opensimplex 0.1.0

/*
 * OpenSimplex (Simplectic) Noise in C.
 * Ported by Stephen M. Cameron from Kurt Spencer's java implementation
 * 
 * v1.1 (October 5, 2014)
 * - Added 2D and 4D implementations.
 * - Proper gradient sets for all dimensions, from a
 *   dimensionally-generalizable scheme with an actual
 *   rhyme and reason behind it.
 * - Removed default permutation array in favor of
 *   default seed.
 * - Changed seed-based constructor to be independent
 *   of any particular randomization library, so results
 *   will be the same when ported to other languages.
 */
#include <math.h>
#include <stdlib.h>
#include <stdint.h>
#include <string.h>
#include <errno.h>

#include "opensimplex.h"

#define STRETCH_CONSTANT_2D (-0.211324865405187)    // (1 / sqrt(2 + 1) - 1 ) / 2;
#define SQUISH_CONSTANT_2D  (0.366025403784439)     // (sqrt(2 + 1) -1) / 2;
#define STRETCH_CONSTANT_3D (-1.0 / 6.0)            // (1 / sqrt(3 + 1) - 1) / 3;
#define SQUISH_CONSTANT_3D  (1.0 / 3.0)             // (sqrt(3+1)-1)/3;
#define STRETCH_CONSTANT_4D (-0.138196601125011)    // (1 / sqrt(4 + 1) - 1) / 4;
#define SQUISH_CONSTANT_4D  (0.309016994374947)     // (sqrt(4 + 1) - 1) / 4;
	
#define NORM_CONSTANT_2D (47.0)
#define NORM_CONSTANT_3D (103.0)
#define NORM_CONSTANT_4D (30.0)
	
#define DEFAULT_SEED (0LL)

struct osn_context {
	int16_t *perm;
	int16_t *permGradIndex3D;
};

#define ARRAYSIZE(x) (sizeof((x)) / sizeof((x)[0]))

/* 
 * Gradients for 2D. They approximate the directions to the
 * vertices of an octagon from the center.
 */
static const int8_t gradients2D[] = {
	 5,  2,    2,  5,
	-5,  2,   -2,  5,
	 5, -2,    2, -5,
	-5, -2,   -2, -5,
};

/*	
 * Gradients for 3D. They approximate the directions to the
 * vertices of a rhombicuboctahedron from the center, skewed so
 * that the triangular and square facets can be inscribed inside
 * circles of the same radius.
 */
static const signed char gradients3D[] = {
	-11,  4,  4,     -4,  11,  4,    -4,  4,  11,
	 11,  4,  4,      4,  11,  4,     4,  4,  11,
	-11, -4,  4,     -4, -11,  4,    -4, -4,  11,
	 11, -4,  4,      4, -11,  4,     4, -4,  11,
	-11,  4, -4,     -4,  11, -4,    -4,  4, -11,
	 11,  4, -4,      4,  11, -4,     4,  4, -11,
	-11, -4, -4,     -4, -11, -4,    -4, -4, -11,
	 11, -4, -4,      4, -11, -4,     4, -4, -11,
};

/*	
 * Gradients for 4D. They approximate the directions to the
 * vertices of a disprismatotesseractihexadecachoron from the center,
 * skewed so that the tetrahedral and cubic facets can be inscribed inside
 * spheres of the same radius.
 */
static const signed char gradients4D[] = {
     3,  1,  1,  1,      1,  3,  1,  1,      1,  1,  3,  1,      1,  1,  1,  3,
    -3,  1,  1,  1,     -1,  3,  1,  1,     -1,  1,  3,  1,     -1,  1,  1,  3,
     3, -1,  1,  1,      1, -3,  1,  1,      1, -1,  3,  1,      1, -1,  1,  3,
    -3, -1,  1,  1,     -1, -3,  1,  1,     -1, -1,  3,  1,     -1, -1,  1,  3,
     3,  1, -1,  1,      1,  3, -1,  1,      1,  1, -3,  1,      1,  1, -1,  3,
    -3,  1, -1,  1,     -1,  3, -1,  1,     -1,  1, -3,  1,     -1,  1, -1,  3,
     3, -1, -1,  1,      1, -3, -1,  1,      1, -1, -3,  1,      1, -1, -1,  3,
    -3, -1, -1,  1,     -1, -3, -1,  1,     -1, -1, -3,  1,     -1, -1, -1,  3,
     3,  1,  1, -1,      1,  3,  1, -1,      1,  1,  3, -1,      1,  1,  1, -3,
    -3,  1,  1, -1,     -1,  3,  1, -1,     -1,  1,  3, -1,     -1,  1,  1, -3,
     3, -1,  1, -1,      1, -3,  1, -1,      1, -1,  3, -1,      1, -1,  1, -3,
    -3, -1,  1, -1,     -1, -3,  1, -1,     -1, -1,  3, -1,     -1, -1,  1, -3,
     3,  1, -1, -1,      1,  3, -1, -1,      1,  1, -3, -1,      1,  1, -1, -3,
    -3,  1, -1, -1,     -1,  3, -1, -1,     -1,  1, -3, -1,     -1,  1, -1, -3,
     3, -1, -1, -1,      1, -3, -1, -1,      1, -1, -3, -1,      1, -1, -1, -3,
    -3, -1, -1, -1,     -1, -3, -1, -1,     -1, -1, -3, -1,     -1, -1, -1, -3,
};

static double extrapolate2(struct osn_context *ctx, int xsb, int ysb, double dx, double dy)
{
	int16_t *perm = ctx->perm;	
	int index = perm[(perm[xsb & 0xFF] + ysb) & 0xFF] & 0x0E;
	return gradients2D[index] * dx
		+ gradients2D[index + 1] * dy;
}
	
static double extrapolate3(struct osn_context *ctx, int xsb, int ysb, int zsb, double dx, double dy, double dz)
{
	int16_t *perm = ctx->perm;	
	int16_t *permGradIndex3D = ctx->permGradIndex3D;
	int index = permGradIndex3D[(perm[(perm[xsb & 0xFF] + ysb) & 0xFF] + zsb) & 0xFF];
	return gradients3D[index] * dx
		+ gradients3D[index + 1] * dy
		+ gradients3D[index + 2] * dz;
}
	
static double extrapolate4(struct osn_context *ctx, int xsb, int ysb, int zsb, int wsb, double dx, double dy, double dz, double dw)
{
	int16_t *perm = ctx->perm;
	int index = perm[(perm[(perm[(perm[xsb & 0xFF] + ysb) & 0xFF] + zsb) & 0xFF] + wsb) & 0xFF] & 0xFC;
	return gradients4D[index] * dx
		+ gradients4D[index + 1] * dy
		+ gradients4D[index + 2] * dz
		+ gradients4D[index + 3] * dw;
}
	
static inline int fastFloor(double x) {
	int xi = (int) x;
	return x < xi ? xi - 1 : xi;
}
	
static int allocate_perm(struct osn_context *ctx, int nperm, int ngrad)
{
	if (ctx->perm)
		free(ctx->perm);
	if (ctx->permGradIndex3D)
		free(ctx->permGradIndex3D);
	ctx->perm = malloc(sizeof(*ctx->perm) * nperm); 
	if (!ctx->perm)
		return -ENOMEM;
	ctx->permGradIndex3D = malloc(sizeof(*ctx->permGradIndex3D) * ngrad);
	if (!ctx->permGradIndex3D) {
		free(ctx->perm);
		return -ENOMEM;
	}
	return 0;
}
	
int open_simplex_noise_init_perm(struct osn_context *ctx, int16_t p[], int nelements)
{
	int i, rc;

	rc = allocate_perm(ctx, nelements, 256);
	if (rc)
		return rc;
	memcpy(ctx->perm, p, sizeof(*ctx->perm) * nelements);
		
	for (i = 0; i < 256; i++) {
		//Since 3D has 24 gradients, simple bitmask won't work, so precompute modulo array.
		ctx->permGradIndex3D[i] = (int16_t)((ctx->perm[i] % (ARRAYSIZE(gradients3D) / 3)) * 3);
	}
	return 0;
}

/*	
 * Initializes using a permutation array generated from a 64-bit seed.
 * Generates a proper permutation (i.e. doesn't merely perform N successive pair
 * swaps on a base array).  Uses a simple 64-bit LCG.
 */
int open_simplex_noise(int64_t seed, struct osn_context **ctx)
{
	int rc;
	int16_t source[256];
	int i;
	int16_t *perm;
	int16_t *permGradIndex3D;

	*ctx = malloc(sizeof(**ctx));
	if (!(*ctx))
		return -ENOMEM;
	(*ctx)->perm = NULL;
	(*ctx)->permGradIndex3D = NULL;

	rc = allocate_perm(*ctx, 256, 256);
	if (rc) {
		free(*ctx);
		return rc;
	}

	perm = (*ctx)->perm;
	permGradIndex3D = (*ctx)->permGradIndex3D;

	for (i = 0; i < 256; i++)
		source[i] = (int16_t) i;
	seed = seed * 6364136223846793005LL + 1442695040888963407LL;
	seed = seed * 6364136223846793005LL + 1442695040888963407LL;
	seed = seed * 6364136223846793005LL + 1442695040888963407LL;
	for (i = 255; i >= 0; i--) {
		seed = seed * 6364136223846793005LL + 1442695040888963407LL;
		int r = (int)((seed + 31) % (i + 1));
		if (r < 0)
			r += (i + 1);
		perm[i] = source[r];
		permGradIndex3D[i] = (short)((perm[i] % (ARRAYSIZE(gradients3D) / 3)) * 3);
		source[r] = source[i];
	}
	return 0;
}

void open_simplex_noise_free(struct osn_context *ctx)
{
	if (!ctx)
		return;
	if (ctx->perm) {
		free(ctx->perm);
		ctx->perm = NULL;	
	}
	if (ctx->permGradIndex3D) {
		free(ctx->permGradIndex3D);
		ctx->permGradIndex3D = NULL;
	}
	free(ctx);
}
	
/* 2D OpenSimplex (Simplectic) Noise. */
double open_simplex_noise2(struct osn_context *ctx, double x, double y) 
{
	
	//Place input coordinates onto grid.
	double stretchOffset = (x + y) * STRETCH_CONSTANT_2D;
	double xs = x + stretchOffset;
	double ys = y + stretchOffset;
		
	//Floor to get grid coordinates of rhombus (stretched square) super-cell origin.
	int xsb = fastFloor(xs);
	int ysb = fastFloor(ys);
		
	//Skew out to get actual coordinates of rhombus origin. We'll need these later.
	double squishOffset = (xsb + ysb) * SQUISH_CONSTANT_2D;
	double xb = xsb + squishOffset;
	double yb = ysb + squishOffset;
		
	//Compute grid coordinates relative to rhombus origin.
	double xins = xs - xsb;
	double yins = ys - ysb;
		
	//Sum those together to get a value that determines which region we're in.
	double inSum = xins + yins;

	//Positions relative to origin point.
	double dx0 = x - xb;
	double dy0 = y - yb;
		
	//We'll be defining these inside the next block and using them afterwards.
	double dx_ext, dy_ext;
	int xsv_ext, ysv_ext;
		
	double value = 0;

