/* SimplexNoise1234, Simplex noise with true analytic
 * derivative in 1D to 4D.
 *
 * Author: Stefan Gustavson, 2003-2005
 * Contact: stegu@itn.liu.se
 */

 /*
This code was GPL licensed until February 2011.
As the original author of this code, I hereby
release it irrevocably into the public domain.
Please feel free to use it for whatever you want.
Credit is appreciated where appropriate, and I also
appreciate being told where this code finds any use,
but you may do as you like. Alternatively, if you want
to have a familiar OSI-approved license, you may use
This code under the terms of the MIT license:

Copyright (C) 2003-2005 by Stefan Gustavson. All rights reserved.
This code is licensed to you under the terms of the MIT license:

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.
*/

/** \file
		\brief C implementation of Perlin Simplex Noise over 1,2,3, and 4 dimensions.
		\author Stefan Gustavson (stegu@itn.liu.se)
*/

/*
 * This implementation is "Simplex Noise" as presented by
 * Ken Perlin at a relatively obscure and not often cited course
 * session "Real-Time Shading" at Siggraph 2001 (before real
 * time shading actually took on), under the title "hardware noise".
 * The 3D function is numerically equivalent to his Java reference
 * code available in the PDF course notes, although I re-implemented
 * it from scratch to get more readable code. The 1D, 2D and 4D cases
 * were implemented from scratch by me from Ken Perlin's text.
 *
 * This file has no dependencies on any other file, not even its own
 * header file. The header file is made for use by external code only.
 */


// We don't need to include this. It does no harm, but no use either.
#include	"simplexnoise1234.h"

#pragma warning(disable: 4244) // conversion double -> float

#define FASTFLOOR(x) ( ((x)>0) ? ((int)x) : (((int)x)-1) )

//---------------------------------------------------------------------
// Static data

/*
 * Permutation table. This is just a random jumble of all numbers 0-255,
 * repeated twice to avoid wrapping the index at 255 for each lookup.
 * This needs to be exactly the same for all instances on all platforms,
 * so it's easiest to just keep it as static explicit data.
 * This also removes the need for any initialisation of this class.
 *
 * Note that making this an int[] instead of a char[] might make the
 * code run faster on platforms with a high penalty for unaligned single
 * byte addressing. Intel x86 is generally single-byte-friendly, but
 * some other CPUs are faster with 4-aligned reads.
 * However, a char[] is smaller, which avoids cache trashing, and that
 * is probably the most important aspect on most architectures.
 * This array is accessed a *lot* by the noise functions.
 * A vector-valued noise over 3D accesses it 96 times, and a
 * float-valued 4D noise 64 times. We want this to fit in the cache!
 */
unsigned char 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 
};

//---------------------------------------------------------------------

/*
 * Helper functions to compute gradients-dot-residualvectors (1D to 4D)
 * Note that these generate gradients of more than unit length. To make
 * a close match with the value range of classic Perlin noise, the final
 * noise values need to be rescaled to fit nicely within [-1,1].
 * (The simplex noise functions as such also have different scaling.)
 * Note also that these noise functions are the most practical and useful
 * signed version of Perlin noise. To return values according to the
 * RenderMan specification from the SL noise() and pnoise() functions,
 * the noise values need to be scaled and offset to [0,1], like this:
 * float SLnoise = (noise(x,y,z) + 1.0) * 0.5;
 */

float  grad1( int hash, float x ) {
    int h = hash & 15;
    float grad = 1.0f + (h & 7);   // Gradient value 1.0, 2.0, ..., 8.0
    if (h&8) grad = -grad;         // Set a random sign for the gradient
    return ( grad * x );           // Multiply the gradient with the distance
}

float  grad2( int hash, float x, float y ) {
    int h = hash & 7;      // Convert low 3 bits of hash code
    float u = h<4 ? x : y;  // into 8 simple gradient directions,
    float v = h<4 ? y : x;  // and compute the dot product with (x,y).
    return ((h&1)? -u : u) + ((h&2)? -2.0f*v : 2.0f*v);
}

float  grad3( int hash, float x, float y , float z ) {
    int h = hash & 15;     // Convert low 4 bits of hash code into 12 simple
    float u = h<8 ? x : y; // gradient directions, and compute dot product.
    float v = h<4 ? y : h==12||h==14 ? x : z; // Fix repeats at h = 12 to 15
    return ((h&1)? -u : u) + ((h&2)? -v : v);
}

float  grad4( int hash, float x, float y, float z, float t ) {
    int h = hash & 31;      // Convert low 5 bits of hash code into 32 simple
    float u = h<24 ? x : y; // gradient directions, and compute dot product.
    float v = h<16 ? y : z;
    float w = h<8 ? z : t;
    return ((h&1)? -u : u) + ((h&2)? -v : v) + ((h&4)? -w : w);
}

