still being developed. - --} -module Numeric.Units.Dimensional.UnitNames -( - -- * Data Types - UnitName, NameAtom, Prefix, PrefixName, Metricality(..), - -- * Construction of Unit Names - atom, applyPrefix, (*), (/), (^), product, reduce, grouped, - -- * Standard Names - baseUnitName, siPrefixes, nOne, - -- * Inspecting Prefixes - prefixName, scaleFactor, - -- * Convenience Type Synonyms for Unit Name Transformations - UnitNameTransformer, UnitNameTransformer2, - -- * Forgetting Unwanted Phantom Types - weaken, strengthen, relax, - name_en, abbreviation_en, asAtomic -) -where - -import Numeric.Units.Dimensional.UnitNames.Internal -import Numeric.Units.Dimensional.Variants -import Prelude hiding ((*), (/), (^), product) +{-# LANGUAGE PatternSynonyms #-}++{- |+ Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter+ License : BSD3++ Maintainer : bjorn@buckwalter.se+ Stability : Stable+ Portability: GHC only++This module provides types and functions for manipulating unit names.++Please note that the details of the name representation may be less stable than the other APIs+provided by this package, as new features using them are still being developed.++-}+module Numeric.Units.Dimensional.UnitNames+(+ -- * Data Types+ UnitName, NameAtom, Prefix, PrefixName, Metricality(..),+ -- * Construction of Unit Names+ atom, applyPrefix, (*), (/), (^), product, reduce, grouped,+ -- * Standard Names+ baseUnitName, siPrefixes, nOne,+ -- * Inspecting Prefixes+ prefixName, scaleFactor,+ -- * Convenience Type Synonyms for Unit Name Transformations+ UnitNameTransformer, UnitNameTransformer2,+ -- * Forgetting Unwanted Phantom Types+ weaken, strengthen, relax,+ name_en, abbreviation_en, asAtomic+)+where++import Numeric.Units.Dimensional.UnitNames.Internal+import Numeric.Units.Dimensional.Variants+import Prelude hiding ((*), (/), (^), product)
src/Numeric/Units/Dimensional/UnitNames/InterchangeNames.hs view
@@ -1,41 +1,41 @@-{-# LANGUAGE DeriveDataTypeable #-} -{-# LANGUAGE DeriveGeneric #-} - -module Numeric.Units.Dimensional.UnitNames.InterchangeNames -( - InterchangeNameAuthority(..), - InterchangeName(..), - HasInterchangeName(..) -) -where - -import Control.DeepSeq -import Data.Data -import GHC.Generics -import Prelude - --- | Represents the authority which issued an interchange name for a unit. -data InterchangeNameAuthority = UCUM -- ^ The interchange name originated with the Unified Code for Units of Measure. - | DimensionalLibrary -- ^ The interchange name originated with the dimensional library. - | Custom -- ^ The interchange name originated with a user of the dimensional library. - deriving (Eq, Ord, Show, Data, Typeable, Generic) - -instance NFData InterchangeNameAuthority where -- instance is derived from Generic instance - -data InterchangeName = InterchangeName { name :: String, authority :: InterchangeNameAuthority, isAtomic :: Bool } - deriving (Eq, Ord, Data, Typeable, Generic) - -instance NFData InterchangeName where -- instance is derived from Generic instance - -instance Show InterchangeName where - show n = name n ++ " (Issued by " ++ show (authority n) ++ ")" - --- | Determines the authority which issued the interchange name of a unit or unit name. --- For composite units, this is the least-authoritative interchange name of any constituent name. --- --- Note that the least-authoritative authority is the one sorted as greatest by the 'Ord' instance of 'InterchangeNameAuthority'. -class HasInterchangeName a where - interchangeName :: a -> InterchangeName - -instance HasInterchangeName InterchangeName where - interchangeName = id +{-# LANGUAGE DeriveDataTypeable #-}+{-# LANGUAGE DeriveGeneric #-}++module Numeric.Units.Dimensional.UnitNames.InterchangeNames+(+ InterchangeNameAuthority(..),+ InterchangeName(..),+ HasInterchangeName(..)+)+where++import Control.DeepSeq (NFData)+import Data.Data+import GHC.Generics+import Prelude++-- | Represents the authority which issued an interchange name for a unit.+data InterchangeNameAuthority = UCUM -- ^ The interchange name originated with the Unified Code for Units of Measure.+ | DimensionalLibrary -- ^ The interchange name originated with the dimensional library.+ | Custom -- ^ The interchange name originated with a user of the dimensional library.+ deriving (Eq, Ord, Show, Data, Typeable, Generic)++instance NFData InterchangeNameAuthority where -- instance is derived from Generic instance++data InterchangeName = InterchangeName { name :: String, authority :: InterchangeNameAuthority, isAtomic :: Bool }+ deriving (Eq, Ord, Data, Typeable, Generic)++instance NFData InterchangeName where -- instance is derived from Generic instance++instance Show InterchangeName where+ show n = name n ++ " (Issued by " ++ show (authority n) ++ ")"++-- | Determines the authority which issued the interchange name of a unit or unit name.+-- For composite units, this is the least-authoritative interchange name of any constituent name.+--+-- Note that the least-authoritative authority is the one sorted as greatest by the 'Ord' instance of 'InterchangeNameAuthority'.+class HasInterchangeName a where+ interchangeName :: a -> InterchangeName++instance HasInterchangeName InterchangeName where+ interchangeName = id
src/Numeric/Units/Dimensional/UnitNames/Internal.hs view
@@ -1,357 +1,365 @@-{-# OPTIONS_HADDOCK not-home #-} - -{-# LANGUAGE AutoDeriveTypeable #-} -{-# LANGUAGE DataKinds #-} -{-# LANGUAGE DeriveDataTypeable #-} -{-# LANGUAGE DeriveGeneric #-} -{-# LANGUAGE FlexibleContexts #-} -{-# LANGUAGE GADTs #-} -{-# LANGUAGE KindSignatures #-} -{-# LANGUAGE NumDecimals #-} -{-# LANGUAGE RankNTypes #-} -{-# LANGUAGE ScopedTypeVariables #-} -{-# LANGUAGE StandaloneDeriving #-} - -module Numeric.Units.Dimensional.UnitNames.Internal -where - -import Control.DeepSeq -import Control.Monad (join) -import Data.Coerce -import Data.Data hiding (Prefix) -import Data.Foldable (toList) -import Data.Ord -import GHC.Generics hiding (Prefix) -import Numeric.Units.Dimensional.Dimensions.TermLevel (Dimension', asList, HasDimension(..)) -import Numeric.Units.Dimensional.UnitNames.InterchangeNames hiding (isAtomic) -import qualified Numeric.Units.Dimensional.UnitNames.InterchangeNames as I -import Numeric.Units.Dimensional.Variants (Metricality(..)) -import Prelude hiding ((*), (/), (^), product) -import qualified Prelude as P - --- | The name of a unit. -data UnitName (m :: Metricality) where - -- The name of the unit of dimensionless values. - One :: UnitName 'NonMetric - -- A name of an atomic unit to which metric prefixes may be applied. - MetricAtomic :: NameAtom ('UnitAtom 'Metric) -> UnitName 'Metric - -- A name of an atomic unit to which metric prefixes may not be applied. - Atomic :: NameAtom ('UnitAtom 'NonMetric) -> UnitName 'NonMetric - -- A name of a prefixed unit. - Prefixed :: PrefixName -> UnitName 'Metric -> UnitName 'NonMetric - -- A compound name formed from the product of two names. - Product :: UnitName 'NonMetric -> UnitName 'NonMetric -> UnitName 'NonMetric - -- A compound name formed from the quotient of two names. - Quotient :: UnitName 'NonMetric -> UnitName 'NonMetric -> UnitName 'NonMetric - -- A compound name formed by raising a unit name to an integer power. - Power :: UnitName 'NonMetric -> Int -> UnitName 'NonMetric - -- A compound name formed by grouping another name, which is generally compound. - Grouped :: UnitName 'NonMetric -> UnitName 'NonMetric - -- A weakened name formed by forgetting that it could accept a metric prefix. - -- - -- Also available is the smart constructor `weaken` which accepts any `UnitName` as input. - Weaken :: UnitName 'Metric -> UnitName 'NonMetric - deriving (Typeable) - -deriving instance Eq (UnitName m) - --- As it is for a GADT, this instance cannot be derived or use the generic default implementation -instance NFData (UnitName m) where - rnf n = case n of - One -> () - MetricAtomic a -> rnf a - Atomic a -> rnf a - Prefixed p n' -> rnf p `seq` rnf n' - Product n1 n2 -> rnf n1 `seq` rnf n2 - Quotient n1 n2 -> rnf n1 `seq` rnf n2 - Power n' e -> rnf n' `seq` rnf e - Grouped n' -> rnf n' - Weaken n' -> rnf n' - --- | `UnitName`s are shown with non-breaking spaces. -instance Show (UnitName m) where - show One = "1" - show (MetricAtomic a) = abbreviation_en a - show (Atomic a) = abbreviation_en a - show (Prefixed a n) = abbreviation_en a ++ show n - show (Product n1 n2) = show n1 ++ "\xA0" ++ show n2 - show (Quotient n1 n2) = show n1 ++ "\xA0/\xA0" ++ show n2 - show (Power x n) = show x ++ "^" ++ show n - show (Grouped n) = "(" ++ show n ++ ")" - show (Weaken n) = show n - -asAtomic :: UnitName m -> Maybe (NameAtom ('UnitAtom m)) -asAtomic (MetricAtomic a) = Just a -asAtomic (Atomic a) = Just a -asAtomic (Weaken n) = coerce <$> asAtomic n -asAtomic _ = Nothing - -isAtomic :: UnitName m -> Bool -isAtomic One = True -isAtomic (MetricAtomic _) = True -isAtomic (Atomic _) = True -isAtomic (Prefixed _ _) = True -isAtomic (Grouped _) = True -isAtomic (Weaken n) = isAtomic n -isAtomic _ = False - -isAtomicOrProduct :: UnitName m -> Bool -isAtomicOrProduct (Product _ _) = True -isAtomicOrProduct n = isAtomic n - --- reduce by algebraic simplifications -reduce :: UnitName m -> UnitName m -reduce One = One -reduce n@(MetricAtomic _) = n -reduce n@(Atomic _) = n -reduce n@(Prefixed _ _) = n -reduce (Product n1 n2) = reduce' (reduce n1 * reduce n2) -reduce (Quotient n1 n2) = reduce' (reduce n1 * reduce n2) -reduce (Power n x) = reduce' (reduce n ^ x) -reduce (Grouped n) = reduce' (Grouped (reduce n)) -reduce (Weaken n) = reduce' (Weaken (reduce n)) - --- reduce, knowing that subterms are already in reduced form -reduce' :: UnitName m -> UnitName m -reduce' (Product One n) = reduce' n -reduce' (Product n One) = reduce' n -reduce' (Power (Power n x1) x2) = reduce (n ^ (x1 P.