# In this post you’ll know:

• What Accelerate is?
• Why it is worth to know it?
• Why SIMD makes calculations even easier?
• How to start research with Accelerate and SIMD?
• How to implement simple custom real-time video filter.

You might be an iOS developer with solid experience. But when it comes to low-level programming you feel scared anyway. Swift shows us all that programming language can be easy to read and just nice looking. On the other hand, low-level programming seems to avoid this purpose.

One of many examples of such an issue is the Accelerate framework. It is not so obvious how, why and when to use it.

When we see such method declaration

vImageConvert_RGBA8888toRGB888(
&sourceBuffer,
&destinationBuffer,
vImage_Flags(kvImageNoFlags))


first thought is: "How to deal with this magic? 😱.

## What is Accelerate? 🤔

TLDR: Accelerate is a framework to make mathematical computations faster. To help us define these computations, Accelerate contains some libraries. With them, we don't have to understand every detail to do some magic stuff. 🧙‍♀️✨

Apple describes this framework with: “Make large-scale mathematical computations and image calculations, optimized for high performance and low-energy consumption. (…) Accelerate provides high-performance, energy-efficient computations on the CPU by leveraging its vector-processing capability.” It’s everywhere when you have a significant workload to run on the CPU. Inside Accelerate there’s a lot of libraries, like vImage for image processing, the Swiss knife of image processing. (WWDC2017-711)

We don’t have to understand what actually happens in every detail, but what we can do is understand what specific sub-library does.

Let’s check the list of sub-libraries below:

• vImage: You can manipulate images, convert them to another format or add a custom filter to the them.
• vDSP: DSP means Digital Signal Processing. When you have some series of numerical data placed in some domain (for example, sound samples in the time domain, or pixels in dimension domain), you can process this data using this library.
• vForce: Calculations done on some vectors can be done so much faster with this library.
• BLAS, LAPACK, LinearAlgebra, Sparse BLAS, Sparse Solvers: Faster matrix computations.
• BNNS: neural networks
• SIMD: Allows us to talk directly with CPU vector units. By directly we mean as fast as possible.
• Compression: Lossless data compression

It is clearly visible that the power of Accelerate cannot be described in a single post. However, a single post can be a great start to begin this inspiring journey! 🧳😄

## Why it is worth to know it? 🤔

TLDR: Accelerate means efficiency in terms of mathematical computation, even these simple ones. Many APIs lead to fewer places to do mistakes because, for many common operations, API has an equivalent method. Accelerate also provides continuous support for the newest Apple hardware. Instead of being angry for not so eye-catching method definitions be thankful that someone implements this in an efficient way. 🔥⏩

To understand why it is worth to know to Accelerate let’s consider the following subjects. If you want try this code, don't forget import Accelerate, if necessary 😄

### Efficiency in even simple operations 👌

The first answer to the question “How to multiply a series of numbers by single value” ...

let x:[Float] = [0,1,2,3,4,5]
let n = x.count
var y = Array.init(repeating: Float(0), count: n)
var scale:Float = 2

... is just “for loop”.

for i in 0..<n {
y[i] = scale * x[i]
}


But with Accelerate this can be done a lot faster.

vDSP_vsmul(x, 1, &scale, &y, 1, vDSP_Length(n))


Yeah, it seems uglier, but it is significantly faster! Apple says that Accelerate, in this case, is 6 times faster and more energy-efficient! Now you can check the docs for this method to check how good you understand all of these things: https://developer.apple.com/documentation/accelerate/1450020-vdsp_vsmul

Note: Apple in 2019 provided some refined methods for swift. One of them is vDSP_vsmul method. You can check documentation here: https://developer.apple.com/documentation/accelerate/vdsp-snv

// Old
vDSP_vsmul(x, 1, &scale, &y, 1, vDSP_Length(n))
// New, but iOS 13 or macOS 10.15 is required.
vDSP.multiply(scale,x)

These updated methods are called by Apple "Swift overlays". So for searching these methods, you should look for such a term 😄

### Far less places to do mistakes ❌🕷

For example please consider multiplication of matrices:

var a:[Float] = [1, 2, 3, 1, 2, 3, 1, 2, 3]
var b:[Float] = [1, 0, 0, 0, 1, 0, 0, 0, 1]
var c:[Float] = [0, 0, 0, 0, 0, 0, 0, 0, 0]
var d:[Float] = [0, 0, 0, 0, 0, 0, 0, 0, 0]
let m = 3
let n = 3
let p = 3

for row in 0..<m {
for col in 0..<n {
for k in 0..<p {
c[row + m * col] += a[row + m * k] * b[k + p * col]
}
}
}


Can you count how many places are prone to errors? I can’t 😄

Let’s check Accelerate’s implementation:

cblas_sgemm(
CblasColMajor, /// This param describes how to parse matrix array.
CblasNoTrans, /// Input matrix can be transposed optionally!
CblasNoTrans,
Int32(m),
Int32(n),
Int32(p),
1.0, // Scaling factor for the product of matrices A and B. Simply multiplification requires that this parameter is equal to one.
&a, // Reference to A matrix.
Int32(m),
&b, // Reference to B matrix
Int32(p),
0.0, // Scaling factor for matrix C. Doesn't matter here.
&c, // Reference to C matrix.
Int32(m) //The size of the first dimension of matrix C)
)


This time code is 100 times faster and 26 times more energy efficient. Really great thing!

