/*
Copyright (c) 2018 Rafał Ziemniewski

Boost Software License - Version 1.0 - August 17th, 2003
Permission is hereby granted, free of charge, to any person or organization
obtaining a copy of the software and accompanying documentation covered by
this license (the "Software") to use, reproduce, display, distribute,
execute, and transmit the Software, and to prepare derivative works of the
Software, and to permit third-parties to whom the Software is furnished to
do so, all subject to the following:

The copyright notices in the Software and this entire statement, including
the above license grant, this restriction and the following disclaimer,
must be included in all copies of the Software, in whole or in part, and
all derivative works of the Software, unless such copies or derivative
works are solely in the form of machine-executable object code generated by
a source language processor.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
DEALINGS IN THE SOFTWARE.
*/

module dagon.graphics.opensimplex;

import std.traits;
import dlib.core.memory;
import dagon.core.ownership;

class OpenSimplexNoise(T): Owner if (isFloatingPoint!T)
{
	enum T STRETCH_CONSTANT_2D = -0.211324865405187;    //(1/Math.sqrt(2+1)-1)/2;
	enum T SQUISH_CONSTANT_2D = 0.366025403784439;      //(Math.sqrt(2+1)-1)/2;
	enum T STRETCH_CONSTANT_3D = -1.0 / 6;              //(1/Math.sqrt(3+1)-1)/3;
	enum T SQUISH_CONSTANT_3D = 1.0 / 3;                //(Math.sqrt(3+1)-1)/3;
	enum T STRETCH_CONSTANT_4D = -0.138196601125011;    //(1/Math.sqrt(4+1)-1)/4;
	enum T SQUISH_CONSTANT_4D = 0.309016994374947;      //(Math.sqrt(4+1)-1)/4;

	enum T NORM_CONSTANT_2D = 47;
	enum T NORM_CONSTANT_3D = 103;
	enum T NORM_CONSTANT_4D = 30;

	enum long DEFAULT_SEED = 0;

	private short[] perm;
	private short[] permGradIndex3D;

	public this(Owner o)
    {
		this(DEFAULT_SEED, o);
	}

/*
	public this(short[] perm)
    {
		this.perm = perm;
		permGradIndex3D = New!(short[])(256);

		for (int i = 0; i < 256; i++)
        {
			//Since 3D has 24 gradients, simple bitmask won't work, so precompute modulo array.
			permGradIndex3D[i] = cast(short)((perm[i] % (gradients3D.length / 3)) * 3);
		}
	}
*/

	//Initializes the class 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.
	public this(long seed, Owner o)
    {
        super(o);
		perm = New!(short[])(256);
		permGradIndex3D = New!(short[])(256);
		short[] source = New!(short[])(256);
		for (short i = 0; i < 256; i++)
			source[i] = i;
		seed = seed * 6_364_136_223_846_793_005L + 1_442_695_040_888_963_407L;
		seed = seed * 6_364_136_223_846_793_005L + 1_442_695_040_888_963_407L;
		seed = seed * 6_364_136_223_846_793_005L + 1_442_695_040_888_963_407L;
		for (int i = 255; i >= 0; i--)
        {
			seed = seed * 6_364_136_223_846_793_005L + 1_442_695_040_888_963_407L;
			int r = cast(int)((seed + 31) % (i + 1));
			if (r < 0)
				r += (i + 1);
			perm[i] = source[r];
			permGradIndex3D[i] = cast(short)((perm[i] % (gradients3D.length / 3)) * 3);
			source[r] = source[i];
		}

        Delete(source);
	}

    public ~this()
    {
        Delete(perm);
        Delete(permGradIndex3D);
    }

	//2D OpenSimplex (Simplectic) Noise.
	public T eval(T x, T y)
    {
		//Place input coordinates onto grid.
		T stretchOffset = (x + y) * STRETCH_CONSTANT_2D;
		T xs = x + stretchOffset;
		T 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.
		T squishOffset = (xsb + ysb) * SQUISH_CONSTANT_2D;
		T xb = xsb + squishOffset;
		T yb = ysb + squishOffset;

		//Compute grid coordinates relative to rhombus origin.
		T xins = xs - xsb;
		T yins = ys - ysb;

		//Sum those together to get a value that determines which region we're in.
		T inSum = xins + yins;

		//Positions relative to origin point.
		T dx0 = x - xb;
		T dy0 = y - yb;

		//We'll be defining these inside the next block and using them afterwards.
		T dx_ext, dy_ext;
		int xsv_ext, ysv_ext;

