inline void zmatmul(float *ain, float *bin, float *cout) {
#ifdef __MIC__
__m512 a,b,c;
__m512 a0,a1,a2,a3;
__m512 b0,b1,b2,b3;
__m512i pa0={ 0, 0, 2, 2, 0, 0, 2, 2, 8, 8,10,10, 8, 8,10,10};
__m512i pa1={ 1, 1, 3, 3, 1, 1, 3, 3, 9, 9,11,11, 9, 9,11,11};
__m512i pa2={ 4, 4, 6, 6, 4, 4, 6, 6,12,12,14,14,12,12,14,14};
__m512i pa3={ 5, 5, 7, 7, 5, 5, 7, 7,13,13,15,15,13,13,15,15};
__m512i pb0={ 0, 1, 0, 1, 4, 5, 4, 5, 0, 1, 0, 1, 4, 5, 4, 5};
__m512i pb1={ 2, 3, 2, 3, 6, 7, 6, 7, 2, 3, 2, 3, 6, 7, 6, 7};
__m512i pb2={ 8, 9, 8, 9,12,13,12,13, 8, 9, 8, 9,12,13,12,13};
__m512i pb3={10,11,10,11,14,15,14,15,10,11,10,11,14,15,14,15};
a=_mm512_load_ps(ain);
b=_mm512_load_ps(bin);
c=_mm512_load_ps(cout);
a0=_mm512_castsi512_ps(_mm512_permutevar_epi32(pa0,_mm512_castps_si512(a)));
a1=_mm512_castsi512_ps(_mm512_permutevar_epi32(pa1,_mm512_castps_si512(a)));
a2=_mm512_castsi512_ps(_mm512_permutevar_epi32(pa2,_mm512_castps_si512(a)));
a3=_mm512_castsi512_ps(_mm512_permutevar_epi32(pa3,_mm512_castps_si512(a)));
b0=_mm512_castsi512_ps(_mm512_permutevar_epi32(pb0,_mm512_castps_si512(b)));
b1=_mm512_castsi512_ps(_mm512_permutevar_epi32(pb1,_mm512_castps_si512(b)));
b2=_mm512_castsi512_ps(_mm512_permutevar_epi32(pb2,_mm512_castps_si512(b)));
b3=_mm512_castsi512_ps(_mm512_permutevar_epi32(pb3,_mm512_castps_si512(b)));
c=_mm512_fmadd_ps(a0,b0,c);
c=_mm512_fmadd_ps(a1,b1,c);
c=_mm512_fmadd_ps(a2,b2,c);
c=_mm512_fmadd_ps(a3,b3,c);
_mm512_store_ps(cout,c);
#else
cout[0] +=ain[0] *bin[0]+ain[1] *bin[2]+ain[4] *bin[8] +ain[5] *bin[10];
cout[1] +=ain[0] *bin[1]+ain[1] *bin[3]+ain[4] *bin[9] +ain[5] *bin[11];
cout[2] +=ain[2] *bin[0]+ain[3] *bin[2]+ain[6] *bin[8] +ain[7] *bin[10];
cout[3] +=ain[2] *bin[1]+ain[3] *bin[3]+ain[6] *bin[9] +ain[7] *bin[11];
cout[4] +=ain[0] *bin[4]+ain[1] *bin[6]+ain[4] *bin[12]+ain[5] *bin[14];
cout[5] +=ain[0] *bin[5]+ain[1] *bin[7]+ain[4] *bin[13]+ain[5] *bin[15];
cout[6] +=ain[2] *bin[4]+ain[3] *bin[6]+ain[6] *bin[12]+ain[7] *bin[14];
cout[7] +=ain[2] *bin[5]+ain[3] *bin[7]+ain[6] *bin[13]+ain[7] *bin[15];
cout[8] +=ain[8] *bin[0]+ain[9] *bin[2]+ain[12]*bin[8] +ain[13]*bin[10];
cout[9] +=ain[8] *bin[1]+ain[9] *bin[3]+ain[12]*bin[9] +ain[13]*bin[11];
cout[10]+=ain[10]*bin[0]+ain[11]*bin[2]+ain[14]*bin[8] +ain[15]*bin[10];
cout[11]+=ain[10]*bin[1]+ain[11]*bin[3]+ain[14]*bin[9] +ain[15]*bin[11];
cout[12]+=ain[8] *bin[4]+ain[9] *bin[6]+ain[12]*bin[12]+ain[13]*bin[14];
cout[13]+=ain[8] *bin[5]+ain[9] *bin[7]+ain[12]*bin[13]+ain[13]*bin[15];
cout[14]+=ain[10]*bin[4]+ain[11]*bin[6]+ain[14]*bin[12]+ain[15]*bin[14];
cout[15]+=ain[10]*bin[5]+ain[11]*bin[7]+ain[14]*bin[13]+ain[15]*bin[15];
#endif
}
// 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()
__attribute__((noinline)) float dot512fma2(float *x1, float *x2, size_t len) {
assert(len % 32 == 0);
__m512 sum = _mm512_setzero_ps();
if (len > 31) {
size_t limit = len - 31;
for (size_t i = 0; i < limit; i += 32) {
__m512 v11 = _mm512_loadu_ps(x1 + i);
__m512 v21 = _mm512_loadu_ps(x2 + i);
__m512 v12 = _mm512_loadu_ps(x1 + i + 16);
__m512 v22 = _mm512_loadu_ps(x2 + i + 16);
sum = _mm512_fmadd_ps(v11, v21, sum);
sum = _mm512_fmadd_ps(v12, v22, sum);
}
}
float buffer[16];
_mm512_storeu_ps(buffer, sum);
return buffer[0] + buffer[1] + buffer[2] + buffer[3] + buffer[4] + buffer[5] +
buffer[6] + buffer[7] + buffer[8] + buffer[9] + buffer[10] +
buffer[11] + buffer[12] + buffer[13] + buffer[14] + buffer[15];
}
inline void mic_sincos_ps(mic_m512_t x, mic_m512_t *s, mic_m512_t *c) {
