// stb_perlin.h - v0.4 - perlin noise
// public domain single-file C implementation by Sean Barrett
//
// LICENSE
//
//   See end of file.
//
//
// to create the implementation,
//     #define STB_PERLIN_IMPLEMENTATION
// in *one* C/CPP file that includes this file.
//
//
// Documentation:
//
// float  stb_perlin_noise3( float x,
//                           float y,
//                           float z,
//                           int   x_wrap=0,
//                           int   y_wrap=0,
//                           int   z_wrap=0)
//
// This function computes a random value at the coordinate (x,y,z).
// Adjacent random values are continuous but the noise fluctuates
// its randomness with period 1, i.e. takes on wholly unrelated values
// at integer points. Specifically, this implements Ken Perlin's
// revised noise function from 2002.
//
// The "wrap" parameters can be used to create wraparound noise that
// wraps at powers of two. The numbers MUST be powers of two. Specify
// 0 to mean "don't care". (The noise always wraps every 256 due
// details of the implementation, even if you ask for larger or no
// wrapping.)
//
// float  stb_perlin_noise3_seed( float x,
//                                float y,
//                                float z,
//                                int   x_wrap=0,
//                                int   y_wrap=0,
//                                int   z_wrap=0,
//                                int   seed)
//
// As above, but 'seed' selects from multiple different variations of the
// noise function. The current implementation only uses the bottom 8 bits
// of 'seed', but possibly in the future more bits will be used.
//
//
// Fractal Noise:
//
// Three common fractal noise functions are included, which produce 
// a wide variety of nice effects depending on the parameters 
// provided. Note that each function will call stb_perlin_noise3 
// 'octaves' times, so this parameter will affect runtime.
//
// float stb_perlin_ridge_noise3(float x, float y, float z,
//                               float lacunarity, float gain, float offset, int octaves)
//
// float stb_perlin_fbm_noise3(float x, float y, float z,
//                             float lacunarity, float gain, int octaves)
//
// float stb_perlin_turbulence_noise3(float x, float y, float z,
//                                    float lacunarity, float gain, int octaves)
//
// Typical values to start playing with:
//     octaves    =   6     -- number of "octaves" of noise3() to sum
//     lacunarity = ~ 2.0   -- spacing between successive octaves (use exactly 2.0 for wrapping output)
//     gain       =   0.5   -- relative weighting applied to each successive octave
//     offset     =   1.0?  -- used to invert the ridges, may need to be larger, not sure
//    
//
// Contributors:
//    Jack Mott - additional noise functions
//    Jordan Peck - seeded noise
//


#ifdef __cplusplus
extern "C" {
#endif
extern float stb_perlin_noise3(float x, float y, float z, int x_wrap, int y_wrap, int z_wrap);
extern float stb_perlin_noise3_seed(float x, float y, float z, int x_wrap, int y_wrap, int z_wrap, int seed);
extern float stb_perlin_ridge_noise3(float x, float y, float z, float lacunarity, float gain, float offset, int octaves);
extern float stb_perlin_fbm_noise3(float x, float y, float z, float lacunarity, float gain, int octaves);
extern float stb_perlin_turbulence_noise3(float x, float y, float z, float lacunarity, float gain, int octaves);
#ifdef __cplusplus
}
#endif

#ifdef STB_PERLIN_IMPLEMENTATION

#include <math.h> // fabs()

