/* sdnoise1234, Simplex noise with true analytic
 * derivative in 1D to 4D.
 *
 * Copyright © 2003-2008, Stefan Gustavson
 *
 * Contact: stefan.gustavson@gmail.com
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public
 * License as published by the Free Software Foundation; either
 * version 2 of the License, or (at your option) any later version.
 *
 * 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.
 *
 * You should have received a copy of the GNU General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 */

/** \file
 \brief C implementation file for Perlin simplex noise with analytic
 derivative over 1, 2, 3 and 4 dimensions.
 \author Stefan Gustavson (stefan.gustavson@gmail.com)
 \author Charl van Deventer (landon.skyfire@gmail.com)
 */

/*
 * This is an implementation of Perlin "simplex noise" over one
 * dimension (x), two dimensions (x,y), three dimensions (x,y,z)
 * and four dimensions (x,y,z,w). The analytic derivative is
 * returned, to make it possible to do lots of fun stuff like
 * flow animations, curl noise, analytic antialiasing and such.
 *
 * Visually, this noise is exactly the same as the plain version of
 * simplex noise provided in the file "snoise1234.c". It just returns
 * all partial derivatives in addition to the scalar noise value.
 *
 */

/*
 * 23 June 2010: Modified by Charl van Deventer to allow periodic arguments
 * Note: It doesn't check for bounds over 255 (wont work) and might fail with
 * negative coords.
 */

#include <math.h>

#include "sdnoise1234.h" /* We strictly don't need this, but play nice. */

#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.
 */
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
};

/*
 * Gradient tables. These could be programmed the Ken Perlin way with
 * some clever bit-twiddling, but this is more clear, and not really slower.
 */
static float grad2lut[8][2] = {
	{ -1.0f, -1.0f }, { 1.0f, 0.0f } , { -1.0f, 0.0f } , { 1.0f, 1.0f } ,
	{ -1.0f, 1.0f } , { 0.0f, -1.0f } , { 0.0f, 1.0f } , { 1.0f, -1.0f }
};

/*
 * Gradient directions for 3D.
 * These vectors are based on the midpoints of the 12 edges of a cube.
 * A larger array of random unit length vectors would also do the job,
 * but these 12 (including 4 repeats to make the array length a power
 * of two) work better. They are not random, they are carefully chosen
 * to represent a small, isotropic set of directions.
 */

static float grad3lut[16][3] = {
	{ 1.0f, 0.0f, 1.0f }, { 0.0f, 1.0f, 1.0f }, // 12 cube edges
	{ -1.0f, 0.0f, 1.0f }, { 0.0f, -1.0f, 1.0f },
	{ 1.0f, 0.0f, -1.0f }, { 0.0f, 1.0f, -1.0f },
	{ -1.0f, 0.0f, -1.0f }, { 0.0f, -1.0f, -1.0f },
	{ 1.0f, -1.0f, 0.0f }, { 1.0f, 1.0f, 0.0f },
	{ -1.0f, 1.0f, 0.0f }, { -1.0f, -1.0f, 0.0f },
	{ 1.0f, 0.0f, 1.0f }, { -1.0f, 0.0f, 1.0f }, // 4 repeats to make 16
	{ 0.0f, 1.0f, -1.0f }, { 0.0f, -1.0f, -1.0f }
};

