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  1. /*
  2.  * Mesa 3-D graphics library
  3.  * Version:  6.5
  4.  *
  5.  * Copyright (C) 2006  Brian Paul   All Rights Reserved.
  6.  *
  7.  * Permission is hereby granted, free of charge, to any person obtaining a
  8.  * copy of this software and associated documentation files (the "Software"),
  9.  * to deal in the Software without restriction, including without limitation
  10.  * the rights to use, copy, modify, merge, publish, distribute, sublicense,
  11.  * and/or sell copies of the Software, and to permit persons to whom the
  12.  * Software is furnished to do so, subject to the following conditions:
  13.  *
  14.  * The above copyright notice and this permission notice shall be included
  15.  * in all copies or substantial portions of the Software.
  16.  *
  17.  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
  18.  * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  19.  * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
  20.  * BRIAN PAUL BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN
  21.  * AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
  22.  * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
  23.  */
  24.  
  25. /*
  26.  * SimplexNoise1234
  27.  * Copyright (c) 2003-2005, Stefan Gustavson
  28.  *
  29.  * Contact: stegu@itn.liu.se
  30.  */
  31.  
  32. /**
  33.  * \file
  34.  * \brief C implementation of Perlin Simplex Noise over 1, 2, 3 and 4 dims.
  35.  * \author Stefan Gustavson (stegu@itn.liu.se)
  36.  *
  37.  *
  38.  * This implementation is "Simplex Noise" as presented by
  39.  * Ken Perlin at a relatively obscure and not often cited course
  40.  * session "Real-Time Shading" at Siggraph 2001 (before real
  41.  * time shading actually took on), under the title "hardware noise".
  42.  * The 3D function is numerically equivalent to his Java reference
  43.  * code available in the PDF course notes, although I re-implemented
  44.  * it from scratch to get more readable code. The 1D, 2D and 4D cases
  45.  * were implemented from scratch by me from Ken Perlin's text.
  46.  *
  47.  * This file has no dependencies on any other file, not even its own
  48.  * header file. The header file is made for use by external code only.
  49.  */
  50.  
  51.  
  52. #include "main/imports.h"
  53. #include "prog_noise.h"
  54.  
  55. #define FASTFLOOR(x) ( ((x)>0) ? ((int)x) : (((int)x)-1) )
  56.  
  57. /*
  58.  * ---------------------------------------------------------------------
  59.  * Static data
  60.  */
  61.  
  62. /**
  63.  * Permutation table. This is just a random jumble of all numbers 0-255,
  64.  * repeated twice to avoid wrapping the index at 255 for each lookup.
  65.  * This needs to be exactly the same for all instances on all platforms,
  66.  * so it's easiest to just keep it as static explicit data.
  67.  * This also removes the need for any initialisation of this class.
  68.  *
  69.  * Note that making this an int[] instead of a char[] might make the
  70.  * code run faster on platforms with a high penalty for unaligned single
  71.  * byte addressing. Intel x86 is generally single-byte-friendly, but
  72.  * some other CPUs are faster with 4-aligned reads.
  73.  * However, a char[] is smaller, which avoids cache trashing, and that
  74.  * is probably the most important aspect on most architectures.
  75.  * This array is accessed a *lot* by the noise functions.
  76.  * A vector-valued noise over 3D accesses it 96 times, and a
  77.  * float-valued 4D noise 64 times. We want this to fit in the cache!
