inline vector4d haddp(const vector4d* row)
{
// row = (a,b,c,d)
// tmp0 = (a0+a1, b0+b1, a2+a3, b2+b3)
__m256d tmp0 = _mm256_hadd_pd(row[0], row[1]);
// tmp1 = (c0+c1, d0+d1, c2+c3, d2+d3)
__m256d tmp1 = _mm256_hadd_pd(row[2], row[3]);
// tmp2 = (a0+a1, b0+b1, c2+c3, d2+d3)
__m256d tmp2 = _mm256_blend_pd(tmp0, tmp1, 0b1100);
// tmp1 = (a2+a3, b2+b3, c2+c3, d2+d3)
tmp1 = _mm256_permute2f128_pd(tmp0, tmp1, 0x21);
return _mm256_add_pd(tmp1, tmp2);
}
inline float64x4_t dot(const float64x4_t ymm1, const float64x4_t ymm2)
{
float64x4_t mul0 = _mm256_mul_pd(ymm1, ymm2);
float64x4_t hadd0 = _mm256_hadd_pd(mul0, mul0);
float64x2_t ext0 = _mm256_extractf128_pd(hadd0, 0);
float64x2_t ext1 = _mm256_extractf128_pd(hadd0, 1);
float64x2_t add0 = _mm_add_pd(ext0, ext1);
return _mm256_broadcast_pd(&add0);
}
irreg_poly_area_func_sign(double, _avx) {
if (__builtin_expect(is_null(cords) || cords_len == 0, 0))
return 0;
__m256d
curr,
forw,
coef_0,
coef_1,
end = _mm256_load_pd((const double *)cords),
accum_sum = _mm256_setzero_pd();
double accum_sum_aux;
unsigned long index;
for (index = 0; index < (cords_len - 4); index += 4) {
curr = end; // x0,y0,x1,y1
forw = _mm256_load_pd((const double *)&cords[index + 2]); // x2,y2,x3,y3
end = _mm256_load_pd((const double *)&cords[index + 4]); // x4,y4,x5,y5
coef_0 = _mm256_permute2f128_pd(curr, forw, 0b00110001); // x1, y1, x3, y3
coef_1 = _mm256_permute2f128_pd(forw, end, 0b00100000); // x2, y2, x4, y4
//_mm256_hsub_pd(a, b) == a0 - a1, b0 - b1, a2 - a3, b2 - b3
accum_sum = _mm256_add_pd(
accum_sum,
_mm256_hsub_pd( // x0*y1 - y0*x1, x1*y2 - y1x2, x2*y3 - y2*x3, x3*y4 - y3*x4
_mm256_mul_pd( // x0*y1, y0*x1, x2*y3, y2*x3
_mm256_permute2f128_pd(curr, forw, 0b00100000), // x0, y0, x2, y2
_mm256_shuffle_pd(coef_0, coef_0, 0b0101) // y1, x1, y3, x3
),
_mm256_mul_pd(coef_0, _mm256_shuffle_pd(coef_1, coef_1, 0b0101)) // y2, x2, y4, x4
// ^^^^^^^^^^^^^^^ x1*y2, y1*x2, x3*y4, y3*x4
)
);
}
accum_sum = _mm256_hadd_pd(accum_sum, _mm256_permute2f128_pd(accum_sum, accum_sum, 1)); // a0+a1, a2+a3, a2+a3, a0+a1
accum_sum = _mm256_hadd_pd(accum_sum, accum_sum); // a0+a1+a2+a3, ...
for (accum_sum_aux = _mm_cvtsd_f64(_mm256_castpd256_pd128(accum_sum)); index < (cords_len - 1); index++)
accum_sum_aux += _calc_diff_of_adj_prods(cords, index);
return accum_sum_aux;
// return scalar_half(scalar_abs(accum_sum_aux));
}
double hadd(const vector4d& rhs)
{
// rhs = (x0, x1, x2, x3)
// tmp = (x2, x3, x0, x1)
__m256d tmp = _mm256_permute2f128_pd(rhs, rhs, 1);
// tmp = (x2+x0, x3+x1, -, -)
tmp = _mm256_add_pd(rhs, tmp);
// tmp = (x2+x0+x3+x1, -, -, -)
tmp = _mm256_hadd_pd(tmp, tmp);
return _mm_cvtsd_f64(_mm256_extractf128_pd(tmp, 0));
}
void gvrotg_avx(double *c, double *s, double *r, double a, double b)
{
register __m256d x0, x1, t0, t2, u0, u1, one, b0, b1;
if (b == 0.0) {
*c = 1.0;
*s = 0.0;
*r = a;
return;
}
if (a == 0.0) {
*c = 0.0;
*s = 1.0;
*r = b;
return;
}
// set_pd() order: [3, 2, 1, 0]
// x[0], x[1]: |a| > |b|, x[2],x[3]: |b| > |a|
x0 = _mm256_set_pd(1.0, a, b, 1.0); // x0 = {1, a, b, 1}
x1 = _mm256_set_pd(1.0, b, a, 1.0); // x0 = {1, b, a, 1}
t0 = _mm256_div_pd(x0, x1); // t0 = {1, a/b, b/a, 1}
x0 = _mm256_mul_pd(t0, t0); // x3 = {1, (a/b)^2, (b/a)^2, 1}
t2 = _mm256_hadd_pd(x0, x0); // x3 = {1+(a/b)^2, ., (b/a)^2+1, ..}
u0 = _mm256_sqrt_pd(t2); // u0 = {sqrt(1+(a/b)^2), .., sqrt((b/a)^2+1)}
one = _mm256_set1_pd(1.0);
u1 = _mm256_div_pd(one, u0);
b0 = _mm256_blend_pd(u0, u1, 0x9); // b0 = {1/u(b), u(b), u(a), 1/u(a)}
b0 = _mm256_mul_pd(b0, x1); // b0 = {1/u(b), b*u(b), a*u(a), 1/u(a)}
b1 = _mm256_mul_pd(t0, u1); // b1 = {1/u(b), t*u(b), t*u(a), 1/u(a)}
if (fabs(b) > fabs(a)) {
*s = b0[3]; // = 1/u(b)
*r = b0[2]; // = b*u(b)
*c = b1[2]; // = t*u(b)
if (signbit(b)) {
*s = -(*s);
*c = -(*c);
*r = -(*r);
}
} else {
*c = b0[0];
*r = b0[1];
*s = b1[1];
}
}
double HodgkinHuxley::dV(double *V, double I) {
const double C = 1.0;
const double gNa = 120.0;
const double gK = 36.0;
const double gL = 0.3;
const double ENa = 50.0;
const double EK = -77.0;
const double EL = -54.4;
#ifdef __AVX__
/*
AVX is an instruction set from Intel which allows simultaneous operation
on 4 doubles. Seems to be slower than optimized FPU, though.
*/
double Va[] __attribute__ ((aligned (32))) = {V[0], V[0], V[0], 1.0},
Ea[] __attribute__ ((aligned (32))) = {EL, ENa, EK, 0.0},
Ga[] __attribute__ ((aligned (32))) = {-gL, -gNa * pow(V[2], 3.0) * V[3], -gK * pow(V[1], 4.0), I};
// load V
__m256d Vr = _mm256_load_pd(Va);
// load E
__m256d Er = _mm256_load_pd(Ea);
// load G
__m256d Gr = _mm256_load_pd(Ga);
// subtract
Vr = _mm256_sub_pd(Vr, Er);
// dot product (why does intel not have _mm256_dp_pd ?)
Vr = _mm256_mul_pd(Vr, Gr);
__m256d temp = _mm256_hadd_pd(Vr, Vr);
__m128d lo128 = _mm256_extractf128_pd(temp, 0);
__m128d hi128 = _mm256_extractf128_pd(temp, 1);
__m128d dotproduct = _mm_add_pd(lo128, hi128);
double sseVal;
// store
_mm_storel_pd(&sseVal, dotproduct);
sseVal /= C;
return sseVal;
#else
return (-gL * (V[0] - EL) - gNa * pow(V[2], 3.0) * V[3] * (V[0] - ENa)
- gK * pow(V[1], 4.0) * (V[0] - EK) + I) / C;
#endif
}
ALGEBRA_INLINE double vector_ps_double (const double* pa,const double* pb,size_t n) {
if(ALGEBRA_IS_ALIGNED(pa) && ALGEBRA_IS_ALIGNED(pb)) {
size_t q = n/4;
size_t r = n%4;
double w = 0;
if(q>0) {
__m256d acc = _mm256_setzero_pd();
__m256d i1 = _mm256_load_pd(pa);
__m256d j1 = _mm256_load_pd(pb);
pa += 4;
pb += 4;
__m256d s = _mm256_mul_pd(i1, j1);
acc = _mm256_add_pd(acc, s);
while(--q != 0) {
// load
i1 = _mm256_load_pd(pa);
j1 = _mm256_load_pd(pb);
pa += 4;
pb += 4;
// multiplie
s = _mm256_mul_pd(i1, j1);
// accumule
acc = _mm256_add_pd(acc, s);
}
// sum finale
// add horizontal
acc = _mm256_hadd_pd(acc, acc);
// échange 128bits haut et bas
__m256d accp = _mm256_permute2f128_pd(acc, acc, 1);
// add vertical
acc = _mm256_add_pd(acc, accp);
// extract
_mm_store_sd(&w, _mm256_extractf128_pd(acc,0));
}
return w + vector_ps_double_basic(pa, pb, r);
}
return vector_ps_double_basic(pa, pb, n);
}
void core::Vector3::normalize(void)
{
#if defined(VTX_USE_AVX)
ALIGNED_32 platform::F64_t vector[] = {this->x, this->y, this->z, 0};
ALIGNED_32 platform::F64_t reciprocalVector[] = {1.0, 1.0, 1.0, 1.0};
__m256d simdvector;
__m256d result;
__m256d recp;
simdvector = _mm256_load_pd(vector);
recp = _mm256_load_pd(reciprocalVector);
result = _mm256_mul_pd(simdvector, simdvector);
result = _mm256_hadd_pd(result, result);
result = _mm256_hadd_pd(result, result);
result = _mm256_sqrt_pd(result);
result = _mm256_div_pd(recp, result);
simdvector = _mm256_mul_pd(simdvector, result);
_mm256_store_pd(vector, simdvector);
this->x = vector[0];
this->y = vector[1];
this->z = vector[2];
#elif defined(VTX_USE_SSE)
// Must pad with a trailing 0, to store in 128-bit register
ALIGNED_16 core::F32_t vector[] = {this->x, this->y, this->z, 0};
__m128 simdvector;
__m128 result;
simdvector = _mm_load_ps(vector);
// (X^2, Y^2, Z^2, 0^2)
result = _mm_mul_ps(simdvector, simdvector);
// Add all elements together, giving us (X^2 + Y^2 + Z^2 + 0^2)
result = _mm_hadd_ps(result, result);
result = _mm_hadd_ps(result, result);
// Calculate square root, giving us sqrt(X^2 + Y^2 + Z^2 + 0^2)
result = _mm_sqrt_ps(result);
// Calculate reciprocal, giving us 1 / sqrt(X^2 + Y^2 + Z^2 + 0^2)
result = _mm_rcp_ps(result);
// Finally, multiply the result with our original vector.
simdvector = _mm_mul_ps(simdvector, result);
_mm_store_ps(vector, simdvector);
this->x = vector[0];
this->y = vector[1];
this->z = vector[2];
#else
core::F64_t num = 1.0 / std::sqrt(std::pow(this->x, 2) + std::pow(this->y, 2) + std::pow(this->z, 2));
this->x *= num;
this->y *= num;
this->z *= num;
#endif
}
/*!
* \brief Perform an horizontal sum of the given vector.
* \param in The input vector type
* \return the horizontal sum of the vector
*/
ETL_STATIC_INLINE(double) hadd(avx_simd_double in) {
const __m256d t1 = _mm256_hadd_pd(in.value, _mm256_permute2f128_pd(in.value, in.value, 1));
const __m256d t2 = _mm256_hadd_pd(t1, t1);
return _mm_cvtsd_f64(_mm256_castpd256_pd128(t2));
}
void kernel_dgemv_t_1_lib4(int kmax, double *A, int sda, double *x, double *y, int alg)
{
if(kmax<=0)
return;
const int lda = 4;
double *tA, *tx;
int k;
int ka = kmax; // number from aligned positon
__m256d
aaxx_temp,
a_00_10_20_30,
x_0_1_2_3,
y_00;
__m128d
ax_temp,
a_00_10,
x_0_1,
y_0, y_1, y_0_1;
y_00 = _mm256_setzero_pd();
y_0 = _mm256_castpd256_pd128(y_00);
k = lda*(ka/lda);
tA = A + (ka/lda)*sda*lda;
tx = x + (ka/lda)*lda;
for(; k<ka; k++)
{
x_0_1 = _mm_load_sd( &tx[0] );
a_00_10 = _mm_load_sd( &tA[0+lda*0] );
/* y_0 += a_00_10 * x_0_1;*/
ax_temp = _mm_mul_sd( a_00_10, x_0_1 );
y_0 = _mm_add_sd (y_0, ax_temp );
tA += 1;
tx += 1;
}
y_00 = _mm256_castpd128_pd256(y_0);
k=0;
for(; k<ka-3; k+=4)
{
x_0_1_2_3 = _mm256_loadu_pd( &x[0] );
a_00_10_20_30 = _mm256_load_pd( &A[0+lda*0] );
/* y_00 += a_00_10_20_30 * x_0_1_2_3;*/
aaxx_temp = _mm256_mul_pd( a_00_10_20_30, x_0_1_2_3 );
y_00 = _mm256_add_pd( y_00, aaxx_temp );
A += 4 + (sda-1)*lda;
x += 4;
}
y_00 = _mm256_hadd_pd(y_00, y_00);
y_1 = _mm256_extractf128_pd(y_00, 1);
y_0 = _mm256_castpd256_pd128(y_00);
/* y_0 += y_1;*/
y_0 = _mm_add_sd( y_0, y_1 );
if(alg==0)
{
_mm_store_sd(&y[0], y_0);
}
else if(alg==1)
{
y_0_1 = _mm_load_sd( &y[0] );
/* y_0_1 += y_0;*/
y_0_1 = _mm_add_sd( y_0_1, y_0 );
_mm_store_sd(&y[0], y_0_1);
}
else // alg==-1
{
y_0_1 = _mm_load_sd( &y[0] );
/* y_0_1 -= y_0;*/
y_0_1 = _mm_sub_sd( y_0_1, y_0 );
_mm_store_sd(&y[0], y_0_1);
}
}
// Computes and returns the dot product of the n-vectors u and v.