static float grad4lut[32][4] = {
	{ 0.0f, 1.0f, 1.0f, 1.0f }, { 0.0f, 1.0f, 1.0f, -1.0f }, { 0.0f, 1.0f, -1.0f, 1.0f }, { 0.0f, 1.0f, -1.0f, -1.0f }, // 32 tesseract edges
	{ 0.0f, -1.0f, 1.0f, 1.0f }, { 0.0f, -1.0f, 1.0f, -1.0f }, { 0.0f, -1.0f, -1.0f, 1.0f }, { 0.0f, -1.0f, -1.0f, -1.0f },
	{ 1.0f, 0.0f, 1.0f, 1.0f }, { 1.0f, 0.0f, 1.0f, -1.0f }, { 1.0f, 0.0f, -1.0f, 1.0f }, { 1.0f, 0.0f, -1.0f, -1.0f },
	{ -1.0f, 0.0f, 1.0f, 1.0f }, { -1.0f, 0.0f, 1.0f, -1.0f }, { -1.0f, 0.0f, -1.0f, 1.0f }, { -1.0f, 0.0f, -1.0f, -1.0f },
	{ 1.0f, 1.0f, 0.0f, 1.0f }, { 1.0f, 1.0f, 0.0f, -1.0f }, { 1.0f, -1.0f, 0.0f, 1.0f }, { 1.0f, -1.0f, 0.0f, -1.0f },
	{ -1.0f, 1.0f, 0.0f, 1.0f }, { -1.0f, 1.0f, 0.0f, -1.0f }, { -1.0f, -1.0f, 0.0f, 1.0f }, { -1.0f, -1.0f, 0.0f, -1.0f },
	{ 1.0f, 1.0f, 1.0f, 0.0f }, { 1.0f, 1.0f, -1.0f, 0.0f }, { 1.0f, -1.0f, 1.0f, 0.0f }, { 1.0f, -1.0f, -1.0f, 0.0f },
	{ -1.0f, 1.0f, 1.0f, 0.0f }, { -1.0f, 1.0f, -1.0f, 0.0f }, { -1.0f, -1.0f, 1.0f, 0.0f }, { -1.0f, -1.0f, -1.0f, 0.0f }
};

// 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}};

/* --------------------------------------------------------------------- */

/*
 * Helper functions to compute gradients in 1D to 4D
 * and gradients-dot-residualvectors in 2D to 4D.
 */

void grad1( int hash, float *gx ) {
	int h = hash & 15;
	*gx = 1.0f + (h & 7);   // Gradient value is one of 1.0, 2.0, ..., 8.0
	if (h&8) *gx = - *gx;   // Make half of the gradients negative
}

void grad2( int hash, float *gx, float *gy ) {
	int h = hash & 7;
	*gx = grad2lut[h][0];
	*gy = grad2lut[h][1];
	return;
}

void grad3( int hash, float *gx, float *gy, float *gz ) {
	int h = hash & 15;
	*gx = grad3lut[h][0];
	*gy = grad3lut[h][1];
	*gz = grad3lut[h][2];
	return;
}

void grad4( int hash, float *gx, float *gy, float *gz, float *gw) {
	int h = hash & 31;
	*gx = grad4lut[h][0];
	*gy = grad4lut[h][1];
	*gz = grad4lut[h][2];
	*gw = grad4lut[h][3];
	return;
}

/** 1D simplex noise with derivative.
 * If the last argument is not null, the analytic derivative
 * is also calculated.
 */
float sdnoise1( float x, int px, float *dnoise_dx)
{
	int i0 = FASTFLOOR(x);
	int i1 = i0 + 1;
	float x0 = x - i0;
	float x1 = x0 - 1.0f;

	float gx0, gx1;
	float n0, n1;
	float t20, t40, t21, t41;

	float x20 = x0*x0;
	float t0 = 1.0f - x20;
	//  if(t0 < 0.0f) t0 = 0.0f; // Never happens for 1D: x0<=1 always
	t20 = t0 * t0;
	t40 = t20 * t20;
	grad1(perm[i0 % px], &gx0);
	n0 = t40 * gx0 * x0;

	float x21 = x1*x1;
	float t1 = 1.0f - x21;
	//  if(t1 < 0.0f) t1 = 0.0f; // Never happens for 1D: |x1|<=1 always
	t21 = t1 * t1;
	t41 = t21 * t21;
	grad1(perm[i1 % px], &gx1);
	n1 = t41 * gx1 * x1;

	/* Compute derivative according to:
	 *  *dnoise_dx = -8.0f * t20 * t0 * x0 * (gx0 * x0) + t40 * gx0;
	 *  *dnoise_dx += -8.0f * t21 * t1 * x1 * (gx1 * x1) + t41 * gx1;
	 */
	*dnoise_dx = t20 * t0 * gx0 * x20;
	*dnoise_dx += t21 * t1 * gx1 * x21;
	*dnoise_dx *= -8.0f;
	*dnoise_dx += t40 * gx0 + t41 * gx1;
	*dnoise_dx *= 0.25f; /* Scale derivative to match the noise scaling */

	// 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
	// to better match classic Perlin noise, we scale it down some more.
	return 0.25f * (n0 + n1);
}

float sdnoise1s( float x, float *dnoise_dx)
{
	return sdnoise1(x, 256, dnoise_dx);
}

