src/mesa/shader/slang/slang_library_noise.c

   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 #include "imports.h"
  26 #include "slang_library_noise.h"
  27
  28 /*
  29  * SimplexNoise1234
  30  * Copyright © 2003-2005, Stefan Gustavson
  31  *
  32  * Contact: stegu@itn.liu.se
  33  *
  34  * This library is free software; you can redistribute it and/or
  35  * modify it under the terms of the GNU General Public
  36  * License as published by the Free Software Foundation; either
  37  * version 2 of the License, or (at your option) any later version.
  38  *
  39  * This library is distributed in the hope that it will be useful,
  40  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  41  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  42  * General Public License for more details.
  43  *
  44  * You should have received a copy of the GNU General Public
  45  * License along with this library; if not, write to the Free Software
  46  * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  47  */
  48
  49 /** \file
  50     \brief C implementation of Perlin Simplex Noise over 1,2,3, and 4 dimensions.
  51     \author Stefan Gustavson (stegu@itn.liu.se)
  52 */
  53
  54 /*
  55  * This implementation is "Simplex Noise" as presented by
  56  * Ken Perlin at a relatively obscure and not often cited course
  57  * session "Real-Time Shading" at Siggraph 2001 (before real
  58  * time shading actually took on), under the title "hardware noise".
  59  * The 3D function is numerically equivalent to his Java reference
  60  * code available in the PDF course notes, although I re-implemented
  61  * it from scratch to get more readable code. The 1D, 2D and 4D cases
  62  * were implemented from scratch by me from Ken Perlin's text.
  63  *
  64  * This file has no dependencies on any other file, not even its own
  65  * header file. The header file is made for use by external code only.
  66  */
  67
  68
  69 #define FASTFLOOR(x) ( ((x)>0) ? ((int)x) : (((int)x)-1) )
  70
  71 /*
  72  * ---------------------------------------------------------------------
  73  * Static data
  74  */
  75
  76 /*
  77  * Permutation table. This is just a random jumble of all numbers 0-255,
  78  * repeated twice to avoid wrapping the index at 255 for each lookup.
  79  * This needs to be exactly the same for all instances on all platforms,
  80  * so it's easiest to just keep it as static explicit data.
  81  * This also removes the need for any initialisation of this class.
  82  *
  83  * Note that making this an int[] instead of a char[] might make the
  84  * code run faster on platforms with a high penalty for unaligned single
  85  * byte addressing. Intel x86 is generally single-byte-friendly, but
  86  * some other CPUs are faster with 4-aligned reads.
  87  * However, a char[] is smaller, which avoids cache trashing, and that
  88  * is probably the most important aspect on most architectures.
  89  * This array is accessed a *lot* by the noise functions.
  90  * A vector-valued noise over 3D accesses it 96 times, and a
  91  * float-valued 4D noise 64 times. We want this to fit in the cache!
  92  */
  93 unsigned char perm[512] = {151,160,137,91,90,15,
  94   131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23,
  95   190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33,
  96   88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166,
  97   77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244,
  98   102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196,
  99   135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123,
 100   5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42,
 101   223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9,
 102   129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228,
 103   251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107,
 104   49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254,
 105   138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180,
 106   151,160,137,91,90,15,
 107   131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23,
 108   190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33,
 109   88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166,
 110   77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244,
 111   102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196,
 112   135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123,
 113   5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42,
 114   223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9,
 115   129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228,
 116   251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107,
 117   49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254,
 118   138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180
 119 };
 120
 121 /*
 122  * ---------------------------------------------------------------------
 123  */
 124
 125 /*
 126  * Helper functions to compute gradients-dot-residualvectors (1D to 4D)
 127  * Note that these generate gradients of more than unit length. To make
 128  * a close match with the value range of classic Perlin noise, the final
 129  * noise values need to be rescaled to fit nicely within [-1,1].
 130  * (The simplex noise functions as such also have different scaling.)