* x2)) -reduce' (Power (Grouped (Power n x1)) x2) = reduce (n ^ (x1 P.* x2)) -reduce' (Power _ 0) = One -reduce' (Power n 1) = reduce' n -reduce' (Grouped n) = reduce' n -reduce' n@(Weaken (MetricAtomic _)) = n -reduce' n = n - -data NameAtomType = UnitAtom Metricality - | PrefixAtom - deriving (Eq, Ord, Data, Typeable, Generic) - -instance NFData NameAtomType where -- instance is derived from Generic instance - --- | The name of a metric prefix. -type PrefixName = NameAtom 'PrefixAtom - -data Prefix = Prefix - { - -- | The name of a metric prefix. - prefixName :: PrefixName, - -- | The scale factor denoted by a metric prefix. - scaleFactor :: Rational - } - deriving (Eq, Data, Typeable, Generic) - -instance Ord Prefix where - compare = comparing scaleFactor - -instance NFData Prefix where -- instance is derived from Generic instance - -instance HasInterchangeName Prefix where - interchangeName = interchangeName . prefixName - --- | The name of the unit of dimensionless values. -nOne :: UnitName 'NonMetric -nOne = One - -nMeter :: UnitName 'Metric -nMeter = ucumMetric "m" "m" "metre" - -nGram :: UnitName 'Metric -nGram = ucumMetric "g" "g" "gram" - -nKilogram :: UnitName 'NonMetric -nKilogram = applyPrefix kilo nGram - -nSecond :: UnitName 'Metric -nSecond = ucumMetric "s" "s" "second" - -nAmpere :: UnitName 'Metric -nAmpere = ucumMetric "A" "A" "Ampere" - -nKelvin :: UnitName 'Metric -nKelvin = ucumMetric "K" "K" "Kelvin" - -nMole :: UnitName 'Metric -nMole = ucumMetric "mol" "mol" "mole" - -nCandela :: UnitName 'Metric -nCandela = ucumMetric "cd" "cd" "candela" - --- | The name of the base unit associated with a specified dimension. -baseUnitName :: Dimension' -> UnitName 'NonMetric -baseUnitName d = let powers = asList $ dimension d - in reduce . product $ zipWith (^) baseUnitNames powers - -baseUnitNames :: [UnitName 'NonMetric] -baseUnitNames = [weaken nMeter, nKilogram, weaken nSecond, weaken nAmpere, weaken nKelvin, weaken nMole, weaken nCandela] - -deka, hecto, kilo, mega, giga, tera, peta, exa, zetta, yotta :: Prefix -deka = prefix "da" "da" "deka" 1e1 -hecto = prefix "h" "h" "hecto" 1e2 -kilo = prefix "k" "k" "kilo" 1e3 -mega = prefix "M" "M" "mega" 1e6 -giga = prefix "G" "G" "giga" 1e9 -tera = prefix "T" "T" "tera" 1e12 -peta = prefix "P" "P" "peta" 1e15 -exa = prefix "E" "E" "exa" 1e18 -zetta = prefix "Z" "Z" "zetta" 1e21 -yotta = prefix "Y" "Y" "yotta" 1e24 -deci, centi, milli, micro, nano, pico, femto, atto, zepto, yocto :: Prefix -deci = prefix "d" "d" "deci" 1e-1 -centi = prefix "c" "c" "centi" 1e-2 -milli = prefix "m" "m" "milli" 1e-3 -micro = prefix "u" "μ" "micro" 1e-6 -nano = prefix "n" "n" "nano" 1e-9 -pico = prefix "p" "p" "pico" 1e-12 -femto = prefix "f" "f" "femto" 1e-15 -atto = prefix "a" "a" "atto" 1e-18 -zepto = prefix "z" "z" "zepto" 1e-21 -yocto = prefix "y" "y" "yocto" 1e-24 - --- | A list of all 'Prefix'es defined by the SI. -siPrefixes :: [Prefix] -siPrefixes = [yocto, zepto, atto, femto, pico, nano, micro, milli, centi, deci, deka, hecto, kilo, mega, giga, tera, peta, exa, zetta, yotta] - --- | Forms a 'UnitName' from a 'Metric' name by applying a metric prefix. -applyPrefix :: Prefix -> UnitName 'Metric -> UnitName 'NonMetric -applyPrefix = Prefixed . prefixName - -{- -We will reuse the operators and function names from the Prelude. -To prevent unpleasant surprises we give operators the same fixity -as the Prelude. --} - -infixr 8 ^ -infixl 7 *, / - --- | Form a 'UnitName' by taking the product of two others. -(*) :: UnitName m1 -> UnitName m2 -> UnitName 'NonMetric -a * b = Product (weaken a) (weaken b) - --- | Form a 'UnitName' by dividing one by another. -(/) :: UnitName m1 -> UnitName m2 -> UnitName 'NonMetric -n1 / n2 | isAtomicOrProduct n1 = Quotient (weaken n1) (weaken n2) - | otherwise = Quotient (grouped n1) (weaken n2) - --- | Form a 'UnitName' by raising a name to an integer power. -(^) :: UnitName m -> Int -> UnitName 'NonMetric -x ^ n | isAtomic x = Power (weaken x) n - | otherwise = Power (grouped x) n - --- | Convert a 'UnitName' which may or may not be 'Metric' to one --- which is certainly 'NonMetric'. -weaken :: UnitName m -> UnitName 'NonMetric -weaken n@(MetricAtomic _) = Weaken n -- we really only need this one case and a catchall, but the typechecker can't see it -weaken n@One = n -weaken n@(Atomic _) = n -weaken n@(Prefixed _ _) = n -weaken n@(Product _ _) = n -weaken n@(Quotient _ _) = n -weaken n@(Power _ _) = n -weaken n@(Grouped _) = n -weaken n@(Weaken _) = n - --- | Attempt to convert a 'UnitName' which may or may not be 'Metric' to one --- which is certainly 'Metric'. -strengthen :: UnitName m -> Maybe (UnitName 'Metric) -strengthen n@(MetricAtomic _) = Just n -strengthen (Weaken n) = strengthen n -strengthen _ = Nothing - --- | Convert a 'UnitName' of one 'Metricality' into a name of another metricality by --- strengthening or weakening if neccessary. Because it may not be possible to strengthen, --- the result is returned in a 'Maybe' wrapper. -relax :: forall m1 m2.(Typeable m1, Typeable m2) => UnitName m1 -> Maybe (UnitName m2) -relax = go (typeRep (Proxy :: Proxy m1)) (typeRep (Proxy :: Proxy m2)) - where - metric = typeRep (Proxy :: Proxy 'Metric) - nonMetric = typeRep (Proxy :: Proxy 'NonMetric) - go :: TypeRep -> TypeRep -> UnitName m1 -> Maybe (UnitName m2) - go p1 p2 | p1 == p2 = cast - | (p1 == nonMetric) && (p2 == metric) = join . fmap gcast . strengthen - | (p1 == metric) && (p2 == nonMetric) = cast . weaken - | otherwise = error "Should be unreachable. TypeRep of an unexpected Metricality encountered." - --- | Constructs a 'UnitName' by applying a grouping operation to --- another 'UnitName', which may be useful to express precedence. -grouped :: UnitName m -> UnitName 'NonMetric -grouped = Grouped . weaken - --- | Represents the name of an atomic unit or prefix. -data NameAtom (m :: NameAtomType) - = NameAtom - { - _interchangeName :: InterchangeName, -- ^ The interchange name of the unit. - abbreviation_en :: String, -- ^ The abbreviated name of the unit in international English - name_en :: String -- ^ The full name of the unit in international English - } - deriving (Eq, Ord, Data, Typeable, Generic) - -instance NFData (NameAtom m) where -- instance is derived from Generic instance - -instance HasInterchangeName (NameAtom m) where - interchangeName = _interchangeName - -instance HasInterchangeName (UnitName m) where - interchangeName One = InterchangeName { name = "1", authority = UCUM, I.isAtomic = True } - interchangeName (MetricAtomic a) = interchangeName a - interchangeName (Atomic a) = interchangeName a - interchangeName (Prefixed p n) = let n' = (name . interchangeName $ p) ++ (name . interchangeName $ n) - a' = max (authority . interchangeName $ p) (authority . interchangeName $ n) - in InterchangeName { name = n', authority = a', I.isAtomic = False } - interchangeName (Product n1 n2) = let n' = (name . interchangeName $ n1) ++ "." ++ (name . interchangeName $ n2) - a' = max (authority . interchangeName $ n1) (authority . interchangeName $ n2) - in InterchangeName { name = n', authority = a', I.isAtomic = False } - interchangeName (Quotient n1 n2) = let n' = (name . interchangeName $ n1) ++ "/" ++ (name . interchangeName $ n2) - a' = max (authority . interchangeName $ n1) (authority . interchangeName $ n2) - in InterchangeName { name = n', authority = a', I.isAtomic = False } - -- TODO #109: note in this case that the UCUM is changing their grammar to not accept exponents after - -- as a result it will become necessary to distribute the exponentiation over the items in the base name - -- prior to generating the interchange name - interchangeName (Power n x) = let n' = (name . interchangeName $ n) ++ show x - in InterchangeName { name = n', authority = authority . interchangeName $ n, I.isAtomic = False } - interchangeName (Grouped n) = let n' = "(" ++ (name . interchangeName $ n) ++ ")" - in InterchangeName { name = n', authority = authority . interchangeName $ n, I.isAtomic = False } - interchangeName (Weaken n) = interchangeName n - -prefix :: String -> String -> String -> Rational -> Prefix -prefix i a f = Prefix n - where - n = NameAtom (InterchangeName i UCUM True) a f - -ucumMetric :: String -> String -> String -> UnitName 'Metric -ucumMetric i a f = MetricAtomic $ NameAtom (InterchangeName i UCUM True) a f - -ucum :: String -> String -> String -> UnitName 'NonMetric -ucum i a f = Atomic $ NameAtom (InterchangeName i UCUM True) a f - -dimensionalAtom :: String -> String -> String -> UnitName 'NonMetric -dimensionalAtom i a f = Atomic $ NameAtom (InterchangeName i DimensionalLibrary True) a f - --- | Constructs an atomic name for a custom unit. -atom :: String -- ^ Interchange name - -> String -- ^ Abbreviated name in international English - -> String -- ^ Full name in international English - -> UnitName 'NonMetric -atom i a f = Atomic $ NameAtom (InterchangeName i Custom True) a f - --- | The type of a unit name transformation that may be associated with an operation that takes a single unit as input. -type UnitNameTransformer = (forall m.UnitName m -> UnitName 'NonMetric) - --- | The type of a unit name transformation that may be associated with an operation that takes two units as input. -type UnitNameTransformer2 = (forall m1 m2.UnitName m1 -> UnitName m2 -> UnitName 'NonMetric) - --- | Forms the product of a list of 'UnitName's. --- --- If you wish to form a heterogenous product of 'Metric' and 'NonMetric' units --- you should apply 'weaken' to the 'Metric' ones. -product :: Foldable f => f (UnitName 'NonMetric) -> UnitName 'NonMetric -product = go . toList - where - -- This is not defined using a simple fold so that it does not complicate the product with - -- valid but meaningless occurences of nOne. - go :: [UnitName 'NonMetric] -> UnitName 'NonMetric - go [] = nOne - go [n] = n - go (n : ns) = n * go ns +{-# OPTIONS_HADDOCK not-home #-}++{-# LANGUAGE DataKinds #-}+{-# LANGUAGE DeriveDataTypeable #-}+{-# LANGUAGE DeriveGeneric #-}+{-# LANGUAGE FlexibleContexts #-}+{-# LANGUAGE GADTs #-}+{-# LANGUAGE KindSignatures #-}+{-# LANGUAGE NumDecimals #-}+{-# LANGUAGE RankNTypes #-}+{-# LANGUAGE ScopedTypeVariables #-}+{-# LANGUAGE StandaloneDeriving #-}++module Numeric.Units.Dimensional.UnitNames.Internal+where++import Control.DeepSeq (NFData(..))+import Control.Monad (join)+import Data.Coerce+import Data.Data hiding (Prefix)+import Data.Foldable (toList)+import Data.Ord+import GHC.Generics hiding (Prefix)+import Numeric.Units.Dimensional.Dimensions.TermLevel (Dimension', asList, HasDimension(..))+import Numeric.Units.Dimensional.UnitNames.InterchangeNames hiding (isAtomic)+import qualified Numeric.Units.Dimensional.UnitNames.InterchangeNames as I+import Numeric.Units.Dimensional.Variants (Metricality(..))+import Prelude hiding ((*), (/), (^), product)+import qualified Prelude as P++-- | The name of a unit.+data UnitName (m :: Metricality) where+ -- | The name of the unit of dimensionless values.+ One :: UnitName 'NonMetric+ -- | A name of an atomic unit to which metric prefixes may be applied.+ MetricAtomic :: NameAtom ('UnitAtom 'Metric) -> UnitName 'Metric+ -- | A name of an atomic unit to which metric prefixes may not be applied.+ Atomic :: NameAtom ('UnitAtom 'NonMetric) -> UnitName 'NonMetric+ -- | A name of a prefixed unit.+ Prefixed :: PrefixName -> UnitName 'Metric -> UnitName 'NonMetric+ -- | A compound name formed from the product of two names.+ Product :: UnitName 'NonMetric -> UnitName 'NonMetric -> UnitName 'NonMetric+ -- | A compound name formed from the quotient of two names.+ Quotient :: UnitName 'NonMetric -> UnitName 'NonMetric -> UnitName 'NonMetric+ -- | A compound name formed by raising a unit name to an integer power.+ Power :: UnitName 'NonMetric -> Int -> UnitName 'NonMetric+ -- | A compound name formed by grouping another name, which is generally compound.+ Grouped :: UnitName 'NonMetric -> UnitName 'NonMetric+ -- | A weakened name formed by forgetting that it could accept a metric prefix.+ --+ -- Also available is the smart constructor `weaken` which accepts any `UnitName` as input.+ Weaken :: UnitName 'Metric -> UnitName 'NonMetric+ deriving (Typeable)++deriving instance Eq (UnitName m)++-- As it is for a GADT, this instance cannot be derived or use the generic default implementation+instance NFData (UnitName m) where+ rnf n = case n of+ One -> ()+ MetricAtomic a -> rnf a+ Atomic a -> rnf a+ Prefixed p n' -> rnf p `seq` rnf n'+ Product n1 n2 -> rnf n1 `seq` rnf n2+ Quotient n1 n2 -> rnf n1 `seq` rnf n2+ Power n' e -> rnf n' `seq` rnf e+ Grouped n' -> rnf n'+ Weaken n' -> rnf n'++-- | `UnitName`s are shown with non-breaking spaces.+instance Show (UnitName m) where+ show One = "1"+ show (MetricAtomic a) = abbreviation_en a+ show (Atomic a) = abbreviation_en a+ show (Prefixed a n) = abbreviation_en a ++ show n+ show (Product n1 n2) = show n1 ++ "\xA0" ++ show n2+ show (Quotient n1 n2) = show n1 ++ "\xA0/\xA0" ++ show n2+ show (Power x n) = show x ++ "^" ++ show n+ show (Grouped n) = "(" ++ show n ++ ")"+ show (Weaken n) = show n++-- | Converts a 'UnitName' to a 'NameAtom', if possible.+asAtomic :: UnitName m -> Maybe (NameAtom ('UnitAtom m))+asAtomic (MetricAtomic a) = Just a+asAtomic (Atomic a) = Just a+asAtomic (Weaken n) = coerce <$> asAtomic n+asAtomic _ = Nothing++-- | Returns 'True' if the 'UnitName' is atomic.+isAtomic :: UnitName m -> Bool+isAtomic One = True+isAtomic (MetricAtomic _) = True+isAtomic (Atomic _) = True+isAtomic (Prefixed _ _) = True+isAtomic (Grouped _) = True+isAtomic (Weaken n) = isAtomic n+isAtomic _ = False++isAtomicOrProduct :: UnitName m -> Bool+isAtomicOrProduct (Product _ _) = True+isAtomicOrProduct n = isAtomic n++-- | Reduce a 'UnitName' by algebraic simplifications.+reduce :: UnitName m -> UnitName m+reduce One = One+reduce n@(MetricAtomic _) = n+reduce n@(Atomic _) = n+reduce n@(Prefixed _ _) = n+reduce (Product n1 n2) = reduce' (reduce n1 * reduce n2)+reduce (Quotient n1 n2) = reduce' (reduce n1 * reduce n2)+reduce (Power n x) = reduce' (reduce n ^ x)+reduce (Grouped n) = reduce' (Grouped (reduce n))+reduce (Weaken n) = reduce' (Weaken (reduce n))++-- reduce, knowing that subterms are already in reduced form+reduce' :: UnitName m -> UnitName m+reduce' (Product One n) = reduce' n+reduce' (Product n One) = reduce' n+reduce' (Power (Power n x1) x2) = reduce (n ^ (x1 P.* x2))+reduce' (Power (Grouped (Power n x1)) x2) = reduce (n ^ (x1 P.* x2))+reduce' (Power _ 0) = One+reduce' (Power n 1) = reduce' n+reduce' (Grouped n) = reduce' n+reduce' n@(Weaken (MetricAtomic _)) = n+reduce' n = n++data NameAtomType = UnitAtom Metricality+ | PrefixAtom+ deriving (Eq, Ord, Data, Typeable, Generic)++instance NFData NameAtomType where -- instance is derived from Generic instance++-- | The name of a metric prefix.+type PrefixName = NameAtom 'PrefixAtom++-- | A metric prefix.+data Prefix = Prefix+ {+ -- | The name of a metric prefix.+ prefixName :: PrefixName,+ -- | The scale factor denoted by a metric prefix.+ scaleFactor :: Rational+ }+ deriving (Eq, Data, Typeable, Generic)++instance Ord Prefix where+ compare = comparing scaleFactor++instance NFData Prefix where -- instance is derived from Generic instance++instance HasInterchangeName Prefix where+ interchangeName = interchangeName . prefixName++-- | The name of the unit of dimensionless values.+nOne :: UnitName 'NonMetric+nOne = One++nMeter :: UnitName 'Metric+nMeter = ucumMetric "m" "m" "metre"++nGram :: UnitName 'Metric+nGram = ucumMetric "g" "g" "gram"++nKilogram :: UnitName 'NonMetric+nKilogram = applyPrefix kilo nGram++nSecond :: UnitName 'Metric+nSecond = ucumMetric "s" "s" "second"++nAmpere :: UnitName 'Metric+nAmpere = ucumMetric "A" "A" "Ampere"++nKelvin :: UnitName 'Metric+nKelvin = ucumMetric "K" "K" "Kelvin"++nMole :: UnitName 'Metric+nMole = ucumMetric "mol" "mol" "mole"++nCandela :: UnitName 'Metric+nCandela = ucumMetric "cd" "cd" "candela"++-- | The name of the base unit associated with a specified dimension.