	//Contribution (1,0)
	double dx1 = dx0 - 1 - SQUISH_CONSTANT_2D;
	double dy1 = dy0 - 0 - SQUISH_CONSTANT_2D;
	double attn1 = 2 - dx1 * dx1 - dy1 * dy1;
	if (attn1 > 0) {
		attn1 *= attn1;
		value += attn1 * attn1 * extrapolate2(ctx, xsb + 1, ysb + 0, dx1, dy1);
	}

	//Contribution (0,1)
	double dx2 = dx0 - 0 - SQUISH_CONSTANT_2D;
	double dy2 = dy0 - 1 - SQUISH_CONSTANT_2D;
	double attn2 = 2 - dx2 * dx2 - dy2 * dy2;
	if (attn2 > 0) {
		attn2 *= attn2;
		value += attn2 * attn2 * extrapolate2(ctx, xsb + 0, ysb + 1, dx2, dy2);
	}
		
	if (inSum <= 1) { //We're inside the triangle (2-Simplex) at (0,0)
		double zins = 1 - inSum;
		if (zins > xins || zins > yins) { //(0,0) is one of the closest two triangular vertices
			if (xins > yins) {
				xsv_ext = xsb + 1;
				ysv_ext = ysb - 1;
				dx_ext = dx0 - 1;
				dy_ext = dy0 + 1;
			} else {
				xsv_ext = xsb - 1;
				ysv_ext = ysb + 1;
				dx_ext = dx0 + 1;
				dy_ext = dy0 - 1;
			}
		} else { //(1,0) and (0,1) are the closest two vertices.
			xsv_ext = xsb + 1;
			ysv_ext = ysb + 1;
			dx_ext = dx0 - 1 - 2 * SQUISH_CONSTANT_2D;
			dy_ext = dy0 - 1 - 2 * SQUISH_CONSTANT_2D;
		}
	} else { //We're inside the triangle (2-Simplex) at (1,1)
		double zins = 2 - inSum;
		if (zins < xins || zins < yins) { //(0,0) is one of the closest two triangular vertices
			if (xins > yins) {
				xsv_ext = xsb + 2;
				ysv_ext = ysb + 0;
				dx_ext = dx0 - 2 - 2 * SQUISH_CONSTANT_2D;
				dy_ext = dy0 + 0 - 2 * SQUISH_CONSTANT_2D;
			} else {
				xsv_ext = xsb + 0;
				ysv_ext = ysb + 2;
				dx_ext = dx0 + 0 - 2 * SQUISH_CONSTANT_2D;
				dy_ext = dy0 - 2 - 2 * SQUISH_CONSTANT_2D;
			}
		} else { //(1,0) and (0,1) are the closest two vertices.
			dx_ext = dx0;
			dy_ext = dy0;
			xsv_ext = xsb;
			ysv_ext = ysb;
		}
		xsb += 1;
		ysb += 1;
		dx0 = dx0 - 1 - 2 * SQUISH_CONSTANT_2D;
		dy0 = dy0 - 1 - 2 * SQUISH_CONSTANT_2D;
	}
		
	//Contribution (0,0) or (1,1)
	double attn0 = 2 - dx0 * dx0 - dy0 * dy0;
	if (attn0 > 0) {
		attn0 *= attn0;
		value += attn0 * attn0 * extrapolate2(ctx, xsb, ysb, dx0, dy0);
	}
	
	//Extra Vertex
	double attn_ext = 2 - dx_ext * dx_ext - dy_ext * dy_ext;
	if (attn_ext > 0) {
		attn_ext *= attn_ext;
		value += attn_ext * attn_ext * extrapolate2(ctx, xsv_ext, ysv_ext, dx_ext, dy_ext);
	}
	
	return value / NORM_CONSTANT_2D;
}
	
/*
 * 3D OpenSimplex (Simplectic) Noise
 */
double open_simplex_noise3(struct osn_context *ctx, double x, double y, double z)
{

	//Place input coordinates on simplectic honeycomb.
	double stretchOffset = (x + y + z) * STRETCH_CONSTANT_3D;
	double xs = x + stretchOffset;
	double ys = y + stretchOffset;
	double zs = z + stretchOffset;
	
	//Floor to get simplectic honeycomb coordinates of rhombohedron (stretched cube) super-cell origin.
	int xsb = fastFloor(xs);
	int ysb = fastFloor(ys);
	int zsb = fastFloor(zs);
	
	//Skew out to get actual coordinates of rhombohedron origin. We'll need these later.
	double squishOffset = (xsb + ysb + zsb) * SQUISH_CONSTANT_3D;
	double xb = xsb + squishOffset;
	double yb = ysb + squishOffset;
	double zb = zsb + squishOffset;
	
	//Compute simplectic honeycomb coordinates relative to rhombohedral origin.
	double xins = xs - xsb;
	double yins = ys - ysb;
	double zins = zs - zsb;
	
	//Sum those together to get a value that determines which region we're in.
	double inSum = xins + yins + zins;

	//Positions relative to origin point.
	double dx0 = x - xb;
	double dy0 = y - yb;
	double dz0 = z - zb;
	
	//We'll be defining these inside the next block and using them afterwards.
	double dx_ext0, dy_ext0, dz_ext0;
	double dx_ext1, dy_ext1, dz_ext1;
	int xsv_ext0, ysv_ext0, zsv_ext0;
	int xsv_ext1, ysv_ext1, zsv_ext1;
	
	double value = 0;
	if (inSum <= 1) { //We're inside the tetrahedron (3-Simplex) at (0,0,0)
		
		//Determine which two of (0,0,1), (0,1,0), (1,0,0) are closest.
		int8_t aPoint = 0x01;
		double aScore = xins;
		int8_t bPoint = 0x02;
		double bScore = yins;
		if (aScore >= bScore && zins > bScore) {
			bScore = zins;
			bPoint = 0x04;
		} else if (aScore < bScore && zins > aScore) {
			aScore = zins;
			aPoint = 0x04;
		}
		
		//Now we determine the two lattice points not part of the tetrahedron that may contribute.
		//This depends on the closest two tetrahedral vertices, including (0,0,0)
		double wins = 1 - inSum;
		if (wins > aScore || wins > bScore) { //(0,0,0) is one of the closest two tetrahedral vertices.
			int8_t c = (bScore > aScore ? bPoint : aPoint); //Our other closest vertex is the closest out of a and b.
			
			if ((c & 0x01) == 0) {
				xsv_ext0 = xsb - 1;
				xsv_ext1 = xsb;
				dx_ext0 = dx0 + 1;
				dx_ext1 = dx0;
			} else {
				xsv_ext0 = xsv_ext1 = xsb + 1;
				dx_ext0 = dx_ext1 = dx0 - 1;
			}

			if ((c & 0x02) == 0) {
				ysv_ext0 = ysv_ext1 = ysb;
				dy_ext0 = dy_ext1 = dy0;
				if ((c & 0x01) == 0) {
					ysv_ext1 -= 1;
					dy_ext1 += 1;
				} else {
					ysv_ext0 -= 1;
					dy_ext0 += 1;
				}
			} else {
				ysv_ext0 = ysv_ext1 = ysb + 1;
				dy_ext0 = dy_ext1 = dy0 - 1;
			}

			if ((c & 0x04) == 0) {
				zsv_ext0 = zsb;
				zsv_ext1 = zsb - 1;
				dz_ext0 = dz0;
				dz_ext1 = dz0 + 1;
			} else {
				zsv_ext0 = zsv_ext1 = zsb + 1;
				dz_ext0 = dz_ext1 = dz0 - 1;
			}
		} else { //(0,0,0) is not one of the closest two tetrahedral vertices.
			int8_t c = (int8_t)(aPoint | bPoint); //Our two extra vertices are determined by the closest two.
			
			if ((c & 0x01) == 0) {
				xsv_ext0 = xsb;
				xsv_ext1 = xsb - 1;
				dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_3D;
				dx_ext1 = dx0 + 1 - SQUISH_CONSTANT_3D;
			} else {
				xsv_ext0 = xsv_ext1 = xsb + 1;
				dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_3D;
				dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_3D;
			}

			if ((c & 0x02) == 0) {
				ysv_ext0 = ysb;
				ysv_ext1 = ysb - 1;
				dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_3D;
				dy_ext1 = dy0 + 1 - SQUISH_CONSTANT_3D;
			} else {
				ysv_ext0 = ysv_ext1 = ysb + 1;
				dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_3D;
				dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_3D;
			}

			if ((c & 0x04) == 0) {
				zsv_ext0 = zsb;
				zsv_ext1 = zsb - 1;
				dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_3D;
				dz_ext1 = dz0 + 1 - SQUISH_CONSTANT_3D;
			} else {
				zsv_ext0 = zsv_ext1 = zsb + 1;
				dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_3D;
				dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_3D;
			}
		}

		//Contribution (0,0,0)
		double attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0;
		if (attn0 > 0) {
			attn0 *= attn0;
			value += attn0 * attn0 * extrapolate3(ctx, xsb + 0, ysb + 0, zsb + 0, dx0, dy0, dz0);
		}

		//Contribution (1,0,0)
		double dx1 = dx0 - 1 - SQUISH_CONSTANT_3D;
		double dy1 = dy0 - 0 - SQUISH_CONSTANT_3D;
		double dz1 = dz0 - 0 - SQUISH_CONSTANT_3D;
		double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1;
		if (attn1 > 0) {
			attn1 *= attn1;
			value += attn1 * attn1 * extrapolate3(ctx, xsb + 1, ysb + 0, zsb + 0, dx1, dy1, dz1);
		}

		//Contribution (0,1,0)
		double dx2 = dx0 - 0 - SQUISH_CONSTANT_3D;
		double dy2 = dy0 - 1 - SQUISH_CONSTANT_3D;
		double dz2 = dz1;
		double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2;
		if (attn2 > 0) {
			attn2 *= attn2;
			value += attn2 * attn2 * extrapolate3(ctx, xsb + 0, ysb + 1, zsb + 0, dx2, dy2, dz2);
		}

		//Contribution (0,0,1)
		double dx3 = dx2;
		double dy3 = dy1;
		double dz3 = dz0 - 1 - SQUISH_CONSTANT_3D;
		double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3;
		if (attn3 > 0) {
			attn3 *= attn3;
			value += attn3 * attn3 * extrapolate3(ctx, xsb + 0, ysb + 0, zsb + 1, dx3, dy3, dz3);
		}
	} else if (inSum >= 2) { //We're inside the tetrahedron (3-Simplex) at (1,1,1)
	
		//Determine which two tetrahedral vertices are the closest, out of (1,1,0), (1,0,1), (0,1,1) but not (1,1,1).
		int8_t aPoint = 0x06;
		double aScore = xins;
		int8_t bPoint = 0x05;
		double bScore = yins;
		if (aScore <= bScore && zins < bScore) {
			bScore = zins;
			bPoint = 0x03;
		} else if (aScore > bScore && zins < aScore) {
			aScore = zins;
			aPoint = 0x03;
		}
		
