```module Math.Noise.VectorTable where
import Data.Maybe
import Data.Array.Unboxed
import qualified Data.Vector.Unboxed as Vector

data NoiseVector = NoiseVector Double Double Double
deriving (Show, Eq)

{- | Generates a normalized vector based on four numbers on the range of [-1.0, 1.0]
- This function uses the Cook (1957) method, and may reject pairs
-}
genNormalized :: (Double,Double,Double,Double) -> Maybe NoiseVector
genNormalized (x0,x1,x2,x3) | x0*x0 + x1*x1 + x2*x2 + x3*x3 >= 1.0 = Nothing
genNormalized (x0,x1,x2,x3) = Just \$ NoiseVector x y z
where x = 2.0 * (x1*x3 + x0*x2) / base
y = 2.0 * (x2*x3 - x0*x1) / base
z = (x0*x0 + x3*x3 - x1*x1 - x2*x2) / base
base = x0*x0 + x1*x1 + x2*x2 + x3*x3

-- just a testing function...
isNormalized :: NoiseVector -> Double
isNormalized (NoiseVector x y z) = x*x + y*y + z*z

-- | Generates a uniform distribution of Double values on the range [-1.0, 1.0]
genUniformDistribution :: Int -> [Double]
genUniformDistribution parts =
[-1.0, (-1.0 + step) .. 1.0]
where step = 1.0 / (fromIntegral parts)

-- | Generates a uniform distribution that has at least n*4 values that won't be rejected by the vector generation function
getSuitableUniformDist :: Int -> Maybe [(Double, Double, Double, Double)]
getSuitableUniformDist n | rem n 4 /= 0 = Nothing
getSuitableUniformDist n | otherwise = Just \$ aux n (vecNumbers n)
where aux current lst | (length lst) == n = lst
aux current lst | otherwise = aux (current + 4) (vecNumbers (current + 4) )
vecNumbers ammount = filter rejectFunc \$ (breakLst . genUniformDistribution) (ammount * 2)
breakLst (a:b:c:d:es) = (a,b,c,d) : breakLst es
breakLst _ = []
rejectFunc (x0,x1,x2,x3) = not \$ x0*x0 + x1*x1 + x2*x2 + x3*x3 >= 1.0

-- | Generates a list of uniformly distributed normalized vectors
genVectors :: Int -> Maybe [NoiseVector]
genVectors ammount = sequence \$ map genNormalized \$ fromMaybe [] \$ getSuitableUniformDist ammount

-- | Creates a list of Doubles with 0.0 separating each set of 3 Doubles
toList :: [NoiseVector] -> [Double]
toList (v:vs) = ((\(NoiseVector x y z) -> [x,y,z,0.0]) v) ++ (toList vs)
toList [] = []

-- | Creates an immutable array from a list of Doubles
listTable :: [Double] -> UArray Int Double
listTable lst = listArray (0, length lst) lst

staticTable :: Vector.Vector Double
staticTable = Vector.fromList constList

-- | An immutable table of predefined vectors
staticTable2 :: UArray Int Double
staticTable2 = listArray (0, 256*4) constList

-- | A constant list of Doubles
constList :: [Double]
constList = [
-0.763874, -0.596439, -0.246489, 0.0,
0.396055, 0.904518, -0.158073, 0.0,
-0.499004, -0.8665, -0.0131631, 0.0,
0.468724, -0.824756, 0.316346, 0.0,
0.829598, 0.43195, 0.353816, 0.0,
-0.454473, 0.629497, -0.630228, 0.0,
-0.162349, -0.869962, -0.465628, 0.0,
0.932805, 0.253451, 0.256198, 0.0,
-0.345419, 0.927299, -0.144227, 0.0,
-0.715026, -0.293698, -0.634413, 0.0,
-0.245997, 0.717467, -0.651711, 0.0,
-0.967409, -0.250435, -0.037451, 0.0,
0.901729, 0.397108, -0.170852, 0.0,