/* Skewing factors for 2D simplex grid:
 * F2 = 0.5*(sqrt(3.0)-1.0)
 * G2 = (3.0-Math.sqrt(3.0))/6.0
 */
#define F2 0.366025403
#define G2 0.211324865

/** 2D simplex noise with derivatives.
 * If the last two arguments are not null, the analytic derivative
 * (the 2D gradient of the scalar noise field) is also calculated.
 */
float sdnoise2( float x, float y, int px, int py, float *dnoise_dx, float *dnoise_dy )
{
	float n0, n1, n2; /* Noise contributions from the three simplex corners */
	float gx0, gy0, gx1, gy1, gx2, gy2; /* Gradients at simplex 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;

	/* 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   */
	float x1 = x0 - i1 + G2; /* Offsets for middle corner in (x,y) unskewed coords */
	float y1 = y0 - j1 + G2;
	float x2 = x0 - 1.0f + 2.0f * G2; /* Offsets for last corner in (x,y) unskewed coords */
	float y2 = y0 - 1.0f + 2.0f * G2;

	/* Wrap the integer indices at 256, to avoid indexing perm[] out of bounds */
	int ii = i % px;
	int jj = j % py;

	/* Calculate the contribution from the three corners */
	float t0 = 0.5f - x0 * x0 - y0 * y0;
	float t20, t40;
	if( t0 < 0.0f ) t40 = t20 = t0 = n0 = gx0 = gy0 = 0.0f; /* No influence */
	else {
		grad2( perm[ii + perm[jj]], &gx0, &gy0 );
		t20 = t0 * t0;
		t40 = t20 * t20;
		n0 = t40 * ( gx0 * x0 + gy0 * y0 );
	}

	float t1 = 0.5f - x1 * x1 - y1 * y1;
	float t21, t41;
	if( t1 < 0.0f ) t21 = t41 = t1 = n1 = gx1 = gy1 = 0.0f; /* No influence */
	else {
		grad2( perm[ii + i1 + perm[jj + j1]], &gx1, &gy1 );
		t21 = t1 * t1;
		t41 = t21 * t21;
		n1 = t41 * ( gx1 * x1 + gy1 * y1 );
	}

	float t2 = 0.5f - x2 * x2 - y2 * y2;
	float t22, t42;
	if( t2 < 0.0f ) t42 = t22 = t2 = n2 = gx2 = gy2 = 0.0f; /* No influence */
	else {
		grad2( perm[ii + 1 + perm[jj + 1]], &gx2, &gy2 );
		t22 = t2 * t2;
		t42 = t22 * t22;
		n2 = t42 * ( gx2 * x2 + gy2 * y2 );
	}

	/* Add contributions from each corner to get the final noise value.
	 * The result is scaled to return values in the interval [-1,1]. */
	float noise = 40.0f * ( n0 + n1 + n2 );

	/* Compute derivative, if requested by supplying non-null pointers
	 * for the last two arguments */
	if( ( dnoise_dx != 0 ) && ( dnoise_dy != 0 ) )
	{
		/*  A straight, unoptimised calculation would be like:
		 *    *dnoise_dx = -8.0f * t20 * t0 * x0 * ( gx0 * x0 + gy0 * y0 ) + t40 * gx0;
		 *    *dnoise_dy = -8.0f * t20 * t0 * y0 * ( gx0 * x0 + gy0 * y0 ) + t40 * gy0;
		 *    *dnoise_dx += -8.0f * t21 * t1 * x1 * ( gx1 * x1 + gy1 * y1 ) + t41 * gx1;
		 *    *dnoise_dy += -8.0f * t21 * t1 * y1 * ( gx1 * x1 + gy1 * y1 ) + t41 * gy1;
		 *    *dnoise_dx += -8.0f * t22 * t2 * x2 * ( gx2 * x2 + gy2 * y2 ) + t42 * gx2;
		 *    *dnoise_dy += -8.0f * t22 * t2 * y2 * ( gx2 * x2 + gy2 * y2 ) + t42 * gy2;
		 */
		float temp0 = t20 * t0 * ( gx0* x0 + gy0 * y0 );
		*dnoise_dx = temp0 * x0;
		*dnoise_dy = temp0 * y0;
		float temp1 = t21 * t1 * ( gx1 * x1 + gy1 * y1 );
		*dnoise_dx += temp1 * x1;
		*dnoise_dy += temp1 * y1;
		float temp2 = t22 * t2 * ( gx2* x2 + gy2 * y2 );
		*dnoise_dx += temp2 * x2;
		*dnoise_dy += temp2 * y2;
		*dnoise_dx *= -8.0f;
		*dnoise_dy *= -8.0f;
		*dnoise_dx += t40 * gx0 + t41 * gx1 + t42 * gx2;
		*dnoise_dy += t40 * gy0 + t41 * gy1 + t42 * gy2;
		*dnoise_dx *= 40.0f; /* Scale derivative to match the noise scaling */
		*dnoise_dy *= 40.0f;
	}
	return noise;
}