		//Now we determine the two lattice points not part of the tetrahedron that may contribute.
		//This depends on the closest two tetrahedral vertices, including (1,1,1)
		double wins = 3 - inSum;
		if (wins < aScore || wins < bScore) { //(1,1,1) is one of the closest two tetrahedral vertices.
			int8_t c = (bScore < aScore ? bPoint : aPoint); //Our other closest vertex is the closest out of a and b.
			
			if ((c & 0x01) != 0) {
				xsv_ext0 = xsb + 2;
				xsv_ext1 = xsb + 1;
				dx_ext0 = dx0 - 2 - 3 * SQUISH_CONSTANT_3D;
				dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_3D;
			} else {
				xsv_ext0 = xsv_ext1 = xsb;
				dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_3D;
			}

			if ((c & 0x02) != 0) {
				ysv_ext0 = ysv_ext1 = ysb + 1;
				dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_3D;
				if ((c & 0x01) != 0) {
					ysv_ext1 += 1;
					dy_ext1 -= 1;
				} else {
					ysv_ext0 += 1;
					dy_ext0 -= 1;
				}
			} else {
				ysv_ext0 = ysv_ext1 = ysb;
				dy_ext0 = dy_ext1 = dy0 - 3 * SQUISH_CONSTANT_3D;
			}

			if ((c & 0x04) != 0) {
				zsv_ext0 = zsb + 1;
				zsv_ext1 = zsb + 2;
				dz_ext0 = dz0 - 1 - 3 * SQUISH_CONSTANT_3D;
				dz_ext1 = dz0 - 2 - 3 * SQUISH_CONSTANT_3D;
			} else {
				zsv_ext0 = zsv_ext1 = zsb;
				dz_ext0 = dz_ext1 = dz0 - 3 * SQUISH_CONSTANT_3D;
			}
		} else { //(1,1,1) is not one of the closest two tetrahedral vertices.
			int8_t c = (int8_t)(aPoint & bPoint); //Our two extra vertices are determined by the closest two.
			
			if ((c & 0x01) != 0) {
				xsv_ext0 = xsb + 1;
				xsv_ext1 = xsb + 2;
				dx_ext0 = dx0 - 1 - SQUISH_CONSTANT_3D;
				dx_ext1 = dx0 - 2 - 2 * SQUISH_CONSTANT_3D;
			} else {
				xsv_ext0 = xsv_ext1 = xsb;
				dx_ext0 = dx0 - SQUISH_CONSTANT_3D;
				dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D;
			}

			if ((c & 0x02) != 0) {
				ysv_ext0 = ysb + 1;
				ysv_ext1 = ysb + 2;
				dy_ext0 = dy0 - 1 - SQUISH_CONSTANT_3D;
				dy_ext1 = dy0 - 2 - 2 * SQUISH_CONSTANT_3D;
			} else {
				ysv_ext0 = ysv_ext1 = ysb;
				dy_ext0 = dy0 - SQUISH_CONSTANT_3D;
				dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D;
			}

			if ((c & 0x04) != 0) {
				zsv_ext0 = zsb + 1;
				zsv_ext1 = zsb + 2;
				dz_ext0 = dz0 - 1 - SQUISH_CONSTANT_3D;
				dz_ext1 = dz0 - 2 - 2 * SQUISH_CONSTANT_3D;
			} else {
				zsv_ext0 = zsv_ext1 = zsb;
				dz_ext0 = dz0 - SQUISH_CONSTANT_3D;
				dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D;
			}
		}
		
		//Contribution (1,1,0)
		double dx3 = dx0 - 1 - 2 * SQUISH_CONSTANT_3D;
		double dy3 = dy0 - 1 - 2 * SQUISH_CONSTANT_3D;
		double dz3 = dz0 - 0 - 2 * SQUISH_CONSTANT_3D;
		double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3;
		if (attn3 > 0) {
			attn3 *= attn3;
			value += attn3 * attn3 * extrapolate3(ctx, xsb + 1, ysb + 1, zsb + 0, dx3, dy3, dz3);
		}

		//Contribution (1,0,1)
		double dx2 = dx3;
		double dy2 = dy0 - 0 - 2 * SQUISH_CONSTANT_3D;
		double dz2 = dz0 - 1 - 2 * SQUISH_CONSTANT_3D;
		double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2;
		if (attn2 > 0) {
			attn2 *= attn2;
			value += attn2 * attn2 * extrapolate3(ctx, xsb + 1, ysb + 0, zsb + 1, dx2, dy2, dz2);
		}

		//Contribution (0,1,1)
		double dx1 = dx0 - 0 - 2 * SQUISH_CONSTANT_3D;
		double dy1 = dy3;
		double dz1 = dz2;
		double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1;
		if (attn1 > 0) {
			attn1 *= attn1;
			value += attn1 * attn1 * extrapolate3(ctx, xsb + 0, ysb + 1, zsb + 1, dx1, dy1, dz1);
		}

		//Contribution (1,1,1)
		dx0 = dx0 - 1 - 3 * SQUISH_CONSTANT_3D;
		dy0 = dy0 - 1 - 3 * SQUISH_CONSTANT_3D;
		dz0 = dz0 - 1 - 3 * SQUISH_CONSTANT_3D;
		double attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0;
		if (attn0 > 0) {
			attn0 *= attn0;
			value += attn0 * attn0 * extrapolate3(ctx, xsb + 1, ysb + 1, zsb + 1, dx0, dy0, dz0);
		}
	} else { //We're inside the octahedron (Rectified 3-Simplex) in between.
		double aScore;
		int8_t aPoint;
		int aIsFurtherSide;
		double bScore;
		int8_t bPoint;
		int bIsFurtherSide;

		//Decide between point (0,0,1) and (1,1,0) as closest
		double p1 = xins + yins;
		if (p1 > 1) {
			aScore = p1 - 1;
			aPoint = 0x03;
			aIsFurtherSide = 1;
		} else {
			aScore = 1 - p1;
			aPoint = 0x04;
			aIsFurtherSide = 0;
		}

		//Decide between point (0,1,0) and (1,0,1) as closest
		double p2 = xins + zins;
		if (p2 > 1) {
			bScore = p2 - 1;
			bPoint = 0x05;
			bIsFurtherSide = 1;
		} else {
			bScore = 1 - p2;
			bPoint = 0x02;
			bIsFurtherSide = 0;
		}
		
		//The closest out of the two (1,0,0) and (0,1,1) will replace the furthest out of the two decided above, if closer.
		double p3 = yins + zins;
		if (p3 > 1) {
			double score = p3 - 1;
			if (aScore <= bScore && aScore < score) {
				aScore = score;
				aPoint = 0x06;
				aIsFurtherSide = 1;
			} else if (aScore > bScore && bScore < score) {
				bScore = score;
				bPoint = 0x06;
				bIsFurtherSide = 1;
			}
		} else {
			double score = 1 - p3;
			if (aScore <= bScore && aScore < score) {
				aScore = score;
				aPoint = 0x01;
				aIsFurtherSide = 0;
			} else if (aScore > bScore && bScore < score) {
				bScore = score;
				bPoint = 0x01;
				bIsFurtherSide = 0;
			}
		}
		
		//Where each of the two closest points are determines how the extra two vertices are calculated.
		if (aIsFurtherSide == bIsFurtherSide) {
			if (aIsFurtherSide) { //Both closest points on (1,1,1) side

				//One of the two extra points is (1,1,1)
				dx_ext0 = dx0 - 1 - 3 * SQUISH_CONSTANT_3D;
				dy_ext0 = dy0 - 1 - 3 * SQUISH_CONSTANT_3D;
				dz_ext0 = dz0 - 1 - 3 * SQUISH_CONSTANT_3D;
				xsv_ext0 = xsb + 1;
				ysv_ext0 = ysb + 1;
				zsv_ext0 = zsb + 1;

				//Other extra point is based on the shared axis.
				int8_t c = (int8_t)(aPoint & bPoint);
				if ((c & 0x01) != 0) {
					dx_ext1 = dx0 - 2 - 2 * SQUISH_CONSTANT_3D;
					dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D;
					dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D;
					xsv_ext1 = xsb + 2;
					ysv_ext1 = ysb;
					zsv_ext1 = zsb;
				} else if ((c & 0x02) != 0) {
					dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D;
					dy_ext1 = dy0 - 2 - 2 * SQUISH_CONSTANT_3D;
					dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D;
					xsv_ext1 = xsb;
					ysv_ext1 = ysb + 2;
					zsv_ext1 = zsb;
				} else {
					dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D;
					dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D;
					dz_ext1 = dz0 - 2 - 2 * SQUISH_CONSTANT_3D;
					xsv_ext1 = xsb;
					ysv_ext1 = ysb;
					zsv_ext1 = zsb + 2;
				}
			} else {//Both closest points on (0,0,0) side

				//One of the two extra points is (0,0,0)
				dx_ext0 = dx0;
				dy_ext0 = dy0;
				dz_ext0 = dz0;
				xsv_ext0 = xsb;
				ysv_ext0 = ysb;
				zsv_ext0 = zsb;

				//Other extra point is based on the omitted axis.
				int8_t c = (int8_t)(aPoint | bPoint);
				if ((c & 0x01) == 0) {
					dx_ext1 = dx0 + 1 - SQUISH_CONSTANT_3D;
					dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_3D;
					dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_3D;
					xsv_ext1 = xsb - 1;
					ysv_ext1 = ysb + 1;
					zsv_ext1 = zsb + 1;
				} else if ((c & 0x02) == 0) {
					dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_3D;
					dy_ext1 = dy0 + 1 - SQUISH_CONSTANT_3D;
					dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_3D;
					xsv_ext1 = xsb + 1;
					ysv_ext1 = ysb - 1;
					zsv_ext1 = zsb + 1;
				} else {
					dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_3D;
					dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_3D;
					dz_ext1 = dz0 + 1 - SQUISH_CONSTANT_3D;
					xsv_ext1 = xsb + 1;
					ysv_ext1 = ysb + 1;
					zsv_ext1 = zsb - 1;
				}
			}
		} else { //One point on (0,0,0) side, one point on (1,1,1) side
			int8_t c1, c2;
			if (aIsFurtherSide) {
				c1 = aPoint;
				c2 = bPoint;
			} else {
				c1 = bPoint;
				c2 = aPoint;
			}

			//One contribution is a permutation of (1,1,-1)
			if ((c1 & 0x01) == 0) {
				dx_ext0 = dx0 + 1 - SQUISH_CONSTANT_3D;
				dy_ext0 = dy0 - 1 - SQUISH_CONSTANT_3D;
				dz_ext0 = dz0 - 1 - SQUISH_CONSTANT_3D;
				xsv_ext0 = xsb - 1;
				ysv_ext0 = ysb + 1;
				zsv_ext0 = zsb + 1;
			} else if ((c1 & 0x02) == 0) {
				dx_ext0 = dx0 - 1 - SQUISH_CONSTANT_3D;
				dy_ext0 = dy0 + 1 - SQUISH_CONSTANT_3D;
				dz_ext0 = dz0 - 1 - SQUISH_CONSTANT_3D;
				xsv_ext0 = xsb + 1;
				ysv_ext0 = ysb - 1;
				zsv_ext0 = zsb + 1;
			} else {
				dx_ext0 = dx0 - 1 - SQUISH_CONSTANT_3D;
				dy_ext0 = dy0 - 1 - SQUISH_CONSTANT_3D;
				dz_ext0 = dz0 + 1 - SQUISH_CONSTANT_3D;
				xsv_ext0 = xsb + 1;
				ysv_ext0 = ysb + 1;
				zsv_ext0 = zsb - 1;
			}

