Vec3 ComputePrincipleComponent( Sym3x3 const& matrix )
{
Vec4 const row0( matrix[0], matrix[1], matrix[2], 0.0f );
Vec4 const row1( matrix[1], matrix[3], matrix[4], 0.0f );
Vec4 const row2( matrix[2], matrix[4], matrix[5], 0.0f );
//Vec4 v = VEC4_CONST( 1.0f );
//Vec4 v = row0; // row1, row2
Vec3 v3 = EstimatePrincipleComponent( matrix );
Vec4 v( v3.X(), v3.Y(), v3.Z(), 0.0f );
for( int i = 0; i < POWER_ITERATION_COUNT; ++i )
{
// matrix multiply
Vec4 w = row0*v.SplatX();
w = MultiplyAdd(row1, v.SplatY(), w);
w = MultiplyAdd(row2, v.SplatZ(), w);
// get max component from xyz in all channels
Vec4 a = Max(w.SplatX(), Max(w.SplatY(), w.SplatZ()));
// divide through and advance
v = w*Reciprocal(a);
}
return v.GetVec3();
}
int main(int /*argc*/, char** /*argv*/) {
std::string opts = ReadFileIntoString("MultiplyAdd.input");
OptionParser parser(opts);
double a = parser.Get<double>("A");
double b = parser.Get<double>("B");
double c = parser.Get<double>("C");
double result = MultiplyAdd(a, b, c);
std::cout << "a is " << a << ", b is " << b << ", c is " << c << std::endl;
std::cout << "The result of MultiplyAdd on a, b, & c is: "
<< result << std::endl;
return EXIT_SUCCESS;
}
Vec4 ClusterFit::SolveLeastSquares( Vec4& start, Vec4& end ) const
{
// accumulate all the quantities we need
int const count = m_colours->GetCount();
Vec4 alpha2_sum = VEC4_CONST( 0.0f );
Vec4 beta2_sum = VEC4_CONST( 0.0f );
Vec4 alphabeta_sum = VEC4_CONST( 0.0f );
Vec4 alphax_sum = VEC4_CONST( 0.0f );
Vec4 betax_sum = VEC4_CONST( 0.0f );
for( int i = 0; i < count; ++i )
{
Vec4 alpha = m_alpha[i];
Vec4 beta = m_beta[i];
Vec4 x = m_weighted[i];
alpha2_sum = MultiplyAdd( alpha, alpha, alpha2_sum );
beta2_sum = MultiplyAdd( beta, beta, beta2_sum );
alphabeta_sum = MultiplyAdd( alpha, beta, alphabeta_sum );
alphax_sum = MultiplyAdd( alpha, x, alphax_sum );
betax_sum = MultiplyAdd( beta, x, betax_sum );
}
// select the results
Vec4 const zero = VEC4_CONST( 0.0f );
Vec4 beta2_sum_zero = CompareEqual( beta2_sum, zero );
Vec4 alpha2_sum_zero = CompareEqual( alpha2_sum, zero );
Vec4 a1 = alphax_sum*Reciprocal( alpha2_sum );
Vec4 b1 = betax_sum*Reciprocal( beta2_sum );
Vec4 factor = Reciprocal( NegativeMultiplySubtract(
alphabeta_sum, alphabeta_sum, alpha2_sum*beta2_sum
) );
Vec4 a2 = NegativeMultiplySubtract(
betax_sum, alphabeta_sum, alphax_sum*beta2_sum
)*factor;
Vec4 b2 = NegativeMultiplySubtract(
alphax_sum, alphabeta_sum, betax_sum*alpha2_sum
)*factor;
Vec4 a = Select( Select( a2, a1, beta2_sum_zero ), zero, alpha2_sum_zero );
Vec4 b = Select( Select( b2, b1, alpha2_sum_zero ), zero, beta2_sum_zero );
// clamp the output to [0, 1]
Vec4 const one = VEC4_CONST( 1.0f );
Vec4 const half = VEC4_CONST( 0.5f );
a = Min( one, Max( zero, a ) );
b = Min( one, Max( zero, b ) );
// clamp to the grid
Vec4 const grid( 31.0f, 63.0f, 31.0f, 0.0f );
Vec4 const gridrcp( 1.0f/31.0f, 1.0f/63.0f, 1.0f/31.0f, 0.0f );
