slang_library_noise.c

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/*
 * 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: 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.
 */


#include "main/imports.h"
#include "slang_library_noise.h"

#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 = (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 */
GLfloat _slang_library_noise1 (GLfloat 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 */
GLfloat _slang_library_noise2 (GLfloat x, GLfloat 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 */
GLfloat _slang_library_noise3 (GLfloat x, GLfloat y, GLfloat 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 */
GLfloat _slang_library_noise4 (GLfloat x, GLfloat y, GLfloat z, GLfloat 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! */
}