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Add Fastor library

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This commit is contained in:
Bassem Girgis
2025-03-22 01:17:52 -05:00
parent 5546e086f6
commit 4dd5939693
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noarch/include/Fastor/backend/inverse.h Normal file
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#ifndef INVERSE_H
#define INVERSE_H
#include "Fastor/config/config.h"
#include "Fastor/meta/meta.h"
#include "Fastor/simd_vector/extintrin.h"
namespace Fastor {
template<typename T, size_t N, enable_if_t_<is_greater_v_<N,4>, bool> = false>
FASTOR_INLINE void _inverse(const T *FASTOR_RESTRICT src, T *FASTOR_RESTRICT dst);
template<typename T, size_t N, enable_if_t_<is_equal_v_<N,1>, bool> = false>
FASTOR_INLINE void _inverse(const T *FASTOR_RESTRICT src, T *FASTOR_RESTRICT dst) {
*dst = T(1) / (*src);
}
#ifdef FASTOR_SSE2_IMPL
template<typename T, size_t N, enable_if_t_<is_equal_v_<N,2> && !is_same_v_<T,float> && !is_same_v_<T,double>, bool> = false>
#else
template<typename T, size_t N, enable_if_t_<is_equal_v_<N,2>, bool> = false>
#endif
FASTOR_INLINE void _inverse(const T *FASTOR_RESTRICT src, T *FASTOR_RESTRICT dst)
{
T det;
T src0 = src[0];
T src1 = src[1];
T src2 = src[2];
T src3 = src[3];
/* Compute adjoint: */
dst[0] = + src3;
dst[1] = - src1;
dst[2] = - src2;
dst[3] = + src0;
/* Compute determinant: */
det = src0 * dst[0] + src1 * dst[2];
/* Multiply adjoint with reciprocal of determinant: */
det = T(1.0) / det;
dst[0] *= det;
dst[1] *= det;
dst[2] *= det;
dst[3] *= det;
}
#ifdef FASTOR_SSE2_IMPL
template<typename T, size_t N, enable_if_t_<is_equal_v_<N,2> && is_same_v_<T,float>, bool> = false>
FASTOR_INLINE void _inverse(const T *FASTOR_RESTRICT src, T *FASTOR_RESTRICT dst)
{
// This is much superior to the scalar code as
// gcc/clang can't auto-vectorise the scalar code
// 6 shuffles + 1 add + 1 mul + 1 div
// Sky 6 + 4 + 4 + 11 = 25
__m128 mat = _mm_loadu_ps(src);
// xor to swap off-diagonals sings
__m128 nmat = _mm_neg_ps(mat);
// two shuffles to get adjoint
__m128 adj = _mm_shuffle_ps(mat, nmat, 0x009C );
adj = _mm_shuffle_ps(adj, adj , 0x39 );
// compute determinat
__m128 tmp0 = _mm_shuffle_ps(mat , mat , 0x00D8);
tmp0 = _mm_mul_ps (adj , tmp0 );
__m128 tmp1 = _mm_shuffle_ps(tmp0, tmp0, 0x1 );
__m128 det = _mm_div_ss (ONEPS, _mm_add_ss(tmp0,tmp1));
// broadcast det to all elements of __m128
det = _mm_shuffle_ps(det, det, 0x0 );
// divide adjoint by determinant
__m128 inv = _mm_mul_ps (adj, det);
_mm_storeu_ps(dst, inv);
}
template<typename T, size_t N, enable_if_t_<is_equal_v_<N,2> && is_same_v_<T,double>, bool> = false>
