inline
short_vec<float, 32> operator-(const short_vec<float, 32>& other) const
{
return short_vec<float, 32>(
_mm512_sub_ps(val1, other.val1),
_mm512_sub_ps(val2, other.val2));
}
// sin()
static inline mic_m512_t mic_sin_ps(mic_m512_t x) {
__m512i sign_bit;
sign_bit = _mm512_and_epi32(_mm512_castps_si512(x), _pi32_sign_mask);
x = _mm512_castsi512_ps(_mm512_and_epi32(_mm512_castps_si512(x), _pi32_inv_sign_mask));
mic_m512_t y = _mm512_mul_ps(x, _ps_cephes_FOPI);
__m512i emm2 = _mm512_cvtfxpnt_round_adjustps_epi32(y, _MM_FROUND_TO_NEAREST_INT, _MM_EXPADJ_NONE);
emm2 = _mm512_add_epi32(emm2, _pi32_1);
emm2 = _mm512_and_epi32(emm2, _pi32_inv1);
y = _mm512_cvtfxpnt_round_adjustepu32_ps(emm2, _MM_FROUND_TO_NEAREST_INT, _MM_EXPADJ_NONE);
__m512i emm0 = _mm512_and_epi32(emm2, _pi32_4);
emm0 = _mm512_slli_epi32(emm0, 29);
emm2 = _mm512_and_epi32(emm2, _pi32_2);
__mmask16 mask = _mm512_cmp_epi32_mask(emm2, _pi32_0, _MM_CMPINT_EQ);
emm2 = _mm512_mask_add_epi32(_pi32_0, mask, _pi32_ffff, _pi32_0);
sign_bit = _mm512_xor_epi32(sign_bit, emm0);
mic_m512_t temp = _ps_minus_cephes_DP123;
temp = _mm512_mul_ps(y, temp);
x = _mm512_add_ps(x, temp);
mic_m512_t x2 = _mm512_mul_ps(x, x);
mic_m512_t x3 = _mm512_mul_ps(x2, x);
mic_m512_t x4 = _mm512_mul_ps(x2, x2);
y = _mm512_mul_ps(_ps_coscof_p0, x2);
mic_m512_t y2 = _mm512_mul_ps(_ps_sincof_p0, x2);
y = _mm512_add_ps(y, _ps_coscof_p1);
y2 = _mm512_add_ps(y2, _ps_sincof_p1);
y = _mm512_mul_ps(y, x2);
y2 = _mm512_mul_ps(y2, x2);
y = _mm512_add_ps(y, _ps_coscof_p2);
y2 = _mm512_add_ps(y2, _ps_sincof_p2);
y = _mm512_mul_ps(y, x4);
y2 = _mm512_mul_ps(y2, x3);
temp = _mm512_mul_ps(x2, _ps_0point5);
temp = _mm512_sub_ps(temp, _ps_1);
y = _mm512_sub_ps(y, temp);
y2 = _mm512_add_ps(y2, x);
y = _mm512_castsi512_ps(_mm512_andnot_epi32(emm2, _mm512_castps_si512(y)));
y2 = _mm512_castsi512_ps(_mm512_and_epi32(emm2, _mm512_castps_si512(y2)));
y = _mm512_add_ps(y, y2);
y = _mm512_castsi512_ps(_mm512_xor_epi32(_mm512_castps_si512(y), sign_bit));
return y;
} // sin_ps()
static inline mic_m512c_t mic_rcp_cps(mic_m512c_t a) {
mic_m512_t temp1 = _mm512_add_ps(_mm512_mul_ps(a.xvec, a.xvec), _mm512_mul_ps(a.yvec, a.yvec));
mic_m512_t temp2 = _mm512_rcp23_ps(temp1);
mic_m512c_t vec;
//__m512 neg_mask = _mm512_castsi512_ps(_mm512_set1_epi32(0x80000000));
vec.xvec = _mm512_mul_ps(a.xvec, temp2);
//vec.yvec = _mm512_xor_ps(_mm512_mul_ps(a.yvec, temp2), neg_mask);
mic_m512_t zero = _mm512_setzero_ps();
vec.yvec = _mm512_sub_ps(zero, _mm512_mul_ps(a.yvec, temp2));
return vec;
} // mic_rcp_cps()
// exp()
inline mic_m512_t mic_exp_ps(mic_m512_t x) {
x = _mm512_min_ps(x, _ps_exp_hi);
x = _mm512_max_ps(x, _ps_exp_lo);
mic_m512_t temp_2 = _mm512_fmadd_ps(x, _ps_cephes_LOG2EF, _ps_0point5);
mic_m512_t temp_1 = _mm512_round_ps(temp_2, _MM_FROUND_TO_NEAREST_INT, _MM_EXPADJ_NONE);
mic_m512_t temp_3 = _mm512_sub_ps(temp_1, temp_2);
