local band = bit32.band
local floor = math.floor
local Perlin = {}
local p = {}

-- Hash lookup table as defined by Ken Perlin
-- This is a randomly arranged array of all numbers from 0-255 inclusive
local permutation = {
    151,
    160,
    137,
    91,
    90,
    15,
    131,
    13,
    201,
    95,
    96,
    53,
    194,
    233,
    7,
    225,
    140,
    36,
    103,
    30,
    69,
    142,
    8,
    99,
    37,
    240,
    21,
    10,
    23,
    190,
    6,
    148,
    247,
    120,
    234,
    75,
    0,
    26,
    197,
    62,
    94,
    252,
    219,
    203,
    117,
    35,
    11,
    32,
    57,
    177,
    33,
    88,
    237,
    149,
    56,
    87,
    174,
    20,
    125,
    136,
    171,
    168,
    68,
    175,
    74,
    165,
    71,
    134,
    139,
    48,
    27,
    166,
    77,
    146,
    158,
    231,
    83,
    111,
    229,
    122,
    60,
    211,
    133,
    230,
    220,
    105,
    92,
    41,
    55,
    46,
    245,
    40,
    244,
    102,
    143,
    54,
    65,
    25,
    63,
    161,
    1,
    216,
    80,
    73,
    209,
    76,
    132,
    187,
    208,
    89,
    18,
    169,
    200,
    196,
    135,
    130,
    116,
    188,
    159,
    86,
    164,
    100,
    109,
    198,
    173,
    186,
    3,
    64,
    52,
    217,
    226,
    250,
    124,
    123,
    5,
    202,
    38,
    147,
    118,
    126,
    255,
    82,
    85,
    212,
    207,
    206,
    59,
    227,
    47,
    16,
    58,
    17,
    182,
    189,
    28,
    42,
    223,
    183,
    170,
    213,
    119,
    248,
    152,
    2,
    44,
    154,
    163,
    70,
    221,
    153,
    101,
    155,
    167,
    43,
    172,
    9,
    129,
    22,
    39,
    253,
    19,
    98,
    108,
    110,
    79,
    113,
    224,
    232,
    178,
    185,
    112,
    104,
    218,
    246,
    97,
    228,
    251,
    34,
    242,
    193,
    238,
    210,
    144,
    12,
    191,
    179,
    162,
    241,
    81,
    51,
    145,
    235,
    249,
    14,
    239,
    107,
    49,
    192,
    214,
    31,
    181,
    199,
    106,
    157,
    184,
    84,
    204,
    176,
    115,
    121,
    50,
    45,
    127,
    4,
    150,
    254,
    138,
    236,
    205,
    93,
    222,
    114,
    67,
    29,
    24,
    72,
    243,
    141,
    128,
    195,
    78,
    66,
    215,
    61,
    156,
    180
}

-- p is used to hash unit cube coordinates to [0, 255]
for i = 0, 255 do
    -- Convert to 0 based index table
    p[i] = permutation[i + 1]
    -- Repeat the array to avoid buffer overflow in hash function
    p[i + 256] = permutation[i + 1]
end

-- Gradient function finds dot product between pseudorandom gradient vector
-- and the vector from input coordinate to a unit cube vertex
local dot_product = {
    [0x0] = function(x, y)
        return x + y
    end,
    [0x1] = function(x, y)
        return -x + y
    end,
    [0x2] = function(x, y)
        return x - y
    end,
    [0x3] = function(x, y)
        return -x - y
    end,
    [0x4] = function(x, z)
        return x + z
    end,
    [0x5] = function(x, z)
        return -x + z
    end,
    [0x6] = function(x, z)
        return x - z
    end,
    [0x7] = function(x, z)
        return -x - z
    end,
    [0x8] = function(y, z)
        return y + z
    end,
    [0x9] = function(y, z)
        return -y + z
    end,
    [0xA] = function(y, z)
        return y - z
    end,
    [0xB] = function(y, z)
        return -y - z
    end,
    [0xC] = function(x, y)
        return y + x
    end,
    [0xD] = function(y, z)
        return -y + z
    end,
    [0xE] = function(x, y)
        return y - x
    end,
    [0xF] = function(y, z)
        return -y - z
    end
}
local function grad(hash, x, y, bit)
    bit = bit or 1
    return dot_product[band(hash, bit)](x, y)
end

-- Fade function is used to smooth final output
local function fade(t)
    return t * t * t * (t * (t * 6 - 15) + 10)
end

local function lerp(t, a, bs)
    return a + t * (bs - a)
end

-- Return range: [-1, 1]
function Perlin.noise(x, y, z, bit)
    y = y or 0
    z = z or 0

    -- This prevents integer inputs returning 0, which casues 'straight line' artifacts.
    x = x - 0.55077056353912
    y = y - 0.131357755512
    z = z - 0.20474238274619

    -- Calculate the "unit cube" that the point asked will be located in
    local xi = band(floor(x), 255)
    local yi = band(floor(y), 255)
    local zi = band(floor(z), 255)

    -- Next we calculate the location (from 0 to 1) in that cube
    x = x - floor(x)
    y = y - floor(y)
    z = z - floor(z)

    -- We also fade the location to smooth the result
    local u = fade(x)
    local v = fade(y)
    local w = fade(z)

    -- Hash all 8 unit cube coordinates surrounding input coordinate
    local A, AA, AB, AAA, ABA, AAB, ABB, B, BA, BB, BAA, BBA, BAB, BBB
    A = p[xi] + yi
    AA = p[A] + zi
    AB = p[A + 1] + zi
    AAA = p[AA]
    ABA = p[AB]
    AAB = p[AA + 1]
    ABB = p[AB + 1]

    B = p[xi + 1] + yi
    BA = p[B] + zi
    BB = p[B + 1] + zi
    BAA = p[BA]
    BBA = p[BB]
    BAB = p[BA + 1]
    BBB = p[BB + 1]

    -- Take the weighted average between all 8 unit cube coordinates
    return lerp(
        w,
        lerp(v, lerp(u, grad(AAA, x, y, bit), grad(BAA, x - 1, y, bit)), lerp(u, grad(ABA, x, y - 1, bit), grad(BBA, x - 1, y - 1, bit))),
        lerp(v, lerp(u, grad(AAB, x, y, bit), grad(BAB, x - 1, y, bit)), lerp(u, grad(ABB, x, y - 1, bit), grad(BBB, x - 1, y - 1, bit)))
    )
end

return Perlin