// noisegen.cpp
//
// Copyright (C) 2003, 2004 Jason Bevins
//
// This library is free software; you can redistribute it and/or modify it
// under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation; either version 2.1 of the License, or (at
// your option) any later version.
//
// This library is distributed in the hope that it will be useful, but WITHOUT
// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
// FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
// License (COPYING.txt) for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with this library; if not, write to the Free Software Foundation,
// Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
//
// The developer's email is jlbezigvins@gmzigail.com (for great email, take
// off every 'zig'.)
//
module noise.noisegen;

import noise.interp;
import noise.vectortable;
import noise.basictypes;
import std.math;

// Specifies the version of the coherent-noise functions to use.
// - Set to 2 to use the current version.
// - Set to 1 to use the flawed version from the original version of libnoise.
// If your application requires coherent-noise values that were generated by
// an earlier version of libnoise, change this constant to the appropriate
// value and recompile libnoise.
const int NOISE_VERSION = 2;

// These constants control certain parameters that all coherent-noise
// functions require.
static if (NOISE_VERSION == 1) { 
  // Constants used by the original version of libnoise.
  // Because X_NOISE_GEN is not relatively prime to the other values, and
  // Z_NOISE_GEN is close to 256 (the number of random gradient vectors),
  // patterns show up in high-frequency coherent noise.
  const int X_NOISE_GEN = 1;
  const int Y_NOISE_GEN = 31337;
  const int Z_NOISE_GEN = 263;
  const int SEED_NOISE_GEN = 1013;
  const int SHIFT_NOISE_GEN = 13;
} else {
  // Constants used by the current version of libnoise.
  const int X_NOISE_GEN = 1619;
  const int Y_NOISE_GEN = 31337;
  const int Z_NOISE_GEN = 6971;
  const int SEED_NOISE_GEN = 1013;
  const int SHIFT_NOISE_GEN = 8;
}

/// Enumerates the noise quality.
enum NoiseQuality
{

  /// Generates coherent noise quickly.  When a coherent-noise function with
  /// this quality setting is used to generate a bump-map image, there are
  /// noticeable "creasing" artifacts in the resulting image.  This is
  /// because the derivative of that function is discontinuous at integer
  /// boundaries.
  QUALITY_FAST = 0,

  /// Generates standard-quality coherent noise.  When a coherent-noise
  /// function with this quality setting is used to generate a bump-map
  /// image, there are some minor "creasing" artifacts in the resulting
  /// image.  This is because the second derivative of that function is
  /// discontinuous at integer boundaries.
  QUALITY_STD = 1,

  /// Generates the best-quality coherent noise.  When a coherent-noise
  /// function with this quality setting is used to generate a bump-map
  /// image, there are no "creasing" artifacts in the resulting image.  This
  /// is because the first and second derivatives of that function are
  /// continuous at integer boundaries.
  QUALITY_BEST = 2

};


/// Generates a gradient-coherent-noise value from the coordinates of a
/// three-dimensional input value.
///
/// @param x The @a x coordinate of the input value.
/// @param y The @a y coordinate of the input value.
/// @param z The @a z coordinate of the input value.
/// @param seed The random number seed.
/// @param noiseQuality The quality of the coherent-noise.
///
/// @returns The generated gradient-coherent-noise value.
///
/// The return value ranges from -1.0 to +1.0.
///
/// For an explanation of the difference between <i>gradient</i> noise and
/// <i>value</i> noise, see the comments for the GradientNoise3D() function.
double GradientCoherentNoise3D (double x, double y, double z, int seed = 0,
  NoiseQuality noiseQuality = NoiseQuality.QUALITY_STD)
{
  // Create a unit-length cube aligned along an integer boundary.  This cube
  // surrounds the input point.
  int x0 = (x > 0.0? cast(int)x: cast(int)x - 1);
  int x1 = x0 + 1;
  int y0 = (y > 0.0? cast(int)y: cast(int)y - 1);
  int y1 = y0 + 1;
  int z0 = (z > 0.0? cast(int)z: cast(int)z - 1);
  int z1 = z0 + 1;

