tahoma2d/toonz/sources/stdfx/iwa_noise1234.cpp

/*-------------------------------------------------------------
iwa_noise1234.cpp
Identical to a public domain code "noise1234.cpp" by Stefan Gustavson.
Just changed file name for handling of files.
-------------------------------------------------------------*/
/*-- The original code starts here --*/

// Noise1234
// Author: Stefan Gustavson (stegu@itn.liu.se)
//
// This library is public domain software, released by the author
// into the public domain in February 2011. You may do anything
// you like with it. You may even remove all attributions,
// but of course I'd appreciate it if you kept my name somewhere.
//
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// General Public License for more details.

/** \file
                \brief Implements the Noise1234 class for producing Perlin
   noise.
                \author Stefan Gustavson (stegu@itn.liu.se)
*/

/*
 * This implementation is "Improved Noise" as presented by
 * Ken Perlin at Siggraph 2002. The 3D function is a direct port
 * of his Java reference code available on www.noisemachine.com
 * (although I cleaned it up and made the code more readable),
 * but the 1D, 2D and 4D cases were implemented from scratch
 * by me.
 *
 * This is a highly reusable class. It has no dependencies
 * on any other file, apart from its own header file.
 */

#include "iwa_noise1234.h"
//#include	"noise1234.h"

// This is the new and improved, C(2) continuous interpolant
#define FADE(t) (t * t * t * (t * (t * 6 - 15) + 10))

#define FASTFLOOR(x) (((x) > 0) ? ((int)x) : ((int)x - 1))
#define LERP(t, a, b) ((a) + (t) * ((b) - (a)))

//---------------------------------------------------------------------
// 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 Noise1234::perm[] = {
    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 match the RenderMan noise in a
 * statistical sense, the approximate scaling values (empirically
 * determined from test renderings) are:
 * 1D noise needs rescaling with 0.188
 * 2D noise needs rescaling with 0.507
 * 3D noise needs rescaling with 0.936
 * 4D noise needs rescaling with 0.87
 * Note 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 = (Noise1234::noise(x,y,z) + 1.0) * 0.5;
 */

float Noise1234::grad(int hash, float x) {
  int h           = hash & 15;
  float grad      = 1.0 + (h & 7);  // Gradient value 1.0, 2.0, ..., 8.0
  if (h & 8) grad = -grad;          // and a random sign for the gradient
  return (grad * x);                // Multiply the gradient with the distance
}

float Noise1234::grad(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) ? -2.0 * v : 2.0 * v);
}

float Noise1234::grad(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 Noise1234::grad(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);
}

//---------------------------------------------------------------------
/** 1D float Perlin noise, SL "noise()"
 */
float Noise1234::noise(float x) {
  int ix0, ix1;
  float fx0, fx1;
  float s, n0, n1;

  ix0 = FASTFLOOR(x);  // Integer part of x
  fx0 = x - ix0;       // Fractional part of x
  fx1 = fx0 - 1.0f;
  ix1 = (ix0 + 1) & 0xff;
  ix0 = ix0 & 0xff;  // Wrap to 0..255

  s = FADE(fx0);

  n0 = grad(perm[ix0], fx0);
  n1 = grad(perm[ix1], fx1);
  return 0.188f * (LERP(s, n0, n1));
}

//---------------------------------------------------------------------
/** 1D float Perlin periodic noise, SL "pnoise()"
 */
float Noise1234::pnoise(float x, int px) {
  int ix0, ix1;
  float fx0, fx1;
  float s, n0, n1;

  ix0 = FASTFLOOR(x);  // Integer part of x
  fx0 = x - ix0;       // Fractional part of x
  fx1 = fx0 - 1.0f;
  ix1 = ((ix0 + 1) % px) & 0xff;  // Wrap to 0..px-1 *and* wrap to 0..255
  ix0 = (ix0 % px) & 0xff;        // (because px might be greater than 256)

  s = FADE(fx0);

  n0 = grad(perm[ix0], fx0);
  n1 = grad(perm[ix1], fx1);
  return 0.188f * (LERP(s, n0, n1));
}

