opensimplex2 1.1.0

/*!
    K.jpg's OpenSimplex 2, faster variant
*/

use std::{num::Wrapping, sync::Once};

const PRIME_X: i64 = 0x5205402B9270C86F;
const PRIME_Y: i64 = 0x598CD327003817B5;
const PRIME_Z: i64 = 0x5BCC226E9FA0BACB;
const PRIME_W: i64 = 0x56CC5227E58F554B;
const HASH_MULTIPLIER: i64 = 0x53A3F72DEEC546F5;
const SEED_FLIP_3D: i64 = -0x52D547B2E96ED629;
const SEED_OFFSET_4D: i64 = 0xE83DC3E0DA7164D;

const ROOT2OVER2: f64 = 0.7071067811865476;
const SKEW_2D: f64 = 0.366025403784439;
const UNSKEW_2D: f64 = -0.21132486540518713;

const ROOT3OVER3: f64 = 0.577350269189626;
const FALLBACK_ROTATE_3D: f64 = 2.0 / 3.0;
const ROTATE_3D_ORTHOGONALIZER: f64 = UNSKEW_2D;

const SKEW_4D: f32 = -0.138196601125011;
const UNSKEW_4D: f32 = 0.309016994374947;
const LATTICE_STEP_4D: f32 = 0.2;

const N_GRADS_2D_EXPONENT: i32 = 7;
const N_GRADS_3D_EXPONENT: i32 = 8;
const N_GRADS_4D_EXPONENT: i32 = 9;
const N_GRADS_2D: i32 = 1 << N_GRADS_2D_EXPONENT;
const N_GRADS_3D: i32 = 1 << N_GRADS_3D_EXPONENT;
const N_GRADS_4D: i32 = 1 << N_GRADS_4D_EXPONENT;

const NORMALIZER_2D: f64 = 0.01001634121365712;
const NORMALIZER_3D: f64 = 0.07969837668935331;
const NORMALIZER_4D: f64 = 0.0220065933241897;

const RSQUARED_2D: f32 = 0.5;
const RSQUARED_3D: f32 = 0.6;
const RSQUARED_4D: f32 = 0.6;

/*
    Noise Evaluators
*/

/**
    2D Simplex noise, standard lattice orientation.
*/
pub fn noise2(seed: i64, x: f64, y: f64) -> f32 {
    // Get points for A2* lattice
    let s = SKEW_2D * (x + y);
    let xs = x + s;
    let ys = y + s;

    noise2_UnskewedBase(seed, xs, ys)
}

/**
    2D Simplex noise, with Y pointing down the main diagonal.
    Might be better for a 2D sandbox style game, where Y is vertical.
    Probably slightly less optimal for heightmaps or continent maps,
    unless your map is centered around an equator. It's a subtle
    difference, but the option is here to make it an easy choice.
*/
pub fn noise2_ImproveX(seed: i64, x: f64, y: f64) -> f32 {
    // Skew transform and rotation baked into one.
    let xx = x * ROOT2OVER2;
    let yy = y * (ROOT2OVER2 * (1.0 + 2.0 * SKEW_2D));

    noise2_UnskewedBase(seed, yy + xx, yy - xx)
}

/**
    2D Simplex noise base.
*/
fn noise2_UnskewedBase(seed: i64, xs: f64, ys: f64) -> f32 {
    let seed = Wrapping(seed);

    // Get base points and offsets.
    let xsb = fastFloor(xs);
    let ysb = fastFloor(ys);
    let xi = (xs - xsb as f64) as f32;
    let yi = (ys - ysb as f64) as f32;

    // Prime pre-multiplication for hash.
    let xsbp = Wrapping(xsb as i64) * Wrapping(PRIME_X);
    let ysbp = Wrapping(ysb as i64) * Wrapping(PRIME_Y);

    // Unskew.
    let t = (xi + yi) * UNSKEW_2D as f32;
    let dx0 = xi + t;
    let dy0 = yi + t;

    // First vertex.
    let mut value = 0.0;
    let a0 = RSQUARED_2D - dx0 * dx0 - dy0 * dy0;
    if a0 > 0.0 {
        value = (a0 * a0) * (a0 * a0) * grad2(seed, xsbp, ysbp, dx0, dy0);
    }

    // Second vertex.
    let a1 = (2.0 * (1.0 + 2.0 * UNSKEW_2D) * (1.0 / UNSKEW_2D + 2.0)) as f32 * t
        + ((-2.0 * (1.0 + 2.0 * UNSKEW_2D) * (1.0 + 2.0 * UNSKEW_2D)) as f32 + a0);
    if a1 > 0.0 {
        let dx1 = dx0 - (1.0 + 2.0 * UNSKEW_2D) as f32;
        let dy1 = dy0 - (1.0 + 2.0 * UNSKEW_2D) as f32;
        value += (a1 * a1)
            * (a1 * a1)
            * grad2(
                seed,
                xsbp + Wrapping(PRIME_X),
                ysbp + Wrapping(PRIME_Y),
                dx1,
                dy1,
            );
    }

