Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
Concept
Multiply–accumulate operation
Summary
In computing, especially digital signal processing, the multiply–accumulate (MAC) or multiply-add (MAD) operation is a common step that computes the product of two numbers and adds that product to an accumulator. The hardware unit that performs the operation is known as a multiplier–accumulator (MAC unit); the operation itself is also often called a MAC or a MAD operation. The MAC operation modifies an accumulator a:
When done with floating point numbers, it might be performed with two roundings (typical in many DSPs), or with a single rounding. When performed with a single rounding, it is called a fused multiply–add (FMA) or fused multiply–accumulate (FMAC).
Modern computers may contain a dedicated MAC, consisting of a multiplier implemented in combinational logic followed by an adder and an accumulator register that stores the result. The output of the register is fed back to one input of the adder, so that on each clock cycle, the output of the multiplier is added to the register. Combinational multipliers require a large amount of logic, but can compute a product much more quickly than the method of shifting and adding typical of earlier computers. Percy Ludgate was the first to conceive a MAC in his Analytical Machine of 1909, and the first to exploit a MAC for division (using multiplication seeded by reciprocal, via the convergent series (1+x)−1). The first modern processors to be equipped with MAC units were digital signal processors, but the technique is now also common in general-purpose processors.
When done with integers, the operation is typically exact (computed modulo some power of two). However, floating-point numbers have only a certain amount of mathematical precision. That is, digital floating-point arithmetic is generally not associative or distributive. (See .)
Therefore, it makes a difference to the result whether the multiply–add is performed with two roundings, or in one operation with a single rounding (a fused multiply–add). IEEE 754-2008 specifies that it must be performed with one rounding, yielding a more accurate result.
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related courses (1)
CS-471: Advanced multiprocessor architecture
Multiprocessors are now the defacto building blocks for all computer systems. This course will build upon the basic concepts offered in Computer Architecture I to cover the architecture and organizati
Related publications (32)
Related people (8)
Related concepts (15)
POWER4
The POWER4 is a microprocessor developed by International Business Machines (IBM) that implemented the 64-bit PowerPC and PowerPC AS instruction set architectures. Released in 2001, the POWER4 succeeded the POWER3 and RS64 microprocessors, enabling RS/6000 and eServer iSeries models of AS/400 computer servers to run on the same processor, as a step toward converging the two lines. The POWER4 was a multicore microprocessor, with two cores on a single die, the first non-embedded microprocessor to do so.
Quadruple-precision floating-point format
In computing, quadruple precision (or quad precision) is a binary floating point–based computer number format that occupies 16 bytes (128 bits) with precision at least twice the 53-bit double precision. This 128-bit quadruple precision is designed not only for applications requiring results in higher than double precision, but also, as a primary function, to allow the computation of double precision results more reliably and accurately by minimising overflow and round-off errors in intermediate calculations and scratch variables.
Kepler (microarchitecture)
Kepler is the codename for a GPU microarchitecture developed by Nvidia, first introduced at retail in April 2012, as the successor to the Fermi microarchitecture. Kepler was Nvidia's first microarchitecture to focus on energy efficiency. Most GeForce 600 series, most GeForce 700 series, and some GeForce 800M series GPUs were based on Kepler, all manufactured in 28 nm. Kepler also found use in the GK20A, the GPU component of the Tegra K1 SoC, as well as in the Quadro Kxxx series, the Quadro NVS 510, and Nvidia Tesla computing modules.