Category Archives: Features

.NET, Features, ILNumerics, Scientific Computing

ILNumerics: High Performance as Default

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ILNumerics releases Version 7.0

The ILNumerics team is proud and excited to announce the availability of a new major release of its ILNumerics Ultimate VS product line. This milestone represents a significant advancement in compiler technology: it introduces the first autonomously parallelizing array compiler, ILNumerics Accelerator.

Array codes, such as numpy and Matlab, are popular within the scientific community. They simplify the description of complex numerical algorithms. However, when these numerical codes are implemented into industrial-grade products, distributed to customers, and maintained by a larger development team for many years, existing tools reveal considerable limitations, with execution speed being possibly the greatest limitation.

ILNumerics Accelerator is here to resolve this issue once and for all. Built on the convenient language of ILNumerics Computing Engine for authoring scientific array codes directly in C# /.NET, our intelligent Accelerator compiler reformulates array codes and executes them in the most efficient manner, unguided and autonomously.

Short Dive: Building an Array Compiler …

The key to optimal hardware utilization today is, of course, the ability to efficiently parallelize the workload. Therefore, ILNumerics Accelerator compiler automatically detects and utilizes parallel potential within subsequent array instructions of your algorithm.

The prevalent approach to automatic parallelization today involves analyzing your code to detect instructions that can execute in parallel. The code is then rewritten to allow these independent instructions to run concurrently. This approach originated at a time when C/C++ and FORTRAN were considered ‘high-level’ languages. While these languages offer some basic array support, numerical algorithms written in them inherently deal with scalar data.

In contrast, the algorithms we handle use n-dimensional arrays as the fundamental data type. When striving for real efficiency, the arrays’ complexity prohibits any compile-time decision about data independence, a suitable execution device, or a low-level implementation using vector instructions, among other factors. Too many variables determine the optimal execution strategy, and their variation is too extensive to identify at development time.

… with a fresh Approach to Parallelization …

ILNumerics takes a data-driven approach to parallelization, making all crucial decisions ‘just in time’ at runtime. This method enables us to implement the low-level internals of array instructions efficiently and eliminates the need for expensive dependency analysis of large program segments. It’s easier to determine at runtime whether an instruction relies on other data and when that data will be available.

However, this increases the compiler’s complexity significantly. Instead of producing fixed code for an array instruction found in the original program, we now generate an intermediate program, often representing several subsequent array instructions. This intermediate program is then transformed at runtime to reflect the original instructions in a manner that respects all influencing factors and enables optimal efficiency.

… with Intelligence and Freedom

These programs all run asynchronously, scheduling themselves onto suitable devices for execution at runtime. They connect with previous and subsequent asynchronous neighbors on the fly, even as they progress in calculating results. They autonomously determine the optimal implementation on the device they select. Significant decision-making power comes with immense responsibility. The final program code builds up asynchronously and autonomously at runtime.

Executing the same code branch twice may result in very different machine instructions. As the creators of the compiler, we can’t predict many details of the final implementation. We can’t even forecast the actual number of asynchronous programs, which we refer to as segments, executing concurrently. The decision now rests with the computer. It has a better understanding of the situation than we do and can process information and make educated decisions much faster and more effectively.

Why another Beta, then?

The first autonomous array compiler has arrived. Are you eager to try it out? Great! Go ahead and test the current beta from nuget.org. Its performance is genuinely impressive.

The majority of our users are building industrial products and have chosen ILNumerics for its reliability and seamless integration into .NET (which means all of .NET, since 2005). The compiler will become a regular part of the ILNumerics Computing Engine once it’s ready. Currently, it’s like a young child, learning new things each day. It’s learning to walk and talk, occasionally stumbling over previously unknown obstacles. Sometimes, it even surprises its creators with unexpected efficiency.

With recent advancements, the Accelerator compiler is now set to ‘always on’ mode. This marks a significant milestone in the development of a compiler. It’s now trusted to be stable and flexible enough to handle all codes, even unseen ones, ensuring it produces correct results and serves its primary purpose: to enhance efficiency.

The compiler will continue to develop until the final release. It will become more stable and gain more real-world exposure. We would greatly appreciate if your feedback contributes to its maturity by then.

All previous modules of ILNumerics have been adapted for the new Accelerator. They are thoroughly tested, have undergone many bugfixes and improvements, and are available for production on nuget.org as of today.

 

Introducing the ILNumerics Accelerator:

[ Video does not show? Download here: https://ilnumerics.net/media/andere/ILNumerics_Segments_2022.mp4 ]

Accelerator, Features, HPC, ILNumerics, Numerical Algorithms, Scientific Computing

ILNumerics Accelerator – A better Approach to faster Array Codes, Part II

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An better Approach to an unsolved Problem

TLDR: Authoring fast numerical array codes on .NET is a complex task. ILNumerics Computing Engine simplifies this task: it brings a convenient syntax, which is fully compatible to numpy and Matlab. And today, we bring back the free lunch: our brand new JIT compiler not only transforms numerical algorithms into highly efficient codes, it also automatically adopts to and parallelizes your workload on any hardware found at runtime. It segments and distributes even small workloads efficiently – more fine grained than any manual configuration could do.