// Uses Intel AVX intrinsics to access the SIMD instruction set.
double DotProductAVX(const double* u, const double* v, int n) {
int max_offset = n - 4;
int offset = 0;
// Accumulate a set of 4 sums in sum, by loading pairs of 4 values from u and
// v, and multiplying them together in parallel.
__m256d sum = _mm256_setzero_pd();
if (offset <= max_offset) {
offset = 4;
// Aligned load is reputedly faster but requires 32 byte aligned input.
if ((reinterpret_cast<const uintptr_t>(u) & 31) == 0 &&
(reinterpret_cast<const uintptr_t>(v) & 31) == 0) {
// Use aligned load.
__m256d floats1 = _mm256_load_pd(u);
__m256d floats2 = _mm256_load_pd(v);
// Multiply.
sum = _mm256_mul_pd(floats1, floats2);
while (offset <= max_offset) {
floats1 = _mm256_load_pd(u + offset);
floats2 = _mm256_load_pd(v + offset);
offset += 4;
__m256d product = _mm256_mul_pd(floats1, floats2);
sum = _mm256_add_pd(sum, product);
}
} else {
// Use unaligned load.
__m256d floats1 = _mm256_loadu_pd(u);
__m256d floats2 = _mm256_loadu_pd(v);
// Multiply.
sum = _mm256_mul_pd(floats1, floats2);
while (offset <= max_offset) {
floats1 = _mm256_loadu_pd(u + offset);
floats2 = _mm256_loadu_pd(v + offset);
offset += 4;
__m256d product = _mm256_mul_pd(floats1, floats2);
sum = _mm256_add_pd(sum, product);
}
}
}
// Add the 4 product sums together horizontally. Not so easy as with sse, as
// there is no add across the upper/lower 128 bit boundary, so permute to
// move the upper 128 bits to lower in another register.
__m256d sum2 = _mm256_permute2f128_pd(sum, sum, 1);
sum = _mm256_hadd_pd(sum, sum2);
sum = _mm256_hadd_pd(sum, sum);
double result;
// _mm256_extract_f64 doesn't exist, but resist the temptation to use an sse
// instruction, as that introduces a 70 cycle delay. All this casting is to
// fool the instrinsics into thinking we are extracting the bottom int64.
auto cast_sum = _mm256_castpd_si256(sum);
*(reinterpret_cast<inT64*>(&result)) =
#if defined(_WIN32) || defined(__i386__)
// This is a very simple workaround that is activated
// for all platforms that do not have _mm256_extract_epi64.
// _mm256_extract_epi64(X, Y) == ((uint64_t*)&X)[Y]
((uint64_t*)&cast_sum)[0]
#else
_mm256_extract_epi64(cast_sum, 0)
#endif
;
while (offset < n) {
result += u[offset] * v[offset];
++offset;
}
return result;
}
void ntt_transform(poly out, const poly o)
{
int s, pos = 0, offset;
__m256d vt,vo0,vo10,vo11,vo20,vo21,vo22,vo23,vc,vp,vpinv,neg2,neg4;
__m256d vx0,vx1,vx2,vx3,vx4,vx5,vx6,vx7;
vpinv = _mm256_set_pd(PARAM_APPROX_P_INVERSE, PARAM_APPROX_P_INVERSE, PARAM_APPROX_P_INVERSE, PARAM_APPROX_P_INVERSE);
vp = _mm256_set_pd(8383489., 8383489., 8383489., 8383489.);
bitrev(out);
vo10 = _mm256_load_pd(o+pos);
vo20 = _mm256_load_pd(o+pos+4);
neg2 = _mm256_load_pd(_neg2);
neg4 = _mm256_load_pd(_neg4);
// m = 2, m = 4, m = 8 (3 levels merged)
for(s = 0; s<POLY_DEG; s+=8)
{
// No multiplication with omega required, respective value is 1
vx0 = _mm256_load_pd(out+s);
vt = _mm256_mul_pd(vx0,neg2);
vx0 = _mm256_hadd_pd(vx0,vt);
vx1 = _mm256_load_pd(out+s+4);
vt = _mm256_mul_pd(vx1,neg2);
vx1 = _mm256_hadd_pd(vx1,vt);
vx0 = _mm256_mul_pd(vx0, vo10);
vc = _mm256_mul_pd(vx0, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vx0 = _mm256_sub_pd(vx0,vc);
vt = _mm256_permute2f128_pd (vx0, vx0, 0x01); // now contains x2,x3,x0,x1
vx0 = _mm256_mul_pd(vx0, neg4);
vx0 = _mm256_add_pd(vx0, vt);
vx1 = _mm256_mul_pd(vx1, vo10);
vc = _mm256_mul_pd(vx1, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vx1 = _mm256_sub_pd(vx1,vc);
vt = _mm256_permute2f128_pd (vx1, vx1, 0x01); // now contains x2,x3,x0,x1
vx1 = _mm256_mul_pd(vx1, neg4);
vx1 = _mm256_add_pd(vx1, vt);
vt = _mm256_mul_pd(vx1, vo20);
vc = _mm256_mul_pd(vt, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vt = _mm256_sub_pd(vt,vc);
vx1 = _mm256_sub_pd(vx0, vt);
_mm256_store_pd(out+s+4, vx1);
vx0 = _mm256_add_pd(vx0, vt);
_mm256_store_pd(out+s+0, vx0);
}
pos += 8;
// m = 16, m = 32, m = 64 (3 levels merged)
for(offset = 0; offset < 8; offset+=4)
{
vo0 = _mm256_load_pd(o+pos+offset);
vo10 = _mm256_load_pd(o+pos+offset+8);
vo11 = _mm256_load_pd(o+pos+offset+16);
for(s = 0; s<POLY_DEG; s+=64)
{
vx1 = _mm256_load_pd(out+offset+s+8);
vt = _mm256_mul_pd(vx1, vo0);
vc = _mm256_mul_pd(vt, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vt = _mm256_sub_pd(vt,vc);
vx0 = _mm256_load_pd(out+offset+s+0);
vx1 = _mm256_sub_pd(vx0, vt);
// _mm256_store_pd(out+offset+s+8, vx1);
vx0 = _mm256_add_pd(vx0, vt);
// _mm256_store_pd(out+offset+s+0, vx0);
vx3 = _mm256_load_pd(out+offset+s+24);
vt = _mm256_mul_pd(vx3, vo0);
vc = _mm256_mul_pd(vt, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vt = _mm256_sub_pd(vt,vc);
vx2 = _mm256_load_pd(out+offset+s+16);
vx3 = _mm256_sub_pd(vx2, vt);
// _mm256_store_pd(out+offset+s+24, vx3);
vx2 = _mm256_add_pd(vx2, vt);
// _mm256_store_pd(out+offset+s+16, vx2);
vx5 = _mm256_load_pd(out+offset+s+40);
vt = _mm256_mul_pd(vx5, vo0);
vc = _mm256_mul_pd(vt, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vt = _mm256_sub_pd(vt,vc);
vx4 = _mm256_load_pd(out+offset+s+32);
vx5 = _mm256_sub_pd(vx4, vt);
// _mm256_store_pd(out+offset+s+40, vx5);
vx4 = _mm256_add_pd(vx4, vt);
// _mm256_store_pd(out+offset+s+32, vx4);
vx7 = _mm256_load_pd(out+offset+s+56);
vt = _mm256_mul_pd(vx7, vo0);
vc = _mm256_mul_pd(vt, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vt = _mm256_sub_pd(vt,vc);
vx6 = _mm256_load_pd(out+offset+s+48);
vx7 = _mm256_sub_pd(vx6, vt);
// _mm256_store_pd(out+offset+s+56, vx7);
vx6 = _mm256_add_pd(vx6, vt);
// _mm256_store_pd(out+offset+s+48, vx6);
// vx2 = _mm256_load_pd(out+offset+s+16);
vt = _mm256_mul_pd(vx2, vo10);
vc = _mm256_mul_pd(vt, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vt = _mm256_sub_pd(vt,vc);
// vx0 = _mm256_load_pd(out+offset+s+0);
vx2 = _mm256_sub_pd(vx0, vt);
// _mm256_store_pd(out+offset+s+16, vx2);
vx0 = _mm256_add_pd(vx0, vt);
// _mm256_store_pd(out+offset+s+0, vx0);
// vx6 = _mm256_load_pd(out+offset+s+48);
vt = _mm256_mul_pd(vx6, vo10);
vc = _mm256_mul_pd(vt, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vt = _mm256_sub_pd(vt,vc);
// vx4 = _mm256_load_pd(out+offset+s+32);
vx6 = _mm256_sub_pd(vx4, vt);
// _mm256_store_pd(out+offset+s+48, vx6);
vx4 = _mm256_add_pd(vx4, vt);
// _mm256_store_pd(out+offset+s+32, vx4);
// vx3 = _mm256_load_pd(out+offset+s+24);
vt = _mm256_mul_pd(vx3, vo11);
vc = _mm256_mul_pd(vt, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vt = _mm256_sub_pd(vt,vc);
// vx1 = _mm256_load_pd(out+offset+s+8);
vx3 = _mm256_sub_pd(vx1, vt);
// _mm256_store_pd(out+offset+s+24, vx3);
vx1 = _mm256_add_pd(vx1, vt);
// _mm256_store_pd(out+offset+s+8, vx1);
// vx7 = _mm256_load_pd(out+offset+s+56);
vt = _mm256_mul_pd(vx7, vo11);
vc = _mm256_mul_pd(vt, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vt = _mm256_sub_pd(vt,vc);
// vx5 = _mm256_load_pd(out+offset+s+40);
vx7 = _mm256_sub_pd(vx5, vt);
// _mm256_store_pd(out+offset+s+56, vx7);
vx5 = _mm256_add_pd(vx5, vt);
// _mm256_store_pd(out+offset+s+40, vx5);
// vx4 = _mm256_load_pd(out+offset+s+32);
vo20 = _mm256_load_pd(o+pos+offset+24);
vt = _mm256_mul_pd(vx4, vo20);
vc = _mm256_mul_pd(vt, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vt = _mm256_sub_pd(vt,vc);
// vx0 = _mm256_load_pd(out+offset+s+0);
vx4 = _mm256_sub_pd(vx0, vt);
_mm256_store_pd(out+offset+s+32, vx4);
vx0 = _mm256_add_pd(vx0, vt);
_mm256_store_pd(out+offset+s+0, vx0);
// vx5 = _mm256_load_pd(out+offset+s+40);
vo21 = _mm256_load_pd(o+pos+offset+32);
vt = _mm256_mul_pd(vx5, vo21);
vc = _mm256_mul_pd(vt, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vt = _mm256_sub_pd(vt,vc);
// vx1 = _mm256_load_pd(out+offset+s+8);
vx5 = _mm256_sub_pd(vx1, vt);
_mm256_store_pd(out+offset+s+40, vx5);
vx1 = _mm256_add_pd(vx1, vt);
_mm256_store_pd(out+offset+s+8, vx1);
// vx6 = _mm256_load_pd(out+offset+s+48);
vo22 = _mm256_load_pd(o+pos+offset+40);
vt = _mm256_mul_pd(vx6, vo22);
vc = _mm256_mul_pd(vt, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vt = _mm256_sub_pd(vt,vc);
// vx2 = _mm256_load_pd(out+offset+s+16);
vx6 = _mm256_sub_pd(vx2, vt);
_mm256_store_pd(out+offset+s+48, vx6);
vx2 = _mm256_add_pd(vx2, vt);
_mm256_store_pd(out+offset+s+16, vx2);
// vx7 = _mm256_load_pd(out+offset+s+56);
vo23 = _mm256_load_pd(o+pos+offset+48);
vt = _mm256_mul_pd(vx7, vo23);
vc = _mm256_mul_pd(vt, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vt = _mm256_sub_pd(vt,vc);
// vx3 = _mm256_load_pd(out+offset+s+24);
vx7 = _mm256_sub_pd(vx3, vt);
_mm256_store_pd(out+offset+s+56, vx7);
vx3 = _mm256_add_pd(vx3, vt);
_mm256_store_pd(out+offset+s+24, vx3);
}
}
pos += 56;
// m = 128, m=256, m=512 (3 levels merged)
