linear-accelerate 0.5.0.1 → 0.6.0.0

raw patch · 19 files changed

+1040/−148 lines, 19 filesdep ~acceleratedep ~doctestPVP ok

version bump matches the API change (PVP)

Dependency ranges changed: accelerate, doctest

API changes (from Hackage documentation)

Files

• .travis.yml +15/−23
• CHANGELOG.markdown +29/−22
• linear-accelerate.cabal +31/−16
• src/Data/Array/Accelerate/Linear.hs +1/−1
• src/Data/Array/Accelerate/Linear/Conjugate.hs +63/−0
• src/Data/Array/Accelerate/Linear/Epsilon.hs +1/−1
• src/Data/Array/Accelerate/Linear/Lift.hs +1/−1
• src/Data/Array/Accelerate/Linear/Matrix.hs +82/−25
• src/Data/Array/Accelerate/Linear/Metric.hs +1/−1
• src/Data/Array/Accelerate/Linear/Plucker.hs +228/−12
• src/Data/Array/Accelerate/Linear/Quaternion.hs +352/−4
• src/Data/Array/Accelerate/Linear/Trace.hs +57/−0
• src/Data/Array/Accelerate/Linear/Type.hs +1/−1
• src/Data/Array/Accelerate/Linear/V0.hs +29/−9
• src/Data/Array/Accelerate/Linear/V1.hs +32/−8
• src/Data/Array/Accelerate/Linear/V2.hs +38/−7
• src/Data/Array/Accelerate/Linear/V3.hs +38/−7
• src/Data/Array/Accelerate/Linear/V4.hs +39/−8
• src/Data/Array/Accelerate/Linear/Vector.hs +2/−2

@@ -3,17 +3,18 @@ # Basic template to test with GHC=[7.8, 7.10, 8.0]. Caches the 'stack' build # directory to speed subsequent compilations. #-language: generic+# https://docs.travis-ci.com/user/reference/overview/+#+language: minimal dist: trusty-sudo: false+sudo: true      # more storage available on sudo-enabled instances  cache:   directories:-    - $HOME/.stack+    - $HOME/.stack/snapshots     - .stack-work/install  before_cache:-  - rm -rf $(stack path --local-install-root)/bin   - rm -rf $(stack path --local-install-root)/doc  addons:@@ -28,10 +29,6 @@  matrix:   include:-    - env: GHC=7.8.4 CABAL=1.24-      compiler: "GHC 7.8"-      addons: { apt: { sources: [ *apt_sources ], packages: [ *apt_packages, cabal-install-1.24 ] }}-     - env: GHC=7.10.3 CABAL=1.24       compiler: "GHC 7.10"       addons: { apt: { sources: [ *apt_sources ], packages: [ *apt_packages, cabal-install-1.24 ] }}@@ -40,10 +37,14 @@       compiler: "GHC 8.0"       addons: { apt: { sources: [ *apt_sources ], packages: [ *apt_packages, cabal-install-1.24 ] }} -    - env: GHC=8.2.0 CABAL=1.24+    - env: GHC=8.2.2 CABAL=2.0       compiler: "GHC 8.2"-      addons: { apt: { sources: [ *apt_sources ], packages: [ *apt_packages, cabal-install-1.24 ] }}+      addons: { apt: { sources: [ *apt_sources ], packages: [ *apt_packages, cabal-install-2.0 ] }} +    - env: GHC=8.4.1 CABAL=2.0+      compiler: "GHC 8.4"+      addons: { apt: { sources: [ *apt_sources ], packages: [ *apt_packages, cabal-install-2.0 ] }}+     # - env: GHC=head CABAL=head     #   compiler: "GHC HEAD"     #   addons: { apt: { sources: [ *apt_sources ], packages: [ *apt_packages, ghc-head, cabal-install-head ] }}@@ -61,21 +62,12 @@   - echo "$(ghc --version) [$(ghc --print-project-git-commit-id 2> /dev/null || echo '?')]"   - cabal --version   - stack --version-  - |-      if [ ${GHC} == head -o ! -e stack.yaml ]; then-        travis_retry cabal install --only-dependencies-      else-        travis_retry stack build --only-dependencies --no-terminal --no-haddock-deps-      fi+  - stack build --no-terminal --dry-run+  - travis_retry travis_wait 60 stack build --fast --test --only-dependencies --no-terminal --no-copy-bins  script:-  - |-      if [ ${GHC} == head -o ! -e stack.yaml ]; then-        cabal install-        cabal haddock-      else-        stack test --no-terminal --haddock --no-haddock-deps-      fi+  - stack build --no-terminal --fast --test --haddock --no-haddock-deps --no-run-tests+  - stack test  after_success:   - source .travis/update-accelerate-buildbot.sh

@@ -6,39 +6,46 @@ project adheres to the [Haskell Package Versioning Policy (PVP)](https://pvp.haskell.org) --## [0.5.0.1]--* Fix [#10]: doctest failure with accelerate-1.1.1.0--## [0.5]--* Fix [#25][acc-llvm#25]: "impossible evaluation" error with accelerate-llvm-native--## [0.4.1]+## [0.6.0.0] - 2018-04-03+### Changed+  * update for accelerate-1.2 -* Support `doctest-0.12`.+### Fixed+  * Disambiguate uses of `fromInteger` and `fromRational`. -## [0.4]+## [0.5.0.1] - 2017-09-29+### Fixed+  * doctest failure with accelerate-1.1.1.0 ([#10]) -* Revamp `Setup.hs` to use `cabal-doctest`. This makes `linear-accelerate`-  build with `Cabal-2.0`.-* Fix handedness of `(-^)` and `(^-)`.-* Re-enable the `doctest`s.+## [0.5] - 2017-08-06+### Fixed+  * "impossible evaluation" error with accelerate-llvm-native ([#25][acc-llvm#25]) -## [0.3]+## [0.4.1] - 2017-07-29+### Added+  * Support `doctest-0.12`. -* Expanded API coverage+## [0.4] - 2017-06-16+### Changed+  * Revamp `Setup.hs` to use `cabal-doctest`. This makes `linear-accelerate` build with `Cabal-2.0`.+  * Re-enable the `doctest`s. -## [0.2]+### Fixed+  * Fix handedness of `(-^)` and `(^-)`. -* Fix [#1]: Move `Data.Complex` instances into the `accelerate` package+## [0.3] - 2017-04-01+### Changed+  * Expanded API coverage -## [0.1]+## [0.2] - 2014-09-15+### Fixed+  * Move `Data.Complex` instances into the `accelerate` package ([#1]) -* Repository initialized+## [0.1] - 2014-03-28+  * Repository initialized  +[0.6.0.0]:          https://github.com/ekmett/linear-accelerate/compare/v0.5.0.1...v0.6.0.0 [0.5.0.1]:          https://github.com/ekmett/linear-accelerate/compare/v0.5...v0.5.0.1 [0.5]:              https://github.com/ekmett/linear-accelerate/compare/v0.4.1...v0.5 [0.4.1]:            https://github.com/ekmett/linear-accelerate/compare/v0.4...v0.4.1

@@ -1,6 +1,6 @@ name:          linear-accelerate category:      Math, Algebra, Compilers/Interpreters, Concurrency, Data, Parallelism-version:       0.5.0.1+version:       0.6.0.0 license:       BSD3 cabal-version: >= 1.10 license-file:  LICENSE@@ -21,12 +21,12 @@   Warning.hs  source-repository head-  type: git+  type:     git   location: git://github.com/ekmett/linear-accelerate.git  source-repository this-  type: git-  tag: v0.5.0.1+  type:     git+  tag:      v0.6.0.0   location: git://github.com/ekmett/linear-accelerate.git  custom-setup@@ -38,15 +38,17 @@ library   build-depends:       base              >= 4.5          && < 5-    , accelerate        >= 0.16+    , accelerate        >= 1.2     , distributive      >= 0.2.2        && < 1     , lens              >= 4            && < 5     , linear            >= 1.10         && < 2    exposed-modules:     Data.Array.Accelerate.Linear+    Data.Array.Accelerate.Linear.Conjugate     Data.Array.Accelerate.Linear.Epsilon     Data.Array.Accelerate.Linear.Matrix+    Data.Array.Accelerate.Linear.Trace     Data.Array.Accelerate.Linear.Metric     Data.Array.Accelerate.Linear.Plucker     Data.Array.Accelerate.Linear.Quaternion@@ -61,19 +63,32 @@   other-modules:     Data.Array.Accelerate.Linear.Lift -  default-language: Haskell2010-  ghc-options: -Wall -fwarn-tabs -O2-  hs-source-dirs: src+  hs-source-dirs:+    src +  default-language:+    Haskell2010++  ghc-options:+    -Wall+    -fwarn-tabs+    -O2+ test-suite doctests-  type:    exitcode-stdio-1.0-  main-is: doctests.hs-  default-language: Haskell2010+  type:               exitcode-stdio-1.0+  hs-source-dirs:     tests+  main-is:            doctests.hs+   build-depends:-    base    == 4.*,-    doctest >= 0.11.1 && < 0.14,-    linear-accelerate-  ghc-options: -Wall -threaded-  hs-source-dirs: tests+      base              == 4.*+    , doctest           >= 0.11.1 && < 0.16+    , linear-accelerate++  default-language:+    Haskell2010++  ghc-options:+    -Wall+    -threaded  -- vim: nospell