__m512i 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 cos_emm2 = _mm512_sub_epi32(emm2, _pi32_2);
__m512i emm0 = _mm512_and_epi32(emm2, _pi32_4);
__m512i cos_emm0 = _mm512_andnot_epi32(cos_emm2, _pi32_4);
emm0 = _mm512_slli_epi32(emm0, 29);
cos_emm0 = _mm512_slli_epi32(cos_emm0, 29);
sign_bit = _mm512_xor_epi32(sign_bit, emm0);
emm2 = _mm512_and_epi32(emm2, _pi32_2);
cos_emm2 = _mm512_and_epi32(cos_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);
__mmask16 cos_mask = _mm512_cmp_epi32_mask(cos_emm2, _pi32_0, _MM_CMPINT_EQ);
cos_emm2 = _mm512_mask_add_epi32(_pi32_0, cos_mask, _pi32_ffff, _pi32_0);
x = _mm512_fmadd_ps(y, _ps_minus_cephes_DP123, 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);
y = _mm512_fmadd_ps(_ps_coscof_p0, x2, _ps_coscof_p1);
y = _mm512_fmadd_ps(y, x2, _ps_coscof_p2);
mic_m512_t temp_2 = _mm512_fmsub_ps(x2, _ps_0point5, _ps_1);
y = _mm512_fmsub_ps(y, x4, temp_2);
mic_m512_t y2 = _mm512_fmadd_ps(_ps_sincof_p0, x2, _ps_sincof_p1);
y2 = _mm512_fmadd_ps(y2, x2, _ps_sincof_p2);
y2 = _mm512_fmadd_ps(y2, x3, x);
mic_m512_t cos_y = y;
mic_m512_t cos_y2 = y2;
y = _mm512_castsi512_ps(_mm512_andnot_epi32(emm2, _mm512_castps_si512(y)));
cos_y = _mm512_castsi512_ps(_mm512_andnot_epi32(cos_emm2, _mm512_castps_si512(cos_y)));
y2 = _mm512_castsi512_ps(_mm512_and_epi32(emm2, _mm512_castps_si512(y2)));
cos_y2 = _mm512_castsi512_ps(_mm512_and_epi32(cos_emm2, _mm512_castps_si512(cos_y2)));
y = _mm512_add_ps(y, y2);
cos_y = _mm512_add_ps(cos_y, cos_y2);
*s = _mm512_castsi512_ps(_mm512_xor_epi32(_mm512_castps_si512(y), sign_bit));
*c = _mm512_castsi512_ps(_mm512_xor_epi32(_mm512_castps_si512(cos_y), cos_emm0));
} // sincos_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;
}
void * avx512_fma(void *args_in)
{
/* Thread input */
struct thread_args *args;
const int n_avx512 = VFMAPS_LATENCY;
const __m512 add0 = _mm512_set1_ps((float) 1e-6);
const __m512 mul0 = _mm512_set1_ps((float) (1. + 1e-6));
__m512 r[n_avx512];
// Declare as volatile to prevent removal during optimisation
volatile float result;
long r_max, i;
int j;
double runtime, flops;
Stopwatch *t;
/* Read inputs */
args = (struct thread_args *) args_in;
t = stopwatch_create(args->timer_type);
for (j = 0; j < n_avx512; j++) {
r[j] = _mm512_set1_ps((float) j);
}
/* Add over registers r0-r4, multiply over r5-r9, and rely on pipelining,
* OOO execution, and latency difference (3 vs 5 cycles) for 2x FLOPs
*/
runtime_flag = 0;
r_max = 1;
do {
pthread_barrier_wait(&timer_barrier);
t->start(t);
for (i = 0; i < r_max; i++) {
#pragma unroll(n_avx512)
for (j = 0; j < n_avx512; j++)
r[j] = _mm512_fmadd_ps(r[j], mul0, add0);
}
t->stop(t);
runtime = t->runtime(t);
/* Set runtime flag if any thread exceeds runtime limit */
if (runtime > args->min_runtime) {
pthread_mutex_lock(&runtime_mutex);
runtime_flag = 1;
pthread_mutex_unlock(&runtime_mutex);
}
pthread_barrier_wait(&timer_barrier);
if (!runtime_flag) r_max *= 2;
} while (!runtime_flag);
/* In order to prevent removal of the prior loop by optimisers,
* sum the register values and save the result as volatile. */
for (j = 0; j < n_avx512; j++)
r[0] = _mm512_add_ps(r[0], r[j]);
result = reduce_AVX512(r[0]);
/* (iter) * (16 instr / reg) * (2 flops / instr) * (n_avx512 reg / iter) */
flops = r_max * 16 * 2 * n_avx512 / runtime;
/* Cleanup */
t->destroy(t);
/* Thread output */
args->runtime = runtime;
args->flops = flops;
args->bw_load = 0.;
args->bw_store = 0.;
pthread_exit(NULL);
}
static batch_type fma(const batch_type& x, const batch_type& y, const batch_type& z)
{
return _mm512_fmadd_ps(x, y, z);
}