for(offset=0;offset<64;offset+=4)
{
vo0 = _mm256_load_pd(o+pos+offset);
vo10 = _mm256_load_pd(o+pos+offset+64);
vo11 = _mm256_load_pd(o+pos+offset+128);
for(s = 0; s<POLY_DEG; s+=512)
{
vx1 = _mm256_load_pd(out+offset+s+64);
vt = _mm256_mul_pd(vx1, vo0);
vc = _mm256_mul_pd(vt, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vt = _mm256_sub_pd(vt,vc);
vx0 = _mm256_load_pd(out+offset+s+0);
vx1 = _mm256_sub_pd(vx0, vt);
//_mm256_store_pd(out+offset+s+64, vx1);
vx0 = _mm256_add_pd(vx0, vt);
//_mm256_store_pd(out+offset+s+0, vx0);
vx3 = _mm256_load_pd(out+offset+s+192);
vt = _mm256_mul_pd(vx3, vo0);
vc = _mm256_mul_pd(vt, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vt = _mm256_sub_pd(vt,vc);
vx2 = _mm256_load_pd(out+offset+s+128);
vx3 = _mm256_sub_pd(vx2, vt);
//_mm256_store_pd(out+offset+s+192, vx3);
vx2 = _mm256_add_pd(vx2, vt);
//_mm256_store_pd(out+offset+s+128, vx2);
vx5 = _mm256_load_pd(out+offset+s+320);
vt = _mm256_mul_pd(vx5, vo0);
vc = _mm256_mul_pd(vt, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vt = _mm256_sub_pd(vt,vc);
vx4 = _mm256_load_pd(out+offset+s+256);
vx5 = _mm256_sub_pd(vx4, vt);
//_mm256_store_pd(out+offset+s+320, vx5);
vx4 = _mm256_add_pd(vx4, vt);
//_mm256_store_pd(out+offset+s+256, vx4);
vx7 = _mm256_load_pd(out+offset+s+448);
vt = _mm256_mul_pd(vx7, vo0);
vc = _mm256_mul_pd(vt, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vt = _mm256_sub_pd(vt,vc);
vx6 = _mm256_load_pd(out+offset+s+384);
vx7 = _mm256_sub_pd(vx6, vt);
//_mm256_store_pd(out+offset+s+448, vx7);
vx6 = _mm256_add_pd(vx6, vt);
//_mm256_store_pd(out+offset+s+384, vx6);
//vx2 = _mm256_load_pd(out+offset+s+128);
vt = _mm256_mul_pd(vx2, vo10);
vc = _mm256_mul_pd(vt, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vt = _mm256_sub_pd(vt,vc);
//vx0 = _mm256_load_pd(out+offset+s+0);
vx2 = _mm256_sub_pd(vx0, vt);
//_mm256_store_pd(out+offset+s+128, vx2);
vx0 = _mm256_add_pd(vx0, vt);
//_mm256_store_pd(out+offset+s+0, vx0);
//vx3 = _mm256_load_pd(out+offset+s+192);
vt = _mm256_mul_pd(vx3, vo11);
vc = _mm256_mul_pd(vt, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vt = _mm256_sub_pd(vt,vc);
//vx1 = _mm256_load_pd(out+offset+s+64);
vx3 = _mm256_sub_pd(vx1, vt);
//_mm256_store_pd(out+offset+s+192, vx3);
vx1 = _mm256_add_pd(vx1, vt);
//_mm256_store_pd(out+offset+s+64, vx1);
//vx6 = _mm256_load_pd(out+offset+s+384);
vt = _mm256_mul_pd(vx6, vo10);
vc = _mm256_mul_pd(vt, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vt = _mm256_sub_pd(vt,vc);
//vx4 = _mm256_load_pd(out+offset+s+256);
vx6 = _mm256_sub_pd(vx4, vt);
//_mm256_store_pd(out+offset+s+384, vx6);
vx4 = _mm256_add_pd(vx4, vt);
//_mm256_store_pd(out+offset+s+256, vx4);
//vx7 = _mm256_load_pd(out+offset+s+448);
vt = _mm256_mul_pd(vx7, vo11);
vc = _mm256_mul_pd(vt, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vt = _mm256_sub_pd(vt,vc);
//vx5 = _mm256_load_pd(out+offset+s+320);
vx7 = _mm256_sub_pd(vx5, vt);
//_mm256_store_pd(out+offset+s+448, vx7);
vx5 = _mm256_add_pd(vx5, vt);
//_mm256_store_pd(out+offset+s+320, vx5);
//vx4 = _mm256_load_pd(out+offset+s+256);
vo20 = _mm256_load_pd(o+pos+offset+192);
vt = _mm256_mul_pd(vx4, vo20);
vc = _mm256_mul_pd(vt, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vt = _mm256_sub_pd(vt,vc);
//vx0 = _mm256_load_pd(out+offset+s+0);
vx4 = _mm256_sub_pd(vx0, vt);
_mm256_store_pd(out+offset+s+256, vx4);
vx0 = _mm256_add_pd(vx0, vt);
_mm256_store_pd(out+offset+s+0, vx0);
//vx5 = _mm256_load_pd(out+offset+s+320);
vo21 = _mm256_load_pd(o+pos+offset+256);
vt = _mm256_mul_pd(vx5, vo21);
vc = _mm256_mul_pd(vt, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vt = _mm256_sub_pd(vt,vc);
//vx1 = _mm256_load_pd(out+offset+s+64);
vx5 = _mm256_sub_pd(vx1, vt);
_mm256_store_pd(out+offset+s+320, vx5);
vx1 = _mm256_add_pd(vx1, vt);
_mm256_store_pd(out+offset+s+64, vx1);
//vx6 = _mm256_load_pd(out+offset+s+384);
vo22 = _mm256_load_pd(o+pos+offset+320);
vt = _mm256_mul_pd(vx6, vo22);
vc = _mm256_mul_pd(vt, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vt = _mm256_sub_pd(vt,vc);
//vx2 = _mm256_load_pd(out+offset+s+128);
vx6 = _mm256_sub_pd(vx2, vt);
_mm256_store_pd(out+offset+s+384, vx6);
vx2 = _mm256_add_pd(vx2, vt);
_mm256_store_pd(out+offset+s+128, vx2);
//vx7 = _mm256_load_pd(out+offset+s+448);
vo23 = _mm256_load_pd(o+pos+offset+384);
vt = _mm256_mul_pd(vx7, vo23);
vc = _mm256_mul_pd(vt, vpinv);
vc = _mm256_round_pd(vc,0x08);
vc = _mm256_mul_pd(vc, vp);
vt = _mm256_sub_pd(vt,vc);
//vx3 = _mm256_load_pd(out+offset+s+192);
vx7 = _mm256_sub_pd(vx3, vt);
_mm256_store_pd(out+offset+s+448, vx7);
vx3 = _mm256_add_pd(vx3, vt);
_mm256_store_pd(out+offset+s+192, vx3);
}
}
}
void AVX2FMA3DNoise(Vector3d& result, const Vector3d& EPoint)
{
#if CHECK_FUNCTIONAL
Vector3d param(EPoint);
#endif
AVX2TABLETYPE *mp;
// TODO FIXME - global statistics reference
// Stats[Calls_To_DNoise]++;
const __m256d ONE_PD = _mm256_set1_pd(1.0);
const __m128i short_si128 = _mm_set1_epi32(0xffff);
const __m256d xyzn = _mm256_setr_pd(EPoint[X], EPoint[Y], EPoint[Z], 0);
const __m256d epsy = _mm256_set1_pd(1.0 - EPSILON);
const __m256d xyzn_e = _mm256_sub_pd(xyzn, epsy);
const __m128i tmp_xyzn = _mm256_cvttpd_epi32(_mm256_blendv_pd(xyzn, xyzn_e, xyzn));
const __m128i noise_min_xyzn = _mm_setr_epi32(NOISE_MINX, NOISE_MINY, NOISE_MINZ, 0);
const __m256d xyz_ixyzn = _mm256_sub_pd(xyzn, _mm256_cvtepi32_pd(tmp_xyzn));
const __m256d xyz_jxyzn = _mm256_sub_pd(xyz_ixyzn, ONE_PD);
const __m128i i_xyzn = _mm_and_si128(_mm_sub_epi32(tmp_xyzn, noise_min_xyzn),
_mm_set1_epi32(0xfff));
const __m256d s_xyzn = _mm256_mul_pd(xyz_ixyzn,
_mm256_mul_pd(xyz_ixyzn,
_mm256_sub_pd(_mm256_set1_pd(3.0),
_mm256_add_pd(xyz_ixyzn, xyz_ixyzn))));
const __m256d t_xyzn = _mm256_sub_pd(ONE_PD, s_xyzn);
const __m256d txtysxsy = _mm256_permute2f128_pd(t_xyzn, s_xyzn, 0x20);
const __m256d txsxtxsx = PERMUTE4x64(txtysxsy, _MM_SHUFFLE(2, 0, 2, 0));
const __m256d tytysysy = PERMUTE4x64(txtysxsy, _MM_SHUFFLE(3, 3, 1, 1));
const __m256d txtysxtytxsysxsy = _mm256_mul_pd(txsxtxsx, tytysysy);
const __m256d incrsump_s1 = _mm256_mul_pd(txtysxtytxsysxsy, PERMUTE4x64(t_xyzn, _MM_SHUFFLE(2, 2, 2, 2)));
const __m256d incrsump_s2 = _mm256_mul_pd(txtysxtytxsysxsy, PERMUTE4x64(s_xyzn, _MM_SHUFFLE(2, 2, 2, 2)));
int ints[4];
_mm_storeu_si128((__m128i*)(ints), i_xyzn);
const int ixiy_hash = Hash2d(ints[0], ints[1]);
const int jxiy_hash = Hash2d(ints[0] + 1, ints[1]);
const int ixjy_hash = Hash2d(ints[0], ints[1] + 1);
const int jxjy_hash = Hash2d(ints[0] + 1, ints[1] + 1);
const int iz = ints[2];
const __m256d iii = _mm256_blend_pd(PERMUTE4x64(xyz_ixyzn, _MM_SHUFFLE(2, 1, 0, 0)), _mm256_set_pd(0, 0, 0, 0.5), 0x1);
const __m256d jjj = _mm256_blend_pd(PERMUTE4x64(xyz_jxyzn, _MM_SHUFFLE(2, 1, 0, 0)), _mm256_set_pd(0, 0, 0, 0.5), 0x1);
__m256d ss;
__m256d blend;
__m256d x = _mm256_setzero_pd(), y = _mm256_setzero_pd(), z = _mm256_setzero_pd();
mp = &AVX2RTable[Hash1dRTableIndexAVX(ixiy_hash, iz)];
ss = PERMUTE4x64(incrsump_s1, _MM_SHUFFLE(0, 0, 0, 0));
// blend = _mm256_blend_pd(iii, jjj, 0);
INCSUMAVX_VECTOR(mp, ss, iii);
mp = &AVX2RTable[Hash1dRTableIndexAVX(jxiy_hash, iz)];
ss = PERMUTE4x64(incrsump_s1, _MM_SHUFFLE(1, 1, 1, 1));
blend = _mm256_blend_pd(iii, jjj, 2);
INCSUMAVX_VECTOR(mp, ss, blend);
mp = &AVX2RTable[Hash1dRTableIndexAVX(jxjy_hash, iz)];
ss = PERMUTE4x64(incrsump_s1, _MM_SHUFFLE(3, 3, 3, 3));
blend = _mm256_blend_pd(iii, jjj, 6);
INCSUMAVX_VECTOR(mp, ss, blend);
mp = &AVX2RTable[Hash1dRTableIndexAVX(ixjy_hash, iz)];
ss = PERMUTE4x64(incrsump_s1, _MM_SHUFFLE(2, 2, 2, 2));
blend = _mm256_blend_pd(iii, jjj, 4);
INCSUMAVX_VECTOR(mp, ss, blend);
mp = &AVX2RTable[Hash1dRTableIndexAVX(ixjy_hash, iz + 1)];
ss = PERMUTE4x64(incrsump_s2, _MM_SHUFFLE(2, 2, 2, 2));
blend = _mm256_blend_pd(iii, jjj, 12);
INCSUMAVX_VECTOR(mp, ss, blend);
mp = &AVX2RTable[Hash1dRTableIndexAVX(jxjy_hash, iz + 1)];
ss = PERMUTE4x64(incrsump_s2, _MM_SHUFFLE(3, 3, 3, 3));
// blend = _mm256_blend_pd(iii, jjj, 14);
INCSUMAVX_VECTOR(mp, ss, jjj);
mp = &AVX2RTable[Hash1dRTableIndexAVX(jxiy_hash, iz + 1)];
ss = PERMUTE4x64(incrsump_s2, _MM_SHUFFLE(1, 1, 1, 1));
blend = _mm256_blend_pd(iii, jjj, 10);
INCSUMAVX_VECTOR(mp, ss, blend);
mp = &AVX2RTable[Hash1dRTableIndexAVX(ixiy_hash, iz + 1)];
ss = PERMUTE4x64(incrsump_s2, _MM_SHUFFLE(0, 0, 0, 0));
blend = _mm256_blend_pd(iii, jjj, 8);
INCSUMAVX_VECTOR(mp, ss, blend);
__m256d xy = _mm256_hadd_pd(x,y);
__m128d xy_up = _mm256_extractf128_pd(xy,1);
xy_up = _mm_add_pd(_mm256_castpd256_pd128(xy),xy_up);
_mm_storeu_pd(&result[X],xy_up);
__m128d z_up = _mm256_extractf128_pd(z,1);
z_up = _mm_add_pd(_mm256_castpd256_pd128(z),z_up);
z_up = _mm_hadd_pd(z_up,z_up);