Vec4 const onethird = VEC4_CONST( 1.0f/3.0f );
Vec4 const twothirds = VEC4_CONST( 2.0f/3.0f );
a = Truncate( MultiplyAdd( grid, a, half ) )*gridrcp;
b = Truncate( MultiplyAdd( grid, b, half ) )*gridrcp;
// compute the error
Vec4 const two = VEC4_CONST( 2.0 );
Vec4 e1 = MultiplyAdd( b*b, beta2_sum, m_xxsum );
Vec4 e2 = MultiplyAdd( a, alphax_sum, b*betax_sum );
Vec4 e3 = MultiplyAdd( a*a, alpha2_sum, e1 );
Vec4 e4 = MultiplyAdd( a*b*alphabeta_sum - e2, two, e3 );
// apply the metric to the error term
Vec4 e5 = e4*m_metricSqr;
Vec4 error = e5.SplatX() + e5.SplatY() + e5.SplatZ();
// save the start and end
start = a;
end = b;
return error;
}
void FastClusterFit::Compress4( void* block )
{
Vec4 const one = VEC4_CONST(1.0f);
Vec4 const zero = VEC4_CONST(0.0f);
Vec4 const half = VEC4_CONST(0.5f);
Vec4 const two = VEC4_CONST(2.0);
Vec4 const onethird = VEC4_CONST( 1.0f/3.0f );
Vec4 const twothirds = VEC4_CONST( 2.0f/3.0f );
// declare variables
Vec4 beststart = VEC4_CONST( 0.0f );
Vec4 bestend = VEC4_CONST( 0.0f );
Vec4 besterror = VEC4_CONST( FLT_MAX );
Vec4 x0 = zero;
int b0 = 0, b1 = 0, b2 = 0;
int i = 0;
// check all possible clusters for this total order
for( int c0 = 0; c0 <= 16; c0++)
{
Vec4 x1 = zero;
for( int c1 = 0; c1 <= 16-c0; c1++)
{
Vec4 x2 = zero;
for( int c2 = 0; c2 <= 16-c0-c1; c2++)
{
Vec4 const constants = Vec4((const float *)&s_fourElement[i]);
Vec4 const alpha2_sum = constants.SplatX();
Vec4 const beta2_sum = constants.SplatY();
Vec4 const alphabeta_sum = constants.SplatZ();
Vec4 const factor = constants.SplatW();
i++;
Vec4 const alphax_sum = x0 + MultiplyAdd(x1, twothirds, x2 * onethird);
Vec4 const betax_sum = m_xsum - alphax_sum;
Vec4 a = NegativeMultiplySubtract(betax_sum, alphabeta_sum, alphax_sum*beta2_sum) * factor;
Vec4 b = NegativeMultiplySubtract(alphax_sum, alphabeta_sum, betax_sum*alpha2_sum) * factor;
// clamp the output to [0, 1]
a = Min( one, Max( zero, a ) );
b = Min( one, Max( zero, b ) );
// clamp to the grid
Vec4 const grid( 31.0f, 63.0f, 31.0f, 0.0f );
Vec4 const gridrcp( 0.03227752766457f, 0.01583151765563f, 0.03227752766457f, 0.0f );
a = Truncate( MultiplyAdd( grid, a, half ) ) * gridrcp;
b = Truncate( MultiplyAdd( grid, b, half ) ) * gridrcp;
// compute the error
Vec4 e1 = MultiplyAdd( a, alphax_sum, b*betax_sum );
Vec4 e2 = MultiplyAdd( a*a, alpha2_sum, b*b*beta2_sum );
Vec4 e3 = MultiplyAdd( a*b*alphabeta_sum - e1, two, e2 );
// apply the metric to the error term
Vec4 e4 = e3 * m_metricSqr;
Vec4 error = e4.SplatX() + e4.SplatY() + e4.SplatZ();
// keep the solution if it wins
if( CompareAnyLessThan( error, besterror ) )
{
besterror = error;
beststart = a;
bestend = b;
b0 = c0;
b1 = c1;
b2 = c2;
}
x2 += m_unweighted[c0+c1+c2];
}
x1 += m_unweighted[c0+c1];
}
x0 += m_unweighted[c0];
}
// save the block if necessary
if( CompareAnyLessThan( besterror, m_besterror ) )
{
// compute indices from cluster sizes.