  // A lookup table to traverse the simplex around a given point in 4D.
  // Details can be found where this table is used, in the 4D noise method.
  /* TODO: This should not be required, backport it from Bill's GLSL code! */
  static unsigned char simplex[64][4] = {
    {0,1,2,3},{0,1,3,2},{0,0,0,0},{0,2,3,1},{0,0,0,0},{0,0,0,0},{0,0,0,0},{1,2,3,0},
    {0,2,1,3},{0,0,0,0},{0,3,1,2},{0,3,2,1},{0,0,0,0},{0,0,0,0},{0,0,0,0},{1,3,2,0},
    {0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},
    {1,2,0,3},{0,0,0,0},{1,3,0,2},{0,0,0,0},{0,0,0,0},{0,0,0,0},{2,3,0,1},{2,3,1,0},
    {1,0,2,3},{1,0,3,2},{0,0,0,0},{0,0,0,0},{0,0,0,0},{2,0,3,1},{0,0,0,0},{2,1,3,0},
    {0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},
    {2,0,1,3},{0,0,0,0},{0,0,0,0},{0,0,0,0},{3,0,1,2},{3,0,2,1},{0,0,0,0},{3,1,2,0},
    {2,1,0,3},{0,0,0,0},{0,0,0,0},{0,0,0,0},{3,1,0,2},{0,0,0,0},{3,2,0,1},{3,2,1,0}};

// 1D simplex noise
float snoise1(float x) {

  int i0 = FASTFLOOR(x);
  int i1 = i0 + 1;
  float x0 = x - i0;
  float x1 = x0 - 1.0f;

  float n0, n1;

  float t0 = 1.0f - x0*x0;
//  if(t0 < 0.0f) t0 = 0.0f; // this never happens for the 1D case
  t0 *= t0;
  n0 = t0 * t0 * grad1(perm[i0 & 0xff], x0);

  float t1 = 1.0f - x1*x1;
//  if(t1 < 0.0f) t1 = 0.0f; // this never happens for the 1D case
  t1 *= t1;
  n1 = t1 * t1 * grad1(perm[i1 & 0xff], x1);
  // The maximum value of this noise is 8*(3/4)^4 = 2.53125
  // A factor of 0.395 would scale to fit exactly within [-1,1], but
  // we want to match PRMan's 1D noise, so we scale it down some more.
  return 0.25f * (n0 + n1);

}

// 2D simplex noise
float snoise2(float x, float y) {

#define F2 0.366025403 // F2 = 0.5*(sqrt(3.0)-1.0)
#define G2 0.211324865 // G2 = (3.0-Math.sqrt(3.0))/6.0

    float n0, n1, n2; // Noise contributions from the three corners

    // Skew the input space to determine which simplex cell we're in
    float s = (x+y)*F2; // Hairy factor for 2D
    float xs = x + s;
    float ys = y + s;
    int i = FASTFLOOR(xs);
    int j = FASTFLOOR(ys);

    float t = (float)(i+j)*G2;
    float X0 = i-t; // Unskew the cell origin back to (x,y) space
    float Y0 = j-t;
    float x0 = x-X0; // The x,y distances from the cell origin
    float y0 = y-Y0;

    // 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

    float x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
    float y1 = y0 - j1 + G2;
    float x2 = x0 - 1.0f + 2.0f * G2; // Offsets for last corner in (x,y) unskewed coords
    float y2 = y0 - 1.0f + 2.0f * G2;

    // Wrap the integer indices at 256, to avoid indexing perm[] out of bounds
    int ii = i & 0xff;
    int jj = j & 0xff;

    // Calculate the contribution from the three corners
    float t0 = 0.5f - x0*x0-y0*y0;
    if(t0 < 0.0f) n0 = 0.0f;
    else {
      t0 *= t0;
      n0 = t0 * t0 * grad2(perm[ii+perm[jj]], x0, y0); 
    }

    float t1 = 0.5f - x1*x1-y1*y1;
    if(t1 < 0.0f) n1 = 0.0f;
    else {
      t1 *= t1;
      n1 = t1 * t1 * grad2(perm[ii+i1+perm[jj+j1]], x1, y1);
    }

    float t2 = 0.5f - x2*x2-y2*y2;
    if(t2 < 0.0f) n2 = 0.0f;
    else {
      t2 *= t2;
      n2 = t2 * t2 * grad2(perm[ii+1+perm[jj+1]], 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 40.0f * (n0 + n1 + n2); // TODO: The scale factor is preliminary!
  }