FASTOR_INLINE void _inverse(const T *FASTOR_RESTRICT src, T *FASTOR_RESTRICT dst)
{
// This is much superior to the scalar code as
// gcc/clang can't auto-vectorise the scalar code
// 8 shuffles + 1 add + 3 mul + 1 div
// Sky 8 + 4 + 12 + 14 = 38
__m128d row0 = _mm_loadu_pd(src);
__m128d row1 = _mm_loadu_pd(src+2);
__m128d tmp = row0;
row0 = _mm_shuffle_pd(row0,_mm_neg_pd(row0),0x2);
row1 = _mm_shuffle_pd(_mm_neg_pd(row1),row1,0x2);
// these two registers hold the adjoint
__m128d irow0 = _mm_shuffle_pd(row1,row0,0x3);
__m128d irow1 = _mm_shuffle_pd(row1,row0,0x0);
// dot product to compute determinant
__m128d det = _mm_mul_pd(tmp,_mm_reverse_pd(row1));
det = _mm_add_pd(det,_mm_reverse_pd(det));
// one by determinant
__m128d invdet = _mm_div_pd(_mm_set1_pd(1.0),det);
// scale
irow0 = _mm_mul_pd(irow0,invdet);
irow1 = _mm_mul_pd(irow1,invdet);
_mm_storeu_pd(dst ,irow0);
_mm_storeu_pd(dst+2,irow1);
}
#endif
template<typename T, size_t N, enable_if_t_<is_equal_v_<N,3>, bool> = false>
FASTOR_INLINE void _inverse(const T *FASTOR_RESTRICT src, T *FASTOR_RESTRICT dst)
{
T det;
T src0 = src[0];
T src1 = src[1];
T src2 = src[2];
T src3 = src[3];
T src4 = src[4];
T src5 = src[5];
T src6 = src[6];
T src7 = src[7];
T src8 = src[8];
/* Compute adjoint: */
dst[0] = + src4 * src8 - src5 * src7;
dst[1] = - src1 * src8 + src2 * src7;
dst[2] = + src1 * src5 - src2 * src4;
dst[3] = - src3 * src8 + src5 * src6;
dst[4] = + src0 * src8 - src2 * src6;
dst[5] = - src0 * src5 + src2 * src3;
dst[6] = + src3 * src7 - src4 * src6;
dst[7] = - src0 * src7 + src1 * src6;
dst[8] = + src0 * src4 - src1 * src3;
/* Compute determinant: */
det = src0 * dst[0] + src1 * dst[3] + src2 * dst[6];
/* Multiply adjoint with reciprocal of determinant: */
det = T(1.0) / det;
dst[0] *= det;
dst[1] *= det;
dst[2] *= det;
dst[3] *= det;
dst[4] *= det;
dst[5] *= det;
dst[6] *= det;
dst[7] *= det;
dst[8] *= det;
}
#ifdef FASTOR_SSE2_IMPL
template<typename T, size_t N, enable_if_t_<is_equal_v_<N,4> && !is_same_v_<T,float> && !is_same_v_<T,double>, bool> = false>
#else
template<typename T, size_t N, enable_if_t_<is_equal_v_<N,4>, bool> = false>
#endif
FASTOR_INLINE void _inverse(const T *FASTOR_RESTRICT src, T *FASTOR_RESTRICT dst)
{
T t1 = src[2*4+2]*src[3*4+3] - src[2*4+3]*src[3*4+2];
T t2 = src[2*4+1]*src[3*4+3] - src[2*4+3]*src[3*4+1];
T t3 = src[2*4+1]*src[3*4+2] - src[2*4+2]*src[3*4+1];
dst[0] = src[1*4+1]*t1 - src[1*4+2]*t2 + src[1*4+3]*t3;
dst[1] = src[0*4+2]*t2 - src[0*4+1]*t1 - src[0*4+3]*t3;
T t4 = src[2*4+0]*src[3*4+3] - src[2*4+3]*src[3*4+0];
T t5 = src[2*4+0]*src[3*4+2] - src[2*4+2]*src[3*4+0];
dst[4] = src[1*4+2]*t4 - src[1*4+0]*t1 - src[1*4+3]*t5;
dst[5] = src[0*4+0]*t1 - src[0*4+2]*t4 + src[0*4+3]*t5;