result[Z] = _mm_cvtsd_f64(z_up);
#if CHECK_FUNCTIONAL
{
Vector3d portable_res;
PortableDNoise(portable_res , param);
if (fabs(portable_res[X] - result[X]) >= EPSILON)
{
throw POV_EXCEPTION_STRING("DNoise X error");
}
if (fabs(portable_res[Y] - result[Y]) >= EPSILON)
{
throw POV_EXCEPTION_STRING("DNoise Y error");
}
if (fabs(portable_res[Z] - result[Z]) >= EPSILON)
{
throw POV_EXCEPTION_STRING("DNoise Z error");
}
}
#endif
_mm256_zeroupper();
return;
}
void kernel_dgemv_t_8_lib4(int kmax, double *A, int sda, double *x, double *y, int alg)
{
if(kmax<=0)
return;
const int lda = 4;
__builtin_prefetch( A + 0*lda );
__builtin_prefetch( A + 2*lda );
__builtin_prefetch( A + 4*lda );
__builtin_prefetch( A + 6*lda );
double *tA, *tx;
int k;
int ka = kmax; // number from aligned positon
__m256d
aaxx_temp,
a_00_10_20_30, a_01_11_21_31, a_02_12_22_32, a_03_13_23_33,
x_0_1_2_3,
y_00, y_11, y_22, y_33, y_44, y_55, y_66, y_77;
__m128d
ax_temp,
a_00_10, a_01_11, a_02_12, a_03_13,
x_0_1,
y_0, y_1, y_2, y_3, y_4, y_5, y_6, y_7;
y_00 = _mm256_setzero_pd();
y_11 = _mm256_setzero_pd();
y_22 = _mm256_setzero_pd();
y_33 = _mm256_setzero_pd();
y_44 = _mm256_setzero_pd();
y_55 = _mm256_setzero_pd();
y_66 = _mm256_setzero_pd();
y_77 = _mm256_setzero_pd();
y_0 = _mm256_castpd256_pd128(y_00);
y_1 = _mm256_castpd256_pd128(y_11);
y_2 = _mm256_castpd256_pd128(y_22);
y_3 = _mm256_castpd256_pd128(y_33);
y_4 = _mm256_castpd256_pd128(y_44);
y_5 = _mm256_castpd256_pd128(y_55);
y_6 = _mm256_castpd256_pd128(y_66);
y_7 = _mm256_castpd256_pd128(y_77);
k = lda*(ka/lda);
tA = A + (ka/lda)*sda*lda;
tx = x + (ka/lda)*lda;
if(ka-k>0) // it can be only ka-k = {1, 2, 3}
{
if((ka-k)>=2)
{
x_0_1 = _mm_load_pd( &tx[0] );
a_00_10 = _mm_load_pd( &tA[0+lda*0] );
a_01_11 = _mm_load_pd( &tA[0+lda*1] );
a_02_12 = _mm_load_pd( &tA[0+lda*2] );
a_03_13 = _mm_load_pd( &tA[0+lda*3] );
ax_temp = _mm_mul_pd( a_00_10, x_0_1 );
y_0 = _mm_add_pd (y_0, ax_temp );
ax_temp = _mm_mul_pd( a_01_11, x_0_1 );
y_1 = _mm_add_pd (y_1, ax_temp );
ax_temp = _mm_mul_pd( a_02_12, x_0_1 );
y_2 = _mm_add_pd (y_2, ax_temp );
ax_temp = _mm_mul_pd( a_03_13, x_0_1 );
y_3 = _mm_add_pd (y_3, ax_temp );
a_00_10 = _mm_load_pd( &tA[0+lda*4] );
a_01_11 = _mm_load_pd( &tA[0+lda*5] );
a_02_12 = _mm_load_pd( &tA[0+lda*6] );
a_03_13 = _mm_load_pd( &tA[0+lda*7] );
ax_temp = _mm_mul_pd( a_00_10, x_0_1 );
y_4 = _mm_add_pd (y_4, ax_temp );
ax_temp = _mm_mul_pd( a_01_11, x_0_1 );
y_5 = _mm_add_pd (y_5, ax_temp );
ax_temp = _mm_mul_pd( a_02_12, x_0_1 );
y_6 = _mm_add_pd (y_6, ax_temp );
ax_temp = _mm_mul_pd( a_03_13, x_0_1 );
y_7 = _mm_add_pd (y_7, ax_temp );
tA += 2;
tx += 2;
k+=2;
}
if((ka-k)==1)
{
x_0_1 = _mm_load_sd( &tx[0] );
a_00_10 = _mm_load_sd( &tA[0+lda*0] );
a_01_11 = _mm_load_sd( &tA[0+lda*1] );
a_02_12 = _mm_load_sd( &tA[0+lda*2] );
a_03_13 = _mm_load_sd( &tA[0+lda*3] );
ax_temp = _mm_mul_sd( a_00_10, x_0_1 );
y_0 = _mm_add_sd (y_0, ax_temp );
ax_temp = _mm_mul_sd( a_01_11, x_0_1 );
y_1 = _mm_add_sd (y_1, ax_temp );
ax_temp = _mm_mul_sd( a_02_12, x_0_1 );
y_2 = _mm_add_sd (y_2, ax_temp );
ax_temp = _mm_mul_sd( a_03_13, x_0_1 );
y_3 = _mm_add_sd (y_3, ax_temp );
a_00_10 = _mm_load_sd( &tA[0+lda*4] );
a_01_11 = _mm_load_sd( &tA[0+lda*5] );
a_02_12 = _mm_load_sd( &tA[0+lda*6] );
a_03_13 = _mm_load_sd( &tA[0+lda*7] );
ax_temp = _mm_mul_sd( a_00_10, x_0_1 );
y_4 = _mm_add_sd (y_4, ax_temp );
ax_temp = _mm_mul_sd( a_01_11, x_0_1 );
y_5 = _mm_add_sd (y_5, ax_temp );
ax_temp = _mm_mul_sd( a_02_12, x_0_1 );
y_6 = _mm_add_sd (y_6, ax_temp );
ax_temp = _mm_mul_sd( a_03_13, x_0_1 );
y_7 = _mm_add_sd (y_7, ax_temp );
tA += 1;
tx += 1;
k++;
}
}
y_00 = _mm256_castpd128_pd256(y_0);
y_11 = _mm256_castpd128_pd256(y_1);
y_22 = _mm256_castpd128_pd256(y_2);
y_33 = _mm256_castpd128_pd256(y_3);
y_44 = _mm256_castpd128_pd256(y_4);
y_55 = _mm256_castpd128_pd256(y_5);
y_66 = _mm256_castpd128_pd256(y_6);
y_77 = _mm256_castpd128_pd256(y_7);
k=0;
for(; k<ka-7; k+=8)
{
__builtin_prefetch( A + sda*lda + 0*lda );
__builtin_prefetch( A + sda*lda + 2*lda );
x_0_1_2_3 = _mm256_loadu_pd( &x[0] );
a_00_10_20_30 = _mm256_load_pd( &A[0+lda*0] );
a_01_11_21_31 = _mm256_load_pd( &A[0+lda*1] );
a_02_12_22_32 = _mm256_load_pd( &A[0+lda*2] );
a_03_13_23_33 = _mm256_load_pd( &A[0+lda*3] );
aaxx_temp = _mm256_mul_pd( a_00_10_20_30, x_0_1_2_3 );
y_00 = _mm256_add_pd( y_00, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_01_11_21_31, x_0_1_2_3 );
y_11 = _mm256_add_pd( y_11, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_02_12_22_32, x_0_1_2_3 );
y_22 = _mm256_add_pd( y_22, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_03_13_23_33, x_0_1_2_3 );
y_33 = _mm256_add_pd( y_33, aaxx_temp );
__builtin_prefetch( A + sda*lda + 4*lda );
__builtin_prefetch( A + sda*lda + 6*lda );
a_00_10_20_30 = _mm256_load_pd( &A[0+lda*4] );
a_01_11_21_31 = _mm256_load_pd( &A[0+lda*5] );
a_02_12_22_32 = _mm256_load_pd( &A[0+lda*6] );
a_03_13_23_33 = _mm256_load_pd( &A[0+lda*7] );
aaxx_temp = _mm256_mul_pd( a_00_10_20_30, x_0_1_2_3 );
y_44 = _mm256_add_pd( y_44, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_01_11_21_31, x_0_1_2_3 );
y_55 = _mm256_add_pd( y_55, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_02_12_22_32, x_0_1_2_3 );
y_66 = _mm256_add_pd( y_66, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_03_13_23_33, x_0_1_2_3 );
y_77 = _mm256_add_pd( y_77, aaxx_temp );
A += 4 + (sda-1)*lda;
x += 4;
__builtin_prefetch( A + sda*lda + 0*lda );
__builtin_prefetch( A + sda*lda + 2*lda );
x_0_1_2_3 = _mm256_loadu_pd( &x[0] );
a_00_10_20_30 = _mm256_load_pd( &A[0+lda*0] );
a_01_11_21_31 = _mm256_load_pd( &A[0+lda*1] );
a_02_12_22_32 = _mm256_load_pd( &A[0+lda*2] );
a_03_13_23_33 = _mm256_load_pd( &A[0+lda*3] );
aaxx_temp = _mm256_mul_pd( a_00_10_20_30, x_0_1_2_3 );
y_00 = _mm256_add_pd( y_00, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_01_11_21_31, x_0_1_2_3 );
y_11 = _mm256_add_pd( y_11, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_02_12_22_32, x_0_1_2_3 );
y_22 = _mm256_add_pd( y_22, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_03_13_23_33, x_0_1_2_3 );
y_33 = _mm256_add_pd( y_33, aaxx_temp );
__builtin_prefetch( A + sda*lda + 4*lda );
__builtin_prefetch( A + sda*lda + 6*lda );
a_00_10_20_30 = _mm256_load_pd( &A[0+lda*4] );
a_01_11_21_31 = _mm256_load_pd( &A[0+lda*5] );
a_02_12_22_32 = _mm256_load_pd( &A[0+lda*6] );
a_03_13_23_33 = _mm256_load_pd( &A[0+lda*7] );
aaxx_temp = _mm256_mul_pd( a_00_10_20_30, x_0_1_2_3 );
y_44 = _mm256_add_pd( y_44, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_01_11_21_31, x_0_1_2_3 );
y_55 = _mm256_add_pd( y_55, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_02_12_22_32, x_0_1_2_3 );
y_66 = _mm256_add_pd( y_66, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_03_13_23_33, x_0_1_2_3 );
y_77 = _mm256_add_pd( y_77, aaxx_temp );
A += 4 + (sda-1)*lda;
x += 4;
}
for(; k<ka-3; k+=4)
{
__builtin_prefetch( A + sda*lda + 0*lda );
__builtin_prefetch( A + sda*lda + 2*lda );
x_0_1_2_3 = _mm256_loadu_pd( &x[0] );
a_00_10_20_30 = _mm256_load_pd( &A[0+lda*0] );
a_01_11_21_31 = _mm256_load_pd( &A[0+lda*1] );
a_02_12_22_32 = _mm256_load_pd( &A[0+lda*2] );
a_03_13_23_33 = _mm256_load_pd( &A[0+lda*3] );
aaxx_temp = _mm256_mul_pd( a_00_10_20_30, x_0_1_2_3 );
y_00 = _mm256_add_pd( y_00, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_01_11_21_31, x_0_1_2_3 );
y_11 = _mm256_add_pd( y_11, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_02_12_22_32, x_0_1_2_3 );
y_22 = _mm256_add_pd( y_22, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_03_13_23_33, x_0_1_2_3 );
y_33 = _mm256_add_pd( y_33, aaxx_temp );
__builtin_prefetch( A + sda*lda + 4*lda );
__builtin_prefetch( A + sda*lda + 6*lda );
a_00_10_20_30 = _mm256_load_pd( &A[0+lda*4] );
a_01_11_21_31 = _mm256_load_pd( &A[0+lda*5] );
a_02_12_22_32 = _mm256_load_pd( &A[0+lda*6] );
a_03_13_23_33 = _mm256_load_pd( &A[0+lda*7] );
aaxx_temp = _mm256_mul_pd( a_00_10_20_30, x_0_1_2_3 );
y_44 = _mm256_add_pd( y_44, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_01_11_21_31, x_0_1_2_3 );
y_55 = _mm256_add_pd( y_55, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_02_12_22_32, x_0_1_2_3 );
y_66 = _mm256_add_pd( y_66, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_03_13_23_33, x_0_1_2_3 );
y_77 = _mm256_add_pd( y_77, aaxx_temp );
A += 4 + (sda-1)*lda;
x += 4;
}
__m256d
y_0_1_2_3, y_4_5_6_7;
y_00 = _mm256_hadd_pd(y_00, y_11);
y_22 = _mm256_hadd_pd(y_22, y_33);
y_44 = _mm256_hadd_pd(y_44, y_55);
y_66 = _mm256_hadd_pd(y_66, y_77);
y_11 = _mm256_permute2f128_pd(y_22, y_00, 2 );
y_00 = _mm256_permute2f128_pd(y_22, y_00, 19);
y_55 = _mm256_permute2f128_pd(y_66, y_44, 2 );
y_44 = _mm256_permute2f128_pd(y_66, y_44, 19);
