MultiplyAccumulate

Multiply-accumulate, often abbreviated MAC, refers to an operation that multiplies two numbers and adds the product to an accumulator. In many systems the canonical form is the simple state update y := y + (a × b). MAC operations are a fundamental primitive in digital signal processing, computer vision, and machine learning workloads because they efficiently combine multiplication and accumulation in a single step.

A MAC unit typically comprises a multiplier, an adder, and an accumulator. It may operate on fixed-point or floating-point data and can implement saturating, modular, or floating-point arithmetic. In practice, MAC units are often pipelined and can be replicated in parallel to boost throughput, enabling large numbers of MACs to execute simultaneously in DSPs, microprocessors, and hardware accelerators.

MACs are central to many algorithms and applications. In digital signal processing, they implement finite impulse response (FIR) filters, where the output is a weighted sum of recent inputs, computed as a sequence of MACs. In neural networks and other AI workloads, MACs compute the weighted sums that form neuron activations, making MAC throughput a critical performance metric for accelerators.

Variants and related concepts include fused multiply-add (FMA), which computes (a × b) + c in one operation with a single rounding, reducing latency and numeric error. Some architectures provide separate MAC and add instructions or specialize MACs for fixed-point saturation behavior. Overall, MACs are a ubiquitous building block across hardware and software for efficient arithmetic-intensive computation.