  78.  */
  79. unsigned char perm[512] = { 151, 160, 137, 91, 90, 15,
  80.    131, 13, 201, 95, 96, 53, 194, 233, 7, 225, 140, 36, 103, 30, 69, 142, 8,
  81.       99, 37, 240, 21, 10, 23,
  82.    190, 6, 148, 247, 120, 234, 75, 0, 26, 197, 62, 94, 252, 219, 203, 117, 35,
  83.       11, 32, 57, 177, 33,
  84.    88, 237, 149, 56, 87, 174, 20, 125, 136, 171, 168, 68, 175, 74, 165, 71,
  85.       134, 139, 48, 27, 166,
  86.    77, 146, 158, 231, 83, 111, 229, 122, 60, 211, 133, 230, 220, 105, 92, 41,
  87.       55, 46, 245, 40, 244,
  88.    102, 143, 54, 65, 25, 63, 161, 1, 216, 80, 73, 209, 76, 132, 187, 208, 89,
  89.       18, 169, 200, 196,
  90.    135, 130, 116, 188, 159, 86, 164, 100, 109, 198, 173, 186, 3, 64, 52, 217,
  91.       226, 250, 124, 123,
  92.    5, 202, 38, 147, 118, 126, 255, 82, 85, 212, 207, 206, 59, 227, 47, 16, 58,
  93.       17, 182, 189, 28, 42,
  94.    223, 183, 170, 213, 119, 248, 152, 2, 44, 154, 163, 70, 221, 153, 101, 155,
  95.       167, 43, 172, 9,
  96.    129, 22, 39, 253, 19, 98, 108, 110, 79, 113, 224, 232, 178, 185, 112, 104,
  97.       218, 246, 97, 228,
  98.    251, 34, 242, 193, 238, 210, 144, 12, 191, 179, 162, 241, 81, 51, 145, 235,
  99.       249, 14, 239, 107,
  100.    49, 192, 214, 31, 181, 199, 106, 157, 184, 84, 204, 176, 115, 121, 50, 45,
  101.       127, 4, 150, 254,
  102.    138, 236, 205, 93, 222, 114, 67, 29, 24, 72, 243, 141, 128, 195, 78, 66,
  103.       215, 61, 156, 180,
  104.    151, 160, 137, 91, 90, 15,
  105.    131, 13, 201, 95, 96, 53, 194, 233, 7, 225, 140, 36, 103, 30, 69, 142, 8,
  106.       99, 37, 240, 21, 10, 23,
  107.    190, 6, 148, 247, 120, 234, 75, 0, 26, 197, 62, 94, 252, 219, 203, 117, 35,
  108.       11, 32, 57, 177, 33,
  109.    88, 237, 149, 56, 87, 174, 20, 125, 136, 171, 168, 68, 175, 74, 165, 71,
  110.       134, 139, 48, 27, 166,
  111.    77, 146, 158, 231, 83, 111, 229, 122, 60, 211, 133, 230, 220, 105, 92, 41,
  112.       55, 46, 245, 40, 244,
  113.    102, 143, 54, 65, 25, 63, 161, 1, 216, 80, 73, 209, 76, 132, 187, 208, 89,
  114.       18, 169, 200, 196,
  115.    135, 130, 116, 188, 159, 86, 164, 100, 109, 198, 173, 186, 3, 64, 52, 217,
  116.       226, 250, 124, 123,
  117.    5, 202, 38, 147, 118, 126, 255, 82, 85, 212, 207, 206, 59, 227, 47, 16, 58,
  118.       17, 182, 189, 28, 42,
  119.    223, 183, 170, 213, 119, 248, 152, 2, 44, 154, 163, 70, 221, 153, 101, 155,
  120.       167, 43, 172, 9,
  121.    129, 22, 39, 253, 19, 98, 108, 110, 79, 113, 224, 232, 178, 185, 112, 104,
  122.       218, 246, 97, 228,
  123.    251, 34, 242, 193, 238, 210, 144, 12, 191, 179, 162, 241, 81, 51, 145, 235,
  124.       249, 14, 239, 107,
  125.    49, 192, 214, 31, 181, 199, 106, 157, 184, 84, 204, 176, 115, 121, 50, 45,
  126.       127, 4, 150, 254,
  127.    138, 236, 205, 93, 222, 114, 67, 29, 24, 72, 243, 141, 128, 195, 78, 66,
  128.       215, 61, 156, 180
  129. };
  130.  
  131. /*
  132.  * ---------------------------------------------------------------------
  133.  */
  134.  
  135. /*
  136.  * Helper functions to compute gradients-dot-residualvectors (1D to 4D)
  137.  * Note that these generate gradients of more than unit length. To make
  138.  * a close match with the value range of classic Perlin noise, the final
  139.  * noise values need to be rescaled to fit nicely within [-1,1].