+baseUnitName :: Dimension' -> UnitName 'NonMetric+baseUnitName d = let powers = asList $ dimension d+ in reduce . product $ zipWith (^) baseUnitNames powers++baseUnitNames :: [UnitName 'NonMetric]+baseUnitNames = [weaken nMeter, nKilogram, weaken nSecond, weaken nAmpere, weaken nKelvin, weaken nMole, weaken nCandela]++deca, hecto, kilo, mega, giga, tera, peta, exa, zetta, yotta, ronna, quetta :: Prefix+deca = prefix "da" "da" "deca" 1e1+hecto = prefix "h" "h" "hecto" 1e2+kilo = prefix "k" "k" "kilo" 1e3+mega = prefix "M" "M" "mega" 1e6+giga = prefix "G" "G" "giga" 1e9+tera = prefix "T" "T" "tera" 1e12+peta = prefix "P" "P" "peta" 1e15+exa = prefix "E" "E" "exa" 1e18+zetta = prefix "Z" "Z" "zetta" 1e21+yotta = prefix "Y" "Y" "yotta" 1e24+ronna = prefix "R" "R" "ronna" 1e27+quetta = prefix "Q" "Q" "quetta" 1e30++deci, centi, milli, micro, nano, pico, femto, atto, zepto, yocto, ronto, quecto :: Prefix+deci = prefix "d" "d" "deci" 1e-1+centi = prefix "c" "c" "centi" 1e-2+milli = prefix "m" "m" "milli" 1e-3+micro = prefix "u" "μ" "micro" 1e-6+nano = prefix "n" "n" "nano" 1e-9+pico = prefix "p" "p" "pico" 1e-12+femto = prefix "f" "f" "femto" 1e-15+atto = prefix "a" "a" "atto" 1e-18+zepto = prefix "z" "z" "zepto" 1e-21+yocto = prefix "y" "y" "yocto" 1e-24+ronto = prefix "r" "r" "ronto" 1e-27+quecto = prefix "q" "q" "quecto" 1e-30+++-- | A list of all 'Prefix'es defined by the SI.+siPrefixes :: [Prefix]+siPrefixes = [quecto, ronto, yocto, zepto, atto, femto, pico, nano, micro, milli, centi, deci, deca, hecto, kilo, mega, giga, tera, peta, exa, zetta, yotta, ronna, quetta]++-- | Forms a 'UnitName' from a 'Metric' name by applying a metric prefix.+applyPrefix :: Prefix -> UnitName 'Metric -> UnitName 'NonMetric+applyPrefix = Prefixed . prefixName++{-+We will reuse the operators and function names from the Prelude.+To prevent unpleasant surprises we give operators the same fixity+as the Prelude.+-}++infixr 8 ^+infixl 7 *, /++-- | Form a 'UnitName' by taking the product of two others.+(*) :: UnitName m1 -> UnitName m2 -> UnitName 'NonMetric+a * b = Product (weaken a) (weaken b)++-- | Form a 'UnitName' by dividing one by another.+(/) :: UnitName m1 -> UnitName m2 -> UnitName 'NonMetric+n1 / n2 | isAtomicOrProduct n1 = Quotient (weaken n1) (weaken n2)+ | otherwise = Quotient (grouped n1) (weaken n2)++-- | Form a 'UnitName' by raising a name to an integer power.+(^) :: UnitName m -> Int -> UnitName 'NonMetric+x ^ n | isAtomic x = Power (weaken x) n+ | otherwise = Power (grouped x) n++-- | Convert a 'UnitName' which may or may not be 'Metric' to one+-- which is certainly 'NonMetric'.+weaken :: UnitName m -> UnitName 'NonMetric+weaken n@(MetricAtomic _) = Weaken n -- we really only need this one case and a catchall, but the typechecker can't see it+weaken n@One = n+weaken n@(Atomic _) = n+weaken n@(Prefixed _ _) = n+weaken n@(Product _ _) = n+weaken n@(Quotient _ _) = n+weaken n@(Power _ _) = n+weaken n@(Grouped _) = n+weaken n@(Weaken _) = n++-- | Attempt to convert a 'UnitName' which may or may not be 'Metric' to one+-- which is certainly 'Metric'.+strengthen :: UnitName m -> Maybe (UnitName 'Metric)+strengthen n@(MetricAtomic _) = Just n+strengthen (Weaken n) = strengthen n+strengthen _ = Nothing++-- | Convert a 'UnitName' of one 'Metricality' into a name of another metricality by+-- strengthening or weakening if neccessary. Because it may not be possible to strengthen,+-- the result is returned in a 'Maybe' wrapper.+relax :: forall m1 m2.(Typeable m1, Typeable m2) => UnitName m1 -> Maybe (UnitName m2)+relax = go (typeRep (Proxy :: Proxy m1)) (typeRep (Proxy :: Proxy m2))+ where+ metric = typeRep (Proxy :: Proxy 'Metric)+ nonMetric = typeRep (Proxy :: Proxy 'NonMetric)+ go :: TypeRep -> TypeRep -> UnitName m1 -> Maybe (UnitName m2)+ go p1 p2 | p1 == p2 = cast+ | (p1 == nonMetric) && (p2 == metric) = join . fmap gcast . strengthen+ | (p1 == metric) && (p2 == nonMetric) = cast . weaken+ | otherwise = error "Should be unreachable. TypeRep of an unexpected Metricality encountered."++-- | Constructs a 'UnitName' by applying a grouping operation to+-- another 'UnitName', which may be useful to express precedence.+grouped :: UnitName m -> UnitName 'NonMetric+grouped = Grouped . weaken++-- | Represents the name of an atomic unit or prefix.+data NameAtom (m :: NameAtomType)+ = NameAtom+ {+ _interchangeName :: InterchangeName, -- ^ The interchange name of the unit.+ abbreviation_en :: String, -- ^ The abbreviated name of the unit in international English.+ name_en :: String -- ^ The full name of the unit in international English.+ }+ deriving (Eq, Ord, Data, Typeable, Generic)++instance NFData (NameAtom m) where -- instance is derived from Generic instance++instance HasInterchangeName (NameAtom m) where+ interchangeName = _interchangeName++instance HasInterchangeName (UnitName m) where+ interchangeName One = InterchangeName { name = "1", authority = UCUM, I.isAtomic = True }+ interchangeName (MetricAtomic a) = interchangeName a+ interchangeName (Atomic a) = interchangeName a+ interchangeName (Prefixed p n) = let n' = (name . interchangeName $ p) ++ (name . interchangeName $ n)+ a' = max (authority . interchangeName $ p) (authority . interchangeName $ n)+ in InterchangeName { name = n', authority = a', I.isAtomic = False }+ interchangeName (Product n1 n2) = let n' = (name . interchangeName $ n1) ++ "." ++ (name . interchangeName $ n2)+ a' = max (authority . interchangeName $ n1) (authority . interchangeName $ n2)+ in InterchangeName { name = n', authority = a', I.isAtomic = False }+ interchangeName (Quotient n1 n2) = let n' = (name . interchangeName $ n1) ++ "/" ++ (name . interchangeName $ n2)+ a' = max (authority . interchangeName $ n1) (authority . interchangeName $ n2)+ in InterchangeName { name = n', authority = a', I.isAtomic = False }+ -- TODO #109: note in this case that the UCUM is changing their grammar to not accept exponents after+ -- as a result it will become necessary to distribute the exponentiation over the items in the base name+ -- prior to generating the interchange name+ interchangeName (Power n x) = let n' = (name . interchangeName $ n) ++ show x+ in InterchangeName { name = n', authority = authority . interchangeName $ n, I.isAtomic = False }+ interchangeName (Grouped n) = let n' = "(" ++ (name . interchangeName $ n) ++ ")"+ in InterchangeName { name = n', authority = authority . interchangeName $ n, I.isAtomic = False }+ interchangeName (Weaken n) = interchangeName n++prefix :: String -> String -> String -> Rational -> Prefix+prefix i a f = Prefix n+ where+ n = NameAtom (InterchangeName i UCUM True) a f++ucumMetric :: String -> String -> String -> UnitName 'Metric+ucumMetric i a f = MetricAtomic $ NameAtom (InterchangeName i UCUM True) a f++ucum :: String -> String -> String -> UnitName 'NonMetric+ucum i a f = Atomic $ NameAtom (InterchangeName i UCUM True) a f++dimensionalAtom :: String -> String -> String -> UnitName 'NonMetric+dimensionalAtom i a f = Atomic $ NameAtom (InterchangeName i DimensionalLibrary True) a f++-- | Constructs an atomic name for a custom unit.+atom :: String -- ^ Interchange name+ -> String -- ^ Abbreviated name in international English+ -> String -- ^ Full name in international English+ -> UnitName 'NonMetric+atom i a f = Atomic $ NameAtom (InterchangeName i Custom True) a f++-- | The type of a unit name transformation that may be associated with an operation that takes a single unit as input.+type UnitNameTransformer = (forall m.UnitName m -> UnitName 'NonMetric)++-- | The type of a unit name transformation that may be associated with an operation that takes two units as input.+type UnitNameTransformer2 = (forall m1 m2.UnitName m1 -> UnitName m2 -> UnitName 'NonMetric)++-- | Forms the product of a list of 'UnitName's.+--+-- If you wish to form a heterogenous product of 'Metric' and 'NonMetric' units+-- you should apply 'weaken' to the 'Metric' ones.+product :: Foldable f => f (UnitName 'NonMetric) -> UnitName 'NonMetric+product = go . toList+ where+ -- This is not defined using a simple fold so that it does not complicate the product with+ -- valid but meaningless occurences of nOne.+ go :: [UnitName 'NonMetric] -> UnitName 'NonMetric+ go [] = nOne+ go [n] = n+ go (n : ns) = n * go ns
src/Numeric/Units/Dimensional/Variants.hs view