/*uint bestindices = 0;
{
int i = b0;
for(; i < b0+b1; i++) {
bestindices = 2 << (2 * m_order[i]);
}
for(; i < b0+b1+b2; i++) {
bestindices = 3 << (2 * m_order[i]);
}
for(; i < 16; i++) {
bestindices = 1 << (2 * m_order[i]);
}
}*/
u8 bestindices[16];
{
int i = 0;
for(; i < b0; i++) {
bestindices[i] = 0;
}
for(; i < b0+b1; i++) {
bestindices[i] = 2;
}
for(; i < b0+b1+b2; i++) {
bestindices[i] = 3;
}
for(; i < 16; i++) {
bestindices[i] = 1;
}
}
// remap the indices
u8 ordered[16];
for( int i = 0; i < 16; ++i )
ordered[m_order[i]] = bestindices[i];
// save the block
WriteColourBlock4( beststart.GetVec3(), bestend.GetVec3(), ordered, block );
// save the error
m_besterror = besterror;
}
}
void WeightedClusterFit::Compress4( void* block )
{
int const count = m_colours->GetCount();
Vec4 const one = VEC4_CONST(1.0f);
Vec4 const zero = VEC4_CONST(0.0f);
Vec4 const half = VEC4_CONST(0.5f);
Vec4 const two = VEC4_CONST(2.0);
Vec4 const onethird( 1.0f/3.0f, 1.0f/3.0f, 1.0f/3.0f, 1.0f/9.0f );
Vec4 const twothirds( 2.0f/3.0f, 2.0f/3.0f, 2.0f/3.0f, 4.0f/9.0f );
Vec4 const twonineths = VEC4_CONST( 2.0f/9.0f );
Vec4 const grid( 31.0f, 63.0f, 31.0f, 0.0f );
Vec4 const gridrcp( 1.0f/31.0f, 1.0f/63.0f, 1.0f/31.0f, 0.0f );
// declare variables
Vec4 beststart = VEC4_CONST( 0.0f );
Vec4 bestend = VEC4_CONST( 0.0f );
Vec4 besterror = VEC4_CONST( FLT_MAX );
Vec4 x0 = zero;
int b0 = 0, b1 = 0, b2 = 0;
// check all possible clusters for this total order
for( int c0 = 0; c0 < count; c0++)
{
Vec4 x1 = zero;
for( int c1 = 0; c1 < count-c0; c1++)
{
Vec4 x2 = zero;
for( int c2 = 0; c2 < count-c0-c1; c2++)
{
Vec4 const x3 = m_xsum - x2 - x1 - x0;
//Vec3 const alphax_sum = x0 + x1 * (2.0f / 3.0f) + x2 * (1.0f / 3.0f);
//float const alpha2_sum = w0 + w1 * (4.0f/9.0f) + w2 * (1.0f/9.0f);
Vec4 const alphax_sum = MultiplyAdd(x2, onethird, MultiplyAdd(x1, twothirds, x0)); // alphax_sum, alpha2_sum
Vec4 const alpha2_sum = alphax_sum.SplatW();
//Vec3 const betax_sum = x3 + x2 * (2.0f / 3.0f) + x1 * (1.0f / 3.0f);
//float const beta2_sum = w3 + w2 * (4.0f/9.0f) + w1 * (1.0f/9.0f);
Vec4 const betax_sum = MultiplyAdd(x2, twothirds, MultiplyAdd(x1, onethird, x3)); // betax_sum, beta2_sum
Vec4 const beta2_sum = betax_sum.SplatW();
//float const alphabeta_sum = (w1 + w2) * (2.0f/9.0f);
Vec4 const alphabeta_sum = twonineths*( x1 + x2 ).SplatW(); // alphabeta_sum
// float const factor = 1.0f / (alpha2_sum * beta2_sum - alphabeta_sum * alphabeta_sum);
Vec4 const factor = Reciprocal( NegativeMultiplySubtract(alphabeta_sum, alphabeta_sum, alpha2_sum*beta2_sum) );
Vec4 a = NegativeMultiplySubtract(betax_sum, alphabeta_sum, alphax_sum*beta2_sum) * factor;
Vec4 b = NegativeMultiplySubtract(alphax_sum, alphabeta_sum, betax_sum*alpha2_sum) * factor;
// clamp to the grid
a = Min( one, Max( zero, a ) );
b = Min( one, Max( zero, b ) );
a = Truncate( MultiplyAdd( grid, a, half ) ) * gridrcp;