// not same permutation table as Perlin's reference to avoid copyright issues;
// Perlin's table can be found at http://mrl.nyu.edu/~perlin/noise/
static unsigned char stb__perlin_randtab[512] =
{
   23, 125, 161, 52, 103, 117, 70, 37, 247, 101, 203, 169, 124, 126, 44, 123, 
   152, 238, 145, 45, 171, 114, 253, 10, 192, 136, 4, 157, 249, 30, 35, 72, 
   175, 63, 77, 90, 181, 16, 96, 111, 133, 104, 75, 162, 93, 56, 66, 240, 
   8, 50, 84, 229, 49, 210, 173, 239, 141, 1, 87, 18, 2, 198, 143, 57, 
   225, 160, 58, 217, 168, 206, 245, 204, 199, 6, 73, 60, 20, 230, 211, 233, 
   94, 200, 88, 9, 74, 155, 33, 15, 219, 130, 226, 202, 83, 236, 42, 172, 
   165, 218, 55, 222, 46, 107, 98, 154, 109, 67, 196, 178, 127, 158, 13, 243, 
   65, 79, 166, 248, 25, 224, 115, 80, 68, 51, 184, 128, 232, 208, 151, 122, 
   26, 212, 105, 43, 179, 213, 235, 148, 146, 89, 14, 195, 28, 78, 112, 76, 
   250, 47, 24, 251, 140, 108, 186, 190, 228, 170, 183, 139, 39, 188, 244, 246, 
   132, 48, 119, 144, 180, 138, 134, 193, 82, 182, 120, 121, 86, 220, 209, 3, 
   91, 241, 149, 85, 205, 150, 113, 216, 31, 100, 41, 164, 177, 214, 153, 231, 
   38, 71, 185, 174, 97, 201, 29, 95, 7, 92, 54, 254, 191, 118, 34, 221, 
   131, 11, 163, 99, 234, 81, 227, 147, 156, 176, 17, 142, 69, 12, 110, 62, 
   27, 255, 0, 194, 59, 116, 242, 252, 19, 21, 187, 53, 207, 129, 64, 135, 
   61, 40, 167, 237, 102, 223, 106, 159, 197, 189, 215, 137, 36, 32, 22, 5,  

   // and a second copy so we don't need an extra mask or static initializer
   23, 125, 161, 52, 103, 117, 70, 37, 247, 101, 203, 169, 124, 126, 44, 123, 
   152, 238, 145, 45, 171, 114, 253, 10, 192, 136, 4, 157, 249, 30, 35, 72, 
   175, 63, 77, 90, 181, 16, 96, 111, 133, 104, 75, 162, 93, 56, 66, 240, 
   8, 50, 84, 229, 49, 210, 173, 239, 141, 1, 87, 18, 2, 198, 143, 57, 
   225, 160, 58, 217, 168, 206, 245, 204, 199, 6, 73, 60, 20, 230, 211, 233, 
   94, 200, 88, 9, 74, 155, 33, 15, 219, 130, 226, 202, 83, 236, 42, 172, 
   165, 218, 55, 222, 46, 107, 98, 154, 109, 67, 196, 178, 127, 158, 13, 243, 
   65, 79, 166, 248, 25, 224, 115, 80, 68, 51, 184, 128, 232, 208, 151, 122, 
   26, 212, 105, 43, 179, 213, 235, 148, 146, 89, 14, 195, 28, 78, 112, 76, 
   250, 47, 24, 251, 140, 108, 186, 190, 228, 170, 183, 139, 39, 188, 244, 246, 
   132, 48, 119, 144, 180, 138, 134, 193, 82, 182, 120, 121, 86, 220, 209, 3, 
   91, 241, 149, 85, 205, 150, 113, 216, 31, 100, 41, 164, 177, 214, 153, 231, 
   38, 71, 185, 174, 97, 201, 29, 95, 7, 92, 54, 254, 191, 118, 34, 221, 
   131, 11, 163, 99, 234, 81, 227, 147, 156, 176, 17, 142, 69, 12, 110, 62, 
   27, 255, 0, 194, 59, 116, 242, 252, 19, 21, 187, 53, 207, 129, 64, 135, 
   61, 40, 167, 237, 102, 223, 106, 159, 197, 189, 215, 137, 36, 32, 22, 5,  
}; 


// perlin's gradient has 12 cases so some get used 1/16th of the time
// and some 2/16ths. We reduce bias by changing those fractions
// to 5/64ths and 6/64ths

