// A direct port of Ken Perlin's Java reference to HLSL
// http://mrl.nyu.edu/~perlin/noise/

// permutation table: 0-255 randomly arranged and then duplicated
static const int p[] = { 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,
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
};

float2 fade(float2 t) { return t * t * t * (t * (t * 6 - 15) + 10); }
float3 fade(float3 t) { return t * t * t * (t * (t * 6 - 15) + 10); }

float grad(int hash, float x, float y) 
{
	int h = hash & 15;
	float u = h<8 ? x : y;
	float v = h<4 ? y : h==12||h==14 ? x : 0;
	return ((h&1) == 0 ? u : -u) + ((h&2) == 0 ? v : -v);
}

float grad(int hash, float x, float y, float z) 
{
	int h = hash & 15; 
	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);
}

float noise(float2 pos)
{
	int2 I = int2(floor(pos)) & 255;
	
	pos = frac(pos);
	
	float2 fades = fade(pos);
	
	int A  = p[I.x] + I.y;
	int AA = p[A];
	int AB = p[A + 1];
	int	B  = p[I.x + 1] + I.y;
	int BA = p[B];
	int BB = p[B + 1]; 

	return lerp(lerp(grad(p[AA], pos.x,     pos.y), 
	                 grad(p[BA], pos.x - 1, pos.y),     fades.x), 
				lerp(grad(p[AB], pos.x,     pos.y - 1), 
				     grad(p[BB], pos.x - 1, pos.y - 1), fades.x), fades.y);
}

float noise(float3 pos) 
{
	int3 I = int3(floor(pos)) & 255;
	  
	pos = frac(pos);
	
	float3 fades = fade(pos);
		  
	int A  = p[I.x  ] + I.y;
	int AA = p[A    ] + I.z;
	int AB = p[A + 1] + I.z; 
	int B  = p[I.x+1] + I.y;
	int BA = p[B    ] + I.z;
	int BB = p[B + 1] + I.z;

	return lerp(lerp(lerp(grad(p[AA  ], pos.x  , pos.y  , pos.z   ),
						  grad(p[BA  ], pos.x-1, pos.y  , pos.z   ), fades.x),
				     lerp(grad(p[AB  ], pos.x  , pos.y-1, pos.z   ), 
						  grad(p[BB  ], pos.x-1, pos.y-1, pos.z   ), fades.x), fades.y),
				lerp(lerp(grad(p[AA+1], pos.x  , pos.y  , pos.z-1 ), 
				   		  grad(p[BA+1], pos.x-1, pos.y  , pos.z-1 ), fades.x),
					 lerp(grad(p[AB+1], pos.x  , pos.y-1, pos.z-1 ),
						  grad(p[BB+1], pos.x-1, pos.y-1, pos.z-1 ), fades.x), fades.y), fades.z);
}

float fBm(float2 pos, int octaves)
{
	float lacunarity = 2.0;
	float gain = 0.5;

	float freq = 1.0;
	float amp = 0.5;
	float sum = 0;
	for (int i = 0; i < octaves; i++)
	{
		sum += noise(pos * freq) * amp;
		freq *= lacunarity;
		amp *= gain;
	}
	return sum;
}

float fBm(float3 pos, int octaves)
{
	float lacunarity = 2.0;
	float gain = 0.5;

	float freq = 1.0;
	float amp = 0.5;
	float sum = 0;
	for (int i = 0; i < octaves; i++)
	{
		sum += noise(pos * freq) * amp;
		freq *= lacunarity;
		amp *= gain;
	}
	return sum;
}