		T value = 0;

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

		//Contribution (0,1)
		T dx2 = dx0 - 0 - SQUISH_CONSTANT_2D;
		T dy2 = dy0 - 1 - SQUISH_CONSTANT_2D;
		T attn2 = 2 - dx2 * dx2 - dy2 * dy2;
		if (attn2 > 0) {
			attn2 *= attn2;
			value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, dx2, dy2);
		}

		if (inSum <= 1) { //We're inside the triangle (2-Simplex) at (0,0)
			T 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)
			T 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)
		T attn0 = 2 - dx0 * dx0 - dy0 * dy0;
		if (attn0 > 0) {
			attn0 *= attn0;
			value += attn0 * attn0 * extrapolate(xsb, ysb, dx0, dy0);
		}

		//Extra Vertex
		T attn_ext = 2 - dx_ext * dx_ext - dy_ext * dy_ext;
		if (attn_ext > 0) {
			attn_ext *= attn_ext;
			value += attn_ext * attn_ext * extrapolate(xsv_ext, ysv_ext, dx_ext, dy_ext);
		}

		return value / NORM_CONSTANT_2D;
	}

	//3D OpenSimplex (Simplectic) Noise.
	public T eval(T x, T y, T z) {

		//Place input coordinates on simplectic honeycomb.
		T stretchOffset = (x + y + z) * STRETCH_CONSTANT_3D;
		T xs = x + stretchOffset;
		T ys = y + stretchOffset;
		T 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.
		T squishOffset = (xsb + ysb + zsb) * SQUISH_CONSTANT_3D;
		T xb = xsb + squishOffset;
		T yb = ysb + squishOffset;
		T zb = zsb + squishOffset;

		//Compute simplectic honeycomb coordinates relative to rhombohedral origin.
		T xins = xs - xsb;
		T yins = ys - ysb;
		T zins = zs - zsb;

		//Sum those together to get a value that determines which region we're in.
		T inSum = xins + yins + zins;

		//Positions relative to origin point.
		T dx0 = x - xb;
		T dy0 = y - yb;
		T dz0 = z - zb;

		//We'll be defining these inside the next block and using them afterwards.
		T dx_ext0, dy_ext0, dz_ext0;
		T dx_ext1, dy_ext1, dz_ext1;
		int xsv_ext0, ysv_ext0, zsv_ext0;
		int xsv_ext1, ysv_ext1, zsv_ext1;

		T 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.
			byte aPoint = 0x01;
			T aScore = xins;
			byte bPoint = 0x02;
			T 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)
			T wins = 1 - inSum;
			if (wins > aScore || wins > bScore) { //(0,0,0) is one of the closest two tetrahedral vertices.
				byte 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.
				byte c = cast(byte)(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)
			T attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0;
			if (attn0 > 0) {
				attn0 *= attn0;
				value += attn0 * attn0 * extrapolate(xsb + 0, ysb + 0, zsb + 0, dx0, dy0, dz0);
			}

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

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

			//Contribution (0,0,1)
			T dx3 = dx2;
			T dy3 = dy1;
			T dz3 = dz0 - 1 - SQUISH_CONSTANT_3D;
			T attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3;
			if (attn3 > 0) {
				attn3 *= attn3;
				value += attn3 * attn3 * extrapolate(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).
			byte aPoint = 0x06;
			T aScore = xins;
			byte bPoint = 0x05;
			T 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)
			T wins = 3 - inSum;
			if (wins < aScore || wins < bScore) { //(1,1,1) is one of the closest two tetrahedral vertices.
				byte 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.
				byte c = cast(byte)(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)
			T dx3 = dx0 - 1 - 2 * SQUISH_CONSTANT_3D;
			T dy3 = dy0 - 1 - 2 * SQUISH_CONSTANT_3D;
			T dz3 = dz0 - 0 - 2 * SQUISH_CONSTANT_3D;
			T attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3;
			if (attn3 > 0) {
				attn3 *= attn3;
				value += attn3 * attn3 * extrapolate(xsb + 1, ysb + 1, zsb + 0, dx3, dy3, dz3);
			}