 131  * Note also that these noise functions are the most practical and useful
 132  * signed version of Perlin noise. To return values according to the
 133  * RenderMan specification from the SL noise() and pnoise() functions,
 134  * the noise values need to be scaled and offset to [0,1], like this:
 135  * float SLnoise = (SimplexNoise1234::noise(x,y,z) + 1.0) * 0.5;
 136  */
 137
 138 static float  grad1( int hash, float x ) {
 139     int h = hash & 15;
 140     float grad = 1.0f + (h & 7);   /* Gradient value 1.0, 2.0, ..., 8.0 */
 141     if (h&8) grad = -grad;         /* Set a random sign for the gradient */
 142     return ( grad * x );           /* Multiply the gradient with the distance */
 143 }
 144
 145 static float  grad2( int hash, float x, float y ) {
 146     int h = hash & 7;      /* Convert low 3 bits of hash code */
 147     float u = h<4 ? x : y;  /* into 8 simple gradient directions, */
 148     float v = h<4 ? y : x;  /* and compute the dot product with (x,y). */
 149     return ((h&1)? -u : u) + ((h&2)? -2.0f*v : 2.0f*v);
 150 }
 151
 152 static float  grad3( int hash, float x, float y , float z ) {
 153     int h = hash & 15;     /* Convert low 4 bits of hash code into 12 simple */
 154     float u = h<8 ? x : y; /* gradient directions, and compute dot product. */
 155     float v = h<4 ? y : h==12||h==14 ? x : z; /* Fix repeats at h = 12 to 15 */
 156     return ((h&1)? -u : u) + ((h&2)? -v : v);
 157 }
 158
 159 static float  grad4( int hash, float x, float y, float z, float t ) {
 160     int h = hash & 31;      /* Convert low 5 bits of hash code into 32 simple */
 161     float u = h<24 ? x : y; /* gradient directions, and compute dot product. */
 162     float v = h<16 ? y : z;
 163     float w = h<8 ? z : t;
 164     return ((h&1)? -u : u) + ((h&2)? -v : v) + ((h&4)? -w : w);
 165 }
 166
 167   /* A lookup table to traverse the simplex around a given point in 4D. */
 168   /* Details can be found where this table is used, in the 4D noise method. */
 169   /* TODO: This should not be required, backport it from Bill's GLSL code! */
 170   static unsigned char simplex[64][4] = {
 171     {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},
 172     {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},
 173     {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},
 174     {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},
 175     {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},
 176     {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},
 177     {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},
 178     {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}};
 179
 180 /* 1D simplex noise */
 181 GLfloat _slang_library_noise1 (GLfloat x)
 182 {
 183   int i0 = FASTFLOOR(x);
 184   int i1 = i0 + 1;
 185   float x0 = x - i0;
 186   float x1 = x0 - 1.0f;
 187   float t1 = 1.0f - x1*x1;
 188   float n0, n1;
 189
 190   float t0 = 1.0f - x0*x0;
 191 /*  if(t0 < 0.0f) t0 = 0.0f; // this never happens for the 1D case */
 192   t0 *= t0;
 193   n0 = t0 * t0 * grad1(perm[i0 & 0xff], x0);
 194
 195 /*  if(t1 < 0.0f) t1 = 0.0f; // this never happens for the 1D case */
 196   t1 *= t1;
 197   n1 = t1 * t1 * grad1(perm[i1 & 0xff], x1);