//---------------------------------------------------------------------
/** 2D float Perlin noise.
 */
float Noise1234::noise(float x, float y) {
  int ix0, iy0, ix1, iy1;
  float fx0, fy0, fx1, fy1;
  float s, t, nx0, nx1, n0, n1;

  ix0 = FASTFLOOR(x);  // Integer part of x
  iy0 = FASTFLOOR(y);  // Integer part of y
  fx0 = x - ix0;       // Fractional part of x
  fy0 = y - iy0;       // Fractional part of y
  fx1 = fx0 - 1.0f;
  fy1 = fy0 - 1.0f;
  ix1 = (ix0 + 1) & 0xff;  // Wrap to 0..255
  iy1 = (iy0 + 1) & 0xff;
  ix0 = ix0 & 0xff;
  iy0 = iy0 & 0xff;

  t = FADE(fy0);
  s = FADE(fx0);

  nx0 = grad(perm[ix0 + perm[iy0]], fx0, fy0);
  nx1 = grad(perm[ix0 + perm[iy1]], fx0, fy1);
  n0  = LERP(t, nx0, nx1);

  nx0 = grad(perm[ix1 + perm[iy0]], fx1, fy0);
  nx1 = grad(perm[ix1 + perm[iy1]], fx1, fy1);
  n1  = LERP(t, nx0, nx1);

  return 0.507f * (LERP(s, n0, n1));
}

//---------------------------------------------------------------------
/** 2D float Perlin periodic noise.
 */
float Noise1234::pnoise(float x, float y, int px, int py) {
  int ix0, iy0, ix1, iy1;
  float fx0, fy0, fx1, fy1;
  float s, t, nx0, nx1, n0, n1;

  ix0 = FASTFLOOR(x);  // Integer part of x
  iy0 = FASTFLOOR(y);  // Integer part of y
  fx0 = x - ix0;       // Fractional part of x
  fy0 = y - iy0;       // Fractional part of y
  fx1 = fx0 - 1.0f;
  fy1 = fy0 - 1.0f;
  ix1 = ((ix0 + 1) % px) & 0xff;  // Wrap to 0..px-1 and wrap to 0..255
  iy1 = ((iy0 + 1) % py) & 0xff;  // Wrap to 0..py-1 and wrap to 0..255
  ix0 = (ix0 % px) & 0xff;
  iy0 = (iy0 % py) & 0xff;

  t = FADE(fy0);
  s = FADE(fx0);

  nx0 = grad(perm[ix0 + perm[iy0]], fx0, fy0);
  nx1 = grad(perm[ix0 + perm[iy1]], fx0, fy1);
  n0  = LERP(t, nx0, nx1);

  nx0 = grad(perm[ix1 + perm[iy0]], fx1, fy0);
  nx1 = grad(perm[ix1 + perm[iy1]], fx1, fy1);
  n1  = LERP(t, nx0, nx1);

  return 0.507f * (LERP(s, n0, n1));
}

//---------------------------------------------------------------------
/** 3D float Perlin noise.
 */
float Noise1234::noise(float x, float y, float z) {
  int ix0, iy0, ix1, iy1, iz0, iz1;
  float fx0, fy0, fz0, fx1, fy1, fz1;
  float s, t, r;
  float nxy0, nxy1, nx0, nx1, n0, n1;

  ix0 = FASTFLOOR(x);  // Integer part of x
  iy0 = FASTFLOOR(y);  // Integer part of y
  iz0 = FASTFLOOR(z);  // Integer part of z
  fx0 = x - ix0;       // Fractional part of x
  fy0 = y - iy0;       // Fractional part of y
  fz0 = z - iz0;       // Fractional part of z
  fx1 = fx0 - 1.0f;
  fy1 = fy0 - 1.0f;
  fz1 = fz0 - 1.0f;
  ix1 = (ix0 + 1) & 0xff;  // Wrap to 0..255
  iy1 = (iy0 + 1) & 0xff;
  iz1 = (iz0 + 1) & 0xff;
  ix0 = ix0 & 0xff;
  iy0 = iy0 & 0xff;
  iz0 = iz0 & 0xff;

  r = FADE(fz0);
  t = FADE(fy0);
  s = FADE(fx0);

  nxy0 = grad(perm[ix0 + perm[iy0 + perm[iz0]]], fx0, fy0, fz0);
  nxy1 = grad(perm[ix0 + perm[iy0 + perm[iz1]]], fx0, fy0, fz1);
  nx0  = LERP(r, nxy0, nxy1);

  nxy0 = grad(perm[ix0 + perm[iy1 + perm[iz0]]], fx0, fy1, fz0);
  nxy1 = grad(perm[ix0 + perm[iy1 + perm[iz1]]], fx0, fy1, fz1);
  nx1  = LERP(r, nxy0, nxy1);

  n0 = LERP(t, nx0, nx1);

  nxy0 = grad(perm[ix1 + perm[iy0 + perm[iz0]]], fx1, fy0, fz0);
  nxy1 = grad(perm[ix1 + perm[iy0 + perm[iz1]]], fx1, fy0, fz1);
  nx0  = LERP(r, nxy0, nxy1);

