Here is a naive implementation of matrix multiplication using a HSA kernel:
@roc.jit def matmul(A, B, C): i = roc.get_global_id(0) j = roc.get_global_id(1) if i >= C.shape or j >= C.shape: return tmp = 0 for k in range(A.shape): 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 cooperatively 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 roc from numba import float32 from time import time as timer blocksize = 16 gridsize = 16 @roc.jit('(float32[:,:], float32[:,:], float32[:,:])') def matmulfast(A, B, C): x = roc.get_global_id(0) y = roc.get_global_id(1) tx = roc.get_local_id(0) ty = roc.get_local_id(1) sA = roc.shared.array(shape=(blocksize, blocksize), dtype=float32) sB = roc.shared.array(shape=(blocksize, blocksize), dtype=float32) if x >= C.shape or y >= C.shape: 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 roc.barrier(1) # compute loop for j in range(blocksize): tmp += sA[tx, j] * sB[j, ty] # wait for compute to end roc.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 roc.register(A, B, C): ts = timer() matmulfast[griddim, blockdim](A, B, C) te = timer() print("1st GPU time:", te - ts) with roc.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 resource, the code preloads a small
block at a time from the input arrays. Then, it calls
barrier() to wait until all threads have finished
preloading 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.