private float ComputeLeastSquares(Vec4 alphax_sum, Vec4 betax_sum, Vec4 alphabeta_sum, out Vec4 a, out Vec4 b)
{
Vec4 alpha2_sum = alphax_sum.SplatW();
Vec4 beta2_sum = betax_sum.SplatW();
// compute the least-squares optimal points
Vec4 factor = alphabeta_sum.NegativeMultiplySubtract(alphabeta_sum, alpha2_sum * beta2_sum).Reciprocal();
a = betax_sum.NegativeMultiplySubtract(alphabeta_sum, alphax_sum * beta2_sum) * factor;
b = alphax_sum.NegativeMultiplySubtract(alphabeta_sum, betax_sum * alpha2_sum) * factor;
// clamp to the grid
a = a.Clamp(Vec4.Zero, Vec4.One);
b = b.Clamp(Vec4.Zero, Vec4.One);
a = GRID.MultiplyAdd(a, HALF).Truncate() * GRIDRCP;
b = GRID.MultiplyAdd(b, HALF).Truncate() * GRIDRCP;
// compute the error (we skip the constant xxsum)
Vec4 e1 = (a * a * alpha2_sum) + (b * b * beta2_sum);
Vec4 e2 = a.NegativeMultiplySubtract(alphax_sum, a * b * alphabeta_sum);
Vec4 e3 = b.NegativeMultiplySubtract(betax_sum, e2);
Vec4 e4 = e3 * 2 + e1;
// apply the metric to the error term
Vec4 e5 = e4 * m_metric;
return(e5.X + e5.Y + e5.Z);
}