b = Truncate( MultiplyAdd( grid, b, half ) ) * gridrcp;
// compute the error (we skip the constant xxsum)
Vec4 e1 = MultiplyAdd( a*a, alpha2_sum, b*b*beta2_sum );
Vec4 e2 = NegativeMultiplySubtract( a, alphax_sum, a*b*alphabeta_sum );
Vec4 e3 = NegativeMultiplySubtract( b, betax_sum, e2 );
Vec4 e4 = MultiplyAdd( two, e3, e1 );
// apply the metric to the error term
Vec4 e5 = e4 * m_metricSqr;
Vec4 error = e5.SplatX() + e5.SplatY() + e5.SplatZ();
// keep the solution if it wins
if( CompareAnyLessThan( error, besterror ) )
{
besterror = error;
beststart = a;
bestend = b;
b0 = c0;
b1 = c1;
b2 = c2;
}
x2 += m_weighted[c0+c1+c2];
}
x1 += m_weighted[c0+c1];
}
x0 += m_weighted[c0];
}
// save the block if necessary
if( CompareAnyLessThan( besterror, m_besterror ) )
{
// compute indices from cluster sizes.
u8 bestindices[16];
{
int i = 0;
for(; i < b0; i++) {
bestindices[i] = 0;
}
for(; i < b0+b1; i++) {
bestindices[i] = 2;
}
for(; i < b0+b1+b2; i++) {
bestindices[i] = 3;
}
for(; i < count; i++) {
bestindices[i] = 1;
}
}
// remap the indices
u8 ordered[16];
for( int i = 0; i < count; ++i )
ordered[m_order[i]] = bestindices[i];
m_colours->RemapIndices( ordered, bestindices );
// save the block
WriteColourBlock4( beststart.GetVec3(), bestend.GetVec3(), bestindices, block );
// save the error
m_besterror = besterror;
}
}
void BitoneClusterFit::ClusterFit4Constant(void* block)
{
// declare variables
int const count = m_bitones->GetCount();
Vec4 const two = VEC4_CONST(2.0f);
Vec4 const one = VEC4_CONST(1.0f);
Vec4 const onethird_onethird2 (1.0f / 3.0f, 1.0f / 3.0f, 1.0f / 3.0f, 1.0f / 9.0f);
Vec4 const twothirds_twothirds2(2.0f / 3.0f, 2.0f / 3.0f, 2.0f / 3.0f, 4.0f / 9.0f);
Vec4 const twonineths = VEC4_CONST(2.0f / 9.0f);
assume((count > 0) && (count <= 16));
// check all possible clusters and iterate on the total order
Vec4 beststart = VEC4_CONST(0.0f);
Vec4 bestend = VEC4_CONST(0.0f);
Scr4 besterror = m_besterror;
u8 bestindices[16];
int bestiteration = 0;
int besti = 0, bestj = 0, bestk = 0;
// prepare an ordering using the principle axis
ConstructOrdering(m_principle, 0);
// loop over iterations (we avoid the case that all points in first or last cluster)
for (int iterationIndex = 0;;) {
// cache some values
Vec4 const xsum_wsum = m_xsum_wsum;
// constants if weights == 1
Vec4 alphabeta_dltas = *((Vec4 *)part2delta[0]);
Vec4 *alphabeta_inits = (Vec4 *)part2inits[0];
float *alphabeta_factors = (float *)part2factors;
#if 0
Vec4 lasta = Vec4(0.0f);
Vec4 lastb = xsum_wsum;
Vec4 lastc = Vec4(0.0f);
#endif
// first cluster [0,i) is at the start
Vec4 part0 = VEC4_CONST(0.0f);
for (int i = 0; i < count; ++i) {
// second cluster [i,j) is one third along
Vec4 part1 = VEC4_CONST(0.0f);
for (int j = i;;) {
// third cluster [j,k) is two thirds along
Vec4 part2 = (j == 0) ? m_points_weights[0] : VEC4_CONST(0.0f);
Vec4 alphabeta_val = *alphabeta_inits++;