@@ -2,7 +2,7 @@ -- | -- Module      : Data.Array.Accelerate.Linear -- Copyright   : 2014 Edward Kmett, Charles Durham,---               2015 Trevor L. McDonell+--               [2015..2018] Trevor L. McDonell -- License     : BSD-style (see the file LICENSE) -- -- Maintainer  : Edward Kmett <ekmett@gmail.com>

@@ -0,0 +1,63 @@+{-# LANGUAGE FlexibleContexts    #-}+{-# LANGUAGE FlexibleInstances   #-}+{-# LANGUAGE ScopedTypeVariables #-}+{-# LANGUAGE ViewPatterns        #-}+{-# OPTIONS_GHC -fno-warn-orphans #-}+-----------------------------------------------------------------------------+-- |+-- Module      : Data.Array.Accelerate.Linear.Conjugate+-- Copyright   : 2018 Trevor L. McDonell+-- License     : BSD-style (see the file LICENSE)+--+-- Maintainer  : Edward Kmett <ekmett@gmail.com>+-- Stability   : experimental+-- Portability : non-portable+--+-- Involutive rings+----------------------------------------------------------------------------++module Data.Array.Accelerate.Linear.Conjugate (++  Conjugate(..),+  TrivialConjugate,++) where++import Data.Array.Accelerate                                        as A+import Data.Array.Accelerate.Data.Complex                           ( Complex(..) )++import Linear.Conjugate++instance Conjugate (Exp Int)+instance Conjugate (Exp Int64)+instance Conjugate (Exp Int32)+instance Conjugate (Exp Int16)+instance Conjugate (Exp Int8)+instance Conjugate (Exp Word)+instance Conjugate (Exp Word64)+instance Conjugate (Exp Word32)+instance Conjugate (Exp Word16)+instance Conjugate (Exp Word8)+instance Conjugate (Exp Double)+instance Conjugate (Exp Float)+instance Conjugate (Exp CFloat)+instance Conjugate (Exp CDouble)++instance (Conjugate (Exp a), A.RealFloat a, Elt (Complex a)) => Conjugate (Exp (Complex a)) where+  conjugate (unlift -> a :+ b :: Complex (Exp a)) = lift $ conjugate a :+ negate b++instance TrivialConjugate (Exp Int)+instance TrivialConjugate (Exp Int64)+instance TrivialConjugate (Exp Int32)+instance TrivialConjugate (Exp Int16)+instance TrivialConjugate (Exp Int8)+instance TrivialConjugate (Exp Word)+instance TrivialConjugate (Exp Word64)+instance TrivialConjugate (Exp Word32)+instance TrivialConjugate (Exp Word16)+instance TrivialConjugate (Exp Word8)+instance TrivialConjugate (Exp Double)+instance TrivialConjugate (Exp Float)+instance TrivialConjugate (Exp CFloat)+instance TrivialConjugate (Exp CDouble)+

@@ -5,7 +5,7 @@ -- | -- Module      : Data.Array.Accelerate.Linear.Epsilon -- Copyright   : 2014 Edward Kmett, Charles Durham,---               2015 Trevor L. McDonell+--               [2015..2018] Trevor L. McDonell -- License     : BSD-style (see the file LICENSE) -- -- Maintainer  : Edward Kmett <ekmett@gmail.com>

@@ -5,7 +5,7 @@ ----------------------------------------------------------------------------- -- | -- Module      : Data.Array.Accelerate.Linear.Lift--- Copyright   : 2015 Trevor L. McDonell+-- Copyright   : [2015..2018] Trevor L. McDonell -- License     : BSD-style (see the file LICENSE) -- -- Maintainer  : Trevor L. McDonell <tmcdonell@cse.unsw.edu.au>

@@ -6,7 +6,7 @@ -- | -- Module      : Data.Array.Accelerate.Linear.Matrix -- Copyright   : 2014 Edward Kmett, Charles Durham,---               2015 Trevor L. McDonell+--               [2015..2018] Trevor L. McDonell -- License     : BSD-style (see the file LICENSE) -- -- Maintainer  : Edward Kmett <ekmett@gmail.com>@@ -18,26 +18,27 @@  module Data.Array.Accelerate.Linear.Matrix ( -  M22, M23, M24, M32, M33, M34, M42, M43, M44,   (!*!), (!+!), (!-!), (!*), (*!), (!!*), (*!!), (!!/),-  transpose,+  M22, M23, M24, M32, M33, M34, M42, M43, M44,+  m33_to_m44, m43_to_m44,+  det22, det33, det44,+  inv22, inv33, inv44,   identity,+  transpose,   Trace(..),+  fromQuaternion,+  mkTransformation,+  mkTransformationMat,  ) where  import Data.Array.Accelerate                    as A hiding ( transpose )-import Data.Array.Accelerate.Data.Complex  import Data.Array.Accelerate.Linear.Lift-import Data.Array.Accelerate.Linear.Plucker-import Data.Array.Accelerate.Linear.Quaternion+import Data.Array.Accelerate.Linear.Trace import Data.Array.Accelerate.Linear.Type-import Data.Array.Accelerate.Linear.V0-import Data.Array.Accelerate.Linear.V1-import Data.Array.Accelerate.Linear.V2+import Data.Array.Accelerate.Linear.Quaternion import Data.Array.Accelerate.Linear.V3-import Data.Array.Accelerate.Linear.V4 import Data.Array.Accelerate.Linear.Vector  import Linear.Matrix                            ( M22, M23, M24, M32, M33, M34, M42, M43, M44 )@@ -51,6 +52,9 @@  -- $setup -- >>> import Data.Array.Accelerate.Interpreter+-- >>> import Data.Array.Accelerate.Linear.V2+-- >>> import Data.Array.Accelerate.Linear.V3+-- >>> import Data.Array.Accelerate.Linear.V4 -- >>> :{ --   let test :: Elt e => Exp e -> e --       test e = indexArray (run (unit e)) Z@@ -185,21 +189,74 @@ transpose = lift . L.transpose . unlift'  -class L.Trace m => Trace m where-  -- | Compute the trace of a matrix-  trace :: (A.Num a, Box2 m m a) => Exp (m (m a)) -> Exp a-  trace = lift . L.trace . unlift'+-- | Build a rotation matrix from a unit 'Quaternion'+--+fromQuaternion :: forall a. A.Num a => Exp (Quaternion a) -> Exp (M33 a)+fromQuaternion = lift1 (L.fromQuaternion :: Quaternion (Exp a) -> M33 (Exp a)) -  -- | Compute the diagonal of a matrix-  diagonal :: Box2 m m a => Exp (m (m a)) -> Exp (m a)-  diagonal = lift . L.diagonal . unlift'+-- | Build a transformation matrix from a rotation expressed as a 'Quaternion'+-- and a translation vector.+--+mkTransformation :: forall a. A.Num a => Exp (Quaternion a) -> Exp (V3 a) -> Exp (M44 a)+mkTransformation = lift2 (L.mkTransformation :: Quaternion (Exp a) -> V3 (Exp a) -> M44 (Exp a)) -instance Trace Complex-instance Trace V0-instance Trace V1-instance Trace V2-instance Trace V3-instance Trace V4-instance Trace Plucker-instance Trace Quaternion+-- | Build a transformation matrix from a rotation matrix and a translation+-- vector.+--+mkTransformationMat :: A.Num a => Exp (M33 a) -> Exp (V3 a) -> Exp (M44 a)+mkTransformationMat m v =+  let r = L.mkTransformationMat (unlift' m) (unlift v)+  in  lift r++-- | Convert a 4x3 matrix to a 4x4 matrix, extending it with @[ 0 0 0 1 ]@+-- column vector+--+m43_to_m44 :: A.Num a => Exp (M43 a) -> Exp (M44 a)+m43_to_m44 m43 =+  let m44 = L.m43_to_m44 (unlift' m43)+  in  lift m44++-- | Convert a 3x3 matrix to a 4x4 matrix extending it with zeros in the new row+-- and column.+--+m33_to_m44 :: A.Num a => Exp (M33 a) -> Exp (M44 a)+m33_to_m44 m33 =+  let m44 = L.m33_to_m44 (unlift' m33)+  in  lift m44++-- | 2x2 matrix determinant+--+det22 :: A.Num a => Exp (M22 a) -> Exp a+det22 = L.det22 . unlift'++-- | 3x3 matrix determinant+--+det33 :: A.Num a => Exp (M33 a) -> Exp a+det33 = L.det33 . unlift'++-- | 4x4 matrix determinant+--+det44 :: A.Num a => Exp (M44 a) -> Exp a+det44 = L.det44 . unlift'++-- | 2x2 matrix inverse+--+inv22 :: A.Fractional a => Exp (M22 a) -> Exp (M22 a)+inv22 m =+  let r = L.inv22 (unlift' m)+  in  lift r++-- | 3x3 matrix inverse+--+inv33 :: A.Fractional a => Exp (M33 a) -> Exp (M33 a)+inv33 m =+  let r = L.inv33 (unlift' m)+  in  lift r++-- | 4x4 matrix inverse+--+inv44 :: A.Fractional a => Exp (M44 a) -> Exp (M44 a)+inv44 m =+  let r = L.inv44 (unlift' m)+  in  lift r 

