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// check out implementation from GPU Gems 1 and 2

float fade( in float x )
{
  return( x * x * x * ( x * ( x * 6.0 - 15.0 ) + 10.0 ));
  //return( x * x * ( 3.0 - 2.0 * x ) );
}

vec2 fade( in vec2 x )
{
  return( x * x * x * ( x * ( x * 6.0 - 15.0 ) + 10.0 ));
  //return( x * x * ( 3.0 - 2.0 * x ) );
}

vec3 fade( in vec3 x )
{
  return( x * x * x * ( x * ( x * 6.0 - 15.0 ) + 10.0 ));
  //return( x * x * ( 3.0 - 2.0 * x ) );
}

vec4 fade( in vec4 x )
{
  return( x * x * x * ( x * ( x * 6.0 - 15.0 ) + 10.0 ));
  //return( x * x * ( 3.0 - 2.0 * x ) );
}

float influence( in int hash, in float x )
{
  return( x * texelFetch( randomGradient1D, ivec2(hash, 0), 0 ).x );
}

float influence( in int hash, in float x, in float y )
{
  return( dot( vec2( x, y ), texelFetch( randomGradient2D, ivec2(hash, 0), 0 ).xy ) );
}

float influence( in int hash, in float x, in float y, in float z )
{
  return( dot( vec3( x, y, z ), texelFetch( randomGradient3D, ivec2(hash, 0), 0 ).xyz ) );
}

float influence( in int hash, in float x, in float y, in float z, in float w )
{
  return( dot( vec4( x, y, z, w ), texelFetch( randomGradient4D, ivec2(hash, 0), 0 ) ) );
}

float perlinNoise( in float pos )
{
  float floorPos = floor( pos );
  int intPos = int( floorPos );
  float fracPos = pos - floorPos;

  return( mix( influence( random255X( intPos ), fracPos ), influence( random255X( intPos+1 ), fracPos - 1.0 ), fade( fracPos ) ) );
}

float perlinNoise( in vec2 pos )
{
  vec2 floorPos = floor( pos );
  vec2 fracPos = pos - floorPos;
  vec2 fadedPos = fade( fracPos );

  int ax = random255X( int(floorPos.x)     );
  int bx = random255X( int(floorPos.x) + 1 );
  int ay = random255Y( int(floorPos.y)     );
  int by = random255Y( int(floorPos.y) + 1 );

  return( mix( mix( influence( ax^ay, fracPos.x,        fracPos.y        )
                  , influence( bx^ay, fracPos.x - 1.0, fracPos.y        ), fadedPos.x )
             , mix( influence( ax^by, fracPos.x,        fracPos.y - 1.0 )
                  , influence( bx^by, fracPos.x - 1.0, fracPos.y - 1.0 ), fadedPos.x ), fadedPos.y ) );
}

float perlinNoise( in vec3 pos )
{
  vec3 floorPos = floor( pos );
  vec3 fracPos = pos - floorPos;
  vec3 fadedPos = fade( fracPos );

  int ax = random255X( int(floorPos.x)     );
  int bx = random255X( int(floorPos.x) + 1 );
  int ay = random255Y( int(floorPos.y)     );
  int by = random255Y( int(floorPos.y) + 1 );
  int az = random255Z( int(floorPos.z)     );
  int bz = random255Z( int(floorPos.z) + 1 );

  int axay = ax ^ ay;
  int bxay = bx ^ ay;
  int axby = ax ^ by;
  int bxby = bx ^ by;

  return( mix( mix( mix( influence( axay^az, fracPos.x,        fracPos.y,        fracPos.z        )
                       , influence( bxay^az, fracPos.x - 1.0, fracPos.y,        fracPos.z        ), fadedPos.x )
                  , mix( influence( axby^az, fracPos.x,        fracPos.y - 1.0, fracPos.z        )
                       , influence( bxby^az, fracPos.x - 1.0, fracPos.y - 1.0, fracPos.z        ), fadedPos.x ), fadedPos.y )
             , mix( mix( influence( axay^bz, fracPos.x,        fracPos.y       , fracPos.z - 1.0 )
                       , influence( bxay^bz, fracPos.x - 1.0, fracPos.y       , fracPos.z - 1.0 ), fadedPos.x )
                  , mix( influence( axby^bz, fracPos.x,        fracPos.y - 1.0, fracPos.z - 1.0 )
                       , influence( bxby^bz, fracPos.x - 1.0, fracPos.y - 1.0, fracPos.z - 1.0 ), fadedPos.x ), fadedPos.y ), fadedPos.z ) );
}