    // Third vertex.
    if dy0 > dx0 {
        let dx2 = dx0 - UNSKEW_2D as f32;
        let dy2 = dy0 - (UNSKEW_2D + 1.0) as f32;
        let a2 = RSQUARED_2D - dx2 * dx2 - dy2 * dy2;
        if a2 > 0.0 {
            value += (a2 * a2) * (a2 * a2) * grad2(seed, xsbp, ysbp + Wrapping(PRIME_Y), dx2, dy2);
        }
    } else {
        let dx2 = dx0 - (UNSKEW_2D + 1.0) as f32;
        let dy2 = dy0 - UNSKEW_2D as f32;
        let a2 = RSQUARED_2D - dx2 * dx2 - dy2 * dy2;
        if a2 > 0.0 {
            value += (a2 * a2) * (a2 * a2) * grad2(seed, xsbp + Wrapping(PRIME_X), ysbp, dx2, dy2);
        }
    }

    value
}

/**
    3D OpenSimplex2 noise, with better visual isotropy in (X, Y).
    Recommended for 3D terrain and time-varied animations.
    The Z coordinate should always be the "different" coordinate in whatever your use case is.
    If Y is vertical in world coordinates, call noise3_ImproveXZ(x, z, Y) or use noise3_XZBeforeY.
    If Z is vertical in world coordinates, call noise3_ImproveXZ(x, y, Z).
    For a time varied animation, call noise3_ImproveXY(x, y, T).
*/
pub fn noise3_ImproveXY(seed: i64, x: f64, y: f64, z: f64) -> f32 {
    // Re-orient the cubic lattices without skewing, so Z points up the main lattice diagonal,
    // and the planes formed by XY are moved far out of alignment with the cube faces.
    // Orthonormal rotation. Not a skew transform.
    let xy = x + y;
    let s2 = xy * ROTATE_3D_ORTHOGONALIZER;
    let zz = z * ROOT3OVER3;
    let xr = x + s2 + zz;
    let yr = y + s2 + zz;
    let zr = xy * -ROOT3OVER3 + zz;

    // Evaluate both lattices to form a BCC lattice.
    noise3_UnrotatedBase(seed, xr, yr, zr)
}

/**
    3D OpenSimplex2 noise, with better visual isotropy in (X, Z).
    Recommended for 3D terrain and time-varied animations.
    The Y coordinate should always be the "different" coordinate in whatever your use case is.
    If Y is vertical in world coordinates, call noise3_ImproveXZ(x, Y, z).
    If Z is vertical in world coordinates, call noise3_ImproveXZ(x, Z, y) or use noise3_ImproveXY.
    For a time varied animation, call noise3_ImproveXZ(x, T, y) or use noise3_ImproveXY.
*/
pub fn noise3_ImproveXZ(seed: i64, x: f64, y: f64, z: f64) -> f32 {
    // Re-orient the cubic lattices without skewing, so Y points up the main lattice diagonal,
    // and the planes formed by XZ are moved far out of alignment with the cube faces.
    // Orthonormal rotation. Not a skew transform.
    let xz = x + z;
    let s2 = xz * ROTATE_3D_ORTHOGONALIZER;
    let yy = y * ROOT3OVER3;
    let xr = x + s2 + yy;
    let zr = z + s2 + yy;
    let yr = xz * -ROOT3OVER3 + yy;

    // Evaluate both lattices to form a BCC lattice.
    noise3_UnrotatedBase(seed, xr, yr, zr)
}

/**
    3D OpenSimplex2 noise, fallback rotation option
    Use noise3_ImproveXY or noise3_ImproveXZ instead, wherever appropriate.
    They have less diagonal bias. This function's best use is as a fallback.
*/
pub fn noise3_Fallback(seed: i64, x: f64, y: f64, z: f64) -> f32 {
    // Re-orient the cubic lattices via rotation, to produce a familiar look.
    // Orthonormal rotation. Not a skew transform.
    let r = FALLBACK_ROTATE_3D * (x + y + z);
    let xr = r - x;
    let yr = r - y;
    let zr = r - z;

    // Evaluate both lattices to form a BCC lattice.
    noise3_UnrotatedBase(seed, xr, yr, zr)
}

/**
    Generate overlapping cubic lattices for 3D OpenSimplex2 noise.
*/
fn noise3_UnrotatedBase(seed: i64, xr: f64, yr: f64, zr: f64) -> f32 {
    let mut seed = Wrapping(seed);

    // Get base points and offsets.
    let xrb = fastRound(xr);
    let yrb = fastRound(yr);
    let zrb = fastRound(zr);
    let mut xri = (xr - xrb as f64) as f32;
    let mut yri = (yr - yrb as f64) as f32;
    let mut zri = (zr - zrb as f64) as f32;

    // -1 if positive, 1 if negative.
    let mut xNSign = (-1.0 - xri) as i32 | 1;
    let mut yNSign = (-1.0 - yri) as i32 | 1;
    let mut zNSign = (-1.0 - zri) as i32 | 1;

    // Compute absolute values, using the above as a shortcut. This was faster in my tests for some reason.
    let mut ax0 = xNSign as f32 * -xri;
    let mut ay0 = yNSign as f32 * -yri;
    let mut az0 = zNSign as f32 * -zri;

    // Prime pre-multiplication for hash.
    let mut xrbp = Wrapping(xrb as i64) * Wrapping(PRIME_X);
    let mut yrbp = Wrapping(yrb as i64) * Wrapping(PRIME_Y);
    let mut zrbp = Wrapping(zrb as i64) * Wrapping(PRIME_Z);

    // Loop: Pick an edge on each lattice copy.
    let mut value = 0.0;
    let mut a = (RSQUARED_3D - xri * xri) - (yri * yri + zri * zri);
    for l in 0.. {
        // Closest point on cube.
        if a > 0.0 {
            value += (a * a) * (a * a) * grad3(seed, xrbp, yrbp, zrbp, xri, yri, zri);
        }