@@ -1,94 +1,98 @@-{-# OPTIONS_HADDOCK not-home, show-extensions #-} - -{-# LANGUAGE AutoDeriveTypeable #-} -{-# LANGUAGE ConstraintKinds #-} -{-# LANGUAGE DataKinds #-} -{-# LANGUAGE DeriveDataTypeable #-} -{-# LANGUAGE DeriveGeneric #-} -{-# LANGUAGE KindSignatures #-} -{-# LANGUAGE TypeFamilies #-} -{-# LANGUAGE TypeOperators #-} - -{- | - Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter - License : BSD3 - - Maintainer : bjorn@buckwalter.se - Stability : Stable - Portability: GHC only - -Provides a type level representation of 'Variant's of dimensional values, -which may be quantities or units. --} -module Numeric.Units.Dimensional.Variants -( - type Variant(..), - Metricality(..), - type (*), type (/), type Weaken, - type CompatibleVariants -) -where - -import Control.DeepSeq -import Data.Data -import qualified Data.ExactPi.TypeLevel as E -import GHC.Generics -import Prelude - --- | Encodes whether a unit is a metric unit, that is, whether it can be combined --- with a metric prefix to form a related unit. -data Metricality = Metric -- ^ Capable of receiving a metric prefix. - | NonMetric -- ^ Incapable of receiving a metric prefix. - deriving (Eq, Ord, Data, Typeable, Generic) - -instance NFData Metricality where -- instance is derived from Generic instance - -{- -The variety 'v' of 'Dimensional' - -The phantom type variable v is used to distinguish between units -and quantities. It must be one of the following: --} - --- | The kind of variants of dimensional values. -data Variant = DQuantity E.ExactPi' -- ^ The value is a quantity, stored as an `ExactPi` multiple of its value in its dimension's SI coherent unit. - | DUnit Metricality -- ^ The value is a unit, possibly a 'Metric' unit. - deriving (Typeable, Generic) - -{- -We will reuse the operators and function names from the Prelude. -To prevent unpleasant surprises we give operators the same fixity -as the Prelude. --} - -infixl 7 * - --- | Forms the product of two 'Variant's. --- --- The product of units is a non-metric unit. --- --- The product of quantities is a quantity. -type family (v1 :: Variant) * (v2 :: Variant) :: Variant where - 'DUnit m1 * 'DUnit m2 = 'DUnit 'NonMetric - 'DQuantity s1 * 'DQuantity s2 = 'DQuantity (s1 E.* s2) - -type family (v1 :: Variant) / (v2 :: Variant) :: Variant where - 'DUnit m1 / 'DUnit m2 = 'DUnit 'NonMetric - 'DQuantity s1 / 'DQuantity s2 = 'DQuantity (s1 E./ s2) - --- | Weakens a 'Variant' by forgetting possibly uninteresting type-level information. -type family Weaken (v :: Variant) :: Variant where - Weaken ('DQuantity s) = 'DQuantity s - Weaken ('DUnit m) = 'DUnit 'NonMetric - --- | Two 'Variant's are compatible when dimensional values of the first may be converted --- into the second merely by changing the representation of their values. -type family AreCompatible (v1 :: Variant) (v2 :: Variant) :: Bool where - AreCompatible ('DQuantity s1) ('DQuantity s2) = 'True - AreCompatible ('DUnit m) ('DUnit 'NonMetric) = 'True - AreCompatible s s = 'True - AreCompatible s1 s2 = 'False - --- | Two 'Variant's are compatible when dimensional values of the first may be converted --- into the second merely by changing the representation of their values. -type CompatibleVariants v1 v2 = ('True ~ AreCompatible v1 v2) +{-# OPTIONS_HADDOCK not-home, show-extensions #-}++{-# LANGUAGE ConstraintKinds #-}+{-# LANGUAGE DataKinds #-}+{-# LANGUAGE DeriveDataTypeable #-}+{-# LANGUAGE DeriveGeneric #-}+{-# LANGUAGE KindSignatures #-}+{-# LANGUAGE TypeFamilies #-}+{-# LANGUAGE TypeOperators #-}++{- |+ Copyright : Copyright (C) 2006-2018 Bjorn Buckwalter+ License : BSD3++ Maintainer : bjorn@buckwalter.se+ Stability : Stable+ Portability: GHC only++Provides a type level representation of 'Variant's of dimensional values,+which may be quantities or units.+-}+module Numeric.Units.Dimensional.Variants+(+ type Variant(..),+ Metricality(..),+ type (*), type (/), type Weaken,+ type CompatibleVariants+)+where++import Control.DeepSeq (NFData)+import Data.Data+import qualified Data.ExactPi.TypeLevel as E+import GHC.Generics+import Prelude++-- | Encodes whether a unit is a metric unit, that is, whether it can be combined+-- with a metric prefix to form a related unit.+data Metricality = Metric -- ^ Capable of receiving a metric prefix.+ | NonMetric -- ^ Incapable of receiving a metric prefix.+ deriving (Eq, Ord, Data, Typeable, Generic)++instance NFData Metricality where -- instance is derived from Generic instance++{-+The variety 'v' of 'Dimensional'++The phantom type variable v is used to distinguish between units+and quantities. It must be one of the following:+-}++-- | The kind of variants of dimensional values.+data Variant = DQuantity E.ExactPi' -- ^ The value is a quantity, stored as an `ExactPi` multiple of its value in its dimension's SI coherent unit.+ | DUnit Metricality -- ^ The value is a unit, possibly a 'Metric' unit.+ deriving (Typeable, Generic)++{-+We will reuse the operators and function names from the Prelude.+To prevent unpleasant surprises we give operators the same fixity+as the Prelude.+-}++infixl 7 *++-- | Forms the product of two 'Variant's.+--+-- The product of units is a non-metric unit.+--+-- The product of quantities is a quantity.+type family (v1 :: Variant) * (v2 :: Variant) :: Variant where+ 'DUnit m1 * 'DUnit m2 = 'DUnit 'NonMetric+ 'DQuantity s1 * 'DQuantity s2 = 'DQuantity (s1 E.* s2)++-- | Forms the quotient of two 'Variant's.+--+-- The quotient of units is a non-metric unit.+--+-- The quotient of quantities is a quantity.+type family (v1 :: Variant) / (v2 :: Variant) :: Variant where+ 'DUnit m1 / 'DUnit m2 = 'DUnit 'NonMetric+ 'DQuantity s1 / 'DQuantity s2 = 'DQuantity (s1 E./ s2)++-- | Weakens a 'Variant' by forgetting possibly uninteresting type-level information.+type family Weaken (v :: Variant) :: Variant where+ Weaken ('DQuantity s) = 'DQuantity s+ Weaken ('DUnit m) = 'DUnit 'NonMetric++-- | Two 'Variant's are compatible when dimensional values of the first may be converted+-- into the second merely by changing the representation of their values.+type family AreCompatible (v1 :: Variant) (v2 :: Variant) :: Bool where+ AreCompatible ('DQuantity s1) ('DQuantity s2) = 'True+ AreCompatible ('DUnit m) ('DUnit 'NonMetric) = 'True+ AreCompatible s s = 'True+ AreCompatible s1 s2 = 'False++-- | Two 'Variant's are compatible when dimensional values of the first may be converted+-- into the second merely by changing the representation of their values.+type CompatibleVariants v1 v2 = ('True ~ AreCompatible v1 v2)
− tests/DocTests.hs
@@ -1,17 +0,0 @@-{-# LANGUAGE CPP #-} -{-# LANGUAGE FlexibleInstances #-} -{-# LANGUAGE TypeSynonymInstances #-} - -module Main (main) where - -import System.FilePath.Glob (glob) -import Test.DocTest (doctest) - -#if MIN_VERSION_base(4,12,0) -doctestFlags = ["-XNoStarIsType"] -#else -doctestFlags = [] -#endif - -main :: IO () -main = glob "src/**/*.hs" >>= (doctest . (doctestFlags++))
tests/Numeric/Units/Dimensional/DynamicSpec.hs view
@@ -1,157 +1,157 @@-module Numeric.Units.Dimensional.DynamicSpec where - -import Numeric.Units.Dimensional.Prelude -import Numeric.Units.Dimensional.Dynamic hiding ((*),(/),(^),(*~),(/~), recip) -import Numeric.Units.Dimensional.Dimensions.TermLevel (hasSomeDimension) -import qualified Numeric.Units.Dimensional.Dynamic as Dyn -import qualified Prelude as P -import Test.Hspec -import Test.QuickCheck - -spec :: Spec -spec = do - describe "Dynamic quantity promotion and demotion" $ do - it "round-trips through AnyQuantity" $ property $ - \x -> let x' = x *~ kilo newton - x'' = demoteQuantity x' :: AnyQuantity Double - in Just x' == promoteQuantity x'' - it "round-trips through DynQuantity" $ property $ - \x -> let x' = x *~ micro watt - x'' = demoteQuantity x' :: DynQuantity Rational - in Just x' == promoteQuantity x'' - it "round-trips through AnyQuantity then DynQuantity" $ property $ - \x -> let x' = x *~ gram - x'' = demoteQuantity x' :: AnyQuantity Double - x''' = demoteQuantity x'' :: DynQuantity Double - in Just x' == promoteQuantity x''' - it "doesn't promote invalid quantities" $ do - (promoteQuantity invalidQuantity :: Maybe (Length Double)) `shouldBe` Nothing - it "doesn't promote AnyQuantity to the wrong dimension" $ do - let x = 12.3 *~ meter - x' = demoteQuantity x :: AnyQuantity Double - (promoteQuantity x' :: Maybe (Mass Double)) `shouldBe` Nothing - it "doesn't promote DynQuantity to the wrong dimension" $ do - let x = 12.3 *~ mole - x' = demoteQuantity x :: DynQuantity Double - (promoteQuantity x' :: Maybe (Time Double)) `shouldBe` Nothing - it "properly combines with dynamic units" $ do - let meter' = demoteUnit' meter - (promoteQuantity (139.4 Dyn.*~ meter' :: AnyQuantity Double)) `shouldBe` Just (139.4 *~ meter) - it "properly eliminates dynamic units" $ do - let ampere' = demoteUnit' ampere - i = demoteQuantity $ 47 *~ ampere :: AnyQuantity Double - i Dyn./~ ampere' `shouldBe` Just 47 - it "doesn't eliminate dynamic units of the wrong dimension" $ do - let ampere' = demoteUnit' ampere - i = demoteQuantity $ 47 *~ joule :: AnyQuantity Double - i Dyn./~ ampere' `shouldBe` Nothing - describe "DynQuantity arithmetic" $ do - -- declare some static quantities and their dynamic counterparts for arithmetic tests - let x1 = 12.3 *~ meter - x2 = (-7.9) *~ meter - a = 93 *~ square (kilo meter) - m = 147 *~ kilo gram - t = 14.9 *~ second - f = 87.2 *~ milli newton - phi = 1.61803398875 *~ one - x1' = demoteQuantity x1 :: DynQuantity Double - x2' = demoteQuantity x2 :: DynQuantity Double - a' = demoteQuantity a :: DynQuantity Double - m' = demoteQuantity m :: DynQuantity Double - t' = demoteQuantity t :: DynQuantity Double - f' = demoteQuantity f :: DynQuantity Double - phi' = demoteQuantity phi :: DynQuantity Double - context "Num instance" $ do - it "matches static addition" $ do - (x1' P.