y_00 = _mm256_add_pd( y_00, y_11 );
y_44 = _mm256_add_pd( y_44, y_55 );
if(alg==0)
{
_mm256_storeu_pd(&y[0], y_00);
_mm256_storeu_pd(&y[4], y_44);
}
else if(alg==1)
{
y_0_1_2_3 = _mm256_loadu_pd( &y[0] );
y_4_5_6_7 = _mm256_loadu_pd( &y[4] );
y_0_1_2_3 = _mm256_add_pd( y_0_1_2_3, y_00 );
y_4_5_6_7 = _mm256_add_pd( y_4_5_6_7, y_44 );
_mm256_storeu_pd(&y[0], y_0_1_2_3);
_mm256_storeu_pd(&y[4], y_4_5_6_7);
}
else // alg==-1
{
y_0_1_2_3 = _mm256_loadu_pd( &y[0] );
y_4_5_6_7 = _mm256_loadu_pd( &y[4] );
y_0_1_2_3 = _mm256_sub_pd( y_0_1_2_3, y_00 );
y_4_5_6_7 = _mm256_sub_pd( y_4_5_6_7, y_44 );
_mm256_storeu_pd(&y[0], y_0_1_2_3);
_mm256_storeu_pd(&y[4], y_4_5_6_7);
}
}
/*
Naive implementation of Matrix Matrix Multiplication
@param A input matrix
@param B input matrix
@param C output matrix
*/
inline
void naive(const Matrix& A, const Matrix& B, Matrix& C){
//preload dimensions for faster access
int dimM = C.getDimM();
int dimN = C.getDimN();
int dimL = A.getDimN();
for (int m = 0; m < dimM; m+=4){ ///rows of c
for (int n = 0; n < dimN; n+=4){ ///cols of c
//do calculation of a 4x4 block
//std::cout << m << "\t" << n << std::endl;
__m256d* pA = A.get(m, 0);
__m256d* pB = A.get(m+1, 0);
__m256d* pC = A.get(m+2, 0);
__m256d* pD = A.get(m+3, 0);
__m256d* pK = B.getT(0, n);
__m256d* pL = B.getT(0, n+1);
__m256d* pM = B.getT(0, n+2);
__m256d* pN = B.getT(0, n+3);
//std::cout << pA << "\t" << pB << "\t" << pC << "\t" << pD << std::endl;
__m256d K = _mm256_setzero_pd();
__m256d L = _mm256_setzero_pd();
__m256d M = _mm256_setzero_pd();
__m256d N = _mm256_setzero_pd();
__m256d O = _mm256_setzero_pd();
__m256d P = _mm256_setzero_pd();
__m256d Q = _mm256_setzero_pd();
__m256d R = _mm256_setzero_pd();
__m256d S = _mm256_setzero_pd();
__m256d T = _mm256_setzero_pd();
__m256d U = _mm256_setzero_pd();
__m256d V = _mm256_setzero_pd();
__m256d W = _mm256_setzero_pd();
__m256d X = _mm256_setzero_pd();
__m256d Y = _mm256_setzero_pd();
__m256d Z = _mm256_setzero_pd();
for (int l = 0; l < dimL; l+=4){
//std::cout <<"mul" << std::endl;
K = K + (*pA) * (*pK);
L = L + (*pA) * (*pL);
M = M + (*pA) * (*pM);
N = N + (*pA) * (*pN);
O = O + (*pB) * (*pK);
P = P + (*pB) * (*pL);
Q = Q + (*pB) * (*pM);
R = R + (*pB) * (*pN);
S = S + (*pC) * (*pK);
T = T + (*pC) * (*pL);
U = U + (*pC) * (*pM);
V = V + (*pC) * (*pN);
W = W + (*pD) * (*pK);
X = X + (*pD) * (*pL);
Y = Y + (*pD) * (*pM);
Z = Z + (*pD) * (*pN);
//std::cout << "inc" <<std::endl;
pA++;
pB++;
pC++;
pD++;
pK++;
pL++;
pM++;
pN++;
}
// {a[0]+a[1], b[0]+b[1], a[2]+a[3], b[2]+b[3]}
__m256d sumab = _mm256_hadd_pd(K, L);
// {c[0]+c[1], d[0]+d[1], c[2]+c[3], d[2]+d[3]}
__m256d sumcd = _mm256_hadd_pd(M, N);
// {a[0]+a[1], b[0]+b[1], c[2]+c[3], d[2]+d[3]}
__m256d blend = _mm256_blend_pd(sumab, sumcd, 0b1100);
// {a[2]+a[3], b[2]+b[3], c[0]+c[1], d[0]+d[1]}
__m256d perm = _mm256_permute2f128_pd(sumab, sumcd, 0x21);
__m256d sum = _mm256_add_pd(perm, blend);
C.set(m, n, sum);
//C(m , n) = K[0] + K[1] + K[2] + K[3];
//C(m , n+1) = L[0] + L[1] + L[2] + L[3];
//C(m , n+2) = M[0] + M[1] + M[2] + M[3];
//C(m , n+3) = N[0] + N[1] + N[2] + N[3];
// {a[0]+a[1], b[0]+b[1], a[2]+a[3], b[2]+b[3]}
sumab = _mm256_hadd_pd(O, P);
// {c[0]+c[1], d[0]+d[1], c[2]+c[3], d[2]+d[3]}
sumcd = _mm256_hadd_pd(Q, R);
// {a[0]+a[1], b[0]+b[1], c[2]+c[3], d[2]+d[3]}
blend = _mm256_blend_pd(sumab, sumcd, 0b1100);
// {a[2]+a[3], b[2]+b[3], c[0]+c[1], d[0]+d[1]}
perm = _mm256_permute2f128_pd(sumab, sumcd, 0x21);
sum = _mm256_add_pd(perm, blend);
C.set(m+1, n, sum);
//C(m+1, n ) = O[0] + O[1] + O[2] + O[3];
//C(m+1, n+1) = P[0] + P[1] + P[2] + P[3];
//C(m+1, n+2) = Q[0] + Q[1] + Q[2] + Q[3];
//C(m+1, n+3) = R[0] + R[1] + R[2] + R[3];
// {a[0]+a[1], b[0]+b[1], a[2]+a[3], b[2]+b[3]}
sumab = _mm256_hadd_pd(S, T);
// {c[0]+c[1], d[0]+d[1], c[2]+c[3], d[2]+d[3]}
sumcd = _mm256_hadd_pd(U, V);
// {a[0]+a[1], b[0]+b[1], c[2]+c[3], d[2]+d[3]}
blend = _mm256_blend_pd(sumab, sumcd, 0b1100);
// {a[2]+a[3], b[2]+b[3], c[0]+c[1], d[0]+d[1]}
perm = _mm256_permute2f128_pd(sumab, sumcd, 0x21);
sum = _mm256_add_pd(perm, blend);
C.set(m+2, n, sum);
//C(m+2, n ) = S[0] + S[1] + S[2] + S[3];
//C(m+2, n+1) = T[0] + T[1] + T[2] + T[3];
//C(m+2, n+2) = U[0] + U[1] + U[2] + U[3];
//C(m+2, n+3) = V[0] + V[1] + V[2] + V[3];
// {a[0]+a[1], b[0]+b[1], a[2]+a[3], b[2]+b[3]}
sumab = _mm256_hadd_pd(W, X);
// {c[0]+c[1], d[0]+d[1], c[2]+c[3], d[2]+d[3]}
sumcd = _mm256_hadd_pd(Y, Z);
// {a[0]+a[1], b[0]+b[1], c[2]+c[3], d[2]+d[3]}
blend = _mm256_blend_pd(sumab, sumcd, 0b1100);
// {a[2]+a[3], b[2]+b[3], c[0]+c[1], d[0]+d[1]}
perm = _mm256_permute2f128_pd(sumab, sumcd, 0x21);
sum = _mm256_add_pd(perm, blend);
C.set(m+3, n, sum);
//C(m+3, n ) = W[0] + W[1] + W[2] + W[3];
//C(m+3, n+1) = X[0] + X[1] + X[2] + X[3];
//C(m+3, n+2) = Y[0] + Y[1] + Y[2] + Y[3];
//C(m+3, n+3) = Z[0] + Z[1] + Z[2] + Z[3];
}
}
}
// it moves vertically across blocks
void kernel_dtrmv_u_t_8_lib4(int kmax, double *A, int sda, double *x, double *y, int alg)
{
/* if(kmax<=0) */
/* return;*/
const int lda = 4;
/* __builtin_prefetch( A + 0*lda );*/
/* __builtin_prefetch( A + 2*lda );*/
/* __builtin_prefetch( A + 4*lda );*/
/* __builtin_prefetch( A + 6*lda );*/
/* double *tA, *tx;*/
int k;
/* int ka = kmax-kna; // number from aligned positon*/
__m256d
zeros,
tmp0, tmp1,
a_00_10_20_30, a_01_11_21_31, a_02_12_22_32, a_03_13_23_33,
x_0_1_2_3,
y_00, y_11, y_22, y_33, y_44, y_55, y_66, y_77;
/* __m128d*/
/* ax_temp,*/
/* a_00_10, a_01_11, a_02_12, a_03_13,*/
/* x_0_1,*/
/* y_0, y_1, y_2, y_3, y_4, y_5, y_6, y_7;*/
y_00 = _mm256_setzero_pd();
y_11 = _mm256_setzero_pd();
y_22 = _mm256_setzero_pd();
y_33 = _mm256_setzero_pd();
y_44 = _mm256_setzero_pd();
y_55 = _mm256_setzero_pd();
y_66 = _mm256_setzero_pd();
y_77 = _mm256_setzero_pd();
k=0;
for(; k<kmax-7; k+=8)
{
/* __builtin_prefetch( A + sda*lda + 0*lda );*/
/* __builtin_prefetch( A + sda*lda + 2*lda );*/
x_0_1_2_3 = _mm256_loadu_pd( &x[0] );
a_00_10_20_30 = _mm256_load_pd( &A[0+lda*0] );
a_01_11_21_31 = _mm256_load_pd( &A[0+lda*1] );
a_02_12_22_32 = _mm256_load_pd( &A[0+lda*2] );
a_03_13_23_33 = _mm256_load_pd( &A[0+lda*3] );
tmp0 = _mm256_mul_pd( a_00_10_20_30, x_0_1_2_3 );
tmp1 = _mm256_mul_pd( a_01_11_21_31, x_0_1_2_3 );
y_00 = _mm256_add_pd( y_00, tmp0 );
y_11 = _mm256_add_pd( y_11, tmp1 );
tmp0 = _mm256_mul_pd( a_02_12_22_32, x_0_1_2_3 );
tmp1 = _mm256_mul_pd( a_03_13_23_33, x_0_1_2_3 );
y_22 = _mm256_add_pd( y_22, tmp0 );
y_33 = _mm256_add_pd( y_33, tmp1 );
/* __builtin_prefetch( A + sda*lda + 4*lda );*/
/* __builtin_prefetch( A + sda*lda + 6*lda );*/
a_00_10_20_30 = _mm256_load_pd( &A[0+lda*4] );
a_01_11_21_31 = _mm256_load_pd( &A[0+lda*5] );
a_02_12_22_32 = _mm256_load_pd( &A[0+lda*6] );
a_03_13_23_33 = _mm256_load_pd( &A[0+lda*7] );
tmp0 = _mm256_mul_pd( a_00_10_20_30, x_0_1_2_3 );
tmp1 = _mm256_mul_pd( a_01_11_21_31, x_0_1_2_3 );
y_44 = _mm256_add_pd( y_44, tmp0 );
y_55 = _mm256_add_pd( y_55, tmp1 );
tmp0 = _mm256_mul_pd( a_02_12_22_32, x_0_1_2_3 );
tmp1 = _mm256_mul_pd( a_03_13_23_33, x_0_1_2_3 );
y_66 = _mm256_add_pd( y_66, tmp0 );
y_77 = _mm256_add_pd( y_77, tmp1 );
A += 4 + (sda-1)*lda;
x += 4;
/* __builtin_prefetch( A + sda*lda + 0*lda );*/
/* __builtin_prefetch( A + sda*lda + 2*lda );*/
x_0_1_2_3 = _mm256_loadu_pd( &x[0] );
a_00_10_20_30 = _mm256_load_pd( &A[0+lda*0] );
a_01_11_21_31 = _mm256_load_pd( &A[0+lda*1] );
a_02_12_22_32 = _mm256_load_pd( &A[0+lda*2] );
a_03_13_23_33 = _mm256_load_pd( &A[0+lda*3] );
tmp0 = _mm256_mul_pd( a_00_10_20_30, x_0_1_2_3 );
tmp1 = _mm256_mul_pd( a_01_11_21_31, x_0_1_2_3 );
y_00 = _mm256_add_pd( y_00, tmp0 );
y_11 = _mm256_add_pd( y_11, tmp1 );
tmp0 = _mm256_mul_pd( a_02_12_22_32, x_0_1_2_3 );
tmp1 = _mm256_mul_pd( a_03_13_23_33, x_0_1_2_3 );
y_22 = _mm256_add_pd( y_22, tmp0 );
y_33 = _mm256_add_pd( y_33, tmp1 );
/* __builtin_prefetch( A + sda*lda + 4*lda );*/
/* __builtin_prefetch( A + sda*lda + 6*lda );*/
a_00_10_20_30 = _mm256_load_pd( &A[0+lda*4] );
a_01_11_21_31 = _mm256_load_pd( &A[0+lda*5] );
a_02_12_22_32 = _mm256_load_pd( &A[0+lda*6] );
a_03_13_23_33 = _mm256_load_pd( &A[0+lda*7] );
tmp0 = _mm256_mul_pd( a_00_10_20_30, x_0_1_2_3 );
tmp1 = _mm256_mul_pd( a_01_11_21_31, x_0_1_2_3 );
y_44 = _mm256_add_pd( y_44, tmp0 );
y_55 = _mm256_add_pd( y_55, tmp1 );
tmp0 = _mm256_mul_pd( a_02_12_22_32, x_0_1_2_3 );
tmp1 = _mm256_mul_pd( a_03_13_23_33, x_0_1_2_3 );
y_66 = _mm256_add_pd( y_66, tmp0 );
y_77 = _mm256_add_pd( y_77, tmp1 );
A += 4 + (sda-1)*lda;
x += 4;
}
/* for(; k<ka-3; k+=4)*/
/* {*/
/* __builtin_prefetch( A + sda*lda + 0*lda );*/
/* __builtin_prefetch( A + sda*lda + 2*lda );*/
/* x_0_1_2_3 = _mm256_loadu_pd( &x[0] );*/
/* a_00_10_20_30 = _mm256_load_pd( &A[0+lda*0] );*/
