/* 4D simplex noise */
GLfloat _slang_library_noise4 (GLfloat x, GLfloat y, GLfloat z, GLfloat w)
{
/* The skewing and unskewing factors are hairy again for the 4D case */
#define F4 0.309016994f /* F4 = (Math.sqrt(5.0)-1.0)/4.0 */
#define G4 0.138196601f /* G4 = (5.0-Math.sqrt(5.0))/20.0 */
float n0, n1, n2, n3, n4; /* Noise contributions from the five corners */
/* Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in */
float s = (x + y + z + w) * F4; /* Factor for 4D skewing */
float xs = x + s;
float ys = y + s;
float zs = z + s;
float ws = w + s;
int i = FASTFLOOR(xs);
int j = FASTFLOOR(ys);
int k = FASTFLOOR(zs);
int l = FASTFLOOR(ws);
float t = (i + j + k + l) * G4; /* Factor for 4D unskewing */
float X0 = i - t; /* Unskew the cell origin back to (x,y,z,w) space */
float Y0 = j - t;
float Z0 = k - t;
float W0 = l - t;
float x0 = x - X0; /* The x,y,z,w distances from the cell origin */
float y0 = y - Y0;
float z0 = z - Z0;
float w0 = w - W0;
/* For the 4D case, the simplex is a 4D shape I won't even try to describe. */
/* To find out which of the 24 possible simplices we're in, we need to */
/* determine the magnitude ordering of x0, y0, z0 and w0. */
/* The method below is a good way of finding the ordering of x,y,z,w and */
/* then find the correct traversal order for the simplex we're in. */
/* First, six pair-wise comparisons are performed between each possible pair */
/* of the four coordinates, and the results are used to add up binary bits */
/* for an integer index. */
int c1 = (x0 > y0) ? 32 : 0;
int c2 = (x0 > z0) ? 16 : 0;
int c3 = (y0 > z0) ? 8 : 0;
int c4 = (x0 > w0) ? 4 : 0;
int c5 = (y0 > w0) ? 2 : 0;
int c6 = (z0 > w0) ? 1 : 0;
int c = c1 + c2 + c3 + c4 + c5 + c6;
int i1, j1, k1, l1; /* The integer offsets for the second simplex corner */
int i2, j2, k2, l2; /* The integer offsets for the third simplex corner */
int i3, j3, k3, l3; /* The integer offsets for the fourth simplex corner */
float x1, y1, z1, w1, x2, y2, z2, w2, x3, y3, z3, w3, x4, y4, z4, w4;
int ii, jj, kk, ll;
float t0, t1, t2, t3, t4;
/* simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order. */
/* Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w */
/* impossible. Only the 24 indices which have non-zero entries make any sense. */
/* We use a thresholding to set the coordinates in turn from the largest magnitude. */
/* The number 3 in the "simplex" array is at the position of the largest coordinate. */
i1 = simplex[c][0]>=3 ? 1 : 0;
j1 = simplex[c][1]>=3 ? 1 : 0;
k1 = simplex[c][2]>=3 ? 1 : 0;
l1 = simplex[c][3]>=3 ? 1 : 0;
/* The number 2 in the "simplex" array is at the second largest coordinate. */
i2 = simplex[c][0]>=2 ? 1 : 0;
j2 = simplex[c][1]>=2 ? 1 : 0;
k2 = simplex[c][2]>=2 ? 1 : 0;
l2 = simplex[c][3]>=2 ? 1 : 0;
/* The number 1 in the "simplex" array is at the second smallest coordinate. */
i3 = simplex[c][0]>=1 ? 1 : 0;
j3 = simplex[c][1]>=1 ? 1 : 0;
k3 = simplex[c][2]>=1 ? 1 : 0;
l3 = simplex[c][3]>=1 ? 1 : 0;
