/*-------------------------------------------------------------
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));
}
//---------------------------------------------------------------------