{-# LANGUAGE DataKinds #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE MagicHash #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeInType #-}
{-# LANGUAGE TypeSynonymInstances #-}
{-# LANGUAGE UnboxedTuples #-}
{-# OPTIONS_GHC -fno-warn-orphans #-}
module Numeric.Quaternion.QDouble
( QDouble, Quater (..)
) where
import Data.Coerce (coerce)
import GHC.Exts
import qualified Control.Monad.ST as ST
import Numeric.DataFrame.Internal.Array.Class
import Numeric.DataFrame.Internal.Array.Family.DoubleX3
import Numeric.DataFrame.Internal.Array.Family.DoubleX4
import qualified Numeric.DataFrame.ST as ST
import Numeric.DataFrame.Type
import Numeric.Dimensions
import qualified Numeric.Dimensions.Fold as ST
import Numeric.PrimBytes (PrimBytes)
import Numeric.Quaternion.Class
import Numeric.Scalar
import Numeric.Vector
type QDouble = Quater Double
deriving instance PrimBytes (Quater Double)
deriving instance PrimArray Double (Quater Double)
instance Quaternion Double where
newtype Quater Double = QDouble DoubleX4
{-# INLINE packQ #-}
packQ (D# x) (D# y) (D# z) (D# w) = QDouble (DoubleX4# x y z w)
{-# INLINE unpackQ #-}
unpackQ (QDouble (DoubleX4# x y z w)) = (D# x, D# y, D# z, D# w)
{-# INLINE fromVecNum #-}
fromVecNum (SingleFrame (DoubleX3# x y z)) (D# w) = QDouble (DoubleX4# x y z w)
{-# INLINE fromVec4 #-}
fromVec4 = coerce
{-# INLINE toVec4 #-}
toVec4 = coerce
{-# INLINE square #-}
square q = D# (qdot q)
{-# INLINE im #-}
im (QDouble (DoubleX4# x y z _)) = QDouble (DoubleX4# x y z 0.0##)
{-# INLINE re #-}
re (QDouble (DoubleX4# _ _ _ w)) = QDouble (DoubleX4# 0.0## 0.0## 0.0## w)
{-# INLINE imVec #-}
imVec (QDouble (DoubleX4# x y z _)) = SingleFrame (DoubleX3# x y z)
{-# INLINE taker #-}
taker (QDouble (DoubleX4# _ _ _ w)) = D# w
{-# INLINE takei #-}
takei (QDouble (DoubleX4# x _ _ _)) = D# x
{-# INLINE takej #-}
takej (QDouble (DoubleX4# _ y _ _)) = D# y
{-# INLINE takek #-}
takek (QDouble (DoubleX4# _ _ z _)) = D# z
{-# INLINE conjugate #-}
conjugate (QDouble (DoubleX4# x y z w)) = QDouble (DoubleX4#
(negateDouble# x)
(negateDouble# y)
(negateDouble# z) w)
{-# INLINE rotScale #-}
rotScale (QDouble (DoubleX4# i j k t))
(SingleFrame (DoubleX3# x y z))
= let l = t*##t -## i*##i -## j*##j -## k*##k
d = 2.0## *## ( i*##x +## j*##y +## k*##z)
t2 = t *## 2.0##
in SingleFrame
( DoubleX3#
(l*##x +## d*##i +## t2 *## (z*##j -## y*##k))
(l*##y +## d*##j +## t2 *## (x*##k -## z*##i))
(l*##z +## d*##k +## t2 *## (y*##i -## x*##j))
)
{-# INLINE getRotScale #-}
getRotScale _ (SingleFrame (DoubleX3# 0.0## 0.0## 0.0##))
= QDouble (DoubleX4# 0.0## 0.0## 0.0## 0.0##)
getRotScale (SingleFrame (DoubleX3# 0.0## 0.0## 0.0##)) _
= case infty of D# x -> QDouble (DoubleX4# x x x x)
getRotScale a@(SingleFrame (DoubleX3# a1 a2 a3))
b@(SingleFrame (DoubleX3# b1 b2 b3))