  // Map the difference between the coordinates of the input value and the
  // coordinates of the cube's outer-lower-left vertex onto an S-curve.
  double xs = 0, ys = 0, zs = 0;
  final switch (noiseQuality) {
    case NoiseQuality.QUALITY_FAST:
      xs = (x - cast(double)x0);
      ys = (y - cast(double)y0);
      zs = (z - cast(double)z0);
      break;
    case NoiseQuality.QUALITY_STD:
      xs = SCurve3 (x - cast(double)x0);
      ys = SCurve3 (y - cast(double)y0);
      zs = SCurve3 (z - cast(double)z0);
      break;
    case NoiseQuality.QUALITY_BEST:
      xs = SCurve5 (x - cast(double)x0);
      ys = SCurve5 (y - cast(double)y0);
      zs = SCurve5 (z - cast(double)z0);
      break;
  }

  // Now calculate the noise values at each vertex of the cube.  To generate
  // the coherent-noise value at the input point, interpolate these eight
  // noise values using the S-curve value as the interpolant (trilinear
  // interpolation.)
  double n0, n1, ix0, ix1, iy0, iy1;
  n0   = GradientNoise3D (x, y, z, x0, y0, z0, seed);
  n1   = GradientNoise3D (x, y, z, x1, y0, z0, seed);
  ix0  = LinearInterp (n0, n1, xs);
  n0   = GradientNoise3D (x, y, z, x0, y1, z0, seed);
  n1   = GradientNoise3D (x, y, z, x1, y1, z0, seed);
  ix1  = LinearInterp (n0, n1, xs);
  iy0  = LinearInterp (ix0, ix1, ys);
  n0   = GradientNoise3D (x, y, z, x0, y0, z1, seed);
  n1   = GradientNoise3D (x, y, z, x1, y0, z1, seed);
  ix0  = LinearInterp (n0, n1, xs);
  n0   = GradientNoise3D (x, y, z, x0, y1, z1, seed);
  n1   = GradientNoise3D (x, y, z, x1, y1, z1, seed);
  ix1  = LinearInterp (n0, n1, xs);
  iy1  = LinearInterp (ix0, ix1, ys);

  return LinearInterp (iy0, iy1, zs);
}

/// Generates a gradient-noise value from the coordinates of a
/// three-dimensional input value and the integer coordinates of a
/// nearby three-dimensional value.
///
/// @param fx The floating-point @a x coordinate of the input value.
/// @param fy The floating-point @a y coordinate of the input value.
/// @param fz The floating-point @a z coordinate of the input value.
/// @param ix The integer @a x coordinate of a nearby value.
/// @param iy The integer @a y coordinate of a nearby value.
/// @param iz The integer @a z coordinate of a nearby value.
/// @param seed The random number seed.
///
/// @returns The generated gradient-noise value.
///
/// @pre The difference between @a fx and @a ix must be less than or equal
/// to one.
///
/// @pre The difference between @a fy and @a iy must be less than or equal
/// to one.
///
/// @pre The difference between @a fz and @a iz must be less than or equal
/// to one.
///
/// A <i>gradient</i>-noise function generates better-quality noise than a
/// <i>value</i>-noise function.  Most noise modules use gradient noise for
/// this reason, although it takes much longer to calculate.
///
/// The return value ranges from -1.0 to +1.0.
///
/// This function generates a gradient-noise value by performing the
/// following steps:
/// - It first calculates a random normalized vector based on the
///   nearby integer value passed to this function.
/// - It then calculates a new value by adding this vector to the
///   nearby integer value passed to this function.
/// - It then calculates the dot product of the above-generated value
///   and the floating-point input value passed to this function.
///
/// A noise function differs from a random-number generator because it
/// always returns the same output value if the same input value is passed
/// to it.
double GradientNoise3D (double fx, double fy, double fz, int ix, int iy,
  int iz, int seed = 0)
{
  // Randomly generate a gradient vector given the integer coordinates of the
  // input value.  This implementation generates a random number and uses it
  // as an index into a normalized-vector lookup table.
  int vectorIndex = (
      X_NOISE_GEN    * ix
    + Y_NOISE_GEN    * iy
    + Z_NOISE_GEN    * iz
    + SEED_NOISE_GEN * seed)
    & 0xffffffff;
  vectorIndex ^= (vectorIndex >> SHIFT_NOISE_GEN);
  vectorIndex &= 0xff;

