Multiply-Accumulate

MADD and MSUB: Fused Multiply-Accumulate

Many real-world computations follow the pattern a + (b * c) or a - (b * c). ARM64 provides dedicated instructions for these patterns that execute in a single cycle.

"Warp 9.975, Mr. La Forge!" -- computing warp factors requires some serious multiply-accumulate math. Fortunately, MADD does it in a single instruction.

MADD -- Multiply-Add

MADD computes Xd = Xa + (Xn * Xm):

MADD X0, X1, X2, X3   // X0 = X3 + (X1 * X2)

The order of operands is: destination, first multiply source, second multiply source, addend.

A common use: computing MUL is actually encoded as MADD Xd, Xn, Xm, XZR (multiply and add zero).

MSUB -- Multiply-Subtract

MSUB computes Xd = Xa - (Xn * Xm):

MSUB X0, X1, X2, X3   // X0 = X3 - (X1 * X2)

This is extremely useful for computing remainders. Remember the remainder pattern?

// Old way: three instructions
UDIV X2, X0, X1       // quotient = a / b
MUL  X3, X2, X1       // temp = quotient * b
SUB  X4, X0, X3       // remainder = a - temp

// New way: two instructions with MSUB
UDIV X2, X0, X1       // quotient = a / b
MSUB X4, X2, X1, X0   // remainder = a - (quotient * b)

Dot Product

The dot product of two vectors is a fundamental operation in linear algebra, graphics, machine learning, and signal processing. For two vectors A and B of length N:

dot = A[0]*B[0] + A[1]*B[1] + ... + A[N-1]*B[N-1]

MADD is perfect for this. Start with an accumulator of 0 and repeatedly multiply-add:

MOV X4, #0             // accumulator = 0
// For each pair (a, b):
MADD X4, Xa, Xb, X4   // accumulator += a * b

Polynomial Evaluation

Another common application is evaluating polynomials. For ax^2 + bx + c, you can use Horner's method: (a*x + b)*x + c:

// Evaluate 3x^2 + 2x + 1 at x=5
MOV X0, #5         // x
MOV X1, #3         // a
MOV X2, #2         // b
MOV X3, #1         // c
MADD X1, X1, X0, X2  // X1 = a*x + b = 17
MADD X1, X1, X0, X3  // X1 = (a*x + b)*x + c = 86

Your Task

Compute the dot product of two 4-element vectors:

• A = [3, 5, 2, 4]
• B = [1, 4, 6, 2]

The dot product is: 31 + 54 + 26 + 42 = 3 + 20 + 12 + 8 = 43.

Use MADD for the accumulation. Print the result (43) followed by a newline.