float sdnoise2s( float x, float y, float *dnoise_dx, float *dnoise_dy )
{
	return sdnoise2( x, y, 256, 256, dnoise_dx, dnoise_dy );
}

/* Skewing factors for 3D simplex grid:
 * F3 = 1/3
 * G3 = 1/6 */
#define F3 0.333333333
#define G3 0.166666667


/** 3D simplex noise with derivatives.
 * If the last tthree arguments are not null, the analytic derivative
 * (the 3D gradient of the scalar noise field) is also calculated.
 */
float sdnoise3( float x, float y, float z, int px, int py, int pz,
	float *dnoise_dx, float *dnoise_dy, float *dnoise_dz )
{
	float n0, n1, n2, n3; /* Noise contributions from the four simplex corners */
	float noise;          /* Return value */
	float gx0, gy0, gz0, gx1, gy1, gz1; /* Gradients at simplex corners */
	float gx2, gy2, gz2, gx3, gy3, gz3;

	/* 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;

	/* 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 */

	/* TODO: 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.   */

	float x1 = x0 - i1 + G3; /* Offsets for second corner in (x,y,z) coords */
	float y1 = y0 - j1 + G3;
	float z1 = z0 - k1 + G3;
	float x2 = x0 - i2 + 2.0f * G3; /* Offsets for third corner in (x,y,z) coords */
	float y2 = y0 - j2 + 2.0f * G3;
	float z2 = z0 - k2 + 2.0f * G3;
	float x3 = x0 - 1.0f + 3.0f * G3; /* Offsets for last corner in (x,y,z) coords */
	float y3 = y0 - 1.0f + 3.0f * G3;
	float z3 = z0 - 1.0f + 3.0f * G3;

	/* Wrap the integer indices at 256, to avoid indexing perm[] out of bounds */
	int ii = i % px;
	int jj = j % py;
	int kk = k % pz;

	/* Calculate the contribution from the four corners */
	float t0 = 0.6f - x0*x0 - y0*y0 - z0*z0;
	float t20, t40;
	if(t0 < 0.0f) n0 = t0 = t20 = t40 = gx0 = gy0 = gz0 = 0.0f;
	else {
		grad3( perm[ii + perm[jj + perm[kk]]], &gx0, &gy0, &gz0 );
		t20 = t0 * t0;
		t40 = t20 * t20;
		n0 = t40 * ( gx0 * x0 + gy0 * y0 + gz0 * z0 );
	}

	float t1 = 0.6f - x1*x1 - y1*y1 - z1*z1;
	float t21, t41;
	if(t1 < 0.0f) n1 = t1 = t21 = t41 = gx1 = gy1 = gz1 = 0.0f;
	else {
		grad3( perm[ii + i1 + perm[jj + j1 + perm[kk + k1]]], &gx1, &gy1, &gz1 );
		t21 = t1 * t1;
		t41 = t21 * t21;
		n1 = t41 * ( gx1 * x1 + gy1 * y1 + gz1 * z1 );
	}

	float t2 = 0.6f - x2*x2 - y2*y2 - z2*z2;
	float t22, t42;
	if(t2 < 0.0f) n2 = t2 = t22 = t42 = gx2 = gy2 = gz2 = 0.0f;
	else {
		grad3( perm[ii + i2 + perm[jj + j2 + perm[kk + k2]]], &gx2, &gy2, &gz2 );
		t22 = t2 * t2;
		t42 = t22 * t22;
		n2 = t42 * ( gx2 * x2 + gy2 * y2 + gz2 * z2 );
	}

	float t3 = 0.6f - x3*x3 - y3*y3 - z3*z3;
	float t23, t43;
	if(t3 < 0.0f) n3 = t3 = t23 = t43 = gx3 = gy3 = gz3 = 0.0f;
	else {
		grad3( perm[ii + 1 + perm[jj + 1 + perm[kk + 1]]], &gx3, &gy3, &gz3 );
		t23 = t3 * t3;
		t43 = t23 * t23;
		n3 = t43 * ( gx3 * x3 + gy3 * y3 + gz3 * z3 );
	}