= let ma = sqrtDouble# (a1*##a1 +## a2*##a2 +## a3*##a3)
mb = sqrtDouble# (b1*##b1 +## b2*##b2 +## b3*##b3)
d = a1*##b1 +## a2*##b2 +## a3*##b3
c = sqrtDouble# (ma*##mb +## d)
ma2 = ma *## sqrtDouble# 2.0##
r = 1.0## /## (ma2 *## c)
in case cross a b of
SingleFrame (DoubleX3# 0.0## 0.0## 0.0##) ->
if isTrue# (d >## 0.0##)
then QDouble (DoubleX4# 0.0## 0.0## 0.0## (sqrtDouble# (mb /## ma)))
else QDouble (DoubleX4# 0.0## 0.0## (sqrtDouble# (mb /## ma)) 0.0##)
SingleFrame (DoubleX3# t1 t2 t3) -> QDouble
( DoubleX4#
(t1 *## r)
(t2 *## r)
(t3 *## r)
(c /## ma2)
)
{-# INLINE axisRotation #-}
axisRotation (SingleFrame (DoubleX3# 0.0## 0.0## 0.0##)) _
= QDouble (DoubleX4# 0.0## 0.0## 0.0## 1.0##)
axisRotation (SingleFrame (DoubleX3# x y z)) (D# a)
= let c = cosDouble# (a *## 0.5##)
s = sinDouble# (a *## 0.5##)
/## sqrtDouble# (x*##x +## y*##y +## z*##z)
in QDouble
( DoubleX4#
(x *## s)
(y *## s)
(z *## s)
c
)
{-# INLINE qArg #-}
qArg (QDouble (DoubleX4# x y z w))
= case atan2 (D# (sqrtDouble# (x*##x +## y*##y +## z*##z)))
(D# w) of
D# a -> D# (a *## 2.0##)
{-# INLINE fromMatrix33 #-}
fromMatrix33 m
= let d =
( ix 0# m *## ( ix 4# m *## ix 8# m -## ix 5# m *## ix 7# m )
-## ix 1# m *## ( ix 3# m *## ix 8# m -## ix 5# m *## ix 6# m )
+## ix 2# m *## ( ix 3# m *## ix 7# m -## ix 4# m *## ix 6# m )
) **## 0.33333333333333333333333333333333##
in QDouble
( DoubleX4#
(sqrtDouble# (max# 0.0## (d +## ix 0# m -## ix 4# m -## ix 8# m )) *## sign# (ix 5# m -## ix 7# m) *## 0.5##)
(sqrtDouble# (max# 0.0## (d -## ix 0# m +## ix 4# m -## ix 8# m )) *## sign# (ix 6# m -## ix 2# m) *## 0.5##)
(sqrtDouble# (max# 0.0## (d -## ix 0# m -## ix 4# m +## ix 8# m )) *## sign# (ix 1# m -## ix 3# m) *## 0.5##)
(sqrtDouble# (max# 0.0## (d +## ix 0# m +## ix 4# m +## ix 8# m )) *## 0.5##)
)
{-# INLINE fromMatrix44 #-}
fromMatrix44 m
= let d =
( ix 0# m *## ( ix 5# m *## ix 10# m -## ix 6# m *## ix 9# m )
-## ix 1# m *## ( ix 4# m *## ix 10# m -## ix 6# m *## ix 8# m )
+## ix 2# m *## ( ix 4# m *## ix 9# m -## ix 5# m *## ix 8# m )
) **## 0.33333333333333333333333333333333##
c = 0.5## /## ix 15# m
in QDouble
( DoubleX4#
(sqrtDouble# (max# 0.0## (d +## ix 0# m -## ix 5# m -## ix 10# m )) *## sign# (ix 6# m -## ix 9# m) *## c)
(sqrtDouble# (max# 0.0## (d -## ix 0# m +## ix 5# m -## ix 10# m )) *## sign# (ix 8# m -## ix 2# m) *## c)
(sqrtDouble# (max# 0.0## (d -## ix 0# m -## ix 5# m +## ix 10# m )) *## sign# (ix 1# m -## ix 4# m) *## c)
(sqrtDouble# (max# 0.0## (d +## ix 0# m +## ix 5# m +## ix 10# m )) *## c)
)
{-# INLINE toMatrix33 #-}
toMatrix33 (QDouble (DoubleX4# 0.0## 0.0## 0.0## w))
= let x = D# (w *## w)
f 0 = (# 3 :: Int , x #)
f k = (# k-1, 0 #)
in case gen# 9# f 0 of
(# _, m #) -> m
toMatrix33 (QDouble (DoubleX4# x' y' z' w')) =
let x = scalar (D# x')