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

			//Contribution (0,1,1)
			T dx1 = dx0 - 0 - 2 * SQUISH_CONSTANT_3D;
			T dy1 = dy3;
			T dz1 = dz2;
			T attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1;
			if (attn1 > 0) {
				attn1 *= attn1;
				value += attn1 * attn1 * extrapolate(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;
			T attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0;
			if (attn0 > 0) {
				attn0 *= attn0;
				value += attn0 * attn0 * extrapolate(xsb + 1, ysb + 1, zsb + 1, dx0, dy0, dz0);
			}
		} else { //We're inside the octahedron (Rectified 3-Simplex) in between.
			T aScore;
			byte aPoint;
			bool aIsFurtherSide;
			T bScore;
			byte bPoint;
			bool bIsFurtherSide;

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

			//Decide between point (0,1,0) and (1,0,1) as closest
			T p2 = xins + zins;
			if (p2 > 1) {
				bScore = p2 - 1;
				bPoint = 0x05;
				bIsFurtherSide = true;
			} else {
				bScore = 1 - p2;
				bPoint = 0x02;
				bIsFurtherSide = false;
			}

			//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.
			T p3 = yins + zins;
			if (p3 > 1) {
				T score = p3 - 1;
				if (aScore <= bScore && aScore < score) {
					aScore = score;
					aPoint = 0x06;
					aIsFurtherSide = true;
				} else if (aScore > bScore && bScore < score) {
					bScore = score;
					bPoint = 0x06;
					bIsFurtherSide = true;
				}
			} else {
				T score = 1 - p3;
				if (aScore <= bScore && aScore < score) {
					aScore = score;
					aPoint = 0x01;
					aIsFurtherSide = false;
				} else if (aScore > bScore && bScore < score) {
					bScore = score;
					bPoint = 0x01;
					bIsFurtherSide = false;
				}
			}

			//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.
					byte c = cast(byte)(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.
					byte c = cast(byte)(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
				byte 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)
			T dx1 = dx0 - 1 - SQUISH_CONSTANT_3D;
			T dy1 = dy0 - 0 - SQUISH_CONSTANT_3D;
			T dz1 = dz0 - 0 - SQUISH_CONSTANT_3D;
			T attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1;
			if (attn1 > 0) {
				attn1 *= attn1;
				value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, dx1, dy1, dz1);
			}

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

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

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

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

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

		//First extra vertex
		T 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 * extrapolate(xsv_ext0, ysv_ext0, zsv_ext0, dx_ext0, dy_ext0, dz_ext0);
		}

		//Second extra vertex
		T 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 * extrapolate(xsv_ext1, ysv_ext1, zsv_ext1, dx_ext1, dy_ext1, dz_ext1);
		}

		return value / NORM_CONSTANT_3D;
	}

	//4D OpenSimplex (Simplectic) Noise.
	public T eval(T x, T y, T z, T w) {

		//Place input coordinates on simplectic honeycomb.
		T stretchOffset = (x + y + z + w) * STRETCH_CONSTANT_4D;
		T xs = x + stretchOffset;
		T ys = y + stretchOffset;
		T zs = z + stretchOffset;
		T 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.
		T squishOffset = (xsb + ysb + zsb + wsb) * SQUISH_CONSTANT_4D;
		T xb = xsb + squishOffset;
		T yb = ysb + squishOffset;
		T zb = zsb + squishOffset;
		T wb = wsb + squishOffset;

		//Compute simplectic honeycomb coordinates relative to rhombo-hypercube origin.
		T xins = xs - xsb;
		T yins = ys - ysb;
		T zins = zs - zsb;
		T wins = ws - wsb;

		//Sum those together to get a value that determines which region we're in.
		T inSum = xins + yins + zins + wins;

		//Positions relative to origin point.
		T dx0 = x - xb;
		T dy0 = y - yb;
		T dz0 = z - zb;
		T dw0 = w - wb;

		//We'll be defining these inside the next block and using them afterwards.
		T dx_ext0, dy_ext0, dz_ext0, dw_ext0;
		T dx_ext1, dy_ext1, dz_ext1, dw_ext1;
		T 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;

		T 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.
			byte aPoint = 0x01;
			T aScore = xins;
			byte bPoint = 0x02;
			T 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)
			T uins = 1 - inSum;
			if (uins > aScore || uins > bScore) { //(0,0,0,0) is one of the closest two pentachoron vertices.
				byte 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.
				byte c = cast(byte)(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)
			T attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 - dw0 * dw0;
			if (attn0 > 0) {
				attn0 *= attn0;
				value += attn0 * attn0 * extrapolate(xsb + 0, ysb + 0, zsb + 0, wsb + 0, dx0, dy0, dz0, dw0);
			}