  double xvGradient = g_randomVectors[(vectorIndex << 2)    ];
  double yvGradient = g_randomVectors[(vectorIndex << 2) + 1];
  double zvGradient = g_randomVectors[(vectorIndex << 2) + 2];

  // Set up us another vector equal to the distance between the two vectors
  // passed to this function.
  double xvPoint = (fx - cast(double)ix);
  double yvPoint = (fy - cast(double)iy);
  double zvPoint = (fz - cast(double)iz);

  // Now compute the dot product of the gradient vector with the distance
  // vector.  The resulting value is gradient noise.  Apply a scaling value
  // so that this noise value ranges from -1.0 to 1.0.
  return ((xvGradient * xvPoint)
    + (yvGradient * yvPoint)
    + (zvGradient * zvPoint)) * 2.12;
}

/// Generates an integer-noise value from the coordinates of a
/// three-dimensional input value.
///
/// @param x The integer @a x coordinate of the input value.
/// @param y The integer @a y coordinate of the input value.
/// @param z The integer @a z coordinate of the input value.
/// @param seed A random number seed.
///
/// @returns The generated integer-noise value.
///
/// The return value ranges from 0 to 2147483647.
///
/// A noise function differs from a random-number generator because it
/// always returns the same output value if the same input value is passed
/// to it.
int IntValueNoise3D (int x, int y, int z, int seed = 0)
{
  // All constants are primes and must remain prime in order for this noise
  // function to work correctly.
  int n = (
      X_NOISE_GEN    * x
    + Y_NOISE_GEN    * y
    + Z_NOISE_GEN    * z
    + SEED_NOISE_GEN * seed)
    & 0x7fffffff;
  n = (n >> 13) ^ n;
  return (n * (n * n * 60493 + 19990303) + 1376312589) & 0x7fffffff;
}

/// Modifies a floating-point value so that it can be stored in a
/// noise::int32 variable.
///
/// @param n A floating-point number.
///
/// @returns The modified floating-point number.
///
/// This function does not modify @a n.
///
/// In libnoise, the noise-generating algorithms are all integer-based;
/// they use variables of type noise::int32.  Before calling a noise
/// function, pass the @a x, @a y, and @a z coordinates to this function to
/// ensure that these coordinates can be cast to a noise::int32 value.
///
/// Although you could do a straight cast from double to noise::int32, the
/// resulting value may differ between platforms.  By using this function,
/// you ensure that the resulting value is identical between platforms.
double MakeInt32Range (double n)
{
  if (n >= 1073741824.0) {
    return (2.0 * fmod (n, 1073741824.0)) - 1073741824.0;
  } else if (n <= -1073741824.0) {
    return (2.0 * fmod (n, 1073741824.0)) + 1073741824.0;
  } else {
    return n;
  }
}