// 3D simplex noise
float snoise3(float x, float y, float z) {

// Simple skewing factors for the 3D case
#define F3 0.333333333
#define G3 0.166666667

    float n0, n1, n2, n3; // Noise contributions from the four corners

    // Skew the input space to determine which simplex cell we're in
    float s = (x+y+z)*F3; // Very nice and simple skew factor for 3D
    float xs = x+s;
    float ys = y+s;
    float zs = z+s;
    int i = FASTFLOOR(xs);
    int j = FASTFLOOR(ys);
    int k = FASTFLOOR(zs);

    float t = (float)(i+j+k)*G3; 
    float X0 = i-t; // Unskew the cell origin back to (x,y,z) space
    float Y0 = j-t;
    float Z0 = k-t;
    float x0 = x-X0; // The x,y,z distances from the cell origin
    float y0 = y-Y0;
    float z0 = z-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

/* This code would benefit from a backport from the GLSL version! */
    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.

    float x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
    float y1 = y0 - j1 + G3;
    float z1 = z0 - k1 + G3;
    float x2 = x0 - i2 + 2.0f*G3; // Offsets for third corner in (x,y,z) coords
    float y2 = y0 - j2 + 2.0f*G3;
    float z2 = z0 - k2 + 2.0f*G3;
    float x3 = x0 - 1.0f + 3.0f*G3; // Offsets for last corner in (x,y,z) coords
    float y3 = y0 - 1.0f + 3.0f*G3;
    float z3 = z0 - 1.0f + 3.0f*G3;

    // Wrap the integer indices at 256, to avoid indexing perm[] out of bounds
    int ii = i & 0xff;
    int jj = j & 0xff;
    int kk = k & 0xff;

    // Calculate the contribution from the four corners
    float t0 = 0.6f - x0*x0 - y0*y0 - z0*z0;
    if(t0 < 0.0f) n0 = 0.0f;
    else {
      t0 *= t0;
      n0 = t0 * t0 * grad3(perm[ii+perm[jj+perm[kk]]], x0, y0, z0);
    }

    float t1 = 0.6f - x1*x1 - y1*y1 - z1*z1;
    if(t1 < 0.0f) n1 = 0.0f;
    else {
      t1 *= t1;
      n1 = t1 * t1 * grad3(perm[ii+i1+perm[jj+j1+perm[kk+k1]]], x1, y1, z1);
    }

    float t2 = 0.6f - x2*x2 - y2*y2 - z2*z2;
    if(t2 < 0.0f) n2 = 0.0f;
    else {
      t2 *= t2;
      n2 = t2 * t2 * grad3(perm[ii+i2+perm[jj+j2+perm[kk+k2]]], x2, y2, z2);
    }

    float t3 = 0.6f - x3*x3 - y3*y3 - z3*z3;
    if(t3<0.0f) n3 = 0.0f;
    else {
      t3 *= t3;
      n3 = t3 * t3 * grad3(perm[ii+1+perm[jj+1+perm[kk+1]]], 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 32.0f * (n0 + n1 + n2 + n3); // TODO: The scale factor is preliminary!
  }


// 4D simplex noise
float snoise4(float x, float y, float z, float w) {
  
  // The skewing and unskewing factors are hairy again for the 4D case
#define F4 0.309016994 // F4 = (Math.sqrt(5.0)-1.0)/4.0
#define G4 0.138196601 // G4 = (5.0-Math.sqrt(5.0))/20.0

    float 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
    float s = (x + y + z + w) * F4; // Factor for 4D skewing
    float xs = x + s;
    float ys = y + s;
    float zs = z + s;
    float ws = w + s;
    int i = FASTFLOOR(xs);
    int j = FASTFLOOR(ys);
    int k = FASTFLOOR(zs);
    int l = FASTFLOOR(ws);

    float t = (i + j + k + l) * G4; // Factor for 4D unskewing
    float X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
    float Y0 = j - t;
    float Z0 = k - t;
    float W0 = l - t;

    float x0 = x - X0;  // The x,y,z,w distances from the cell origin
    float y0 = y - Y0;
    float z0 = z - Z0;
    float 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.
    // The method below is a good way of finding the ordering of x,y,z,w and
    // then find the correct traversal order for the simplex we’re in.
    // First, six pair-wise comparisons are performed between each possible pair
    // of the four coordinates, and the results are used to add up binary bits
    // for an integer index.
    int c1 = (x0 > y0) ? 32 : 0;
    int c2 = (x0 > z0) ? 16 : 0;
    int c3 = (y0 > z0) ? 8 : 0;
    int c4 = (x0 > w0) ? 4 : 0;
    int c5 = (y0 > w0) ? 2 : 0;
    int c6 = (z0 > w0) ? 1 : 0;
    int c = c1 + c2 + c3 + c4 + c5 + c6;