 198   /* The maximum value of this noise is 8*(3/4)^4 = 2.53125 */
 199   /* A factor of 0.395 would scale to fit exactly within [-1,1], but */
 200   /* we want to match PRMan's 1D noise, so we scale it down some more. */
 201   return 0.25f * (n0 + n1);
 202 }
 203
 204 /* 2D simplex noise */
 205 GLfloat _slang_library_noise2 (GLfloat x, GLfloat y)
 206 {
 207 #define F2 0.366025403f /* F2 = 0.5*(sqrt(3.0)-1.0) */
 208 #define G2 0.211324865f /* G2 = (3.0-Math.sqrt(3.0))/6.0 */
 209
 210     float n0, n1, n2; /* Noise contributions from the three corners */
 211
 212     /* Skew the input space to determine which simplex cell we're in */
 213     float s = (x+y)*F2; /* Hairy factor for 2D */
 214     float xs = x + s;
 215     float ys = y + s;
 216     int i = FASTFLOOR(xs);
 217     int j = FASTFLOOR(ys);
 218
 219     float t = (float)(i+j)*G2;
 220     float X0 = i-t; /* Unskew the cell origin back to (x,y) space */
 221     float Y0 = j-t;
 222     float x0 = x-X0; /* The x,y distances from the cell origin */
 223     float y0 = y-Y0;
 224
 225     float x1, y1, x2, y2;
 226     int ii, jj;
 227     float t0, t1, t2;
 228
 229     /* For the 2D case, the simplex shape is an equilateral triangle. */
 230     /* Determine which simplex we are in. */
 231     int i1, j1; /* Offsets for second (middle) corner of simplex in (i,j) coords */
 232     if(x0>y0) {i1=1; j1=0;} /* lower triangle, XY order: (0,0)->(1,0)->(1,1) */
 233     else {i1=0; j1=1;}      /* upper triangle, YX order: (0,0)->(0,1)->(1,1) */
 234
 235     /* A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and */
 236     /* a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where */
 237     /* c = (3-sqrt(3))/6 */
 238
 239     x1 = x0 - i1 + G2; /* Offsets for middle corner in (x,y) unskewed coords */
 240     y1 = y0 - j1 + G2;
 241     x2 = x0 - 1.0f + 2.0f * G2; /* Offsets for last corner in (x,y) unskewed coords */
 242     y2 = y0 - 1.0f + 2.0f * G2;
 243
 244     /* Wrap the integer indices at 256, to avoid indexing perm[] out of bounds */
 245     ii = i % 256;
 246     jj = j % 256;
 247
 248     /* Calculate the contribution from the three corners */
 249     t0 = 0.5f - x0*x0-y0*y0;
 250     if(t0 < 0.0f) n0 = 0.0f;
 251     else {
 252       t0 *= t0;
 253       n0 = t0 * t0 * grad2(perm[ii+perm[jj]], x0, y0);
 254     }
 255
 256     t1 = 0.5f - x1*x1-y1*y1;
 257     if(t1 < 0.0f) n1 = 0.0f;
 258     else {
 259       t1 *= t1;
 260       n1 = t1 * t1 * grad2(perm[ii+i1+perm[jj+j1]], x1, y1);
 261     }
 262
 263     t2 = 0.5f - x2*x2-y2*y2;
 264     if(t2 < 0.0f) n2 = 0.0f;
 265     else {
 266       t2 *= t2;
 267       n2 = t2 * t2 * grad2(perm[ii+1+perm[jj+1]], x2, y2);
 268     }
 269
 270     /* Add contributions from each corner to get the final noise value. */
 271     /* The result is scaled to return values in the interval [-1,1]. */
 272     return 40.0f * (n0 + n1 + n2); /* TODO: The scale factor is preliminary! */
 273 }
 274
 275 /* 3D simplex noise */
 276 GLfloat _slang_library_noise3 (GLfloat x, GLfloat y, GLfloat z)
 277 {
 278 /* Simple skewing factors for the 3D case */
 279 #define F3 0.333333333f
 280 #define G3 0.166666667f
 281
 282     float n0, n1, n2, n3; /* Noise contributions from the four corners */