/// Generates a value-coherent-noise value from the coordinates of a
/// three-dimensional input value.
///
/// @param x The @a x coordinate of the input value.
/// @param y The @a y coordinate of the input value.
/// @param z The @a z coordinate of the input value.
/// @param seed The random number seed.
/// @param noiseQuality The quality of the coherent-noise.
///
/// @returns The generated value-coherent-noise value.
///
/// The return value ranges from -1.0 to +1.0.
///
/// For an explanation of the difference between <i>gradient</i> noise and
/// <i>value</i> noise, see the comments for the GradientNoise3D() function.
double ValueCoherentNoise3D (double x, double y, double z, int seed = 0,
  NoiseQuality noiseQuality = NoiseQuality.QUALITY_STD)
{
  // Create a unit-length cube aligned along an integer boundary.  This cube
  // surrounds the input point.
  int x0 = (x > 0.0? cast(int)x: cast(int)x - 1);
  int x1 = x0 + 1;
  int y0 = (y > 0.0? cast(int)y: cast(int)y - 1);
  int y1 = y0 + 1;
  int z0 = (z > 0.0? cast(int)z: cast(int)z - 1);
  int z1 = z0 + 1;

  // Map the difference between the coordinates of the input value and the
  // coordinates of the cube's outer-lower-left vertex onto an S-curve.
  double xs = 0, ys = 0, zs = 0;
  final switch (noiseQuality) {
    case NoiseQuality.QUALITY_FAST:
      xs = (x - cast(double)x0);
      ys = (y - cast(double)y0);
      zs = (z - cast(double)z0);
      break;
    case NoiseQuality.QUALITY_STD:
      xs = SCurve3 (x - cast(double)x0);
      ys = SCurve3 (y - cast(double)y0);
      zs = SCurve3 (z - cast(double)z0);
      break;
    case NoiseQuality.QUALITY_BEST:
      xs = SCurve5 (x - cast(double)x0);
      ys = SCurve5 (y - cast(double)y0);
      zs = SCurve5 (z - cast(double)z0);
      break;
  }

  // Now calculate the noise values at each vertex of the cube.  To generate
  // the coherent-noise value at the input point, interpolate these eight
  // noise values using the S-curve value as the interpolant (trilinear
  // interpolation.)
  double n0, n1, ix0, ix1, iy0, iy1;
  n0   = ValueNoise3D (x0, y0, z0, seed);
  n1   = ValueNoise3D (x1, y0, z0, seed);
  ix0  = LinearInterp (n0, n1, xs);
  n0   = ValueNoise3D (x0, y1, z0, seed);
  n1   = ValueNoise3D (x1, y1, z0, seed);
  ix1  = LinearInterp (n0, n1, xs);
  iy0  = LinearInterp (ix0, ix1, ys);
  n0   = ValueNoise3D (x0, y0, z1, seed);
  n1   = ValueNoise3D (x1, y0, z1, seed);
  ix0  = LinearInterp (n0, n1, xs);
  n0   = ValueNoise3D (x0, y1, z1, seed);
  n1   = ValueNoise3D (x1, y1, z1, seed);
  ix1  = LinearInterp (n0, n1, xs);
  iy1  = LinearInterp (ix0, ix1, ys);
  return LinearInterp (iy0, iy1, zs);
}

/// Generates a value-noise value from the coordinates of a
/// three-dimensional input value.
///
/// @param x The @a x coordinate of the input value.
/// @param y The @a y coordinate of the input value.
/// @param z The @a z coordinate of the input value.
/// @param seed A random number seed.
///
/// @returns The generated value-noise value.
///
/// The return value ranges from -1.0 to +1.0.
///
/// A noise function differs from a random-number generator because it
/// always returns the same output value if the same input value is passed
/// to it.
double ValueNoise3D (int x, int y, int z, int seed = 0)
{
  return 1.0 - (cast(double)IntValueNoise3D (x, y, z, seed) / 1073741824.0);
}