			//One contribution is a permutation of (0,0,2)
			dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D;
			dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D;
			dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D;
			xsv_ext1 = xsb;
			ysv_ext1 = ysb;
			zsv_ext1 = zsb;
			if ((c2 & 0x01) != 0) {
				dx_ext1 -= 2;
				xsv_ext1 += 2;
			} else if ((c2 & 0x02) != 0) {
				dy_ext1 -= 2;
				ysv_ext1 += 2;
			} else {
				dz_ext1 -= 2;
				zsv_ext1 += 2;
			}
		}

		//Contribution (1,0,0)
		double dx1 = dx0 - 1 - SQUISH_CONSTANT_3D;
		double dy1 = dy0 - 0 - SQUISH_CONSTANT_3D;
		double dz1 = dz0 - 0 - SQUISH_CONSTANT_3D;
		double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1;
		if (attn1 > 0) {
			attn1 *= attn1;
			value += attn1 * attn1 * extrapolate3(ctx, xsb + 1, ysb + 0, zsb + 0, dx1, dy1, dz1);
		}

		//Contribution (0,1,0)
		double dx2 = dx0 - 0 - SQUISH_CONSTANT_3D;
		double dy2 = dy0 - 1 - SQUISH_CONSTANT_3D;
		double dz2 = dz1;
		double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2;
		if (attn2 > 0) {
			attn2 *= attn2;
			value += attn2 * attn2 * extrapolate3(ctx, xsb + 0, ysb + 1, zsb + 0, dx2, dy2, dz2);
		}

		//Contribution (0,0,1)
		double dx3 = dx2;
		double dy3 = dy1;
		double dz3 = dz0 - 1 - SQUISH_CONSTANT_3D;
		double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3;
		if (attn3 > 0) {
			attn3 *= attn3;
			value += attn3 * attn3 * extrapolate3(ctx, xsb + 0, ysb + 0, zsb + 1, dx3, dy3, dz3);
		}

		//Contribution (1,1,0)
		double dx4 = dx0 - 1 - 2 * SQUISH_CONSTANT_3D;
		double dy4 = dy0 - 1 - 2 * SQUISH_CONSTANT_3D;
		double dz4 = dz0 - 0 - 2 * SQUISH_CONSTANT_3D;
		double attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4;
		if (attn4 > 0) {
			attn4 *= attn4;
			value += attn4 * attn4 * extrapolate3(ctx, xsb + 1, ysb + 1, zsb + 0, dx4, dy4, dz4);
		}

		//Contribution (1,0,1)
		double dx5 = dx4;
		double dy5 = dy0 - 0 - 2 * SQUISH_CONSTANT_3D;
		double dz5 = dz0 - 1 - 2 * SQUISH_CONSTANT_3D;
		double attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5;
		if (attn5 > 0) {
			attn5 *= attn5;
			value += attn5 * attn5 * extrapolate3(ctx, xsb + 1, ysb + 0, zsb + 1, dx5, dy5, dz5);
		}

		//Contribution (0,1,1)
		double dx6 = dx0 - 0 - 2 * SQUISH_CONSTANT_3D;
		double dy6 = dy4;
		double dz6 = dz5;
		double attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6;
		if (attn6 > 0) {
			attn6 *= attn6;
			value += attn6 * attn6 * extrapolate3(ctx, xsb + 0, ysb + 1, zsb + 1, dx6, dy6, dz6);
		}
	}

	//First extra vertex
	double attn_ext0 = 2 - dx_ext0 * dx_ext0 - dy_ext0 * dy_ext0 - dz_ext0 * dz_ext0;
	if (attn_ext0 > 0)
	{
		attn_ext0 *= attn_ext0;
		value += attn_ext0 * attn_ext0 * extrapolate3(ctx, xsv_ext0, ysv_ext0, zsv_ext0, dx_ext0, dy_ext0, dz_ext0);
	}

	//Second extra vertex
	double attn_ext1 = 2 - dx_ext1 * dx_ext1 - dy_ext1 * dy_ext1 - dz_ext1 * dz_ext1;
	if (attn_ext1 > 0)
	{
		attn_ext1 *= attn_ext1;
		value += attn_ext1 * attn_ext1 * extrapolate3(ctx, xsv_ext1, ysv_ext1, zsv_ext1, dx_ext1, dy_ext1, dz_ext1);
	}
	
	return value / NORM_CONSTANT_3D;
}
	
/* 
 * 4D OpenSimplex (Simplectic) Noise.
 */
double open_simplex_noise4(struct osn_context *ctx, double x, double y, double z, double w)
{

	//Place input coordinates on simplectic honeycomb.
	double stretchOffset = (x + y + z + w) * STRETCH_CONSTANT_4D;
	double xs = x + stretchOffset;
	double ys = y + stretchOffset;
	double zs = z + stretchOffset;
	double ws = w + stretchOffset;
	
	//Floor to get simplectic honeycomb coordinates of rhombo-hypercube super-cell origin.
	int xsb = fastFloor(xs);
	int ysb = fastFloor(ys);
	int zsb = fastFloor(zs);
	int wsb = fastFloor(ws);
	
	//Skew out to get actual coordinates of stretched rhombo-hypercube origin. We'll need these later.
	double squishOffset = (xsb + ysb + zsb + wsb) * SQUISH_CONSTANT_4D;
	double xb = xsb + squishOffset;
	double yb = ysb + squishOffset;
	double zb = zsb + squishOffset;
	double wb = wsb + squishOffset;
	
	//Compute simplectic honeycomb coordinates relative to rhombo-hypercube origin.
	double xins = xs - xsb;
	double yins = ys - ysb;
	double zins = zs - zsb;
	double wins = ws - wsb;
	
	//Sum those together to get a value that determines which region we're in.
	double inSum = xins + yins + zins + wins;

	//Positions relative to origin point.
	double dx0 = x - xb;
	double dy0 = y - yb;
	double dz0 = z - zb;
	double dw0 = w - wb;
	
	//We'll be defining these inside the next block and using them afterwards.
	double dx_ext0, dy_ext0, dz_ext0, dw_ext0;
	double dx_ext1, dy_ext1, dz_ext1, dw_ext1;
	double dx_ext2, dy_ext2, dz_ext2, dw_ext2;
	int xsv_ext0, ysv_ext0, zsv_ext0, wsv_ext0;
	int xsv_ext1, ysv_ext1, zsv_ext1, wsv_ext1;
	int xsv_ext2, ysv_ext2, zsv_ext2, wsv_ext2;
	
	double value = 0;
	if (inSum <= 1) { //We're inside the pentachoron (4-Simplex) at (0,0,0,0)

		//Determine which two of (0,0,0,1), (0,0,1,0), (0,1,0,0), (1,0,0,0) are closest.
		int8_t aPoint = 0x01;
		double aScore = xins;
		int8_t bPoint = 0x02;
		double bScore = yins;
		if (aScore >= bScore && zins > bScore) {
			bScore = zins;
			bPoint = 0x04;
		} else if (aScore < bScore && zins > aScore) {
			aScore = zins;
			aPoint = 0x04;
		}
		if (aScore >= bScore && wins > bScore) {
			bScore = wins;
			bPoint = 0x08;
		} else if (aScore < bScore && wins > aScore) {
			aScore = wins;
			aPoint = 0x08;
		}
		
		//Now we determine the three lattice points not part of the pentachoron that may contribute.
		//This depends on the closest two pentachoron vertices, including (0,0,0,0)
		double uins = 1 - inSum;
		if (uins > aScore || uins > bScore) { //(0,0,0,0) is one of the closest two pentachoron vertices.
			int8_t c = (bScore > aScore ? bPoint : aPoint); //Our other closest vertex is the closest out of a and b.
			if ((c & 0x01) == 0) {
				xsv_ext0 = xsb - 1;
				xsv_ext1 = xsv_ext2 = xsb;
				dx_ext0 = dx0 + 1;
				dx_ext1 = dx_ext2 = dx0;
			} else {
				xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1;
				dx_ext0 = dx_ext1 = dx_ext2 = dx0 - 1;
			}

			if ((c & 0x02) == 0) {
				ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb;
				dy_ext0 = dy_ext1 = dy_ext2 = dy0;
				if ((c & 0x01) == 0x01) {
					ysv_ext0 -= 1;
					dy_ext0 += 1;
				} else {
					ysv_ext1 -= 1;
					dy_ext1 += 1;
				}
			} else {
				ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1;
				dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 1;
			}
			
			if ((c & 0x04) == 0) {
				zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb;
				dz_ext0 = dz_ext1 = dz_ext2 = dz0;
				if ((c & 0x03) != 0) {
					if ((c & 0x03) == 0x03) {
						zsv_ext0 -= 1;
						dz_ext0 += 1;
					} else {
						zsv_ext1 -= 1;
						dz_ext1 += 1;
					}
				} else {
					zsv_ext2 -= 1;
					dz_ext2 += 1;
				}
			} else {
				zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1;
				dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 1;
			}
			
			if ((c & 0x08) == 0) {
				wsv_ext0 = wsv_ext1 = wsb;
				wsv_ext2 = wsb - 1;
				dw_ext0 = dw_ext1 = dw0;
				dw_ext2 = dw0 + 1;
			} else {
				wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1;
				dw_ext0 = dw_ext1 = dw_ext2 = dw0 - 1;
			}
		} else { //(0,0,0,0) is not one of the closest two pentachoron vertices.
			int8_t c = (int8_t)(aPoint | bPoint); //Our three extra vertices are determined by the closest two.
			
			if ((c & 0x01) == 0) {
				xsv_ext0 = xsv_ext2 = xsb;
				xsv_ext1 = xsb - 1;
				dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_4D;
				dx_ext1 = dx0 + 1 - SQUISH_CONSTANT_4D;
				dx_ext2 = dx0 - SQUISH_CONSTANT_4D;
			} else {
				xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1;
				dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
				dx_ext1 = dx_ext2 = dx0 - 1 - SQUISH_CONSTANT_4D;
			}
			
			if ((c & 0x02) == 0) {
				ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb;
				dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_4D;
				dy_ext1 = dy_ext2 = dy0 - SQUISH_CONSTANT_4D;
				if ((c & 0x01) == 0x01) {
					ysv_ext1 -= 1;
					dy_ext1 += 1;
				} else {
					ysv_ext2 -= 1;
					dy_ext2 += 1;
				}
			} else {
				ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1;
				dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
				dy_ext1 = dy_ext2 = dy0 - 1 - SQUISH_CONSTANT_4D;
			}
			
			if ((c & 0x04) == 0) {
				zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb;
				dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_4D;
				dz_ext1 = dz_ext2 = dz0 - SQUISH_CONSTANT_4D;
				if ((c & 0x03) == 0x03) {
					zsv_ext1 -= 1;
					dz_ext1 += 1;
				} else {
					zsv_ext2 -= 1;
					dz_ext2 += 1;
				}
			} else {
				zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1;
				dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
				dz_ext1 = dz_ext2 = dz0 - 1 - SQUISH_CONSTANT_4D;
			}
			
			if ((c & 0x08) == 0) {
				wsv_ext0 = wsv_ext1 = wsb;
				wsv_ext2 = wsb - 1;
				dw_ext0 = dw0 - 2 * SQUISH_CONSTANT_4D;
				dw_ext1 = dw0 - SQUISH_CONSTANT_4D;
				dw_ext2 = dw0 + 1 - SQUISH_CONSTANT_4D;
			} else {
				wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1;
				dw_ext0 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
				dw_ext1 = dw_ext2 = dw0 - 1 - SQUISH_CONSTANT_4D;
			}
		}