t1 = src[2*4+0]*src[3*4+1] - src[2*4+1]*src[3*4+0];
dst[8] = src[1*4+0]*t2 - src[1*4+1]*t4 + src[1*4+3]*t1;
dst[9] = src[0*4+1]*t4 - src[0*4+0]*t2 - src[0*4+3]*t1;
dst[12] = src[1*4+1]*t5 - src[1*4+0]*t3 - src[1*4+2]*t1;
dst[13] = src[0*4+0]*t3 - src[0*4+1]*t5 + src[0*4+2]*t1;
t1 = src[0*4+2]*src[1*4+3] - src[0*4+3]*src[1*4+2];
t2 = src[0*4+1]*src[1*4+3] - src[0*4+3]*src[1*4+1];
t3 = src[0*4+1]*src[1*4+2] - src[0*4+2]*src[1*4+1];
dst[2] = src[3*4+1]*t1 - src[3*4+2]*t2 + src[3*4+3]*t3;
dst[3] = src[2*4+2]*t2 - src[2*4+1]*t1 - src[2*4+3]*t3;
t4 = src[0*4+0]*src[1*4+3] - src[0*4+3]*src[1*4+0];
t5 = src[0*4+0]*src[1*4+2] - src[0*4+2]*src[1*4+0];
dst[6] = src[3*4+2]*t4 - src[3*4+0]*t1 - src[3*4+3]*t5;
dst[7] = src[2*4+0]*t1 - src[2*4+2]*t4 + src[2*4+3]*t5;
t1 = src[0*4+0]*src[1*4+1] - src[0*4+1]*src[1*4+0];
dst[10] = src[3*4+0]*t2 - src[3*4+1]*t4 + src[3*4+3]*t1;
dst[11] = src[2*4+1]*t4 - src[2*4+0]*t2 - src[2*4+3]*t1;
dst[14] = src[3*4+1]*t5 - src[3*4+0]*t3 - src[3*4+2]*t1;
dst[15] = src[2*4+0]*t3 - src[2*4+1]*t5 + src[2*4+2]*t1;
const T __det = src[0]*dst[0] + src[1]*dst[4] + src[2]*dst[8] + src[3]*dst[12];
const T __invdet = T(1)/__det;
for (int i=0; i<16; ++i)
dst[i] *= __invdet;
}
#ifdef FASTOR_SSE2_IMPL
template<typename T, size_t N, enable_if_t_<is_equal_v_<N,4> && is_same_v_<T,float>, bool> = false>
FASTOR_INLINE void _inverse(const T *FASTOR_RESTRICT src, T *FASTOR_RESTRICT dst)
{
// From Intel's SSE matrix library
// The inverse is calculated using "Divide and Conquer" technique. The
// original matrix is divide into four 2x2 sub-matrices. Since each
// register of the matrix holds two elements, the smaller matrices are
// consisted of two registers. Hence we get a better locality of the
// calculations.
const __m128 p4f_sign_PNNP = _mm_castsi128_ps(_mm_set_epi32(0x00000000, 0x80000000, 0x80000000, 0x00000000));
// Load the full matrix into registers
__m128 _L1 = _mm_loadu_ps(src + 0);
__m128 _L2 = _mm_loadu_ps(src + 4);
__m128 _L3 = _mm_loadu_ps(src + 8);
__m128 _L4 = _mm_loadu_ps(src + 12);
__m128 A, B, C, D; // the four sub-matrices
A = _mm_movelh_ps(_L1, _L2);
B = _mm_movehl_ps(_L2, _L1);
C = _mm_movelh_ps(_L3, _L4);
D = _mm_movehl_ps(_L4, _L3);
// partial inverse of the sub-matrices
__m128 iA, iB, iC, iD, DC, AB;
__m128 dA, dB, dC, dD; // determinant of the sub-matrices
__m128 det, d, d1, d2;
__m128 rd; // reciprocal of the determinant
// AB = A# * B
AB = _mm_mul_ps(_mm_shuffle_ps(A,A,0x0F), B);
AB = _mm_sub_ps(AB,_mm_mul_ps(_mm_shuffle_ps(A,A,0xA5), _mm_shuffle_ps(B,B,0x4E)));
// DC = D# * C
DC = _mm_mul_ps(_mm_shuffle_ps(D,D,0x0F), C);
DC = _mm_sub_ps(DC,_mm_mul_ps(_mm_shuffle_ps(D,D,0xA5), _mm_shuffle_ps(C,C,0x4E)));