0.892657, -0.0720622, -0.444938, 0.0,
0.0260084, -0.0361701, 0.999007, 0.0,
0.949107, -0.19486, 0.247439, 0.0,
0.471803, -0.807064, -0.355036, 0.0,
0.879737, 0.141845, 0.453809, 0.0,
0.570747, 0.696415, 0.435033, 0.0,
-0.141751, -0.988233, -0.0574584, 0.0,
-0.58219, -0.0303005, 0.812488, 0.0,
-0.60922, 0.239482, -0.755975, 0.0,
0.299394, -0.197066, -0.933557, 0.0,
-0.851615, -0.220702, -0.47544, 0.0,
0.848886, 0.341829, -0.403169, 0.0,
-0.156129, -0.687241, 0.709453, 0.0,
-0.665651, 0.626724, 0.405124, 0.0,
0.595914, -0.674582, 0.43569, 0.0,
0.171025, -0.509292, 0.843428, 0.0,
0.78605, 0.536414, -0.307222, 0.0,
0.18905, -0.791613, 0.581042, 0.0,
-0.294916, 0.844994, 0.446105, 0.0,
0.342031, -0.58736, -0.7335, 0.0,
0.57155, 0.7869, 0.232635, 0.0,
0.885026, -0.408223, 0.223791, 0.0,
-0.789518, 0.571645, 0.223347, 0.0,
0.774571, 0.31566, 0.548087, 0.0,
-0.79695, -0.0433603, -0.602487, 0.0,
-0.142425, -0.473249, -0.869339, 0.0,
-0.0698838, 0.170442, 0.982886, 0.0,
0.687815, -0.484748, 0.540306, 0.0,
0.543703, -0.534446, -0.647112, 0.0,
0.97186, 0.184391, -0.146588, 0.0,
0.707084, 0.485713, -0.513921, 0.0,
0.942302, 0.331945, 0.043348, 0.0,
0.499084, 0.599922, 0.625307, 0.0,
-0.289203, 0.211107, 0.9337, 0.0,
0.412433, -0.71667, -0.56239, 0.0,
0.87721, -0.082816, 0.47291, 0.0,
-0.420685, -0.214278, 0.881538, 0.0,
0.752558, -0.0391579, 0.657361, 0.0,
0.0765725, -0.996789, 0.0234082, 0.0,
-0.544312, -0.309435, -0.779727, 0.0,
-0.455358, -0.415572, 0.787368, 0.0,
-0.874586, 0.483746, 0.0330131, 0.0,
0.245172, -0.0838623, 0.965846, 0.0,
0.382293, -0.432813, 0.81641, 0.0,
-0.287735, -0.905514, 0.311853, 0.0,
-0.667704, 0.704955, -0.239186, 0.0,
0.717885, -0.464002, -0.518983, 0.0,
0.976342, -0.214895, 0.0240053, 0.0,
-0.0733096, -0.921136, 0.382276, 0.0,
-0.986284, 0.151224, -0.0661379, 0.0,
-0.899319, -0.429671, 0.0812908, 0.0,
0.652102, -0.724625, 0.222893, 0.0,
0.203761, 0.458023, -0.865272, 0.0,
-0.030396, 0.698724, -0.714745, 0.0,
-0.460232, 0.839138, 0.289887, 0.0,
-0.0898602, 0.837894, 0.538386, 0.0,
-0.731595, 0.0793784, 0.677102, 0.0,
-0.447236, -0.788397, 0.422386, 0.0,
0.186481, 0.645855, -0.740335, 0.0,
-0.259006, 0.935463, 0.240467, 0.0,
0.445839, 0.819655, -0.359712, 0.0,
0.349962, 0.755022, -0.554499, 0.0,
-0.997078, -0.0359577, 0.0673977, 0.0,
-0.431163, -0.147516, -0.890133, 0.0,
0.299648, -0.63914, 0.708316, 0.0,
0.397043, 0.566526, -0.722084, 0.0,
-0.502489, 0.438308, -0.745246, 0.0,
0.0687235, 0.354097, 0.93268, 0.0,
-0.0476651, -0.462597, 0.885286, 0.0,
-0.221934, 0.900739, -0.373383, 0.0,
-0.956107, -0.225676, 0.186893, 0.0,
-0.187627, 0.391487, -0.900852, 0.0,
-0.224209, -0.315405, 0.92209, 0.0,
-0.730807, -0.537068, 0.421283, 0.0,
-0.0353135, -0.816748, 0.575913, 0.0,
-0.941391, 0.176991, -0.287153, 0.0,
-0.154174, 0.390458, 0.90762, 0.0,
-0.283847, 0.533842, 0.796519, 0.0,
-0.482737, -0.850448, 0.209052, 0.0,
-0.649175, 0.477748, 0.591886, 0.0,
0.885373, -0.405387, -0.227543, 0.0,
-0.147261, 0.181623, -0.972279, 0.0,
0.0959236, -0.115847, -0.988624, 0.0,