/* The fifth corner has all coordinate offsets = 1, so no need to look that up. */
x1 = x0 - i1 + G4; /* Offsets for second corner in (x,y,z,w) coords */
y1 = y0 - j1 + G4;
z1 = z0 - k1 + G4;
w1 = w0 - l1 + G4;
x2 = x0 - i2 + 2.0f*G4; /* Offsets for third corner in (x,y,z,w) coords */
y2 = y0 - j2 + 2.0f*G4;
z2 = z0 - k2 + 2.0f*G4;
w2 = w0 - l2 + 2.0f*G4;
x3 = x0 - i3 + 3.0f*G4; /* Offsets for fourth corner in (x,y,z,w) coords */
y3 = y0 - j3 + 3.0f*G4;
z3 = z0 - k3 + 3.0f*G4;
w3 = w0 - l3 + 3.0f*G4;
x4 = x0 - 1.0f + 4.0f*G4; /* Offsets for last corner in (x,y,z,w) coords */
y4 = y0 - 1.0f + 4.0f*G4;
z4 = z0 - 1.0f + 4.0f*G4;
w4 = w0 - 1.0f + 4.0f*G4;
/* Wrap the integer indices at 256, to avoid indexing perm[] out of bounds */
ii = i % 256;
jj = j % 256;
kk = k % 256;
ll = l % 256;
/* Calculate the contribution from the five corners */
t0 = 0.6f - x0*x0 - y0*y0 - z0*z0 - w0*w0;
if(t0 < 0.0f) n0 = 0.0f;
else {
t0 *= t0;
n0 = t0 * t0 * grad4(perm[ii+perm[jj+perm[kk+perm[ll]]]], x0, y0, z0, w0);
}
t1 = 0.6f - x1*x1 - y1*y1 - z1*z1 - w1*w1;
if(t1 < 0.0f) n1 = 0.0f;
else {
t1 *= t1;
n1 = t1 * t1 * grad4(perm[ii+i1+perm[jj+j1+perm[kk+k1+perm[ll+l1]]]], x1, y1, z1, w1);
}
t2 = 0.6f - x2*x2 - y2*y2 - z2*z2 - w2*w2;
if(t2 < 0.0f) n2 = 0.0f;
else {
t2 *= t2;
n2 = t2 * t2 * grad4(perm[ii+i2+perm[jj+j2+perm[kk+k2+perm[ll+l2]]]], x2, y2, z2, w2);
}
t3 = 0.6f - x3*x3 - y3*y3 - z3*z3 - w3*w3;
if(t3 < 0.0f) n3 = 0.0f;
else {
t3 *= t3;
n3 = t3 * t3 * grad4(perm[ii+i3+perm[jj+j3+perm[kk+k3+perm[ll+l3]]]], x3, y3, z3, w3);
}
t4 = 0.6f - x4*x4 - y4*y4 - z4*z4 - w4*w4;
if(t4 < 0.0f) n4 = 0.0f;
else {
t4 *= t4;
n4 = t4 * t4 * grad4(perm[ii+1+perm[jj+1+perm[kk+1+perm[ll+1]]]], x4, y4, z4, w4);
}
/* Sum up and scale the result to cover the range [-1,1] */
return 27.0f * (n0 + n1 + n2 + n3 + n4); /* TODO: The scale factor is preliminary! */
}
float snoise(vec4 v)
{
const vec4 C = vec4( 0.138196601125011, // (5 - sqrt(5))/20 G4
0.276393202250021, // 2 * G4
0.414589803375032, // 3 * G4
-0.447213595499958); // -1 + 4 * G4
// First corner
vec4 i = floor(v + dot(v, vec4(F4)) );
vec4 x0 = v - i + dot(i, C.xxxx);
// Other corners
// Rank sorting originally contributed by Bill Licea-Kane, AMD (formerly ATI)
vec4 i0;
vec3 isX = step( x0.yzw, x0.xxx );
vec3 isYZ = step( x0.zww, x0.yyz );
// i0.x = dot( isX, vec3( 1.0 ) );
i0.x = isX.x + isX.y + isX.z;
i0.yzw = 1.0 - isX;
// i0.y += dot( isYZ.xy, vec2( 1.0 ) );
i0.y += isYZ.x + isYZ.y;
i0.zw += 1.0 - isYZ.xy;
i0.z += isYZ.z;
i0.w += 1.0 - isYZ.z;
// i0 now contains the unique values 0,1,2,3 in each channel
vec4 i3 = clamp( i0, 0.0, 1.0 );
vec4 i2 = clamp( i0-1.0, 0.0, 1.0 );
vec4 i1 = clamp( i0-2.0, 0.0, 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
vec4 x1 = x0 - i1 + C.xxxx;
vec4 x2 = x0 - i2 + C.yyyy;
vec4 x3 = x0 - i3 + C.zzzz;
vec4 x4 = x0 + C.wwww;
// Permutations
i = mod289(i);
float j0 = permute( permute( permute( permute(i.w) + i.z) + i.y) + i.x);
vec4 j1 = permute( permute( permute( permute (
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.