        // Second-closest point.
        if ax0 >= ay0 && ax0 >= az0 {
            let mut b = a + ax0 + ax0;
            if b > 1.0 {
                b -= 1.0;
                value += (b * b)
                    * (b * b)
                    * grad3(
                        seed,
                        xrbp - Wrapping(xNSign as i64) * Wrapping(PRIME_X),
                        yrbp,
                        zrbp,
                        xri + xNSign as f32,
                        yri,
                        zri,
                    );
            }
        } else if ay0 > ax0 && ay0 >= az0 {
            let mut b = a + ay0 + ay0;
            if b > 1.0 {
                b -= 1.0;
                value += (b * b)
                    * (b * b)
                    * grad3(
                        seed,
                        xrbp,
                        yrbp - Wrapping(yNSign as i64) * Wrapping(PRIME_Y),
                        zrbp,
                        xri,
                        yri + yNSign as f32,
                        zri,
                    );
            }
        } else {
            let mut b = a + az0 + az0;
            if b > 1.0 {
                b -= 1.0;
                value += (b * b)
                    * (b * b)
                    * grad3(
                        seed,
                        xrbp,
                        yrbp,
                        zrbp - Wrapping(zNSign as i64) * Wrapping(PRIME_Z),
                        xri,
                        yri,
                        zri + zNSign as f32,
                    );
            }
        }

        // Break from loop if we're done, skipping updates below.
        if l == 1 {
            break;
        }

        // Update absolute value.
        ax0 = 0.5 - ax0;
        ay0 = 0.5 - ay0;
        az0 = 0.5 - az0;

        // Update relative coordinate.
        xri = xNSign as f32 * ax0;
        yri = yNSign as f32 * ay0;
        zri = zNSign as f32 * az0;

        // Update falloff.
        a += (0.75 - ax0) - (ay0 + az0);

        // Update prime for hash.
        xrbp += (xNSign as i64 >> 1) & PRIME_X;
        yrbp += (yNSign as i64 >> 1) & PRIME_Y;
        zrbp += (zNSign as i64 >> 1) & PRIME_Z;

        // Update the reverse sign indicators.
        xNSign = -xNSign;
        yNSign = -yNSign;
        zNSign = -zNSign;

        // And finally update the seed for the other lattice copy.
        seed ^= SEED_FLIP_3D;
    }

    value
}

/**
    4D OpenSimplex2 noise, with XYZ oriented like noise3_ImproveXY
    and W for an extra degree of freedom. W repeats eventually.
    Recommended for time-varied animations which texture a 3D object (W=time)
    in a space where Z is vertical
*/
pub fn noise4_ImproveXYZ_ImproveXY(seed: i64, x: f64, y: f64, z: f64, w: f64) -> f32 {
    let xy = x + y;
    let s2 = xy * -0.21132486540518699998;
    let zz = z * 0.28867513459481294226;
    let ww = w * 0.2236067977499788;
    let xr = x + (zz + ww + s2);
    let yr = y + (zz + ww + s2);
    let zr = xy * -0.57735026918962599998 + (zz + ww);
    let wr = z * -0.866025403784439 + ww;

    noise4_UnskewedBase(seed, xr, yr, zr, wr)
}

/**
    4D OpenSimplex2 noise, with XYZ oriented like noise3_ImproveXZ
    and W for an extra degree of freedom. W repeats eventually.
    Recommended for time-varied animations which texture a 3D object (W=time)
    in a space where Y is vertical
*/
pub fn noise4_ImproveXYZ_ImproveXZ(seed: i64, x: f64, y: f64, z: f64, w: f64) -> f32 {
    let xz = x + z;
    let s2 = xz * -0.21132486540518699998;
    let yy = y * 0.28867513459481294226;
    let ww = w * 0.2236067977499788;
    let xr = x + (yy + ww + s2);
    let zr = z + (yy + ww + s2);
    let yr = xz * -0.57735026918962599998 + (yy + ww);
    let wr = y * -0.866025403784439 + ww;

    noise4_UnskewedBase(seed, xr, yr, zr, wr)
}

/**
    4D OpenSimplex2 noise, with XYZ oriented like noise3_Fallback
    and W for an extra degree of freedom. W repeats eventually.
    Recommended for time-varied animations which texture a 3D object (W=time)
    where there isn't a clear distinction between horizontal and vertical
*/
pub fn noise4_ImproveXYZ(seed: i64, x: f64, y: f64, z: f64, w: f64) -> f32 {
    let xyz = x + y + z;
    let ww = w * 0.2236067977499788;
    let s2 = xyz * -0.16666666666666666 + ww;
    let xs = x + s2;
    let ys = y + s2;
    let zs = z + s2;
    let ws = -0.5 * xyz + ww;

    noise4_UnskewedBase(seed, xs, ys, zs, ws)
}

/**
    4D OpenSimplex2 noise, with XY and ZW forming orthogonal triangular-based planes.
    Recommended for 3D terrain, where X and Y (or Z and W) are horizontal.
    Recommended for noise(x, y, sin(time), cos(time)) trick.
*/
pub fn noise4_ImproveXY_ImproveZW(seed: i64, x: f64, y: f64, z: f64, w: f64) -> f32 {
    let s2 = (x + y) * -0.178275657951399372 + (z + w) * 0.215623393288842828;
    let t2 = (z + w) * -0.403949762580207112 + (x + y) * -0.375199083010075342;
    let xs = x + s2;
    let ys = y + s2;
    let zs = z + t2;
    let ws = w + t2;

