2010-08-19

Calculate PerlinNoise faster with an optimization to grad()

A simple optimization to the gradient function makes the noise function twice as fast.

PerlinNoise.grad()
inline float grad(int hash, float x, float y, float z)
   {  
 //float u = (h < 8) ? x : y;
 //float v = (h < 4) ? y : ((h == 12 || h == 14) ? x : z);
 //return ((h & 1) == 0 ? u : -u) + ((h & 2) == 0 ? v : -v);

 switch(hash & 0xF)
 {
  case 0x0: return  x + y;
  case 0x1: return -x + y;
  case 0x2: return  x - y;
  case 0x3: return -x - y;
  case 0x4: return  x + z;
  case 0x5: return -x + z;
  case 0x6: return  x - z;
  case 0x7: return -x - z;
  case 0x8: return  y + z;
  case 0x9: return -y + z;
  case 0xA: return  y - z;
  case 0xB: return -y - z;
  case 0xC: return  y + x;
  case 0xD: return -y + z;
  case 0xE: return  y - x;
  case 0xF: return -y - z;
  default: return 0; // never happens
 }
   }

PerlinNoise.noise() (click code to expand)
int   perm[512];

   void initPerlinNoise()
   {
      int i, 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 };

      for (i = 0; i < 256; i++)
         perm[256 + i] = perm[i] = permutation[i];
   }


   inline float fade(float t)
   {
      return t * t * t * (t * (t * 6.0f - 15.0f) + 10.0f);
   }

   inline float lerp(float t, float a, float b)
   {
      return a + t * (b - a);
   }

   inline float grad(int hash, float x, float y, float z)
   {  
 //float u = (h < 8) ? x : y;
 //float v = (h < 4) ? y : ((h == 12 || h == 14) ? x : z);
 //return ((h & 1) == 0 ? u : -u) + ((h & 2) == 0 ? v : -v);

 switch(hash & 0xF)
 {
  case 0x0: return  x + y;
  case 0x1: return -x + y;
  case 0x2: return  x - y;
  case 0x3: return -x - y;
  case 0x4: return  x + x;
  case 0x5: return -x + x;
  case 0x6: return  x - x;
  case 0x7: return -x - x;
  case 0x8: return  y + x;
  case 0x9: return -y + x;
  case 0xA: return  y - x;
  case 0xB: return -y - x;
  case 0xC: return  y + z;
  case 0xD: return -y + x;
  case 0xE: return  y - x;
  case 0xF: return -y - z;
  default: return 0; // never happens
 }
   }

   static inline float __fastcall noise(float x, float y, float z)
   {
      jint ix,iy,iz,gx,gy,gz;
      jint a0,b0,aa,ab,ba,bb;

      float aa0,ab0,ba0,bb0;
      float aa1,ab1,ba1,bb1;
      float a1,a2,a3,a4,a5,a6,a7,a8;
      float u,v,w,a8_5,a4_1;

      ix = (jint)x; x-=ix;
      iy = (jint)y; y-=iy;
      iz = (jint)z; z-=iz;

      gx = ix & 0xFF;
      gy = iy & 0xFF;
      gz = iz & 0xFF;
      
      a0 = gy+perm[gx];
      b0 = gy+perm[gx + 1];
      aa = gz+perm[a0];
      ab = gz+perm[a0 + 1];
      ba = gz+perm[b0];
      bb = gz+perm[b0 + 1];

      aa0 = perm[aa]; aa1 = perm[aa + 1];
      ab0 = perm[ab]; ab1 = perm[ab + 1];
      ba0 = perm[ba]; ba1 = perm[ba + 1];
      bb0 = perm[bb]; bb1 = perm[bb + 1];

      a1 = grad(bb1, x-1, y-1, z-1);
      a2 = grad(ab1, x  , y-1, z-1);
      a3 = grad(ba1, x-1, y  , z-1);
      a4 = grad(aa1, x  , y  , z-1);
      a5 = grad(bb0, x-1, y-1, z  );
      a6 = grad(ab0, x  , y-1, z  );
      a7 = grad(ba0, x-1, y  , z  );
      a8 = grad(aa0, x  , y  , z  );

      u = fade(x);
      v = fade(y);
      w = fade(z);

      a8_5 = lerp(v, lerp(u, a8, a7), lerp(u, a6, a5));
      a4_1 = lerp(v, lerp(u, a4, a3), lerp(u, a2, a1));
      return lerp(w, a8_5, a4_1);
   }