__mmask16 mask = _mm512_cmp_ps_mask(temp_3, _ps_0, _MM_CMPINT_GT);
temp_2 = _mm512_mask_sub_ps(temp_1, mask, temp_1, _ps_1);
__m512i emm0 = _mm512_cvtfxpnt_round_adjustps_epi32(temp_2, _MM_FROUND_TO_NEAREST_INT, _MM_EXPADJ_NONE);
x = _mm512_fnmadd_ps(temp_2, _ps_cephes_exp_C12, x);
mic_m512_t x2 = _mm512_mul_ps(x, x);
mic_m512_t x3 = _mm512_mul_ps(x2, x);
mic_m512_t x4 = _mm512_mul_ps(x2, x2);
temp_1 = _mm512_add_ps(x, _ps_1);
temp_1 = _mm512_fmadd_ps(x2, _ps_cephes_exp_p5, temp_1);
temp_1 = _mm512_fmadd_ps(x3, _ps_cephes_exp_p4, temp_1);
temp_2 = _mm512_mul_ps(x3, _ps_cephes_exp_p0);
temp_3 = _mm512_mul_ps(x2, _ps_cephes_exp_p1);
mic_m512_t temp_4 = _mm512_mul_ps(x, _ps_cephes_exp_p2);
emm0 = _mm512_add_epi32(emm0, _pi32_0x7f);
temp_2 = _mm512_add_ps(temp_2, temp_3);
temp_3 = _mm512_add_ps(temp_3, temp_4);
temp_2 = _mm512_add_ps(temp_2, temp_3);
emm0 = _mm512_slli_epi32(emm0, 23);
mic_m512_t pow2n = _mm512_castsi512_ps(emm0);
temp_2 = _mm512_mul_ps(temp_2, x4);
mic_m512_t y = _mm512_add_ps(temp_1, temp_2);
y = _mm512_mul_ps(y, pow2n);
return y;
} // newexp_ps()
int main() {
// Initialize
int N = 1 << 16;
int NALIGN = 64;
int i, j;
float OPS = 20. * N * N * 1e-9;
float EPS2 = 1e-6;
double tic, toc;
float * x = (float*) _mm_malloc(N * sizeof(float), NALIGN);
float * y = (float*) _mm_malloc(N * sizeof(float), NALIGN);
float * z = (float*) _mm_malloc(N * sizeof(float), NALIGN);
float * m = (float*) _mm_malloc(N * sizeof(float), NALIGN);
float * p = (float*) _mm_malloc(N * sizeof(float), NALIGN);
float * ax = (float*) _mm_malloc(N * sizeof(float), NALIGN);
float * ay = (float*) _mm_malloc(N * sizeof(float), NALIGN);
float * az = (float*) _mm_malloc(N * sizeof(float), NALIGN);
#pragma omp parallel for
for (i=0; i<N; i++) {
x[i] = drand48();
y[i] = drand48();
z[i] = drand48();
m[i] = drand48() / N;
p[i] = ax[i] = ay[i] = az[i] = 0;
}
printf("N : %d\n",N);
#pragma omp parallel private(j)
{
#pragma omp single
tic = get_time();
// Vectorize target with intrinsics
#pragma omp for
for (i=0; i<N; i+=16) {
__m512 pi = _mm512_setzero_ps();
__m512 axi = _mm512_setzero_ps();
__m512 ayi = _mm512_setzero_ps();
__m512 azi = _mm512_setzero_ps();
__m512 xi = _mm512_load_ps(x+i);
__m512 yi = _mm512_load_ps(y+i);
__m512 zi = _mm512_load_ps(z+i);
for (j=0; j<N; j++) {
__m512 xj = _mm512_set1_ps(x[j]);
xj = _mm512_sub_ps(xj, xi);
__m512 yj = _mm512_set1_ps(y[j]);
yj = _mm512_sub_ps(yj, yi);
__m512 zj = _mm512_set1_ps(z[j]);
zj = _mm512_sub_ps(zj, zi);
__m512 R2 = _mm512_set1_ps(EPS2);
R2 = _mm512_fmadd_ps(xj, xj, R2);
R2 = _mm512_fmadd_ps(yj, yj, R2);
R2 = _mm512_fmadd_ps(zj, zj, R2);
__m512 mj = _mm512_set1_ps(m[j]);
__m512 invR = _mm512_rsqrt23_ps(R2);
mj = _mm512_mul_ps(mj, invR);
pi = _mm512_add_ps(pi, mj);
invR = _mm512_mul_ps(invR, invR);
invR = _mm512_mul_ps(invR, mj);
axi = _mm512_fmadd_ps(xj, invR, axi);
ayi = _mm512_fmadd_ps(yj, invR, ayi);