    noise4_UnskewedBase(seed, xs, ys, zs, ws)
}

/**
    4D OpenSimplex2 noise, fallback lattice orientation.
*/
pub fn noise4_Fallback(seed: i64, x: f64, y: f64, z: f64, w: f64) -> f32 {
    // Get points for A4 lattice
    let s = SKEW_4D as f64 * (x + y + z + w);
    let xs = x + s;
    let ys = y + s;
    let zs = z + s;
    let ws = w + s;

    noise4_UnskewedBase(seed, xs, ys, zs, ws)
}

/**
    4D OpenSimplex2 noise base.
*/
fn noise4_UnskewedBase(seed: i64, xs: f64, ys: f64, zs: f64, ws: f64) -> f32 {
    let mut seed = Wrapping(seed);

    // Get base points and offsets
    let xsb = fastFloor(xs);
    let ysb = fastFloor(ys);
    let zsb = fastFloor(zs);
    let wsb = fastFloor(ws);
    let mut xsi = (xs - xsb as f64) as f32;
    let mut ysi = (ys - ysb as f64) as f32;
    let mut zsi = (zs - zsb as f64) as f32;
    let mut wsi = (ws - wsb as f64) as f32;

    // Determine which lattice we can be confident has a contributing point its corresponding cell's base simplex.
    // We only look at the spaces between the diagonal planes. This proved effective in all of my tests.
    let siSum = (xsi + ysi) + (zsi + wsi);
    let startingLattice = (siSum * 1.25) as i32;

    // Offset for seed based on first lattice copy.
    seed += Wrapping(startingLattice as i64) * Wrapping(SEED_OFFSET_4D);

    // Offset for lattice point relative positions (skewed)
    let startingLatticeOffset = startingLattice as f32 * -LATTICE_STEP_4D;
    xsi += startingLatticeOffset;
    ysi += startingLatticeOffset;
    zsi += startingLatticeOffset;
    wsi += startingLatticeOffset;

    // Prep for vertex contributions.
    let mut ssi = (siSum + startingLatticeOffset * 4.0) * UNSKEW_4D;

    // Prime pre-multiplication for hash.
    let mut xsvp = Wrapping(xsb as i64) * Wrapping(PRIME_X);
    let mut ysvp = Wrapping(ysb as i64) * Wrapping(PRIME_Y);
    let mut zsvp = Wrapping(zsb as i64) * Wrapping(PRIME_Z);
    let mut wsvp = Wrapping(wsb as i64) * Wrapping(PRIME_W);

    // Five points to add, total, from five copies of the A4 lattice.
    let mut value = 0.0;
    for i in 0.. {
        // Next point is the closest vertex on the 4-simplex whose base vertex is the aforementioned vertex.
        let score0 = 1.0 + ssi * (-1.0 / UNSKEW_4D); // Seems slightly faster than 1.0-xsi-ysi-zsi-wsi
        if xsi >= ysi && xsi >= zsi && xsi >= wsi && xsi >= score0 {
            xsvp += PRIME_X;
            xsi -= 1.0;
            ssi -= UNSKEW_4D;
        } else if ysi > xsi && ysi >= zsi && ysi >= wsi && ysi >= score0 {
            ysvp += PRIME_Y;
            ysi -= 1.0;
            ssi -= UNSKEW_4D;
        } else if zsi > xsi && zsi > ysi && zsi >= wsi && zsi >= score0 {
            zsvp += PRIME_Z;
            zsi -= 1.0;
            ssi -= UNSKEW_4D;
        } else if wsi > xsi && wsi > ysi && wsi > zsi && wsi >= score0 {
            wsvp += PRIME_W;
            wsi -= 1.0;
            ssi -= UNSKEW_4D;
        }

        // gradient contribution with falloff.
        let dx = xsi + ssi;
        let dy = ysi + ssi;
        let dz = zsi + ssi;
        let dw = wsi + ssi;
        let mut a = (dx * dx + dy * dy) + (dz * dz + dw * dw);
        if a < RSQUARED_4D {
            a -= RSQUARED_4D;
            a *= a;
            value += a * a * grad4(seed, xsvp, ysvp, zsvp, wsvp, dx, dy, dz, dw);
        }

        // Break from loop if we're done, skipping updates below.
        if i == 4 {
            break;
        }

        // Update for next lattice copy shifted down by <-0.2, -0.2, -0.2, -0.2>.
        xsi += LATTICE_STEP_4D;
        ysi += LATTICE_STEP_4D;
        zsi += LATTICE_STEP_4D;
        wsi += LATTICE_STEP_4D;
        ssi += LATTICE_STEP_4D * 4.0 * UNSKEW_4D;
        seed -= SEED_OFFSET_4D;