vec4 ip = vec4(1.0/294.0, 1.0/49.0, 1.0/7.0, 0.0) ;
vec4 p0 = grad4(j0, ip);
vec4 p1 = grad4(j1.x, ip);
vec4 p2 = grad4(j1.y, ip);
vec4 p3 = grad4(j1.z, ip);
vec4 p4 = grad4(j1.w, ip);
// Normalise gradients
vec4 norm = taylorInvSqrt(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 *= taylorInvSqrt(dot(p4,p4));
// Mix contributions from the five corners
vec3 m0 = max(0.6 - vec3(dot(x0,x0), dot(x1,x1), dot(x2,x2)), 0.0);
vec2 m1 = max(0.6 - vec2(dot(x3,x3), dot(x4,x4) ), 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 ) ) ) ) ;
}
float pnoise4( float x, float y, float z, float w,
int px, int py, int pz, int pw )
{
int ix0, iy0, iz0, iw0, ix1, iy1, iz1, iw1;
float fx0, fy0, fz0, fw0, fx1, fy1, fz1, fw1;
float s, t, r, q;
float nxyz0, nxyz1, nxy0, nxy1, nx0, nx1, n0, n1;
ix0 = FASTFLOOR( x ); // Integer part of x
iy0 = FASTFLOOR( y ); // Integer part of y
iz0 = FASTFLOOR( z ); // Integer part of y
iw0 = FASTFLOOR( w ); // Integer part of w
fx0 = x - ix0; // Fractional part of x
fy0 = y - iy0; // Fractional part of y
fz0 = z - iz0; // Fractional part of z
fw0 = w - iw0; // Fractional part of w
fx1 = fx0 - 1.0f;
fy1 = fy0 - 1.0f;
fz1 = fz0 - 1.0f;
fw1 = fw0 - 1.0f;
ix1 = (( ix0 + 1 ) % px ) & 0xff; // Wrap to 0..px-1 and wrap to 0..255
iy1 = (( iy0 + 1 ) % py ) & 0xff; // Wrap to 0..py-1 and wrap to 0..255
iz1 = (( iz0 + 1 ) % pz ) & 0xff; // Wrap to 0..pz-1 and wrap to 0..255
iw1 = (( iw0 + 1 ) % pw ) & 0xff; // Wrap to 0..pw-1 and wrap to 0..255
ix0 = ( ix0 % px ) & 0xff;
iy0 = ( iy0 % py ) & 0xff;
iz0 = ( iz0 % pz ) & 0xff;
iw0 = ( iw0 % pw ) & 0xff;
q = FADE( fw0 );
r = FADE( fz0 );
t = FADE( fy0 );
s = FADE( fx0 );
nxyz0 = grad4(perm[ix0 + perm[iy0 + perm[iz0 + perm[iw0]]]], fx0, fy0, fz0, fw0);
nxyz1 = grad4(perm[ix0 + perm[iy0 + perm[iz0 + perm[iw1]]]], fx0, fy0, fz0, fw1);
nxy0 = LERP( q, nxyz0, nxyz1 );
nxyz0 = grad4(perm[ix0 + perm[iy0 + perm[iz1 + perm[iw0]]]], fx0, fy0, fz1, fw0);
nxyz1 = grad4(perm[ix0 + perm[iy0 + perm[iz1 + perm[iw1]]]], fx0, fy0, fz1, fw1);
nxy1 = LERP( q, nxyz0, nxyz1 );
nx0 = LERP ( r, nxy0, nxy1 );
nxyz0 = grad4(perm[ix0 + perm[iy1 + perm[iz0 + perm[iw0]]]], fx0, fy1, fz0, fw0);
nxyz1 = grad4(perm[ix0 + perm[iy1 + perm[iz0 + perm[iw1]]]], fx0, fy1, fz0, fw1);
nxy0 = LERP( q, nxyz0, nxyz1 );
nxyz0 = grad4(perm[ix0 + perm[iy1 + perm[iz1 + perm[iw0]]]], fx0, fy1, fz1, fw0);
nxyz1 = grad4(perm[ix0 + perm[iy1 + perm[iz1 + perm[iw1]]]], fx0, fy1, fz1, fw1);
nxy1 = LERP( q, nxyz0, nxyz1 );
nx1 = LERP ( r, nxy0, nxy1 );