### Many APIs 🔌🔌🔌

Accelerate provides 2800 APIs approximately, which leads to less code, more efficiency, more performance. Accelerate take care of multithreading, hardware architecture compatibility and whatsoever. Exploring Accelerate possibilities can lead to really great apps.

### Apple’s support 🍏

As it is Apple’s framework, you can be sure that with releasing new hardware, solutions implemented in Accelerate will benefit fully from the power of new hardware.

## What is SIMD? 🤔

I guess you have noted that Accelerate methods require passing additional parameters that seem redundant For example, in matrix multiplication, we also need to pass the size of this matrix. Let’s consider the following calculation:

$\ \begin{bmatrix} 1 & 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 3 \end{bmatrix} *\ \ \begin{bmatrix} 1\\ 1\\ 1 \end{bmatrix} =\ \begin{bmatrix} 1\\ 2\\ 3 \end{bmatrix}$

With accelerate:

import Accelerate
var A: [Float] = [1,0,0,0,2,0,0,0,3]
var x: [Float] = [1,1,1]
var y = [Float](repeating:0, count:3)
cblas_sgemv(CblasColMajor, CblasNoTrans, 3, 3, 1, &A, 3, &x, 1, 0, &y, 1)


With GLKit:

import GLKit
let A = GLKMatrix3(m: (1, 0, 0, 0, 2, 0, 0, 0, 3))
let x = GLKVector3(v: (1, 1, 1))
let y = GLKMatrix3MultiplyVector3(A, x)


With SIMD:

import simd
let A = float3x3(diagonal: [1,2,3])
let x = float3(1, 1, 1)
let y = A*x


Do you see differences? Usable initializers for diagonal matrices and vertical vectors and straightforward multiplication operators.

Doing countless operations like that makes our appreciation for SIMD stronger and stronger 😄

## Where to start?

TLDR: Apple provides a nice set of documentation. Some of these articles are strictly mathematical, but most of them are focused on practical stuff.

Apple provides set of example projects to show us, how to use Accelerate. What these terms actually mean? Let’s do some overview of Accelerate documentation (https://developer.apple.com/documentation/accelerate) What we can find there?

• Image Processing Essentials.
• Image processing takes conversion between format that we got, and formats that Accelerate works with.
• vImage works on buffers, so separate article is about how to work with them.
• As the user wants to see results as quickly as possible, vImage allows creating a displayable representation of buffers.
• Image processing is an entire workflow. You must get from somewhere an image, process it to usable form, do some operations on it, and create displayable form. Basically. How to connect all these steps? This is described in a separate article.
• Not always we want to process the entire image, but just some separate regions. It is also possible!
• Accelerate gives a huge boost in performance, but on our side always can be done some improvements. The documentation covers also this subject.
• Signal Processing Essentials. Raw signal processing.
• Operate selectively on the elements of a vector at regular intervals.
• Data interpolation! With this, you can “fill the gaps in arrays of numerical data.”. Really great feature, when your signal is incomplete and instead of displaying gaps you want to make your graph smoother.
• Resampling a Signal with Decimation. It is a great feature. If you want to reduce the resolution of the signal and loose as few details as possible.
• Core Video Interoperation. Image processing is not limited only to static images, but can be used as real-time video effects!
• Vectors, Matrices, and Quaternions. Imagine defining some 3d objects. How to make them move or rotate smoothly? The answer you will find here.
• Fourier and Cosine Transforms. Imagine that you what to remove the noise effect from the image. Fourier and Cosine transform allows you to do that. Allows mathematically to find items in a set of data that don’t really matter and removing them won’t change signal or image significantly at first sight.
• Audio Processing. Accelerate contains cosine transform implementation, which is really useful with audio processing. Separate articles from Apple will show us how it works.
• Conversion Between Image Formats. This is not so short subject. Many formats of images, many color spaces (RGB, CMYK, etc.) force us to do many conversions, so I do not wonder that separate article is for that.
• Image Resampling. In processing images in various ways we must control result size of our results. Resampling is basically for that.
• Convolution and Morphology. Blurring or bokeh effect takes into account not some specific pixel, but also pixels around that pixel. That type of processing is addressed here.
• Color and Tone Adjustment. Here Apple introduces us histograms. For example, you can align colours from one image to another. This makes both images have the same colour palette.
• vImage / vDSP Interoperability. Finding the sharpest image in a sequence of captured images. Really awesome!
• Sparse Matrices. If you remember equations with unknowns, here is the topic for you.
• Compression. In my opinion it is great that we can compress data by ourselves. That means whole new level of security 😃

Now we have idea what we can achieve with Accelerate. Let’s do some example. Easy as possible. 😎

## Image Processing 🖼

TLDR: Apple provides a demo project, where we can learn how to implement custom image processing, and analyze differences between used data formats.