 283
 284     /* Skew the input space to determine which simplex cell we're in */
 285     float s = (x+y+z)*F3; /* Very nice and simple skew factor for 3D */
 286     float xs = x+s;
 287     float ys = y+s;
 288     float zs = z+s;
 289     int i = FASTFLOOR(xs);
 290     int j = FASTFLOOR(ys);
 291     int k = FASTFLOOR(zs);
 292
 293     float t = (float)(i+j+k)*G3;
 294     float X0 = i-t; /* Unskew the cell origin back to (x,y,z) space */
 295     float Y0 = j-t;
 296     float Z0 = k-t;
 297     float x0 = x-X0; /* The x,y,z distances from the cell origin */
 298     float y0 = y-Y0;
 299     float z0 = z-Z0;
 300
 301     float x1, y1, z1, x2, y2, z2, x3, y3, z3;
 302     int ii, jj, kk;
 303     float t0, t1, t2, t3;
 304
 305     /* For the 3D case, the simplex shape is a slightly irregular tetrahedron. */
 306     /* Determine which simplex we are in. */
 307     int i1, j1, k1; /* Offsets for second corner of simplex in (i,j,k) coords */
 308     int i2, j2, k2; /* Offsets for third corner of simplex in (i,j,k) coords */
 309
 310 /* This code would benefit from a backport from the GLSL version! */
 311     if(x0>=y0) {
 312       if(y0>=z0)
 313         { i1=1; j1=0; k1=0; i2=1; j2=1; k2=0; } /* X Y Z order */
 314         else if(x0>=z0) { i1=1; j1=0; k1=0; i2=1; j2=0; k2=1; } /* X Z Y order */
 315         else { i1=0; j1=0; k1=1; i2=1; j2=0; k2=1; } /* Z X Y order */
 316       }
 317     else { /* x0<y0 */
 318       if(y0<z0) { i1=0; j1=0; k1=1; i2=0; j2=1; k2=1; } /* Z Y X order */
 319       else if(x0<z0) { i1=0; j1=1; k1=0; i2=0; j2=1; k2=1; } /* Y Z X order */
 320       else { i1=0; j1=1; k1=0; i2=1; j2=1; k2=0; } /* Y X Z order */
 321     }
 322
 323     /* A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z), */
 324     /* a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and */
 325     /* a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where */
 326     /* c = 1/6. */
 327
 328     x1 = x0 - i1 + G3; /* Offsets for second corner in (x,y,z) coords */
 329     y1 = y0 - j1 + G3;
 330     z1 = z0 - k1 + G3;
 331     x2 = x0 - i2 + 2.0f*G3; /* Offsets for third corner in (x,y,z) coords */
 332     y2 = y0 - j2 + 2.0f*G3;
 333     z2 = z0 - k2 + 2.0f*G3;
 334     x3 = x0 - 1.0f + 3.0f*G3; /* Offsets for last corner in (x,y,z) coords */
 335     y3 = y0 - 1.0f + 3.0f*G3;
 336     z3 = z0 - 1.0f + 3.0f*G3;
 337
 338     /* Wrap the integer indices at 256, to avoid indexing perm[] out of bounds */
 339     ii = i % 256;
 340     jj = j % 256;
 341     kk = k % 256;
 342
 343     /* Calculate the contribution from the four corners */
 344     t0 = 0.6f - x0*x0 - y0*y0 - z0*z0;
 345     if(t0 < 0.0f) n0 = 0.0f;
 346     else {
 347       t0 *= t0;
 348       n0 = t0 * t0 * grad3(perm[ii+perm[jj+perm[kk]]], x0, y0, z0);
 349     }
 350
 351     t1 = 0.6f - x1*x1 - y1*y1 - z1*z1;
 352     if(t1 < 0.0f) n1 = 0.0f;
 353     else {
 354       t1 *= t1;
 355       n1 = t1 * t1 * grad3(perm[ii+i1+perm[jj+j1+perm[kk+k1]]], x1, y1, z1);
 356     }
 357
 358     t2 = 0.6f - x2*x2 - y2*y2 - z2*z2;
 359     if(t2 < 0.0f) n2 = 0.0f;
 360     else {
 361       t2 *= t2;
 362       n2 = t2 * t2 * grad3(perm[ii+i2+perm[jj+j2+perm[kk+k2]]], x2, y2, z2);