		//Contribution (0,0,0,0)
		double attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 - dw0 * dw0;
		if (attn0 > 0) {
			attn0 *= attn0;
			value += attn0 * attn0 * extrapolate4(ctx, xsb + 0, ysb + 0, zsb + 0, wsb + 0, dx0, dy0, dz0, dw0);
		}

		//Contribution (1,0,0,0)
		double dx1 = dx0 - 1 - SQUISH_CONSTANT_4D;
		double dy1 = dy0 - 0 - SQUISH_CONSTANT_4D;
		double dz1 = dz0 - 0 - SQUISH_CONSTANT_4D;
		double dw1 = dw0 - 0 - SQUISH_CONSTANT_4D;
		double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1;
		if (attn1 > 0) {
			attn1 *= attn1;
			value += attn1 * attn1 * extrapolate4(ctx, xsb + 1, ysb + 0, zsb + 0, wsb + 0, dx1, dy1, dz1, dw1);
		}

		//Contribution (0,1,0,0)
		double dx2 = dx0 - 0 - SQUISH_CONSTANT_4D;
		double dy2 = dy0 - 1 - SQUISH_CONSTANT_4D;
		double dz2 = dz1;
		double dw2 = dw1;
		double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2;
		if (attn2 > 0) {
			attn2 *= attn2;
			value += attn2 * attn2 * extrapolate4(ctx, xsb + 0, ysb + 1, zsb + 0, wsb + 0, dx2, dy2, dz2, dw2);
		}

		//Contribution (0,0,1,0)
		double dx3 = dx2;
		double dy3 = dy1;
		double dz3 = dz0 - 1 - SQUISH_CONSTANT_4D;
		double dw3 = dw1;
		double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3;
		if (attn3 > 0) {
			attn3 *= attn3;
			value += attn3 * attn3 * extrapolate4(ctx, xsb + 0, ysb + 0, zsb + 1, wsb + 0, dx3, dy3, dz3, dw3);
		}

		//Contribution (0,0,0,1)
		double dx4 = dx2;
		double dy4 = dy1;
		double dz4 = dz1;
		double dw4 = dw0 - 1 - SQUISH_CONSTANT_4D;
		double attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4;
		if (attn4 > 0) {
			attn4 *= attn4;
			value += attn4 * attn4 * extrapolate4(ctx, xsb + 0, ysb + 0, zsb + 0, wsb + 1, dx4, dy4, dz4, dw4);
		}
	} else if (inSum >= 3) { //We're inside the pentachoron (4-Simplex) at (1,1,1,1)
		//Determine which two of (1,1,1,0), (1,1,0,1), (1,0,1,1), (0,1,1,1) are closest.
		int8_t aPoint = 0x0E;
		double aScore = xins;
		int8_t bPoint = 0x0D;
		double bScore = yins;
		if (aScore <= bScore && zins < bScore) {
			bScore = zins;
			bPoint = 0x0B;
		} else if (aScore > bScore && zins < aScore) {
			aScore = zins;
			aPoint = 0x0B;
		}
		if (aScore <= bScore && wins < bScore) {
			bScore = wins;
			bPoint = 0x07;
		} else if (aScore > bScore && wins < aScore) {
			aScore = wins;
			aPoint = 0x07;
		}
		
		//Now we determine the three lattice points not part of the pentachoron that may contribute.
		//This depends on the closest two pentachoron vertices, including (0,0,0,0)
		double uins = 4 - inSum;
		if (uins < aScore || uins < bScore) { //(1,1,1,1) is one of the closest two pentachoron vertices.
			int8_t c = (bScore < aScore ? bPoint : aPoint); //Our other closest vertex is the closest out of a and b.
			
			if ((c & 0x01) != 0) {
				xsv_ext0 = xsb + 2;
				xsv_ext1 = xsv_ext2 = xsb + 1;
				dx_ext0 = dx0 - 2 - 4 * SQUISH_CONSTANT_4D;
				dx_ext1 = dx_ext2 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D;
			} else {
				xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb;
				dx_ext0 = dx_ext1 = dx_ext2 = dx0 - 4 * SQUISH_CONSTANT_4D;
			}

			if ((c & 0x02) != 0) {
				ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1;
				dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D;
				if ((c & 0x01) != 0) {
					ysv_ext1 += 1;
					dy_ext1 -= 1;
				} else {
					ysv_ext0 += 1;
					dy_ext0 -= 1;
				}
			} else {
				ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb;
				dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 4 * SQUISH_CONSTANT_4D;
			}
			
			if ((c & 0x04) != 0) {
				zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1;
				dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D;
				if ((c & 0x03) != 0x03) {
					if ((c & 0x03) == 0) {
						zsv_ext0 += 1;
						dz_ext0 -= 1;
					} else {
						zsv_ext1 += 1;
						dz_ext1 -= 1;
					}
				} else {
					zsv_ext2 += 1;
					dz_ext2 -= 1;
				}
			} else {
				zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb;
				dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 4 * SQUISH_CONSTANT_4D;
			}
			
			if ((c & 0x08) != 0) {
				wsv_ext0 = wsv_ext1 = wsb + 1;
				wsv_ext2 = wsb + 2;
				dw_ext0 = dw_ext1 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D;
				dw_ext2 = dw0 - 2 - 4 * SQUISH_CONSTANT_4D;
			} else {
				wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb;
				dw_ext0 = dw_ext1 = dw_ext2 = dw0 - 4 * SQUISH_CONSTANT_4D;
			}
		} else { //(1,1,1,1) is not one of the closest two pentachoron vertices.
			int8_t c = (int8_t)(aPoint & bPoint); //Our three extra vertices are determined by the closest two.
			
			if ((c & 0x01) != 0) {
				xsv_ext0 = xsv_ext2 = xsb + 1;
				xsv_ext1 = xsb + 2;
				dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
				dx_ext1 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D;
				dx_ext2 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D;
			} else {
				xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb;
				dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_4D;
				dx_ext1 = dx_ext2 = dx0 - 3 * SQUISH_CONSTANT_4D;
			}
			
			if ((c & 0x02) != 0) {
				ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1;
				dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
				dy_ext1 = dy_ext2 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D;
				if ((c & 0x01) != 0) {
					ysv_ext2 += 1;
					dy_ext2 -= 1;
				} else {
					ysv_ext1 += 1;
					dy_ext1 -= 1;
				}
			} else {
				ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb;
				dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_4D;
				dy_ext1 = dy_ext2 = dy0 - 3 * SQUISH_CONSTANT_4D;
			}
			
			if ((c & 0x04) != 0) {
				zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1;
				dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
				dz_ext1 = dz_ext2 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D;
				if ((c & 0x03) != 0) {
					zsv_ext2 += 1;
					dz_ext2 -= 1;
				} else {
					zsv_ext1 += 1;
					dz_ext1 -= 1;
				}
			} else {
				zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb;
				dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_4D;
				dz_ext1 = dz_ext2 = dz0 - 3 * SQUISH_CONSTANT_4D;
			}
			
			if ((c & 0x08) != 0) {
				wsv_ext0 = wsv_ext1 = wsb + 1;
				wsv_ext2 = wsb + 2;
				dw_ext0 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
				dw_ext1 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D;
				dw_ext2 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D;
			} else {
				wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb;
				dw_ext0 = dw0 - 2 * SQUISH_CONSTANT_4D;
				dw_ext1 = dw_ext2 = dw0 - 3 * SQUISH_CONSTANT_4D;
			}
		}

		//Contribution (1,1,1,0)
		double dx4 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D;
		double dy4 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D;
		double dz4 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D;
		double dw4 = dw0 - 3 * SQUISH_CONSTANT_4D;
		double attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4;
		if (attn4 > 0) {
			attn4 *= attn4;
			value += attn4 * attn4 * extrapolate4(ctx, xsb + 1, ysb + 1, zsb + 1, wsb + 0, dx4, dy4, dz4, dw4);
		}

		//Contribution (1,1,0,1)
		double dx3 = dx4;
		double dy3 = dy4;
		double dz3 = dz0 - 3 * SQUISH_CONSTANT_4D;
		double dw3 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D;
		double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3;
		if (attn3 > 0) {
			attn3 *= attn3;
			value += attn3 * attn3 * extrapolate4(ctx, xsb + 1, ysb + 1, zsb + 0, wsb + 1, dx3, dy3, dz3, dw3);
		}

		//Contribution (1,0,1,1)
		double dx2 = dx4;
		double dy2 = dy0 - 3 * SQUISH_CONSTANT_4D;
		double dz2 = dz4;
		double dw2 = dw3;
		double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2;
		if (attn2 > 0) {
			attn2 *= attn2;
			value += attn2 * attn2 * extrapolate4(ctx, xsb + 1, ysb + 0, zsb + 1, wsb + 1, dx2, dy2, dz2, dw2);
		}

		//Contribution (0,1,1,1)
		double dx1 = dx0 - 3 * SQUISH_CONSTANT_4D;
		double dz1 = dz4;
		double dy1 = dy4;
		double dw1 = dw3;
		double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1;
		if (attn1 > 0) {
			attn1 *= attn1;
			value += attn1 * attn1 * extrapolate4(ctx, xsb + 0, ysb + 1, zsb + 1, wsb + 1, dx1, dy1, dz1, dw1);
		}

		//Contribution (1,1,1,1)
		dx0 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D;
		dy0 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D;
		dz0 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D;
		dw0 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D;
		double attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 - dw0 * dw0;
		if (attn0 > 0) {
			attn0 *= attn0;
			value += attn0 * attn0 * extrapolate4(ctx, xsb + 1, ysb + 1, zsb + 1, wsb + 1, dx0, dy0, dz0, dw0);
		}
	} else if (inSum <= 2) { //We're inside the first dispentachoron (Rectified 4-Simplex)
		double aScore;
		int8_t aPoint;
		int aIsBiggerSide = 1;
		double bScore;
		int8_t bPoint;
		int bIsBiggerSide = 1;
		
		//Decide between (1,1,0,0) and (0,0,1,1)
		if (xins + yins > zins + wins) {
			aScore = xins + yins;
			aPoint = 0x03;
		} else {
			aScore = zins + wins;
			aPoint = 0x0C;
		}
		