  nxy0 = grad(perm[ix1 + perm[iy1 + perm[iz0]]], fx1, fy1, fz0);
  nxy1 = grad(perm[ix1 + perm[iy1 + perm[iz1]]], fx1, fy1, fz1);
  nx1  = LERP(r, nxy0, nxy1);

  n1 = LERP(t, nx0, nx1);

  return 0.936f * (LERP(s, n0, n1));
}

//---------------------------------------------------------------------
/** 3D float Perlin periodic noise.
 */
float Noise1234::pnoise(float x, float y, float z, int px, int py, int pz) {
  int ix0, iy0, ix1, iy1, iz0, iz1;
  float fx0, fy0, fz0, fx1, fy1, fz1;
  float s, t, r;
  float nxy0, nxy1, nx0, nx1, n0, n1;

  ix0 = FASTFLOOR(x);  // Integer part of x
  iy0 = FASTFLOOR(y);  // Integer part of y
  iz0 = FASTFLOOR(z);  // Integer part of z
  fx0 = x - ix0;       // Fractional part of x
  fy0 = y - iy0;       // Fractional part of y
  fz0 = z - iz0;       // Fractional part of z
  fx1 = fx0 - 1.0f;
  fy1 = fy0 - 1.0f;
  fz1 = fz0 - 1.0f;
  ix1 = ((ix0 + 1) % px) & 0xff;  // Wrap to 0..px-1 and wrap to 0..255
  iy1 = ((iy0 + 1) % py) & 0xff;  // Wrap to 0..py-1 and wrap to 0..255
  iz1 = ((iz0 + 1) % pz) & 0xff;  // Wrap to 0..pz-1 and wrap to 0..255
  ix0 = (ix0 % px) & 0xff;
  iy0 = (iy0 % py) & 0xff;
  iz0 = (iz0 % pz) & 0xff;

  r = FADE(fz0);
  t = FADE(fy0);
  s = FADE(fx0);

  nxy0 = grad(perm[ix0 + perm[iy0 + perm[iz0]]], fx0, fy0, fz0);
  nxy1 = grad(perm[ix0 + perm[iy0 + perm[iz1]]], fx0, fy0, fz1);
  nx0  = LERP(r, nxy0, nxy1);

  nxy0 = grad(perm[ix0 + perm[iy1 + perm[iz0]]], fx0, fy1, fz0);
  nxy1 = grad(perm[ix0 + perm[iy1 + perm[iz1]]], fx0, fy1, fz1);
  nx1  = LERP(r, nxy0, nxy1);

  n0 = LERP(t, nx0, nx1);

  nxy0 = grad(perm[ix1 + perm[iy0 + perm[iz0]]], fx1, fy0, fz0);
  nxy1 = grad(perm[ix1 + perm[iy0 + perm[iz1]]], fx1, fy0, fz1);
  nx0  = LERP(r, nxy0, nxy1);

  nxy0 = grad(perm[ix1 + perm[iy1 + perm[iz0]]], fx1, fy1, fz0);
  nxy1 = grad(perm[ix1 + perm[iy1 + perm[iz1]]], fx1, fy1, fz1);
  nx1  = LERP(r, nxy0, nxy1);

  n1 = LERP(t, nx0, nx1);

  return 0.936f * (LERP(s, n0, n1));
}

//---------------------------------------------------------------------
/** 4D float Perlin noise.
 */

float Noise1234::noise(float x, float y, float z, float w) {
  int ix0, iy0, iz0, iw0, ix1, iy1, iz1, iw1;
  float fx0, fy0, fz0, fw0, fx1, fy1, fz1, fw1;
  float s, t, r, q;
  float nxyz0, nxyz1, nxy0, nxy1, nx0, nx1, n0, n1;

  ix0 = FASTFLOOR(x);  // Integer part of x
  iy0 = FASTFLOOR(y);  // Integer part of y
  iz0 = FASTFLOOR(z);  // Integer part of y
  iw0 = FASTFLOOR(w);  // Integer part of w
  fx0 = x - ix0;       // Fractional part of x
  fy0 = y - iy0;       // Fractional part of y
  fz0 = z - iz0;       // Fractional part of z
  fw0 = w - iw0;       // Fractional part of w
  fx1 = fx0 - 1.0f;
  fy1 = fy0 - 1.0f;
  fz1 = fz0 - 1.0f;
  fw1 = fw0 - 1.0f;
  ix1 = (ix0 + 1) & 0xff;  // Wrap to 0..255
  iy1 = (iy0 + 1) & 0xff;
  iz1 = (iz0 + 1) & 0xff;
  iw1 = (iw0 + 1) & 0xff;
  ix0 = ix0 & 0xff;
  iy0 = iy0 & 0xff;
  iz0 = iz0 & 0xff;
  iw0 = iw0 & 0xff;