    // 2D simplex noise
     double SimplexNoise(double xin, double yin) { //727.20, 131.32
        double n0, n1, n2; // Noise contributions from the three corners
        // Skew the input space to determine which simplex cell we're in
        double s = (xin+yin)*F2; // Hairy factor for 2D //s = 314.196
        int i = fastfloor(xin+s); //1041
        int j = fastfloor(yin+s); //445
        double t = (i+j)*G2; //314.028
        double X0 = i-t; // Unskew the cell origin back to (x,y) space //726.972
        double Y0 = j-t; //130.972
        double x0 = xin-X0; // The x,y distances from the cell origin //0.228
        double y0 = yin-Y0; // 0.348
        // For the 2D case, the simplex shape is an equilateral triangle.
        // Determine which simplex we are in.
        int i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords
        if(x0>y0) {i1=1; j1=0;} // lower triangle, XY order: (0,0)->(1,0)->(1,1)
        else {i1=0; j1=1;}      // upper triangle, YX order: (0,0)->(0,1)->(1,1)
        // A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
        // a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
        // c = (3-sqrt(3))/6
        double x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
        double y1 = y0 - j1 + G2;
        double x2 = x0 - 1.0 + 2.0 * G2; // Offsets for last corner in (x,y) unskewed coords
        double y2 = y0 - 1.0 + 2.0 * G2;
        // Work out the hashed gradient indices of the three simplex corners
        int ii = i & 255;
        int jj = j & 255;
        int gi0 = permMod12[ii+perm[jj]];
        int gi1 = permMod12[ii+i1+perm[jj+j1]];
        int gi2 = permMod12[ii+1+perm[jj+1]];
        // Calculate the contribution from the three corners
        double t0 = 0.5 - (x0*x0) - (y0*y0);
        if(t0<0) n0 = 0.0;
        else {
          t0 *= t0;
          n0 = t0 * t0 * dot(grad3[gi0], x0, y0);  // (x,y) of grad3 used for 2D gradient
        }
        double t1 = 0.5 - (x1*x1) - (y1*y1);
        if(t1<0) n1 = 0.0;
        else {
          t1 *= t1;
          n1 = t1 * t1 * dot(grad3[gi1], x1, y1);
        }
        double t2 = 0.5 - (x2*x2) - (y2*y2);
        if(t2<0) n2 = 0.0;
        else {
          t2 *= t2;
          n2 = t2 * t2 * dot(grad3[gi2], x2, y2);
        }
        // Add contributions from each corner to get the final noise value.
        // The result is scaled to return values in the interval [-1,1].
        return 70.1043345 * (n0 + n1 + n2);
    }