@@ -7,7 +7,7 @@ -- | -- Module      : Data.Array.Accelerate.Linear.Metric -- Copyright   : 2014 Edward Kmett, Charles Durham,---               2015 Trevor L. McDonell+--               [2015..2018] Trevor L. McDonell -- License     : BSD-style (see the file LICENSE) -- -- Maintainer  : Edward Kmett <ekmett@gmail.com>

@@ -3,16 +3,19 @@ {-# LANGUAGE FlexibleContexts      #-} {-# LANGUAGE FlexibleInstances     #-} {-# LANGUAGE MultiParamTypeClasses #-}+{-# LANGUAGE RebindableSyntax      #-} {-# LANGUAGE ScopedTypeVariables   #-} {-# LANGUAGE StandaloneDeriving    #-} {-# LANGUAGE TypeFamilies          #-} {-# LANGUAGE UndecidableInstances  #-}-{-# OPTIONS_GHC -fno-warn-orphans #-}+{-# LANGUAGE ViewPatterns          #-}+{-# OPTIONS_GHC -fno-warn-name-shadowing #-}+{-# OPTIONS_GHC -fno-warn-orphans        #-} ----------------------------------------------------------------------------- -- | -- Module      : Data.Array.Accelerate.Linear.Plucker -- Copyright   : 2014 Edward Kmett, Charles Durham,---               2015 Trevor L. McDonell+--               [2015..2018] Trevor L. McDonell -- License     : BSD-style (see the file LICENSE) -- -- Maintainer  : Edward Kmett <ekmett@gmail.com>@@ -24,25 +27,52 @@  module Data.Array.Accelerate.Linear.Plucker ( -  Plucker(..), squaredError, (><), plucker, plucker3D,+  Plucker(..), +  squaredError,+  isotropic,+  (><),+  plucker,+  plucker3D,++  -- * operations on lines+  LinePass(..),+  parallel,+  intersects,+  passes,+  quadranceToOrigin,+  closestToOrigin,+  isLine,++  -- * Basis elements+       p01, p02, p03,+  p10,      p12, p13,+  p20, p21,      p23,+  p30, p31, p32,+ ) where -import Data.Array.Accelerate                    as A+import Data.Array.Accelerate                    hiding ( fromInteger )+import Data.Array.Accelerate.Data.Functor import Data.Array.Accelerate.Smart import Data.Array.Accelerate.Product import Data.Array.Accelerate.Array.Sugar +import Data.Array.Accelerate.Linear.Epsilon import Data.Array.Accelerate.Linear.Lift import Data.Array.Accelerate.Linear.Metric-import Data.Array.Accelerate.Linear.Vector+import Data.Array.Accelerate.Linear.V2 import Data.Array.Accelerate.Linear.V3 import Data.Array.Accelerate.Linear.V4+import Data.Array.Accelerate.Linear.Vector -import Data.Typeable import Control.Lens-import Linear.Plucker                           ( Plucker(..) )+import Data.Function+import Data.Typeable+import Linear.Plucker                           ( Plucker(..), LinePass(..) )+import Prelude                                  ( fromInteger ) import qualified Linear.Plucker                 as L+import qualified Prelude                        as P   -- | Valid Plücker coordinates @p@ will have @'squaredError' p '==' 0@@@ -50,30 +80,136 @@ -- That said, floating point makes a mockery of this claim, so you may want to -- use 'nearZero'. ---squaredError :: forall a. A.Num a => Exp (Plucker a) -> Exp a+squaredError :: forall a. Num a => Exp (Plucker a) -> Exp a squaredError = lift1 (L.squaredError :: Plucker (Exp a) -> Exp a)  -- | This isn't the actual metric because this bilinear form gives rise to an--- isotropic quadratic space+-- isotropic quadratic space. -- infixl 5 ><-(><) :: forall a. A.Num a => Exp (Plucker a) -> Exp (Plucker a) -> Exp a+(><) :: forall a. Num a => Exp (Plucker a) -> Exp (Plucker a) -> Exp a (><) = lift2 ((L.><) :: Plucker (Exp a) -> Plucker (Exp a) -> Exp a) +-- | Checks if the line is near-isotropic (isotropic vectors in this quadratic+-- space represent lines in real 3D space).+--+isotropic :: Epsilon a => Exp (Plucker a) -> Exp Bool+isotropic a = nearZero (a >< a)+ -- | Given a pair of points represented by homogeneous coordinates generate -- Plücker coordinates for the line through them, directed from the second -- towards the first. ---plucker :: forall a. A.Num a => Exp (V4 a) -> Exp (V4 a) -> Exp (Plucker a)+plucker :: forall a. Num a => Exp (V4 a) -> Exp (V4 a) -> Exp (Plucker a) plucker = lift2 (L.plucker :: V4 (Exp a) -> V4 (Exp a) -> Plucker (Exp a))  -- | Given a pair of 3D points, generate Plücker coordinates for the line -- through them, directed from the second towards the first. ---plucker3D :: forall a. A.Num a => Exp (V3 a) -> Exp (V3 a) -> Exp (Plucker a)+plucker3D :: forall a. Num a => Exp (V3 a) -> Exp (V3 a) -> Exp (Plucker a) plucker3D = lift2 (L.plucker3D :: V3 (Exp a) -> V3 (Exp a) -> Plucker (Exp a)) +-- | Checks if two lines intersect (or nearly intersect).+--+intersects :: (Epsilon a, Ord a) => Exp (Plucker a) -> Exp (Plucker a) -> Exp Bool+intersects a b = not (a `parallel` b) && passes a b == constant Coplanar +-- | Check how two lines pass each other. @passes l1 l2@ describes @l2@ when+-- looking down @l1@.+--+passes :: (Epsilon a, Ord a) => Exp (Plucker a) -> Exp (Plucker a) -> Exp LinePass+passes a b =+  if nearZero s then constant Coplanar else+  if s > 0      then constant Counterclockwise+                else constant Clockwise+  where+    s        = (lift u1 `dot` lift v2) + (lift u2 `dot` lift v1)+    V2 u1 v1 = toUV a+    V2 u2 v2 = toUV b++-- | Checks if two lines are parallel.+--+parallel :: Epsilon a => Exp (Plucker a) -> Exp (Plucker a) -> Exp Bool+parallel a b = nearZero $ lift u1 `cross` lift u2+  where+    V2 u1 _ = toUV a+    V2 u2 _ = toUV b++-- | Represent a Plücker coordinate as a pair of 3-tuples, typically denoted+-- U and V.+--+toUV :: Elt a => Exp (Plucker a) -> V2 (V3 (Exp a))+toUV (unlift -> Plucker a b c d e f) = V2 (V3 a b c) (V3 d e f)++-- | The minimum squared distance of a line from the origin.+--+quadranceToOrigin :: Fractional a => Exp (Plucker a) -> Exp a+quadranceToOrigin p = (lift v `dot` lift v) / (lift u `dot` lift u)+  where+    V2 u v = toUV p++-- | The point where a line is closest to the origin.+--+closestToOrigin :: Fractional a => Exp (Plucker a) -> Exp (V3 a)+closestToOrigin p = normalizePoint . lift $ V4 x y z (lift u `dot` lift u)+  where+    V2 u v   = toUV p+    V3 x y z = unlift $ lift v `cross` lift u++-- | Not all 6-dimensional points correspond to a line in 3D. This predicate+-- tests that a Plücker coordinate lies on the Grassmann manifold, and does+-- indeed represent a 3D line.+--+isLine :: Epsilon a => Exp (Plucker a) -> Exp Bool+isLine p = nearZero $ lift u `dot` lift v+  where+    V2 u v = toUV p+++-- | These elements form a basis for the Plücker space, or the Grassmanian+-- manifold @Gr(2,V4)@.+--+-- @+-- 'p01' :: 'Lens'' ('Plucker' a) a+-- 'p02' :: 'Lens'' ('Plucker' a) a+-- 'p03' :: 'Lens'' ('Plucker' a) a+-- 'p23' :: 'Lens'' ('Plucker' a) a+-- 'p31' :: 'Lens'' ('Plucker' a) a+-- 'p12' :: 'Lens'' ('Plucker' a) a+-- @+--+p01, p02, p03, p23, p31, p12 :: Elt a => Lens' (Exp (Plucker a)) (Exp a)+p01 = liftLens (L.p01 :: Lens' (Plucker (Exp a)) (Exp a))+p02 = liftLens (L.p02 :: Lens' (Plucker (Exp a)) (Exp a))+p03 = liftLens (L.p03 :: Lens' (Plucker (Exp a)) (Exp a))+p23 = liftLens (L.p23 :: Lens' (Plucker (Exp a)) (Exp a))+p31 = liftLens (L.p31 :: Lens' (Plucker (Exp a)) (Exp a))+p12 = liftLens (L.p12 :: Lens' (Plucker (Exp a)) (Exp a))++-- | These elements form an alternate basis for the Plücker space, or the+-- Grassmanian manifold @Gr(2,V4)@.+--+-- @+-- 'p10' :: 'Num' a => 'Lens'' ('Plucker' a) a+-- 'p20' :: 'Num' a => 'Lens'' ('Plucker' a) a+-- 'p30' :: 'Num' a => 'Lens'' ('Plucker' a) a+-- 'p32' :: 'Num' a => 'Lens'' ('Plucker' a) a+-- 'p13' :: 'Num' a => 'Lens'' ('Plucker' a) a+-- 'p21' :: 'Num' a => 'Lens'' ('Plucker' a) a+-- @+--+p10, p20, p30, p32, p13, p21 :: Num a => Lens' (Exp (Plucker a)) (Exp a)+p10 = anti p01+p20 = anti p02+p30 = anti p03+p32 = anti p23+p13 = anti p31+p21 = anti p21++anti :: (P.Functor f, Num a) => ((Exp a -> f (Exp a)) -> r) -> (Exp a -> f (Exp a)) -> r+anti k f = k (P.fmap negate . f . negate)++ -- Instances -- --------- @@ -120,4 +256,84 @@  instance (Elt a, Elt b) => Each (Exp (Plucker a)) (Exp (Plucker b)) (Exp a) (Exp b) where   each = liftLens (each :: Traversal (Plucker (Exp a)) (Plucker (Exp b)) (Exp a) (Exp b))++instance Eq a => Eq (Plucker a) where+  (==) = (==) `on` t6+  (/=) = (/=) `on` t6++instance Ord a => Ord (Plucker a) where+  (<)  = (<) `on` t6+  (>)  = (>) `on` t6+  (<=) = (<=) `on` t6+  (>=) = (>=) `on` t6+  min  = pl $$ on min t6+  max  = pl $$ on max t6++t6 :: Elt a => Exp (Plucker a) -> Exp (a,a,a,a,a,a)+t6 (unlift -> Plucker a b c d e f) = tup6 (a,b,c,d,e,f)++pl :: Elt a => Exp (a,a,a,a,a,a) -> Exp (Plucker a)+pl (untup6 -> (a,b,c,d,e,f)) = lift (Plucker a b c d e f)++instance Num a => P.Num (Exp (Plucker a)) where+  (+)           = lift2 ((+) :: Plucker (Exp a) -> Plucker (Exp a) -> Plucker (Exp a))+  (-)           = lift2 ((-) :: Plucker (Exp a) -> Plucker (Exp a) -> Plucker (Exp a))+  (*)           = lift2 ((*) :: Plucker (Exp a) -> Plucker (Exp a) -> Plucker (Exp a))+  negate        = fmap negate+  abs           = fmap abs+  signum        = fmap signum+  fromInteger x = lift (P.fromInteger x :: Plucker (Exp a))++instance Fractional a => P.Fractional (Exp (Plucker a)) where+  recip          = fmap recip+  (/)            = lift2 ((/) :: Plucker (Exp a) -> Plucker (Exp a) -> Plucker (Exp a))+  fromRational x = lift (P.fromRational x :: Plucker (Exp a))++instance Floating a => P.Floating (Exp (Plucker a)) where+  pi      = lift (pi :: Plucker (Exp a))+  exp     = fmap exp+  sqrt    = fmap sqrt+  log     = fmap log+  (**)    = lift2 ((**) :: Plucker (Exp a) -> Plucker (Exp a) -> Plucker (Exp a))+  logBase = lift2 (logBase :: Plucker (Exp a) -> Plucker (Exp a) -> Plucker (Exp a))+  sin     = fmap sin+  tan     = fmap tan+  cos     = fmap cos+  asin    = fmap asin+  atan    = fmap atan+  acos    = fmap acos+  sinh    = fmap sinh+  tanh    = fmap tanh+  cosh    = fmap cosh+  asinh   = fmap asinh+  atanh   = fmap atanh+  acosh   = fmap acosh++instance Epsilon a => Epsilon (Plucker a) where+  nearZero = nearZero . quadrance++instance Functor Plucker where+  fmap g (unlift -> Plucker a b c d e f) = lift (Plucker (g a) (g b) (g c) (g d) (g e) (g f))+  x <$ _                                 = lift (Plucker x x x x x x)+++type instance EltRepr LinePass = Int8++instance Elt LinePass where+  eltType _ = eltType (undefined::Int8)++  toElt x = let (==) = (P.==)   -- -XRebindableSyntax hax+            in  case x of+                  0 -> Coplanar+                  1 -> Clockwise+                  2 -> Counterclockwise+                  _ -> P.error "LinePass: unhandled constructor"++  fromElt Coplanar         = 0+  fromElt Clockwise        = 1+  fromElt Counterclockwise = 2++instance Eq LinePass where+  x == y = bitcast x == (bitcast y :: Exp Int8)+  x /= y = bitcast x /= (bitcast y :: Exp Int8) 