y = scalar (D# y')
z = scalar (D# z')
w = scalar (D# w')
x2 = x * x
y2 = y * y
z2 = z * z
w2 = w * w
l2 = x2 + y2 + z2 + w2
in ST.runST $ do
df <- ST.newDataFrame
ST.writeDataFrameOff df 0 $ l2 - 2*(z2 + y2)
ST.writeDataFrameOff df 1 $ 2*(x*y + z*w)
ST.writeDataFrameOff df 2 $ 2*(x*z - y*w)
ST.writeDataFrameOff df 3 $ 2*(x*y - z*w)
ST.writeDataFrameOff df 4 $ l2 - 2*(z2 + x2)
ST.writeDataFrameOff df 5 $ 2*(y*z + x*w)
ST.writeDataFrameOff df 6 $ 2*(x*z + y*w)
ST.writeDataFrameOff df 7 $ 2*(y*z - x*w)
ST.writeDataFrameOff df 8 $ l2 - 2*(y2 + x2)
ST.unsafeFreezeDataFrame df
{-# INLINE toMatrix44 #-}
toMatrix44 (QDouble (DoubleX4# 0.0## 0.0## 0.0## w)) = ST.runST $ do
df <- ST.newDataFrame
ST.overDimOff_ (dims :: Dims '[4,4]) (\i -> ST.writeDataFrameOff df i 0) 0 1
let w2 = scalar (D# (w *## w))
ST.writeDataFrameOff df 0 w2
ST.writeDataFrameOff df 5 w2
ST.writeDataFrameOff df 10 w2
ST.writeDataFrameOff df 15 1
ST.unsafeFreezeDataFrame df
toMatrix44 (QDouble (DoubleX4# x' y' z' w')) =
let x = scalar (D# x')
y = scalar (D# y')
z = scalar (D# z')
w = scalar (D# w')
x2 = x * x
y2 = y * y
z2 = z * z
w2 = w * w
l2 = x2 + y2 + z2 + w2
in ST.runST $ do
df <- ST.newDataFrame
ST.writeDataFrameOff df 0 $ l2 - 2*(z2 + y2)
ST.writeDataFrameOff df 1 $ 2*(x*y + z*w)
ST.writeDataFrameOff df 2 $ 2*(x*z - y*w)
ST.writeDataFrameOff df 3 0
ST.writeDataFrameOff df 4 $ 2*(x*y - z*w)
ST.writeDataFrameOff df 5 $ l2 - 2*(z2 + x2)
ST.writeDataFrameOff df 6 $ 2*(y*z + x*w)
ST.writeDataFrameOff df 7 0
ST.writeDataFrameOff df 8 $ 2*(x*z + y*w)
ST.writeDataFrameOff df 9 $ 2*(y*z - x*w)
ST.writeDataFrameOff df 10 $ l2 - 2*(y2 + x2)
ST.writeDataFrameOff df 11 0
ST.writeDataFrameOff df 12 0
ST.writeDataFrameOff df 13 0
ST.writeDataFrameOff df 14 0
ST.writeDataFrameOff df 15 1
ST.unsafeFreezeDataFrame df
qdot :: QDouble -> Double#
qdot (QDouble (DoubleX4# x y z w)) = (x *## x) +##
(y *## y) +##
(z *## z) +##
(w *## w)
{-# INLINE qdot #-}
infty :: Double
infty = read "Infinity"
max# :: Double# -> Double# -> Double#
max# a b | isTrue# (a >## b) = a
| otherwise = b
{-# INLINE max# #-}
sign# :: Double# -> Double#
sign# a | isTrue# (a >## 0.0##) = 1.0##
| isTrue# (a <## 0.0##) = negateDouble# 1.0##
| otherwise = 0.0##
{-# INLINE sign# #-}
ix :: PrimArray Double a => Int# -> a -> Double#
ix i a = case ix# i a of D# r -> r
{-# INLINE ix #-}
instance Num QDouble where
QDouble a + QDouble b
= QDouble (a + b)
{-# INLINE (+) #-}
QDouble a - QDouble b
= QDouble (a - b)
{-# INLINE (-) #-}
QDouble (DoubleX4# a1 a2 a3 a4) * QDouble (DoubleX4# b1 b2 b3 b4)
= QDouble
( DoubleX4#
((a4 *## b1) +##
(a1 *## b4) +##
(a2 *## b3) -##
(a3 *## b2)
)
((a4 *## b2) -##
(a1 *## b3) +##
(a2 *## b4) +##
(a3 *## b1)
)
((a4 *## b3) +##
(a1 *## b2) -##
(a2 *## b1) +##
(a3 *## b4)
)
((a4 *## b4) -##
(a1 *## b1) -##