		//Decide between (1,0,1,0) and (0,1,0,1)
		if (xins + zins > yins + wins) {
			bScore = xins + zins;
			bPoint = 0x05;
		} else {
			bScore = yins + wins;
			bPoint = 0x0A;
		}
		
		//Closer between (1,0,0,1) and (0,1,1,0) will replace the further of a and b, if closer.
		if (xins + wins > yins + zins) {
			double score = xins + wins;
			if (aScore >= bScore && score > bScore) {
				bScore = score;
				bPoint = 0x09;
			} else if (aScore < bScore && score > aScore) {
				aScore = score;
				aPoint = 0x09;
			}
		} else {
			double score = yins + zins;
			if (aScore >= bScore && score > bScore) {
				bScore = score;
				bPoint = 0x06;
			} else if (aScore < bScore && score > aScore) {
				aScore = score;
				aPoint = 0x06;
			}
		}
		
		//Decide if (1,0,0,0) is closer.
		double p1 = 2 - inSum + xins;
		if (aScore >= bScore && p1 > bScore) {
			bScore = p1;
			bPoint = 0x01;
			bIsBiggerSide = 0;
		} else if (aScore < bScore && p1 > aScore) {
			aScore = p1;
			aPoint = 0x01;
			aIsBiggerSide = 0;
		}
		
		//Decide if (0,1,0,0) is closer.
		double p2 = 2 - inSum + yins;
		if (aScore >= bScore && p2 > bScore) {
			bScore = p2;
			bPoint = 0x02;
			bIsBiggerSide = 0;
		} else if (aScore < bScore && p2 > aScore) {
			aScore = p2;
			aPoint = 0x02;
			aIsBiggerSide = 0;
		}
		
		//Decide if (0,0,1,0) is closer.
		double p3 = 2 - inSum + zins;
		if (aScore >= bScore && p3 > bScore) {
			bScore = p3;
			bPoint = 0x04;
			bIsBiggerSide = 0;
		} else if (aScore < bScore && p3 > aScore) {
			aScore = p3;
			aPoint = 0x04;
			aIsBiggerSide = 0;
		}
		
		//Decide if (0,0,0,1) is closer.
		double p4 = 2 - inSum + wins;
		if (aScore >= bScore && p4 > bScore) {
			bScore = p4;
			bPoint = 0x08;
			bIsBiggerSide = 0;
		} else if (aScore < bScore && p4 > aScore) {
			aScore = p4;
			aPoint = 0x08;
			aIsBiggerSide = 0;
		}
		
		//Where each of the two closest points are determines how the extra three vertices are calculated.
		if (aIsBiggerSide == bIsBiggerSide) {
			if (aIsBiggerSide) { //Both closest points on the bigger side
				int8_t c1 = (int8_t)(aPoint | bPoint);
				int8_t c2 = (int8_t)(aPoint & bPoint);
				if ((c1 & 0x01) == 0) {
					xsv_ext0 = xsb;
					xsv_ext1 = xsb - 1;
					dx_ext0 = dx0 - 3 * SQUISH_CONSTANT_4D;
					dx_ext1 = dx0 + 1 - 2 * SQUISH_CONSTANT_4D;
				} else {
					xsv_ext0 = xsv_ext1 = xsb + 1;
					dx_ext0 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D;
					dx_ext1 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
				}
				
				if ((c1 & 0x02) == 0) {
					ysv_ext0 = ysb;
					ysv_ext1 = ysb - 1;
					dy_ext0 = dy0 - 3 * SQUISH_CONSTANT_4D;
					dy_ext1 = dy0 + 1 - 2 * SQUISH_CONSTANT_4D;
				} else {
					ysv_ext0 = ysv_ext1 = ysb + 1;
					dy_ext0 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D;
					dy_ext1 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
				}
				
				if ((c1 & 0x04) == 0) {
					zsv_ext0 = zsb;
					zsv_ext1 = zsb - 1;
					dz_ext0 = dz0 - 3 * SQUISH_CONSTANT_4D;
					dz_ext1 = dz0 + 1 - 2 * SQUISH_CONSTANT_4D;
				} else {
					zsv_ext0 = zsv_ext1 = zsb + 1;
					dz_ext0 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D;
					dz_ext1 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
				}
				
				if ((c1 & 0x08) == 0) {
					wsv_ext0 = wsb;
					wsv_ext1 = wsb - 1;
					dw_ext0 = dw0 - 3 * SQUISH_CONSTANT_4D;
					dw_ext1 = dw0 + 1 - 2 * SQUISH_CONSTANT_4D;
				} else {
					wsv_ext0 = wsv_ext1 = wsb + 1;
					dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D;
					dw_ext1 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
				}
				
				//One combination is a permutation of (0,0,0,2) based on c2
				xsv_ext2 = xsb;
				ysv_ext2 = ysb;
				zsv_ext2 = zsb;
				wsv_ext2 = wsb;
				dx_ext2 = dx0 - 2 * SQUISH_CONSTANT_4D;
				dy_ext2 = dy0 - 2 * SQUISH_CONSTANT_4D;
				dz_ext2 = dz0 - 2 * SQUISH_CONSTANT_4D;
				dw_ext2 = dw0 - 2 * SQUISH_CONSTANT_4D;
				if ((c2 & 0x01) != 0) {
					xsv_ext2 += 2;
					dx_ext2 -= 2;
				} else if ((c2 & 0x02) != 0) {
					ysv_ext2 += 2;
					dy_ext2 -= 2;
				} else if ((c2 & 0x04) != 0) {
					zsv_ext2 += 2;
					dz_ext2 -= 2;
				} else {
					wsv_ext2 += 2;
					dw_ext2 -= 2;
				}
				
			} else { //Both closest points on the smaller side
				//One of the two extra points is (0,0,0,0)
				xsv_ext2 = xsb;
				ysv_ext2 = ysb;
				zsv_ext2 = zsb;
				wsv_ext2 = wsb;
				dx_ext2 = dx0;
				dy_ext2 = dy0;
				dz_ext2 = dz0;
				dw_ext2 = dw0;
				
				//Other two points are based on the omitted axes.
				int8_t c = (int8_t)(aPoint | bPoint);
				
				if ((c & 0x01) == 0) {
					xsv_ext0 = xsb - 1;
					xsv_ext1 = xsb;
					dx_ext0 = dx0 + 1 - SQUISH_CONSTANT_4D;
					dx_ext1 = dx0 - SQUISH_CONSTANT_4D;
				} else {
					xsv_ext0 = xsv_ext1 = xsb + 1;
					dx_ext0 = dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_4D;
				}
				
				if ((c & 0x02) == 0) {
					ysv_ext0 = ysv_ext1 = ysb;
					dy_ext0 = dy_ext1 = dy0 - SQUISH_CONSTANT_4D;
					if ((c & 0x01) == 0x01)
					{
						ysv_ext0 -= 1;
						dy_ext0 += 1;
					} else {
						ysv_ext1 -= 1;
						dy_ext1 += 1;
					}
				} else {
					ysv_ext0 = ysv_ext1 = ysb + 1;
					dy_ext0 = dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_4D;
				}
				
				if ((c & 0x04) == 0) {
					zsv_ext0 = zsv_ext1 = zsb;
					dz_ext0 = dz_ext1 = dz0 - SQUISH_CONSTANT_4D;
					if ((c & 0x03) == 0x03)
					{
						zsv_ext0 -= 1;
						dz_ext0 += 1;
					} else {
						zsv_ext1 -= 1;
						dz_ext1 += 1;
					}
				} else {
					zsv_ext0 = zsv_ext1 = zsb + 1;
					dz_ext0 = dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_4D;
				}
				
				if ((c & 0x08) == 0)
				{
					wsv_ext0 = wsb;
					wsv_ext1 = wsb - 1;
					dw_ext0 = dw0 - SQUISH_CONSTANT_4D;
					dw_ext1 = dw0 + 1 - SQUISH_CONSTANT_4D;
				} else {
					wsv_ext0 = wsv_ext1 = wsb + 1;
					dw_ext0 = dw_ext1 = dw0 - 1 - SQUISH_CONSTANT_4D;
				}
				
			}
		} else { //One point on each "side"
			int8_t c1, c2;
			if (aIsBiggerSide) {
				c1 = aPoint;
				c2 = bPoint;
			} else {
				c1 = bPoint;
				c2 = aPoint;
			}
			
			//Two contributions are the bigger-sided point with each 0 replaced with -1.
			if ((c1 & 0x01) == 0) {
				xsv_ext0 = xsb - 1;
				xsv_ext1 = xsb;
				dx_ext0 = dx0 + 1 - SQUISH_CONSTANT_4D;
				dx_ext1 = dx0 - SQUISH_CONSTANT_4D;
			} else {
				xsv_ext0 = xsv_ext1 = xsb + 1;
				dx_ext0 = dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_4D;
			}
			
			if ((c1 & 0x02) == 0) {
				ysv_ext0 = ysv_ext1 = ysb;
				dy_ext0 = dy_ext1 = dy0 - SQUISH_CONSTANT_4D;
				if ((c1 & 0x01) == 0x01) {
					ysv_ext0 -= 1;
					dy_ext0 += 1;
				} else {
					ysv_ext1 -= 1;
					dy_ext1 += 1;
				}
			} else {
				ysv_ext0 = ysv_ext1 = ysb + 1;
				dy_ext0 = dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_4D;
			}
			
			if ((c1 & 0x04) == 0) {
				zsv_ext0 = zsv_ext1 = zsb;
				dz_ext0 = dz_ext1 = dz0 - SQUISH_CONSTANT_4D;
				if ((c1 & 0x03) == 0x03) {
					zsv_ext0 -= 1;
					dz_ext0 += 1;
				} else {
					zsv_ext1 -= 1;
					dz_ext1 += 1;
				}
			} else {
				zsv_ext0 = zsv_ext1 = zsb + 1;
				dz_ext0 = dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_4D;
			}
			
			if ((c1 & 0x08) == 0) {
				wsv_ext0 = wsb;
				wsv_ext1 = wsb - 1;
				dw_ext0 = dw0 - SQUISH_CONSTANT_4D;
				dw_ext1 = dw0 + 1 - SQUISH_CONSTANT_4D;
			} else {
				wsv_ext0 = wsv_ext1 = wsb + 1;
				dw_ext0 = dw_ext1 = dw0 - 1 - SQUISH_CONSTANT_4D;
			}

			//One contribution is a permutation of (0,0,0,2) based on the smaller-sided point
			xsv_ext2 = xsb;
			ysv_ext2 = ysb;
			zsv_ext2 = zsb;
			wsv_ext2 = wsb;
			dx_ext2 = dx0 - 2 * SQUISH_CONSTANT_4D;
			dy_ext2 = dy0 - 2 * SQUISH_CONSTANT_4D;
			dz_ext2 = dz0 - 2 * SQUISH_CONSTANT_4D;
			dw_ext2 = dw0 - 2 * SQUISH_CONSTANT_4D;
			if ((c2 & 0x01) != 0) {
				xsv_ext2 += 2;
				dx_ext2 -= 2;
			} else if ((c2 & 0x02) != 0) {
				ysv_ext2 += 2;
				dy_ext2 -= 2;
			} else if ((c2 & 0x04) != 0) {
				zsv_ext2 += 2;
				dz_ext2 -= 2;
			} else {
				wsv_ext2 += 2;
				dw_ext2 -= 2;
			}
		}
		