    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.
    // The number 3 in the "simplex" array is at the position of the largest coordinate.
    i1 = simplex[c][0]>=3 ? 1 : 0;
    j1 = simplex[c][1]>=3 ? 1 : 0;
    k1 = simplex[c][2]>=3 ? 1 : 0;
    l1 = simplex[c][3]>=3 ? 1 : 0;
    // The number 2 in the "simplex" array is at the second largest coordinate.
    i2 = simplex[c][0]>=2 ? 1 : 0;
    j2 = simplex[c][1]>=2 ? 1 : 0;
    k2 = simplex[c][2]>=2 ? 1 : 0;
    l2 = simplex[c][3]>=2 ? 1 : 0;
    // The number 1 in the "simplex" array is at the second smallest coordinate.
    i3 = simplex[c][0]>=1 ? 1 : 0;
    j3 = simplex[c][1]>=1 ? 1 : 0;
    k3 = simplex[c][2]>=1 ? 1 : 0;
    l3 = simplex[c][3]>=1 ? 1 : 0;
    // The fifth corner has all coordinate offsets = 1, so no need to look that up.

    float x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
    float y1 = y0 - j1 + G4;
    float z1 = z0 - k1 + G4;
    float w1 = w0 - l1 + G4;
    float x2 = x0 - i2 + 2.0f*G4; // Offsets for third corner in (x,y,z,w) coords
    float y2 = y0 - j2 + 2.0f*G4;
    float z2 = z0 - k2 + 2.0f*G4;
    float w2 = w0 - l2 + 2.0f*G4;
    float x3 = x0 - i3 + 3.0f*G4; // Offsets for fourth corner in (x,y,z,w) coords
    float y3 = y0 - j3 + 3.0f*G4;
    float z3 = z0 - k3 + 3.0f*G4;
    float w3 = w0 - l3 + 3.0f*G4;
    float x4 = x0 - 1.0f + 4.0f*G4; // Offsets for last corner in (x,y,z,w) coords
    float y4 = y0 - 1.0f + 4.0f*G4;
    float z4 = z0 - 1.0f + 4.0f*G4;
    float w4 = w0 - 1.0f + 4.0f*G4;

    // Wrap the integer indices at 256, to avoid indexing perm[] out of bounds
    int ii = i & 0xff;
    int jj = j & 0xff;
    int kk = k & 0xff;
    int ll = l & 0xff;

    // Calculate the contribution from the five corners
    float t0 = 0.6f - x0*x0 - y0*y0 - z0*z0 - w0*w0;
    if(t0 < 0.0f) n0 = 0.0f;
    else {
      t0 *= t0;
      n0 = t0 * t0 * grad4(perm[ii+perm[jj+perm[kk+perm[ll]]]], x0, y0, z0, w0);
    }

   float t1 = 0.6f - x1*x1 - y1*y1 - z1*z1 - w1*w1;
    if(t1 < 0.0f) n1 = 0.0f;
    else {
      t1 *= t1;
      n1 = t1 * t1 * grad4(perm[ii+i1+perm[jj+j1+perm[kk+k1+perm[ll+l1]]]], x1, y1, z1, w1);
    }

   float t2 = 0.6f - x2*x2 - y2*y2 - z2*z2 - w2*w2;
    if(t2 < 0.0f) n2 = 0.0f;
    else {
      t2 *= t2;
      n2 = t2 * t2 * grad4(perm[ii+i2+perm[jj+j2+perm[kk+k2+perm[ll+l2]]]], x2, y2, z2, w2);
    }

   float t3 = 0.6f - x3*x3 - y3*y3 - z3*z3 - w3*w3;
    if(t3 < 0.0f) n3 = 0.0f;
    else {
      t3 *= t3;
      n3 = t3 * t3 * grad4(perm[ii+i3+perm[jj+j3+perm[kk+k3+perm[ll+l3]]]], x3, y3, z3, w3);
    }

   float t4 = 0.6f - x4*x4 - y4*y4 - z4*z4 - w4*w4;
    if(t4 < 0.0f) n4 = 0.0f;
    else {
      t4 *= t4;
      n4 = t4 * t4 * grad4(perm[ii+1+perm[jj+1+perm[kk+1+perm[ll+1]]]], x4, y4, z4, w4);
    }

    // Sum up and scale the result to cover the range [-1,1]
    return 27.0f * (n0 + n1 + n2 + n3 + n4); // TODO: The scale factor is preliminary!
  }
//---------------------------------------------------------------------