	/*  Add contributions from each corner to get the final noise value.
	 * The result is scaled to return values in the range [-1,1] */
	noise = 28.0f * (n0 + n1 + n2 + n3);

	/* Compute derivative, if requested by supplying non-null pointers
	 * for the last three arguments */
	if( ( dnoise_dx != 0 ) && ( dnoise_dy != 0 ) && ( dnoise_dz != 0 ))
	{
		/*  A straight, unoptimised calculation would be like:
		 *     *dnoise_dx = -8.0f * t20 * t0 * x0 * dot(gx0, gy0, gz0, x0, y0, z0) + t40 * gx0;
		 *    *dnoise_dy = -8.0f * t20 * t0 * y0 * dot(gx0, gy0, gz0, x0, y0, z0) + t40 * gy0;
		 *    *dnoise_dz = -8.0f * t20 * t0 * z0 * dot(gx0, gy0, gz0, x0, y0, z0) + t40 * gz0;
		 *    *dnoise_dx += -8.0f * t21 * t1 * x1 * dot(gx1, gy1, gz1, x1, y1, z1) + t41 * gx1;
		 *    *dnoise_dy += -8.0f * t21 * t1 * y1 * dot(gx1, gy1, gz1, x1, y1, z1) + t41 * gy1;
		 *    *dnoise_dz += -8.0f * t21 * t1 * z1 * dot(gx1, gy1, gz1, x1, y1, z1) + t41 * gz1;
		 *    *dnoise_dx += -8.0f * t22 * t2 * x2 * dot(gx2, gy2, gz2, x2, y2, z2) + t42 * gx2;
		 *    *dnoise_dy += -8.0f * t22 * t2 * y2 * dot(gx2, gy2, gz2, x2, y2, z2) + t42 * gy2;
		 *    *dnoise_dz += -8.0f * t22 * t2 * z2 * dot(gx2, gy2, gz2, x2, y2, z2) + t42 * gz2;
		 *    *dnoise_dx += -8.0f * t23 * t3 * x3 * dot(gx3, gy3, gz3, x3, y3, z3) + t43 * gx3;
		 *    *dnoise_dy += -8.0f * t23 * t3 * y3 * dot(gx3, gy3, gz3, x3, y3, z3) + t43 * gy3;
		 *    *dnoise_dz += -8.0f * t23 * t3 * z3 * dot(gx3, gy3, gz3, x3, y3, z3) + t43 * gz3;
		 */
		float temp0 = t20 * t0 * ( gx0 * x0 + gy0 * y0 + gz0 * z0 );
		*dnoise_dx = temp0 * x0;
		*dnoise_dy = temp0 * y0;
		*dnoise_dz = temp0 * z0;
		float temp1 = t21 * t1 * ( gx1 * x1 + gy1 * y1 + gz1 * z1 );
		*dnoise_dx += temp1 * x1;
		*dnoise_dy += temp1 * y1;
		*dnoise_dz += temp1 * z1;
		float temp2 = t22 * t2 * ( gx2 * x2 + gy2 * y2 + gz2 * z2 );
		*dnoise_dx += temp2 * x2;
		*dnoise_dy += temp2 * y2;
		*dnoise_dz += temp2 * z2;
		float temp3 = t23 * t3 * ( gx3 * x3 + gy3 * y3 + gz3 * z3 );
		*dnoise_dx += temp3 * x3;
		*dnoise_dy += temp3 * y3;
		*dnoise_dz += temp3 * z3;
		*dnoise_dx *= -8.0f;
		*dnoise_dy *= -8.0f;
		*dnoise_dz *= -8.0f;
		*dnoise_dx += t40 * gx0 + t41 * gx1 + t42 * gx2 + t43 * gx3;
		*dnoise_dy += t40 * gy0 + t41 * gy1 + t42 * gy2 + t43 * gy3;
		*dnoise_dz += t40 * gz0 + t41 * gz1 + t42 * gz2 + t43 * gz3;
		*dnoise_dx *= 28.0f; /* Scale derivative to match the noise scaling */
		*dnoise_dy *= 28.0f;
		*dnoise_dz *= 28.0f;
	}
	return noise;
}

float sdnoise3s( float x, float y, float z, float *dnoise_dx, float *dnoise_dy, float *dnoise_dz )
{
	return sdnoise3(x, y, z, 256, 256, 256, dnoise_dx, dnoise_dy, dnoise_dz);
}

