Community Core Vision

#pragma once

/*

 * Mesa 3-D graphics library

 * Version:  6.5

 *

 * Copyright (C) 2006  Brian Paul   All Rights Reserved.

 *

 * 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

 * BRIAN PAUL 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.

 */

/*

 * SimplexNoise1234

 * Copyright (c) 2003-2005, Stefan Gustavson

 *

 * Contact: [email protected]

 */

/** \file

    \brief C implementation of Perlin Simplex Noise over 1,2,3, and 4 dimensions.

    \author Stefan Gustavson ([email protected])

*/

/*

 * 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.

 */

#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!

 */

static 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 = (SimplexNoise1234::noise(x,y,z) + 1.0) * 0.5;

 */

static 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 */

}

static 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);

}

static 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);

}

static 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 */

static float _slang_library_noise1 (float x)

{

  int i0 = FASTFLOOR(x);

  int i1 = i0 + 1;

  float x0 = x - i0;

  float x1 = x0 - 1.0f;

  float t1 = 1.0f - x1*x1;

  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);

/*  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 */

static float _slang_library_noise2 (float x, float y)

{

#define F2 0.366025403f /* F2 = 0.5*(sqrt(3.0)-1.0) */

#define G2 0.211324865f /* 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;

    float x1, y1, x2, y2;

    int ii, jj;

    float t0, t1, t2;

    /* 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 */

    x1 = x0 - i1 + G2; /* Offsets for middle corner in (x,y) unskewed coords */

    y1 = y0 - j1 + G2;

    x2 = x0 - 1.0f + 2.0f * G2; /* Offsets for last corner in (x,y) unskewed coords */

    y2 = y0 - 1.0f + 2.0f * G2;

    /* Wrap the integer indices at 256, to avoid indexing perm[] out of bounds */

    ii = i % 256;

    jj = j % 256;

    /* Calculate the contribution from the three corners */

    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);

    }

    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);

    }

    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 */

static float _slang_library_noise3 (float x, float y, float z)

{

/* Simple skewing factors for the 3D case */

#define F3 0.333333333f

#define G3 0.166666667f

    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;

    float x1, y1, z1, x2, y2, z2, x3, y3, z3;

    int ii, jj, kk;

    float t0, t1, t2, t3;

    /* 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. */

    x1 = x0 - i1 + G3; /* Offsets for second corner in (x,y,z) coords */

    y1 = y0 - j1 + G3;

    z1 = z0 - k1 + G3;

    x2 = x0 - i2 + 2.0f*G3; /* Offsets for third corner in (x,y,z) coords */

    y2 = y0 - j2 + 2.0f*G3;

    z2 = z0 - k2 + 2.0f*G3;

    x3 = x0 - 1.0f + 3.0f*G3; /* Offsets for last corner in (x,y,z) coords */

    y3 = y0 - 1.0f + 3.0f*G3;

    z3 = z0 - 1.0f + 3.0f*G3;

    /* Wrap the integer indices at 256, to avoid indexing perm[] out of bounds */

    ii = i % 256;

    jj = j % 256;

    kk = k % 256;

    /* Calculate the contribution from the four corners */

    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);

    }

    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);

    }

    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);

    }

    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 */

static float _slang_library_noise4 (float x, float y, float z, float w)

{

  /* The skewing and unskewing factors are hairy again for the 4D case */

#define F4 0.309016994f /* F4 = (Math.sqrt(5.0)-1.0)/4.0 */

#define G4 0.138196601f /* 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 */

    float x1, y1, z1, w1, x2, y2, z2, w2, x3, y3, z3, w3, x4, y4, z4, w4;

    int ii, jj, kk, ll;

    float t0, t1, t2, t3, t4;

    /* 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. */

    x1 = x0 - i1 + G4; /* Offsets for second corner in (x,y,z,w) coords */

    y1 = y0 - j1 + G4;

    z1 = z0 - k1 + G4;

    w1 = w0 - l1 + G4;

    x2 = x0 - i2 + 2.0f*G4; /* Offsets for third corner in (x,y,z,w) coords */

    y2 = y0 - j2 + 2.0f*G4;

    z2 = z0 - k2 + 2.0f*G4;

    w2 = w0 - l2 + 2.0f*G4;

    x3 = x0 - i3 + 3.0f*G4; /* Offsets for fourth corner in (x,y,z,w) coords */

    y3 = y0 - j3 + 3.0f*G4;

    z3 = z0 - k3 + 3.0f*G4;

    w3 = w0 - l3 + 3.0f*G4;

    x4 = x0 - 1.0f + 4.0f*G4; /* Offsets for last corner in (x,y,z,w) coords */

    y4 = y0 - 1.0f + 4.0f*G4;

    z4 = z0 - 1.0f + 4.0f*G4;

    w4 = w0 - 1.0f + 4.0f*G4;

    /* Wrap the integer indices at 256, to avoid indexing perm[] out of bounds */

    ii = i % 256;

    jj = j % 256;

    kk = k % 256;

    ll = l % 256;

    /* Calculate the contribution from the five corners */

    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);

    }

   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);

    }

   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);

    }

   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);

    }

   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! */

}