  q = FADE(fw0);
  r = FADE(fz0);
  t = FADE(fy0);
  s = FADE(fx0);

  nxyz0 =
      grad(perm[ix0 + perm[iy0 + perm[iz0 + perm[iw0]]]], fx0, fy0, fz0, fw0);
  nxyz1 =
      grad(perm[ix0 + perm[iy0 + perm[iz0 + perm[iw1]]]], fx0, fy0, fz0, fw1);
  nxy0 = LERP(q, nxyz0, nxyz1);

  nxyz0 =
      grad(perm[ix0 + perm[iy0 + perm[iz1 + perm[iw0]]]], fx0, fy0, fz1, fw0);
  nxyz1 =
      grad(perm[ix0 + perm[iy0 + perm[iz1 + perm[iw1]]]], fx0, fy0, fz1, fw1);
  nxy1 = LERP(q, nxyz0, nxyz1);

  nx0 = LERP(r, nxy0, nxy1);

  nxyz0 =
      grad(perm[ix0 + perm[iy1 + perm[iz0 + perm[iw0]]]], fx0, fy1, fz0, fw0);
  nxyz1 =
      grad(perm[ix0 + perm[iy1 + perm[iz0 + perm[iw1]]]], fx0, fy1, fz0, fw1);
  nxy0 = LERP(q, nxyz0, nxyz1);

  nxyz0 =
      grad(perm[ix0 + perm[iy1 + perm[iz1 + perm[iw0]]]], fx0, fy1, fz1, fw0);
  nxyz1 =
      grad(perm[ix0 + perm[iy1 + perm[iz1 + perm[iw1]]]], fx0, fy1, fz1, fw1);
  nxy1 = LERP(q, nxyz0, nxyz1);

  nx1 = LERP(r, nxy0, nxy1);

  n0 = LERP(t, nx0, nx1);

  nxyz0 =
      grad(perm[ix1 + perm[iy0 + perm[iz0 + perm[iw0]]]], fx1, fy0, fz0, fw0);
  nxyz1 =
      grad(perm[ix1 + perm[iy0 + perm[iz0 + perm[iw1]]]], fx1, fy0, fz0, fw1);
  nxy0 = LERP(q, nxyz0, nxyz1);

  nxyz0 =
      grad(perm[ix1 + perm[iy0 + perm[iz1 + perm[iw0]]]], fx1, fy0, fz1, fw0);
  nxyz1 =
      grad(perm[ix1 + perm[iy0 + perm[iz1 + perm[iw1]]]], fx1, fy0, fz1, fw1);
  nxy1 = LERP(q, nxyz0, nxyz1);

  nx0 = LERP(r, nxy0, nxy1);

  nxyz0 =
      grad(perm[ix1 + perm[iy1 + perm[iz0 + perm[iw0]]]], fx1, fy1, fz0, fw0);
  nxyz1 =
      grad(perm[ix1 + perm[iy1 + perm[iz0 + perm[iw1]]]], fx1, fy1, fz0, fw1);
  nxy0 = LERP(q, nxyz0, nxyz1);

  nxyz0 =
      grad(perm[ix1 + perm[iy1 + perm[iz1 + perm[iw0]]]], fx1, fy1, fz1, fw0);
  nxyz1 =
      grad(perm[ix1 + perm[iy1 + perm[iz1 + perm[iw1]]]], fx1, fy1, fz1, fw1);
  nxy1 = LERP(q, nxyz0, nxyz1);

  nx1 = LERP(r, nxy0, nxy1);

  n1 = LERP(t, nx0, nx1);

  return 0.87f * (LERP(s, n0, n1));
}

//---------------------------------------------------------------------
/** 4D float Perlin periodic noise.
 */

float Noise1234::pnoise(float x, float y, float z, float w, int px, int py,
                        int pz, int pw) {
  int ix0, iy0, iz0, iw0, ix1, iy1, iz1, iw1;
  float fx0, fy0, fz0, fw0, fx1, fy1, fz1, fw1;
  float s, t, r, q;
  float nxyz0, nxyz1, nxy0, nxy1, nx0, nx1, n0, n1;