  140.  * (The simplex noise functions as such also have different scaling.)
  141.  * Note also that these noise functions are the most practical and useful
  142.  * signed version of Perlin noise. To return values according to the
  143.  * RenderMan specification from the SL noise() and pnoise() functions,
  144.  * the noise values need to be scaled and offset to [0,1], like this:
  145.  * float SLnoise = (SimplexNoise1234::noise(x,y,z) + 1.0) * 0.5;
  146.  */
  147.  
  148. static float
  149. grad1(int hash, float x)
  150. {
  151.    int h = hash & 15;
  152.    float grad = 1.0f + (h & 7); /* Gradient value 1.0, 2.0, ..., 8.0 */
  153.    if (h & 8)
  154.       grad = -grad;             /* Set a random sign for the gradient */
  155.    return (grad * x);           /* Multiply the gradient with the distance */
  156. }
  157.  
  158. static float
  159. grad2(int hash, float x, float y)
  160. {
  161.    int h = hash & 7;            /* Convert low 3 bits of hash code */
  162.    float u = h < 4 ? x : y;     /* into 8 simple gradient directions, */
  163.    float v = h < 4 ? y : x;     /* and compute the dot product with (x,y). */
  164.    return ((h & 1) ? -u : u) + ((h & 2) ? -2.0f * v : 2.0f * v);
  165. }
  166.  
  167. static float
  168. grad3(int hash, float x, float y, float z)
  169. {
  170.    int h = hash & 15;           /* Convert low 4 bits of hash code into 12 simple */
  171.    float u = h < 8 ? x : y;     /* gradient directions, and compute dot product. */
  172.    float v = h < 4 ? y : h == 12 || h == 14 ? x : z;    /* Fix repeats at h = 12 to 15 */
  173.    return ((h & 1) ? -u : u) + ((h & 2) ? -v : v);
  174. }
  175.  
  176. static float
  177. grad4(int hash, float x, float y, float z, float t)
  178. {
  179.    int h = hash & 31;           /* Convert low 5 bits of hash code into 32 simple */
  180.    float u = h < 24 ? x : y;    /* gradient directions, and compute dot product. */
  181.    float v = h < 16 ? y : z;
  182.    float w = h < 8 ? z : t;
  183.    return ((h & 1) ? -u : u) + ((h & 2) ? -v : v) + ((h & 4) ? -w : w);
  184. }
  185.  
  186. /**
  187.  * A lookup table to traverse the simplex around a given point in 4D.
  188.  * Details can be found where this table is used, in the 4D noise method.
  189.  * TODO: This should not be required, backport it from Bill's GLSL code!
  190.  */
  191. static unsigned char simplex[64][4] = {
  192.    {0, 1, 2, 3}, {0, 1, 3, 2}, {0, 0, 0, 0}, {0, 2, 3, 1},
  193.    {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {1, 2, 3, 0},
  194.    {0, 2, 1, 3}, {0, 0, 0, 0}, {0, 3, 1, 2}, {0, 3, 2, 1},
  195.    {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {1, 3, 2, 0},
  196.    {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0},
  197.    {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0},
  198.    {1, 2, 0, 3}, {0, 0, 0, 0}, {1, 3, 0, 2}, {0, 0, 0, 0},
  199.    {0, 0, 0, 0}, {0, 0, 0, 0}, {2, 3, 0, 1}, {2, 3, 1, 0},
  200.    {1, 0, 2, 3}, {1, 0, 3, 2}, {0, 0, 0, 0}, {0, 0, 0, 0},
  201.    {0, 0, 0, 0}, {2, 0, 3, 1}, {0, 0, 0, 0}, {2, 1, 3, 0},
  202.    {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0},
  203.    {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0},
  204.    {2, 0, 1, 3}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0},
  205.    {3, 0, 1, 2}, {3, 0, 2, 1}, {0, 0, 0, 0}, {3, 1, 2, 0},
  206.    {2, 1, 0, 3}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0},
  207.    {3, 1, 0, 2}, {0, 0, 0, 0}, {3, 2, 0, 1}, {3, 2, 1, 0}
  208. };
  209.  
  210.  