// dA = |A|
dA = _mm_mul_ps(_mm_shuffle_ps(A, A, 0x5F),A);
dA = _mm_sub_ss(dA, _mm_movehl_ps(dA,dA));
// dB = |B|
dB = _mm_mul_ps(_mm_shuffle_ps(B, B, 0x5F),B);
dB = _mm_sub_ss(dB, _mm_movehl_ps(dB,dB));
// dC = |C|
dC = _mm_mul_ps(_mm_shuffle_ps(C, C, 0x5F),C);
dC = _mm_sub_ss(dC, _mm_movehl_ps(dC,dC));
// dD = |D|
dD = _mm_mul_ps(_mm_shuffle_ps(D, D, 0x5F),D);
dD = _mm_sub_ss(dD, _mm_movehl_ps(dD,dD));
// d = trace(AB*DC) = trace(A#*B*D#*C)
d = _mm_mul_ps(_mm_shuffle_ps(DC,DC,0xD8),AB);
// iD = C*A#*B
iD = _mm_mul_ps(_mm_shuffle_ps(C,C,0xA0), _mm_movelh_ps(AB,AB));
iD = _mm_add_ps(iD,_mm_mul_ps(_mm_shuffle_ps(C,C,0xF5), _mm_movehl_ps(AB,AB)));
// iA = B*D#*C
iA = _mm_mul_ps(_mm_shuffle_ps(B,B,0xA0), _mm_movelh_ps(DC,DC));
iA = _mm_add_ps(iA,_mm_mul_ps(_mm_shuffle_ps(B,B,0xF5), _mm_movehl_ps(DC,DC)));
// d = trace(AB*DC) = trace(A#*B*D#*C) [continue]
d = _mm_add_ps(d, _mm_movehl_ps(d, d));
d = _mm_add_ss(d, _mm_shuffle_ps(d, d, 1));
d1 = _mm_mul_ss(dA,dD);
d2 = _mm_mul_ss(dB,dC);
// iD = D*|A| - C*A#*B
iD = _mm_sub_ps(_mm_mul_ps(D,_mm_shuffle_ps(dA,dA,0)), iD);
// iA = A*|D| - B*D#*C;
iA = _mm_sub_ps(_mm_mul_ps(A,_mm_shuffle_ps(dD,dD,0)), iA);
// det = |A|*|D| + |B|*|C| - trace(A#*B*D#*C)
det = _mm_sub_ss(_mm_add_ss(d1,d2),d);
rd = _mm_div_ss(_mm_set_ss(1.0f), det);
// iB = D * (A#B)# = D*B#*A
iB = _mm_mul_ps(D, _mm_shuffle_ps(AB,AB,0x33));
iB = _mm_sub_ps(iB, _mm_mul_ps(_mm_shuffle_ps(D,D,0xB1), _mm_shuffle_ps(AB,AB,0x66)));
// iC = A * (D#C)# = A*C#*D
iC = _mm_mul_ps(A, _mm_shuffle_ps(DC,DC,0x33));
iC = _mm_sub_ps(iC, _mm_mul_ps(_mm_shuffle_ps(A,A,0xB1), _mm_shuffle_ps(DC,DC,0x66)));
rd = _mm_shuffle_ps(rd,rd,0);
rd = _mm_xor_ps(rd, p4f_sign_PNNP);
// iB = C*|B| - D*B#*A
iB = _mm_sub_ps(_mm_mul_ps(C,_mm_shuffle_ps(dB,dB,0)), iB);
// iC = B*|C| - A*C#*D;
iC = _mm_sub_ps(_mm_mul_ps(B,_mm_shuffle_ps(dC,dC,0)), iC);
// iX = iX / det
iA = _mm_mul_ps(rd,iA);
iB = _mm_mul_ps(rd,iB);
iC = _mm_mul_ps(rd,iC);
iD = _mm_mul_ps(rd,iD);
_mm_storeu_ps(dst+0, _mm_shuffle_ps(iA,iB,0x77));
_mm_storeu_ps(dst+4, _mm_shuffle_ps(iA,iB,0x22));
_mm_storeu_ps(dst+8, _mm_shuffle_ps(iC,iD,0x77));
_mm_storeu_ps(dst+12, _mm_shuffle_ps(iC,iD,0x22));
}
template<typename T, size_t N, enable_if_t_<is_equal_v_<N,4> && is_same_v_<T,double>, bool> = false>
FASTOR_INLINE void _inverse(const T *FASTOR_RESTRICT src, T *FASTOR_RESTRICT dst)
{
// From Intel's SSE matrix library
// The inverse is calculated using "Divide and Conquer" technique. The
// original matrix is divide into four 2x2 sub-matrices. Since each
// register of the matrix holds two elements, the smaller matrices are
// consisted of two registers. Hence we get a better locality of the
// calculations.
