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Add simd power solver.

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pull/216/head
castano 15 years ago
parent 8365df0adf
commit a5faf51738
1 changed files with 35 additions and 167 deletions
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202
src/nvtt/squish/maths.cpp
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@ -24,6 +24,7 @@
-------------------------------------------------------------------------- */
#include "maths.h"
#include "simd.h"
#include <cfloat>
namespace nvsquish {
@ -59,189 +60,56 @@ Sym3x3 ComputeWeightedCovariance( int n, Vec3 const* points, float const* weight
return covariance;
}
#if 1
#define POWER_ITERATION_COUNT 8
#if SQUISH_USE_SIMD
Vec3 ComputePrincipleComponent( Sym3x3 const& matrix )
{
const int NUM = 8;
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 );
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();
}
#else
Vec3 ComputePrincipleComponent( Sym3x3 const& matrix )
{
Vec3 v(1, 1, 1);
for (int i = 0; i < NUM; i++)
{
for (int i = 0; i < POWER_ITERATION_COUNT; i++)
{
float x = v.X() * matrix[0] + v.Y() * matrix[1] + v.Z() * matrix[2];
float y = v.X() * matrix[1] + v.Y() * matrix[3] + v.Z() * matrix[4];
float z = v.X() * matrix[2] + v.Y() * matrix[4] + v.Z() * matrix[5];
float norm = std::max(std::max(x, y), z);
float iv = 1.0f / norm;
if (norm == 0.0f) { // @@ I think this is not necessary in this case!!
return Vec3(0.0f);
}
v = Vec3(x*iv, y*iv, z*iv);
}
return v;
}
#else
static Vec3 GetMultiplicity1Evector( Sym3x3 const& matrix, float evalue )
{
// compute M
Sym3x3 m;
m[0] = matrix[0] - evalue;
m[1] = matrix[1];
m[2] = matrix[2];
m[3] = matrix[3] - evalue;
m[4] = matrix[4];
m[5] = matrix[5] - evalue;
// compute U
Sym3x3 u;
u[0] = m[3]*m[5] - m[4]*m[4];
u[1] = m[2]*m[4] - m[1]*m[5];
u[2] = m[1]*m[4] - m[2]*m[3];
u[3] = m[0]*m[5] - m[2]*m[2];
u[4] = m[1]*m[2] - m[4]*m[0];
u[5] = m[0]*m[3] - m[1]*m[1];
// find the largest component
float mc = std::fabs( u[0] );
int mi = 0;
for( int i = 1; i < 6; ++i )
{
float c = std::fabs( u[i] );
if( c > mc )
{
mc = c;
mi = i;
}
}
// pick the column with this component
switch( mi )
{
case 0:
return Vec3( u[0], u[1], u[2] );
case 1:
case 3:
return Vec3( u[1], u[3], u[4] );
default:
return Vec3( u[2], u[4], u[5] );
}
}
static Vec3 GetMultiplicity2Evector( Sym3x3 const& matrix, float evalue )
{
// compute M
Sym3x3 m;
m[0] = matrix[0] - evalue;
m[1] = matrix[1];
m[2] = matrix[2];
m[3] = matrix[3] - evalue;
m[4] = matrix[4];
m[5] = matrix[5] - evalue;
// find the largest component
float mc = std::fabs( m[0] );
int mi = 0;
for( int i = 1; i < 6; ++i )
{
float c = std::fabs( m[i] );
if( c > mc )
{
mc = c;
mi = i;
}
}
// pick the first eigenvector based on this index
switch( mi )
{
case 0:
case 1:
return Vec3( -m[1], m[0], 0.0f );
case 2:
return Vec3( m[2], 0.0f, -m[0] );
case 3:
case 4:
return Vec3( 0.0f, -m[4], m[3] );
default:
return Vec3( 0.0f, -m[5], m[4] );
}
}
Vec3 ComputePrincipleComponent( Sym3x3 const& matrix )
{
// compute the cubic coefficients
float c0 = matrix[0]*matrix[3]*matrix[5]
+ 2.0f*matrix[1]*matrix[2]*matrix[4]
- matrix[0]*matrix[4]*matrix[4]
- matrix[3]*matrix[2]*matrix[2]
- matrix[5]*matrix[1]*matrix[1];
float c1 = matrix[0]*matrix[3] + matrix[0]*matrix[5] + matrix[3]*matrix[5]
- matrix[1]*matrix[1] - matrix[2]*matrix[2] - matrix[4]*matrix[4];
float c2 = matrix[0] + matrix[3] + matrix[5];
// compute the quadratic coefficients
float a = c1 - ( 1.0f/3.0f )*c2*c2;
float b = ( -2.0f/27.0f )*c2*c2*c2 + ( 1.0f/3.0f )*c1*c2 - c0;
// compute the root count check
float Q = 0.25f*b*b + ( 1.0f/27.0f )*a*a*a;
// test the multiplicity
if( FLT_EPSILON < Q )
{
// only one root, which implies we have a multiple of the identity
return Vec3( 1.0f );
}
else if( Q < -FLT_EPSILON )
{
// three distinct roots
float theta = std::atan2( std::sqrt( -Q ), -0.5f*b );
float rho = std::sqrt( 0.25f*b*b - Q );
float rt = std::pow( rho, 1.0f/3.0f );
float ct = std::cos( theta/3.0f );
float st = std::sin( theta/3.0f );
float l1 = ( 1.0f/3.0f )*c2 + 2.0f*rt*ct;
float l2 = ( 1.0f/3.0f )*c2 - rt*( ct + ( float )sqrt( 3.0f )*st );
float l3 = ( 1.0f/3.0f )*c2 - rt*( ct - ( float )sqrt( 3.0f )*st );
// pick the larger
if( std::fabs( l2 ) > std::fabs( l1 ) )
l1 = l2;
if( std::fabs( l3 ) > std::fabs( l1 ) )
l1 = l3;
// get the eigenvector
return GetMultiplicity1Evector( matrix, l1 );
}
else // if( -FLT_EPSILON <= Q && Q <= FLT_EPSILON )
{
// two roots
float rt;
if( b < 0.0f )
rt = -std::pow( -0.5f*b, 1.0f/3.0f );
else
rt = std::pow( 0.5f*b, 1.0f/3.0f );
float l1 = ( 1.0f/3.0f )*c2 + rt; // repeated
float l2 = ( 1.0f/3.0f )*c2 - 2.0f*rt;
// get the eigenvector
if( std::fabs( l1 ) > std::fabs( l2 ) )
return GetMultiplicity2Evector( matrix, l1 );
else
return GetMultiplicity1Evector( matrix, l2 );
}
}
#endif
} // namespace squish
} // namespace nvsquish

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