(a2 *## b2) -##
(a3 *## b3)
)
)
{-# INLINE (*) #-}
negate (QDouble a) = QDouble (negate a)
{-# INLINE negate #-}
abs q = QDouble (DoubleX4# 0.0## 0.0## 0.0## (sqrtDouble# (qdot q)))
{-# INLINE abs #-}
signum q@(QDouble (DoubleX4# x y z w))
= case qdot q of
0.0## -> QDouble (DoubleX4# 0.0## 0.0## 0.0## 0.0##)
qd -> case 1.0## /## sqrtDouble# qd of
s -> QDouble
( DoubleX4#
(x *## s)
(y *## s)
(z *## s)
(w *## s)
)
{-# INLINE signum #-}
fromInteger n = case fromInteger n of
D# x -> QDouble (DoubleX4# 0.0## 0.0## 0.0## x)
{-# INLINE fromInteger #-}
instance Fractional QDouble where
{-# INLINE recip #-}
recip q@(QDouble (DoubleX4# x y z w)) = case -1.0## /## qdot q of
c -> QDouble
( DoubleX4#
(x *## c)
(y *## c)
(z *## c)
(negateDouble# (w *## c))
)
{-# INLINE (/) #-}
a / b = a * recip b
{-# INLINE fromRational #-}
fromRational q = case fromRational q of
D# x -> QDouble (DoubleX4# 0.0## 0.0## 0.0## x)
instance Floating QDouble where
{-# INLINE pi #-}
pi = QDouble (DoubleX4# 0.0## 0.0## 0.0##
3.141592653589793##)
{-# INLINE exp #-}
exp (QDouble (DoubleX4# x y z w))
= case (# (x *## x) +##
(y *## y) +##
(z *## z)
, expDouble# w
#) of
(# 0.0##, et #) -> QDouble (DoubleX4# 0.0## 0.0## 0.0## et)
(# mv2, et #) -> case sqrtDouble# mv2 of
mv -> case et *## sinDouble# mv
/## mv of
l -> QDouble
( DoubleX4#
(x *## l)
(y *## l)
(z *## l)
(et *## cosDouble# mv)
)
{-# INLINE log #-}
log (QDouble (DoubleX4# x y z w))
= case (x *## x) +##
(y *## y) +##
(z *## z) of
0.0## -> if isTrue# (w >=## 0.0##)
then QDouble (DoubleX4# 0.0## 0.0## 0.0## (logDouble# w))
else QDouble (DoubleX4# 3.141592653589793## 0.0## 0.0##
(logDouble# (negateDouble# w)))
mv2 -> case (# sqrtDouble# (mv2 +## (w *## w))
, sqrtDouble# mv2
#) of
(# mq, mv #) -> case atan2 (D# mv) (D# w) / D# mv of
D# l -> QDouble
( DoubleX4#
(x *## l)
(y *## l)
(z *## l)
(logDouble# mq)
)
{-# INLINE sqrt #-}
sqrt (QDouble (DoubleX4# x y z w))
= case (x *## x) +##
(y *## y) +##
(z *## z) of
0.0## -> if isTrue# (w >=## 0.0##)
then QDouble (DoubleX4# 0.0## 0.0## 0.0## (sqrtDouble# w))
else QDouble (DoubleX4# (sqrtDouble# (negateDouble# w)) 0.0## 0.0## 0.0##)
mv2 ->
let mq = sqrtDouble# (mv2 +## w *## w)
l2 = sqrtDouble# mq
tq = w /## (mq *## 2.0##)
sina = sqrtDouble# (0.5## -## tq) *## l2 /## sqrtDouble# mv2
in QDouble
( DoubleX4#
(x *## sina)
(y *## sina)
(z *## sina)
(sqrtDouble# (0.5## +## tq) *## l2)
)
{-# INLINE sin #-}
sin (QDouble (DoubleX4# x y z w))
= case (x *## x) +##
(y *## y) +##
(z *## z) of
0.0## -> QDouble (DoubleX4# 0.0## 0.0## 0.0## (sinDouble# w))
mv2 -> case sqrtDouble# mv2 of
mv -> case cosDouble# w *## sinhDouble# mv
/## mv of
l -> QDouble
( DoubleX4#
(x *## l)
(y *## l)
(z *## l)
(sinDouble# w *## coshDouble# mv)
)
{-# INLINE cos #-}
cos (QDouble (DoubleX4# x y z w))
= case (x *## x) +##