n0 = LERP( t, nx0, nx1 );
nxyz0 = grad4(perm[ix1 + perm[iy0 + perm[iz0 + perm[iw0]]]], fx1, fy0, fz0, fw0);
nxyz1 = grad4(perm[ix1 + perm[iy0 + perm[iz0 + perm[iw1]]]], fx1, fy0, fz0, fw1);
nxy0 = LERP( q, nxyz0, nxyz1 );
nxyz0 = grad4(perm[ix1 + perm[iy0 + perm[iz1 + perm[iw0]]]], fx1, fy0, fz1, fw0);
nxyz1 = grad4(perm[ix1 + perm[iy0 + perm[iz1 + perm[iw1]]]], fx1, fy0, fz1, fw1);
nxy1 = LERP( q, nxyz0, nxyz1 );
nx0 = LERP ( r, nxy0, nxy1 );
nxyz0 = grad4(perm[ix1 + perm[iy1 + perm[iz0 + perm[iw0]]]], fx1, fy1, fz0, fw0);
nxyz1 = grad4(perm[ix1 + perm[iy1 + perm[iz0 + perm[iw1]]]], fx1, fy1, fz0, fw1);
nxy0 = LERP( q, nxyz0, nxyz1 );
nxyz0 = grad4(perm[ix1 + perm[iy1 + perm[iz1 + perm[iw0]]]], fx1, fy1, fz1, fw0);
nxyz1 = grad4(perm[ix1 + perm[iy1 + perm[iz1 + perm[iw1]]]], fx1, fy1, fz1, fw1);
nxy1 = LERP( q, nxyz0, nxyz1 );
nx1 = LERP ( r, nxy0, nxy1 );
n1 = LERP( t, nx0, nx1 );
return 0.87f * ( LERP( s, n0, n1 ) );
}
/** 4D simplex noise with derivatives.
* If the last four arguments are not null, the analytic derivative
* (the 4D gradient of the scalar noise field) is also calculated.
*/
float sdnoise4( float x, float y, float z, float w,
float *dnoise_dx, float *dnoise_dy,
float *dnoise_dz, float *dnoise_dw)
{
float n0, n1, n2, n3, n4; // Noise contributions from the five corners
float noise; // Return value
float gx0, gy0, gz0, gw0, gx1, gy1, gz1, gw1; /* Gradients at simplex corners */
float gx2, gy2, gz2, gw2, gx3, gy3, gz3, gw3, gx4, gy4, gz4, gw4;
float t20, t21, t22, t23, t24;
float t40, t41, t42, t43, t44;
// Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in
float s = (x + y + z + w) * F4; // Factor for 4D skewing
float xs = x + s;
float ys = y + s;
float zs = z + s;
float ws = w + s;
int i = FASTFLOOR(xs);
int j = FASTFLOOR(ys);
int k = FASTFLOOR(zs);
int l = FASTFLOOR(ws);
float t = (i + j + k + l) * G4; // Factor for 4D unskewing
float X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
float Y0 = j - t;
float Z0 = k - t;
float W0 = l - t;
float x0 = x - X0; // The x,y,z,w distances from the cell origin
float y0 = y - Y0;
float z0 = z - Z0;
float w0 = w - W0;
// For the 4D case, the simplex is a 4D shape I won't even try to describe.
// To find out which of the 24 possible simplices we're in, we need to
// determine the magnitude ordering of x0, y0, z0 and w0.
// The method below is a reasonable way of finding the ordering of x,y,z,w
// and then find the correct traversal order for the simplex we’re in.