+ x2') `shouldBe` demoteQuantity (x1 + x2) - it "allows addition with polydimensional zero" $ do - (t' P.+ polydimensionalZero) `shouldBe` t' - (polydimensionalZero P.+ t') `shouldBe` t' - (polydimensionalZero P.+ polydimensionalZero) `shouldBe` (polydimensionalZero :: DynQuantity Double) - it "propagates witnesses to zero during addition" $ do - -- We want to test that the witness for polymorphic zero was actually added to the other addend. - -- The reason for this property is that if the other addend is some element of the underlying type - -- which can't act as a divisor (such as a propagating nAn), then we want that information to still - -- be around when we go to promote the result. - let nan = 0 P./ 0 :: Double - x = demoteQuantity $ nan *~ meter - Just y = promoteQuantity (polydimensionalZero P.+ x) :: Maybe (Length Double) - (y /~ meter) `shouldSatisfy` P.isNaN - it "matches static subtraction" $ do - (x2' P.- x1') `shouldBe` demoteQuantity (x2 - x1) - it "allows subtraction with polydimensional zero" $ do - (m' P.- polydimensionalZero) `shouldBe` m' - (polydimensionalZero P.- m') `shouldBe` (P.negate m') - (polydimensionalZero P.- polydimensionalZero) `shouldBe` (polydimensionalZero :: DynQuantity Double) - it "matches static multiplication" $ do - promoteQuantity (x1' P.* f') `shouldBe` Just (x1 * f) - it "allows multiplication with polydimensional zero" $ do - (f' P.* polydimensionalZero) `shouldBe` polydimensionalZero - (polydimensionalZero P.* m') `shouldBe` polydimensionalZero - (polydimensionalZero P.* polydimensionalZero) `shouldBe` (polydimensionalZero :: DynQuantity Double) - it "matches static negation" $ do - (P.negate m') `shouldBe` demoteQuantity (negate m) - it "negates polydimensional zero" $ do - (P.negate polydimensionalZero) `shouldBe` (polydimensionalZero :: DynQuantity Double) - it "matches static absolute value" $ do - (P.abs x2') `shouldBe` demoteQuantity (abs x2) - it "takes absolute value of polydimensional zero" $ do - (P.abs polydimensionalZero) `shouldBe` (polydimensionalZero :: DynQuantity Double) - it "matches static signum" $ do - (P.signum x1') `shouldBe` demoteQuantity (signum x1) - (P.signum x2') `shouldBe` demoteQuantity (signum x2) - it "takes signum of polydimensional zero" $ do - (P.signum polydimensionalZero) `shouldBe` demoteQuantity (_0 :: Dimensionless Double) - it "implements fromInteger with dimensionless result" $ do - (P.fromInteger 7 :: DynQuantity Double) `shouldBe` demoteQuantity _7 - context "Fractional instance" $ do - it "matches static division" $ do - ((f' P.* x1') P./ t') `shouldBe` demoteQuantity ((f * x1) / t) - it "matches static reciprocal" $ do - (P.recip m') `shouldBe` demoteQuantity (recip m) - it "implements fromRational with dimensionless result" $ do - let pi' = 22 P./ 7 :: Rational - (P.fromRational pi' :: DynQuantity Rational) `shouldBe` demoteQuantity (pi' *~ one) - it "permits polydimensional zero as a dividend" $ do - (polydimensionalZero P./ m') `shouldBe` polydimensionalZero - it "propagates witnesses to zero during division" $ do - -- We want to test that the witness for polymorphic zero was actually divided by the divisor. - -- The reason for this property is that if the divisor is itself zero (but not polydimensionalZero), - -- or some other element of the underlying type which can't act as a divisor (such as a propagating nAn), - -- then we want that information to still be around when we go to promote the result. - let nan = 0 P./ 0 :: Double - x = demoteQuantity $ nan *~ meter - y = polydimensionalZero P./ x - Just y' = promoteQuantity y :: Maybe (Length Double) - (y' /~ meter) `shouldSatisfy` P.isNaN - context "Floating instance" $ do - it "implements dimensionless pi" $ do - (P.pi :: DynQuantity Double) `shouldBe` demoteQuantity pi - it "implements dimensionless sin" $ do - -- this will serve as a test for all the single-argument dimensionless functions - (P.sin phi') `shouldBe` demoteQuantity (sin phi) - it "rejects non-dimensionless arguments to sin" $ do - (P.sin m') `shouldBe` invalidQuantity - it "implements dimensionless sin of polydimensional zero" $ do - (P.sin polydimensionalZero) `shouldBe` (0 :: DynQuantity Double) - it "matches static square root" $ do - (P.sqrt a') `shouldBe` demoteQuantity (sqrt a) - it "rejects arguments to square root with non-square dimensions" $ do - (P.sqrt f') `shouldNotSatisfy` hasSomeDimension - it "takes the square root of polydimensional zero" $ do - (P.sqrt polydimensionalZero) `shouldBe` (polydimensionalZero :: DynQuantity Double) - it "matches static dimensionless exponentiation" $ do - (phi' P.** phi') `shouldBe` demoteQuantity (phi ** phi) - it "rejects non-dimensionless arguments to dimensionless exponentiation" $ do - (phi' P.** m') `shouldNotSatisfy` hasSomeDimension - (x1' P.** phi') `shouldNotSatisfy` hasSomeDimension - it "matches static logBase" $ do - (P.logBase 10 phi') `shouldBe` demoteQuantity (logBase (10 *~ one) phi) - it "rejects non-dimensionless arguments to logBase" $ do - (P.logBase 10 x1') `shouldNotSatisfy` hasSomeDimension - (P.logBase x1' 10) `shouldNotSatisfy` hasSomeDimension - describe "Dynamic units" $ do - describe "Promotion and demotion" $ do - return () - describe "Arithmetic" $ do - return () +module Numeric.Units.Dimensional.DynamicSpec where++import Numeric.Units.Dimensional.Prelude+import Numeric.Units.Dimensional.Dynamic hiding ((*),(/),(^),(*~),(/~), recip)+import Numeric.Units.Dimensional.Dimensions.TermLevel (hasSomeDimension)+import qualified Numeric.Units.Dimensional.Dynamic as Dyn+import qualified Prelude as P+import Test.Hspec+import Test.QuickCheck++spec :: Spec+spec = do+ describe "Dynamic quantity promotion and demotion" $ do+ it "round-trips through AnyQuantity" $ property $+ \x -> let x' = x *~ kilo newton+ x'' = demoteQuantity x' :: AnyQuantity Double+ in Just x' == promoteQuantity x''+ it "round-trips through DynQuantity" $ property $+ \x -> let x' = x *~ micro watt+ x'' = demoteQuantity x' :: DynQuantity Rational+ in Just x' == promoteQuantity x''+ it "round-trips through AnyQuantity then DynQuantity" $ property $+ \x -> let x' = x *~ gram+ x'' = demoteQuantity x' :: AnyQuantity Double+ x''' = demoteQuantity x'' :: DynQuantity Double+ in Just x' == promoteQuantity x'''+ it "doesn't promote invalid quantities" $ do+ (promoteQuantity invalidQuantity :: Maybe (Length Double)) `shouldBe` Nothing+ it "doesn't promote AnyQuantity to the wrong dimension" $ do+ let x = 12.3 *~ meter+ x' = demoteQuantity x :: AnyQuantity Double+ (promoteQuantity x' :: Maybe (Mass Double)) `shouldBe` Nothing+ it "doesn't promote DynQuantity to the wrong dimension" $ do+ let x = 12.3 *~ mole+ x' = demoteQuantity x :: DynQuantity Double+ (promoteQuantity x' :: Maybe (Time Double)) `shouldBe` Nothing+ it "properly combines with dynamic units" $ do+ let meter' = demoteUnit' meter+ (promoteQuantity (139.4 Dyn.*~ meter' :: AnyQuantity Double)) `shouldBe` Just (139.4 *~ meter)+ it "properly eliminates dynamic units" $ do+ let ampere' = demoteUnit' ampere+ i = demoteQuantity $ 47 *~ ampere :: AnyQuantity Double+ i Dyn./~ ampere' `shouldBe` Just 47+ it "doesn't eliminate dynamic units of the wrong dimension" $ do+ let ampere' = demoteUnit' ampere+ i = demoteQuantity $ 47 *~ joule :: AnyQuantity Double+ i Dyn./~ ampere' `shouldBe` Nothing+ describe "DynQuantity arithmetic" $ do+ -- declare some static quantities and their dynamic counterparts for arithmetic tests+ let x1 = 12.3 *~ meter+ x2 = (-7.9) *~ meter+ a = 93 *~ square (kilo meter)+ m = 147 *~ kilo gram+ t = 14.9 *~ second+ f = 87.2 *~ milli newton+ phi = 1.61803398875 *~ one+ x1' = demoteQuantity x1 :: DynQuantity Double+ x2' = demoteQuantity x2 :: DynQuantity Double+ a' = demoteQuantity a :: DynQuantity Double+ m' = demoteQuantity m :: DynQuantity Double+ t' = demoteQuantity t :: DynQuantity Double+ f' = demoteQuantity f :: DynQuantity Double+ phi' = demoteQuantity phi :: DynQuantity Double+ context "Num instance" $ do+ it "matches static addition" $ do+ (x1' P.+ x2') `shouldBe` demoteQuantity (x1 + x2)+ it "allows addition with polydimensional zero" $ do+ (t' P.+ polydimensionalZero) `shouldBe` t'+ (polydimensionalZero P.+ t') `shouldBe` t'+ (polydimensionalZero P.+ polydimensionalZero) `shouldBe` (polydimensionalZero :: DynQuantity Double) + it "propagates witnesses to zero during addition" $ do+ -- We want to test that the witness for polymorphic zero was actually added to the other addend.