        // Because we don't always start on the same lattice copy, there's a special reset case.
        if i == startingLattice {
            xsvp -= PRIME_X;
            ysvp -= PRIME_Y;
            zsvp -= PRIME_Z;
            wsvp -= PRIME_W;
            seed += SEED_OFFSET_4D * 5;
        }
    }

    value
}

/*
    Utility
*/

fn grad2(seed: Wrapping<i64>, xsvp: Wrapping<i64>, ysvp: Wrapping<i64>, dx: f32, dy: f32) -> f32 {
    let mut hash = seed ^ xsvp ^ ysvp;
    hash *= HASH_MULTIPLIER;
    hash ^= hash.0 >> (64 - N_GRADS_2D_EXPONENT + 1);
    let gi = (hash.0 as i32 & ((N_GRADS_2D - 1) << 1)) as usize;
    let grads = &getGradients().gradients2D;
    grads[gi | 0] * dx + grads[gi | 1] * dy
}

fn grad3(
    seed: Wrapping<i64>,
    xrvp: Wrapping<i64>,
    yrvp: Wrapping<i64>,
    zrvp: Wrapping<i64>,
    dx: f32,
    dy: f32,
    dz: f32,
) -> f32 {
    let mut hash = (seed ^ xrvp) ^ (yrvp ^ zrvp);
    hash *= HASH_MULTIPLIER;
    hash ^= hash.0 >> (64 - N_GRADS_3D_EXPONENT + 2);
    let gi = (hash.0 as i32 & ((N_GRADS_3D - 1) << 2)) as usize;
    let grads = &getGradients().gradients3D;
    grads[gi | 0] * dx + grads[gi | 1] * dy + grads[gi | 2] * dz
}

fn grad4(
    seed: Wrapping<i64>,
    xsvp: Wrapping<i64>,
    ysvp: Wrapping<i64>,
    zsvp: Wrapping<i64>,
    wsvp: Wrapping<i64>,
    dx: f32,
    dy: f32,
    dz: f32,
    dw: f32,
) -> f32 {
    let mut hash = seed ^ (xsvp ^ ysvp) ^ (zsvp ^ wsvp);
    hash *= HASH_MULTIPLIER;
    hash ^= hash.0 >> (64 - N_GRADS_4D_EXPONENT + 2);
    let gi = (hash.0 as i32 & ((N_GRADS_4D - 1) << 2)) as usize;
    let grads = &getGradients().gradients4D;
    (grads[gi | 0] * dx + grads[gi | 1] * dy) + (grads[gi | 2] * dz + grads[gi | 3] * dw)
}

fn fastFloor(x: f64) -> i32 {
    let xi = x as i32;
    if x < xi as f64 {
        xi - 1
    } else {
        xi
    }
}

fn fastRound(x: f64) -> i32 {
    if x < 0.0 {
        (x - 0.5) as i32
    } else {
        (x + 0.5) as i32
    }
}

/*
    gradients
*/

struct Gradients {
    gradients2D: Vec<f32>,
    gradients3D: Vec<f32>,
    gradients4D: Vec<f32>,
}

static mut GRADIENTS: (Once, Option<Gradients>) = (Once::new(), None);

fn getGradients() -> &'static Gradients {
    unsafe {
        GRADIENTS.0.call_once(|| {
            GRADIENTS.1 = Some(initGradients());
        });
        GRADIENTS.1.as_ref().unwrap()
    }
}

fn initGradients() -> Gradients {
    let gradients2D: Vec<_> = GRAD2_SRC
        .into_iter()
        .map(|v| (v / NORMALIZER_2D) as f32)
        .collect::<Vec<_>>() // cache divisions
        .into_iter()
        .cycle()
        .take((N_GRADS_2D * 2) as usize)
        .collect();

    let gradients3D: Vec<_> = GRAD3_SRC
        .into_iter()
        .map(|v| (v / NORMALIZER_3D) as f32)
        .collect::<Vec<_>>() // cache divisions
        .into_iter()
        .cycle()
        .take((N_GRADS_3D * 4) as usize)
        .collect();

    let gradients4D: Vec<_> = GRAD4_SRC
        .into_iter()
        .map(|v| (v / NORMALIZER_4D) as f32)
        .collect::<Vec<_>>() // cache divisions
        .into_iter()
        .cycle()
        .take((N_GRADS_4D * 4) as usize)
        .collect();

    Gradients {
        gradients2D,
        gradients3D,
        gradients4D,
    }
}

#[rustfmt::skip]
const GRAD2_SRC: &[f64] = &[
     0.38268343236509,   0.923879532511287,
     0.923879532511287,  0.38268343236509,
     0.923879532511287, -0.38268343236509,
     0.38268343236509,  -0.923879532511287,
    -0.38268343236509,  -0.923879532511287,
    -0.923879532511287, -0.38268343236509,
    -0.923879532511287,  0.38268343236509,
    -0.38268343236509,   0.923879532511287,
    //-------------------------------------//
     0.130526192220052,  0.99144486137381,
     0.608761429008721,  0.793353340291235,
     0.793353340291235,  0.608761429008721,
     0.99144486137381,   0.130526192220051,
     0.99144486137381,  -0.130526192220051,
     0.793353340291235, -0.60876142900872,
     0.608761429008721, -0.793353340291235,
     0.130526192220052, -0.99144486137381,
    -0.130526192220052, -0.99144486137381,
    -0.608761429008721, -0.793353340291235,
    -0.793353340291235, -0.608761429008721,
    -0.99144486137381,  -0.130526192220052,
    -0.99144486137381,   0.130526192220051,
    -0.793353340291235,  0.608761429008721,
    -0.608761429008721,  0.793353340291235,
    -0.130526192220052,  0.99144486137381,
];