int kmin = (j == 0) ? 1 : j;
for (int k = kmin;;) {
// TODO: the inner alphabeta_sum seems always to be the same sequence
Vec4 alphabeta_factor = alphabeta_val * Vec4(*alphabeta_factors++);
// compute least squares terms directly
Vec4 const alphax_sum = MultiplyAdd(part2, onethird_onethird2, MultiplyAdd(part1, twothirds_twothirds2, part0));
Vec4 const betax_sum = /*MultiplyAdd(part1, onethird_onethird2, MultiplyAdd(part2, twothirds_twothirds2, part3))*/ xsum_wsum - alphax_sum;
Vec4 const alpha2_sum = alphabeta_val.SplatX();
Vec4 const beta2_sum = alphabeta_val.SplatY();
Vec4 const alphabeta_sum = alphabeta_val.SplatZ();
Vec4 a = NegativeMultiplySubtract( betax_sum, alphabeta_factor.SplatZ(), alphax_sum * alphabeta_factor.SplatY());
Vec4 b = NegativeMultiplySubtract(alphax_sum, alphabeta_factor.SplatZ(), betax_sum * alphabeta_factor.SplatX());
#if 0
// last cluster [k,count) is at the end
Vec4 part3 = xsum_wsum - part2 - part1 - part0;
// compute least squares terms directly
Vec4 const _alphax_sum = MultiplyAdd(part2, onethird_onethird2, MultiplyAdd(part1, twothirds_twothirds2, part0));
Vec4 const _betax_sum = MultiplyAdd(part1, onethird_onethird2, MultiplyAdd(part2, twothirds_twothirds2, part3));
// Vec4 const _betac_sum = xsum_wsum - _alphax_sum;
Vec4 const _alpha2_sum = _alphax_sum.SplatW();
Vec4 const _beta2_sum = _betax_sum.SplatW();
Vec4 const _alphabeta_sum = twonineths * (part1 + part2).SplatW();
// compute the least-squares optimal points
Vec4 _factor = Reciprocal(NegativeMultiplySubtract(_alphabeta_sum, _alphabeta_sum, _alpha2_sum * _beta2_sum));
Vec4 _a = NegativeMultiplySubtract( _betax_sum, _alphabeta_sum, _alphax_sum * _beta2_sum) * _factor;
Vec4 _b = NegativeMultiplySubtract(_alphax_sum, _alphabeta_sum, _betax_sum * _alpha2_sum) * _factor;
#undef limit
#define limit 2e-5
assert(fabs(_alpha2_sum.W() - alpha2_sum.X()) < limit);
assert(fabs(_beta2_sum.W() - beta2_sum.X()) < limit);
assert(fabs(_alphabeta_sum.W() - alphabeta_sum.X()) < limit);
if (alphabeta_factors[-1] != FLT_MAX) {
assert(fabs(_factor.W() - alphabeta_factors[-1]) < limit);
assert(fabs(_alpha2_sum.W() * _factor.W() - alphabeta_factor.X()) < limit);
assert(fabs(_beta2_sum.W() * _factor.W() - alphabeta_factor.Y()) < limit);
assert(fabs(_alphabeta_sum.W() * _factor.W() - alphabeta_factor.Z()) < limit);
assert(fabs(a.X() - _a.X()) < limit);
assert(fabs(a.Y() - _a.Y()) < limit);
assert(fabs(a.Z() - _a.Z()) < limit);
assert(fabs(b.X() - _b.X()) < limit);
assert(fabs(b.Y() - _b.Y()) < limit);
assert(fabs(b.Z() - _b.Z()) < limit);
}
#if 0
fprintf(stderr, "{%.9ff},", _factor.W());
if (k == kmin)
fprintf(stderr, "{%.9f, %.9f, %.9f},\n", alpha2_sum.W(), beta2_sum.W(), alphabeta_sum.W());
fprintf(stderr, "{%.9f/*%.9f*/,%.9f/*%.9f*/,%.9f,%.9f},\n",
alpha2_sum.W(), lasta.W() - alpha2_sum.W(),
beta2_sum.W(), lastb.W() - beta2_sum.W(),
