# SIMD

May 20, 2023

**SIMD** (*Single Instruction Multiple Data*) is a technique used in computer architecture to perform parallel processing on large sets of data. It is a type of instruction level parallelism that allows for the execution of multiple computations simultaneously.

The purpose of SIMD is to increase the speed and efficiency of computations by processing multiple data points at the same time, instead of processing them one-by-one. SIMD instructions are commonly used in multimedia and graphics applications, as well as in scientific and numerical computations.

## How SIMD Works

The basic idea behind SIMD is to use a single instruction to operate on multiple data elements simultaneously. This is achieved by using special registers, called vector registers, which can hold multiple data elements at once. SIMD instructions use these vector registers to perform a single operation on all the data elements at once.

For example, consider the following code snippet:

```
for (int i = 0; i < n; i++) {
c[i] = a[i] + b[i];
}
```

This code performs an element-wise addition of two arrays `a`

and `b`

, storing the result in array `c`

. Without SIMD, this code would execute the addition operation `n`

times, once for each element in the arrays. However, with SIMD, the addition operation can be performed on multiple elements at the same time, using a single instruction.

To use SIMD instructions, the data elements must be stored in a special format called a vector. A vector is a contiguous block of memory that contains multiple data elements packed tightly together. The size of a vector depends on the processor architecture, but is typically 128 or 256 bits.

To perform an operation on a vector, the vector is loaded into a vector register, and the SIMD instruction operates on the entire vector register. The result is then stored back into memory as a vector.

## Types of SIMD Instructions

There are two main types of SIMD instructions: integer SIMD and floating-point SIMD. Integer SIMD instructions operate on integers, while floating-point SIMD instructions operate on floating-point numbers.

In addition to these two types, there are also SIMD instructions that operate on Boolean values (logical SIMD), as well as instructions that perform other operations such as shuffling and packing/unpacking data.

## SIMD Implementations

SIMD instructions are implemented in various processor architectures, including x86, ARM, and PowerPC. Each architecture has its own set of SIMD instructions, which are optimized for that architecture.

One of the most widely used SIMD instruction sets is Intel’s SSE (*Streaming SIMD Extensions*) instruction set, which was introduced in the late 1990s. SSE provides a set of instructions for performing SIMD operations on both floating-point and integer data types.

In addition to SSE, Intel has also introduced newer SIMD instruction sets, including AVX (*Advanced Vector Extensions*) and AVX2, which provide even more powerful SIMD instructions.

Other processor manufacturers also have their own SIMD instruction sets. For example, ARM processors have the NEON instruction set, which provides SIMD instructions for both floating-point and integer data types.

## SIMD in Multimedia Applications

One of the most common uses of SIMD is in multimedia applications, such as video and audio processing. These applications require the manipulation of large sets of data, and SIMD instructions can greatly improve the performance of these operations.

For example, video decoding involves the decoding of multiple frames of video data, each of which contains millions of pixels. Without SIMD, the decoding process would be slow and inefficient. However, with SIMD, the decoding process can be performed much more quickly, as the same operation can be applied to multiple pixels at once.

Similarly, audio processing applications such as digital signal processing (DSP) and audio synthesis can benefit greatly from SIMD instructions. These applications typically require the manipulation of large sets of audio samples, and SIMD can greatly improve the performance of these operations.

## SIMD in Scientific and Numerical Applications

In addition to multimedia applications, SIMD instructions are also commonly used in scientific and numerical applications. These applications often involve the manipulation of large data sets, and SIMD can greatly improve the performance of these operations.

For example, matrix multiplication is a common operation in numerical computations. Without SIMD, matrix multiplication would be slow and inefficient, as each element of the resulting matrix would need to be computed one-by-one. However, with SIMD, multiple elements of the resulting matrix can be computed simultaneously, resulting in a significant performance improvement.

Other common numerical operations that can benefit from SIMD include vector addition, dot product, and Fast Fourier Transform (FFT).