		//Contribution (1,0,0,0)
		double dx1 = dx0 - 1 - SQUISH_CONSTANT_4D;
		double dy1 = dy0 - 0 - SQUISH_CONSTANT_4D;
		double dz1 = dz0 - 0 - SQUISH_CONSTANT_4D;
		double dw1 = dw0 - 0 - SQUISH_CONSTANT_4D;
		double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1;
		if (attn1 > 0) {
			attn1 *= attn1;
			value += attn1 * attn1 * extrapolate4(ctx, xsb + 1, ysb + 0, zsb + 0, wsb + 0, dx1, dy1, dz1, dw1);
		}

		//Contribution (0,1,0,0)
		double dx2 = dx0 - 0 - SQUISH_CONSTANT_4D;
		double dy2 = dy0 - 1 - SQUISH_CONSTANT_4D;
		double dz2 = dz1;
		double dw2 = dw1;
		double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2;
		if (attn2 > 0) {
			attn2 *= attn2;
			value += attn2 * attn2 * extrapolate4(ctx, xsb + 0, ysb + 1, zsb + 0, wsb + 0, dx2, dy2, dz2, dw2);
		}

		//Contribution (0,0,1,0)
		double dx3 = dx2;
		double dy3 = dy1;
		double dz3 = dz0 - 1 - SQUISH_CONSTANT_4D;
		double dw3 = dw1;
		double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3;
		if (attn3 > 0) {
			attn3 *= attn3;
			value += attn3 * attn3 * extrapolate4(ctx, xsb + 0, ysb + 0, zsb + 1, wsb + 0, dx3, dy3, dz3, dw3);
		}

		//Contribution (0,0,0,1)
		double dx4 = dx2;
		double dy4 = dy1;
		double dz4 = dz1;
		double dw4 = dw0 - 1 - SQUISH_CONSTANT_4D;
		double attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4;
		if (attn4 > 0) {
			attn4 *= attn4;
			value += attn4 * attn4 * extrapolate4(ctx, xsb + 0, ysb + 0, zsb + 0, wsb + 1, dx4, dy4, dz4, dw4);
		}
		
		//Contribution (1,1,0,0)
		double dx5 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
		double dy5 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
		double dz5 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D;
		double dw5 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D;
		double attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5 - dw5 * dw5;
		if (attn5 > 0) {
			attn5 *= attn5;
			value += attn5 * attn5 * extrapolate4(ctx, xsb + 1, ysb + 1, zsb + 0, wsb + 0, dx5, dy5, dz5, dw5);
		}
		
		//Contribution (1,0,1,0)
		double dx6 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
		double dy6 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D;
		double dz6 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
		double dw6 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D;
		double attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6 - dw6 * dw6;
		if (attn6 > 0) {
			attn6 *= attn6;
			value += attn6 * attn6 * extrapolate4(ctx, xsb + 1, ysb + 0, zsb + 1, wsb + 0, dx6, dy6, dz6, dw6);
		}

		//Contribution (1,0,0,1)
		double dx7 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
		double dy7 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D;
		double dz7 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D;
		double dw7 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
		double attn7 = 2 - dx7 * dx7 - dy7 * dy7 - dz7 * dz7 - dw7 * dw7;
		if (attn7 > 0) {
			attn7 *= attn7;
			value += attn7 * attn7 * extrapolate4(ctx, xsb + 1, ysb + 0, zsb + 0, wsb + 1, dx7, dy7, dz7, dw7);
		}
		
		//Contribution (0,1,1,0)
		double dx8 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D;
		double dy8 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
		double dz8 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
		double dw8 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D;
		double attn8 = 2 - dx8 * dx8 - dy8 * dy8 - dz8 * dz8 - dw8 * dw8;
		if (attn8 > 0) {
			attn8 *= attn8;
			value += attn8 * attn8 * extrapolate4(ctx, xsb + 0, ysb + 1, zsb + 1, wsb + 0, dx8, dy8, dz8, dw8);
		}
		
		//Contribution (0,1,0,1)
		double dx9 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D;
		double dy9 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
		double dz9 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D;
		double dw9 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
		double attn9 = 2 - dx9 * dx9 - dy9 * dy9 - dz9 * dz9 - dw9 * dw9;
		if (attn9 > 0) {
			attn9 *= attn9;
			value += attn9 * attn9 * extrapolate4(ctx, xsb + 0, ysb + 1, zsb + 0, wsb + 1, dx9, dy9, dz9, dw9);
		}
		
		//Contribution (0,0,1,1)
		double dx10 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D;
		double dy10 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D;
		double dz10 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
		double dw10 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
		double attn10 = 2 - dx10 * dx10 - dy10 * dy10 - dz10 * dz10 - dw10 * dw10;
		if (attn10 > 0) {
			attn10 *= attn10;
			value += attn10 * attn10 * extrapolate4(ctx, xsb + 0, ysb + 0, zsb + 1, wsb + 1, dx10, dy10, dz10, dw10);
		}
	} else { //We're inside the second dispentachoron (Rectified 4-Simplex)
		double aScore;
		int8_t aPoint;
		int aIsBiggerSide = 1;
		double bScore;
		int8_t bPoint;
		int bIsBiggerSide = 1;
		
		//Decide between (0,0,1,1) and (1,1,0,0)
		if (xins + yins < zins + wins) {
			aScore = xins + yins;
			aPoint = 0x0C;
		} else {
			aScore = zins + wins;
			aPoint = 0x03;
		}
		
		//Decide between (0,1,0,1) and (1,0,1,0)
		if (xins + zins < yins + wins) {
			bScore = xins + zins;
			bPoint = 0x0A;
		} else {
			bScore = yins + wins;
			bPoint = 0x05;
		}
		
		//Closer between (0,1,1,0) and (1,0,0,1) will replace the further of a and b, if closer.
		if (xins + wins < yins + zins) {
			double score = xins + wins;
			if (aScore <= bScore && score < bScore) {
				bScore = score;
				bPoint = 0x06;
			} else if (aScore > bScore && score < aScore) {
				aScore = score;
				aPoint = 0x06;
			}
		} else {
			double score = yins + zins;
			if (aScore <= bScore && score < bScore) {
				bScore = score;
				bPoint = 0x09;
			} else if (aScore > bScore && score < aScore) {
				aScore = score;
				aPoint = 0x09;
			}
		}
		
		//Decide if (0,1,1,1) is closer.
		double p1 = 3 - inSum + xins;
		if (aScore <= bScore && p1 < bScore) {
			bScore = p1;
			bPoint = 0x0E;
			bIsBiggerSide = 0;
		} else if (aScore > bScore && p1 < aScore) {
			aScore = p1;
			aPoint = 0x0E;
			aIsBiggerSide = 0;
		}
		
		//Decide if (1,0,1,1) is closer.
		double p2 = 3 - inSum + yins;
		if (aScore <= bScore && p2 < bScore) {
			bScore = p2;
			bPoint = 0x0D;
			bIsBiggerSide = 0;
		} else if (aScore > bScore && p2 < aScore) {
			aScore = p2;
			aPoint = 0x0D;
			aIsBiggerSide = 0;
		}
		
		//Decide if (1,1,0,1) is closer.
		double p3 = 3 - inSum + zins;
		if (aScore <= bScore && p3 < bScore) {
			bScore = p3;
			bPoint = 0x0B;
			bIsBiggerSide = 0;
		} else if (aScore > bScore && p3 < aScore) {
			aScore = p3;
			aPoint = 0x0B;
			aIsBiggerSide = 0;
		}
		
		//Decide if (1,1,1,0) is closer.
		double p4 = 3 - inSum + wins;
		if (aScore <= bScore && p4 < bScore) {
			bScore = p4;
			bPoint = 0x07;
			bIsBiggerSide = 0;
		} else if (aScore > bScore && p4 < aScore) {
			aScore = p4;
			aPoint = 0x07;
			aIsBiggerSide = 0;
		}
		
		//Where each of the two closest points are determines how the extra three vertices are calculated.
		if (aIsBiggerSide == bIsBiggerSide) {
			if (aIsBiggerSide) { //Both closest points on the bigger side
				int8_t c1 = (int8_t)(aPoint & bPoint);
				int8_t c2 = (int8_t)(aPoint | bPoint);
				
				//Two contributions are permutations of (0,0,0,1) and (0,0,0,2) based on c1
				xsv_ext0 = xsv_ext1 = xsb;
				ysv_ext0 = ysv_ext1 = ysb;
				zsv_ext0 = zsv_ext1 = zsb;
				wsv_ext0 = wsv_ext1 = wsb;
				dx_ext0 = dx0 - SQUISH_CONSTANT_4D;
				dy_ext0 = dy0 - SQUISH_CONSTANT_4D;
				dz_ext0 = dz0 - SQUISH_CONSTANT_4D;
				dw_ext0 = dw0 - SQUISH_CONSTANT_4D;
				dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_4D;
				dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_4D;
				dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_4D;
				dw_ext1 = dw0 - 2 * SQUISH_CONSTANT_4D;
				if ((c1 & 0x01) != 0) {
					xsv_ext0 += 1;
					dx_ext0 -= 1;
					xsv_ext1 += 2;
					dx_ext1 -= 2;
				} else if ((c1 & 0x02) != 0) {
					ysv_ext0 += 1;
					dy_ext0 -= 1;
					ysv_ext1 += 2;
					dy_ext1 -= 2;
				} else if ((c1 & 0x04) != 0) {
					zsv_ext0 += 1;
					dz_ext0 -= 1;
					zsv_ext1 += 2;
					dz_ext1 -= 2;
				} else {
					wsv_ext0 += 1;
					dw_ext0 -= 1;
					wsv_ext1 += 2;
					dw_ext1 -= 2;
				}
				
				//One contribution is a permutation of (1,1,1,-1) based on c2
				xsv_ext2 = xsb + 1;
				ysv_ext2 = ysb + 1;
				zsv_ext2 = zsb + 1;
				wsv_ext2 = wsb + 1;
				dx_ext2 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
				dy_ext2 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
				dz_ext2 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
				dw_ext2 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
				if ((c2 & 0x01) == 0) {
					xsv_ext2 -= 2;
					dx_ext2 += 2;
				} else if ((c2 & 0x02) == 0) {
					ysv_ext2 -= 2;
					dy_ext2 += 2;
				} else if ((c2 & 0x04) == 0) {
					zsv_ext2 -= 2;
					dz_ext2 += 2;
				} else {
					wsv_ext2 -= 2;
					dw_ext2 += 2;
				}
			} else { //Both closest points on the smaller side
				//One of the two extra points is (1,1,1,1)
				xsv_ext2 = xsb + 1;
				ysv_ext2 = ysb + 1;
				zsv_ext2 = zsb + 1;
				wsv_ext2 = wsb + 1;
				dx_ext2 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D;
				dy_ext2 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D;
				dz_ext2 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D;
				dw_ext2 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D;
				