azi = _mm512_fmadd_ps(zj, invR, azi);
}
_mm512_store_ps(p+i, pi);
_mm512_store_ps(ax+i, axi);
_mm512_store_ps(ay+i, ayi);
_mm512_store_ps(az+i, azi);
}
#pragma omp single
{
toc = get_time();
printf("Vectorize target with intrinsics : %e s : %lf GFlops\n",toc-tic, OPS/(toc-tic));
// Vectorize source with intrinsics
tic = get_time();
}
#pragma omp for
for (i=0; i<N; i++) {
__m512 pi = _mm512_setzero_ps();
__m512 axi = _mm512_setzero_ps();
__m512 ayi = _mm512_setzero_ps();
__m512 azi = _mm512_setzero_ps();
__m512 xi = _mm512_set1_ps(x[i]);
__m512 yi = _mm512_set1_ps(y[i]);
__m512 zi = _mm512_set1_ps(z[i]);
for (j=0; j<N; j+=16) {
__m512 xj = _mm512_load_ps(x+j);
xj = _mm512_sub_ps(xj, xi);
__m512 yj = _mm512_load_ps(y+j);
yj = _mm512_sub_ps(yj, yi);
__m512 zj = _mm512_load_ps(z+j);
zj = _mm512_sub_ps(zj, zi);
__m512 R2 = _mm512_set1_ps(EPS2);
R2 = _mm512_fmadd_ps(xj, xj, R2);
R2 = _mm512_fmadd_ps(yj, yj, R2);
R2 = _mm512_fmadd_ps(zj, zj, R2);
__m512 mj = _mm512_load_ps(m+j);
__m512 invR = _mm512_rsqrt23_ps(R2);
mj = _mm512_mul_ps(mj, invR);
pi = _mm512_add_ps(pi, mj);
invR = _mm512_mul_ps(invR, invR);
invR = _mm512_mul_ps(invR, mj);
axi = _mm512_fmadd_ps(xj, invR, axi);
ayi = _mm512_fmadd_ps(yj, invR, ayi);
azi = _mm512_fmadd_ps(zj, invR, azi);
}
p[i] = _mm512_reduce_add_ps(pi);
ax[i] = _mm512_reduce_add_ps(axi);
ay[i] = _mm512_reduce_add_ps(ayi);
az[i] = _mm512_reduce_add_ps(azi);
}
#pragma omp single
{
toc = get_time();
printf("Vectorize source with intrinsics : %e s : %lf GFlops\n",toc-tic, OPS/(toc-tic));
// Vectorize target with pragma simd
tic = get_time();
}
#pragma simd
#pragma omp for
for (i=0; i<N; i++) {
float pi = 0;
float axi = 0;
float ayi = 0;
float azi = 0;
float xi = x[i];
float yi = y[i];
float zi = z[i];
for (j=0; j<N; j++) {
float dx = x[j] - xi;
float dy = y[j] - yi;
float dz = z[j] - zi;
float R2 = dx * dx + dy * dy + dz * dz + EPS2;
float invR = 1.0f / sqrtf(R2);
float invR3 = m[j] * invR * invR * invR;
pi += m[j] * invR;
axi += dx * invR3;
ayi += dy * invR3;
azi += dz * invR3;
}
p[i] = pi;
ax[i] = axi;
ay[i] = ayi;
az[i] = azi;
}
#pragma omp single
{
toc = get_time();
printf("Vectorize target with pragma simd: %e s : %lf GFlops\n",toc-tic, OPS/(toc-tic));
// Vectorize source with pragma simd
tic = get_time();
}
#pragma omp for
for (i=0; i<N; i++) {
float pi = 0;
float axi = 0;
float ayi = 0;
float azi = 0;
float xi = x[i];
float yi = y[i];
float zi = z[i];
#pragma simd
for (j=0; j<N; j++) {
float dx = x[j] - xi;
float dy = y[j] - yi;
float dz = z[j] - zi;
float R2 = dx * dx + dy * dy + dz * dz + EPS2;
float invR = 1.0f / sqrtf(R2);
float invR3 = m[j] * invR * invR * invR;
pi += m[j] * invR;
axi += dx * invR3;
ayi += dy * invR3;
azi += dz * invR3;
}
p[i] = pi;
ax[i] = axi;
ay[i] = ayi;
az[i] = azi;
}
#pragma omp single
{
toc = get_time();
printf("Vectorize source with pragma simd: %e s : %lf GFlops\n",toc-tic, OPS/(toc-tic));