@@ -1,15 +1,18 @@ {-# LANGUAGE ConstraintKinds       #-}+{-# LANGUAGE FlexibleContexts      #-} {-# LANGUAGE FlexibleInstances     #-} {-# LANGUAGE MultiParamTypeClasses #-}+{-# LANGUAGE RebindableSyntax      #-} {-# LANGUAGE ScopedTypeVariables   #-} {-# LANGUAGE TypeFamilies          #-} {-# LANGUAGE UndecidableInstances  #-}+{-# LANGUAGE ViewPatterns          #-} {-# OPTIONS_GHC -fno-warn-orphans #-} ----------------------------------------------------------------------------- -- | -- Module      : Data.Array.Accelerate.Linear.Quaternion -- Copyright   : 2014 Edward Kmett, Charles Durham,---               2015 Trevor L. McDonell+--               [2015..2018] Trevor L. McDonell -- License     : BSD-style (see the file LICENSE) -- -- Maintainer  : Edward Kmett <ekmett@gmail.com>@@ -23,22 +26,139 @@    Quaternion(..), +  slerp,+  asinq,+  acosq,+  atanq,+  asinhq,+  acoshq,+  atanhq,+  absi,+  pow,+  rotate,+  axisAngle,+ ) where  import Data.Array.Accelerate-import Data.Array.Accelerate.Smart-import Data.Array.Accelerate.Product import Data.Array.Accelerate.Array.Sugar+import Data.Array.Accelerate.Data.Complex       hiding ( conjugate )+import Data.Array.Accelerate.Data.Functor+import Data.Array.Accelerate.Product+import Data.Array.Accelerate.Smart +import Data.Array.Accelerate.Linear.Conjugate+import Data.Array.Accelerate.Linear.Epsilon import Data.Array.Accelerate.Linear.Lift import Data.Array.Accelerate.Linear.Metric-import Data.Array.Accelerate.Linear.Vector import Data.Array.Accelerate.Linear.V3+import Data.Array.Accelerate.Linear.Vector  import Control.Lens+import Data.Function import Linear.Quaternion                        ( Quaternion(..) )+import qualified Prelude                        as P  +-- | Spherical linear interpolation between two quaternions+--+slerp :: RealFloat a => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp a -> Exp (Quaternion a)+slerp q p t =+  if 1.0 - cosphi < 1.0e-8+    then q+    else ((sin ((1-t)*phi) *^ q) + sin (t*phi) *^ fp) ^/ sin phi+  where+    dqp = dot q p+    phi = acos cosphi+    (cosphi, fp) = unlift $ if dqp < 0 then tup2 (-dqp, negate p)+                                       else tup2 (dqp, p)++-- | 'asin' with a specified branch cut+--+asinq :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a)+asinq q@(unlift -> Quaternion e _) u =+  if qiq /= 0.0 || e >= -1 && e <= 1+    then asin q+    else cutWith (asin (lift $ e :+ sqrt qiq)) u+  where+    qiq = qi q++-- | 'acos' with a specified branch cut+--+acosq :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a)+acosq q@(unlift -> Quaternion e _) u =+  if qiq /= 0.0 || e >= -1 && e <= 1+    then acos q+    else cutWith (acos (lift $ e :+ sqrt qiq)) u+  where+    qiq = qi q++-- | 'atan' with a specified branch cut+--+atanq :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a)+atanq q@(unlift -> Quaternion e _) u =+  if e /= 0.0 || qiq >= -1 && qiq <= 1+    then atan q+    else cutWith (atan (lift $ e :+ sqrt qiq)) u+  where+    qiq = qi q++-- | 'asinh' with a specified branch cut+--+asinhq :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a)+asinhq q@(unlift -> Quaternion e _) u =+  if e /= 0.0 || qiq >= -1 && qiq <= 1+    then asinh q+    else cutWith (asinh (lift $ e :+ sqrt qiq)) u+  where+    qiq = qi q++-- | 'acosh' with a specified branch cut+--+acoshq :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a)+acoshq q@(unlift -> Quaternion e _) u =+  if qiq /= 0.0 || e >= 1+    then asinh q+    else cutWith (acosh (lift $ e :+ sqrt qiq)) u+  where+    qiq = qi q++-- | 'atanh' with a specified branch cut+--+atanhq :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a)+atanhq q@(unlift -> Quaternion e _) u =+  if qiq /= 0.0 || e > -1 && e < 1+    then atanh q+    else cutWith (atanh (lift $ e :+ sqrt qiq)) u+  where+    qiq = qi q++-- | norm of the imaginary component+--+absi :: Floating a => Exp (Quaternion a) -> Exp a+absi = sqrt . qi++-- | raise a 'Quaternion' to a scalar power+--+pow :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp a -> Exp (Quaternion a)+pow q t = exp (t *^ log q)++-- | Apply a rotation to a vector+--+rotate :: forall a. (Conjugate (Exp a), RealFloat a) => Exp (Quaternion a) -> Exp (V3 a) -> Exp (V3 a)+rotate q v = lift ijk+  where+    Quaternion _ ijk = unlift $ q * (lift (Quaternion 0 (unlift v))) * conjugate q :: Quaternion (Exp a)++-- | @'axisAngle' axis theta@ builds a 'Quaternion' representing a rotation of+-- @theta@ radians about @axis@.+--+axisAngle :: (Epsilon a, Floating a) => Exp (V3 a) -> Exp a -> Exp (Quaternion a)+axisAngle axis theta = lift $ Quaternion (cos half) (unlift (sin half *^ normalize axis))+  where+    half = theta / 2++ -- Instances -- --------- @@ -77,4 +197,232 @@  instance (Elt a, Elt b) => Each (Exp (Quaternion a)) (Exp (Quaternion b)) (Exp a) (Exp b) where   each = liftLens (each :: Traversal (Quaternion (Exp a)) (Quaternion (Exp b)) (Exp a) (Exp b))++instance Eq a => Eq (Quaternion a) where+  (==) = (==) `on` t4+  (/=) = (/=) `on` t4++instance Ord a => Ord (Quaternion a) where+  (<)  = (<) `on` t4+  (>)  = (>) `on` t4+  (<=) = (<=) `on` t4+  (>=) = (>=) `on` t4+  min  = qu $$ on min t4+  max  = qu $$ on max t4++t4 :: Elt a => Exp (Quaternion a) -> Exp (a,a,a,a)+t4 (unlift -> Quaternion x (V3 y z w)) = tup4 (x,y,z,w)++qu :: Elt a => Exp (a,a,a,a) -> Exp (Quaternion a)+qu (untup4 -> (x,y,z,w)) = lift (Quaternion x (V3 y z w))++instance RealFloat a => P.Num (Exp (Quaternion a)) where+  (+)           = lift2 ((+) :: Quaternion (Exp a) -> Quaternion (Exp a) -> Quaternion (Exp a))+  (-)           = lift2 ((-) :: Quaternion (Exp a) -> Quaternion (Exp a) -> Quaternion (Exp a))+  negate        = fmap negate+  abs z         = lift (Quaternion (norm z) (V3 0 0 0))+  fromInteger x = lift (Quaternion (fromInteger x) (V3 0 0 0))++  z1 * z2       = let Quaternion s1 v1' = unlift z1; v1 = lift v1'+                      Quaternion s2 v2' = unlift z2; v2 = lift v2'+                  in+                  lift $ Quaternion (s1*s2 - (v1 `dot` v2))+                                    (unlift ((v1 `cross` v2) + s1*^v2 + s2*^v1))++  signum q@(unlift -> Quaternion e (V3 i j k)) =+    if m == 0.0                      then q else+    if not (isInfinite m || isNaN m) then q ^/ sqrt m else+    if ne || ni || nj || nk          then qNaN else+    if not (ii || ij || ik)          then lift $ Quaternion 1 (V3 0 0 0) else+    if not (ie || ij || ik)          then lift $ Quaternion 0 (V3 1 0 0) else+    if not (ie || ii || ik)          then lift $ Quaternion 0 (V3 0 1 0) else+    if not (ie || ii || ij)          then lift $ Quaternion 0 (V3 0 0 1)+                                     else qNaN+    where+      m  = quadrance q+      ie = isInfinite e+      ii = isInfinite i+      ij = isInfinite j+      ik = isInfinite k+      ne = isNaN e+      ni = isNaN i+      nj = isNaN j+      nk = isNaN k+      --+      qNaN = lift $ Quaternion fNaN (V3 fNaN fNaN fNaN)+      fNaN = 0/0++instance RealFloat a => P.Fractional (Exp (Quaternion a)) where+  z1 / z2 =+    let Quaternion q0 (V3 q1 q2 q3) = unlift z1+        Quaternion r0 (V3 r1 r2 r3) = unlift z2+    in+    lift (Quaternion (r0*q0+r1*q1+r2*q2+r3*q3)+                     (V3 (r0*q1-r1*q0-r2*q3+r3*q2)+                         (r0*q2+r1*q3-r2*q0-r3*q1)+                         (r0*q3-r1*q2+r2*q1-r3*q0)))+      ^/ (r0*r0 + r1*r1 + r2*r2 + r3*r3)++  recip q = let Quaternion e v = unlift q :: Quaternion (Exp a)+            in  lift (Quaternion e (P.fmap negate v)) ^/ quadrance q++  fromRational x = lift (Quaternion (fromRational x) (V3 0 0 0))++instance (RealFloat a, Elt (Complex a)) => P.Floating (Exp (Quaternion a)) where+  pi = lift (Quaternion pi (V3 0 0 0))++  exp q@(unlift -> Quaternion e v) =+    if qiq == 0+      then lift (Quaternion exe v)+      else reimagine (exe * cos ai) (exe * (sin ai / ai)) q+    where+      qiq = qi q+      ai  = sqrt qiq+      exe = exp e++  log q@(unlift -> Quaternion e v@(V3 _i j k)) =+    if qiq == 0+      then if e >= 0+             then lift $ Quaternion (log e) v+             else lift $ Quaternion (log (negate e)) (V3 pi j k) -- mmm, pi+      else reimagine (log m) (atan2 m e / ai) q+    where+      qiq = qi q+      ai  = sqrt qiq+      m   = sqrte2pqiq e qiq++  x ** y = exp (y * log x)++  sqrt q@(unlift -> Quaternion e v) =+    if m   == 0 then q else+    if qiq == 0 then if e > 0+                        then lift $ Quaternion (sqrt e) (V3 0 0 0)+                        else lift $ Quaternion 0 (V3 (sqrt (negate e)) 0 0)+                else lift $ Quaternion (0.5*(m+e)) (unlift (lift v ^* im))+    where+      qiq = qi q+      im  = sqrt (0.5*(m-e)) / sqrt qiq+      m   = sqrte2pqiq e qiq++  cos q@(unlift -> Quaternion e v) =+    if qiq == 0 then lift $ Quaternion (cos e) v+                else reimagine (cos e * cosh ai) (- sin e / ai / sinh ai) q -- 0.15 bits error+                  -- reimagine (cos e * cosh ai) (- sin e * sinh ai / ai) q -- 13.5 bits worse+    where+      qiq = qi q+      ai  = sqrt qiq++  sin q@(unlift -> Quaternion e v) =+    if qiq == 0 then lift $ Quaternion (sin e) v+                else reimagine (sin e * cosh ai) (cos e * sinh ai / ai) q+    where+      qiq = qi q+      ai  = sqrt qiq++  tan q@(unlift -> Quaternion e v) =+    if qiq == 0 then lift $ Quaternion (tan e) v+                else reimagine (ce * sin e / d) (tanrhs sai ai d) q+    where+      qiq = qi q+      ai  = sqrt qiq+      ce  = cos e+      sai = sinh ai+      d   = ce*ce + sai*sai++  sinh q@(unlift -> Quaternion e v) =+    if qiq == 0 then lift $ Quaternion (sinh e) v+                else reimagine (sinh e * cos ai) (cosh e * sin ai / ai) q+    where+      qiq = qi q+      ai  = sqrt qiq++  cosh q@(unlift -> Quaternion e v) =+    if qiq == 0 then lift $ Quaternion (cosh e) v+                else reimagine (cosh e * cos ai) (sin ai * (sinh e / ai)) q+    where+      qiq = qi q+      ai  = sqrt qiq++  tanh q@(unlift -> Quaternion e v) =+    if qiq == 0 then lift $ Quaternion (tanh e) v+                else reimagine (cosh e * se / d) (tanhrhs cai ai d) q+    where+      qiq = qi q+      ai  = sqrt qiq+      se  = sinh e+      cai = cos ai+      d   = se*se + cai*cai++  asin = cut asin+  acos = cut acos+  atan = cut atan++  asinh = cut asinh+  acosh = cut acosh+  atanh = cut atanh+++reimagine :: RealFloat a => Exp a -> Exp a -> Exp (Quaternion a) -> Exp (Quaternion a)+reimagine r s (unlift -> Quaternion _ v) =+  if isNaN s || isInfinite s+    then let aux x = if x == 0 then 0+                               else s * x+         in lift $ Quaternion r (P.fmap aux v)+    else    lift $ Quaternion r (unlift (lift v ^* s))++-- | Helper for calculating with specific branch cuts+--+cut :: (RealFloat a, Elt (Complex a)) => (Exp (Complex a) -> Exp (Complex a)) -> Exp (Quaternion a) -> Exp (Quaternion a)+cut f q@(unlift -> Quaternion e (V3 _ y z)) =+  if qiq == 0 then lift $ Quaternion a (V3 b y z)+              else reimagine a (b / ai) q+  where+    qiq    = qi q+    ai     = sqrt qiq+    a :+ b = unlift $ f (lift (e :+ ai))++-- | Helper for calculating with specific branch cuts+--+cutWith :: (RealFloat a, Elt (Complex a)) => Exp (Complex a) -> Exp (Quaternion a) -> Exp (Quaternion a)+cutWith (unlift -> r :+ im) q@(unlift -> Quaternion e v) =+  if e /= 0 || qiq == 0 || isNaN qiq || isInfinite qiq+    then 0/0 -- error "bad cut"  -- TLM: argh+    else lift $ Quaternion r (unlift (lift v ^* s))+  where+    qiq = qi q+    s   = im / sqrt qiq++-- | quadrance of the imaginary component+--+qi :: Num a => Exp (Quaternion a) -> Exp a+qi (unlift -> Quaternion _ v :: Quaternion (Exp a)) = quadrance (lift v)++sqrte2pqiq :: (Floating a, Ord a) => Exp a -> Exp a -> Exp a+sqrte2pqiq e qiq = -- = sqrt (e*e) + qiq+  if e < - 1.5097698010472593e153 then -(qiq/e) - e else+  if e < 5.582399551122541e57     then sqrt ((e*e) + qiq) -- direct definition+                                  else (qiq/e) + e++tanrhs :: (Floating a, Ord a) => Exp a -> Exp a -> Exp a -> Exp a+tanrhs sai ai d = -- = cosh ai * (sai / ai) / d -- improved from 6.04 bits of error to 0.19 bits+  if sai < -4.618902267687042e-52 then (sai / d / ai) * cosh ai else+  if sai < 1.038530535935153e-39  then (cosh ai * sai) / ai / d+                                  else (sai / d / ai) * cosh ai++tanhrhs :: (Floating a, Ord a) => Exp a -> Exp a -> Exp a -> Exp a+tanhrhs cai ai d = -- = cai * (sin ai / ai) / d+  if d >= -4.2173720203427147e-29 && d < 4.446702369113811e64+    then cai / (d * (ai / sin ai))+    else cai * (1 / ai / sin ai) / d++instance (RealFloat a, Epsilon a) => Epsilon (Quaternion a) where+  nearZero = nearZero . quadrance++instance (RealFloat a, Conjugate (Exp a)) => Conjugate (Exp (Quaternion a)) where+  conjugate (unlift -> Quaternion e v :: Quaternion (Exp a)) =+    lift (Quaternion (conjugate e) (unlift (negate (lift v :: Exp (V3 a)))))++instance Functor Quaternion where+  fmap f (unlift -> Quaternion e v) = lift (Quaternion (f e) (P.fmap f v))+  x <$ _                            = lift (Quaternion x (V3 x x x)) 

