// This file is part of the ustl library, an STL implementation.
//
// Copyright (C) 2005 by Mike Sharov <msharov@users.sourceforge.net>
// This file is free software, distributed under the MIT License.
//
// ulaalgo.h
//
#ifndef ULAALGO_H_2E403D182E83FB596AFB800E68B255A1
#define ULAALGO_H_2E403D182E83FB596AFB800E68B255A1
#include "umatrix.h"
#include "simd.h"
namespace ustl {
/// \brief Creates an identity matrix in \p m
/// \ingroup NumericAlgorithms
template <size_t NX, size_t NY, typename T>
void load_identity (matrix<NX,NY,T>& m)
{
fill_n (m.begin(), NX * NY, 0);
for (typename matrix<NX,NY,T>::iterator i = m.begin(); i < m.end(); i += NX + 1)
*i = 1;
}
/// \brief Multiplies two matrices
/// \ingroup NumericAlgorithms
template <size_t NX, size_t NY, typename T>
matrix<NY,NY,T> operator* (const matrix<NX,NY,T>& m1, const matrix<NY,NX,T>& m2)
{
matrix<NY,NY,T> mr;
for (uoff_t ry = 0; ry < NY; ++ ry) {
for (uoff_t rx = 0; rx < NY; ++ rx) {
T dpv (0);
for (uoff_t x = 0; x < NX; ++ x)
dpv += m1[ry][x] * m2[x][rx];
mr[ry][rx] = dpv;
}
}
return (mr);
}
/// \brief Transforms vector \p t with matrix \p m
/// \ingroup NumericAlgorithms
template <size_t NX, size_t NY, typename T>
tuple<NX,T> operator* (const tuple<NY,T>& t, const matrix<NX,NY,T>& m)
{
tuple<NX,T> tr;
for (uoff_t x = 0; x < NX; ++ x) {
T dpv (0);
for (uoff_t y = 0; y < NY; ++ y)
dpv += t[y] * m[y][x];
tr[x] = dpv;
}
return (tr);
}
/// \brief Transposes (exchanges rows and columns) matrix \p m.
/// \ingroup NumericAlgorithms
template <size_t N, typename T>
void transpose (matrix<N,N,T>& m)
{
for (uoff_t x = 0; x < N; ++ x)
for (uoff_t y = x; y < N; ++ y)
swap (m[x][y], m[y][x]);
}
#if WANT_UNROLLED_COPY
#if CPU_HAS_SSE
#if linux // Non-linux gcc versions (BSD, Solaris) can't handle "x" constraint and provide no alternative.
template <>
inline void load_identity (matrix<4,4,float>& m)
{
asm (
"movaps %4, %%xmm1 \n\t" // 1 0 0 0
"movups %4, %0 \n\t" // 1 0 0 0
"shufps $0xB1,%%xmm1,%%xmm1 \n\t" // 0 1 0 0
"movups %%xmm1, %1 \n\t" // 0 1 0 0
"shufps $0x4F,%4,%%xmm1 \n\t" // 0 0 1 0
"shufps $0x1B,%4,%4 \n\t" // 0 0 0 1
"movups %%xmm1, %2 \n\t" // 0 0 1 0
"movups %4, %3" // 0 0 0 1
: "=m"(m[0][0]), "=m"(m[1][0]), "=m"(m[2][0]), "=m"(m[3][0])
: "x"(1.0f)
: "xmm1"
);
}
#endif
inline void _sse_load_matrix (const float* m)
{
asm (
"movups %0, %%xmm4 \n\t" // xmm4 = m[1 2 3 4]
"movups %1, %%xmm5 \n\t" // xmm5 = m[1 2 3 4]
"movups %2, %%xmm6 \n\t" // xmm6 = m[1 2 3 4]
"movups %3, %%xmm7" // xmm7 = m[1 2 3 4]
: : "m"(m[0]), "m"(m[4]), "m"(m[8]), "m"(m[12])
: "xmm4", "xmm5", "xmm6", "xmm7"
);
}
inline void _sse_transform_to_vector (float* result)
{
asm (
"movaps %%xmm0, %%xmm1 \n\t" // xmm1 = t[0 1 2 3]
"movaps %%xmm0, %%xmm2 \n\t" // xmm1 = t[0 1 2 3]
"movaps %%xmm0, %%xmm3 \n\t" // xmm1 = t[0 1 2 3]
"shufps $0x00, %%xmm0, %%xmm0 \n\t" // xmm0 = t[0 0 0 0]
"shufps $0x66, %%xmm1, %%xmm1 \n\t" // xmm1 = t[1 1 1 1]
"shufps $0xAA, %%xmm2, %%xmm2 \n\t" // xmm2 = t[2 2 2 2]
"shufps $0xFF, %%xmm3, %%xmm3 \n\t" // xmm3 = t[3 3 3 3]
"mulps %%xmm4, %%xmm0 \n\t" // xmm0 = t[0 0 0 0] * m[0 1 2 3]
"mulps %%xmm5, %%xmm1 \n\t" // xmm1 = t[1 1 1 1] * m[0 1 2 3]
"addps %%xmm1, %%xmm0 \n\t" // xmm0 = xmm0 + xmm1
"mulps %%xmm6, %%xmm2 \n\t" // xmm2 = t[2 2 2 2] * m[0 1 2 3]
"mulps %%xmm7, %%xmm3 \n\t" // xmm3 = t[3 3 3 3] * m[0 1 2 3]
"addps %%xmm3, %%xmm2 \n\t" // xmm2 = xmm2 + xmm3
"addps %%xmm2, %%xmm0 \n\t" // xmm0 = result
"movups %%xmm0, %0"
: "=m"(result[0]) :
: "xmm0", "xmm1", "xmm2", "xmm3", "xmm4", "xmm5", "xmm6", "xmm7"
);
}
template <>
tuple<4,float> operator* (const tuple<4,float>& t, const matrix<4,4,float>& m)
{
tuple<4,float> result;
_sse_load_matrix (m.begin());
asm ("movups %0, %%xmm0" : : "m"(t[0]) : "xmm0");
_sse_transform_to_vector (result.begin());
return (result);
}
template <>
matrix<4,4,float> operator* (const matrix<4,4,float>& m1, const matrix<4,4,float>& m2)
{
matrix<4,4,float> result;
_sse_load_matrix (m2.begin());
for (uoff_t r = 0; r < 4; ++ r) {
asm ("movups %0, %%xmm0" : : "m"(m1[r][0]) : "xmm0");
_sse_transform_to_vector (result[r]);
}
return (result);
}
#elif CPU_HAS_3DNOW
/// Specialization for 4-component vector transform, the slow part of 3D graphics.