  211. /** 1D simplex noise */
  212. GLfloat
  213. _mesa_noise1(GLfloat x)
  214. {
  215.    int i0 = FASTFLOOR(x);
  216.    int i1 = i0 + 1;
  217.    float x0 = x - i0;
  218.    float x1 = x0 - 1.0f;
  219.    float t1 = 1.0f - x1 * x1;
  220.    float n0, n1;
  221.  
  222.    float t0 = 1.0f - x0 * x0;
  223. /*  if(t0 < 0.0f) t0 = 0.0f; // this never happens for the 1D case */
  224.    t0 *= t0;
  225.    n0 = t0 * t0 * grad1(perm[i0 & 0xff], x0);
  226.  
  227. /*  if(t1 < 0.0f) t1 = 0.0f; // this never happens for the 1D case */
  228.    t1 *= t1;
  229.    n1 = t1 * t1 * grad1(perm[i1 & 0xff], x1);
  230.    /* The maximum value of this noise is 8*(3/4)^4 = 2.53125 */
  231.    /* A factor of 0.395 would scale to fit exactly within [-1,1], but */
  232.    /* we want to match PRMan's 1D noise, so we scale it down some more. */
  233.    return 0.25f * (n0 + n1);
  234. }
  235.  
  236.  
  237. /** 2D simplex noise */
  238. GLfloat
  239. _mesa_noise2(GLfloat x, GLfloat y)
  240. {
  241. #define F2 0.366025403f         /* F2 = 0.5*(sqrt(3.0)-1.0) */
  242. #define G2 0.211324865f         /* G2 = (3.0-Math.sqrt(3.0))/6.0 */
  243.  
  244.    float n0, n1, n2;            /* Noise contributions from the three corners */
  245.  
  246.    /* Skew the input space to determine which simplex cell we're in */
  247.    float s = (x + y) * F2;      /* Hairy factor for 2D */
  248.    float xs = x + s;
  249.    float ys = y + s;
  250.    int i = FASTFLOOR(xs);
  251.    int j = FASTFLOOR(ys);
  252.  
  253.    float t = (float) (i + j) * G2;
  254.    float X0 = i - t;            /* Unskew the cell origin back to (x,y) space */
  255.    float Y0 = j - t;
  256.    float x0 = x - X0;           /* The x,y distances from the cell origin */
  257.    float y0 = y - Y0;
  258.  
  259.    float x1, y1, x2, y2;
  260.    int ii, jj;
  261.    float t0, t1, t2;
  262.  
  263.    /* For the 2D case, the simplex shape is an equilateral triangle. */
  264.    /* Determine which simplex we are in. */
  265.    int i1, j1;                  /* Offsets for second (middle) corner of simplex in (i,j) coords */
  266.    if (x0 > y0) {
  267.       i1 = 1;
  268.       j1 = 0;
  269.    }                            /* lower triangle, XY order: (0,0)->(1,0)->(1,1) */
  270.    else {
  271.       i1 = 0;
  272.       j1 = 1;
  273.    }                            /* upper triangle, YX order: (0,0)->(0,1)->(1,1) */
  274.  
  275.    /* A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and */
  276.    /* a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where */
  277.    /* c = (3-sqrt(3))/6 */
  278.  
  279.    x1 = x0 - i1 + G2;           /* Offsets for middle corner in (x,y) unskewed coords */
  280.    y1 = y0 - j1 + G2;
  281.    x2 = x0 - 1.0f + 2.0f * G2;  /* Offsets for last corner in (x,y) unskewed coords */
  282.    y2 = y0 - 1.0f + 2.0f * G2;
  283.  
  284.    /* Wrap the integer indices at 256, to avoid indexing perm[] out of bounds */
  285.    ii = i % 256;
  286.    jj = j % 256;
  287.  
  288.    /* Calculate the contribution from the three corners */
  289.    t0 = 0.5f - x0 * x0 - y0 * y0;
  290.    if (t0 < 0.0f)
  291.       n0 = 0.0f;
  292.    else {
  293.       t0 *= t0;
  294.       n0 = t0 * t0 * grad2(perm[ii + perm[jj]], x0, y0);
  295.    }
  296.  