alphabeta_sum.W(), lastc.W() - alphabeta_sum.W(),
factor.W());
lasta = alpha2_sum;
lastb = beta2_sum;
lastc = alphabeta_sum;
#endif
#endif
// snap floating-point-values to the integer-lattice
a = Truncate(a * 255.0f) * (1.0f / 255.0f);
b = Truncate(b * 255.0f) * (1.0f / 255.0f);
// compute the error (we skip the constant xxsum)
Vec4 e1 = MultiplyAdd(a * a, alpha2_sum, b * b * beta2_sum);
Vec4 e2 = NegativeMultiplySubtract(a, alphax_sum, a * b * alphabeta_sum);
Vec4 e3 = NegativeMultiplySubtract(b, betax_sum, e2);
Vec4 e4 = MultiplyAdd(two, e3, e1);
// apply the metric to the error term
Scr4 eS = e4;
// keep the solution if it wins
if (besterror > eS) {
besterror = eS;
beststart = a;
bestend = b;
bestiteration = iterationIndex;
besti = i;
bestj = j;
bestk = k;
}
alphabeta_val += alphabeta_dltas;
// advance
if (k == count) break;
part2 += m_points_weights[k]; ++k; }
// advance
if (j == count) break;
part1 += m_points_weights[j]; ++j; }
// advance
part0 += m_points_weights[i];
}
// stop if we didn't improve in this iteration
if (bestiteration != iterationIndex)
break;
// advance if possible
++iterationIndex;
if (iterationIndex == m_iterationCount)
break;
// stop if a new iteration is an ordering that has already been tried
Vec3 axis = (bestend - beststart).GetVec3();
if (!ConstructOrdering(axis, iterationIndex))
break;
}
// save the block if necessary
if (besterror < m_besterror) {
// save the error
m_besterror = besterror;
// remap the indices
u8 const* order = (u8*)m_order + 16 * bestiteration;
u8 unordered[16];
for (int m = 0; m < besti; ++m)
unordered[order[m]] = 0;
for (int m = besti; m < bestj; ++m)
unordered[order[m]] = 2;
for (int m = bestj; m < bestk; ++m)
unordered[order[m]] = 3;
for (int m = bestk; m < count; ++m)
unordered[order[m]] = 1;
m_bitones->RemapIndices(unordered, bestindices);
// save the block
WriteBitoneBlock4(beststart.GetVec3(), bestend.GetVec3(), bestindices, block);
}
}
void BitoneClusterFit::ClusterFit4(void* block)
{
// declare variables
int const count = m_bitones->GetCount();
Vec4 const two = VEC4_CONST(2.0f);
Vec4 const one = VEC4_CONST(1.0f);
Vec4 const onethird_onethird2 (1.0f / 3.0f, 1.0f / 3.0f, 1.0f / 3.0f, 1.0f / 9.0f);
Vec4 const twothirds_twothirds2(2.0f / 3.0f, 2.0f / 3.0f, 2.0f / 3.0f, 4.0f / 9.0f);
Vec4 const twonineths = VEC4_CONST(2.0f / 9.0f);
assume((count > 0) && (count <= 16));
// prepare an ordering using the principle axis
ConstructOrdering(m_principle, 0);
// check all possible clusters and iterate on the total order
Vec4 beststart = VEC4_CONST(0.0f);
Vec4 bestend = VEC4_CONST(0.0f);
Scr4 besterror = m_besterror;
u8 bestindices[16];
int bestiteration = 0;
int besti = 0, bestj = 0, bestk = 0;
// loop over iterations (we avoid the case that all points in first or last cluster)
for (int iterationIndex = 0;;) {
// first cluster [0,i) is at the start
Vec4 part0 = VEC4_CONST(0.0f);