@@ -0,0 +1,57 @@+{-# LANGUAGE ConstraintKinds  #-}+{-# LANGUAGE FlexibleContexts #-}+{-# LANGUAGE TypeFamilies     #-}+-----------------------------------------------------------------------------+-- |+-- Module      : Data.Array.Accelerate.Linear.Trace+-- Copyright   : 2014 Edward Kmett+--               [2015..2018] Trevor L. McDonell+-- License     : BSD-style (see the file LICENSE)+--+-- Maintainer  : Edward Kmett <ekmett@gmail.com>+-- Stability   : experimental+-- Portability : non-portable+--+-- Simple matrix operations for low-dimensional primitives+----------------------------------------------------------------------------++module Data.Array.Accelerate.Linear.Trace (++  Trace(..),++) where++import Data.Array.Accelerate                                        as A+import Data.Array.Accelerate.Data.Complex++import Data.Array.Accelerate.Linear.Lift+import Data.Array.Accelerate.Linear.Plucker+import Data.Array.Accelerate.Linear.Quaternion+import Data.Array.Accelerate.Linear.Type+import Data.Array.Accelerate.Linear.V0+import Data.Array.Accelerate.Linear.V1+import Data.Array.Accelerate.Linear.V2+import Data.Array.Accelerate.Linear.V3+import Data.Array.Accelerate.Linear.V4++import qualified Linear.Trace                                       as L+++class L.Trace m => Trace m where+  -- | Compute the trace of a matrix+  trace :: (A.Num a, Box2 m m a) => Exp (m (m a)) -> Exp a+  trace = lift . L.trace . unlift'++  -- | Compute the diagonal of a matrix+  diagonal :: Box2 m m a => Exp (m (m a)) -> Exp (m a)+  diagonal = lift . L.diagonal . unlift'++instance Trace Complex+instance Trace V0+instance Trace V1+instance Trace V2+instance Trace V3+instance Trace V4+instance Trace Plucker+instance Trace Quaternion+