-0.89724, -0.191348, 0.397928, 0.0,
0.903553, -0.428461, -0.00350461, 0.0,
0.849072, -0.295807, -0.437693, 0.0,
0.65551, 0.741754, -0.141804, 0.0,
0.61598, -0.178669, 0.767232, 0.0,
0.0112967, 0.932256, -0.361623, 0.0,
-0.793031, 0.258012, 0.551845, 0.0,
0.421933, 0.454311, 0.784585, 0.0,
-0.319993, 0.0401618, -0.946568, 0.0,
-0.81571, 0.551307, -0.175151, 0.0,
-0.377644, 0.00322313, 0.925945, 0.0,
0.129759, -0.666581, -0.734052, 0.0,
0.601901, -0.654237, -0.457919, 0.0,
-0.927463, -0.0343576, -0.372334, 0.0,
-0.438663, -0.868301, -0.231578, 0.0,
-0.648845, -0.749138, -0.133387, 0.0,
0.507393, -0.588294, 0.629653, 0.0,
0.726958, 0.623665, 0.287358, 0.0,
0.411159, 0.367614, -0.834151, 0.0,
0.806333, 0.585117, -0.0864016, 0.0,
0.263935, -0.880876, 0.392932, 0.0,
0.421546, -0.201336, 0.884174, 0.0,
-0.683198, -0.569557, -0.456996, 0.0,
-0.117116, -0.0406654, -0.992285, 0.0,
-0.643679, -0.109196, -0.757465, 0.0,
-0.561559, -0.62989, 0.536554, 0.0,
0.0628422, 0.104677, -0.992519, 0.0,
0.480759, -0.2867, -0.828658, 0.0,
-0.228559, -0.228965, -0.946222, 0.0,
-0.10194, -0.65706, -0.746914, 0.0,
0.0689193, -0.678236, 0.731605, 0.0,
0.401019, -0.754026, 0.52022, 0.0,
-0.742141, 0.547083, -0.387203, 0.0,
-0.00210603, -0.796417, -0.604745, 0.0,
0.296725, -0.409909, -0.862513, 0.0,
-0.260932, -0.798201, 0.542945, 0.0,
-0.641628, 0.742379, 0.192838, 0.0,
-0.186009, -0.101514, 0.97729, 0.0,
0.106711, -0.962067, 0.251079, 0.0,
-0.743499, 0.30988, -0.592607, 0.0,
-0.795853, -0.605066, -0.0226607, 0.0,
-0.828661, -0.419471, -0.370628, 0.0,
0.0847218, -0.489815, -0.8677, 0.0,
-0.381405, 0.788019, -0.483276, 0.0,
0.282042, -0.953394, 0.107205, 0.0,
0.530774, 0.847413, 0.0130696, 0.0,
0.0515397, 0.922524, 0.382484, 0.0,
-0.631467, -0.709046, 0.313852, 0.0,
0.688248, 0.517273, 0.508668, 0.0,
0.646689, -0.333782, -0.685845, 0.0,
-0.932528, -0.247532, -0.262906, 0.0,
0.630609, 0.68757, -0.359973, 0.0,
0.577805, -0.394189, 0.714673, 0.0,
-0.887833, -0.437301, -0.14325, 0.0,
0.690982, 0.174003, 0.701617, 0.0,
-0.866701, 0.0118182, 0.498689, 0.0,
-0.482876, 0.727143, 0.487949, 0.0,
-0.577567, 0.682593, -0.447752, 0.0,
0.373768, 0.0982991, 0.922299, 0.0,
0.170744, 0.964243, -0.202687, 0.0,
0.993654, -0.035791, -0.106632, 0.0,
0.587065, 0.4143, -0.695493, 0.0,
-0.396509, 0.26509, -0.878924, 0.0,
-0.0866853, 0.83553, -0.542563, 0.0,
0.923193, 0.133398, -0.360443, 0.0,
0.00379108, -0.258618, 0.965972, 0.0,
0.239144, 0.245154, -0.939526, 0.0,
0.758731, -0.555871, 0.33961, 0.0,
0.295355, 0.309513, 0.903862, 0.0,
0.0531222, -0.91003, -0.411124, 0.0,
0.270452, 0.0229439, -0.96246, 0.0,
0.563634, 0.0324352, 0.825387, 0.0,
0.156326, 0.147392, 0.976646, 0.0,
-0.0410141, 0.981824, 0.185309, 0.0,
-0.385562, -0.576343, -0.720535, 0.0,
0.388281, 0.904441, 0.176702, 0.0,
0.945561, -0.192859, -0.262146, 0.0,
0.844504, 0.520193, 0.127325, 0.0,
0.0330893, 0.999121, -0.0257505, 0.0,
-0.592616, -0.482475, -0.644999, 0.0,
0.539471, 0.631024, -0.557476, 0.0,
0.655851, -0.027319, -0.754396, 0.0,
