public static uint hash(double4x4 v)
{
return(csum(fold_to_uint(v.c0) * uint4(0x4DDC6509u, 0x7CF083CBu, 0x5C4D6CEDu, 0xF9137117u) +
fold_to_uint(v.c1) * uint4(0xE857DCE1u, 0xF62213C5u, 0x9CDAA959u, 0xAA269ABFu) +
fold_to_uint(v.c2) * uint4(0xD54BA36Fu, 0xFD0847B9u, 0x8189A683u, 0xB139D651u) +
fold_to_uint(v.c3) * uint4(0xE7579997u, 0xEF7D56C7u, 0x66F38F0Bu, 0x624256A3u)) + 0x5292ADE1u);
}
public static uint4 hashwide(double4x4 v)
{
return((fold_to_uint(v.c0) * uint4(0xD2E590E5u, 0xF25BE857u, 0x9BC17CE7u, 0xC8B86851u) +
fold_to_uint(v.c1) * uint4(0x64095221u, 0xADF428FFu, 0xA3977109u, 0x745ED837u) +
fold_to_uint(v.c2) * uint4(0x9CDC88F5u, 0xFA62D721u, 0x7E4DB1CFu, 0x68EEE0F5u) +
fold_to_uint(v.c3) * uint4(0xBC3B0A59u, 0x816EFB5Du, 0xA24E82B7u, 0x45A22087u)) + 0xFC104C3Bu);
}
public uint4x4(double4x4 v)
{
this.c0 = (uint4)v.c0;
this.c1 = (uint4)v.c1;
this.c2 = (uint4)v.c2;
this.c3 = (uint4)v.c3;
}
public float4x4(double4x4 v)
{
this.c0 = (float4)v.c0;
this.c1 = (float4)v.c1;
this.c2 = (float4)v.c2;
this.c3 = (float4)v.c3;
}
public static double4x4 transpose(double4x4 v)
{
return(double4x4(
v.c0.x, v.c0.y, v.c0.z, v.c0.w,
v.c1.x, v.c1.y, v.c1.z, v.c1.w,
v.c2.x, v.c2.y, v.c2.z, v.c2.w,
v.c3.x, v.c3.y, v.c3.z, v.c3.w));
}
/// <summary>\n\t\t/// Returns the determinant of a double4x4 matrix.\n\t\t/// </summary>
public static double determinant(double4x4 m)
{
double4 c0 = m.c0;
double4 c1 = m.c1;
double4 c2 = m.c2;
double4 c3 = m.c3;
double m00 = c1.y * (c2.z * c3.w - c2.w * c3.z) - c2.y * (c1.z * c3.w - c1.w * c3.z) + c3.y * (c1.z * c2.w - c1.w * c2.z);
double m01 = c0.y * (c2.z * c3.w - c2.w * c3.z) - c2.y * (c0.z * c3.w - c0.w * c3.z) + c3.y * (c0.z * c2.w - c0.w * c2.z);
double m02 = c0.y * (c1.z * c3.w - c1.w * c3.z) - c1.y * (c0.z * c3.w - c0.w * c3.z) + c3.y * (c0.z * c1.w - c0.w * c1.z);
double m03 = c0.y * (c1.z * c2.w - c1.w * c2.z) - c1.y * (c0.z * c2.w - c0.w * c2.z) + c2.y * (c0.z * c1.w - c0.w * c1.z);
return(c0.x * m00 - c1.x * m01 + c2.x * m02 - c3.x * m03);
}
// Fast matrix inverse for rigid transforms (Orthonormal basis and translation)
public static double4x4 fastinverse(double4x4 m)
{
double4 c0 = m.c0;
double4 c1 = m.c1;
double4 c2 = m.c2;
double4 pos = m.c3;
double4 zero = double4(0);
double4 t0 = unpacklo(c0, c2);
double4 t1 = unpacklo(c1, zero);
double4 t2 = unpackhi(c0, c2);
double4 t3 = unpackhi(c1, zero);
double4 r0 = unpacklo(t0, t1);
double4 r1 = unpackhi(t0, t1);
double4 r2 = unpacklo(t2, t3);
pos = -(r0 * pos.x + r1 * pos.y + r2 * pos.z);
pos.w = 1.0f;
return(double4x4(r0, r1, r2, pos));
}
/// <summary>\n\t\t/// Returns the double4x4 full inverse of a double4x4 matrix.\n\t\t/// </summary>
public static double4x4 inverse(double4x4 m)
{
double4 c0 = m.c0;
double4 c1 = m.c1;
double4 c2 = m.c2;
double4 c3 = m.c3;
double4 r0y_r1y_r0x_r1x = movelh(c1, c0);
double4 r0z_r1z_r0w_r1w = movelh(c2, c3);
double4 r2y_r3y_r2x_r3x = movehl(c0, c1);
double4 r2z_r3z_r2w_r3w = movehl(c3, c2);
double4 r1y_r2y_r1x_r2x = shuffle(c1, c0, ShuffleComponent.LeftY, ShuffleComponent.LeftZ, ShuffleComponent.RightY, ShuffleComponent.RightZ);
double4 r1z_r2z_r1w_r2w = shuffle(c2, c3, ShuffleComponent.LeftY, ShuffleComponent.LeftZ, ShuffleComponent.RightY, ShuffleComponent.RightZ);
double4 r3y_r0y_r3x_r0x = shuffle(c1, c0, ShuffleComponent.LeftW, ShuffleComponent.LeftX, ShuffleComponent.RightW, ShuffleComponent.RightX);
double4 r3z_r0z_r3w_r0w = shuffle(c2, c3, ShuffleComponent.LeftW, ShuffleComponent.LeftX, ShuffleComponent.RightW, ShuffleComponent.RightX);
double4 r0_wzyx = shuffle(r0z_r1z_r0w_r1w, r0y_r1y_r0x_r1x, ShuffleComponent.LeftZ, ShuffleComponent.LeftX, ShuffleComponent.RightX, ShuffleComponent.RightZ);
double4 r1_wzyx = shuffle(r0z_r1z_r0w_r1w, r0y_r1y_r0x_r1x, ShuffleComponent.LeftW, ShuffleComponent.LeftY, ShuffleComponent.RightY, ShuffleComponent.RightW);
double4 r2_wzyx = shuffle(r2z_r3z_r2w_r3w, r2y_r3y_r2x_r3x, ShuffleComponent.LeftZ, ShuffleComponent.LeftX, ShuffleComponent.RightX, ShuffleComponent.RightZ);
double4 r3_wzyx = shuffle(r2z_r3z_r2w_r3w, r2y_r3y_r2x_r3x, ShuffleComponent.LeftW, ShuffleComponent.LeftY, ShuffleComponent.RightY, ShuffleComponent.RightW);
double4 r0_xyzw = shuffle(r0y_r1y_r0x_r1x, r0z_r1z_r0w_r1w, ShuffleComponent.LeftZ, ShuffleComponent.LeftX, ShuffleComponent.RightX, ShuffleComponent.RightZ);
// Calculate remaining inner term pairs. inner terms have zw=-xy, so we only have to calculate xy and can pack two pairs per vector.