for (int i = 0; i < count; ++i) {
// second cluster [i,j) is one third along
Vec4 part1 = VEC4_CONST(0.0f);
for (int j = i;;) {
// third cluster [j,k) is two thirds along
Vec4 part2 = (j == 0) ? m_points_weights[0] : VEC4_CONST(0.0f);
int kmin = (j == 0) ? 1 : j;
for (int k = kmin;;) {
// last cluster [k,count) is at the end
Vec4 part3 = m_xsum_wsum - part2 - part1 - part0;
// compute least squares terms directly
Vec4 const alphax_sum = MultiplyAdd(part2, onethird_onethird2, MultiplyAdd(part1, twothirds_twothirds2, part0));
Vec4 const betax_sum = MultiplyAdd(part1, onethird_onethird2, MultiplyAdd(part2, twothirds_twothirds2, part3));
Vec4 const alpha2_sum = alphax_sum.SplatW();
Vec4 const beta2_sum = betax_sum.SplatW();
Vec4 const alphabeta_sum = twonineths * (part1 + part2).SplatW();
// compute the least-squares optimal points
Vec4 factor = Reciprocal(NegativeMultiplySubtract(alphabeta_sum, alphabeta_sum, alpha2_sum * beta2_sum));
Vec4 a = NegativeMultiplySubtract( betax_sum, alphabeta_sum, alphax_sum * beta2_sum) * factor;
Vec4 b = NegativeMultiplySubtract(alphax_sum, alphabeta_sum, betax_sum * alpha2_sum) * factor;
// snap floating-point-values to the integer-lattice
a = Truncate(a * 255.0f) * (1.0f / 255.0f);
b = Truncate(b * 255.0f) * (1.0f / 255.0f);
// compute the error (we skip the constant xxsum)
Vec4 e1 = MultiplyAdd(a * a, alpha2_sum, b * b * beta2_sum);
Vec4 e2 = NegativeMultiplySubtract(a, alphax_sum, a * b * alphabeta_sum);
Vec4 e3 = NegativeMultiplySubtract(b, betax_sum, e2);
Vec4 e4 = MultiplyAdd(two, e3, e1);
// apply the metric to the error term
Scr4 eS = e4;
// keep the solution if it wins
if (besterror > eS) {
besterror = eS;
beststart = a;
bestend = b;
besti = i;
bestj = j;
bestk = k;
bestiteration = iterationIndex;
}
// advance
if (k == count) break;
part2 += m_points_weights[k]; ++k;
}
// advance
if (j == count) break;
part1 += m_points_weights[j]; ++j;
}
// advance
part0 += m_points_weights[i];
}
// stop if we didn't improve in this iteration
if (bestiteration != iterationIndex)
break;
// advance if possible
++iterationIndex;
if (iterationIndex == m_iterationCount)
break;
// stop if a new iteration is an ordering that has already been tried
Vec3 axis = (bestend - beststart).GetVec3();
if (!ConstructOrdering(axis, iterationIndex))
break;
}
// save the block if necessary
if (besterror < m_besterror) {
// save the error
m_besterror = besterror;
// remap the indices
u8 const* order = (u8*)m_order + 16 * bestiteration;
u8 unordered[16];
for (int m = 0; m < besti; ++m)
unordered[order[m]] = 0;
for (int m = besti; m < bestj; ++m)
unordered[order[m]] = 2;
for (int m = bestj; m < bestk; ++m)
unordered[order[m]] = 3;
for (int m = bestk; m < count; ++m)
unordered[order[m]] = 1;
m_bitones->RemapIndices(unordered, bestindices);
// save the block
WriteBitoneBlock4(beststart.GetVec3(), bestend.GetVec3(), bestindices, block);
}
}