@@ -4,7 +4,7 @@ ----------------------------------------------------------------------------- -- | -- Module      : Data.Array.Accelerate.Linear.Type--- Copyright   : 2015 Trevor L. McDonell+-- Copyright   : [2015..2018] Trevor L. McDonell -- License     : BSD-style (see the file LICENSE) -- -- Maintainer  : Edward Kmett <ekmett@gmail.com>

@@ -1,6 +1,5 @@ {-# LANGUAGE ConstraintKinds       #-} {-# LANGUAGE FlexibleInstances     #-}-{-# LANGUAGE IncoherentInstances   #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE ScopedTypeVariables   #-} {-# LANGUAGE TypeFamilies          #-}@@ -10,7 +9,7 @@ -- | -- Module      : Data.Array.Accelerate.Linear.V0 -- Copyright   : 2014 Edward Kmett, Charles Durham,---               2015 Trevor L. McDonell+--               [2015..2018] Trevor L. McDonell -- License     : BSD-style (see the file LICENSE) -- -- Maintainer  : Edward Kmett <ekmett@gmail.com>@@ -27,6 +26,7 @@ ) where  import Data.Array.Accelerate                    as A+import Data.Array.Accelerate.Data.Functor       as A import Data.Array.Accelerate.Smart import Data.Array.Accelerate.Product import Data.Array.Accelerate.Array.Sugar@@ -66,14 +66,34 @@ instance Unlift Exp (V0 a) where   unlift _ = V0 +instance (Elt a, Elt b) => Each (Exp (V0 a)) (Exp (V0 b)) (Exp a) (Exp b) where+  each _ _ = pure (constant V0)+ instance A.Num a => P.Num (Exp (V0 a)) where-  _ + _ = constant V0-  _ - _ = constant V0-  _ * _ = constant V0-  abs _ = constant V0-  signum _ = constant V0+  _ + _         = constant V0+  _ - _         = constant V0+  _ * _         = constant V0+  abs _         = constant V0+  signum _      = constant V0   fromInteger _ = constant V0 -instance (Elt a, Elt b) => Each (Exp (V0 a)) (Exp (V0 b)) (Exp a) (Exp b) where-  each _ _ = pure (constant V0)+instance Elt a => A.Eq (V0 a) where+  _ == _ = constant True+  _ /= _ = constant False++instance Elt a => A.Ord (V0 a) where+  _ < _   = constant False+  _ > _   = constant False+  _ <= _  = constant True+  _ >= _  = constant True+  min _ _ = constant V0+  max _ _ = constant V0++instance Elt a => P.Bounded (Exp (V0 a)) where+  minBound = constant V0+  maxBound = constant V0++instance A.Functor V0 where+  fmap _ _ = constant V0+  _ <$ _   = constant V0 

@@ -1,7 +1,6 @@ {-# LANGUAGE ConstraintKinds       #-} {-# LANGUAGE FlexibleContexts      #-} {-# LANGUAGE FlexibleInstances     #-}-{-# LANGUAGE IncoherentInstances   #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE ScopedTypeVariables   #-} {-# LANGUAGE TypeFamilies          #-}@@ -12,7 +11,7 @@ -- | -- Module      : Data.Array.Accelerate.Linear.V1 -- Copyright   : 2014 Edward Kmett, Charles Durham,---               2015 Trevor L. McDonell+--               [2015..2018] Trevor L. McDonell -- License     : BSD-style (see the file LICENSE) -- -- Maintainer  : Edward Kmett <ekmett@gmail.com>@@ -29,11 +28,13 @@ ) where  import Data.Array.Accelerate                    as A+import Data.Array.Accelerate.Data.Functor       as A import Data.Array.Accelerate.Array.Sugar import Data.Array.Accelerate.Product import Data.Array.Accelerate.Smart import Data.Array.Accelerate.Type +import Data.Array.Accelerate.Linear.Epsilon import Data.Array.Accelerate.Linear.Lift import Data.Array.Accelerate.Linear.Metric import Data.Array.Accelerate.Linear.Type@@ -41,8 +42,8 @@  import Control.Lens import Linear.V1                                ( V1(..) )-import qualified Linear.V1                      as L import Prelude                                  as P+import qualified Linear.V1                      as L  -- $setup -- >>> import Data.Array.Accelerate.Interpreter@@ -80,7 +81,7 @@ type instance EltRepr (V1 a) = ((), EltRepr a)  instance Elt a => Elt (V1 a) where-  eltType _ = PairTuple UnitTuple (eltType (undefined :: a))+  eltType _ = TypeRpair TypeRunit (eltType (undefined :: a))   toElt ((), x) = V1 (toElt x)   fromElt (V1 x) = ((), fromElt x) @@ -97,6 +98,25 @@ instance Elt a => Unlift Exp (V1 (Exp a)) where   unlift t = V1 $ Exp $ ZeroTupIdx `Prj` t +instance (Elt a, Elt b) => Each (Exp (V1 a)) (Exp (V1 b)) (Exp a) (Exp b) where+  each = liftLens (each :: Traversal (V1 (Exp a)) (V1 (Exp b)) (Exp a) (Exp b))++instance A.Eq a => A.Eq (V1 a) where+  (unlift -> V1 x) == (unlift -> V1 y) = x A.== y+  (unlift -> V1 x) /= (unlift -> V1 y) = x A./= y++instance A.Ord a => A.Ord (V1 a) where+  (unlift -> V1 x) <  (unlift -> V1 y) = x A.< y+  (unlift -> V1 x) >  (unlift -> V1 y) = x A.> y+  (unlift -> V1 x) >= (unlift -> V1 y) = x A.>= y+  (unlift -> V1 x) <= (unlift -> V1 y) = x A.<= y+  min (unlift -> V1 x) (unlift -> V1 y) = lift $ V1 (A.min x y)+  max (unlift -> V1 x) (unlift -> V1 y) = lift $ V1 (A.max x y)++instance A.Bounded a => P.Bounded (Exp (V1 a)) where+  minBound = lift (V1 (minBound :: Exp a))+  maxBound = lift (V1 (maxBound :: Exp a))+ instance A.Num a => P.Num (Exp (V1 a)) where   (+)             = lift2 ((+) :: V1 (Exp a) -> V1 (Exp a) -> V1 (Exp a))   (-)             = lift2 ((-) :: V1 (Exp a) -> V1 (Exp a) -> V1 (Exp a))@@ -104,12 +124,12 @@   negate          = lift1 (negate :: V1 (Exp a) -> V1 (Exp a))   signum          = lift1 (signum :: V1 (Exp a) -> V1 (Exp a))   abs             = lift1 (signum :: V1 (Exp a) -> V1 (Exp a))-  fromInteger x   = lift (fromInteger x :: V1 (Exp a))+  fromInteger x   = lift (P.fromInteger x :: V1 (Exp a))  instance A.Floating a => P.Fractional (Exp (V1 a)) where   (/)             = lift2 ((/) :: V1 (Exp a) -> V1 (Exp a) -> V1 (Exp a))   recip           = lift1 (recip :: V1 (Exp a) -> V1 (Exp a))-  fromRational x  = lift (fromRational x :: V1 (Exp a))+  fromRational x  = lift (P.fromRational x :: V1 (Exp a))  instance A.Floating a => P.Floating (Exp (V1 a)) where   pi              = lift (pi :: V1 (Exp a))@@ -128,6 +148,10 @@   acosh           = lift1 (acosh :: V1 (Exp a) -> V1 (Exp a))   atanh           = lift1 (atanh :: V1 (Exp a) -> V1 (Exp a)) -instance (Elt a, Elt b) => Each (Exp (V1 a)) (Exp (V1 b)) (Exp a) (Exp b) where-  each = liftLens (each :: Traversal (V1 (Exp a)) (V1 (Exp b)) (Exp a) (Exp b))+instance Epsilon a => Epsilon (V1 a) where+  nearZero (unlift -> V1 x) = nearZero x++instance A.Functor V1 where+  fmap f (unlift -> V1 x) = lift (V1 (f x))+  x <$ _                  = lift (V1 x) 