  297.    t1 = 0.5f - x1 * x1 - y1 * y1;
  298.    if (t1 < 0.0f)
  299.       n1 = 0.0f;
  300.    else {
  301.       t1 *= t1;
  302.       n1 = t1 * t1 * grad2(perm[ii + i1 + perm[jj + j1]], x1, y1);
  303.    }
  304.  
  305.    t2 = 0.5f - x2 * x2 - y2 * y2;
  306.    if (t2 < 0.0f)
  307.       n2 = 0.0f;
  308.    else {
  309.       t2 *= t2;
  310.       n2 = t2 * t2 * grad2(perm[ii + 1 + perm[jj + 1]], x2, y2);
  311.    }
  312.  
  313.    /* Add contributions from each corner to get the final noise value. */
  314.    /* The result is scaled to return values in the interval [-1,1]. */
  315.    return 40.0f * (n0 + n1 + n2);       /* TODO: The scale factor is preliminary! */
  316. }
  317.  
  318.  
  319. /** 3D simplex noise */
  320. GLfloat
  321. _mesa_noise3(GLfloat x, GLfloat y, GLfloat z)
  322. {
  323. /* Simple skewing factors for the 3D case */
  324. #define F3 0.333333333f
  325. #define G3 0.166666667f
  326.  
  327.    float n0, n1, n2, n3;        /* Noise contributions from the four corners */
  328.  
  329.    /* Skew the input space to determine which simplex cell we're in */
  330.    float s = (x + y + z) * F3;  /* Very nice and simple skew factor for 3D */
  331.    float xs = x + s;
  332.    float ys = y + s;
  333.    float zs = z + s;
  334.    int i = FASTFLOOR(xs);
  335.    int j = FASTFLOOR(ys);
  336.    int k = FASTFLOOR(zs);
  337.  
  338.    float t = (float) (i + j + k) * G3;
  339.    float X0 = i - t;            /* Unskew the cell origin back to (x,y,z) space */
  340.    float Y0 = j - t;
  341.    float Z0 = k - t;
  342.    float x0 = x - X0;           /* The x,y,z distances from the cell origin */
  343.    float y0 = y - Y0;
  344.    float z0 = z - Z0;
  345.  
  346.    float x1, y1, z1, x2, y2, z2, x3, y3, z3;
  347.    int ii, jj, kk;
  348.    float t0, t1, t2, t3;
  349.  
  350.    /* For the 3D case, the simplex shape is a slightly irregular tetrahedron. */
  351.    /* Determine which simplex we are in. */
  352.    int i1, j1, k1;              /* Offsets for second corner of simplex in (i,j,k) coords */
  353.    int i2, j2, k2;              /* Offsets for third corner of simplex in (i,j,k) coords */
  354.  
  355. /* This code would benefit from a backport from the GLSL version! */
  356.    if (x0 >= y0) {
  357.       if (y0 >= z0) {
  358.          i1 = 1;
  359.          j1 = 0;
  360.          k1 = 0;
  361.          i2 = 1;
  362.          j2 = 1;
  363.          k2 = 0;
  364.       }                         /* X Y Z order */
  365.       else if (x0 >= z0) {
  366.          i1 = 1;
  367.          j1 = 0;
  368.          k1 = 0;
  369.          i2 = 1;
  370.          j2 = 0;
  371.          k2 = 1;
  372.       }                         /* X Z Y order */
  373.       else {
  374.          i1 = 0;
  375.          j1 = 0;
  376.          k1 = 1;
  377.          i2 = 1;
  378.          j2 = 0;
  379.          k2 = 1;
  380.       }                         /* Z X Y order */
  381.    }
  382.    else {                       /* x0<y0 */
  383.       if (y0 < z0) {
  384.          i1 = 0;
  385.          j1 = 0;
  386.          k1 = 1;
  387.          i2 = 0;
  388.          j2 = 1;
  389.          k2 = 1;
  390.       }                         /* Z Y X order */
  391.       else if (x0 < z0) {
  392.          i1 = 0;
  393.          j1 = 1;
  394.          k1 = 0;
  395.          i2 = 0;
  396.          j2 = 1;
  397.          k2 = 1;
  398.       }                         /* Y Z X order */
  399.       else {
  400.          i1 = 0;
  401.          j1 = 1;
  402.          k1 = 0;
  403.          i2 = 1;
  404.          j2 = 1;
  405.          k2 = 0;
  406.       }                         /* Y X Z order */
  407.    }
  408.  