const __m128d _Sign_NP = _mm_castsi128_pd(_mm_set_epi32(0x0,0x0,0x80000000,0x0));
const __m128d _Sign_PN = _mm_castsi128_pd(_mm_set_epi32(0x80000000,0x0,0x0,0x0));
// the four sub-matrices
__m128d A1, A2, B1, B2, C1, C2, D1, D2;
A1 = _mm_loadu_pd(src + 0); B1 = _mm_loadu_pd(src + 2);
A2 = _mm_loadu_pd(src + 4); B2 = _mm_loadu_pd(src + 6);
C1 = _mm_loadu_pd(src + 8); D1 = _mm_loadu_pd(src +10);
C2 = _mm_loadu_pd(src +12); D2 = _mm_loadu_pd(src +14);
// partial inverse of the sub-matrices
__m128d iA1, iA2, iB1, iB2, iC1, iC2, iD1, iD2, DC1, DC2, AB1, AB2;
__m128d dA, dB, dC, dD; // determinant of the sub-matrices
__m128d det, d1, d2, rd;
// dA = |A|
dA = _mm_shuffle_pd(A2, A2, 1);
dA = _mm_mul_pd(A1, dA);
dA = _mm_sub_sd(dA, _mm_shuffle_pd(dA,dA,3));
// dB = |B|
dB = _mm_shuffle_pd(B2, B2, 1);
dB = _mm_mul_pd(B1, dB);
dB = _mm_sub_sd(dB, _mm_shuffle_pd(dB,dB,3));
// AB = A# * B
AB1 = _mm_mul_pd(B1, _mm_shuffle_pd(A2,A2,3));
AB2 = _mm_mul_pd(B2, _mm_shuffle_pd(A1,A1,0));
AB1 = _mm_sub_pd(AB1, _mm_mul_pd(B2, _mm_shuffle_pd(A1,A1,3)));
AB2 = _mm_sub_pd(AB2, _mm_mul_pd(B1, _mm_shuffle_pd(A2,A2,0)));
// dC = |C|
dC = _mm_shuffle_pd(C2, C2, 1);
dC = _mm_mul_pd(C1, dC);
dC = _mm_sub_sd(dC, _mm_shuffle_pd(dC,dC,3));
// dD = |D|
dD = _mm_shuffle_pd(D2, D2, 1);
dD = _mm_mul_pd(D1, dD);
dD = _mm_sub_sd(dD, _mm_shuffle_pd(dD,dD,3));
// DC = D# * C
DC1 = _mm_mul_pd(C1, _mm_shuffle_pd(D2,D2,3));
DC2 = _mm_mul_pd(C2, _mm_shuffle_pd(D1,D1,0));
DC1 = _mm_sub_pd(DC1, _mm_mul_pd(C2, _mm_shuffle_pd(D1,D1,3)));
DC2 = _mm_sub_pd(DC2, _mm_mul_pd(C1, _mm_shuffle_pd(D2,D2,0)));
// rd = trace(AB*DC) = trace(A#*B*D#*C)
d1 = _mm_mul_pd(AB1, _mm_shuffle_pd(DC1, DC2, 0));
d2 = _mm_mul_pd(AB2, _mm_shuffle_pd(DC1, DC2, 3));
rd = _mm_add_pd(d1, d2);
rd = _mm_add_sd(rd, _mm_shuffle_pd(rd, rd,3));
// iD = C*A#*B
iD1 = _mm_mul_pd(AB1, _mm_shuffle_pd(C1,C1,0));
iD2 = _mm_mul_pd(AB1, _mm_shuffle_pd(C2,C2,0));
iD1 = _mm_add_pd(iD1, _mm_mul_pd(AB2, _mm_shuffle_pd(C1,C1,3)));
iD2 = _mm_add_pd(iD2, _mm_mul_pd(AB2, _mm_shuffle_pd(C2,C2,3)));
// iA = B*D#*C
iA1 = _mm_mul_pd(DC1, _mm_shuffle_pd(B1,B1,0));
iA2 = _mm_mul_pd(DC1, _mm_shuffle_pd(B2,B2,0));