// this array is designed to match the previous implementation
// of gradient hash: indices[stb__perlin_randtab[i]&63]
static unsigned char stb__perlin_randtab_grad_idx[512] =
{
    7, 9, 5, 0, 11, 1, 6, 9, 3, 9, 11, 1, 8, 10, 4, 7,
    8, 6, 1, 5, 3, 10, 9, 10, 0, 8, 4, 1, 5, 2, 7, 8,
    7, 11, 9, 10, 1, 0, 4, 7, 5, 0, 11, 6, 1, 4, 2, 8,
    8, 10, 4, 9, 9, 2, 5, 7, 9, 1, 7, 2, 2, 6, 11, 5,
    5, 4, 6, 9, 0, 1, 1, 0, 7, 6, 9, 8, 4, 10, 3, 1,
    2, 8, 8, 9, 10, 11, 5, 11, 11, 2, 6, 10, 3, 4, 2, 4,
    9, 10, 3, 2, 6, 3, 6, 10, 5, 3, 4, 10, 11, 2, 9, 11,
    1, 11, 10, 4, 9, 4, 11, 0, 4, 11, 4, 0, 0, 0, 7, 6,
    10, 4, 1, 3, 11, 5, 3, 4, 2, 9, 1, 3, 0, 1, 8, 0,
    6, 7, 8, 7, 0, 4, 6, 10, 8, 2, 3, 11, 11, 8, 0, 2,
    4, 8, 3, 0, 0, 10, 6, 1, 2, 2, 4, 5, 6, 0, 1, 3,
    11, 9, 5, 5, 9, 6, 9, 8, 3, 8, 1, 8, 9, 6, 9, 11,
    10, 7, 5, 6, 5, 9, 1, 3, 7, 0, 2, 10, 11, 2, 6, 1,
    3, 11, 7, 7, 2, 1, 7, 3, 0, 8, 1, 1, 5, 0, 6, 10,
    11, 11, 0, 2, 7, 0, 10, 8, 3, 5, 7, 1, 11, 1, 0, 7,
    9, 0, 11, 5, 10, 3, 2, 3, 5, 9, 7, 9, 8, 4, 6, 5,

    // and a second copy so we don't need an extra mask or static initializer
    7, 9, 5, 0, 11, 1, 6, 9, 3, 9, 11, 1, 8, 10, 4, 7,
    8, 6, 1, 5, 3, 10, 9, 10, 0, 8, 4, 1, 5, 2, 7, 8,
    7, 11, 9, 10, 1, 0, 4, 7, 5, 0, 11, 6, 1, 4, 2, 8,
    8, 10, 4, 9, 9, 2, 5, 7, 9, 1, 7, 2, 2, 6, 11, 5,
    5, 4, 6, 9, 0, 1, 1, 0, 7, 6, 9, 8, 4, 10, 3, 1,
    2, 8, 8, 9, 10, 11, 5, 11, 11, 2, 6, 10, 3, 4, 2, 4,
    9, 10, 3, 2, 6, 3, 6, 10, 5, 3, 4, 10, 11, 2, 9, 11,
    1, 11, 10, 4, 9, 4, 11, 0, 4, 11, 4, 0, 0, 0, 7, 6,
    10, 4, 1, 3, 11, 5, 3, 4, 2, 9, 1, 3, 0, 1, 8, 0,
    6, 7, 8, 7, 0, 4, 6, 10, 8, 2, 3, 11, 11, 8, 0, 2,
    4, 8, 3, 0, 0, 10, 6, 1, 2, 2, 4, 5, 6, 0, 1, 3,
    11, 9, 5, 5, 9, 6, 9, 8, 3, 8, 1, 8, 9, 6, 9, 11,
    10, 7, 5, 6, 5, 9, 1, 3, 7, 0, 2, 10, 11, 2, 6, 1,
    3, 11, 7, 7, 2, 1, 7, 3, 0, 8, 1, 1, 5, 0, 6, 10,
    11, 11, 0, 2, 7, 0, 10, 8, 3, 5, 7, 1, 11, 1, 0, 7,
    9, 0, 11, 5, 10, 3, 2, 3, 5, 9, 7, 9, 8, 4, 6, 5,
};