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

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

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

			//Contribution (0,0,0,1)
			T dx4 = dx2;
			T dy4 = dy1;
			T dz4 = dz1;
			T dw4 = dw0 - 1 - SQUISH_CONSTANT_4D;
			T attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4;
			if (attn4 > 0) {
				attn4 *= attn4;
				value += attn4 * attn4 * extrapolate(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.
			byte aPoint = 0x0E;
			T aScore = xins;
			byte bPoint = 0x0D;
			T 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)
			T uins = 4 - inSum;
			if (uins < aScore || uins < bScore) { //(1,1,1,1) is one of the closest two pentachoron vertices.
				byte 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.
				byte c = cast(byte)(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)
			T dx4 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D;
			T dy4 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D;
			T dz4 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D;
			T dw4 = dw0 - 3 * SQUISH_CONSTANT_4D;
			T attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4;
			if (attn4 > 0) {
				attn4 *= attn4;
				value += attn4 * attn4 * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 0, dx4, dy4, dz4, dw4);
			}

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

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

			//Contribution (0,1,1,1)
			T dx1 = dx0 - 3 * SQUISH_CONSTANT_4D;
			T dz1 = dz4;
			T dy1 = dy4;
			T dw1 = dw3;
			T attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1;
			if (attn1 > 0) {
				attn1 *= attn1;
				value += attn1 * attn1 * extrapolate(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;
			T attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 - dw0 * dw0;
			if (attn0 > 0) {
				attn0 *= attn0;
				value += attn0 * attn0 * extrapolate(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)
			T aScore;
			byte aPoint;
			bool aIsBiggerSide = true;
			T bScore;
			byte bPoint;
			bool bIsBiggerSide = true;

			//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) {
				T score = xins + wins;
				if (aScore >= bScore && score > bScore) {
					bScore = score;
					bPoint = 0x09;
				} else if (aScore < bScore && score > aScore) {
					aScore = score;
					aPoint = 0x09;
				}
			} else {
				T 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.
			T p1 = 2 - inSum + xins;
			if (aScore >= bScore && p1 > bScore) {
				bScore = p1;
				bPoint = 0x01;
				bIsBiggerSide = false;
			} else if (aScore < bScore && p1 > aScore) {
				aScore = p1;
				aPoint = 0x01;
				aIsBiggerSide = false;
			}

			//Decide if (0,1,0,0) is closer.
			T p2 = 2 - inSum + yins;
			if (aScore >= bScore && p2 > bScore) {
				bScore = p2;
				bPoint = 0x02;
				bIsBiggerSide = false;
			} else if (aScore < bScore && p2 > aScore) {
				aScore = p2;
				aPoint = 0x02;
				aIsBiggerSide = false;
			}

			//Decide if (0,0,1,0) is closer.
			T p3 = 2 - inSum + zins;
			if (aScore >= bScore && p3 > bScore) {
				bScore = p3;
				bPoint = 0x04;
				bIsBiggerSide = false;
			} else if (aScore < bScore && p3 > aScore) {
				aScore = p3;
				aPoint = 0x04;
				aIsBiggerSide = false;
			}

			//Decide if (0,0,0,1) is closer.
			T p4 = 2 - inSum + wins;
			if (aScore >= bScore && p4 > bScore) {
				bScore = p4;
				bPoint = 0x08;
				bIsBiggerSide = false;
			} else if (aScore < bScore && p4 > aScore) {
				aScore = p4;
				aPoint = 0x08;
				aIsBiggerSide = false;
			}

			//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
					byte c1 = cast(byte)(aPoint | bPoint);
					byte c2 = cast(byte)(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.
					byte c = cast(byte)(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"
				byte 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)
			T dx1 = dx0 - 1 - SQUISH_CONSTANT_4D;
			T dy1 = dy0 - 0 - SQUISH_CONSTANT_4D;
			T dz1 = dz0 - 0 - SQUISH_CONSTANT_4D;
			T dw1 = dw0 - 0 - SQUISH_CONSTANT_4D;
			T attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1;
			if (attn1 > 0) {
				attn1 *= attn1;
				value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 0, dx1, dy1, dz1, dw1);
			}

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

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

			//Contribution (0,0,0,1)
			T dx4 = dx2;
			T dy4 = dy1;
			T dz4 = dz1;
			T dw4 = dw0 - 1 - SQUISH_CONSTANT_4D;
			T attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4;
			if (attn4 > 0) {
				attn4 *= attn4;
				value += attn4 * attn4 * extrapolate(xsb + 0, ysb + 0, zsb + 0, wsb + 1, dx4, dy4, dz4, dw4);
			}