/* a_01_11_21_31 = _mm256_load_pd( &A[0+lda*1] );*/
/* a_02_12_22_32 = _mm256_load_pd( &A[0+lda*2] );*/
/* a_03_13_23_33 = _mm256_load_pd( &A[0+lda*3] );*/
/* */
/* aaxx_temp = _mm256_mul_pd( a_00_10_20_30, x_0_1_2_3 );*/
/* y_00 = _mm256_add_pd( y_00, aaxx_temp );*/
/* aaxx_temp = _mm256_mul_pd( a_01_11_21_31, x_0_1_2_3 );*/
/* y_11 = _mm256_add_pd( y_11, aaxx_temp );*/
/* aaxx_temp = _mm256_mul_pd( a_02_12_22_32, x_0_1_2_3 );*/
/* y_22 = _mm256_add_pd( y_22, aaxx_temp );*/
/* aaxx_temp = _mm256_mul_pd( a_03_13_23_33, x_0_1_2_3 );*/
/* y_33 = _mm256_add_pd( y_33, aaxx_temp );*/
/* */
/* __builtin_prefetch( A + sda*lda + 4*lda );*/
/* __builtin_prefetch( A + sda*lda + 6*lda );*/
/* a_00_10_20_30 = _mm256_load_pd( &A[0+lda*4] );*/
/* a_01_11_21_31 = _mm256_load_pd( &A[0+lda*5] );*/
/* a_02_12_22_32 = _mm256_load_pd( &A[0+lda*6] );*/
/* a_03_13_23_33 = _mm256_load_pd( &A[0+lda*7] );*/
/* */
/* aaxx_temp = _mm256_mul_pd( a_00_10_20_30, x_0_1_2_3 );*/
/* y_44 = _mm256_add_pd( y_44, aaxx_temp );*/
/* aaxx_temp = _mm256_mul_pd( a_01_11_21_31, x_0_1_2_3 );*/
/* y_55 = _mm256_add_pd( y_55, aaxx_temp );*/
/* aaxx_temp = _mm256_mul_pd( a_02_12_22_32, x_0_1_2_3 );*/
/* y_66 = _mm256_add_pd( y_66, aaxx_temp );*/
/* aaxx_temp = _mm256_mul_pd( a_03_13_23_33, x_0_1_2_3 );*/
/* y_77 = _mm256_add_pd( y_77, aaxx_temp );*/
/* A += 4 + (sda-1)*lda;*/
/* x += 4;*/
/* }*/
zeros = _mm256_setzero_pd();
// top triangle
x_0_1_2_3 = _mm256_loadu_pd( &x[0] );
a_00_10_20_30 = _mm256_load_pd( &A[0+lda*0] );
a_00_10_20_30 = _mm256_blend_pd( a_00_10_20_30, zeros, 0xe );
a_01_11_21_31 = _mm256_load_pd( &A[0+lda*1] );
a_01_11_21_31 = _mm256_blend_pd( a_01_11_21_31, zeros, 0xc );
a_02_12_22_32 = _mm256_load_pd( &A[0+lda*2] );
a_02_12_22_32 = _mm256_blend_pd( a_02_12_22_32, zeros, 0x8 );
a_03_13_23_33 = _mm256_load_pd( &A[0+lda*3] );
tmp0 = _mm256_mul_pd( a_00_10_20_30, x_0_1_2_3 );
tmp1 = _mm256_mul_pd( a_01_11_21_31, x_0_1_2_3 );
y_00 = _mm256_add_pd( y_00, tmp0 );
y_11 = _mm256_add_pd( y_11, tmp1 );
tmp0 = _mm256_mul_pd( a_02_12_22_32, x_0_1_2_3 );
tmp1 = _mm256_mul_pd( a_03_13_23_33, x_0_1_2_3 );
y_22 = _mm256_add_pd( y_22, tmp0 );
y_33 = _mm256_add_pd( y_33, tmp1 );
// top square
a_00_10_20_30 = _mm256_load_pd( &A[0+lda*4] );
a_01_11_21_31 = _mm256_load_pd( &A[0+lda*5] );
a_02_12_22_32 = _mm256_load_pd( &A[0+lda*6] );
a_03_13_23_33 = _mm256_load_pd( &A[0+lda*7] );
tmp0 = _mm256_mul_pd( a_00_10_20_30, x_0_1_2_3 );
tmp1 = _mm256_mul_pd( a_01_11_21_31, x_0_1_2_3 );
y_44 = _mm256_add_pd( y_44, tmp0 );
y_55 = _mm256_add_pd( y_55, tmp1 );
tmp0 = _mm256_mul_pd( a_02_12_22_32, x_0_1_2_3 );
tmp1 = _mm256_mul_pd( a_03_13_23_33, x_0_1_2_3 );
y_66 = _mm256_add_pd( y_66, tmp0 );
y_77 = _mm256_add_pd( y_77, tmp1 );
A += 4 + (sda-1)*lda;
x += 4;
// bottom triangle
x_0_1_2_3 = _mm256_loadu_pd( &x[0] );
a_00_10_20_30 = _mm256_load_pd( &A[0+lda*4] );
a_00_10_20_30 = _mm256_blend_pd( a_00_10_20_30, zeros, 0xe );
a_01_11_21_31 = _mm256_load_pd( &A[0+lda*5] );
a_01_11_21_31 = _mm256_blend_pd( a_01_11_21_31, zeros, 0xc );
a_02_12_22_32 = _mm256_load_pd( &A[0+lda*6] );
a_02_12_22_32 = _mm256_blend_pd( a_02_12_22_32, zeros, 0x8 );
a_03_13_23_33 = _mm256_load_pd( &A[0+lda*7] );
tmp0 = _mm256_mul_pd( a_00_10_20_30, x_0_1_2_3 );
tmp1 = _mm256_mul_pd( a_01_11_21_31, x_0_1_2_3 );
y_44 = _mm256_add_pd( y_44, tmp0 );
y_55 = _mm256_add_pd( y_55, tmp1 );
tmp0 = _mm256_mul_pd( a_02_12_22_32, x_0_1_2_3 );
tmp1 = _mm256_mul_pd( a_03_13_23_33, x_0_1_2_3 );
y_66 = _mm256_add_pd( y_66, tmp0 );
y_77 = _mm256_add_pd( y_77, tmp1 );
// store
__m256d
y_0_1_2_3, y_4_5_6_7;
y_00 = _mm256_hadd_pd(y_00, y_11);
y_22 = _mm256_hadd_pd(y_22, y_33);
y_44 = _mm256_hadd_pd(y_44, y_55);
y_66 = _mm256_hadd_pd(y_66, y_77);
y_11 = _mm256_permute2f128_pd(y_22, y_00, 2 );
y_00 = _mm256_permute2f128_pd(y_22, y_00, 19);
y_55 = _mm256_permute2f128_pd(y_66, y_44, 2 );
y_44 = _mm256_permute2f128_pd(y_66, y_44, 19);
y_00 = _mm256_add_pd( y_00, y_11 );
y_44 = _mm256_add_pd( y_44, y_55 );
if(alg==0)
{
_mm256_storeu_pd(&y[0], y_00);
_mm256_storeu_pd(&y[4], y_44);
}
else if(alg==1)
{
y_0_1_2_3 = _mm256_loadu_pd( &y[0] );
y_4_5_6_7 = _mm256_loadu_pd( &y[4] );
y_0_1_2_3 = _mm256_add_pd( y_0_1_2_3, y_00 );
y_4_5_6_7 = _mm256_add_pd( y_4_5_6_7, y_44 );
_mm256_storeu_pd(&y[0], y_0_1_2_3);
_mm256_storeu_pd(&y[4], y_4_5_6_7);
}
else // alg==-1
{
y_0_1_2_3 = _mm256_loadu_pd( &y[0] );
y_4_5_6_7 = _mm256_loadu_pd( &y[4] );
y_0_1_2_3 = _mm256_sub_pd( y_0_1_2_3, y_00 );
y_4_5_6_7 = _mm256_sub_pd( y_4_5_6_7, y_44 );
_mm256_storeu_pd(&y[0], y_0_1_2_3);
_mm256_storeu_pd(&y[4], y_4_5_6_7);
}
}
// it moves vertically across blocks
void kernel_dtrmv_u_t_4_lib4(int kmax, double *A, int sda, double *x, double *y, int alg)
{
/* if(kmax<=0) */
/* return;*/
const int lda = 4;
/* __builtin_prefetch( A + 0*lda );*/
/* __builtin_prefetch( A + 2*lda );*/
/* double *tA, *tx;*/
int k;
__m256d
zeros,
tmp0, tmp1,
a_00_10_20_30, a_01_11_21_31, a_02_12_22_32, a_03_13_23_33,
x_0_1_2_3,
y_00, y_11, y_22, y_33;
y_00 = _mm256_setzero_pd();
y_11 = _mm256_setzero_pd();
y_22 = _mm256_setzero_pd();
y_33 = _mm256_setzero_pd();
k=0;
for(; k<kmax-7; k+=8)
{
/* __builtin_prefetch( A + sda*lda + 0*lda );*/
/* __builtin_prefetch( A + sda*lda + 2*lda );*/
x_0_1_2_3 = _mm256_loadu_pd( &x[0] );
a_00_10_20_30 = _mm256_load_pd( &A[0+lda*0] );
a_01_11_21_31 = _mm256_load_pd( &A[0+lda*1] );
a_02_12_22_32 = _mm256_load_pd( &A[0+lda*2] );
a_03_13_23_33 = _mm256_load_pd( &A[0+lda*3] );
tmp0 = _mm256_mul_pd( a_00_10_20_30, x_0_1_2_3 );
tmp1 = _mm256_mul_pd( a_01_11_21_31, x_0_1_2_3 );
y_00 = _mm256_add_pd( y_00, tmp0 );
y_11 = _mm256_add_pd( y_11, tmp1 );
tmp0 = _mm256_mul_pd( a_02_12_22_32, x_0_1_2_3 );
tmp1 = _mm256_mul_pd( a_03_13_23_33, x_0_1_2_3 );
y_22 = _mm256_add_pd( y_22, tmp0 );
y_33 = _mm256_add_pd( y_33, tmp1 );
A += 4 + (sda-1)*lda;
x += 4;
/* __builtin_prefetch( A + sda*lda + 0*lda );*/
/* __builtin_prefetch( A + sda*lda + 2*lda );*/
x_0_1_2_3 = _mm256_loadu_pd( &x[0] );
a_00_10_20_30 = _mm256_load_pd( &A[0+lda*0] );
a_01_11_21_31 = _mm256_load_pd( &A[0+lda*1] );
a_02_12_22_32 = _mm256_load_pd( &A[0+lda*2] );
a_03_13_23_33 = _mm256_load_pd( &A[0+lda*3] );
tmp0 = _mm256_mul_pd( a_00_10_20_30, x_0_1_2_3 );
tmp1 = _mm256_mul_pd( a_01_11_21_31, x_0_1_2_3 );
y_00 = _mm256_add_pd( y_00, tmp0 );
y_11 = _mm256_add_pd( y_11, tmp1 );
tmp0 = _mm256_mul_pd( a_02_12_22_32, x_0_1_2_3 );
tmp1 = _mm256_mul_pd( a_03_13_23_33, x_0_1_2_3 );
y_22 = _mm256_add_pd( y_22, tmp0 );
y_33 = _mm256_add_pd( y_33, tmp1 );
A += 4 + (sda-1)*lda;
x += 4;
}
for(; k<kmax-3; k+=4)
{
/* __builtin_prefetch( A + sda*lda + 0*lda );*/
/* __builtin_prefetch( A + sda*lda + 2*lda );*/
x_0_1_2_3 = _mm256_loadu_pd( &x[0] );
a_00_10_20_30 = _mm256_load_pd( &A[0+lda*0] );
a_01_11_21_31 = _mm256_load_pd( &A[0+lda*1] );
a_02_12_22_32 = _mm256_load_pd( &A[0+lda*2] );
a_03_13_23_33 = _mm256_load_pd( &A[0+lda*3] );
tmp0 = _mm256_mul_pd( a_00_10_20_30, x_0_1_2_3 );
tmp1 = _mm256_mul_pd( a_01_11_21_31, x_0_1_2_3 );
y_00 = _mm256_add_pd( y_00, tmp0 );
y_11 = _mm256_add_pd( y_11, tmp1 );
tmp0 = _mm256_mul_pd( a_02_12_22_32, x_0_1_2_3 );
tmp1 = _mm256_mul_pd( a_03_13_23_33, x_0_1_2_3 );
y_22 = _mm256_add_pd( y_22, tmp0 );
y_33 = _mm256_add_pd( y_33, tmp1 );
A += 4 + (sda-1)*lda;
x += 4;
}
zeros = _mm256_setzero_pd();
x_0_1_2_3 = _mm256_loadu_pd( &x[0] );
a_00_10_20_30 = _mm256_load_pd( &A[0+lda*0] );
a_00_10_20_30 = _mm256_blend_pd( a_00_10_20_30, zeros, 0xe );
a_01_11_21_31 = _mm256_load_pd( &A[0+lda*1] );
a_01_11_21_31 = _mm256_blend_pd( a_01_11_21_31, zeros, 0xc );
a_02_12_22_32 = _mm256_load_pd( &A[0+lda*2] );
a_02_12_22_32 = _mm256_blend_pd( a_02_12_22_32, zeros, 0x8 );
a_03_13_23_33 = _mm256_load_pd( &A[0+lda*3] );
tmp0 = _mm256_mul_pd( a_00_10_20_30, x_0_1_2_3 );
tmp1 = _mm256_mul_pd( a_01_11_21_31, x_0_1_2_3 );
y_00 = _mm256_add_pd( y_00, tmp0 );
y_11 = _mm256_add_pd( y_11, tmp1 );
tmp0 = _mm256_mul_pd( a_02_12_22_32, x_0_1_2_3 );
tmp1 = _mm256_mul_pd( a_03_13_23_33, x_0_1_2_3 );
y_22 = _mm256_add_pd( y_22, tmp0 );
y_33 = _mm256_add_pd( y_33, tmp1 );
__m256d
y_0_1_2_3;
y_00 = _mm256_hadd_pd(y_00, y_11);
y_22 = _mm256_hadd_pd(y_22, y_33);
y_11 = _mm256_permute2f128_pd(y_22, y_00, 2 );
y_00 = _mm256_permute2f128_pd(y_22, y_00, 19);
y_00 = _mm256_add_pd( y_00, y_11 );
if(alg==0)
{
_mm256_storeu_pd(&y[0], y_00);
}
else if(alg==1)
{
y_0_1_2_3 = _mm256_loadu_pd( &y[0] );
y_0_1_2_3 = _mm256_add_pd( y_0_1_2_3, y_00 );
_mm256_storeu_pd(&y[0], y_0_1_2_3);
}
else // alg==-1
{
y_0_1_2_3 = _mm256_loadu_pd( &y[0] );
y_0_1_2_3 = _mm256_sub_pd( y_0_1_2_3, y_00 );
_mm256_storeu_pd(&y[0], y_0_1_2_3);
}
}
// it moves vertically across blocks
