MOD: add comments to a53 zgemm kernel
This commit is contained in:
parent
9f59b19fcd
commit
5c1cd5e0c2
|
@ -25,9 +25,120 @@ OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
|
|||
USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
*****************************************************************************/
|
||||
|
||||
#include <common.h>
|
||||
#include "common.h"
|
||||
#include <arm_neon.h>
|
||||
|
||||
/*******************************************************************************
|
||||
The complex GEMM kernels in OpenBLAS use static configuration of conjugation
|
||||
modes via specific macros:
|
||||
|
||||
MACRO_NAME | conjugation on matrix A | conjugation on matrix B |
|
||||
---------- | ----------------------- | ----------------------- |
|
||||
NN/NT/TN/TT | No | No |
|
||||
NR/NC/TR/TC | No | Yes |
|
||||
RN/RT/CN/CT | Yes | No |
|
||||
RR/RC/CR/CC | Yes | Yes |
|
||||
|
||||
"conjugation on matrix A" means the complex conjugates of elements from
|
||||
matrix A are used for matmul (rather than the original elements). "conjugation
|
||||
on matrix B" means the complex conjugate of each element from matrix B is taken
|
||||
for matrix multiplication, respectively.
|
||||
|
||||
Complex numbers in arrays or matrices are usually packed together as an
|
||||
array of struct (without padding):
|
||||
struct complex_number {
|
||||
FLOAT real_part;
|
||||
FLOAT imag_part;
|
||||
};
|
||||
|
||||
For a double complex array ARR[] which is usually DEFINED AS AN ARRAY OF
|
||||
DOUBLE, the real part of its Kth complex number can be accessed as
|
||||
ARR[K * 2], the imaginary part of the Kth complex number is ARR[2 * K + 1].
|
||||
|
||||
This file uses 2 ways to vectorize matrix multiplication of complex numbers:
|
||||
|
||||
(1) Expanded-form
|
||||
|
||||
During accumulation along direction K:
|
||||
|
||||
Σk(a[0][k].real b[k][n].real)
|
||||
accumulate Σk(a[0][k].imag b[k][n].real)
|
||||
-------------------> .
|
||||
| * b[k][n].real .
|
||||
| (broadcasted) .
|
||||
a[0][k].real Σk(a[v-1][k].real b[k][n].real)
|
||||
a[0][k].imag Σk(a[v-1][k].imag b[k][n].real)
|
||||
. VECTOR I
|
||||
(vec_a) .
|
||||
.
|
||||
a[v-1][k].real Σk(a[0][k].real b[k][n].imag)
|
||||
a[v-1][k].imag Σk(a[0][k].imag b[k][n].imag)
|
||||
| .
|
||||
| accumulate .
|
||||
-------------------> .
|
||||
* b[k][n].imag Σk(a[v-1][k].real b[k][n].imag)
|
||||
(broadcasted) Σk(a[v-1][k].imag b[k][n].imag)
|
||||
VECTOR II
|
||||
|
||||
After accumulation, prior to storage:
|
||||
|
||||
-1 -Σk(a[0][k].imag b[k][n].imag)
|
||||
1 Σk(a[0][k].real b[k][n].imag)
|
||||
. .
|
||||
VECTOR II permute and multiply . to get .
|
||||
. .
|
||||
-1 -Σk(a[v-1][k].imag b[k][n].imag)
|
||||
1 Σk(a[v-1][k].real b[k][n].imag)
|
||||
|
||||
then add with VECTOR I to get the result vector of elements of C.
|
||||
|
||||
2 vector registers are needed for every v elements of C, with
|
||||
v == sizeof(vector) / sizeof(complex)
|
||||
|
||||
(2) Contracted-form
|
||||
|
||||
During accumulation along direction K:
|
||||
|
||||
(the K coordinate is not shown, since the operation is identical for each k)
|
||||
|
||||
(load vector in mem) (load vector in mem)
|
||||
a[0].r a[0].i ... a[v-1].r a[v-1].i a[v].r a[v].i ... a[2v-1].r a[2v-1]i
|
||||
| |
|
||||
| unzip operation (or VLD2 in arm neon) |
|
||||
-----------------------------------------------------
|
||||
|
|
||||
|
|
||||
--------------------------------------------------
|
||||
| |
|
||||
| |
|
||||
v v
|
||||
a[0].real ... a[2v-1].real a[0].imag ... a[2v-1].imag
|
||||
| | | |
|
||||
| | * b[i].imag(broadcast) | |
|
||||
* b[i].real | -----------------------------|---- | * b[i].real
|
||||
(broadcast) | | | | (broadcast)
|
||||
| ------------------------------ | |
|
||||
+ | - | * b[i].imag(broadcast) + | + |
|
||||
v v v v
|
||||
(accumulate) (accumulate)
|
||||
c[0].real ... c[2v-1].real c[0].imag ... c[2v-1].imag
|
||||
VECTOR_REAL VECTOR_IMAG
|
||||
|
||||
After accumulation, VECTOR_REAL and VECTOR_IMAG are zipped (interleaved)
|
||||
then stored to matrix C directly.
|
||||
|
||||
For 2v elements of C, only 2 vector registers are needed, while
|
||||
4 registers are required for expanded-form.
|
||||
(v == sizeof(vector) / sizeof(complex))
|
||||
|
||||
For AArch64 zgemm, 4x4 kernel needs 32 128-bit NEON registers
|
||||
to store elements of C when using expanded-form calculation, where
|
||||
the register spilling will occur. So contracted-form operation is
|
||||
selected for 4x4 kernel. As for all other combinations of unroll parameters
|
||||
(2x4, 4x2, 2x2, and so on), expanded-form mode is used to bring more
|
||||
NEON registers into usage to hide latency of multiply-add instructions.
|
||||
******************************************************************************/
|
||||
|
||||
static inline float64x2_t set_f64x2(double lo, double hi) {
|
||||
float64x2_t ret = vdupq_n_f64(0);
|
||||
ret = vsetq_lane_f64(lo, ret, 0);
|
||||
|
|
Loading…
Reference in New Issue