// The skewing and unskewing factors are hairy again for the 4D case
#define F4 0.309016994 // F4 = (Math.sqrt(5.0)-1.0)/4.0
#define G4 0.138196601 // G4 = (5.0-Math.sqrt(5.0))/20.0

/** 4D simplex noise with derivatives.
 * If the last four arguments are not null, the analytic derivative
 * (the 4D gradient of the scalar noise field) is also calculated.
 */
float sdnoise4( float x, float y, float z, float w,
	int px, int py, int pz, int pw,
	float *dnoise_dx, float *dnoise_dy,
	float *dnoise_dz, float *dnoise_dw)
{
	float n0, n1, n2, n3, n4; // Noise contributions from the five corners
	float noise; // Return value
	float gx0, gy0, gz0, gw0, gx1, gy1, gz1, gw1; /* Gradients at simplex corners */
	float gx2, gy2, gz2, gw2, gx3, gy3, gz3, gw3, gx4, gy4, gz4, gw4;
	float t20, t21, t22, t23, t24;
	float t40, t41, t42, t43, t44;

	// 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 reasonable way of finding the ordering of x,y,z,w
	// and then find the correct traversal order for the simplex were in.
	// First, six pair-wise comparisons are performed between each possible pair
	// of the four coordinates, and then the results are used to add up binary
	// bits for an integer index into a precomputed lookup table, simplex[].
	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; // '|' is mostly faster than '+'

	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

	// 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.

	float x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
	float y1 = y0 - j1 + G4;
	float z1 = z0 - k1 + G4;
	float w1 = w0 - l1 + G4;
	float x2 = x0 - i2 + 2.0f * G4; // Offsets for third corner in (x,y,z,w) coords
	float y2 = y0 - j2 + 2.0f * G4;
	float z2 = z0 - k2 + 2.0f * G4;
	float w2 = w0 - l2 + 2.0f * G4;
	float x3 = x0 - i3 + 3.0f * G4; // Offsets for fourth corner in (x,y,z,w) coords
	float y3 = y0 - j3 + 3.0f * G4;
	float z3 = z0 - k3 + 3.0f * G4;
	float w3 = w0 - l3 + 3.0f * G4;
	float x4 = x0 - 1.0f + 4.0f * G4; // Offsets for last corner in (x,y,z,w) coords
	float y4 = y0 - 1.0f + 4.0f * G4;
	float z4 = z0 - 1.0f + 4.0f * G4;
	float w4 = w0 - 1.0f + 4.0f * G4;

	// Wrap the integer indices at 256, to avoid indexing perm[] out of bounds
	int ii = i % px;
	int jj = j % py;
	int kk = k % pz;
	int ll = l % pw;

	// Calculate the contribution from the five corners
	float t0 = 0.6f - x0*x0 - y0*y0 - z0*z0 - w0*w0;
	if(t0 < 0.0f) n0 = t0 = t20 = t40 = gx0 = gy0 = gz0 = gw0 = 0.0f;
	else {
		t20 = t0 * t0;
		t40 = t20 * t20;
		grad4(perm[ii+perm[jj+perm[kk+perm[ll]]]], &gx0, &gy0, &gz0, &gw0);
		n0 = t40 * ( gx0 * x0 + gy0 * y0 + gz0 * z0 + gw0 * w0 );
	}

	float t1 = 0.6f - x1*x1 - y1*y1 - z1*z1 - w1*w1;
	if(t1 < 0.0f) n1 = t1 = t21 = t41 = gx1 = gy1 = gz1 = gw1 = 0.0f;
	else {
		t21 = t1 * t1;
		t41 = t21 * t21;
		grad4(perm[ii+i1+perm[jj+j1+perm[kk+k1+perm[ll+l1]]]], &gx1, &gy1, &gz1, &gw1);
		n1 = t41 * ( gx1 * x1 + gy1 * y1 + gz1 * z1 + gw1 * w1 );
	}