void kernel_dsymv_4_lib4(int kmax, double *A, int sda, double *x_n, double *y_n, double *z_n, double *x_t, double *y_t, double *z_t, int tri, int alg)
{
if(kmax<=0)
return;
/*printf("\nciao %d\n", kmax); */
const int bs = 4;
__builtin_prefetch( A + bs*0 );
__builtin_prefetch( A + bs*2 );
int k, ka;
ka = kmax; // number from aligned positon
double k_left;
// double *sA, *sy_n, *sx_t;
static double d_mask[4] = {0.5, 1.5, 2.5, 3.5};
__m256d
v_mask,
zeros, temp,
a_00, a_01, a_02, a_03,
x_n_0, x_n_1, x_n_2, x_n_3, y_n_0,
x_t_0, y_t_0, y_t_1, y_t_2, y_t_3;
__m256i
i_mask;
#if 0
__m128d
stemp,
sa_00, sa_01, sa_02, sa_03,
sx_n_0, sx_n_1, sx_n_2, sx_n_3, sy_n_0,
sx_t_0, sy_t_0, sy_t_1, sy_t_2, sy_t_3;
#endif
zeros = _mm256_setzero_pd();
x_n_0 = _mm256_broadcast_sd( &x_n[0] );
x_n_1 = _mm256_broadcast_sd( &x_n[1] );
x_n_2 = _mm256_broadcast_sd( &x_n[2] );
x_n_3 = _mm256_broadcast_sd( &x_n[3] );
if(alg==-1) // TODO xor
{
x_n_0 = _mm256_sub_pd( zeros, x_n_0 );
x_n_1 = _mm256_sub_pd( zeros, x_n_1 );
x_n_2 = _mm256_sub_pd( zeros, x_n_2 );
x_n_3 = _mm256_sub_pd( zeros, x_n_3 );
}
y_t_0 = _mm256_setzero_pd();
y_t_1 = _mm256_setzero_pd();
y_t_2 = _mm256_setzero_pd();
y_t_3 = _mm256_setzero_pd();
#if 0
sx_n_0 = _mm256_castpd256_pd128( x_n_0 );
sx_n_1 = _mm256_castpd256_pd128( x_n_1 );
sx_n_2 = _mm256_castpd256_pd128( x_n_2 );
sx_n_3 = _mm256_castpd256_pd128( x_n_3 );
sy_t_0 = _mm256_castpd256_pd128( y_t_0 );
sy_t_1 = _mm256_castpd256_pd128( y_t_1 );
sy_t_2 = _mm256_castpd256_pd128( y_t_2 );
sy_t_3 = _mm256_castpd256_pd128( y_t_3 );
k = bs*(ka/bs);
sA = A + (ka/bs)*sda*bs;
sy_n = y_n + (ka/bs)*bs;
sx_t = x_t + (ka/bs)*bs;
for(; k<ka; k++)
{
sy_n_0 = _mm_load_sd( &sy_n[0] );
sx_t_0 = _mm_load_sd( &sx_t[0] );
sa_00 = _mm_load_sd( &sA[0+bs*0] );
sa_01 = _mm_load_sd( &sA[0+bs*1] );
sa_02 = _mm_load_sd( &sA[0+bs*2] );
sa_03 = _mm_load_sd( &sA[0+bs*3] );
stemp = _mm_mul_sd( sa_00, sx_n_0 );
sy_n_0 = _mm_add_sd( sy_n_0, stemp );
stemp = _mm_mul_sd( sa_00, sx_t_0 );
sy_t_0 = _mm_add_sd( sy_t_0, stemp );
stemp = _mm_mul_sd( sa_01, sx_n_1 );
sy_n_0 = _mm_add_sd( sy_n_0, stemp );
stemp = _mm_mul_sd( sa_01, sx_t_0 );
sy_t_1 = _mm_add_sd( sy_t_1, stemp );
stemp = _mm_mul_sd( sa_02, sx_n_2 );
sy_n_0 = _mm_add_sd( sy_n_0, stemp );
stemp = _mm_mul_sd( sa_02, sx_t_0 );
sy_t_2 = _mm_add_sd( sy_t_2, stemp );
stemp = _mm_mul_sd( sa_03, sx_n_3 );
sy_n_0 = _mm_add_sd( sy_n_0, stemp );
stemp = _mm_mul_sd( sa_03, sx_t_0 );
sy_t_3 = _mm_add_sd( sy_t_3, stemp );
_mm_store_sd( &sy_n[0], sy_n_0 );
sA += 1;
sy_n += 1;
sx_t += 1;
}
y_t_0 = _mm256_castpd128_pd256( sy_t_0 );
y_t_1 = _mm256_castpd128_pd256( sy_t_1 );
y_t_2 = _mm256_castpd128_pd256( sy_t_2 );
y_t_3 = _mm256_castpd128_pd256( sy_t_3 );
#endif
k=0;
// corner
if(tri==1)
{
__builtin_prefetch( A + sda*bs +bs*0 );
__builtin_prefetch( A + sda*bs +bs*2 );
y_n_0 = _mm256_loadu_pd( &y_n[0] );
x_t_0 = _mm256_loadu_pd( &x_t[0] );
a_00 = _mm256_load_pd( &A[0+bs*0] );
a_01 = _mm256_load_pd( &A[0+bs*1] );
a_02 = _mm256_load_pd( &A[0+bs*2] );
a_03 = _mm256_load_pd( &A[0+bs*3] );
temp = _mm256_mul_pd( a_00, x_n_0 );
y_n_0 = _mm256_add_pd( y_n_0, temp );
temp = _mm256_mul_pd( a_00, x_t_0 );
temp = _mm256_blend_pd( zeros, temp, 14 );
y_t_0 = _mm256_add_pd( y_t_0, temp );
temp = _mm256_mul_pd( a_01, x_n_1 );
temp = _mm256_blend_pd( zeros, temp, 14 );
y_n_0 = _mm256_add_pd( y_n_0, temp );
temp = _mm256_mul_pd( a_01, x_t_0 );
temp = _mm256_blend_pd( zeros, temp, 12 );
y_t_1 = _mm256_add_pd( y_t_1, temp );
temp = _mm256_mul_pd( a_02, x_n_2 );
temp = _mm256_blend_pd( zeros, temp, 12 );
y_n_0 = _mm256_add_pd( y_n_0, temp );
temp = _mm256_mul_pd( a_02, x_t_0 );
temp = _mm256_blend_pd( zeros, temp, 8 );
y_t_2 = _mm256_add_pd( y_t_2, temp );
temp = _mm256_mul_pd( a_03, x_n_3 );
temp = _mm256_blend_pd( zeros, temp, 8 );
y_n_0 = _mm256_add_pd( y_n_0, temp );
_mm256_storeu_pd( &z_n[0], y_n_0 );
A += sda*bs;
y_n += 4;
z_n += 4;
x_t += 4;
k += 4;
}
for(; k<ka-7; k+=2*bs)
{
__builtin_prefetch( A + sda*bs +bs*0 );
__builtin_prefetch( A + sda*bs +bs*2 );
y_n_0 = _mm256_loadu_pd( &y_n[0] );
x_t_0 = _mm256_loadu_pd( &x_t[0] );
a_00 = _mm256_load_pd( &A[0+bs*0] );
a_01 = _mm256_load_pd( &A[0+bs*1] );
a_02 = _mm256_load_pd( &A[0+bs*2] );
a_03 = _mm256_load_pd( &A[0+bs*3] );
temp = _mm256_mul_pd( a_00, x_n_0 );
y_n_0 = _mm256_add_pd( y_n_0, temp );
temp = _mm256_mul_pd( a_00, x_t_0 );
y_t_0 = _mm256_add_pd( y_t_0, temp );
temp = _mm256_mul_pd( a_01, x_n_1 );
y_n_0 = _mm256_add_pd( y_n_0, temp );
temp = _mm256_mul_pd( a_01, x_t_0 );
y_t_1 = _mm256_add_pd( y_t_1, temp );
temp = _mm256_mul_pd( a_02, x_n_2 );
y_n_0 = _mm256_add_pd( y_n_0, temp );
temp = _mm256_mul_pd( a_02, x_t_0 );
y_t_2 = _mm256_add_pd( y_t_2, temp );
temp = _mm256_mul_pd( a_03, x_n_3 );
y_n_0 = _mm256_add_pd( y_n_0, temp );
temp = _mm256_mul_pd( a_03, x_t_0 );
y_t_3 = _mm256_add_pd( y_t_3, temp );
_mm256_storeu_pd( &z_n[0], y_n_0 );
A += sda*bs;
y_n += 4;
z_n += 4;
x_t += 4;
__builtin_prefetch( A + sda*bs +bs*0 );
__builtin_prefetch( A + sda*bs +bs*2 );
y_n_0 = _mm256_loadu_pd( &y_n[0] );
x_t_0 = _mm256_loadu_pd( &x_t[0] );
a_00 = _mm256_load_pd( &A[0+bs*0] );
a_01 = _mm256_load_pd( &A[0+bs*1] );
a_02 = _mm256_load_pd( &A[0+bs*2] );
a_03 = _mm256_load_pd( &A[0+bs*3] );
temp = _mm256_mul_pd( a_00, x_n_0 );
y_n_0 = _mm256_add_pd( y_n_0, temp );
temp = _mm256_mul_pd( a_00, x_t_0 );
y_t_0 = _mm256_add_pd( y_t_0, temp );
temp = _mm256_mul_pd( a_01, x_n_1 );
y_n_0 = _mm256_add_pd( y_n_0, temp );
temp = _mm256_mul_pd( a_01, x_t_0 );
y_t_1 = _mm256_add_pd( y_t_1, temp );
temp = _mm256_mul_pd( a_02, x_n_2 );
y_n_0 = _mm256_add_pd( y_n_0, temp );
temp = _mm256_mul_pd( a_02, x_t_0 );
y_t_2 = _mm256_add_pd( y_t_2, temp );
temp = _mm256_mul_pd( a_03, x_n_3 );
y_n_0 = _mm256_add_pd( y_n_0, temp );
temp = _mm256_mul_pd( a_03, x_t_0 );
y_t_3 = _mm256_add_pd( y_t_3, temp );
_mm256_storeu_pd( &z_n[0], y_n_0 );
A += sda*bs;
y_n += 4;
z_n += 4;
x_t += 4;
}
for(; k<ka-3; k+=bs)
{
__builtin_prefetch( A + sda*bs +bs*0 );
__builtin_prefetch( A + sda*bs +bs*2 );
y_n_0 = _mm256_loadu_pd( &y_n[0] );
x_t_0 = _mm256_loadu_pd( &x_t[0] );
a_00 = _mm256_load_pd( &A[0+bs*0] );
a_01 = _mm256_load_pd( &A[0+bs*1] );
a_02 = _mm256_load_pd( &A[0+bs*2] );
a_03 = _mm256_load_pd( &A[0+bs*3] );
temp = _mm256_mul_pd( a_00, x_n_0 );
y_n_0 = _mm256_add_pd( y_n_0, temp );
temp = _mm256_mul_pd( a_00, x_t_0 );
y_t_0 = _mm256_add_pd( y_t_0, temp );
temp = _mm256_mul_pd( a_01, x_n_1 );
y_n_0 = _mm256_add_pd( y_n_0, temp );
temp = _mm256_mul_pd( a_01, x_t_0 );
y_t_1 = _mm256_add_pd( y_t_1, temp );
temp = _mm256_mul_pd( a_02, x_n_2 );
y_n_0 = _mm256_add_pd( y_n_0, temp );
temp = _mm256_mul_pd( a_02, x_t_0 );
y_t_2 = _mm256_add_pd( y_t_2, temp );
temp = _mm256_mul_pd( a_03, x_n_3 );
y_n_0 = _mm256_add_pd( y_n_0, temp );
temp = _mm256_mul_pd( a_03, x_t_0 );
y_t_3 = _mm256_add_pd( y_t_3, temp );
_mm256_storeu_pd( &z_n[0], y_n_0 );
A += sda*bs;
y_n += 4;
z_n += 4;
x_t += 4;
}
if(k<ka)
{
k_left = ka-k;
v_mask = _mm256_sub_pd( _mm256_loadu_pd( d_mask ), _mm256_broadcast_sd( &k_left ) );
i_mask = _mm256_castpd_si256( v_mask );
// __builtin_prefetch( A + sda*bs +bs*0 );
// __builtin_prefetch( A + sda*bs +bs*2 );
y_n_0 = _mm256_loadu_pd( &y_n[0] );
x_t_0 = _mm256_maskload_pd( &x_t[0], i_mask );
a_00 = _mm256_load_pd( &A[0+bs*0] );
a_01 = _mm256_load_pd( &A[0+bs*1] );
a_02 = _mm256_load_pd( &A[0+bs*2] );
a_03 = _mm256_load_pd( &A[0+bs*3] );
temp = _mm256_mul_pd( a_00, x_n_0 );
y_n_0 = _mm256_add_pd( y_n_0, temp );
temp = _mm256_mul_pd( a_00, x_t_0 );
y_t_0 = _mm256_add_pd( y_t_0, temp );
temp = _mm256_mul_pd( a_01, x_n_1 );
y_n_0 = _mm256_add_pd( y_n_0, temp );
temp = _mm256_mul_pd( a_01, x_t_0 );
y_t_1 = _mm256_add_pd( y_t_1, temp );
temp = _mm256_mul_pd( a_02, x_n_2 );
y_n_0 = _mm256_add_pd( y_n_0, temp );
temp = _mm256_mul_pd( a_02, x_t_0 );
y_t_2 = _mm256_add_pd( y_t_2, temp );
temp = _mm256_mul_pd( a_03, x_n_3 );
y_n_0 = _mm256_add_pd( y_n_0, temp );
temp = _mm256_mul_pd( a_03, x_t_0 );
y_t_3 = _mm256_add_pd( y_t_3, temp );
_mm256_maskstore_pd( &z_n[0], i_mask, y_n_0 );
// A += sda*bs;
// y_n += 4;
// z_n += 4;
// x_t += 4;
}
__m256d
y_0_1_2_3;
y_t_0 = _mm256_hadd_pd( y_t_0, y_t_1 );
y_t_2 = _mm256_hadd_pd( y_t_2, y_t_3 );
y_t_1 = _mm256_permute2f128_pd( y_t_2, y_t_0, 2 );
y_t_0 = _mm256_permute2f128_pd( y_t_2, y_t_0, 19 );
y_t_0 = _mm256_add_pd( y_t_0, y_t_1 );
if(alg==1)
{
y_0_1_2_3 = _mm256_loadu_pd( &y_t[0] );
y_0_1_2_3 = _mm256_add_pd( y_0_1_2_3, y_t_0 );
_mm256_storeu_pd( &z_t[0], y_0_1_2_3 );
}
else // alg==-1
{
y_0_1_2_3 = _mm256_loadu_pd( &y_t[0] );
y_0_1_2_3 = _mm256_sub_pd( y_0_1_2_3, y_t_0 );
_mm256_storeu_pd( &z_t[0], y_0_1_2_3 );
}
}
/**
* Calculate all values in one step per pixel. Requires grabbing the neighboring pixels.
