(* Fade function *)
fade[t_] := t^3 (t (t 6 - 15) + 10)

(* Linear interpolation *)
lerp[t_, a_, b_] := a + t (b - a)

(* Gradient function *)
grad[hash_, x_, y_, z_] :=
  Module[{h, u, v},
    h = BitAnd[hash, 15];
    u = If[h < 8, x, y];
    v = If[h < 4, y, If[MemberQ[{12, 14}, h], x, z]];
    (If[BitAnd[h, 1] == 0, u, -u]) + (If[BitAnd[h, 2] == 0, v, -v])
  ]

(* Permutation table *)
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
};

(* Double the permutation to avoid wrap-around *)
p = Join[permutation, permutation];

(* Perlin noise function *)
perlinNoise[x_, y_, z_] :=
  Module[{X, Y, Z, u, v, w, A, AA, AB, B, BA, BB, xf, yf, zf},
    X = BitAnd[Floor[x], 255];
    Y = BitAnd[Floor[y], 255];
    Z = BitAnd[Floor[z], 255];
    xf = x - Floor[x];
    yf = y - Floor[y];
    zf = z - Floor[z];
    u = fade[xf];
    v = fade[yf];
    w = fade[zf];
    A = p[[X + 1]] + Y;
    AA = p[[A + 1]] + Z;
    AB = p[[A + 2]] + Z;
    B = p[[X + 2]] + Y;
    BA = p[[B + 1]] + Z;
    BB = p[[B + 2]] + Z;

    lerp[w,
      lerp[v,
        lerp[u, grad[p[[AA + 1]], xf, yf, zf],
             grad[p[[BA + 1]], xf - 1, yf, zf]],
        lerp[u, grad[p[[AB + 1]], xf, yf - 1, zf],
             grad[p[[BB + 1]], xf - 1, yf - 1, zf]]
      ],
      lerp[v,
        lerp[u, grad[p[[AA + 2]], xf, yf, zf - 1],
             grad[p[[BA + 2]], xf - 1, yf, zf - 1]],
        lerp[u, grad[p[[AB + 2]], xf, yf - 1, zf - 1],
             grad[p[[BB + 2]], xf - 1, yf - 1, zf - 1]]
      ]
    ]
  ]

(* Example usage *)
perlinNoise[3.14, 42, 7] // N[#, 17] & //Print