 363     }
 364
 365     t3 = 0.6f - x3*x3 - y3*y3 - z3*z3;
 366     if(t3<0.0f) n3 = 0.0f;
 367     else {
 368       t3 *= t3;
 369       n3 = t3 * t3 * grad3(perm[ii+1+perm[jj+1+perm[kk+1]]], x3, y3, z3);
 370     }
 371
 372     /* Add contributions from each corner to get the final noise value. */
 373     /* The result is scaled to stay just inside [-1,1] */
 374     return 32.0f * (n0 + n1 + n2 + n3); /* TODO: The scale factor is preliminary! */
 375 }
 376
 377 /* 4D simplex noise */
 378 GLfloat _slang_library_noise4 (GLfloat x, GLfloat y, GLfloat z, GLfloat w)
 379 {
 380   /* The skewing and unskewing factors are hairy again for the 4D case */
 381 #define F4 0.309016994f /* F4 = (Math.sqrt(5.0)-1.0)/4.0 */
 382 #define G4 0.138196601f /* G4 = (5.0-Math.sqrt(5.0))/20.0 */
 383
 384     float n0, n1, n2, n3, n4; /* Noise contributions from the five corners */
 385
 386     /* Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in */
 387     float s = (x + y + z + w) * F4; /* Factor for 4D skewing */
 388     float xs = x + s;
 389     float ys = y + s;
 390     float zs = z + s;
 391     float ws = w + s;
 392     int i = FASTFLOOR(xs);
 393     int j = FASTFLOOR(ys);
 394     int k = FASTFLOOR(zs);
 395     int l = FASTFLOOR(ws);
 396
 397     float t = (i + j + k + l) * G4; /* Factor for 4D unskewing */
 398     float X0 = i - t; /* Unskew the cell origin back to (x,y,z,w) space */
 399     float Y0 = j - t;
 400     float Z0 = k - t;
 401     float W0 = l - t;
 402
 403     float x0 = x - X0;  /* The x,y,z,w distances from the cell origin */
 404     float y0 = y - Y0;
 405     float z0 = z - Z0;
 406     float w0 = w - W0;
 407
 408     /* For the 4D case, the simplex is a 4D shape I won't even try to describe. */
 409     /* To find out which of the 24 possible simplices we're in, we need to */
 410     /* determine the magnitude ordering of x0, y0, z0 and w0. */
 411     /* The method below is a good way of finding the ordering of x,y,z,w and */
 412     /* then find the correct traversal order for the simplex we\92re in. */
 413     /* First, six pair-wise comparisons are performed between each possible pair */
 414     /* of the four coordinates, and the results are used to add up binary bits */
 415     /* for an integer index. */
 416     int c1 = (x0 > y0) ? 32 : 0;
 417     int c2 = (x0 > z0) ? 16 : 0;
 418     int c3 = (y0 > z0) ? 8 : 0;
 419     int c4 = (x0 > w0) ? 4 : 0;
 420     int c5 = (y0 > w0) ? 2 : 0;
 421     int c6 = (z0 > w0) ? 1 : 0;
 422     int c = c1 + c2 + c3 + c4 + c5 + c6;
 423
 424     int i1, j1, k1, l1; /* The integer offsets for the second simplex corner */
 425     int i2, j2, k2, l2; /* The integer offsets for the third simplex corner */
 426     int i3, j3, k3, l3; /* The integer offsets for the fourth simplex corner */
 427
 428     float x1, y1, z1, w1, x2, y2, z2, w2, x3, y3, z3, w3, x4, y4, z4, w4;
 429     int ii, jj, kk, ll;
 430     float t0, t1, t2, t3, t4;
 431
 432     /* simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order. */
 433     /* Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w */
 434     /* impossible. Only the 24 indices which have non-zero entries make any sense. */