+ -- The reason for this property is that if the other addend is some element of the underlying type+ -- which can't act as a divisor (such as a propagating nAn), then we want that information to still+ -- be around when we go to promote the result.+ let nan = 0 P./ 0 :: Double+ x = demoteQuantity $ nan *~ meter+ Just y = promoteQuantity (polydimensionalZero P.+ x) :: Maybe (Length Double)+ (y /~ meter) `shouldSatisfy` P.isNaN+ it "matches static subtraction" $ do+ (x2' P.- x1') `shouldBe` demoteQuantity (x2 - x1)+ it "allows subtraction with polydimensional zero" $ do+ (m' P.- polydimensionalZero) `shouldBe` m'+ (polydimensionalZero P.- m') `shouldBe` (P.negate m')+ (polydimensionalZero P.- polydimensionalZero) `shouldBe` (polydimensionalZero :: DynQuantity Double) + it "matches static multiplication" $ do+ promoteQuantity (x1' P.* f') `shouldBe` Just (x1 * f)+ it "allows multiplication with polydimensional zero" $ do+ (f' P.* polydimensionalZero) `shouldBe` polydimensionalZero+ (polydimensionalZero P.* m') `shouldBe` polydimensionalZero+ (polydimensionalZero P.* polydimensionalZero) `shouldBe` (polydimensionalZero :: DynQuantity Double)+ it "matches static negation" $ do+ (P.negate m') `shouldBe` demoteQuantity (negate m)+ it "negates polydimensional zero" $ do+ (P.negate polydimensionalZero) `shouldBe` (polydimensionalZero :: DynQuantity Double)+ it "matches static absolute value" $ do+ (P.abs x2') `shouldBe` demoteQuantity (abs x2)+ it "takes absolute value of polydimensional zero" $ do+ (P.abs polydimensionalZero) `shouldBe` (polydimensionalZero :: DynQuantity Double)+ it "matches static signum" $ do+ (P.signum x1') `shouldBe` demoteQuantity (signum x1)+ (P.signum x2') `shouldBe` demoteQuantity (signum x2)+ it "takes signum of polydimensional zero" $ do+ (P.signum polydimensionalZero) `shouldBe` demoteQuantity (_0 :: Dimensionless Double)+ it "implements fromInteger with dimensionless result" $ do+ (P.fromInteger 7 :: DynQuantity Double) `shouldBe` demoteQuantity _7+ context "Fractional instance" $ do+ it "matches static division" $ do+ ((f' P.* x1') P./ t') `shouldBe` demoteQuantity ((f * x1) / t)+ it "matches static reciprocal" $ do+ (P.recip m') `shouldBe` demoteQuantity (recip m)+ it "implements fromRational with dimensionless result" $ do+ let pi' = 22 P./ 7 :: Rational+ (P.fromRational pi' :: DynQuantity Rational) `shouldBe` demoteQuantity (pi' *~ one)+ it "permits polydimensional zero as a dividend" $ do+ (polydimensionalZero P./ m') `shouldBe` polydimensionalZero+ it "propagates witnesses to zero during division" $ do+ -- We want to test that the witness for polymorphic zero was actually divided by the divisor.+ -- The reason for this property is that if the divisor is itself zero (but not polydimensionalZero),+ -- or some other element of the underlying type which can't act as a divisor (such as a propagating nAn),+ -- then we want that information to still be around when we go to promote the result.+ let nan = 0 P./ 0 :: Double+ x = demoteQuantity $ nan *~ meter+ y = polydimensionalZero P./ x+ Just y' = promoteQuantity y :: Maybe (Length Double)+ (y' /~ meter) `shouldSatisfy` P.isNaN+ context "Floating instance" $ do+ it "implements dimensionless pi" $ do+ (P.pi :: DynQuantity Double) `shouldBe` demoteQuantity pi+ it "implements dimensionless sin" $ do+ -- this will serve as a test for all the single-argument dimensionless functions+ (P.sin phi') `shouldBe` demoteQuantity (sin phi)+ it "rejects non-dimensionless arguments to sin" $ do+ (P.sin m') `shouldBe` invalidQuantity+ it "implements dimensionless sin of polydimensional zero" $ do+ (P.sin polydimensionalZero) `shouldBe` (0 :: DynQuantity Double)+ it "matches static square root" $ do+ (P.sqrt a') `shouldBe` demoteQuantity (sqrt a)+ it "rejects arguments to square root with non-square dimensions" $ do+ (P.sqrt f') `shouldNotSatisfy` hasSomeDimension+ it "takes the square root of polydimensional zero" $ do+ (P.sqrt polydimensionalZero) `shouldBe` (polydimensionalZero :: DynQuantity Double)+ it "matches static dimensionless exponentiation" $ do+ (phi' P.** phi') `shouldBe` demoteQuantity (phi ** phi)+ it "rejects non-dimensionless arguments to dimensionless exponentiation" $ do+ (phi' P.** m') `shouldNotSatisfy` hasSomeDimension+ (x1' P.** phi') `shouldNotSatisfy` hasSomeDimension+ it "matches static logBase" $ do+ (P.logBase 10 phi') `shouldBe` demoteQuantity (logBase (10 *~ one) phi)+ it "rejects non-dimensionless arguments to logBase" $ do+ (P.logBase 10 x1') `shouldNotSatisfy` hasSomeDimension+ (P.logBase x1' 10) `shouldNotSatisfy` hasSomeDimension+ describe "Dynamic units" $ do+ describe "Promotion and demotion" $ do+ return ()+ describe "Arithmetic" $ do+ return ()
tests/Numeric/Units/Dimensional/QuantitiesSpec.hs view
@@ -1,137 +1,137 @@-module Numeric.Units.Dimensional.QuantitiesSpec where - -import Numeric.Units.Dimensional.Prelude -import Test.Hspec - -spec :: Spec -spec = do - describe "Quantity synonyms" $ do - it "compile with correct dimensions" $ do - success -- If I compiled I'm OK! - -success :: IO () -success = return () - --- These definitions simply verify that the type synonyms are --- consistent with the appropriate units from table 2. If the --- definitions compile the type synonyms are good. - -x1 :: Area Double -x1 = 1 *~ meter ^ pos2 -x2 :: Volume Double -x2 = 1 *~ meter ^ pos3 -x3 :: Velocity Double -x3 = 1 *~ (meter / second) -x4 :: Acceleration Double -x4 = 1 *~ (meter / second ^ pos2) -x5 :: WaveNumber Double -x5 = 1 *~ meter ^ neg1 -x6 :: Density Double -x6 = 1 *~ (kilo gram / meter ^ pos3) -x7 :: SpecificVolume Double -x7 = 1 *~ (meter ^ pos3 / kilo gram) -x8 :: CurrentDensity Double -x8 = 1 *~ (ampere / meter ^ pos2) -x9 :: MagneticFieldStrength Double -x9 = 1 *~ (ampere / meter) -x10 :: Concentration Double -x10 = 1 *~ (mole / meter ^ pos3) -x11 :: Luminance Double -x11 = 1 *~ (candela / meter ^ pos2) - --- These definitions simply verify that the type synonyms are --- consistent with the appropriate units from table 3. If the --- definitions compile the type synonyms are good. - -y1 :: PlaneAngle Double -y1 = 1 *~ (meter / meter) -y2 :: SolidAngle Double -y2 = 1 *~ (meter ^ pos2 / meter ^ pos2) -y3 :: Frequency Double -y3 = 1 *~ (one / second) -y4 :: Force Double -y4 = 1 *~ (meter * kilo gram / second ^ pos2) -y5 :: Pressure Double -y5 = 1 *~ (newton / meter ^ pos2) -y6 :: Energy Double -y6 = 1 *~ (newton * meter) -y7 :: Power Double -y7 = 1 *~ (joule / second) -y8 :: ElectricCharge Double -y8 = 1 *~ (second * ampere) -y9 :: ElectricPotential Double -y9 = 1 *~ (watt / ampere) -y10 :: Capacitance Double -y10 = 1 *~ (coulomb / volt) -y11 :: ElectricResistance Double -y11 = 1 *~ (volt / ampere) -y12 :: ElectricConductance Double -y12 = 1 *~ (ampere / volt) -y13 :: MagneticFlux Double -y13 = 1 *~ (volt * second) -y14 :: MagneticFluxDensity Double -y14 = 1 *~ (weber / meter ^ pos2) -y15 :: Inductance Double -y15 = 1 *~ (weber / ampere) -y16 :: LuminousFlux Double -y16 = 1 *~ (candela * steradian) -y17 :: Illuminance Double -y17 = 1 *~ (lumen / meter ^ pos2) -y18 :: Activity Double -y18 = 1 *~ (one / second) -y19 :: AbsorbedDose Double -y19 = 1 *~ (joule / kilo gram) -y20 :: DoseEquivalent Double -y20 = 1 *~ (joule / kilo gram) -y21 :: CatalyticActivity Double -y21 = 1 *~ (mole / second) - --- Verification of table 4. If the definitions compile the type --- synonyms are good. - -z1 :: AngularVelocity Double -z1 = 1 *~ (radian / second) -z2 :: AngularAcceleration Double -z2 = 1 *~ (radian / second ^ pos2) -z3 :: DynamicViscosity Double -z3 = 1 *~ (pascal * second) -z4 :: MomentOfForce Double -z4 = 1 *~ (newton * meter) -z5 :: SurfaceTension Double -z5 = 1 *~ (newton / meter) -z6 :: HeatFluxDensity Double -z6 = 1 *~ (watt / meter ^ pos2) -z7 :: RadiantIntensity Double -z7 = 1 *~ (watt / steradian) -z8 :: Radiance Double -z8 = 1 *~ (watt / (meter ^ pos2 * steradian)) -z9 :: HeatCapacity Double -z9 = 1 *~ (joule / kelvin) -z10 :: SpecificHeatCapacity Double -z10 = 1 *~ (joule / (kilo gram * kelvin)) -z11 :: ThermalConductivity Double -z11 = 1 *~ (watt / (meter * kelvin)) -z12 :: EnergyDensity Double -z12 = 1 *~ (joule / meter ^ pos3) -z13 :: ElectricFieldStrength Double -z13 = 1 *~ (volt / meter) -z14 :: ElectricChargeDensity Double -z14 = 1 *~ (coulomb / meter ^ pos3) -z15 :: ElectricFluxDensity Double -z15 = 1 *~ (coulomb / meter ^ pos2) -z16 :: Permittivity Double -z16 = 1 *~ (farad / meter) -z17 :: Permeability Double -z17 = 1 *~ (henry / meter) -z18 :: MolarEnergy Double -z18 = 1 *~ (joule / mole) -z19 :: MolarEntropy Double -z19 = 1 *~ (joule / (mole * kelvin)) -z20 :: Exposure Double -z20 = 1 *~ (coulomb / kilo gram) -z21 :: AbsorbedDoseRate Double -z21 = 1 *~ (gray / second) - --- Other quantitites. -mu :: GravitationalParameter Double -mu = 398600.4418 *~ (kilo meter ^ pos3 / second ^ pos2) +module Numeric.Units.Dimensional.QuantitiesSpec where++import Numeric.Units.Dimensional.Prelude+import Test.Hspec++spec :: Spec+spec = do+ describe "Quantity synonyms" $ do+ it "compile with correct dimensions" $ do+ success -- If I compiled I'm OK!