All these things can be useful for making complex calculations, but in my opinion, the most convenient way to make this knowledge really practical is by doing some image processing. Let’s go to the Real-Time Video Effects with vImage Apple’s tutorial and just download example project. You will find a lot of detailed information how it works.

Basically this example app provides a set of custom video filters. I made some screenshots of this app for you. Let’s add another filter!

Open project and ViewController.swift file. Find DemoMode enum. Let’s add another case for this enum, for our filtering type.

enum DemoMode: String {
case saturation = "Saturation"
case rotation = "Rotation"
case blur = "Blurring"
case dither = "Dither"
case lookupTable = "Lookup Table"
case custom = "Custom" // Our custom type.
}


Find let modeSegmentedControlItem declaration. Here we implement add our custom type to segmented control.

let segmentedControl = UISegmentedControl(items:[
DemoMode.saturation.rawValue,
DemoMode.rotation.rawValue,
DemoMode.blur.rawValue,
DemoMode.dither.rawValue,
DemoMode.lookupTable.rawValue,
DemoMode.custom.rawValue
])


Find func displayYpCbCrToRGB(pixelBuffer: CVPixelBuffer). Here we will implement our custom filter.

Find switch statement.

        switch mode {
case .rotation:
let backcolor: [UInt8] = [255, 255, 255, 255]


Add our custom filter by implementing case .custom.

case .custom:
// Change these coefficient constants and check result!
let redCoefficient: Float = 0.2126
let greenCoefficient: Float = 0.7152
let blueCoefficient: Float = 0.0722
// Divisior is used for normalisation.
// By using this value we take care about cases when a computed pixel is above the displayable value
// (for example in RGB format, color (255,250,700) is invalid)
let divisor: Int32 = 0x1000
let fDivisor = Float(divisor)

// Each pixel will be multiplied by these values.
var coefficientsMatrix = [
Int16(redCoefficient * fDivisor),
Int16(greenCoefficient * fDivisor),
Int16(blueCoefficient * fDivisor)
]
let preBias: [Int16] = [0, 0, 0, 0] // These values will be added before processing to each channel of a pixel.
let postBias: Int32 = 2 // This value will be added to each pixel at the end of processing.

// Fill our temporary buffer with initial data
var tmpBuffer = vImage_Buffer()
vImageBuffer_Init(&tmpBuffer,
destinationBuffer.height,
destinationBuffer.width,
cgImageFormat.bitsPerPixel,
vImage_Flags(kvImageNoFlags))
// Fill our temporary buffer with initial data
vImageCopyBuffer(&destinationBuffer,
&tmpBuffer,
4,
vImage_Flags(kvImageNoFlags))
// Produce single channel data.
vImageMatrixMultiply_ARGB8888ToPlanar8(&tmpBuffer,
&destinationBuffer,
&coefficientsMatrix,
divisor,
preBias,
postBias,
vImage_Flags(kvImageNoFlags))

free(tmpBuffer.data) // Skip this line, and app will crash!


After this, we also need to implement another type conversion to displayable type, because we switched to single channel image (monochromatic images can be represented by just one channel for each pixel). Let’s handle this issue quickly as possible, by just catching this case by swapping image format in vImageCreateCGImageFromBuffer.

        let monoFormat = vImage_CGImageFormat(
bitsPerComponent: 8,
bitsPerPixel: 8,
colorSpace: Unmanaged.passUnretained(CGColorSpaceCreateDeviceGray()),
bitmapInfo: CGBitmapInfo(rawValue: CGImageAlphaInfo.none.rawValue),
version: 0,
decode: nil,
renderingIntent: .defaultIntent
)

var format = mode == .custom ? monoFormat : cgImageFormat

let cgImage = vImageCreateCGImageFromBuffer(&destinationBuffer,
&format,
nil,
nil,
vImage_Flags(kvImageNoFlags),
&error)

if let cgImage = cgImage, error == kvImageNoError {
DispatchQueue.main.async {
self.imageView.image = UIImage(cgImage: cgImage.takeRetainedValue())
}
}


Yeah! It works 😃

It is just simple example. For a start I recommend just to download Apple’s demos, mix them, analyse differences.

Most of the difficulties with understanding all of these things are caused by different data domains. We convert some data from one domain to another to make possible doing some special processing. The key to understanding the power of Accelerate is understanding how each domain works. We can save images as three two-dimensional arrays of basic colors (Red, Green, Blue), we can save images as a result of the Fourier transform, we can save images as series of compressed data. Each format has different advantages. Use them to do some magic! 😄🧙🏻‍♂️✨

And that’s it. 😅

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