// First, six pair-wise comparisons are performed between each possible pair
// of the four coordinates, and then the results are used to add up binary
// bits for an integer index into a precomputed lookup table, simplex[].
int c1 = (x0 > y0) ? 32 : 0;
int c2 = (x0 > z0) ? 16 : 0;
int c3 = (y0 > z0) ? 8 : 0;
int c4 = (x0 > w0) ? 4 : 0;
int c5 = (y0 > w0) ? 2 : 0;
int c6 = (z0 > w0) ? 1 : 0;
int c = c1 | c2 | c3 | c4 | c5 | c6; // '|' is mostly faster than '+'
int i1, j1, k1, l1; // The integer offsets for the second simplex corner
int i2, j2, k2, l2; // The integer offsets for the third simplex corner
int i3, j3, k3, l3; // The integer offsets for the fourth simplex corner
// simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order.
// Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w
// impossible. Only the 24 indices which have non-zero entries make any sense.
// We use a thresholding to set the coordinates in turn from the largest magnitude.
// The number 3 in the "simplex" array is at the position of the largest coordinate.
i1 = simplex[c][0]>=3 ? 1 : 0;
j1 = simplex[c][1]>=3 ? 1 : 0;
k1 = simplex[c][2]>=3 ? 1 : 0;
l1 = simplex[c][3]>=3 ? 1 : 0;
// The number 2 in the "simplex" array is at the second largest coordinate.
i2 = simplex[c][0]>=2 ? 1 : 0;
j2 = simplex[c][1]>=2 ? 1 : 0;
k2 = simplex[c][2]>=2 ? 1 : 0;
l2 = simplex[c][3]>=2 ? 1 : 0;
// The number 1 in the "simplex" array is at the second smallest coordinate.
i3 = simplex[c][0]>=1 ? 1 : 0;
j3 = simplex[c][1]>=1 ? 1 : 0;
k3 = simplex[c][2]>=1 ? 1 : 0;
l3 = simplex[c][3]>=1 ? 1 : 0;
// The fifth corner has all coordinate offsets = 1, so no need to look that up.
float x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
float y1 = y0 - j1 + G4;
float z1 = z0 - k1 + G4;
float w1 = w0 - l1 + G4;
float x2 = x0 - i2 + 2.0f * G4; // Offsets for third corner in (x,y,z,w) coords
float y2 = y0 - j2 + 2.0f * G4;
float z2 = z0 - k2 + 2.0f * G4;
float w2 = w0 - l2 + 2.0f * G4;
float x3 = x0 - i3 + 3.0f * G4; // Offsets for fourth corner in (x,y,z,w) coords
float y3 = y0 - j3 + 3.0f * G4;
float z3 = z0 - k3 + 3.0f * G4;
float w3 = w0 - l3 + 3.0f * G4;
float x4 = x0 - 1.0f + 4.0f * G4; // Offsets for last corner in (x,y,z,w) coords
float y4 = y0 - 1.0f + 4.0f * G4;
float z4 = z0 - 1.0f + 4.0f * G4;
float w4 = w0 - 1.0f + 4.0f * G4;
// Wrap the integer indices at 256, to avoid indexing perm[] out of bounds
int ii = i & 0xff;
int jj = j & 0xff;
int kk = k & 0xff;
int ll = l & 0xff;
// Calculate the contribution from the five corners