  409.    /* A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in
  410.     * (x,y,z), a step of (0,1,0) in (i,j,k) means a step of
  411.     * (-c,1-c,-c) in (x,y,z), and a step of (0,0,1) in (i,j,k) means a
  412.     * step of (-c,-c,1-c) in (x,y,z), where c = 1/6.
  413.     */
  414.  
  415.    x1 = x0 - i1 + G3;         /* Offsets for second corner in (x,y,z) coords */
  416.    y1 = y0 - j1 + G3;
  417.    z1 = z0 - k1 + G3;
  418.    x2 = x0 - i2 + 2.0f * G3;  /* Offsets for third corner in (x,y,z) coords */
  419.    y2 = y0 - j2 + 2.0f * G3;
  420.    z2 = z0 - k2 + 2.0f * G3;
  421.    x3 = x0 - 1.0f + 3.0f * G3;/* Offsets for last corner in (x,y,z) coords */
  422.    y3 = y0 - 1.0f + 3.0f * G3;
  423.    z3 = z0 - 1.0f + 3.0f * G3;
  424.  
  425.    /* Wrap the integer indices at 256 to avoid indexing perm[] out of bounds */
  426.    ii = i % 256;
  427.    jj = j % 256;
  428.    kk = k % 256;
  429.  
  430.    /* Calculate the contribution from the four corners */
  431.    t0 = 0.6f - x0 * x0 - y0 * y0 - z0 * z0;
  432.    if (t0 < 0.0f)
  433.       n0 = 0.0f;
  434.    else {
  435.       t0 *= t0;
  436.       n0 = t0 * t0 * grad3(perm[ii + perm[jj + perm[kk]]], x0, y0, z0);
  437.    }
  438.  
  439.    t1 = 0.6f - x1 * x1 - y1 * y1 - z1 * z1;
  440.    if (t1 < 0.0f)
  441.       n1 = 0.0f;
  442.    else {
  443.       t1 *= t1;
  444.       n1 =
  445.          t1 * t1 * grad3(perm[ii + i1 + perm[jj + j1 + perm[kk + k1]]], x1,
  446.                          y1, z1);
  447.    }
  448.  
  449.    t2 = 0.6f - x2 * x2 - y2 * y2 - z2 * z2;
  450.    if (t2 < 0.0f)
  451.       n2 = 0.0f;
  452.    else {
  453.       t2 *= t2;
  454.       n2 =
  455.          t2 * t2 * grad3(perm[ii + i2 + perm[jj + j2 + perm[kk + k2]]], x2,
  456.                          y2, z2);
  457.    }
  458.  
  459.    t3 = 0.6f - x3 * x3 - y3 * y3 - z3 * z3;
  460.    if (t3 < 0.0f)
  461.       n3 = 0.0f;
  462.    else {
  463.       t3 *= t3;
  464.       n3 =
  465.          t3 * t3 * grad3(perm[ii + 1 + perm[jj + 1 + perm[kk + 1]]], x3, y3,
  466.                          z3);
  467.    }
  468.  
  469.    /* Add contributions from each corner to get the final noise value.
  470.     * The result is scaled to stay just inside [-1,1]
  471.     */
  472.    return 32.0f * (n0 + n1 + n2 + n3);  /* TODO: The scale factor is preliminary! */
  473. }
  474.  
  475.  
  476. /** 4D simplex noise */
  477. GLfloat
  478. _mesa_noise4(GLfloat x, GLfloat y, GLfloat z, GLfloat w)
  479. {
  480.    /* The skewing and unskewing factors are hairy again for the 4D case */
  481. #define F4 0.309016994f         /* F4 = (Math.sqrt(5.0)-1.0)/4.0 */
  482. #define G4 0.138196601f         /* G4 = (5.0-Math.sqrt(5.0))/20.0 */
  483.  