			//Contribution (1,1,0,0)
			T dx5 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
			T dy5 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
			T dz5 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D;
			T dw5 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D;
			T attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5 - dw5 * dw5;
			if (attn5 > 0) {
				attn5 *= attn5;
				value += attn5 * attn5 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 0, dx5, dy5, dz5, dw5);
			}

			//Contribution (1,0,1,0)
			T dx6 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
			T dy6 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D;
			T dz6 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
			T dw6 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D;
			T attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6 - dw6 * dw6;
			if (attn6 > 0) {
				attn6 *= attn6;
				value += attn6 * attn6 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 0, dx6, dy6, dz6, dw6);
			}

			//Contribution (1,0,0,1)
			T dx7 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
			T dy7 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D;
			T dz7 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D;
			T dw7 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
			T attn7 = 2 - dx7 * dx7 - dy7 * dy7 - dz7 * dz7 - dw7 * dw7;
			if (attn7 > 0) {
				attn7 *= attn7;
				value += attn7 * attn7 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 1, dx7, dy7, dz7, dw7);
			}

			//Contribution (0,1,1,0)
			T dx8 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D;
			T dy8 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
			T dz8 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
			T dw8 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D;
			T attn8 = 2 - dx8 * dx8 - dy8 * dy8 - dz8 * dz8 - dw8 * dw8;
			if (attn8 > 0) {
				attn8 *= attn8;
				value += attn8 * attn8 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 0, dx8, dy8, dz8, dw8);
			}

			//Contribution (0,1,0,1)
			T dx9 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D;
			T dy9 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
			T dz9 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D;
			T dw9 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
			T attn9 = 2 - dx9 * dx9 - dy9 * dy9 - dz9 * dz9 - dw9 * dw9;
			if (attn9 > 0) {
				attn9 *= attn9;
				value += attn9 * attn9 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 1, dx9, dy9, dz9, dw9);
			}

			//Contribution (0,0,1,1)
			T dx10 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D;
			T dy10 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D;
			T dz10 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
			T dw10 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
			T attn10 = 2 - dx10 * dx10 - dy10 * dy10 - dz10 * dz10 - dw10 * dw10;
			if (attn10 > 0) {
				attn10 *= attn10;
				value += attn10 * attn10 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 1, dx10, dy10, dz10, dw10);
			}
		} else { //We're inside the second dispentachoron (Rectified 4-Simplex)
			T aScore;
			byte aPoint;
			bool aIsBiggerSide = true;
			T bScore;
			byte bPoint;
			bool bIsBiggerSide = true;

			//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) {
				T score = xins + wins;
				if (aScore <= bScore && score < bScore) {
					bScore = score;
					bPoint = 0x06;
				} else if (aScore > bScore && score < aScore) {
					aScore = score;
					aPoint = 0x06;
				}
			} else {
				T 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.
			T p1 = 3 - inSum + xins;
			if (aScore <= bScore && p1 < bScore) {
				bScore = p1;
				bPoint = 0x0E;
				bIsBiggerSide = false;
			} else if (aScore > bScore && p1 < aScore) {
				aScore = p1;
				aPoint = 0x0E;
				aIsBiggerSide = false;
			}

			//Decide if (1,0,1,1) is closer.
			T p2 = 3 - inSum + yins;
			if (aScore <= bScore && p2 < bScore) {
				bScore = p2;
				bPoint = 0x0D;
				bIsBiggerSide = false;
			} else if (aScore > bScore && p2 < aScore) {
				aScore = p2;
				aPoint = 0x0D;
				aIsBiggerSide = false;
			}

			//Decide if (1,1,0,1) is closer.
			T p3 = 3 - inSum + zins;
			if (aScore <= bScore && p3 < bScore) {
				bScore = p3;
				bPoint = 0x0B;
				bIsBiggerSide = false;
			} else if (aScore > bScore && p3 < aScore) {
				aScore = p3;
				aPoint = 0x0B;
				aIsBiggerSide = false;
			}

			//Decide if (1,1,1,0) is closer.
			T p4 = 3 - inSum + wins;
			if (aScore <= bScore && p4 < bScore) {
				bScore = p4;
				bPoint = 0x07;
				bIsBiggerSide = false;
			} else if (aScore > bScore && p4 < aScore) {
				aScore = p4;
				aPoint = 0x07;
				aIsBiggerSide = false;
			}