#[rustfmt::skip]
const GRAD3_SRC: &[f64] = &[
     2.22474487139,       2.22474487139,      -1.0,                 0.0,
     2.22474487139,       2.22474487139,       1.0,                 0.0,
     3.0862664687972017,  1.1721513422464978,  0.0,                 0.0,
     1.1721513422464978,  3.0862664687972017,  0.0,                 0.0,
    -2.22474487139,       2.22474487139,      -1.0,                 0.0,
    -2.22474487139,       2.22474487139,       1.0,                 0.0,
    -1.1721513422464978,  3.0862664687972017,  0.0,                 0.0,
    -3.0862664687972017,  1.1721513422464978,  0.0,                 0.0,
    -1.0,                -2.22474487139,      -2.22474487139,       0.0,
     1.0,                -2.22474487139,      -2.22474487139,       0.0,
     0.0,                -3.0862664687972017, -1.1721513422464978,  0.0,
     0.0,                -1.1721513422464978, -3.0862664687972017,  0.0,
    -1.0,                -2.22474487139,       2.22474487139,       0.0,
     1.0,                -2.22474487139,       2.22474487139,       0.0,
     0.0,                -1.1721513422464978,  3.0862664687972017,  0.0,
     0.0,                -3.0862664687972017,  1.1721513422464978,  0.0,
    //--------------------------------------------------------------------//
    -2.22474487139,      -2.22474487139,      -1.0,                 0.0,
    -2.22474487139,      -2.22474487139,       1.0,                 0.0,
    -3.0862664687972017, -1.1721513422464978,  0.0,                 0.0,
    -1.1721513422464978, -3.0862664687972017,  0.0,                 0.0,
    -2.22474487139,      -1.0,                -2.22474487139,       0.0,
    -2.22474487139,       1.0,                -2.22474487139,       0.0,
    -1.1721513422464978,  0.0,                -3.0862664687972017,  0.0,
    -3.0862664687972017,  0.0,                -1.1721513422464978,  0.0,
    -2.22474487139,      -1.0,                 2.22474487139,       0.0,
    -2.22474487139,       1.0,                 2.22474487139,       0.0,
    -3.0862664687972017,  0.0,                 1.1721513422464978,  0.0,
    -1.1721513422464978,  0.0,                 3.0862664687972017,  0.0,
    -1.0,                 2.22474487139,      -2.22474487139,       0.0,
     1.0,                 2.22474487139,      -2.22474487139,       0.0,
     0.0,                 1.1721513422464978, -3.0862664687972017,  0.0,
     0.0,                 3.0862664687972017, -1.1721513422464978,  0.0,
    -1.0,                 2.22474487139,       2.22474487139,       0.0,
     1.0,                 2.22474487139,       2.22474487139,       0.0,
     0.0,                 3.0862664687972017,  1.1721513422464978,  0.0,
     0.0,                 1.1721513422464978,  3.0862664687972017,  0.0,
     2.22474487139,      -2.22474487139,      -1.0,                 0.0,
     2.22474487139,      -2.22474487139,       1.0,                 0.0,
     1.1721513422464978, -3.0862664687972017,  0.0,                 0.0,
     3.0862664687972017, -1.1721513422464978,  0.0,                 0.0,
     2.22474487139,      -1.0,                -2.22474487139,       0.0,
     2.22474487139,       1.0,                -2.22474487139,       0.0,
     3.0862664687972017,  0.0,                -1.1721513422464978,  0.0,
     1.1721513422464978,  0.0,                -3.0862664687972017,  0.0,
     2.22474487139,      -1.0,                 2.22474487139,       0.0,
     2.22474487139,       1.0,                 2.22474487139,       0.0,
     1.1721513422464978,  0.0,                 3.0862664687972017,  0.0,
     3.0862664687972017,  0.0,                 1.1721513422464978,  0.0,
];