    // 3D simplex noise
    double SimplexNoise(double xin, double yin, double zin) {
        double n0, n1, n2, n3; // Noise contributions from the four corners
        // Skew the input space to determine which simplex cell we're in
        double s = (xin+yin+zin)*F3; // Very nice and simple skew factor for 3D
        int i = fastfloor(xin+s);
        int j = fastfloor(yin+s);
        int k = fastfloor(zin+s);
        double t = (i+j+k)*G3;
        double X0 = i-t; // Unskew the cell origin back to (x,y,z) space
        double Y0 = j-t;
        double Z0 = k-t;
        double x0 = xin-X0; // The x,y,z distances from the cell origin
        double y0 = yin-Y0;
        double z0 = zin-Z0;
        // For the 3D case, the simplex shape is a slightly irregular tetrahedron.
        // Determine which simplex we are in.
        int i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords
        int i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords
        if(x0>=y0) {
          if(y0>=z0) { i1=1; j1=0; k1=0; i2=1; j2=1; k2=0; } // X Y Z order
            else if(x0>=z0) { i1=1; j1=0; k1=0; i2=1; j2=0; k2=1; } // X Z Y order
            else { i1=0; j1=0; k1=1; i2=1; j2=0; k2=1; } // Z X Y order
          }
        else { // x0<y0
          if(y0<z0) { i1=0; j1=0; k1=1; i2=0; j2=1; k2=1; } // Z Y X order
          else if(x0<z0) { i1=0; j1=1; k1=0; i2=0; j2=1; k2=1; } // Y Z X order
          else { i1=0; j1=1; k1=0; i2=1; j2=1; k2=0; } // Y X Z order
        }
        // A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z),
        // a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and
        // a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where
        // c = 1/6.
        double x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
        double y1 = y0 - j1 + G3;
        double z1 = z0 - k1 + G3;
        double x2 = x0 - i2 + 2.0*G3; // Offsets for third corner in (x,y,z) coords
        double y2 = y0 - j2 + 2.0*G3;
        double z2 = z0 - k2 + 2.0*G3;
        double x3 = x0 - 1.0 + 3.0*G3; // Offsets for last corner in (x,y,z) coords
        double y3 = y0 - 1.0 + 3.0*G3;
        double z3 = z0 - 1.0 + 3.0*G3;
        // Work out the hashed gradient indices of the four simplex corners
        int ii = i & 255;
        int jj = j & 255;
        int kk = k & 255;
        int gi0 = permMod12[ii+perm[jj+perm[kk]]];
        int gi1 = permMod12[ii+i1+perm[jj+j1+perm[kk+k1]]];
        int gi2 = permMod12[ii+i2+perm[jj+j2+perm[kk+k2]]];
        int gi3 = permMod12[ii+1+perm[jj+1+perm[kk+1]]];
        // Calculate the contribution from the four corners
        double t0 = 0.5 - x0*x0 - y0*y0 - z0*z0;
        if(t0<0) n0 = 0.0;
        else {
          n0 = t0 * t0 * t0 * dot(grad3[gi0], x0, y0, z0);
        }
        double t1 = 0.5 - x1*x1 - y1*y1 - z1*z1;
        if(t1<0) n1 = 0.0;
        else {
          n1 = t1 * t1 * t1 * dot(grad3[gi1], x1, y1, z1);
        }
        double t2 = 0.5 - x2*x2 - y2*y2 - z2*z2;
        if(t2<0) n2 = 0.0;
        else {
          n2 = t2 * t2 * t2 * dot(grad3[gi2], x2, y2, z2);
        }
        double t3 = 0.5 - x3*x3 - y3*y3 - z3*z3;
        if(t3<0) n3 = 0.0;
        else {
          n3 = t3 * t3 * t3 * dot(grad3[gi3], x3, y3, z3);
        }
        // Add contributions from each corner to get the final noise value.
        // The result is scaled to stay just inside [-1,1]
        return 31.6*(n0 + n1 + n2 + n3);
    }

    // 4D simplex noise, better simplex rank ordering method 2012-03-09
     double SimplexNoise(double x, double y, double z, double w) {

