I ran into this question when writing a program. I need to generate two matrices, and calculate their product.
However, I must ensure all entries are within 8-bit signed integer range, i.e. $[-128, 128)$. Is there a way to algorithmically achieve this?
Furthermore, what if I need every intermediate result during calculation is also within such range?
Besides, I think the algorithm needs not to be deterministic, but with high probability is enough. For example, is there a way to randomly generate the initial $A$ and $B$, so that the entries of product $AB$ are highly likely to within $[-128, 127)$? If so, I can run the program several times to be lucky.
The dimensions of $A$ and $B$ are inputs of the program, which are typically 1K ~ 5K.