# 5.7. Examples¶

## 5.7.1. Matrix multiplication¶

Here is a naive implementation of matrix multiplication using a HSA kernel:

```
@hsa.jit
def matmul(A, B, C):
i = hsa.get_global_id(0)
j = hsa.get_global_id(1)
if i >= C.shape[0] or j >= C.shape[1]:
return
tmp = 0
for k in range(A.shape[1]):
tmp += A[i, k] * B[k, j]
C[i, j] = tmp
```

This implementation is straightforward and intuitive but performs poorly, because the same matrix elements will be loaded multiple times from device memory, which is slow (some devices may have transparent data caches, but they may not be large enough to hold the entire inputs at once).

It will be faster if we use a blocked algorithm to reduce accesses to the
device memory. HSA provides a fast *shared memory*
for workitems in a group to cooperately compute on a task. The following
implements a faster version of the square matrix multiplication using shared
memory:

```
import numpy as np
from numba import hsa
blocksize = 20
gridsize = 20
@hsa.jit
def matmulfast(A, B, C):
x = hsa.get_global_id(0)
y = hsa.get_global_id(1)
tx = hsa.get_local_id(0)
ty = hsa.get_local_id(1)
sA = hsa.shared.array(shape=(blocksize, blocksize), dtype=float32)
sB = hsa.shared.array(shape=(blocksize, blocksize), dtype=float32)
if x >= C.shape[0] or y >= C.shape[1]:
return
tmp = 0
for i in range(gridsize):
# preload
sA[tx, ty] = A[x, ty + i * blocksize]
sB[tx, ty] = B[tx + i * blocksize, y]
# wait for preload to end
hsa.barrier(1)
# compute loop
for j in range(blocksize):
tmp += sA[tx, j] * sB[j, ty]
# wait for compute to end
hsa.barrier(1)
C[x, y] = tmp
N = gridsize * blocksize
A = np.random.random((N, N)).astype(np.float32)
B = np.random.random((N, N)).astype(np.float32)
C = np.zeros_like(A)
griddim = gridsize, gridsize
blockdim = blocksize, blocksize
with hsa.register(A, B, C):
ts = timer()
matmulfast[griddim, blockdim](A, B, C)
te = timer()
print("1st GPU time:", te - ts)
with hsa.register(A, B, C):
ts = timer()
matmulfast[griddim, blockdim](A, B, C)
te = timer()
print("2nd GPU time:", te - ts)
ts = timer()
ans = np.dot(A, B)
te = timer()
print("CPU time:", te - ts)
np.testing.assert_allclose(ans, C, rtol=1e-5)
```

Because the shared memory is a limited resources, the code preloads small
block at a time from the input arrays. Then, it calls
`barrier()` to wait until all threads have finished
preloading and before doing the computation on the shared memory.
It synchronizes again after the computation to ensure all threads
have finished with the data in shared memory before overwriting it
in the next loop iteration.