        double n0, n1, n2, n3, n4; // Noise contributions from the five corners
        // Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in
        double s = (x + y + z + w) * F4; // Factor for 4D skewing
        int i = fastfloor(x + s);
        int j = fastfloor(y + s);
        int k = fastfloor(z + s);
        int l = fastfloor(w + s);
        double t = (i + j + k + l) * G4; // Factor for 4D unskewing
        double X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
        double Y0 = j - t;
        double Z0 = k - t;
        double W0 = l - t;
        double x0 = x - X0;  // The x,y,z,w distances from the cell origin
        double y0 = y - Y0;
        double z0 = z - Z0;
        double w0 = w - W0;
        // For the 4D case, the simplex is a 4D shape I won't even try to describe.
        // To find out which of the 24 possible simplices we're in, we need to
        // determine the magnitude ordering of x0, y0, z0 and w0.
        // Six pair-wise comparisons are performed between each possible pair
        // of the four coordinates, and the results are used to rank the numbers.
        int rankx = 0;
        int ranky = 0;
        int rankz = 0;
        int rankw = 0;
        if(x0 > y0) rankx++; else ranky++;
        if(x0 > z0) rankx++; else rankz++;
        if(x0 > w0) rankx++; else rankw++;
        if(y0 > z0) ranky++; else rankz++;
        if(y0 > w0) ranky++; else rankw++;
        if(z0 > w0) rankz++; else rankw++;
        int i1, j1, k1, l1; // The integer offsets for the second simplex corner
        int i2, j2, k2, l2; // The integer offsets for the third simplex corner
        int i3, j3, k3, l3; // The integer offsets for the fourth simplex corner
        // simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order.
        // Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w
        // impossible. Only the 24 indices which have non-zero entries make any sense.
        // We use a thresholding to set the coordinates in turn from the largest magnitude.
        // Rank 3 denotes the largest coordinate.
        i1 = rankx >= 3 ? 1 : 0;
        j1 = ranky >= 3 ? 1 : 0;
        k1 = rankz >= 3 ? 1 : 0;
        l1 = rankw >= 3 ? 1 : 0;
        // Rank 2 denotes the second largest coordinate.
        i2 = rankx >= 2 ? 1 : 0;
        j2 = ranky >= 2 ? 1 : 0;
        k2 = rankz >= 2 ? 1 : 0;
        l2 = rankw >= 2 ? 1 : 0;
        // Rank 1 denotes the second smallest coordinate.
        i3 = rankx >= 1 ? 1 : 0;
        j3 = ranky >= 1 ? 1 : 0;
        k3 = rankz >= 1 ? 1 : 0;
        l3 = rankw >= 1 ? 1 : 0;
        // The fifth corner has all coordinate offsets = 1, so no need to compute that.
        double x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
        double y1 = y0 - j1 + G4;
        double z1 = z0 - k1 + G4;
        double w1 = w0 - l1 + G4;
        double x2 = x0 - i2 + 2.0*G4; // Offsets for third corner in (x,y,z,w) coords
        double y2 = y0 - j2 + 2.0*G4;
        double z2 = z0 - k2 + 2.0*G4;
        double w2 = w0 - l2 + 2.0*G4;
        double x3 = x0 - i3 + 3.0*G4; // Offsets for fourth corner in (x,y,z,w) coords
        double y3 = y0 - j3 + 3.0*G4;
        double z3 = z0 - k3 + 3.0*G4;
        double w3 = w0 - l3 + 3.0*G4;
        double x4 = x0 - 1.0 + 4.0*G4; // Offsets for last corner in (x,y,z,w) coords
        double y4 = y0 - 1.0 + 4.0*G4;
        double z4 = z0 - 1.0 + 4.0*G4;
        double w4 = w0 - 1.0 + 4.0*G4;
        // Work out the hashed gradient indices of the five simplex corners
        int ii = i & 255;
        int jj = j & 255;
        int kk = k & 255;
        int ll = l & 255;
        int gi0 = permMod32[ii+perm[jj+perm[kk+perm[ll]]]];
        int gi1 = permMod32[ii+i1+perm[jj+j1+perm[kk+k1+perm[ll+l1]]]];
        int gi2 = permMod32[ii+i2+perm[jj+j2+perm[kk+k2+perm[ll+l2]]]];
        int gi3 = permMod32[ii+i3+perm[jj+j3+perm[kk+k3+perm[ll+l3]]]];
        int gi4 = permMod32[ii+1+perm[jj+1+perm[kk+1+perm[ll+1]]]];
        // Calculate the contribution from the five corners
        double t0 = 0.6 - x0*x0 - y0*y0 - z0*z0 - w0*w0;
        if(t0<0) n0 = 0.0;
        else {
          t0 *= t0;
          n0 = t0 * t0 * dot(grad4[gi0], x0, y0, z0, w0);
        }
        double t1 = 0.6 - x1*x1 - y1*y1 - z1*z1 - w1*w1;
        if(t1<0) n1 = 0.0;
        else {
          t1 *= t1;
          n1 = t1 * t1 * dot(grad4[gi1], x1, y1, z1, w1);
        }
        double t2 = 0.6 - x2*x2 - y2*y2 - z2*z2 - w2*w2;
        if(t2<0) n2 = 0.0;
        else {
          t2 *= t2;
          n2 = t2 * t2 * dot(grad4[gi2], x2, y2, z2, w2);
        }
        double t3 = 0.6 - x3*x3 - y3*y3 - z3*z3 - w3*w3;
        if(t3<0) n3 = 0.0;
        else {
          t3 *= t3;
          n3 = t3 * t3 * dot(grad4[gi3], x3, y3, z3, w3);
        }
        double t4 = 0.6 - x4*x4 - y4*y4 - z4*z4 - w4*w4;
        if(t4<0) n4 = 0.0;
        else {
          t4 *= t4;
          n4 = t4 * t4 * dot(grad4[gi4], x4, y4, z4, w4);
        }
        // Sum up and scale the result to cover the range [-1,1]
        return 27.0 * (n0 + n1 + n2 + n3 + n4);
    }