float t0 = 0.6f - x0*x0 - y0*y0 - z0*z0 - w0*w0;
if(t0 < 0.0f) n0 = t0 = t20 = t40 = gx0 = gy0 = gz0 = gw0 = 0.0f;
else {
t20 = t0 * t0;
t40 = t20 * t20;
grad4(perm[ii+perm[jj+perm[kk+perm[ll]]]], &gx0, &gy0, &gz0, &gw0);
n0 = t40 * ( gx0 * x0 + gy0 * y0 + gz0 * z0 + gw0 * w0 );
}
float t1 = 0.6f - x1*x1 - y1*y1 - z1*z1 - w1*w1;
if(t1 < 0.0f) n1 = t1 = t21 = t41 = gx1 = gy1 = gz1 = gw1 = 0.0f;
else {
t21 = t1 * t1;
t41 = t21 * t21;
grad4(perm[ii+i1+perm[jj+j1+perm[kk+k1+perm[ll+l1]]]], &gx1, &gy1, &gz1, &gw1);
n1 = t41 * ( gx1 * x1 + gy1 * y1 + gz1 * z1 + gw1 * w1 );
}
float t2 = 0.6f - x2*x2 - y2*y2 - z2*z2 - w2*w2;
if(t2 < 0.0f) n2 = t2 = t22 = t42 = gx2 = gy2 = gz2 = gw2 = 0.0f;
else {
t22 = t2 * t2;
t42 = t22 * t22;
grad4(perm[ii+i2+perm[jj+j2+perm[kk+k2+perm[ll+l2]]]], &gx2, &gy2, &gz2, &gw2);
n2 = t42 * ( gx2 * x2 + gy2 * y2 + gz2 * z2 + gw2 * w2 );
}
float t3 = 0.6f - x3*x3 - y3*y3 - z3*z3 - w3*w3;
if(t3 < 0.0f) n3 = t3 = t23 = t43 = gx3 = gy3 = gz3 = gw3 = 0.0f;
else {
t23 = t3 * t3;
t43 = t23 * t23;
grad4(perm[ii+i3+perm[jj+j3+perm[kk+k3+perm[ll+l3]]]], &gx3, &gy3, &gz3, &gw3);
n3 = t43 * ( gx3 * x3 + gy3 * y3 + gz3 * z3 + gw3 * w3 );
}
float t4 = 0.6f - x4*x4 - y4*y4 - z4*z4 - w4*w4;
if(t4 < 0.0f) n4 = t4 = t24 = t44 = gx4 = gy4 = gz4 = gw4 = 0.0f;
else {
t24 = t4 * t4;
t44 = t24 * t24;
grad4(perm[ii+1+perm[jj+1+perm[kk+1+perm[ll+1]]]], &gx4, &gy4, &gz4, &gw4);
n4 = t44 * ( gx4 * x4 + gy4 * y4 + gz4 * z4 + gw4 * w4 );
}
// Sum up and scale the result to cover the range [-1,1]
noise = 27.0f * (n0 + n1 + n2 + n3 + n4); // TODO: The scale factor is preliminary!
/* Compute derivative, if requested by supplying non-null pointers
* for the last four arguments */
if( ( dnoise_dx != 0 ) && ( dnoise_dy != 0 ) && ( dnoise_dz != 0 ) && ( dnoise_dw != 0 ) )
{
/* A straight, unoptimised calculation would be like:
* *dnoise_dx = -8.0f * t20 * t0 * x0 * dot(gx0, gy0, gz0, gw0, x0, y0, z0, w0) + t40 * gx0;
* *dnoise_dy = -8.0f * t20 * t0 * y0 * dot(gx0, gy0, gz0, gw0, x0, y0, z0, w0) + t40 * gy0;
* *dnoise_dz = -8.0f * t20 * t0 * z0 * dot(gx0, gy0, gz0, gw0, x0, y0, z0, w0) + t40 * gz0;
* *dnoise_dw = -8.0f * t20 * t0 * w0 * dot(gx0, gy0, gz0, gw0, x0, y0, z0, w0) + t40 * gw0;
* *dnoise_dx += -8.0f * t21 * t1 * x1 * dot(gx1, gy1, gz1, gw1, x1, y1, z1, w1) + t41 * gx1;
* *dnoise_dy += -8.0f * t21 * t1 * y1 * dot(gx1, gy1, gz1, gw1, x1, y1, z1, w1) + t41 * gy1;
* *dnoise_dz += -8.0f * t21 * t1 * z1 * dot(gx1, gy1, gz1, gw1, x1, y1, z1, w1) + t41 * gz1;
* *dnoise_dw = -8.0f * t21 * t1 * w1 * dot(gx1, gy1, gz1, gw1, x1, y1, z1, w1) + t41 * gw1;