(y *## y) +##
(z *## z) of
0.0## -> QDouble (DoubleX4# 0.0## 0.0## 0.0## (cosDouble# w))
mv2 -> case sqrtDouble# mv2 of
mv -> case sinDouble# w *## sinhDouble# mv
/## negateDouble# mv of
l -> QDouble
( DoubleX4#
(x *## l)
(y *## l)
(z *## l)
(cosDouble# w *## coshDouble# mv)
)
{-# INLINE tan #-}
tan (QDouble (DoubleX4# x y z w))
= case (x *## x) +##
(y *## y) +##
(z *## z) of
0.0## -> QDouble (DoubleX4# 0.0## 0.0## 0.0## (tanDouble# w))
mv2 ->
let mv = sqrtDouble# mv2
chv = coshDouble# mv
shv = sinhDouble# mv
ct = cosDouble# w
st = sinDouble# w
cq = 1.0## /##
( (ct *## ct *## chv *## chv)
+##
(st *## st *## shv *## shv)
)
l = chv *## shv *## cq
/## mv
in QDouble
( DoubleX4#
(x *## l)
(y *## l)
(z *## l)
(ct *## st *## cq)
)
{-# INLINE sinh #-}
sinh (QDouble (DoubleX4# x y z w))
= case (x *## x) +##
(y *## y) +##
(z *## z) of
0.0## -> QDouble (DoubleX4# 0.0## 0.0## 0.0## (sinhDouble# w))
mv2 -> case sqrtDouble# mv2 of
mv -> case coshDouble# w *## sinDouble# mv
/## mv of
l -> QDouble
( DoubleX4#
(x *## l)
(y *## l)
(z *## l)
(sinhDouble# w *## cosDouble# mv)
)
{-# INLINE cosh #-}
cosh (QDouble (DoubleX4# x y z w))
= case (x *## x) +##
(y *## y) +##
(z *## z) of
0.0## -> QDouble (DoubleX4# 0.0## 0.0## 0.0## (coshDouble# w))
mv2 -> case sqrtDouble# mv2 of
mv -> case sinhDouble# w *## sinDouble# mv
/## mv of
l -> QDouble
( DoubleX4#
(x *## l)
(y *## l)
(z *## l)
(coshDouble# w *## cosDouble# mv)
)
{-# INLINE tanh #-}
tanh (QDouble (DoubleX4# x y z w))
= case (x *## x) +##
(y *## y) +##
(z *## z) of
0.0## -> QDouble (DoubleX4# 0.0## 0.0## 0.0## (tanhDouble# w))
mv2 ->
let mv = sqrtDouble# mv2
cv = cosDouble# mv
sv = sinDouble# mv
cht = coshDouble# w
sht = sinhDouble# w
cq = 1.0## /##
( (cht *## cht *## cv *## cv)
+##
(sht *## sht *## sv *## sv)
)
l = cv *## sv *## cq
/## mv
in QDouble
( DoubleX4#
(x *## l)
(y *## l)
(z *## l)
(cht *## sht *## cq)
)
{-# INLINE asin #-}
asin q = -i * log (i*q + sqrt (1 - q*q))
where
i = case signum . im $ q of
0 -> QDouble (DoubleX4# 1.0## 0.0## 0.0## 0.0##)
i' -> i'
{-# INLINE acos #-}
acos q = pi/2 - asin q
{-# INLINE atan #-}
atan q@(QDouble (DoubleX4# _ _ _ w))
= if square imq == 0
then QDouble (DoubleX4# 0.0## 0.0## 0.0## (atanDouble# w))
else i / 2 * log ( (i + q) / (i - q) )
where
i = signum imq
imq = im q
{-# INLINE asinh #-}
asinh q = log (q + sqrt (q*q + 1))
{-# INLINE acosh #-}
acosh q = log (q + sqrt (q*q - 1))
{-# INLINE atanh #-}
atanh q = 0.5 * log ((1+q)/(1-q))
instance Eq QDouble where
{-# INLINE (==) #-}
QDouble a == QDouble b = a == b
{-# INLINE (/=) #-}
QDouble a /= QDouble b = a /= b
instance Show QDouble where
show (QDouble (DoubleX4# x y z w)) =
show (D# w) ++ ss x ++ "i"
++ ss y ++ "j"
++ ss z ++ "k"
where
ss a# = case D# a# of
a -> if a >= 0 then " + " ++ show a
else " - " ++ show (negate a)