static float stb__perlin_lerp(float a, float b, float t)
{
   return a + (b-a) * t;
}

static int stb__perlin_fastfloor(float a)
{
    int ai = (int) a;
    return (a < ai) ? ai-1 : ai;
}

// different grad function from Perlin's, but easy to modify to match reference
static float stb__perlin_grad(int grad_idx, float x, float y, float z)
{
   static float basis[12][4] =
   {
      {  1, 1, 0 },
      { -1, 1, 0 },
      {  1,-1, 0 },
      { -1,-1, 0 },
      {  1, 0, 1 },
      { -1, 0, 1 },
      {  1, 0,-1 },
      { -1, 0,-1 },
      {  0, 1, 1 },
      {  0,-1, 1 },
      {  0, 1,-1 },
      {  0,-1,-1 },
   };

   float *grad = basis[grad_idx];
   return grad[0]*x + grad[1]*y + grad[2]*z;
}

float stb_perlin_noise3_internal(float x, float y, float z, int x_wrap, int y_wrap, int z_wrap, unsigned char seed)
{
   float u,v,w;
   float n000,n001,n010,n011,n100,n101,n110,n111;
   float n00,n01,n10,n11;
   float n0,n1;

   unsigned int x_mask = (x_wrap-1) & 255;
   unsigned int y_mask = (y_wrap-1) & 255;
   unsigned int z_mask = (z_wrap-1) & 255;
   int px = stb__perlin_fastfloor(x);
   int py = stb__perlin_fastfloor(y);
   int pz = stb__perlin_fastfloor(z);
   int x0 = px & x_mask, x1 = (px+1) & x_mask;
   int y0 = py & y_mask, y1 = (py+1) & y_mask;
   int z0 = pz & z_mask, z1 = (pz+1) & z_mask;
   int r0,r1, r00,r01,r10,r11;

   #define stb__perlin_ease(a)   (((a*6-15)*a + 10) * a * a * a)

   x -= px; u = stb__perlin_ease(x);
   y -= py; v = stb__perlin_ease(y);
   z -= pz; w = stb__perlin_ease(z);

   r0 = stb__perlin_randtab[x0+seed];
   r1 = stb__perlin_randtab[x1+seed];

   r00 = stb__perlin_randtab[r0+y0];
   r01 = stb__perlin_randtab[r0+y1];
   r10 = stb__perlin_randtab[r1+y0];
   r11 = stb__perlin_randtab[r1+y1];

   n000 = stb__perlin_grad(stb__perlin_randtab_grad_idx[r00+z0], x  , y  , z   );
   n001 = stb__perlin_grad(stb__perlin_randtab_grad_idx[r00+z1], x  , y  , z-1 );
   n010 = stb__perlin_grad(stb__perlin_randtab_grad_idx[r01+z0], x  , y-1, z   );
   n011 = stb__perlin_grad(stb__perlin_randtab_grad_idx[r01+z1], x  , y-1, z-1 );
   n100 = stb__perlin_grad(stb__perlin_randtab_grad_idx[r10+z0], x-1, y  , z   );
   n101 = stb__perlin_grad(stb__perlin_randtab_grad_idx[r10+z1], x-1, y  , z-1 );
   n110 = stb__perlin_grad(stb__perlin_randtab_grad_idx[r11+z0], x-1, y-1, z   );
   n111 = stb__perlin_grad(stb__perlin_randtab_grad_idx[r11+z1], x-1, y-1, z-1 );