     double dot(Grad g, double x, double y) {
        return g.x*x + g.y*y; 
    }

     double dot(Grad g, double x, double y, double z) {
        return g.x*x + g.y*y + g.z*z; 
    }

     double dot(Grad g, double x, double y, double z, double w) {
        return g.x*x + g.y*y + g.z*z + g.w*w; 
    }

     int fastfloor(double x) {
        int xi = cast(int)x;
        return x<xi ? xi-1 : xi;
    }

     short[512] modulo_lookup(immutable int modulo) {
        short temp[512];
        for(int i = 0; i < perm.length; i++) {
            temp[i] = perm[i] % modulo;
        }
        return temp;
    }

    //lookup table for selecting gradients, doubled to avoid having to deal
    //with index wrapping.
     immutable short perm[512] = [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];

     immutable short permMod12[] = modulo_lookup(12);
     immutable short permMod32[] = modulo_lookup(32);

    //gradient tables
     immutable Grad grad3[12] = [ Grad(1,1,0),Grad(-1,1,0),Grad(1,-1,0),Grad(-1,-1,0),
                                                Grad(1,0,1),Grad(-1,0,1),Grad(1,0,-1),Grad(-1,0,-1),
                                                Grad(0,1,1),Grad(0,-1,1),Grad(0,1,-1),Grad(0,-1,-1)];

     immutable Grad grad4[32] = [ Grad(0,1,1,1),Grad(0,1,1,-1),Grad(0,1,-1,1),Grad(0,1,-1,-1),
                                                Grad(0,-1,1,1),Grad(0,-1,1,-1),Grad(0,-1,-1,1),Grad(0,-1,-1,-1),
                                                Grad(1,0,1,1),Grad(1,0,1,-1),Grad(1,0,-1,1),Grad(1,0,-1,-1),
                                                Grad(-1,0,1,1),Grad(-1,0,1,-1),Grad(-1,0,-1,1),Grad(-1,0,-1,-1),
                                                Grad(1,1,0,1),Grad(1,1,0,-1),Grad(1,-1,0,1),Grad(1,-1,0,-1),
                                                Grad(-1,1,0,1),Grad(-1,1,0,-1),Grad(-1,-1,0,1),Grad(-1,-1,0,-1),
                                                Grad(1,1,1,0),Grad(1,1,-1,0),Grad(1,-1,1,0),Grad(1,-1,-1,0),
                                                Grad(-1,1,1,0),Grad(-1,1,-1,0),Grad(-1,-1,1,0),Grad(-1,-1,-1,0)];

    // Skewing and unskewing factors for 2, 3, and 4 dimensions
     const double F2 = 0.5*(sqrt(cast(real)3.0)-1.0);
     const double G2 = (3.0-sqrt(cast(real)3.0))/6.0;
     const double F3 = 1.0/3.0;
     const double G3 = 1.0/6.0;
     const double F4 = (sqrt(cast(real)5.0)-1.0)/4.0;
     const double G4 = (5.0-sqrt(cast(real)5.0))/20.0;

private {
  struct Grad {
    int x = 0;
    int y = 0;
    int z = 0;
    int w = 0;
    this(int x, int y, int z) {
      this.x = x;
      this.y = y;
      this.z = z;
    }

    this(int x, int y, int z, int w) {
      this.x = x;
      this.y = y;
      this.z = z;
      this.w = w;
    }
  }
}