Matrix matrix multiplication

For your first foray into chisel you will design a matrix matrix multiplication unit. Matrix multiplication is fairly straight forward, however on hardware it's a little trickier than the standard for loops normally employed..

Task 1 - Vector

The first component you should implement is a register bank for storing a vector.

In Vector.scala you will find the skeleton code for this component. Unlike the standard Chisel.Vec our custom vector has a read enable which means that the memory pointed to by idx will only be overWritten when readEnable is true.

Implement the vector and test that it works by running testOnly Ex0.VectorSpec in your sbt console.

Task 2 - Matrix

The matrix works just like the vector only in two dimensions. The skeleton code and associated tests should make the purpose of this module obvious. Run the tests with testOnly Ex0.VectorSpec

Task 3 - Dot Product

This component differs from the two previous in that it has no explicit control input, which might at first be rather confusing.

With only two inputs for data, how do we know when the dotproduct has been calculated? The answer to this is the elements argument, which tells the dot product calculator the size of the input vectors. Consequently, the resulting hardware can only (at least on its own) compute dotproducts for one size of vector, which is fine in our circuit.

To get a better understanding we can model this behavior in regular scala:

case class DotProdCalculator(vectorLen: Int, timeStep: Int, accumulator: Int){
  def update(inputA: Int, inputB: Int): (Int, Boolean, DotProdCalculator) = {
    val product = inputA * inputB
    if(((timeStep + 1) % vectorLen) == 0){
      (accumulator + product, true, this.copy(timeStep = 0, accumulator = 0))
    else
      (accumulator + product, false, this.copy(timeStep = this.timeStep + 1, accumulator = accumulator + product))
    }
  }
}

To see it in action run testOnly Ex0.DPCsimulatorSpec in your sbt console.

As with the previous tasks, the dot product calculator must pass the tests with testOnly Ex0.DotProdSpec

Task 4 - Matrix Matrix multiplication

With our matrix modules and dot product calculators we have every piece needed to implement the matrix multiplier.

When performing matrix multiplication on a computer transposing the second matrix can help us reduce complexity by quite a lot. To examplify, consider

    | 2,  5 |
A = | 7, -1 |
    | 0,  4 |
    

B = | 1,  1,  2 |
    | 0,  4,  0 |

It would be much simpler to just have two modules with the same dimensions, and we can do this by transposing B so we get

     | 2,  5 |
A  = | 7, -1 |
     | 0,  4 |
    
     | 1,  0 |
BT = | 1,  4 |
     | 2,  0 |

Now we need to do is calculate the dot products for the final matrix:

if A*B = C then

     |  A[0] × BT[0],   A[0] × BT[1],   A[0] × BT[2] |
C  = |  A[1] × BT[0],   ...         ,   ...          |
     |  ...         ,   ...         ,   A[2] × BT[2] |

where 
A[0] × BT[0] is the dot product of [2, 5] and [1, 0]
and
A[0] × BT[1] is the dot product of [2, 5] and [1, 4]
and so forth..

Because of this, the input for matrix B will be supplied transposed, thus you do not have to worry about this. For B the input would be [1, 0, 1, 4, 2, 0]

The skeleton code for the matrix multiplier is less detailed, with only one test. You're encouraged to write your own tests to make this easier. Additionally, if you feel like you're getting stuck you can take a look at MatMulTips.org

Bonus exercise - Introspection on code quality and design choices

This last exercise has no deliverable, but you should spend some time thinking about where you spent most of your efforts.

A common saying is "A few hours of work can save you from several minutes of planning", and this holds especially true for writing chisel!!

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