   n00 = stb__perlin_lerp(n000,n001,w);
   n01 = stb__perlin_lerp(n010,n011,w);
   n10 = stb__perlin_lerp(n100,n101,w);
   n11 = stb__perlin_lerp(n110,n111,w);

   n0 = stb__perlin_lerp(n00,n01,v);
   n1 = stb__perlin_lerp(n10,n11,v);

   return stb__perlin_lerp(n0,n1,u);
}

float stb_perlin_noise3(float x, float y, float z, int x_wrap, int y_wrap, int z_wrap)
{
    return stb_perlin_noise3_internal(x,y,z,x_wrap,y_wrap,z_wrap,0);
}

float stb_perlin_noise3_seed(float x, float y, float z, int x_wrap, int y_wrap, int z_wrap, int seed)
{
    return stb_perlin_noise3_internal(x,y,z,x_wrap,y_wrap,z_wrap, (unsigned char) seed);
}

float stb_perlin_ridge_noise3(float x, float y, float z, float lacunarity, float gain, float offset, int octaves)
{
   int i;
   float frequency = 1.0f;
   float prev = 1.0f;
   float amplitude = 0.5f;
   float sum = 0.0f;

   for (i = 0; i < octaves; i++) {
      float r = stb_perlin_noise3_internal(x*frequency,y*frequency,z*frequency,0,0,0,(unsigned char)i);
      r = offset - (float) fabs(r);
      r = r*r;
      sum += r*amplitude*prev;
      prev = r;
      frequency *= lacunarity;
      amplitude *= gain;
   }
   return sum;
}

float stb_perlin_fbm_noise3(float x, float y, float z, float lacunarity, float gain, int octaves)
{
   int i;
   float frequency = 1.0f;
   float amplitude = 1.0f;
   float sum = 0.0f;
   
   for (i = 0; i < octaves; i++) {
      sum += stb_perlin_noise3_internal(x*frequency,y*frequency,z*frequency,0,0,0,(unsigned char)i)*amplitude;
      frequency *= lacunarity;
      amplitude *= gain;
   }
   return sum;
}

float stb_perlin_turbulence_noise3(float x, float y, float z, float lacunarity, float gain, int octaves)
{
   int i;
   float frequency = 1.0f;
   float amplitude = 1.0f;
   float sum = 0.0f;
   
   for (i = 0; i < octaves; i++) {
      float r = stb_perlin_noise3_internal(x*frequency,y*frequency,z*frequency,0,0,0,(unsigned char)i)*amplitude;
      sum += (float) fabs(r);
      frequency *= lacunarity;
      amplitude *= gain;
   }
   return sum;
}

#endif  // STB_PERLIN_IMPLEMENTATION

/*
------------------------------------------------------------------------------
This software is available under 2 licenses -- choose whichever you prefer.
------------------------------------------------------------------------------
ALTERNATIVE A - MIT License
Copyright (c) 2017 Sean Barrett
Permission is hereby granted, free of charge, to any person obtaining a copy of 
this software and associated documentation files (the "Software"), to deal in 
the Software without restriction, including without limitation the rights to 
use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies 
of the Software, and to permit persons to whom the Software is furnished to do 
so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all 
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 
SOFTWARE.
------------------------------------------------------------------------------
ALTERNATIVE B - Public Domain (www.unlicense.org)
This is free and unencumbered software released into the public domain.
Anyone is free to copy, modify, publish, use, compile, sell, or distribute this 
software, either in source code form or as a compiled binary, for any purpose, 
commercial or non-commercial, and by any means.
In jurisdictions that recognize copyright laws, the author or authors of this 
software dedicate any and all copyright interest in the software to the public 
domain. We make this dedication for the benefit of the public at large and to 
the detriment of our heirs and successors. We intend this dedication to be an 
overt act of relinquishment in perpetuity of all present and future rights to 
this software under copyright law.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 
AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN 
ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION 
WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
------------------------------------------------------------------------------
*/