simplexNoise4D

//! requires mod289 taylorInvSqrt4
fn snoise_permute4(x: vec4<f32>) -> vec4<f32> {
    return mod289(((x * 34.0) + 10.0) * x);
}

fn snoise_mod289f(x: f32) -> f32 {
    return x - floor(x * (1.0 / 289.0)) * 289.0;
}

fn snoise_permute(x: f32) -> f32 {
    return snoise_mod289f(((x * 34.0) + 10.0) * x);
}

fn snoise_taylorInvSqrt(r: f32) -> f32 {
    return 1.79284291400159 - 0.85373472095314 * r;
}

fn snoise_grad4(j: f32, ip: vec4<f32>) -> vec4<f32> {
    let ones = vec4(1.0, 1.0, 1.0, -1.0);

    var p: vec4<f32>;
    var s: vec4<f32>;

    p = vec4(floor(fract(vec3(j) * ip.xyz) * 7.0) * ip.z - 1.0, p.w);
    p.w = 1.5 - dot(abs(p.xyz), ones.xyz);
    s = select(vec4(0.0), vec4(1.0), p < vec4(0.0));
    p = vec4(p.xyz + (s.xyz * 2.0 - 1.0) * s.www, p.w);

    return p;
}

fn snoise(v: vec4<f32>) -> f32 {
    let C: vec4<f32> = vec4(
        0.138196601125011, // (5 - sqrt(5))/20  G4
        0.276393202250021, // 2 * G4
        0.414589803375032, // 3 * G4
        -0.447213595499958 // -1 + 4 * G4
    );

    // (sqrt(5) - 1)/4 = F4, used once below
    let F4: f32 = 0.309016994374947451;

    // First corner
    var i: vec4<f32> = floor(v + dot(v, vec4(F4)));
    var x0: vec4<f32> = v - i + dot(i, C.xxxx);

    // Other corners

    // Rank sorting originally contributed by Bill Licea-Kane, AMD (formerly ATI)
    var i0: vec4<f32>;
    var isX: vec3<f32> = step(x0.yzw, x0.xxx);
    var isYZ: vec3<f32> = step(x0.zww, x0.yyz);

    //  i0.x = dot( isX, vec3( 1.0 ) );
    i0.x = isX.x + isX.y + isX.z;
    var minusX = 1.0 - isX;
    i0.y = minusX.x;
    i0.z = minusX.y;
    i0.w = minusX.z;

    //  i0.y += dot( isYZ.xy, vec2( 1.0 ) );
    i0.y += isYZ.x + isYZ.y;
    var minusY = 1.0 - isYZ;
    i0.z += minusY.x;
    i0.w += minusY.y;
    i0.z += isYZ.z;
    i0.w += minusY.z;

    // i0 now contains the unique values 0,1,2,3 in each channel
    var i3: vec4<f32> = vec4<f32>(clamp(i0, vec4(0.0), vec4(1.0)));
    var i2: vec4<f32> = clamp(i0 - vec4(1.0), vec4(0.0), vec4(1.0));
    var i1: vec4<f32> = clamp(i0 - vec4(2.0), vec4(0.0), vec4(1.0));

    //  x0 = x0 - 0.0 + 0.0 * C.xxxx
    //  x1 = x0 - i1  + 1.0 * C.xxxx
    //  x2 = x0 - i2  + 2.0 * C.xxxx
    //  x3 = x0 - i3  + 3.0 * C.xxxx
    //  x4 = x0 - 1.0 + 4.0 * C.xxxx
    var x1: vec4<f32> = x0 - i1 + C.xxxx;
    var x2: vec4<f32> = x0 - i2 + C.yyyy;
    var x3: vec4<f32> = x0 - i3 + C.zzzz;
    var x4: vec4<f32> = x0 + C.wwww;

    // Permutations
    i = mod289(i);
    var j0: f32 = snoise_permute(snoise_permute(snoise_permute(snoise_permute(i.w) + i.z) + i.y) + i.x);
    var j1: vec4<f32> = snoise_permute4(snoise_permute4(snoise_permute4(snoise_permute4(i.w + vec4(i1.w, i2.w, i3.w, 1.0)) + i.z + vec4(i1.z, i2.z, i3.z, 1.0)) + i.y + vec4(i1.y, i2.y, i3.y, 1.0)) + i.x + vec4(i1.x, i2.x, i3.x, 1.0));

    // Gradients: 7x7x6 points over a cube, mapped onto a 4-cross polytope
    // 7*7*6 = 294, which is close to the ring size 17*17 = 289.
    var ip: vec4<f32> = vec4(1.0 / 294.0, 1.0 / 49.0, 1.0 / 7.0, 0.0);

    var p0: vec4<f32> = snoise_grad4(j0, ip);
    var p1: vec4<f32> = snoise_grad4(j1.x, ip);
    var p2: vec4<f32> = snoise_grad4(j1.y, ip);
    var p3: vec4<f32> = snoise_grad4(j1.z, ip);
    var p4: vec4<f32> = snoise_grad4(j1.w, ip);

    // Normalise gradients
    var norm: vec4<f32> = taylorInvSqrt4(vec4(dot(p0, p0), dot(p1, p1), dot(p2, p2), dot(p3, p3)));
    p0 *= norm.x;
    p1 *= norm.y;
    p2 *= norm.z;
    p3 *= norm.w;
    p4 *= snoise_taylorInvSqrt(dot(p4, p4));

    // Mix contributions from the five corners
    var m0: vec3<f32> = max(0.6 - vec3(dot(x0, x0), dot(x1, x1), dot(x2, x2)), vec3(0.0));
    var m1: vec2<f32> = max(0.6 - vec2(dot(x3, x3), dot(x4, x4)), vec2(0.0));
    m0 = m0 * m0;
    m1 = m1 * m1;
    return 49.0 * (dot(m0 * m0, vec3(dot(p0, x0), dot(p1, x1), dot(p2, x2))) + dot(m1 * m1, vec2(dot(p3, x3), dot(p4, x4))));
}