  484.    float n0, n1, n2, n3, n4;    /* Noise contributions from the five corners */
  485.  
  486.    /* Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in */
  487.    float s = (x + y + z + w) * F4;      /* Factor for 4D skewing */
  488.    float xs = x + s;
  489.    float ys = y + s;
  490.    float zs = z + s;
  491.    float ws = w + s;
  492.    int i = FASTFLOOR(xs);
  493.    int j = FASTFLOOR(ys);
  494.    int k = FASTFLOOR(zs);
  495.    int l = FASTFLOOR(ws);
  496.  
  497.    float t = (i + j + k + l) * G4;      /* Factor for 4D unskewing */
  498.    float X0 = i - t;            /* Unskew the cell origin back to (x,y,z,w) space */
  499.    float Y0 = j - t;
  500.    float Z0 = k - t;
  501.    float W0 = l - t;
  502.  
  503.    float x0 = x - X0;           /* The x,y,z,w distances from the cell origin */
  504.    float y0 = y - Y0;
  505.    float z0 = z - Z0;
  506.    float w0 = w - W0;
  507.  
  508.    /* For the 4D case, the simplex is a 4D shape I won't even try to describe.
  509.     * To find out which of the 24 possible simplices we're in, we need to
  510.     * determine the magnitude ordering of x0, y0, z0 and w0.
  511.     * The method below is a good way of finding the ordering of x,y,z,w and
  512.     * then find the correct traversal order for the simplex we're in.
  513.     * First, six pair-wise comparisons are performed between each possible pair
  514.     * of the four coordinates, and the results are used to add up binary bits
  515.     * for an integer index.
  516.     */
  517.    int c1 = (x0 > y0) ? 32 : 0;
  518.    int c2 = (x0 > z0) ? 16 : 0;
  519.    int c3 = (y0 > z0) ? 8 : 0;
  520.    int c4 = (x0 > w0) ? 4 : 0;
  521.    int c5 = (y0 > w0) ? 2 : 0;
  522.    int c6 = (z0 > w0) ? 1 : 0;
  523.    int c = c1 + c2 + c3 + c4 + c5 + c6;
  524.  
  525.    int i1, j1, k1, l1;  /* The integer offsets for the second simplex corner */
  526.    int i2, j2, k2, l2;  /* The integer offsets for the third simplex corner */
  527.    int i3, j3, k3, l3;  /* The integer offsets for the fourth simplex corner */
  528.  
  529.    float x1, y1, z1, w1, x2, y2, z2, w2, x3, y3, z3, w3, x4, y4, z4, w4;
  530.    int ii, jj, kk, ll;
  531.    float t0, t1, t2, t3, t4;
  532.  
  533.    /*
  534.     * simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some
  535.     * order.  Many values of c will never occur, since e.g. x>y>z>w
  536.     * makes x<z, y<w and x<w impossible. Only the 24 indices which
  537.     * have non-zero entries make any sense.  We use a thresholding to
  538.     * set the coordinates in turn from the largest magnitude.  The
  539.     * number 3 in the "simplex" array is at the position of the
  540.     * largest coordinate.
  541.     */
  542.    i1 = simplex[c][0] >= 3 ? 1 : 0;
  543.    j1 = simplex[c][1] >= 3 ? 1 : 0;
  544.    k1 = simplex[c][2] >= 3 ? 1 : 0;
  545.    l1 = simplex[c][3] >= 3 ? 1 : 0;
  546.    /* The number 2 in the "simplex" array is at the second largest coordinate. */
  547.    i2 = simplex[c][0] >= 2 ? 1 : 0;
  548.    j2 = simplex[c][1] >= 2 ? 1 : 0;
  549.    k2 = simplex[c][2] >= 2 ? 1 : 0;
  550.    l2 = simplex[c][3] >= 2 ? 1 : 0;
  551.    /* The number 1 in the "simplex" array is at the second smallest coordinate. */
  552.    i3 = simplex[c][0] >= 1 ? 1 : 0;
  553.    j3 = simplex[c][1] >= 1 ? 1 : 0;
  554.    k3 = simplex[c][2] >= 1 ? 1 : 0;
  555.    l3 = simplex[c][3] >= 1 ? 1 : 0;
  556.    /* The fifth corner has all coordinate offsets = 1, so no need to look that up. */
  557.  