#[rustfmt::skip]
const GRAD4_SRC: &[f64] = &[
    -0.6740059517812944,   -0.3239847771997537,   -0.3239847771997537,    0.5794684678643381,
    -0.7504883828755602,   -0.4004672082940195,    0.15296486218853164,   0.5029860367700724,
    -0.7504883828755602,    0.15296486218853164,  -0.4004672082940195,    0.5029860367700724,
    -0.8828161875373585,    0.08164729285680945,   0.08164729285680945,   0.4553054119602712,
    -0.4553054119602712,   -0.08164729285680945,  -0.08164729285680945,   0.8828161875373585,
    -0.5029860367700724,   -0.15296486218853164,   0.4004672082940195,    0.7504883828755602,
    -0.5029860367700724,    0.4004672082940195,   -0.15296486218853164,   0.7504883828755602,
    -0.5794684678643381,    0.3239847771997537,    0.3239847771997537,    0.6740059517812944,
    -0.6740059517812944,   -0.3239847771997537,    0.5794684678643381,   -0.3239847771997537,
    -0.7504883828755602,   -0.4004672082940195,    0.5029860367700724,    0.15296486218853164,
    -0.7504883828755602,    0.15296486218853164,   0.5029860367700724,   -0.4004672082940195,
    -0.8828161875373585,    0.08164729285680945,   0.4553054119602712,    0.08164729285680945,
    -0.4553054119602712,   -0.08164729285680945,   0.8828161875373585,   -0.08164729285680945,
    -0.5029860367700724,   -0.15296486218853164,   0.7504883828755602,    0.4004672082940195,
    -0.5029860367700724,    0.4004672082940195,    0.7504883828755602,   -0.15296486218853164,
    -0.5794684678643381,    0.3239847771997537,    0.6740059517812944,    0.3239847771997537,
    -0.6740059517812944,    0.5794684678643381,   -0.3239847771997537,   -0.3239847771997537,
    -0.7504883828755602,    0.5029860367700724,   -0.4004672082940195,    0.15296486218853164,
    -0.7504883828755602,    0.5029860367700724,    0.15296486218853164,  -0.4004672082940195,
    -0.8828161875373585,    0.4553054119602712,    0.08164729285680945,   0.08164729285680945,
    -0.4553054119602712,    0.8828161875373585,   -0.08164729285680945,  -0.08164729285680945,
    -0.5029860367700724,    0.7504883828755602,   -0.15296486218853164,   0.4004672082940195,
    -0.5029860367700724,    0.7504883828755602,    0.4004672082940195,   -0.15296486218853164,
    -0.5794684678643381,    0.6740059517812944,    0.3239847771997537,    0.3239847771997537,
     0.5794684678643381,   -0.6740059517812944,   -0.3239847771997537,   -0.3239847771997537,
     0.5029860367700724,   -0.7504883828755602,   -0.4004672082940195,    0.15296486218853164,
     0.5029860367700724,   -0.7504883828755602,    0.15296486218853164,  -0.4004672082940195,
     0.4553054119602712,   -0.8828161875373585,    0.08164729285680945,   0.08164729285680945,
     0.8828161875373585,   -0.4553054119602712,   -0.08164729285680945,  -0.08164729285680945,
     0.7504883828755602,   -0.5029860367700724,   -0.15296486218853164,   0.4004672082940195,
     0.7504883828755602,   -0.5029860367700724,    0.4004672082940195,   -0.15296486218853164,
     0.6740059517812944,   -0.5794684678643381,    0.3239847771997537,    0.3239847771997537,
    //------------------------------------------------------------------------------------------//
    -0.753341017856078,    -0.37968289875261624,  -0.37968289875261624,  -0.37968289875261624,
    -0.7821684431180708,   -0.4321472685365301,   -0.4321472685365301,    0.12128480194602098,
    -0.7821684431180708,   -0.4321472685365301,    0.12128480194602098,  -0.4321472685365301,
    -0.7821684431180708,    0.12128480194602098,  -0.4321472685365301,   -0.4321472685365301,
    -0.8586508742123365,   -0.508629699630796,     0.044802370851755174,  0.044802370851755174,
    -0.8586508742123365,    0.044802370851755174, -0.508629699630796,     0.044802370851755174,
    -0.8586508742123365,    0.044802370851755174,  0.044802370851755174, -0.508629699630796,
    -0.9982828964265062,   -0.03381941603233842,  -0.03381941603233842,  -0.03381941603233842,
    -0.37968289875261624,  -0.753341017856078,    -0.37968289875261624,  -0.37968289875261624,
    -0.4321472685365301,   -0.7821684431180708,   -0.4321472685365301,    0.12128480194602098,
    -0.4321472685365301,   -0.7821684431180708,    0.12128480194602098,  -0.4321472685365301,
     0.12128480194602098,  -0.7821684431180708,   -0.4321472685365301,   -0.4321472685365301,
    -0.508629699630796,    -0.8586508742123365,    0.044802370851755174,  0.044802370851755174,
     0.044802370851755174, -0.8586508742123365,   -0.508629699630796,     0.044802370851755174,
     0.044802370851755174, -0.8586508742123365,    0.044802370851755174, -0.508629699630796,
    -0.03381941603233842,  -0.9982828964265062,   -0.03381941603233842,  -0.03381941603233842,
    -0.37968289875261624,  -0.37968289875261624,  -0.753341017856078,    -0.37968289875261624,
    -0.4321472685365301,   -0.4321472685365301,   -0.7821684431180708,    0.12128480194602098,
    -0.4321472685365301,    0.12128480194602098,  -0.7821684431180708,   -0.4321472685365301,
     0.12128480194602098,  -0.4321472685365301,   -0.7821684431180708,   -0.4321472685365301,
    -0.508629699630796,     0.044802370851755174, -0.8586508742123365,    0.044802370851755174,
     0.044802370851755174, -0.508629699630796,    -0.8586508742123365,    0.044802370851755174,
     0.044802370851755174,  0.044802370851755174, -0.8586508742123365,   -0.508629699630796,
    -0.03381941603233842,  -0.03381941603233842,  -0.9982828964265062,   -0.03381941603233842,
    -0.37968289875261624,  -0.37968289875261624,  -0.37968289875261624,  -0.753341017856078,
    -0.4321472685365301,   -0.4321472685365301,    0.12128480194602098,  -0.7821684431180708,
