/* discontinuous pseudorandom uniformly distributed in [-0.5, +0.5]^3 */
vec3 random3(vec3 c) {
    float j = 4096.0 * sin(dot(c, vec3(17.0, 59.4, 15.0)));
    vec3 r;
    r.z = fract(512.0 * j);
    j *= .125;
    r.x = fract(512.0 * j);
    j *= .125;
    r.y = fract(512.0 * j);
    return r - 0.5;
}

const float F3 = 0.3333333;
const float G3 = 0.1666667;

/* 3d simplex noise */
float simplex3d(vec3 p) {
	 /* 1. find current tetrahedron T and it's four vertices */
	 /* s, s+i1, s+i2, s+1.0 - absolute skewed (integer) coordinates of T vertices */
	 /* x, x1, x2, x3 - unskewed coordinates of p relative to each of T vertices*/

	 /* calculate s and x */
    vec3 s = floor(p + dot(p, vec3(F3)));
    vec3 x = p - s + dot(s, vec3(G3));

	 /* calculate i1 and i2 */
    vec3 e = step(vec3(0.0), x - x.yzx);
    vec3 i1 = e * (1.0 - e.zxy);
    vec3 i2 = 1.0 - e.zxy * (1.0 - e);

	 /* x1, x2, x3 */
    vec3 x1 = x - i1 + G3;
    vec3 x2 = x - i2 + 2.0 * G3;
    vec3 x3 = x - 1.0 + 3.0 * G3;

	 /* 2. find four surflets and store them in d */
    vec4 w, d;

	 /* calculate surflet weights */
    w.x = dot(x, x);
    w.y = dot(x1, x1);
    w.z = dot(x2, x2);
    w.w = dot(x3, x3);

	 /* w fades from 0.6 at the center of the surflet to 0.0 at the margin */
    w = max(0.6 - w, 0.0);

	 /* calculate surflet components */
    d.x = dot(random3(s), x);
    d.y = dot(random3(s + i1), x1);
    d.z = dot(random3(s + i2), x2);
    d.w = dot(random3(s + 1.0), x3);

	 /* multiply d by w^4 */
    w *= w;
    w *= w;
    d *= w;

	 /* 3. return the sum of the four surflets */
    return dot(d, vec4(52.0));
}