0.274465, 0.887659, 0.369772, 0.0,
-0.123419, 0.975177, -0.183842, 0.0,
-0.223429, 0.708045, 0.66989, 0.0,
-0.908654, 0.196302, 0.368528, 0.0,
-0.95759, -0.00863708, 0.288005, 0.0,
0.960535, 0.030592, 0.276472, 0.0,
-0.413146, 0.907537, 0.0754161, 0.0,
-0.847992, 0.350849, -0.397259, 0.0,
0.614736, 0.395841, 0.68221, 0.0,
-0.503504, -0.666128, -0.550234, 0.0,
-0.268833, -0.738524, -0.618314, 0.0,
0.792737, -0.60001, -0.107502, 0.0,
-0.637582, 0.508144, -0.579032, 0.0,
0.750105, 0.282165, -0.598101, 0.0,
-0.351199, -0.392294, -0.850155, 0.0,
0.250126, -0.960993, -0.118025, 0.0,
-0.732341, 0.680909, -0.0063274, 0.0,
-0.760674, -0.141009, 0.633634, 0.0,
0.222823, -0.304012, 0.926243, 0.0,
0.209178, 0.505671, 0.836984, 0.0,
0.757914, -0.56629, -0.323857, 0.0,
-0.782926, -0.339196, 0.52151, 0.0,
-0.462952, 0.585565, 0.665424, 0.0,
0.61879, 0.194119, -0.761194, 0.0,
0.741388, -0.276743, 0.611357, 0.0,
0.707571, 0.702621, 0.0752872, 0.0,
0.156562, 0.819977, 0.550569, 0.0,
-0.793606, 0.440216, 0.42, 0.0,
0.234547, 0.885309, -0.401517, 0.0,
0.132598, 0.80115, -0.58359, 0.0,
-0.377899, -0.639179, 0.669808, 0.0,
-0.865993, -0.396465, 0.304748, 0.0,
-0.624815, -0.44283, 0.643046, 0.0,
-0.485705, 0.825614, -0.287146, 0.0,
-0.971788, 0.175535, 0.157529, 0.0,
-0.456027, 0.392629, 0.798675, 0.0,
-0.0104443, 0.521623, -0.853112, 0.0,
-0.660575, -0.74519, 0.091282, 0.0,
-0.0157698, -0.307475, -0.951425, 0.0,
-0.603467, -0.250192, 0.757121, 0.0,
0.506876, 0.25006, 0.824952, 0.0,
0.255404, 0.966794, 0.00884498, 0.0,
0.466764, -0.874228, -0.133625, 0.0,
0.475077, -0.0682351, -0.877295, 0.0,
-0.224967, -0.938972, -0.260233, 0.0,
-0.377929, -0.814757, -0.439705, 0.0,
-0.305847, 0.542333, -0.782517, 0.0,
0.26658, -0.902905, -0.337191, 0.0,
0.0275773, 0.322158, -0.946284, 0.0,
0.0185422, 0.716349, 0.697496, 0.0,
-0.20483, 0.978416, 0.0273371, 0.0,
-0.898276, 0.373969, 0.230752, 0.0,
-0.00909378, 0.546594, 0.837349, 0.0,
0.6602, -0.751089, 0.000959236, 0.0,
0.855301, -0.303056, 0.420259, 0.0,
0.797138, 0.0623013, -0.600574, 0.0,
0.48947, -0.866813, 0.0951509, 0.0,
0.251142, 0.674531, 0.694216, 0.0,
-0.578422, -0.737373, -0.348867, 0.0,
-0.254689, -0.514807, 0.818601, 0.0,
0.374972, 0.761612, 0.528529, 0.0,
0.640303, -0.734271, -0.225517, 0.0,
-0.638076, 0.285527, 0.715075, 0.0,
0.772956, -0.15984, -0.613995, 0.0,
0.798217, -0.590628, 0.118356, 0.0,
-0.986276, -0.0578337, -0.154644, 0.0,
-0.312988, -0.94549, 0.0899272, 0.0,
-0.497338, 0.178325, 0.849032, 0.0,
-0.101136, -0.981014, 0.165477, 0.0,
-0.521688, 0.0553434, -0.851339, 0.0,
-0.786182, -0.583814, 0.202678, 0.0,
-0.565191, 0.821858, -0.0714658, 0.0,
0.437895, 0.152598, -0.885981, 0.0,
-0.92394, 0.353436, -0.14635, 0.0,
0.212189, -0.815162, -0.538969, 0.0,
-0.859262, 0.143405, -0.491024, 0.0,
0.991353, 0.112814, 0.0670273, 0.0,
0.0337884, -0.979891, -0.196654, 0.0
]

{-
-- generates the table based on the functions defined above
vectorTable :: (Double, Double, Double)
vectorTable = listArray (0, 255) \$ fromMaybe [] \$ genVectors 256
-}
```