Populates arrayA[] with 64 values

arrayA[i] = 0x0100 + (rand() & 0x001F);

In this step, we are generating 64 random values between 0x0100 and 0x011F (because we have added a pseudo-random integral number in the range between 0 and 0x001F to our original 0x0100).

Populates arrayB[] with 64 values

arrayB[i] = 0x0040 + (rand() & 0x000F);

In this step, we are generating 64 random values between 0x0040 and 0x004F (because we have added a pseudo-random integral number in the range between 0 and 0x000F to our original 0x0040).

After we have populated our arrays, we need to pass those parameters from C to assembly. The C functions pass their parameters to other functions (including assembly functions) through the W registers. It is important to note that the W registers are used in the order that the parameters are passed to the function.

In order to be able to pass both coefficients to just one W register (W0), we created an array of 2 elements called coeffs. As we can see in the code above, the parameter coeffs in the linearize function doesn't need the '&' symbol (which indicates we are passing an address) because C automatically passes the address of the first element inside an array. To access the second coefficient we then just increment W0 as can be seen below:

• Passed to linearize.S:
  • • W0 : polynomial coefficient a1
    • W0+2 : polynomial coefficient a2
    • W1 : pointer to averagedArrays

• Returned from linearize.S:
  • • W2 : pointer to linearOut

$linearOut = ($ 0x2C3C $* (averagedArrays) )- ($ 0x0179 $* (averagedArrays)^2))$

[w2] = ( [w0] * [w1] ) - ([w0+2] * [w1]²)

In the assembly code below, we can observe that the first step is to PUSH our registers onto the stack. Then, after configuring accumulators A and B, we move the addresses of coefficients a1 and a2 into W8 and W9 respectively. Lastly, we move the address of averagedArrays into W10 which is a pointer to Y data space.

To calculate the first part of the linearization, we clear Accumulator A, preload W4 with a1, and pre-load W5 with averagedArrays, all in a single instruction. After that, using the MPY instruction, we multiply a1 with averagedArrays and store the result in Accumulator A.

For the second part of the linearization, we first need to square averagedArrays. To do this, we will multiply W5 by W5 since averagedArrays was previously loaded into this register, and store the result in Accumulator B. During that same MPY instruction we are also going to pre-load W4 with the second coefficient, a2. The next step is to store averagedArrays² into W5.

Lastly, in line 38, we multiply a2 by averagedArrays² and subtract that from Accumulator A, which previously contained the result of multiplying a1 and averagedArrays together. That result gets stored back into ACCA. Line 42 then stores the result in Accumulator A into W2 which points to the function linearOut.