iA1 = _mm_add_pd(iA1, _mm_mul_pd(DC2, _mm_shuffle_pd(B1,B1,3)));
iA2 = _mm_add_pd(iA2, _mm_mul_pd(DC2, _mm_shuffle_pd(B2,B2,3)));
// iD = D*|A| - C*A#*B
dA = _mm_shuffle_pd(dA,dA,0);
iD1 = _mm_sub_pd(_mm_mul_pd(D1, dA), iD1);
iD2 = _mm_sub_pd(_mm_mul_pd(D2, dA), iD2);
// iA = A*|D| - B*D#*C;
dD = _mm_shuffle_pd(dD,dD,0);
iA1 = _mm_sub_pd(_mm_mul_pd(A1, dD), iA1);
iA2 = _mm_sub_pd(_mm_mul_pd(A2, dD), iA2);
d1 = _mm_mul_sd(dA, dD);
d2 = _mm_mul_sd(dB, dC);
// iB = D * (A#B)# = D*B#*A
iB1 = _mm_mul_pd(D1, _mm_shuffle_pd(AB2,AB1,1));
iB2 = _mm_mul_pd(D2, _mm_shuffle_pd(AB2,AB1,1));
iB1 = _mm_sub_pd(iB1, _mm_mul_pd(_mm_shuffle_pd(D1,D1,1), _mm_shuffle_pd(AB2,AB1,2)));
iB2 = _mm_sub_pd(iB2, _mm_mul_pd(_mm_shuffle_pd(D2,D2,1), _mm_shuffle_pd(AB2,AB1,2)));
// det = |A|*|D| + |B|*|C| - trace(A#*B*D#*C)
det = _mm_add_sd(d1, d2);
det = _mm_sub_sd(det, rd);
// iC = A * (D#C)# = A*C#*D
iC1 = _mm_mul_pd(A1, _mm_shuffle_pd(DC2,DC1,1));
iC2 = _mm_mul_pd(A2, _mm_shuffle_pd(DC2,DC1,1));
iC1 = _mm_sub_pd(iC1, _mm_mul_pd(_mm_shuffle_pd(A1,A1,1), _mm_shuffle_pd(DC2,DC1,2)));
iC2 = _mm_sub_pd(iC2, _mm_mul_pd(_mm_shuffle_pd(A2,A2,1), _mm_shuffle_pd(DC2,DC1,2)));
rd = _mm_div_sd(_mm_set_sd(1.0), det);
rd = _mm_shuffle_pd(rd,rd,0);
// iB = C*|B| - D*B#*A
dB = _mm_shuffle_pd(dB,dB,0);
iB1 = _mm_sub_pd(_mm_mul_pd(C1, dB), iB1);
iB2 = _mm_sub_pd(_mm_mul_pd(C2, dB), iB2);
d1 = _mm_xor_pd(rd, _Sign_PN);
d2 = _mm_xor_pd(rd, _Sign_NP);
// iC = B*|C| - A*C#*D;
dC = _mm_shuffle_pd(dC,dC,0);
iC1 = _mm_sub_pd(_mm_mul_pd(B1, dC), iC1);
iC2 = _mm_sub_pd(_mm_mul_pd(B2, dC), iC2);
_mm_storeu_pd(dst+0, _mm_mul_pd(_mm_shuffle_pd(iA2, iA1, 3), d1));
_mm_storeu_pd(dst+4, _mm_mul_pd(_mm_shuffle_pd(iA2, iA1, 0), d2));
_mm_storeu_pd(dst+2, _mm_mul_pd(_mm_shuffle_pd(iB2, iB1, 3), d1));
_mm_storeu_pd(dst+4+2, _mm_mul_pd(_mm_shuffle_pd(iB2, iB1, 0), d2));
_mm_storeu_pd(dst+2*4, _mm_mul_pd(_mm_shuffle_pd(iC2, iC1, 3), d1));
_mm_storeu_pd(dst+3*4, _mm_mul_pd(_mm_shuffle_pd(iC2, iC1, 0), d2));
_mm_storeu_pd(dst+2*4+2,_mm_mul_pd(_mm_shuffle_pd(iD2, iD1, 3), d1));
_mm_storeu_pd(dst+3*4+2,_mm_mul_pd(_mm_shuffle_pd(iD2, iD1, 0), d2));
}
#endif
} // end of namespace Fastor
#endif // INVERSE_H