  ix0 = FASTFLOOR(x);  // Integer part of x
  iy0 = FASTFLOOR(y);  // Integer part of y
  iz0 = FASTFLOOR(z);  // Integer part of y
  iw0 = FASTFLOOR(w);  // Integer part of w
  fx0 = x - ix0;       // Fractional part of x
  fy0 = y - iy0;       // Fractional part of y
  fz0 = z - iz0;       // Fractional part of z
  fw0 = w - iw0;       // Fractional part of w
  fx1 = fx0 - 1.0f;
  fy1 = fy0 - 1.0f;
  fz1 = fz0 - 1.0f;
  fw1 = fw0 - 1.0f;
  ix1 = ((ix0 + 1) % px) & 0xff;  // Wrap to 0..px-1 and wrap to 0..255
  iy1 = ((iy0 + 1) % py) & 0xff;  // Wrap to 0..py-1 and wrap to 0..255
  iz1 = ((iz0 + 1) % pz) & 0xff;  // Wrap to 0..pz-1 and wrap to 0..255
  iw1 = ((iw0 + 1) % pw) & 0xff;  // Wrap to 0..pw-1 and wrap to 0..255
  ix0 = (ix0 % px) & 0xff;
  iy0 = (iy0 % py) & 0xff;
  iz0 = (iz0 % pz) & 0xff;
  iw0 = (iw0 % pw) & 0xff;

  q = FADE(fw0);
  r = FADE(fz0);
  t = FADE(fy0);
  s = FADE(fx0);

  nxyz0 =
      grad(perm[ix0 + perm[iy0 + perm[iz0 + perm[iw0]]]], fx0, fy0, fz0, fw0);
  nxyz1 =
      grad(perm[ix0 + perm[iy0 + perm[iz0 + perm[iw1]]]], fx0, fy0, fz0, fw1);
  nxy0 = LERP(q, nxyz0, nxyz1);

  nxyz0 =
      grad(perm[ix0 + perm[iy0 + perm[iz1 + perm[iw0]]]], fx0, fy0, fz1, fw0);
  nxyz1 =
      grad(perm[ix0 + perm[iy0 + perm[iz1 + perm[iw1]]]], fx0, fy0, fz1, fw1);
  nxy1 = LERP(q, nxyz0, nxyz1);

  nx0 = LERP(r, nxy0, nxy1);

  nxyz0 =
      grad(perm[ix0 + perm[iy1 + perm[iz0 + perm[iw0]]]], fx0, fy1, fz0, fw0);
  nxyz1 =
      grad(perm[ix0 + perm[iy1 + perm[iz0 + perm[iw1]]]], fx0, fy1, fz0, fw1);
  nxy0 = LERP(q, nxyz0, nxyz1);

  nxyz0 =
      grad(perm[ix0 + perm[iy1 + perm[iz1 + perm[iw0]]]], fx0, fy1, fz1, fw0);
  nxyz1 =
      grad(perm[ix0 + perm[iy1 + perm[iz1 + perm[iw1]]]], fx0, fy1, fz1, fw1);
  nxy1 = LERP(q, nxyz0, nxyz1);

  nx1 = LERP(r, nxy0, nxy1);

  n0 = LERP(t, nx0, nx1);

  nxyz0 =
      grad(perm[ix1 + perm[iy0 + perm[iz0 + perm[iw0]]]], fx1, fy0, fz0, fw0);
  nxyz1 =
      grad(perm[ix1 + perm[iy0 + perm[iz0 + perm[iw1]]]], fx1, fy0, fz0, fw1);
  nxy0 = LERP(q, nxyz0, nxyz1);

  nxyz0 =
      grad(perm[ix1 + perm[iy0 + perm[iz1 + perm[iw0]]]], fx1, fy0, fz1, fw0);
  nxyz1 =
      grad(perm[ix1 + perm[iy0 + perm[iz1 + perm[iw1]]]], fx1, fy0, fz1, fw1);
  nxy1 = LERP(q, nxyz0, nxyz1);

  nx0 = LERP(r, nxy0, nxy1);

  nxyz0 =
      grad(perm[ix1 + perm[iy1 + perm[iz0 + perm[iw0]]]], fx1, fy1, fz0, fw0);
  nxyz1 =
      grad(perm[ix1 + perm[iy1 + perm[iz0 + perm[iw1]]]], fx1, fy1, fz0, fw1);
  nxy0 = LERP(q, nxyz0, nxyz1);

  nxyz0 =
      grad(perm[ix1 + perm[iy1 + perm[iz1 + perm[iw0]]]], fx1, fy1, fz1, fw0);
  nxyz1 =
      grad(perm[ix1 + perm[iy1 + perm[iz1 + perm[iw1]]]], fx1, fy1, fz1, fw1);
  nxy1 = LERP(q, nxyz0, nxyz1);

  nx1 = LERP(r, nxy0, nxy1);

  n1 = LERP(t, nx0, nx1);

  return 0.87f * (LERP(s, n0, n1));
}

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