    -0.4321472685365301,    0.12128480194602098,  -0.4321472685365301,   -0.7821684431180708,
     0.12128480194602098,  -0.4321472685365301,   -0.4321472685365301,   -0.7821684431180708,
    -0.508629699630796,     0.044802370851755174,  0.044802370851755174, -0.8586508742123365,
     0.044802370851755174, -0.508629699630796,     0.044802370851755174, -0.8586508742123365,
     0.044802370851755174,  0.044802370851755174, -0.508629699630796,    -0.8586508742123365,
    -0.03381941603233842,  -0.03381941603233842,  -0.03381941603233842,  -0.9982828964265062,
    -0.3239847771997537,   -0.6740059517812944,   -0.3239847771997537,    0.5794684678643381,
    -0.4004672082940195,   -0.7504883828755602,    0.15296486218853164,   0.5029860367700724,
     0.15296486218853164,  -0.7504883828755602,   -0.4004672082940195,    0.5029860367700724,
     0.08164729285680945,  -0.8828161875373585,    0.08164729285680945,   0.4553054119602712,
    -0.08164729285680945,  -0.4553054119602712,   -0.08164729285680945,   0.8828161875373585,
    -0.15296486218853164,  -0.5029860367700724,    0.4004672082940195,    0.7504883828755602,
     0.4004672082940195,   -0.5029860367700724,   -0.15296486218853164,   0.7504883828755602,
     0.3239847771997537,   -0.5794684678643381,    0.3239847771997537,    0.6740059517812944,
    -0.3239847771997537,   -0.3239847771997537,   -0.6740059517812944,    0.5794684678643381,
    -0.4004672082940195,    0.15296486218853164,  -0.7504883828755602,    0.5029860367700724,
     0.15296486218853164,  -0.4004672082940195,   -0.7504883828755602,    0.5029860367700724,
     0.08164729285680945,   0.08164729285680945,  -0.8828161875373585,    0.4553054119602712,
    -0.08164729285680945,  -0.08164729285680945,  -0.4553054119602712,    0.8828161875373585,
    -0.15296486218853164,   0.4004672082940195,   -0.5029860367700724,    0.7504883828755602,
     0.4004672082940195,   -0.15296486218853164,  -0.5029860367700724,    0.7504883828755602,
     0.3239847771997537,    0.3239847771997537,   -0.5794684678643381,    0.6740059517812944,
    -0.3239847771997537,   -0.6740059517812944,    0.5794684678643381,   -0.3239847771997537,
    -0.4004672082940195,   -0.7504883828755602,    0.5029860367700724,    0.15296486218853164,
     0.15296486218853164,  -0.7504883828755602,    0.5029860367700724,   -0.4004672082940195,
     0.08164729285680945,  -0.8828161875373585,    0.4553054119602712,    0.08164729285680945,
    -0.08164729285680945,  -0.4553054119602712,    0.8828161875373585,   -0.08164729285680945,
    -0.15296486218853164,  -0.5029860367700724,    0.7504883828755602,    0.4004672082940195,
     0.4004672082940195,   -0.5029860367700724,    0.7504883828755602,   -0.15296486218853164,
     0.3239847771997537,   -0.5794684678643381,    0.6740059517812944,    0.3239847771997537,
    -0.3239847771997537,   -0.3239847771997537,    0.5794684678643381,   -0.6740059517812944,
    -0.4004672082940195,    0.15296486218853164,   0.5029860367700724,   -0.7504883828755602,
     0.15296486218853164,  -0.4004672082940195,    0.5029860367700724,   -0.7504883828755602,
     0.08164729285680945,   0.08164729285680945,   0.4553054119602712,   -0.8828161875373585,
    -0.08164729285680945,  -0.08164729285680945,   0.8828161875373585,   -0.4553054119602712,
    -0.15296486218853164,   0.4004672082940195,    0.7504883828755602,   -0.5029860367700724,
     0.4004672082940195,   -0.15296486218853164,   0.7504883828755602,   -0.5029860367700724,
     0.3239847771997537,    0.3239847771997537,    0.6740059517812944,   -0.5794684678643381,
    -0.3239847771997537,    0.5794684678643381,   -0.6740059517812944,   -0.3239847771997537,
    -0.4004672082940195,    0.5029860367700724,   -0.7504883828755602,    0.15296486218853164,
     0.15296486218853164,   0.5029860367700724,   -0.7504883828755602,   -0.4004672082940195,
     0.08164729285680945,   0.4553054119602712,   -0.8828161875373585,    0.08164729285680945,
    -0.08164729285680945,   0.8828161875373585,   -0.4553054119602712,   -0.08164729285680945,
    -0.15296486218853164,   0.7504883828755602,   -0.5029860367700724,    0.4004672082940195,
     0.4004672082940195,    0.7504883828755602,   -0.5029860367700724,   -0.15296486218853164,
     0.3239847771997537,    0.6740059517812944,   -0.5794684678643381,    0.3239847771997537,
    -0.3239847771997537,    0.5794684678643381,   -0.3239847771997537,   -0.6740059517812944,
    -0.4004672082940195,    0.5029860367700724,    0.15296486218853164,  -0.7504883828755602,
     0.15296486218853164,   0.5029860367700724,   -0.4004672082940195,   -0.7504883828755602,
     0.08164729285680945,   0.4553054119602712,    0.08164729285680945,  -0.8828161875373585,
    -0.08164729285680945,   0.8828161875373585,   -0.08164729285680945,  -0.4553054119602712,
    -0.15296486218853164,   0.7504883828755602,    0.4004672082940195,   -0.5029860367700724,
     0.4004672082940195,    0.7504883828755602,   -0.15296486218853164,  -0.5029860367700724,
     0.3239847771997537,    0.6740059517812944,    0.3239847771997537,   -0.5794684678643381,
     0.5794684678643381,   -0.3239847771997537,   -0.6740059517812944,   -0.3239847771997537,
     0.5029860367700724,   -0.4004672082940195,   -0.7504883828755602,    0.15296486218853164,
     0.5029860367700724,    0.15296486218853164,  -0.7504883828755602,   -0.4004672082940195,
     0.4553054119602712,    0.08164729285680945,  -0.8828161875373585,    0.08164729285680945,
     0.8828161875373585,   -0.08164729285680945,  -0.4553054119602712,   -0.08164729285680945,
     0.7504883828755602,   -0.15296486218853164,  -0.5029860367700724,    0.4004672082940195,
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