				//Other two points are based on the shared axes.
				int8_t c = (int8_t)(aPoint & bPoint);
				
				if ((c & 0x01) != 0) {
					xsv_ext0 = xsb + 2;
					xsv_ext1 = xsb + 1;
					dx_ext0 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D;
					dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D;
				} else {
					xsv_ext0 = xsv_ext1 = xsb;
					dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_4D;
				}
				
				if ((c & 0x02) != 0) {
					ysv_ext0 = ysv_ext1 = ysb + 1;
					dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D;
					if ((c & 0x01) == 0)
					{
						ysv_ext0 += 1;
						dy_ext0 -= 1;
					} else {
						ysv_ext1 += 1;
						dy_ext1 -= 1;
					}
				} else {
					ysv_ext0 = ysv_ext1 = ysb;
					dy_ext0 = dy_ext1 = dy0 - 3 * SQUISH_CONSTANT_4D;
				}
				
				if ((c & 0x04) != 0) {
					zsv_ext0 = zsv_ext1 = zsb + 1;
					dz_ext0 = dz_ext1 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D;
					if ((c & 0x03) == 0)
					{
						zsv_ext0 += 1;
						dz_ext0 -= 1;
					} else {
						zsv_ext1 += 1;
						dz_ext1 -= 1;
					}
				} else {
					zsv_ext0 = zsv_ext1 = zsb;
					dz_ext0 = dz_ext1 = dz0 - 3 * SQUISH_CONSTANT_4D;
				}
				
				if ((c & 0x08) != 0)
				{
					wsv_ext0 = wsb + 1;
					wsv_ext1 = wsb + 2;
					dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D;
					dw_ext1 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D;
				} else {
					wsv_ext0 = wsv_ext1 = wsb;
					dw_ext0 = dw_ext1 = dw0 - 3 * SQUISH_CONSTANT_4D;
				}
			}
		} else { //One point on each "side"
			int8_t c1, c2;
			if (aIsBiggerSide) {
				c1 = aPoint;
				c2 = bPoint;
			} else {
				c1 = bPoint;
				c2 = aPoint;
			}
			
			//Two contributions are the bigger-sided point with each 1 replaced with 2.
			if ((c1 & 0x01) != 0) {
				xsv_ext0 = xsb + 2;
				xsv_ext1 = xsb + 1;
				dx_ext0 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D;
				dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D;
			} else {
				xsv_ext0 = xsv_ext1 = xsb;
				dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_4D;
			}
			
			if ((c1 & 0x02) != 0) {
				ysv_ext0 = ysv_ext1 = ysb + 1;
				dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D;
				if ((c1 & 0x01) == 0) {
					ysv_ext0 += 1;
					dy_ext0 -= 1;
				} else {
					ysv_ext1 += 1;
					dy_ext1 -= 1;
				}
			} else {
				ysv_ext0 = ysv_ext1 = ysb;
				dy_ext0 = dy_ext1 = dy0 - 3 * SQUISH_CONSTANT_4D;
			}
			
			if ((c1 & 0x04) != 0) {
				zsv_ext0 = zsv_ext1 = zsb + 1;
				dz_ext0 = dz_ext1 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D;
				if ((c1 & 0x03) == 0) {
					zsv_ext0 += 1;
					dz_ext0 -= 1;
				} else {
					zsv_ext1 += 1;
					dz_ext1 -= 1;
				}
			} else {
				zsv_ext0 = zsv_ext1 = zsb;
				dz_ext0 = dz_ext1 = dz0 - 3 * SQUISH_CONSTANT_4D;
			}
			
			if ((c1 & 0x08) != 0) {
				wsv_ext0 = wsb + 1;
				wsv_ext1 = wsb + 2;
				dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D;
				dw_ext1 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D;
			} else {
				wsv_ext0 = wsv_ext1 = wsb;
				dw_ext0 = dw_ext1 = dw0 - 3 * SQUISH_CONSTANT_4D;
			}

			//One contribution is a permutation of (1,1,1,-1) based on the smaller-sided point
			xsv_ext2 = xsb + 1;
			ysv_ext2 = ysb + 1;
			zsv_ext2 = zsb + 1;
			wsv_ext2 = wsb + 1;
			dx_ext2 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
			dy_ext2 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
			dz_ext2 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
			dw_ext2 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
			if ((c2 & 0x01) == 0) {
				xsv_ext2 -= 2;
				dx_ext2 += 2;
			} else if ((c2 & 0x02) == 0) {
				ysv_ext2 -= 2;
				dy_ext2 += 2;
			} else if ((c2 & 0x04) == 0) {
				zsv_ext2 -= 2;
				dz_ext2 += 2;
			} else {
				wsv_ext2 -= 2;
				dw_ext2 += 2;
			}
		}
		
		//Contribution (1,1,1,0)
		double dx4 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D;
		double dy4 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D;
		double dz4 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D;
		double dw4 = dw0 - 3 * SQUISH_CONSTANT_4D;
		double attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4;
		if (attn4 > 0) {
			attn4 *= attn4;
			value += attn4 * attn4 * extrapolate4(ctx, xsb + 1, ysb + 1, zsb + 1, wsb + 0, dx4, dy4, dz4, dw4);
		}

		//Contribution (1,1,0,1)
		double dx3 = dx4;
		double dy3 = dy4;
		double dz3 = dz0 - 3 * SQUISH_CONSTANT_4D;
		double dw3 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D;
		double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3;
		if (attn3 > 0) {
			attn3 *= attn3;
			value += attn3 * attn3 * extrapolate4(ctx, xsb + 1, ysb + 1, zsb + 0, wsb + 1, dx3, dy3, dz3, dw3);
		}

		//Contribution (1,0,1,1)
		double dx2 = dx4;
		double dy2 = dy0 - 3 * SQUISH_CONSTANT_4D;
		double dz2 = dz4;
		double dw2 = dw3;
		double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2;
		if (attn2 > 0) {
			attn2 *= attn2;
			value += attn2 * attn2 * extrapolate4(ctx, xsb + 1, ysb + 0, zsb + 1, wsb + 1, dx2, dy2, dz2, dw2);
		}

		//Contribution (0,1,1,1)
		double dx1 = dx0 - 3 * SQUISH_CONSTANT_4D;
		double dz1 = dz4;
		double dy1 = dy4;
		double dw1 = dw3;
		double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1;
		if (attn1 > 0) {
			attn1 *= attn1;
			value += attn1 * attn1 * extrapolate4(ctx, xsb + 0, ysb + 1, zsb + 1, wsb + 1, dx1, dy1, dz1, dw1);
		}
		
		//Contribution (1,1,0,0)
		double dx5 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
		double dy5 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
		double dz5 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D;
		double dw5 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D;
		double attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5 - dw5 * dw5;
		if (attn5 > 0) {
			attn5 *= attn5;
			value += attn5 * attn5 * extrapolate4(ctx, xsb + 1, ysb + 1, zsb + 0, wsb + 0, dx5, dy5, dz5, dw5);
		}
		
		//Contribution (1,0,1,0)
		double dx6 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
		double dy6 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D;
		double dz6 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
		double dw6 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D;
		double attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6 - dw6 * dw6;
		if (attn6 > 0) {
			attn6 *= attn6;
			value += attn6 * attn6 * extrapolate4(ctx, xsb + 1, ysb + 0, zsb + 1, wsb + 0, dx6, dy6, dz6, dw6);
		}

		//Contribution (1,0,0,1)
		double dx7 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
		double dy7 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D;
		double dz7 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D;
		double dw7 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
		double attn7 = 2 - dx7 * dx7 - dy7 * dy7 - dz7 * dz7 - dw7 * dw7;
		if (attn7 > 0) {
			attn7 *= attn7;
			value += attn7 * attn7 * extrapolate4(ctx, xsb + 1, ysb + 0, zsb + 0, wsb + 1, dx7, dy7, dz7, dw7);
		}
		
		//Contribution (0,1,1,0)
		double dx8 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D;
		double dy8 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
		double dz8 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
		double dw8 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D;
		double attn8 = 2 - dx8 * dx8 - dy8 * dy8 - dz8 * dz8 - dw8 * dw8;
		if (attn8 > 0) {
			attn8 *= attn8;
			value += attn8 * attn8 * extrapolate4(ctx, xsb + 0, ysb + 1, zsb + 1, wsb + 0, dx8, dy8, dz8, dw8);
		}
		
		//Contribution (0,1,0,1)
		double dx9 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D;
		double dy9 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
		double dz9 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D;
		double dw9 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
		double attn9 = 2 - dx9 * dx9 - dy9 * dy9 - dz9 * dz9 - dw9 * dw9;
		if (attn9 > 0) {
			attn9 *= attn9;
			value += attn9 * attn9 * extrapolate4(ctx, xsb + 0, ysb + 1, zsb + 0, wsb + 1, dx9, dy9, dz9, dw9);
		}
		
		//Contribution (0,0,1,1)
		double dx10 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D;
		double dy10 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D;
		double dz10 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
		double dw10 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
		double attn10 = 2 - dx10 * dx10 - dy10 * dy10 - dz10 * dz10 - dw10 * dw10;
		if (attn10 > 0) {
			attn10 *= attn10;
			value += attn10 * attn10 * extrapolate4(ctx, xsb + 0, ysb + 0, zsb + 1, wsb + 1, dx10, dy10, dz10, dw10);
		}
	}

	//First extra vertex
	double attn_ext0 = 2 - dx_ext0 * dx_ext0 - dy_ext0 * dy_ext0 - dz_ext0 * dz_ext0 - dw_ext0 * dw_ext0;
	if (attn_ext0 > 0)
	{
		attn_ext0 *= attn_ext0;
		value += attn_ext0 * attn_ext0 * extrapolate4(ctx, xsv_ext0, ysv_ext0, zsv_ext0, wsv_ext0, dx_ext0, dy_ext0, dz_ext0, dw_ext0);
	}

	//Second extra vertex
	double attn_ext1 = 2 - dx_ext1 * dx_ext1 - dy_ext1 * dy_ext1 - dz_ext1 * dz_ext1 - dw_ext1 * dw_ext1;
	if (attn_ext1 > 0)
	{
		attn_ext1 *= attn_ext1;
		value += attn_ext1 * attn_ext1 * extrapolate4(ctx, xsv_ext1, ysv_ext1, zsv_ext1, wsv_ext1, dx_ext1, dy_ext1, dz_ext1, dw_ext1);
	}

	//Third extra vertex
	double attn_ext2 = 2 - dx_ext2 * dx_ext2 - dy_ext2 * dy_ext2 - dz_ext2 * dz_ext2 - dw_ext2 * dw_ext2;
	if (attn_ext2 > 0)
	{
		attn_ext2 *= attn_ext2;
		value += attn_ext2 * attn_ext2 * extrapolate4(ctx, xsv_ext2, ysv_ext2, zsv_ext2, wsv_ext2, dx_ext2, dy_ext2, dz_ext2, dw_ext2);
	}

	return value / NORM_CONSTANT_4D;
}