In a programming language of your choice (but preferably C++), implement 2-D convolution that uses a small 8-bit signed vector-matrix multiplier.
The functionality should be similar to that seen in tf.nn.conv2d, though just the base functionality is sufficient - not all options need to be considered (e.g. pick single values for padding, data_format, etc).
Assume the input to the Conv2D op is a 8-bit image of width W and height H, C input channels, D output channels, and batch size of 1. So the entire operation will have two inputs: a 3D input matrix [H, W, C] and a 4D filter [kh, kw, C, D]. The output is a 3D matrix created by the convolution of the input matrix with the filter. Remember, all the inputs and outputs should be 8-bit integers. For the multiplier unit, assume you have a function similar to (in no particular language):
z = mult(x, y)
Where:
z – An 8-bit matrix of shape [N, P], where [zi = xi * y]. i.e. the results of N vector-matrix multiplications
x – An 8-bit matrix of shape [N, P], essentially N P-sized vectors.
y – An 8-bit matrix of shape [P, P].
Assume P is fixed, as if we’ve made hardware specifically for that size, but allow input and kernel with any size width/height to the Conv2D operation.
Pretend we can only do 8-bit signed arithmetic for operations outside of the core multiplier. Annotate the code to point out where this may be an issue.
Test it.