			//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
					byte c1 = cast(byte)(aPoint & bPoint);
					byte c2 = cast(byte)(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.
					byte c = cast(byte)(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"
				byte 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)
			T dx4 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D;
			T dy4 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D;
			T dz4 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D;
			T dw4 = dw0 - 3 * SQUISH_CONSTANT_4D;
			T attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4;
			if (attn4 > 0) {
				attn4 *= attn4;
				value += attn4 * attn4 * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 0, dx4, dy4, dz4, dw4);
			}

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

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

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

			//Contribution (1,1,0,0)
			T dx5 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
			T dy5 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
			T dz5 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D;
			T dw5 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D;
			T attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5 - dw5 * dw5;
			if (attn5 > 0) {
				attn5 *= attn5;
				value += attn5 * attn5 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 0, dx5, dy5, dz5, dw5);
			}

			//Contribution (1,0,1,0)
			T dx6 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
			T dy6 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D;
			T dz6 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
			T dw6 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D;
			T attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6 - dw6 * dw6;
			if (attn6 > 0) {
				attn6 *= attn6;
				value += attn6 * attn6 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 0, dx6, dy6, dz6, dw6);
			}

			//Contribution (1,0,0,1)
			T dx7 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
			T dy7 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D;
			T dz7 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D;
			T dw7 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
			T attn7 = 2 - dx7 * dx7 - dy7 * dy7 - dz7 * dz7 - dw7 * dw7;
			if (attn7 > 0) {
				attn7 *= attn7;
				value += attn7 * attn7 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 1, dx7, dy7, dz7, dw7);
			}

			//Contribution (0,1,1,0)
			T dx8 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D;
			T dy8 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
			T dz8 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
			T dw8 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D;
			T attn8 = 2 - dx8 * dx8 - dy8 * dy8 - dz8 * dz8 - dw8 * dw8;
			if (attn8 > 0) {
				attn8 *= attn8;
				value += attn8 * attn8 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 0, dx8, dy8, dz8, dw8);
			}

			//Contribution (0,1,0,1)
			T dx9 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D;
			T dy9 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
			T dz9 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D;
			T dw9 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
			T attn9 = 2 - dx9 * dx9 - dy9 * dy9 - dz9 * dz9 - dw9 * dw9;
			if (attn9 > 0) {
				attn9 *= attn9;
				value += attn9 * attn9 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 1, dx9, dy9, dz9, dw9);
			}

			//Contribution (0,0,1,1)
			T dx10 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D;
			T dy10 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D;
			T dz10 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
			T dw10 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
			T attn10 = 2 - dx10 * dx10 - dy10 * dy10 - dz10 * dz10 - dw10 * dw10;
			if (attn10 > 0) {
				attn10 *= attn10;
				value += attn10 * attn10 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 1, dx10, dy10, dz10, dw10);
			}
		}

		//First extra vertex
		T 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 * extrapolate(xsv_ext0, ysv_ext0, zsv_ext0, wsv_ext0, dx_ext0, dy_ext0, dz_ext0, dw_ext0);
		}

		//Second extra vertex
		T 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 * extrapolate(xsv_ext1, ysv_ext1, zsv_ext1, wsv_ext1, dx_ext1, dy_ext1, dz_ext1, dw_ext1);
		}

		//Third extra vertex
		T 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 * extrapolate(xsv_ext2, ysv_ext2, zsv_ext2, wsv_ext2, dx_ext2, dy_ext2, dz_ext2, dw_ext2);
		}

		return value / NORM_CONSTANT_4D;
	}

	private T extrapolate(int xsb, int ysb, T dx, T dy)
	{
		int index = perm[(perm[xsb & 0xFF] + ysb) & 0xFF] & 0x0E;
		return gradients2D[index] * dx
			+ gradients2D[index + 1] * dy;
	}

	private T extrapolate(int xsb, int ysb, int zsb, T dx, T dy, T dz)
	{
		int index = permGradIndex3D[(perm[(perm[xsb & 0xFF] + ysb) & 0xFF] + zsb) & 0xFF];
		return gradients3D[index] * dx
			+ gradients3D[index + 1] * dy
			+ gradients3D[index + 2] * dz;
	}

	private T extrapolate(int xsb, int ysb, int zsb, int wsb, T dx, T dy, T dz, T dw)
	{
		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;
	}

	private static int fastFloor(T x) {
		int xi = cast(int)x;
		return x < xi ? xi - 1 : xi;
	}

	//Gradients for 2D. They approximate the directions to the
	//vertices of an octagon from the center.
	private static immutable byte[] 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.
	private static immutable byte[] 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.
	private static immutable byte[] 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,
	];
}