  558.    x1 = x0 - i1 + G4;           /* Offsets for second corner in (x,y,z,w) coords */
  559.    y1 = y0 - j1 + G4;
  560.    z1 = z0 - k1 + G4;
  561.    w1 = w0 - l1 + G4;
  562.    x2 = x0 - i2 + 2.0f * G4;    /* Offsets for third corner in (x,y,z,w) coords */
  563.    y2 = y0 - j2 + 2.0f * G4;
  564.    z2 = z0 - k2 + 2.0f * G4;
  565.    w2 = w0 - l2 + 2.0f * G4;
  566.    x3 = x0 - i3 + 3.0f * G4;    /* Offsets for fourth corner in (x,y,z,w) coords */
  567.    y3 = y0 - j3 + 3.0f * G4;
  568.    z3 = z0 - k3 + 3.0f * G4;
  569.    w3 = w0 - l3 + 3.0f * G4;
  570.    x4 = x0 - 1.0f + 4.0f * G4;  /* Offsets for last corner in (x,y,z,w) coords */
  571.    y4 = y0 - 1.0f + 4.0f * G4;
  572.    z4 = z0 - 1.0f + 4.0f * G4;
  573.    w4 = w0 - 1.0f + 4.0f * G4;
  574.  
  575.    /* Wrap the integer indices at 256, to avoid indexing perm[] out of bounds */
  576.    ii = i % 256;
  577.    jj = j % 256;
  578.    kk = k % 256;
  579.    ll = l % 256;
  580.  
  581.    /* Calculate the contribution from the five corners */
  582.    t0 = 0.6f - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0;
  583.    if (t0 < 0.0f)
  584.       n0 = 0.0f;
  585.    else {
  586.       t0 *= t0;
  587.       n0 =
  588.          t0 * t0 * grad4(perm[ii + perm[jj + perm[kk + perm[ll]]]], x0, y0,
  589.                          z0, w0);
  590.    }
  591.  
  592.    t1 = 0.6f - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1;
  593.    if (t1 < 0.0f)
  594.       n1 = 0.0f;
  595.    else {
  596.       t1 *= t1;
  597.       n1 =
  598.          t1 * t1 *
  599.          grad4(perm[ii + i1 + perm[jj + j1 + perm[kk + k1 + perm[ll + l1]]]],
  600.                x1, y1, z1, w1);
  601.    }
  602.  
  603.    t2 = 0.6f - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2;
  604.    if (t2 < 0.0f)
  605.       n2 = 0.0f;
  606.    else {
  607.       t2 *= t2;
  608.       n2 =
  609.          t2 * t2 *
  610.          grad4(perm[ii + i2 + perm[jj + j2 + perm[kk + k2 + perm[ll + l2]]]],
  611.                x2, y2, z2, w2);
  612.    }
  613.  
  614.    t3 = 0.6f - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3;
  615.    if (t3 < 0.0f)
  616.       n3 = 0.0f;
  617.    else {
  618.       t3 *= t3;
  619.       n3 =
  620.          t3 * t3 *
  621.          grad4(perm[ii + i3 + perm[jj + j3 + perm[kk + k3 + perm[ll + l3]]]],
  622.                x3, y3, z3, w3);
  623.    }
  624.  
  625.    t4 = 0.6f - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4;
  626.    if (t4 < 0.0f)
  627.       n4 = 0.0f;
  628.    else {
  629.       t4 *= t4;
  630.       n4 =
  631.          t4 * t4 *
  632.          grad4(perm[ii + 1 + perm[jj + 1 + perm[kk + 1 + perm[ll + 1]]]], x4,
  633.                y4, z4, w4);
  634.    }
  635.  
  636.    /* Sum up and scale the result to cover the range [-1,1] */
  637.    return 27.0f * (n0 + n1 + n2 + n3 + n4);     /* TODO: The scale factor is preliminary! */
  638. }
  639.