	float t2 = 0.6f - x2*x2 - y2*y2 - z2*z2 - w2*w2;
	if(t2 < 0.0f) n2 = t2 = t22 = t42 = gx2 = gy2 = gz2 = gw2 = 0.0f;
	else {
		t22 = t2 * t2;
		t42 = t22 * t22;
		grad4(perm[ii+i2+perm[jj+j2+perm[kk+k2+perm[ll+l2]]]], &gx2, &gy2, &gz2, &gw2);
		n2 = t42 * ( gx2 * x2 + gy2 * y2 + gz2 * z2 + gw2 * w2 );
	}

	float t3 = 0.6f - x3*x3 - y3*y3 - z3*z3 - w3*w3;
	if(t3 < 0.0f) n3 = t3 = t23 = t43 = gx3 = gy3 = gz3 = gw3 = 0.0f;
	else {
		t23 = t3 * t3;
		t43 = t23 * t23;
		grad4(perm[ii+i3+perm[jj+j3+perm[kk+k3+perm[ll+l3]]]], &gx3, &gy3, &gz3, &gw3);
		n3 = t43 * ( gx3 * x3 + gy3 * y3 + gz3 * z3 + gw3 * w3 );
	}

	float t4 = 0.6f - x4*x4 - y4*y4 - z4*z4 - w4*w4;
	if(t4 < 0.0f) n4 = t4 = t24 = t44 = gx4 = gy4 = gz4 = gw4 = 0.0f;
	else {
		t24 = t4 * t4;
		t44 = t24 * t24;
		grad4(perm[ii+1+perm[jj+1+perm[kk+1+perm[ll+1]]]], &gx4, &gy4, &gz4, &gw4);
		n4 = t44 * ( gx4 * x4 + gy4 * y4 + gz4 * z4 + gw4 * w4 );
	}

	// Sum up and scale the result to cover the range [-1,1]
	noise = 27.0f * (n0 + n1 + n2 + n3 + n4); // TODO: The scale factor is preliminary!