++success :: IO ()+success = return ()++-- These definitions simply verify that the type synonyms are+-- consistent with the appropriate units from table 2. If the+-- definitions compile the type synonyms are good.++x1 :: Area Double+x1 = 1 *~ meter ^ pos2+x2 :: Volume Double+x2 = 1 *~ meter ^ pos3+x3 :: Velocity Double+x3 = 1 *~ (meter / second)+x4 :: Acceleration Double+x4 = 1 *~ (meter / second ^ pos2)+x5 :: WaveNumber Double+x5 = 1 *~ meter ^ neg1+x6 :: Density Double+x6 = 1 *~ (kilo gram / meter ^ pos3)+x7 :: SpecificVolume Double+x7 = 1 *~ (meter ^ pos3 / kilo gram)+x8 :: CurrentDensity Double+x8 = 1 *~ (ampere / meter ^ pos2)+x9 :: MagneticFieldStrength Double+x9 = 1 *~ (ampere / meter)+x10 :: Concentration Double+x10 = 1 *~ (mole / meter ^ pos3)+x11 :: Luminance Double+x11 = 1 *~ (candela / meter ^ pos2)++-- These definitions simply verify that the type synonyms are+-- consistent with the appropriate units from table 3. If the+-- definitions compile the type synonyms are good.++y1 :: PlaneAngle Double+y1 = 1 *~ (meter / meter)+y2 :: SolidAngle Double+y2 = 1 *~ (meter ^ pos2 / meter ^ pos2)+y3 :: Frequency Double+y3 = 1 *~ (one / second)+y4 :: Force Double+y4 = 1 *~ (meter * kilo gram / second ^ pos2)+y5 :: Pressure Double+y5 = 1 *~ (newton / meter ^ pos2)+y6 :: Energy Double+y6 = 1 *~ (newton * meter)+y7 :: Power Double+y7 = 1 *~ (joule / second)+y8 :: ElectricCharge Double+y8 = 1 *~ (second * ampere)+y9 :: ElectricPotential Double+y9 = 1 *~ (watt / ampere)+y10 :: Capacitance Double+y10 = 1 *~ (coulomb / volt)+y11 :: ElectricResistance Double+y11 = 1 *~ (volt / ampere)+y12 :: ElectricConductance Double+y12 = 1 *~ (ampere / volt)+y13 :: MagneticFlux Double+y13 = 1 *~ (volt * second)+y14 :: MagneticFluxDensity Double+y14 = 1 *~ (weber / meter ^ pos2)+y15 :: Inductance Double+y15 = 1 *~ (weber / ampere)+y16 :: LuminousFlux Double+y16 = 1 *~ (candela * steradian)+y17 :: Illuminance Double+y17 = 1 *~ (lumen / meter ^ pos2)+y18 :: Activity Double+y18 = 1 *~ (one / second)+y19 :: AbsorbedDose Double+y19 = 1 *~ (joule / kilo gram)+y20 :: DoseEquivalent Double+y20 = 1 *~ (joule / kilo gram)+y21 :: CatalyticActivity Double+y21 = 1 *~ (mole / second)++-- Verification of table 4. If the definitions compile the type+-- synonyms are good.++z1 :: AngularVelocity Double+z1 = 1 *~ (radian / second)+z2 :: AngularAcceleration Double+z2 = 1 *~ (radian / second ^ pos2)+z3 :: DynamicViscosity Double+z3 = 1 *~ (pascal * second)+z4 :: MomentOfForce Double+z4 = 1 *~ (newton * meter)+z5 :: SurfaceTension Double+z5 = 1 *~ (newton / meter)+z6 :: HeatFluxDensity Double+z6 = 1 *~ (watt / meter ^ pos2)+z7 :: RadiantIntensity Double+z7 = 1 *~ (watt / steradian)+z8 :: Radiance Double+z8 = 1 *~ (watt / (meter ^ pos2 * steradian))+z9 :: HeatCapacity Double+z9 = 1 *~ (joule / kelvin)+z10 :: SpecificHeatCapacity Double+z10 = 1 *~ (joule / (kilo gram * kelvin))+z11 :: ThermalConductivity Double+z11 = 1 *~ (watt / (meter * kelvin))+z12 :: EnergyDensity Double+z12 = 1 *~ (joule / meter ^ pos3)+z13 :: ElectricFieldStrength Double+z13 = 1 *~ (volt / meter)+z14 :: ElectricChargeDensity Double+z14 = 1 *~ (coulomb / meter ^ pos3)+z15 :: ElectricFluxDensity Double+z15 = 1 *~ (coulomb / meter ^ pos2)+z16 :: Permittivity Double+z16 = 1 *~ (farad / meter)+z17 :: Permeability Double+z17 = 1 *~ (henry / meter)+z18 :: MolarEnergy Double+z18 = 1 *~ (joule / mole)+z19 :: MolarEntropy Double+z19 = 1 *~ (joule / (mole * kelvin))+z20 :: Exposure Double+z20 = 1 *~ (coulomb / kilo gram)+z21 :: AbsorbedDoseRate Double+z21 = 1 *~ (gray / second)++-- Other quantitites.+mu :: GravitationalParameter Double+mu = 398600.4418 *~ (kilo meter ^ pos3 / second ^ pos2)
tests/Numeric/Units/DimensionalSpec.hs view
@@ -1,49 +1,49 @@-module Numeric.Units.DimensionalSpec where - -import Numeric.Units.Dimensional.Prelude -import Test.Hspec -import qualified Prelude as P - -spec :: Spec -spec = do - describe "Exponentiation operators" $ do - it "correctly exponentiate quantities with integer exponents" $ do - ((9::Double) *~ one) `shouldBe` (3 *~ one) ^ pos2 - ((1::Double) *~ one) `shouldBe` (12.1231 *~ one) ^ zero - ((0.25::Double) *~ one) `shouldBe` (2 *~ one) ^ neg2 - it "correctly exponentiate dimensionless quantities with floating point exponents" $ do - (3 P.** 2::Double) *~ one `shouldBe` (3 *~ one) ** (2 *~ one) - (3 P.** (-2.231)::Double) *~ one `shouldBe` (3 *~ one) ** ((-2.231) *~ one) - - describe "Show instance" $ do - it "properly prints basic quantities" $ do - -- note: these comparison literals use non-breaking spaces - show ((1.0::Double) *~ one) `shouldBe` "1.0" - show ((2.0::Double) *~ meter) `shouldBe` "2.0 m" - show ((2.0::Double) *~ (meter / second)) `shouldBe` "2.0 m s^-1" - show ((2.0::Double) *~ (meter ^ pos2 / second ^ pos2)) `shouldBe` "2.0 m^2 s^-2" - - describe "Ord instance" $ do - it "properly sorts quantities" $ do - compare ((1 :: Integer) *~ one) (3 *~ one) `shouldBe` LT - compare ((1 :: Double) *~ (kilo meter)) (1 *~ meter) `shouldBe` GT - compare ((0 :: Double) *~ second) (_0) `shouldBe` EQ - - describe "Enumeration function nFromTo" $ do - it "handles zero intermediate values" $ do - nFromTo' _1 _6 0 `shouldBe` [_1, _6] - it "handles negative number of intermediate values" $ do - nFromTo' _1 _6 (-1) `shouldBe` [_1, _6] - it "handles straightforward cases" $ do - nFromTo' _1 _3 1 `shouldBe` [_1, _2, _3] - nFromTo' _1 _6 4 `shouldBe` [_1, _2, _3, _4, _5, _6] - nFromTo' _0 _6 2 `shouldBe` [_0, _2, _4, _6] - it "handles decreasing intervals" $ do - nFromTo' _5 _2 2 `shouldBe` [_5, _4, _3, _2] - nFromTo' _6 _0 2 `shouldBe` [_6, _4, _2, _0] - it "handles empty intervals" $ do - nFromTo' _1 _1 0 `shouldBe` [_1, _1] - nFromTo' _0 _0 2 `shouldBe` [_0, _0, _0, _0] - -nFromTo' :: Dimensionless Double -> Dimensionless Double -> Int -> [Dimensionless Double] -nFromTo' = nFromTo +module Numeric.Units.DimensionalSpec where++import Numeric.Units.Dimensional.Prelude+import Test.Hspec+import qualified Prelude as P++spec :: Spec+spec = do+ describe "Exponentiation operators" $ do+ it "correctly exponentiate quantities with integer exponents" $ do+ ((9::Double) *~ one) `shouldBe` (3 *~ one) ^ pos2+ ((1::Double) *~ one) `shouldBe` (12.1231 *~ one) ^ zero+ ((0.25::Double) *~ one) `shouldBe` (2 *~ one) ^ neg2+ it "correctly exponentiate dimensionless quantities with floating point exponents" $ do+ (3 P.** 2::Double) *~ one `shouldBe` (3 *~ one) ** (2 *~ one)+ (3 P.** (-2.231)::Double) *~ one `shouldBe` (3 *~ one) ** ((-2.231) *~ one)++ describe "Show instance" $ do+ it "properly prints basic quantities" $ do+ -- note: these comparison literals use non-breaking spaces+ show ((1.0::Double) *~ one) `shouldBe` "1.0"+ show ((2.0::Double) *~ meter) `shouldBe` "2.0 m"+ show ((2.0::Double) *~ (meter / second)) `shouldBe` "2.0 m s^-1"+ show ((2.0::Double) *~ (meter ^ pos2 / second ^ pos2)) `shouldBe` "2.0 m^2 s^-2"++ describe "Ord instance" $ do+ it "properly sorts quantities" $ do+ compare ((1 :: Integer) *~ one) (3 *~ one) `shouldBe` LT+ compare ((1 :: Double) *~ (kilo meter)) (1 *~ meter) `shouldBe` GT+ compare ((0 :: Double) *~ second) (_0) `shouldBe` EQ++ describe "Enumeration function nFromTo" $ do+ it "handles zero intermediate values" $ do+ nFromTo' _1 _6 0 `shouldBe` [_1, _6]+ it "handles negative number of intermediate values" $ do+ nFromTo' _1 _6 (-1) `shouldBe` [_1, _6]+ it "handles straightforward cases" $ do+ nFromTo' _1 _3 1 `shouldBe` [_1, _2, _3]+ nFromTo' _1 _6 4 `shouldBe` [_1, _2, _3, _4, _5, _6]+ nFromTo' _0 _6 2 `shouldBe` [_0, _2, _4, _6]+ it "handles decreasing intervals" $ do+ nFromTo' _5 _2 2 `shouldBe` [_5, _4, _3, _2]+ nFromTo' _6 _0 2 `shouldBe` [_6, _4, _2, _0]+ it "handles empty intervals" $ do+ nFromTo' _1 _1 0 `shouldBe` [_1, _1]+ nFromTo' _0 _0 2 `shouldBe` [_0, _0, _0, _0]++nFromTo' :: Dimensionless Double -> Dimensionless Double -> Int -> [Dimensionless Double]+nFromTo' = nFromTo
tests/Spec.hs view
@@ -1,4 +1,4 @@-{-# OPTIONS_GHC -F -pgmF hspec-discover #-} - --- This module will automatically pull in all the Spec modules. --- See http://hspec.github.io/hspec-discover.html for a summary of how it works. +{-# OPTIONS_GHC -F -pgmF hspec-discover #-}++-- This module will automatically pull in all the Spec modules.+-- See https://hspec.github.io/hspec-discover.html for a summary of how it works.