template <>
tuple<4,float> operator* (const tuple<4,float>& t, const matrix<4,4,float>& m)
{
tuple<4,float> result;
// This is taken from "AMD Athlon Code Optimization Guide" from AMD. 18 cycles!
// If you are writing a 3D engine, you may want to copy it instead of calling it
// because of the femms instruction at the end, which takes 2 cycles.
asm (
"movq %2, %%mm0 \n\t" // y | x
"movq %3, %%mm1 \n\t" // w | z
"movq %%mm0, %%mm2 \n\t" // y | x
"movq %4, %%mm3 \n\t" // m[0][1] | m[0][0]
"punpckldq %%mm0, %%mm0 \n\t" // x | x
"movq %6, %%mm4 \n\t" // m[1][1] | m[1][0]
"pfmul %%mm0, %%mm3 \n\t" // x*m[0][1] | x*m[0][0]
"punpckhdq %%mm2, %%mm2 \n\t" // y | y
"pfmul %%mm2, %%mm4 \n\t" // y*m[1][1] | y*m[1][0]
"movq %5, %%mm5 \n\t" // m[0][3] | m[0][2]
"movq %7, %%mm7 \n\t" // m[1][3] | m[1][2]
"movq %%mm1, %%mm6 \n\t" // w | z
"pfmul %%mm0, %%mm5 \n\t" // x*m[0][3] | v0>x*m[0][2]
"movq %8, %%mm0 \n\t" // m[2][1] | m[2][0]
"punpckldq %%mm1, %%mm1 \n\t" // z | z
"pfmul %%mm2, %%mm7 \n\t" // y*m[1][3] | y*m[1][2]
"movq %9, %%mm2 \n\t" // m[2][3] | m[2][2]
"pfmul %%mm1, %%mm0 \n\t" // z*m[2][1] | z*m[2][0]
"pfadd %%mm4, %%mm3 \n\t" // x*m[0][1]+y*m[1][1] | x*m[0][0]+y*m[1][0]
"movq %10, %%mm4 \n\t" // m[3][1] | m[3][0]
"pfmul %%mm1, %%mm2 \n\t" // z*m[2][3] | z*m[2][2]
"pfadd %%mm7, %%mm5 \n\t" // x*m[0][3]+y*m[1][3] | x*m[0][2]+y*m[1][2]
"movq %11, %%mm1 \n\t" // m[3][3] | m[3][2]
"punpckhdq %%mm6, %%mm6 \n\t" // w | w
"pfadd %%mm0, %%mm3 \n\t" // x*m[0][1]+y*m[1][1]+z*m[2][1] | x*m[0][0]+y*m[1][0]+z*m[2][0]
"pfmul %%mm6, %%mm4 \n\t" // w*m[3][1] | w*m[3][0]
"pfmul %%mm6, %%mm1 \n\t" // w*m[3][3] | w*m[3][2]
"pfadd %%mm2, %%mm5 \n\t" // x*m[0][3]+y*m[1][3]+z*m[2][3] | x*m[0][2]+y*m[1][2]+z*m[2][2]
"pfadd %%mm4, %%mm3 \n\t" // x*m[0][1]+y*m[1][1]+z*m[2][1]+w*m[3][1] | x*m[0][0]+y*m[1][0]+z*m[2][0]+w*m[3][0]
"movq %%mm3, %0 \n\t" // store result->y | result->x
"pfadd %%mm1, %%mm5 \n\t" // x*m[0][3]+y*m[1][3]+z*m[2][3]+w*m[3][3] | x*m[0][2]+y*m[1][2]+z*m[2][2]+w*m[3][2]
"movq %%mm5, %1" // store result->w | result->z
: "=m"(result[0]), "=m"(result[2])
: "m"(t[0]), "m"(t[2]),
"m"(m[0][0]), "m"(m[0][2]),
"m"(m[1][0]), "m"(m[1][2]),
"m"(m[2][0]), "m"(m[2][2]),
"m"(m[3][0]), "m"(m[3][2])
: "mm0","mm1","mm2","mm3","mm4","mm5","mm6","mm7"
);
simd::reset_mmx();
return (result);
}
#else // If no processor extensions, just unroll the multiplication
/// Specialization for 4-component vector transform, the slow part of 3D graphics.
template <>
tuple<4,float> operator* (const tuple<4,float>& t, const matrix<4,4,float>& m)
{
tuple<4,float> tr;
for (uoff_t i = 0; i < 4; ++ i)
tr[i] = t[0] * m[0][i] + t[1] * m[1][i] + t[2] * m[2][i] + t[3] * m[3][i];
return (tr);
}
#endif // CPU_HAS_3DNOW
#endif // WANT_UNROLLED_COPY
} // namespace ustl
#endif