	/* Compute derivative, if requested by supplying non-null pointers
	 * for the last four arguments */
	if( ( dnoise_dx != 0 ) && ( dnoise_dy != 0 ) && ( dnoise_dz != 0 ) && ( dnoise_dw != 0 ) )
	{
		/*  A straight, unoptimised calculation would be like:
		 *     *dnoise_dx = -8.0f * t20 * t0 * x0 * dot(gx0, gy0, gz0, gw0, x0, y0, z0, w0) + t40 * gx0;
		 *    *dnoise_dy = -8.0f * t20 * t0 * y0 * dot(gx0, gy0, gz0, gw0, x0, y0, z0, w0) + t40 * gy0;
		 *    *dnoise_dz = -8.0f * t20 * t0 * z0 * dot(gx0, gy0, gz0, gw0, x0, y0, z0, w0) + t40 * gz0;
		 *    *dnoise_dw = -8.0f * t20 * t0 * w0 * dot(gx0, gy0, gz0, gw0, x0, y0, z0, w0) + t40 * gw0;
		 *    *dnoise_dx += -8.0f * t21 * t1 * x1 * dot(gx1, gy1, gz1, gw1, x1, y1, z1, w1) + t41 * gx1;
		 *    *dnoise_dy += -8.0f * t21 * t1 * y1 * dot(gx1, gy1, gz1, gw1, x1, y1, z1, w1) + t41 * gy1;
		 *    *dnoise_dz += -8.0f * t21 * t1 * z1 * dot(gx1, gy1, gz1, gw1, x1, y1, z1, w1) + t41 * gz1;
		 *    *dnoise_dw = -8.0f * t21 * t1 * w1 * dot(gx1, gy1, gz1, gw1, x1, y1, z1, w1) + t41 * gw1;
		 *    *dnoise_dx += -8.0f * t22 * t2 * x2 * dot(gx2, gy2, gz2, gw2, x2, y2, z2, w2) + t42 * gx2;
		 *    *dnoise_dy += -8.0f * t22 * t2 * y2 * dot(gx2, gy2, gz2, gw2, x2, y2, z2, w2) + t42 * gy2;
		 *    *dnoise_dz += -8.0f * t22 * t2 * z2 * dot(gx2, gy2, gz2, gw2, x2, y2, z2, w2) + t42 * gz2;
		 *    *dnoise_dw += -8.0f * t22 * t2 * w2 * dot(gx2, gy2, gz2, gw2, x2, y2, z2, w2) + t42 * gw2;
		 *    *dnoise_dx += -8.0f * t23 * t3 * x3 * dot(gx3, gy3, gz3, gw3, x3, y3, z3, w3) + t43 * gx3;
		 *    *dnoise_dy += -8.0f * t23 * t3 * y3 * dot(gx3, gy3, gz3, gw3, x3, y3, z3, w3) + t43 * gy3;
		 *    *dnoise_dz += -8.0f * t23 * t3 * z3 * dot(gx3, gy3, gz3, gw3, x3, y3, z3, w3) + t43 * gz3;
		 *    *dnoise_dw += -8.0f * t23 * t3 * w3 * dot(gx3, gy3, gz3, gw3, x3, y3, z3, w3) + t43 * gw3;
		 *    *dnoise_dx += -8.0f * t24 * t4 * x4 * dot(gx4, gy4, gz4, gw4, x4, y4, z4, w4) + t44 * gx4;
		 *    *dnoise_dy += -8.0f * t24 * t4 * y4 * dot(gx4, gy4, gz4, gw4, x4, y4, z4, w4) + t44 * gy4;
		 *    *dnoise_dz += -8.0f * t24 * t4 * z4 * dot(gx4, gy4, gz4, gw4, x4, y4, z4, w4) + t44 * gz4;
		 *    *dnoise_dw += -8.0f * t24 * t4 * w4 * dot(gx4, gy4, gz4, gw4, x4, y4, z4, w4) + t44 * gw4;
		 */
		float temp0 = t20 * t0 * ( gx0 * x0 + gy0 * y0 + gz0 * z0 + gw0 * w0 );
		*dnoise_dx = temp0 * x0;
		*dnoise_dy = temp0 * y0;
		*dnoise_dz = temp0 * z0;
		*dnoise_dw = temp0 * w0;
		float temp1 = t21 * t1 * ( gx1 * x1 + gy1 * y1 + gz1 * z1 + gw1 * w1 );
		*dnoise_dx += temp1 * x1;
		*dnoise_dy += temp1 * y1;
		*dnoise_dz += temp1 * z1;
		*dnoise_dw += temp1 * w1;
		float temp2 = t22 * t2 * ( gx2 * x2 + gy2 * y2 + gz2 * z2 + gw2 * w2 );
		*dnoise_dx += temp2 * x2;
		*dnoise_dy += temp2 * y2;
		*dnoise_dz += temp2 * z2;
		*dnoise_dw += temp2 * w2;
		float temp3 = t23 * t3 * ( gx3 * x3 + gy3 * y3 + gz3 * z3 + gw3 * w3 );
		*dnoise_dx += temp3 * x3;
		*dnoise_dy += temp3 * y3;
		*dnoise_dz += temp3 * z3;
		*dnoise_dw += temp3 * w3;
		float temp4 = t24 * t4 * ( gx4 * x4 + gy4 * y4 + gz4 * z4 + gw4 * w4 );
		*dnoise_dx += temp4 * x4;
		*dnoise_dy += temp4 * y4;
		*dnoise_dz += temp4 * z4;
		*dnoise_dw += temp4 * w4;
		*dnoise_dx *= -8.0f;
		*dnoise_dy *= -8.0f;
		*dnoise_dz *= -8.0f;
		*dnoise_dw *= -8.0f;
		*dnoise_dx += t40 * gx0 + t41 * gx1 + t42 * gx2 + t43 * gx3 + t44 * gx4;
		*dnoise_dy += t40 * gy0 + t41 * gy1 + t42 * gy2 + t43 * gy3 + t44 * gy4;
		*dnoise_dz += t40 * gz0 + t41 * gz1 + t42 * gz2 + t43 * gz3 + t44 * gz4;
		*dnoise_dw += t40 * gw0 + t41 * gw1 + t42 * gw2 + t43 * gw3 + t44 * gw4;

		*dnoise_dx *= 28.0f; /* Scale derivative to match the noise scaling */
		*dnoise_dy *= 28.0f;
		*dnoise_dz *= 28.0f;
		*dnoise_dw *= 28.0f;
	}

	return noise;
}

float sdnoise4s( float x, float y, float z, float w,
	float *dnoise_dx, float *dnoise_dy,
	float *dnoise_dz, float *dnoise_dw)
{
	return sdnoise4( x, y, z, w,
		256, 256, 256, 256,
		dnoise_dx, dnoise_dy,
		dnoise_dz, dnoise_dw);
}