float perlinNoise( in vec4 pos )
{
  vec4 floorPos = floor( pos );
  vec4 fracPos = pos - floorPos;
  vec4 fadedPos = fade( fracPos );

  int ax = random255X( int(floorPos.x)     );
  int bx = random255X( int(floorPos.x) + 1 );
  int ay = random255Y( int(floorPos.y)     );
  int by = random255Y( int(floorPos.y) + 1 );
  int az = random255Z( int(floorPos.z)     );
  int bz = random255Z( int(floorPos.z) + 1 );
  int aw = random255W( int(floorPos.w)     );

  int axay = ax ^ ay;
  int bxay = bx ^ ay;
  int axby = ax ^ by;
  int bxby = bx ^ by;

  float result[2];
  for ( int i=0 ; i<2 ; i++ )
  {
    int azaw = az ^ aw;
    int bzaw = bz ^ aw;

    result[i] = mix( mix( mix( influence( axay^azaw, fracPos.x,        fracPos.y,        fracPos.z,        fracPos.w )
                             , influence( bxay^azaw, fracPos.x - 1.0, fracPos.y,        fracPos.z,        fracPos.w ), fadedPos.x )
                        , mix( influence( axby^azaw, fracPos.x,        fracPos.y - 1.0, fracPos.z,        fracPos.w )
                             , influence( bxby^azaw, fracPos.x - 1.0, fracPos.y - 1.0, fracPos.z,        fracPos.w ), fadedPos.x ), fadedPos.y )
                   , mix( mix( influence( axay^bzaw, fracPos.x,        fracPos.y,        fracPos.z - 1.0, fracPos.w )
                             , influence( bxay^bzaw, fracPos.x - 1.0, fracPos.y,        fracPos.z - 1.0, fracPos.w ), fadedPos.x )
                        , mix( influence( axby^bzaw, fracPos.x,        fracPos.y - 1.0, fracPos.z - 1.0, fracPos.w )
                             , influence( bxby^bzaw, fracPos.x - 1.0, fracPos.y - 1.0, fracPos.z - 1.0, fracPos.w ), fadedPos.x ), fadedPos.y ), fadedPos.z );
    aw = random255W( int(floorPos.w) + 1 );
    fracPos.w -= 1.0;
  }
  return( mix( result[0], result[1], fadedPos.w ) );
}

float summedPerlinNoise( in vec3 pos, in int terms, in bool absNoise )
{
  float sum = 0.0;
  float weight = 1.0;
  vec3 p = pos;
  while ( terms-- != 0 )
  {
    float noise = perlinNoise( p );
    sum += weight * ( absNoise ? abs(noise) : noise );
    p += p;
    weight *= 0.5;
  }
  return( sum );
}

float summedPerlinNoise( in vec4 pos, in int terms, in bool absNoise )
{
  float sum = 0.0;
  float weight = 1.0;
  vec4 p = pos;
  while ( terms-- != 0 )
  {
    float noise = perlinNoise( p );
    sum += weight * ( absNoise ? abs(noise) : noise );
    p += p;
    weight *= 0.5;
  }
  return( sum );
}

float perlinNoise( in vec3 pos, in float time, in int terms, in vec3 turbulenceWeight, in bool absoluteNoise, in bool applyMarble
                 , in bool applyDent, in float noiseBands, in float noiseThresholdHigh, in float noiseThresholdLow )
{
  float noise = ( time == 0.0 ) ? summedPerlinNoise( pos, terms, absoluteNoise ) : summedPerlinNoise( vec4( pos, time ), terms, absoluteNoise );
  if ( turbulenceWeight != vec3( 0.0, 0.0, 0.0 ) )
  {
    noise = sin( dot( pos, turbulenceWeight ) + noise );
  }
  if ( ! absoluteNoise )
  {
    noise = 0.5 * noise + 0.5;    // scale [-1,1] to [0,1]
  }
  if ( applyMarble )
  {
    noise = cos( pos.x + 5.0 * noise );    // classic Perlin marble function, with magic 5.0
  }
  if ( applyDent )
  {
    noise = cube( noise );
  }
  if ( noiseBands != 1.0 )
  {
    // Create banding/stripes by using the fraction component only
    noise *= noiseBands;
    noise -= floor( noise );
    noise += pow( 1.0 - noise, 20.0 );
  }
  if ( noiseThresholdLow < noiseThresholdHigh )
  {
    // clamp the noise
    noise = clamp( ( noise - noiseThresholdLow ) / ( noiseThresholdHigh - noiseThresholdLow ), 0.0, 1.0 );
  }
  return( noise );
}