 435     /* We use a thresholding to set the coordinates in turn from the largest magnitude. */
 436     /* The number 3 in the "simplex" array is at the position of the largest coordinate. */
 437     i1 = simplex[c][0]>=3 ? 1 : 0;
 438     j1 = simplex[c][1]>=3 ? 1 : 0;
 439     k1 = simplex[c][2]>=3 ? 1 : 0;
 440     l1 = simplex[c][3]>=3 ? 1 : 0;
 441     /* The number 2 in the "simplex" array is at the second largest coordinate. */
 442     i2 = simplex[c][0]>=2 ? 1 : 0;
 443     j2 = simplex[c][1]>=2 ? 1 : 0;
 444     k2 = simplex[c][2]>=2 ? 1 : 0;
 445     l2 = simplex[c][3]>=2 ? 1 : 0;
 446     /* The number 1 in the "simplex" array is at the second smallest coordinate. */
 447     i3 = simplex[c][0]>=1 ? 1 : 0;
 448     j3 = simplex[c][1]>=1 ? 1 : 0;
 449     k3 = simplex[c][2]>=1 ? 1 : 0;
 450     l3 = simplex[c][3]>=1 ? 1 : 0;
 451     /* The fifth corner has all coordinate offsets = 1, so no need to look that up. */
 452
 453     x1 = x0 - i1 + G4; /* Offsets for second corner in (x,y,z,w) coords */
 454     y1 = y0 - j1 + G4;
 455     z1 = z0 - k1 + G4;
 456     w1 = w0 - l1 + G4;
 457     x2 = x0 - i2 + 2.0f*G4; /* Offsets for third corner in (x,y,z,w) coords */
 458     y2 = y0 - j2 + 2.0f*G4;
 459     z2 = z0 - k2 + 2.0f*G4;
 460     w2 = w0 - l2 + 2.0f*G4;
 461     x3 = x0 - i3 + 3.0f*G4; /* Offsets for fourth corner in (x,y,z,w) coords */
 462     y3 = y0 - j3 + 3.0f*G4;
 463     z3 = z0 - k3 + 3.0f*G4;
 464     w3 = w0 - l3 + 3.0f*G4;
 465     x4 = x0 - 1.0f + 4.0f*G4; /* Offsets for last corner in (x,y,z,w) coords */
 466     y4 = y0 - 1.0f + 4.0f*G4;
 467     z4 = z0 - 1.0f + 4.0f*G4;
 468     w4 = w0 - 1.0f + 4.0f*G4;
 469
 470     /* Wrap the integer indices at 256, to avoid indexing perm[] out of bounds */
 471     ii = i % 256;
 472     jj = j % 256;
 473     kk = k % 256;
 474     ll = l % 256;
 475
 476     /* Calculate the contribution from the five corners */
 477     t0 = 0.6f - x0*x0 - y0*y0 - z0*z0 - w0*w0;
 478     if(t0 < 0.0f) n0 = 0.0f;
 479     else {
 480       t0 *= t0;
 481       n0 = t0 * t0 * grad4(perm[ii+perm[jj+perm[kk+perm[ll]]]], x0, y0, z0, w0);
 482     }
 483
 484    t1 = 0.6f - x1*x1 - y1*y1 - z1*z1 - w1*w1;
 485     if(t1 < 0.0f) n1 = 0.0f;
 486     else {
 487       t1 *= t1;
 488       n1 = t1 * t1 * grad4(perm[ii+i1+perm[jj+j1+perm[kk+k1+perm[ll+l1]]]], x1, y1, z1, w1);
 489     }
 490
 491    t2 = 0.6f - x2*x2 - y2*y2 - z2*z2 - w2*w2;
 492     if(t2 < 0.0f) n2 = 0.0f;
 493     else {
 494       t2 *= t2;
 495       n2 = t2 * t2 * grad4(perm[ii+i2+perm[jj+j2+perm[kk+k2+perm[ll+l2]]]], x2, y2, z2, w2);
 496     }
 497
 498    t3 = 0.6f - x3*x3 - y3*y3 - z3*z3 - w3*w3;
 499     if(t3 < 0.0f) n3 = 0.0f;
 500     else {
 501       t3 *= t3;
 502       n3 = t3 * t3 * grad4(perm[ii+i3+perm[jj+j3+perm[kk+k3+perm[ll+l3]]]], x3, y3, z3, w3);
 503     }
 504
 505    t4 = 0.6f - x4*x4 - y4*y4 - z4*z4 - w4*w4;
 506     if(t4 < 0.0f) n4 = 0.0f;
 507     else {
 508       t4 *= t4;
 509       n4 = t4 * t4 * grad4(perm[ii+1+perm[jj+1+perm[kk+1+perm[ll+1]]]], x4, y4, z4, w4);
 510     }
 511
 512     /* Sum up and scale the result to cover the range [-1,1] */
 513     return 27.0f * (n0 + n1 + n2 + n3 + n4); /* TODO: The scale factor is preliminary! */
 514 }
 515