* *dnoise_dx += -8.0f * t22 * t2 * x2 * dot(gx2, gy2, gz2, gw2, x2, y2, z2, w2) + t42 * gx2;
* *dnoise_dy += -8.0f * t22 * t2 * y2 * dot(gx2, gy2, gz2, gw2, x2, y2, z2, w2) + t42 * gy2;
* *dnoise_dz += -8.0f * t22 * t2 * z2 * dot(gx2, gy2, gz2, gw2, x2, y2, z2, w2) + t42 * gz2;
* *dnoise_dw += -8.0f * t22 * t2 * w2 * dot(gx2, gy2, gz2, gw2, x2, y2, z2, w2) + t42 * gw2;
* *dnoise_dx += -8.0f * t23 * t3 * x3 * dot(gx3, gy3, gz3, gw3, x3, y3, z3, w3) + t43 * gx3;
* *dnoise_dy += -8.0f * t23 * t3 * y3 * dot(gx3, gy3, gz3, gw3, x3, y3, z3, w3) + t43 * gy3;
* *dnoise_dz += -8.0f * t23 * t3 * z3 * dot(gx3, gy3, gz3, gw3, x3, y3, z3, w3) + t43 * gz3;
* *dnoise_dw += -8.0f * t23 * t3 * w3 * dot(gx3, gy3, gz3, gw3, x3, y3, z3, w3) + t43 * gw3;
* *dnoise_dx += -8.0f * t24 * t4 * x4 * dot(gx4, gy4, gz4, gw4, x4, y4, z4, w4) + t44 * gx4;
* *dnoise_dy += -8.0f * t24 * t4 * y4 * dot(gx4, gy4, gz4, gw4, x4, y4, z4, w4) + t44 * gy4;
* *dnoise_dz += -8.0f * t24 * t4 * z4 * dot(gx4, gy4, gz4, gw4, x4, y4, z4, w4) + t44 * gz4;
* *dnoise_dw += -8.0f * t24 * t4 * w4 * dot(gx4, gy4, gz4, gw4, x4, y4, z4, w4) + t44 * gw4;
*/
float temp0 = t20 * t0 * ( gx0 * x0 + gy0 * y0 + gz0 * z0 + gw0 * w0 );
*dnoise_dx = temp0 * x0;
*dnoise_dy = temp0 * y0;
*dnoise_dz = temp0 * z0;
*dnoise_dw = temp0 * w0;
float temp1 = t21 * t1 * ( gx1 * x1 + gy1 * y1 + gz1 * z1 + gw1 * w1 );
*dnoise_dx += temp1 * x1;
*dnoise_dy += temp1 * y1;
*dnoise_dz += temp1 * z1;
*dnoise_dw += temp1 * w1;
float temp2 = t22 * t2 * ( gx2 * x2 + gy2 * y2 + gz2 * z2 + gw2 * w2 );
*dnoise_dx += temp2 * x2;
*dnoise_dy += temp2 * y2;
*dnoise_dz += temp2 * z2;
*dnoise_dw += temp2 * w2;
float temp3 = t23 * t3 * ( gx3 * x3 + gy3 * y3 + gz3 * z3 + gw3 * w3 );
*dnoise_dx += temp3 * x3;
*dnoise_dy += temp3 * y3;
*dnoise_dz += temp3 * z3;
*dnoise_dw += temp3 * w3;
float temp4 = t24 * t4 * ( gx4 * x4 + gy4 * y4 + gz4 * z4 + gw4 * w4 );
*dnoise_dx += temp4 * x4;
*dnoise_dy += temp4 * y4;
*dnoise_dz += temp4 * z4;
*dnoise_dw += temp4 * w4;
*dnoise_dx *= -8.0f;
*dnoise_dy *= -8.0f;
*dnoise_dz *= -8.0f;
*dnoise_dw *= -8.0f;
*dnoise_dx += t40 * gx0 + t41 * gx1 + t42 * gx2 + t43 * gx3 + t44 * gx4;
*dnoise_dy += t40 * gy0 + t41 * gy1 + t42 * gy2 + t43 * gy3 + t44 * gy4;
*dnoise_dz += t40 * gz0 + t41 * gz1 + t42 * gz2 + t43 * gz3 + t44 * gz4;
*dnoise_dw += t40 * gw0 + t41 * gw1 + t42 * gw2 + t43 * gw3 + t44 * gw4;
*dnoise_dx *= 28.0f; /* Scale derivative to match the noise scaling */
*dnoise_dy *= 28.0f;
*dnoise_dz *= 28.0f;
*dnoise_dw *= 28.0f;
}
return noise;
}