@@ -1,7 +1,6 @@ {-# LANGUAGE ConstraintKinds       #-} {-# LANGUAGE FlexibleContexts      #-} {-# LANGUAGE FlexibleInstances     #-}-{-# LANGUAGE IncoherentInstances   #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE ScopedTypeVariables   #-} {-# LANGUAGE TypeFamilies          #-}@@ -12,7 +11,7 @@ -- | -- Module      : Data.Array.Accelerate.Linear.V2 -- Copyright   : 2014 Edward Kmett, Charles Durham,---               2015 Trevor L. McDonell+--               [2015..2018] Trevor L. McDonell -- License     : BSD-style (see the file LICENSE) -- -- Maintainer  : Edward Kmett <ekmett@gmail.com>@@ -32,10 +31,12 @@ ) where  import Data.Array.Accelerate                    as A+import Data.Array.Accelerate.Data.Functor       as A import Data.Array.Accelerate.Smart import Data.Array.Accelerate.Product import Data.Array.Accelerate.Array.Sugar +import Data.Array.Accelerate.Linear.Epsilon import Data.Array.Accelerate.Linear.Lift import Data.Array.Accelerate.Linear.Metric import Data.Array.Accelerate.Linear.Type@@ -43,9 +44,10 @@ import Data.Array.Accelerate.Linear.Vector  import Control.Lens+import Data.Function import Linear.V2                                ( V2(..) )-import qualified Linear.V2                      as L import Prelude                                  as P+import qualified Linear.V2                      as L  -- $setup -- >>> import Data.Array.Accelerate.Interpreter@@ -131,6 +133,31 @@   unlift t = V2 (Exp $ SuccTupIdx ZeroTupIdx `Prj` t)                 (Exp $ ZeroTupIdx `Prj` t) +instance (Elt a, Elt b) => Each (Exp (V2 a)) (Exp (V2 b)) (Exp a) (Exp b) where+  each = liftLens (each :: Traversal (V2 (Exp a)) (V2 (Exp b)) (Exp a) (Exp b))++instance A.Eq a => A.Eq (V2 a) where+  (==) = (A.==) `on` t2+  (/=) = (A./=) `on` t2++instance A.Ord a => A.Ord (V2 a) where+  (<)  = (A.<) `on` t2+  (>)  = (A.>) `on` t2+  (<=) = (A.<=) `on` t2+  (>=) = (A.>=) `on` t2+  min  = v2 $$ on A.min t2+  max  = v2 $$ on A.max t2++t2 :: Elt a => Exp (V2 a) -> Exp (a,a)+t2 (unlift -> V2 x y) = tup2 (x,y)++v2 :: Elt a => Exp (a,a) -> Exp (V2 a)+v2 (untup2 -> (x,y)) = lift (V2 x y)++instance A.Bounded a => P.Bounded (Exp (V2 a)) where+  minBound = lift (V2 (minBound :: Exp a) (minBound :: Exp a))+  maxBound = lift (V2 (maxBound :: Exp a) (maxBound :: Exp a))+ instance A.Num a => P.Num (Exp (V2 a)) where   (+)             = lift2 ((+) :: V2 (Exp a) -> V2 (Exp a) -> V2 (Exp a))   (-)             = lift2 ((-) :: V2 (Exp a) -> V2 (Exp a) -> V2 (Exp a))@@ -138,12 +165,12 @@   negate          = lift1 (negate :: V2 (Exp a) -> V2 (Exp a))   signum          = lift1 (signum :: V2 (Exp a) -> V2 (Exp a))   abs             = lift1 (signum :: V2 (Exp a) -> V2 (Exp a))-  fromInteger x   = lift (fromInteger x :: V2 (Exp a))+  fromInteger x   = lift (P.fromInteger x :: V2 (Exp a))  instance A.Floating a => P.Fractional (Exp (V2 a)) where   (/)             = lift2 ((/) :: V2 (Exp a) -> V2 (Exp a) -> V2 (Exp a))   recip           = lift1 (recip :: V2 (Exp a) -> V2 (Exp a))-  fromRational x  = lift (fromRational x :: V2 (Exp a))+  fromRational x  = lift (P.fromRational x :: V2 (Exp a))  instance A.Floating a => P.Floating (Exp (V2 a)) where   pi              = lift (pi :: V2 (Exp a))@@ -162,6 +189,10 @@   acosh           = lift1 (acosh :: V2 (Exp a) -> V2 (Exp a))   atanh           = lift1 (atanh :: V2 (Exp a) -> V2 (Exp a)) -instance (Elt a, Elt b) => Each (Exp (V2 a)) (Exp (V2 b)) (Exp a) (Exp b) where-  each = liftLens (each :: Traversal (V2 (Exp a)) (V2 (Exp b)) (Exp a) (Exp b))+instance Epsilon a => Epsilon (V2 a) where+  nearZero = nearZero . quadrance++instance A.Functor V2 where+  fmap f (unlift -> V2 x y) = lift (V2 (f x) (f y))+  x <$ _                    = lift (V2 x x) 