*/
FORCE_INLINE double single_pixel(
double *im, int center, int top, int left, int right, int bottom,
const __m256i mask1110,
const __m256d rgb0W,
const __m256d onehalf,
const __m256d minustwelvehalf){
// double r = im[center];
// double g = im[center+1];
// double b = im[center+2];
// double r1 = im[top];
// double g1 = im[top+1];
// double b1 = im[top+2];
// double r2 = im[left];
// double g2 = im[left+1];
// double b2 = im[left+2];
// double r3 = im[right];
// double g3 = im[right+1];
// double b3 = im[right+2];
// double r4 = im[bottom];
// double g4 = im[bottom+1];
// double b4 = im[bottom+2];
__m256d c = _mm256_maskload_pd(&(im[center]),mask1110);
__m256d c1 = _mm256_loadu_pd(&(im[top]));
__m256d c2 = _mm256_loadu_pd(&(im[left]));
__m256d c3 = _mm256_loadu_pd(&(im[right]));
__m256d c4 = _mm256_loadu_pd(&(im[bottom]));
COST_INC_LOAD(20);
// double grey = rw * r + gw * g + bw * b;
// double grey1 = rw * r1 + gw * g1 + bw * b1;
// double grey2 = rw * r2 + gw * g2 + bw * b2;
// double grey3 = rw * r3 + gw * g3 + bw * b3;
// double grey4 = rw * r4 + gw * g4 + bw * b4;
__m256d greyc = _mm256_mul_pd(c,rgb0W);
__m256d grey1 = _mm256_mul_pd(c1,rgb0W);
__m256d grey2 = _mm256_mul_pd(c2,rgb0W);
__m256d grey3 = _mm256_mul_pd(c3,rgb0W);
__m256d grey4 = _mm256_mul_pd(c4,rgb0W);
//AVX: double: horizontal add for 1 vector
__m256d c_perm = _mm256_permute2f128_pd(c, c, 0b00100001);//1,2
__m256d c_h = _mm256_hadd_pd(c,c_perm);
__m128d c_h_lo = _mm256_extractf128_pd (c_h, 0);// lo
__m128d c_h_hi = _mm256_extractf128_pd (c_h, 1);// hi
double c_hsum_lo = _mm_cvtsd_f64(c_h_lo);
double c_hsum_hi = _mm_cvtsd_f64(c_h_hi);
double c_hsum = c_hsum_lo + c_hsum_hi;
//AVX: double: horizontal add for 1 vector
__m256d greyc_perm = _mm256_permute2f128_pd(greyc, greyc, 0b00100001);//1,2
__m256d greyc_h = _mm256_hadd_pd(greyc,greyc_perm);
__m128d greyc_h_lo = _mm256_extractf128_pd (greyc_h, 0);// lo
__m128d greyc_h_hi = _mm256_extractf128_pd (greyc_h, 1);// hi
double greyc_hsum_lo = _mm_cvtsd_f64(greyc_h_lo);
double greyc_hsum_hi = _mm_cvtsd_f64(greyc_h_hi);
double greyc_hsum = greyc_hsum_lo + greyc_hsum_hi;
//AVX: _m256d: horizontal add for 4 vectors at once
__m256d grey12 = _mm256_hadd_pd(grey1,grey2);
__m256d grey34 = _mm256_hadd_pd(grey3,grey4);
__m256d grey_1234_blend = _mm256_blend_pd(grey12, grey34, 0b1100); //0011
__m256d grey_1234_perm = _mm256_permute2f128_pd(grey12, grey34, 0b00100001);//1,2
__m256d grey_1234 = _mm256_add_pd(grey_1234_perm, grey_1234_blend);
//AVX: double: horizontal add for 1 vector
__m256d grey1234_perm = _mm256_permute2f128_pd(grey_1234, grey_1234, 0b00100001);//1,2
__m256d grey1234_h = _mm256_hadd_pd(grey_1234,grey1234_perm);
__m128d grey1234_h_lo = _mm256_extractf128_pd (grey1234_h, 0);// lo
__m128d grey1234_h_hi = _mm256_extractf128_pd (grey1234_h, 1);// hi
double grey1234_hsum_lo = _mm_cvtsd_f64(grey1234_h_lo);
double grey1234_hsum_hi = _mm_cvtsd_f64(grey1234_h_hi);
double grey1234_sum = grey1234_hsum_lo + grey1234_hsum_hi;
COST_INC_ADD(10); //+ operations wasted on AVX
COST_INC_MUL(15); //+ operations wasted on AVX
double mu = c_hsum / 3.0;
COST_INC_ADD(2);
COST_INC_DIV(1);
// double rmu = r-mu;
// double gmu = g-mu;
// double bmu = b-mu;
__m256d c_mu = _mm256_set1_pd(mu);
__m256d c_rgbmu = _mm256_sub_pd(c,c_mu);
COST_INC_ADD(3); //+1 operations wasted on AVX
// double rz = r-0.5;
// double gz = g-0.5;
// double bz = b-0.5;
__m256d c_rgbz = _mm256_sub_pd(c,onehalf);
COST_INC_ADD(3); //+1 operations wasted on AVX
// double rzrz = rz*rz;
// double gzgz = gz*gz;
// double bzbz = bz*bz;
__m256d c_rgbz_sq = _mm256_mul_pd(c_rgbz,c_rgbz);
COST_INC_MUL(3); //+1 operations wasted on AVX
// double re = exp(-12.5*rzrz);
// double ge = exp(-12.5*gzgz);
// double be = exp(-12.5*bzbz);
__m256d c_rgbe_tmp = _mm256_mul_pd(minustwelvehalf,c_rgbz_sq);
__m128 c_rgbe_tmp_ps = _mm256_cvtpd_ps(c_rgbe_tmp);
__m128 c_rgbe_ps = exp_ps(c_rgbe_tmp_ps);
__m256d c_rgbe = _mm256_cvtps_pd(c_rgbe_ps);
COST_INC_EXP(3);
COST_INC_MUL(3); //+1 operations wasted on AVX
// double t1 = sqrt((rmu*rmu + gmu*gmu + bmu*bmu)/3.0);
__m256d c_rgbmu_sq = _mm256_mul_pd(c_rgbmu,c_rgbmu);
__m128d t1_tmp1_lo = _mm256_extractf128_pd (c_rgbmu_sq, 0);// lo
__m128d t1_tmp1_hi = _mm256_extractf128_pd (c_rgbmu_sq, 1);// hi
__m128d t1_tmp1_lo_sum = _mm_hadd_pd (t1_tmp1_lo, t1_tmp1_lo);
double t1_tmp1_hi_lo = _mm_cvtsd_f64(t1_tmp1_hi);
double t1_tmp1_lo_sum_lo = _mm_cvtsd_f64(t1_tmp1_lo_sum);
double t1_tmp1 = t1_tmp1_lo_sum_lo + t1_tmp1_hi_lo;
double t1_tmp2 = t1_tmp1 / 3.0;
double t1 = sqrt(t1_tmp2);
COST_INC_SQRT(1);
COST_INC_ADD(3);
COST_INC_MUL(3); //+1 operations wasted on AVX
COST_INC_DIV(1);
double t2 = fabs(t1);
COST_INC_ABS(1);
// double t3 = re*ge*be;
__m128d t3_tmp1_lo = _mm256_extractf128_pd (c_rgbe, 0);// lo
__m128d t3_tmp1_hi = _mm256_extractf128_pd (c_rgbe, 1);// hi
double t3_tmp1_lo_lo = _mm_cvtsd_f64(t3_tmp1_lo);
double t3_tmp1_hi_lo = _mm_cvtsd_f64(t3_tmp1_hi);
__m128d t3_tmp1_lo_swapped = _mm_permute_pd(t3_tmp1_lo, 1);// swap
double t3_tmp1_lo_hi = _mm_cvtsd_f64(t3_tmp1_lo_swapped);
double t3 = t3_tmp1_lo_lo * t3_tmp1_lo_hi * t3_tmp1_hi_lo;
COST_INC_MUL(2);
double t4 = fabs(t3);
COST_INC_ABS(1);
double t5 = t2 * t4;
COST_INC_MUL(1);
// double t6 = -4.0*grey+grey1+grey2+grey3+grey4;
double minusfour_times_grey = -4.0*greyc_hsum;
double t6 = minusfour_times_grey+grey1234_sum;
COST_INC_MUL(1);
COST_INC_ADD(2); //2 operations saved due to AVX
double t7 = fabs(t6);
COST_INC_ABS(1);
double t8 = t5 * t7;
COST_INC_MUL(1);
double t9 = t8 + 1.0E-12;
COST_INC_ADD(1);
return t9;
}
void kernel_dgemv_t_4_lib4(int kmax, double *A, int sda, double *x, double *y, int alg)
{
if(kmax<=0)
return;
const int lda = 4;
__builtin_prefetch( A + 0*lda );
__builtin_prefetch( A + 2*lda );
double *tA, *tx;
int k;
int ka = kmax; // number from aligned positon
__m256d
aaxx_temp,
a_00_10_20_30, a_01_11_21_31, a_02_12_22_32, a_03_13_23_33,
x_0_1_2_3,
y_00, y_11, y_22, y_33;
__m128d
ax_temp,
a_00_10, a_01_11, a_02_12, a_03_13,
x_0_1,
y_0, y_1, y_2, y_3;
y_00 = _mm256_setzero_pd();
y_11 = _mm256_setzero_pd();
y_22 = _mm256_setzero_pd();
y_33 = _mm256_setzero_pd();
y_0 = _mm256_castpd256_pd128(y_00);
y_1 = _mm256_castpd256_pd128(y_11);
y_2 = _mm256_castpd256_pd128(y_22);
y_3 = _mm256_castpd256_pd128(y_33);
k = lda*(ka/lda);
tA = A + (ka/lda)*sda*lda;
tx = x + (ka/lda)*lda;
for(; k<ka; k++)
{
x_0_1 = _mm_load_sd( &tx[0] );
a_00_10 = _mm_load_sd( &tA[0+lda*0] );
a_01_11 = _mm_load_sd( &tA[0+lda*1] );
a_02_12 = _mm_load_sd( &tA[0+lda*2] );
a_03_13 = _mm_load_sd( &tA[0+lda*3] );
ax_temp = _mm_mul_sd( a_00_10, x_0_1 );
y_0 = _mm_add_sd (y_0, ax_temp );
ax_temp = _mm_mul_sd( a_01_11, x_0_1 );
y_1 = _mm_add_sd (y_1, ax_temp );
ax_temp = _mm_mul_sd( a_02_12, x_0_1 );
y_2 = _mm_add_sd (y_2, ax_temp );
ax_temp = _mm_mul_sd( a_03_13, x_0_1 );
y_3 = _mm_add_sd (y_3, ax_temp );
tA += 1;
tx += 1;
}
y_00 = _mm256_castpd128_pd256(y_0);
y_11 = _mm256_castpd128_pd256(y_1);
y_22 = _mm256_castpd128_pd256(y_2);
y_33 = _mm256_castpd128_pd256(y_3);
k=0;
for(; k<ka-7; k+=8)
{
__builtin_prefetch( A + sda*lda + 0*lda );
__builtin_prefetch( A + sda*lda + 2*lda );
x_0_1_2_3 = _mm256_loadu_pd( &x[0] );
a_00_10_20_30 = _mm256_load_pd( &A[0+lda*0] );
a_01_11_21_31 = _mm256_load_pd( &A[0+lda*1] );
a_02_12_22_32 = _mm256_load_pd( &A[0+lda*2] );
a_03_13_23_33 = _mm256_load_pd( &A[0+lda*3] );
aaxx_temp = _mm256_mul_pd( a_00_10_20_30, x_0_1_2_3 );
y_00 = _mm256_add_pd( y_00, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_01_11_21_31, x_0_1_2_3 );
y_11 = _mm256_add_pd( y_11, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_02_12_22_32, x_0_1_2_3 );
y_22 = _mm256_add_pd( y_22, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_03_13_23_33, x_0_1_2_3 );
y_33 = _mm256_add_pd( y_33, aaxx_temp );
A += 4 + (sda-1)*lda;
x += 4;
__builtin_prefetch( A + sda*lda + 0*lda );
__builtin_prefetch( A + sda*lda + 2*lda );
x_0_1_2_3 = _mm256_loadu_pd( &x[0] );
a_00_10_20_30 = _mm256_load_pd( &A[0+lda*0] );
a_01_11_21_31 = _mm256_load_pd( &A[0+lda*1] );
a_02_12_22_32 = _mm256_load_pd( &A[0+lda*2] );
a_03_13_23_33 = _mm256_load_pd( &A[0+lda*3] );
aaxx_temp = _mm256_mul_pd( a_00_10_20_30, x_0_1_2_3 );
y_00 = _mm256_add_pd( y_00, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_01_11_21_31, x_0_1_2_3 );
y_11 = _mm256_add_pd( y_11, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_02_12_22_32, x_0_1_2_3 );
y_22 = _mm256_add_pd( y_22, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_03_13_23_33, x_0_1_2_3 );
y_33 = _mm256_add_pd( y_33, aaxx_temp );
A += 4 + (sda-1)*lda;
x += 4;
}
for(; k<ka-3; k+=4)
{
__builtin_prefetch( A + sda*lda + 0*lda );
__builtin_prefetch( A + sda*lda + 2*lda );
x_0_1_2_3 = _mm256_loadu_pd( &x[0] );
a_00_10_20_30 = _mm256_load_pd( &A[0+lda*0] );
a_01_11_21_31 = _mm256_load_pd( &A[0+lda*1] );
a_02_12_22_32 = _mm256_load_pd( &A[0+lda*2] );
a_03_13_23_33 = _mm256_load_pd( &A[0+lda*3] );
aaxx_temp = _mm256_mul_pd( a_00_10_20_30, x_0_1_2_3 );
y_00 = _mm256_add_pd( y_00, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_01_11_21_31, x_0_1_2_3 );
y_11 = _mm256_add_pd( y_11, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_02_12_22_32, x_0_1_2_3 );
y_22 = _mm256_add_pd( y_22, aaxx_temp );
aaxx_temp = _mm256_mul_pd( a_03_13_23_33, x_0_1_2_3 );
y_33 = _mm256_add_pd( y_33, aaxx_temp );
A += 4 + (sda-1)*lda;
x += 4;
}
__m256d
y_0_1_2_3;
y_00 = _mm256_hadd_pd(y_00, y_11);
y_22 = _mm256_hadd_pd(y_22, y_33);
y_11 = _mm256_permute2f128_pd(y_22, y_00, 2 );
y_00 = _mm256_permute2f128_pd(y_22, y_00, 19);
y_00 = _mm256_add_pd( y_00, y_11 );
if(alg==0)
{
_mm256_storeu_pd(&y[0], y_00);
}
else if(alg==1)
{
y_0_1_2_3 = _mm256_loadu_pd( &y[0] );
y_0_1_2_3 = _mm256_add_pd( y_0_1_2_3, y_00 );
_mm256_storeu_pd(&y[0], y_0_1_2_3);
}
else // alg==-1
{
y_0_1_2_3 = _mm256_loadu_pd( &y[0] );
y_0_1_2_3 = _mm256_sub_pd( y_0_1_2_3, y_00 );
_mm256_storeu_pd(&y[0], y_0_1_2_3);
}
}