double4 inner12_23 = r1y_r2y_r1x_r2x * r2z_r3z_r2w_r3w - r1z_r2z_r1w_r2w * r2y_r3y_r2x_r3x;
double4 inner02_13 = r0y_r1y_r0x_r1x * r2z_r3z_r2w_r3w - r0z_r1z_r0w_r1w * r2y_r3y_r2x_r3x;
double4 inner30_01 = r3z_r0z_r3w_r0w * r0y_r1y_r0x_r1x - r3y_r0y_r3x_r0x * r0z_r1z_r0w_r1w;
// Expand inner terms back to 4 components. zw signs still need to be flipped
double4 inner12 = shuffle(inner12_23, inner12_23, ShuffleComponent.LeftX, ShuffleComponent.LeftZ, ShuffleComponent.RightZ, ShuffleComponent.RightX);
double4 inner23 = shuffle(inner12_23, inner12_23, ShuffleComponent.LeftY, ShuffleComponent.LeftW, ShuffleComponent.RightW, ShuffleComponent.RightY);
double4 inner02 = shuffle(inner02_13, inner02_13, ShuffleComponent.LeftX, ShuffleComponent.LeftZ, ShuffleComponent.RightZ, ShuffleComponent.RightX);
double4 inner13 = shuffle(inner02_13, inner02_13, ShuffleComponent.LeftY, ShuffleComponent.LeftW, ShuffleComponent.RightW, ShuffleComponent.RightY);
// Calculate minors
double4 minors0 = r3_wzyx * inner12 - r2_wzyx * inner13 + r1_wzyx * inner23;
double4 denom = r0_xyzw * minors0;
// Horizontal sum of denominator. Free sign flip of z and w compensates for missing flip in inner terms.
denom = denom + shuffle(denom, denom, ShuffleComponent.LeftY, ShuffleComponent.LeftX, ShuffleComponent.RightW, ShuffleComponent.RightZ); // x+y x+y z+w z+w
denom = denom - shuffle(denom, denom, ShuffleComponent.LeftZ, ShuffleComponent.LeftZ, ShuffleComponent.RightX, ShuffleComponent.RightX); // x+y-z-w x+y-z-w z+w-x-y z+w-x-y
double4 rcp_denom_ppnn = double4(1.0) / denom;
double4x4 res;
res.c0 = minors0 * rcp_denom_ppnn;
double4 inner30 = shuffle(inner30_01, inner30_01, ShuffleComponent.LeftX, ShuffleComponent.LeftZ, ShuffleComponent.RightZ, ShuffleComponent.RightX);
double4 inner01 = shuffle(inner30_01, inner30_01, ShuffleComponent.LeftY, ShuffleComponent.LeftW, ShuffleComponent.RightW, ShuffleComponent.RightY);
double4 minors1 = r2_wzyx * inner30 - r0_wzyx * inner23 - r3_wzyx * inner02;
res.c1 = minors1 * rcp_denom_ppnn;
double4 minors2 = r0_wzyx * inner13 - r1_wzyx * inner30 - r3_wzyx * inner01;
res.c2 = minors2 * rcp_denom_ppnn;
double4 minors3 = r1_wzyx * inner02 - r0_wzyx * inner12 + r2_wzyx * inner01;
res.c3 = minors3 * rcp_denom_ppnn;
return(res);
}
public static double3 transform(double4x4 a, double3 b)
{
return((a.c0 * b.x + a.c1 * b.y + a.c2 * b.z + a.c3).xyz);
}
public static double3 rotate(double4x4 a, double3 b)
{
return((a.c0 * b.x + a.c1 * b.y + a.c2 * b.z).xyz);
}
public static uint4x4 uint4x4(double4x4 v)
{
return(new uint4x4(v));
}
public static int4x4 int4x4(double4x4 v)
{
return(new int4x4(v));
}
public static float4x4 float4x4(double4x4 v)
{
return(new float4x4(v));
}