@@ -1,7 +1,6 @@ {-# LANGUAGE ConstraintKinds       #-} {-# LANGUAGE FlexibleContexts      #-} {-# LANGUAGE FlexibleInstances     #-}-{-# LANGUAGE IncoherentInstances   #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE ScopedTypeVariables   #-} {-# LANGUAGE TypeFamilies          #-}@@ -12,7 +11,7 @@ -- | -- Module      : Data.Array.Accelerate.Linear.V3 -- Copyright   : 2014 Edward Kmett, Charles Durham,---               2015 Trevor L. McDonell+--               [2015..2018] Trevor L. McDonell -- License     : BSD-style (see the file LICENSE) -- -- Maintainer  : Edward Kmett <ekmett@gmail.com>@@ -36,10 +35,12 @@ ) where  import Data.Array.Accelerate                    as A+import Data.Array.Accelerate.Data.Functor       as A import Data.Array.Accelerate.Smart import Data.Array.Accelerate.Product import Data.Array.Accelerate.Array.Sugar +import Data.Array.Accelerate.Linear.Epsilon import Data.Array.Accelerate.Linear.Lift import Data.Array.Accelerate.Linear.Metric import Data.Array.Accelerate.Linear.Type@@ -48,9 +49,10 @@ import Data.Array.Accelerate.Linear.Vector  import Control.Lens+import Data.Function import Linear.V3                                ( V3(..) )-import qualified Linear.V3                      as L import Prelude                                  as P+import qualified Linear.V3                      as L  -- $setup -- >>> import Data.Array.Accelerate.Interpreter@@ -140,6 +142,31 @@                 (Exp $ SuccTupIdx ZeroTupIdx `Prj` t)                 (Exp $ ZeroTupIdx `Prj` t) +instance (Elt a, Elt b) => Each (Exp (V3 a)) (Exp (V3 b)) (Exp a) (Exp b) where+  each = liftLens (each :: Traversal (V3 (Exp a)) (V3 (Exp b)) (Exp a) (Exp b))++instance A.Eq a => A.Eq (V3 a) where+  (==) = (A.==) `on` t3+  (/=) = (A./=) `on` t3++instance A.Ord a => A.Ord (V3 a) where+  (<)  = (A.<) `on` t3+  (>)  = (A.>) `on` t3+  (<=) = (A.<=) `on` t3+  (>=) = (A.>=) `on` t3+  min  = v3 $$ on A.min t3+  max  = v3 $$ on A.max t3++t3 :: Elt a => Exp (V3 a) -> Exp (a,a,a)+t3 (unlift -> V3 x y z) = tup3 (x,y,z)++v3 :: Elt a => Exp (a,a,a) -> Exp (V3 a)+v3 (untup3 -> (x,y,z)) = lift (V3 x y z)++instance A.Bounded a => P.Bounded (Exp (V3 a)) where+  minBound = lift (V3 (minBound :: Exp a) (minBound :: Exp a) (minBound :: Exp a))+  maxBound = lift (V3 (maxBound :: Exp a) (maxBound :: Exp a) (maxBound :: Exp a))+ instance A.Num a => P.Num (Exp (V3 a)) where   (+)             = lift2 ((+) :: V3 (Exp a) -> V3 (Exp a) -> V3 (Exp a))   (-)             = lift2 ((-) :: V3 (Exp a) -> V3 (Exp a) -> V3 (Exp a))@@ -147,12 +174,12 @@   negate          = lift1 (negate :: V3 (Exp a) -> V3 (Exp a))   signum          = lift1 (signum :: V3 (Exp a) -> V3 (Exp a))   abs             = lift1 (signum :: V3 (Exp a) -> V3 (Exp a))-  fromInteger x   = lift (fromInteger x :: V3 (Exp a))+  fromInteger x   = lift (P.fromInteger x :: V3 (Exp a))  instance A.Floating a => P.Fractional (Exp (V3 a)) where   (/)             = lift2 ((/) :: V3 (Exp a) -> V3 (Exp a) -> V3 (Exp a))   recip           = lift1 (recip :: V3 (Exp a) -> V3 (Exp a))-  fromRational x  = lift (fromRational x :: V3 (Exp a))+  fromRational x  = lift (P.fromRational x :: V3 (Exp a))  instance A.Floating a => P.Floating (Exp (V3 a)) where   pi              = lift (pi :: V3 (Exp a))@@ -171,8 +198,12 @@   acosh           = lift1 (acosh :: V3 (Exp a) -> V3 (Exp a))   atanh           = lift1 (atanh :: V3 (Exp a) -> V3 (Exp a)) -instance (Elt a, Elt b) => Each (Exp (V3 a)) (Exp (V3 b)) (Exp a) (Exp b) where-  each = liftLens (each :: Traversal (V3 (Exp a)) (V3 (Exp b)) (Exp a) (Exp b))+instance Epsilon a => Epsilon (V3 a) where+  nearZero = nearZero . quadrance++instance A.Functor V3 where+  fmap f (unlift -> V3 x y z) = lift (V3 (f x) (f y) (f z))+  x <$ _                      = lift (V3 x x x)  -- $liftAcc --

@@ -1,7 +1,6 @@ {-# LANGUAGE ConstraintKinds       #-} {-# LANGUAGE FlexibleContexts      #-} {-# LANGUAGE FlexibleInstances     #-}-{-# LANGUAGE IncoherentInstances   #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE ScopedTypeVariables   #-} {-# LANGUAGE TypeFamilies          #-}@@ -12,7 +11,7 @@ -- | -- Module      : Data.Array.Accelerate.Linear.V4 -- Copyright   : 2014 Edward Kmett, Charles Durham,---               2015 Trevor L. McDonell+--               [2015..2018] Trevor L. McDonell -- License     : BSD-style (see the file LICENSE) -- -- Maintainer  : Edward Kmett <ekmett@gmail.com>@@ -43,10 +42,12 @@ ) where  import Data.Array.Accelerate                    as A+import Data.Array.Accelerate.Data.Functor       as A import Data.Array.Accelerate.Smart import Data.Array.Accelerate.Product import Data.Array.Accelerate.Array.Sugar +import Data.Array.Accelerate.Linear.Epsilon import Data.Array.Accelerate.Linear.Lift import Data.Array.Accelerate.Linear.Metric import Data.Array.Accelerate.Linear.Type@@ -56,9 +57,10 @@ import Data.Array.Accelerate.Linear.Vector  import Control.Lens+import Data.Function import Linear.V4                                ( V4(..) )-import qualified Linear.V4                      as L import Prelude                                  as P+import qualified Linear.V4                      as L  -- $setup -- >>> import Data.Array.Accelerate.Interpreter@@ -85,7 +87,7 @@ -- the projective, homogenous, coordinate @[x:y:z:w]@ is one of many associated -- with a single point @(x\/w, y\/w, z\/w)@. ---normalizePoint :: forall a. A.Floating a => Exp (V4 a) -> Exp (V3 a)+normalizePoint :: forall a. A.Fractional a => Exp (V4 a) -> Exp (V3 a) normalizePoint = lift1 (L.normalizePoint :: V4 (Exp a) -> V3 (Exp a))  -- | A space that distinguishes orthogonal basis vectors '_x', '_y', '_z', and '_w'.@@ -210,6 +212,31 @@                 (Exp $ SuccTupIdx ZeroTupIdx `Prj` t)                 (Exp $ ZeroTupIdx `Prj` t) +instance (Elt a, Elt b) => Each (Exp (V4 a)) (Exp (V4 b)) (Exp a) (Exp b) where+  each = liftLens (each :: Traversal (V4 (Exp a)) (V4 (Exp b)) (Exp a) (Exp b))++instance A.Eq a => A.Eq (V4 a) where+  (==) = (A.==) `on` t4+  (/=) = (A./=) `on` t4++instance A.Ord a => A.Ord (V4 a) where+  (<)  = (A.<) `on` t4+  (>)  = (A.>) `on` t4+  (<=) = (A.<=) `on` t4+  (>=) = (A.>=) `on` t4+  min  = v4 $$ on A.min t4+  max  = v4 $$ on A.max t4++t4 :: Elt a => Exp (V4 a) -> Exp (a,a,a,a)+t4 (unlift -> V4 x y z w) = tup4 (x,y,z,w)++v4 :: Elt a => Exp (a,a,a,a) -> Exp (V4 a)+v4 (untup4 -> (x,y,z,w)) = lift (V4 x y z w)++instance A.Bounded a => P.Bounded (Exp (V4 a)) where+  minBound = lift (V4 (minBound :: Exp a) (minBound :: Exp a) (minBound :: Exp a) (minBound :: Exp a))+  maxBound = lift (V4 (maxBound :: Exp a) (maxBound :: Exp a) (maxBound :: Exp a) (maxBound :: Exp a))+ instance A.Num a => P.Num (Exp (V4 a)) where   (+)             = lift2 ((+) :: V4 (Exp a) -> V4 (Exp a) -> V4 (Exp a))   (-)             = lift2 ((-) :: V4 (Exp a) -> V4 (Exp a) -> V4 (Exp a))@@ -217,12 +244,12 @@   negate          = lift1 (negate :: V4 (Exp a) -> V4 (Exp a))   signum          = lift1 (signum :: V4 (Exp a) -> V4 (Exp a))   abs             = lift1 (signum :: V4 (Exp a) -> V4 (Exp a))-  fromInteger x   = lift (fromInteger x :: V4 (Exp a))+  fromInteger x   = lift (P.fromInteger x :: V4 (Exp a))  instance A.Floating a => P.Fractional (Exp (V4 a)) where   (/)             = lift2 ((/) :: V4 (Exp a) -> V4 (Exp a) -> V4 (Exp a))   recip           = lift1 (recip :: V4 (Exp a) -> V4 (Exp a))-  fromRational x  = lift (fromRational x :: V4 (Exp a))+  fromRational x  = lift (P.fromRational x :: V4 (Exp a))  instance A.Floating a => P.Floating (Exp (V4 a)) where   pi              = lift (pi :: V4 (Exp a))@@ -241,6 +268,10 @@   acosh           = lift1 (acosh :: V4 (Exp a) -> V4 (Exp a))   atanh           = lift1 (atanh :: V4 (Exp a) -> V4 (Exp a)) -instance (Elt a, Elt b) => Each (Exp (V4 a)) (Exp (V4 b)) (Exp a) (Exp b) where-  each = liftLens (each :: Traversal (V4 (Exp a)) (V4 (Exp b)) (Exp a) (Exp b))+instance Epsilon a => Epsilon (V4 a) where+  nearZero = nearZero . quadrance++instance A.Functor V4 where+  fmap f (unlift -> V4 x y z w) = lift (V4 (f x) (f y) (f z) (f w))+  x <$ _                        = lift (V4 x x x x) 

@@ -8,7 +8,7 @@ -- | -- Module      : Data.Array.Accelerate.Linear.Vector -- Copyright   : 2014 Edward Kmett, Charles Durham,---               2015 Trevor L. McDonell+--               [2015..2018] Trevor L. McDonell -- License     : BSD-style (see the file LICENSE) -- -- Maintainer  : Edward Kmett <ekmett@gmail.com>@@ -83,7 +83,7 @@   lerp = lift3 (L.lerp :: Exp a -> f (Exp a) -> f (Exp a) -> f (Exp a))  -type IsAdditive f a = (Additive f, Box f a)+-- type IsAdditive f a = (Additive f, Box f a)   -- | Basis element