}
}
_mm_free(x);
_mm_free(y);
_mm_free(z);
_mm_free(m);
_mm_free(p);
_mm_free(ax);
_mm_free(ay);
_mm_free(az);
return 0;
}
static inline mic_m512c_t mic_mul_ccps(mic_m512c_t a, mic_m512c_t b) {
mic_m512c_t vec;
vec.xvec = _mm512_sub_ps(_mm512_mul_ps(a.xvec, b.xvec), _mm512_mul_ps(a.yvec, b.yvec));
vec.yvec = _mm512_add_ps(_mm512_mul_ps(a.xvec, b.yvec), _mm512_mul_ps(a.yvec, b.xvec));
return vec;
} // mic_mul_ccps()
static batch_type sub(const batch_type& lhs, const batch_type& rhs)
{
return _mm512_sub_ps(lhs, rhs);
}
static batch_type neg(const batch_type& rhs)
{
return _mm512_sub_ps(_mm512_setzero_ps(), rhs);
}
void AVX512BW_mandelbrot(
float Re_min, float Re_max,
float Im_min, float Im_max,
float threshold,
int maxiters,
int width, int height,
uint8_t *data)
{
float dRe, dIm;
int x, y;
__m128i* ptr = (__m128i*)data;
// step on Re and Im axis
dRe = (Re_max - Re_min)/width;
dIm = (Im_max - Im_min)/height;
// prepare vectors
// 1. threshold
const __m512 vec_threshold = _mm512_set1_ps(threshold);
// 2. Cim
__m512 Cim = _mm512_set1_ps(Im_min);
// 3. Re advance every x iteration
const __m512 vec_dRe = _mm512_set1_ps(16*dRe);
// 4. Im advance every y iteration
const __m512 vec_dIm = _mm512_set1_ps(dIm);
// calculations
for (y=0; y < height; y++) {
__m512 Cre = _mm512_setr_ps(
Re_min + 0*dRe, Re_min + 1*dRe, Re_min + 2*dRe, Re_min + 3*dRe,
Re_min + 4*dRe, Re_min + 5*dRe, Re_min + 6*dRe, Re_min + 7*dRe,
Re_min + 8*dRe, Re_min + 9*dRe, Re_min + 10*dRe, Re_min + 11*dRe,
Re_min + 12*dRe, Re_min + 13*dRe, Re_min + 14*dRe, Re_min + 15*dRe
);
for (x=0; x < width; x+=16) {
__m512 Xre = _mm512_setzero_ps();
__m512 Xim = _mm512_setzero_ps();
__m128i itercount = _mm_setzero_si128();
int i;
for (i=0; i < maxiters; i++) {
// Tre = Xre^2 - Xim^2 + Cim
const __m512 Xre2 = _mm512_mul_ps(Xre, Xre);
const __m512 Xim2 = _mm512_mul_ps(Xim, Xim);
const __m512 Tre = _mm512_add_ps(Cre, _mm512_sub_ps(Xre2, Xim2));
// Tim = 2*Xre*Xim + Cre
const __m512 t1 = _mm512_mul_ps(Xre, Xim);
const __m512 Tim = _mm512_add_ps(Cim, _mm512_add_ps(t1, t1));
// sqr_dist = Tre^2 + Tim^2
__m512 Tre2 = _mm512_mul_ps(Tre, Tre);
__m512 Tim2 = _mm512_mul_ps(Tim, Tim);
__m512 sqr_dist = _mm512_add_ps(Tre2, Tim2);
// sqr_dist < threshold => 16-bit mask
__mmask16 mask = _mm512_cmp_ps_mask(sqr_dist, vec_threshold, _CMP_LE_OS);
if (mask == 0) {
break;
}
// Note: unlike SSE/AVX2 versions itercount is a packed byte vector,
// thus conversion packed dword -> byte is not needed.
itercount = _mm_sub_epi8(itercount, _mm_movm_epi8(mask));
Xre = Tre;
Xim = Tim;
} // for
*ptr++ = itercount;
// advance Cre vector
Cre = _mm512_add_ps(Cre, vec_dRe);
}
// advance Cim vector
Cim = _mm512_add_ps(Cim, vec_dIm);
}
}
inline
void operator-=(const short_vec<float, 32>& other)
{
val1 = _mm512_sub_ps(val1, other.val1);
val2 = _mm512_sub_ps(val2, other.val2);
}