Author: H. Kutschbach (ILNumerics)  Reading time: 12 min

Since its introduction in 2007 ILNumerics has led innovation for technical computing in the .NET world. We have enabled a short, expressive syntax for authors of numerical algorithms. Writing array based algorithms with ILNumerics feels very similar (and is compatible) to well known prototyping systems, namely: Matlab, numpy and all its successors.

Another focus of ILNumerics has always been: performance. In fact, we started the company in 2013 with the goal to build the fastest technology on earth. Today we propose a better, faster approach to array code execution: ILNumerics Accelerator.

This is part 2 of an article series on ILNumerics Accelerator. In the first part we’ve explained why automatic parallelization was too large a problem for the existing compiler landscape. In the following we start by describing the problem ILNumerics Accelerator solves. Then we’ll explain how it works.

The Problem Space

Math drives the world. High tech companies, financial institutions, medical instruments, rocket science … The most innovative projects do all have one thing in common: they are driven by numerical data and complex mathematical algorithms working on these data. Most data can be represented as n-dimensional arrays. They allow to implement great complexity without great effort. Consequently, array based algorithms play a huge role in todays most innovative industries.

Over the years we have seen many different attempts to realize the advantage of numerical arrays for small and large developer teams, working on .NET. Some large teams have even built their own solution. And indeed: building a math library in C# is easy to start with! You’ll see many low hanging fruits. With a few lines of code, you are able to create matrices and to sum them in short expressions, like ‘A + B’! Woooh!! If this is all you need then you can safely skip the rest of this article…

Often enough managers loose enthusiasm when after some months huge device codes built with such trivial ‘solution’ eventually show execution speed far below their requirements.

Optimal execution speed is only realized by efficient utilization of all compute resources.

What may sound simple is actually a problem that has been waiting for a solution for more than two decades. Todays hardware is mostly heterogeneous. Even inside a single CPU there are at least two levels of parallelism. Often, there is also at least one GPU around.

The only working way to utilize heterogeneous computing resources today was to manually distribute manually selected parts of an algorithm and its data to manually selected devices. Many tools exist which aim to help the programming expert to decide, write and fine-tune the required codes at development time. This still requires expert knowledge and intimate insights into the data flow of your algorithms. And it requires time. A lot of time! The large codes created this way need testing and maintenance.

Nevertheless, this demanding approach still cannot harness all performance potential! Needless to say that such results are far from being expressive and easy to understand. ILNumerics Accelerator is here to solve this problem for the large domain of numerical array codes.

The Big Performance Picture

Let’s widen our perspective on the performance topic! Three major factors influence execution speed:

1. The Algorithm

Basically, a program performs a transformation of data from one representation (input) into another representation (result). The transformation is described by the program´s algorithm(s). This high-level, business view on software is ‘lowered’ by the programmer when she writes the concrete program code, enabling a compiler to understand the intent. In subsequent compilation steps the code is then further lowered by one or more compilers into other representations, which can be better understood by the hardware. So, the programmer and the compiler(s) share responsibility to implement the intended transformation in a way that it is carried out on the available hardware and produces the correct result in the shortest time possible.

2. The Hardware

An optimally fast program must recognize and utilize all available hardware resources. The exact configuration and properties of all devices, however, is typically only known at runtime. This implies that a significant amount of transformation can only be done at runtime (-> JIT compiler). One may say, a program could be specialized for one specific set of computing resources. This is of course true, but it only shifts issues to the next time the hardware is to be renewed. Further, some properties of the hardware are inherently only known at runtime. Two examples: resource utilization rate and influences by other programs / threads running concurrently on the computer. If the final executable program fails to keep all parts of the hardware busy with useful instructions the program will require more time to run than necessary.

3. The Data

In general technical data is made out of individual numbers, or ‘scalars’. Traditionally, processor instructions deal with scalar data only. In array algorithms data forms arrays with arbitrary shape, size and dimensionality. This can be seen as an extension to the traditional scalar data model, since n-dimensional arrays include scalar data as a special case.

The array extension introduces great new complexity. Instead of a single number, having a type and a value, an array instruction deals with input data which may have one or many, often several million individual values! But arrays can also be empty…

While there is often exactly one way to execute a scalar instruction, to execute an array instruction efficiently requires careful plan and order and to select and align the execution strategy to the (greatly varying) data and hardware properties. Again, failing to do so (at runtime) will lead to sub-optimal execution times.

Workload & Segmentation

Together with the algorithm data forms another important factor: ‘workload’. It is a measure of the number of computational steps required to perform a certain data transform. Let’s say: the number of clock cycles of a CPU core required to compute the result of the ‘sin(A)’ instruction for a matrix A of a certain size. Mapping the workload onto a concrete hardware device yields the effort or cost (in terms of minimal time or energy) required to complete the transform on this device.

Obviously, throughout a program´s execution there are many intermediate steps, transforming various data with varying properties (-sizes, etc.). The overall workload – in a slightly simplified view – is the aggregation of all workloads of all intermediate steps.

To keep a program´s execution time small, all intermediate steps must be carefully adopted to and execute on the fastest hardware resource(s) currently available, yielding the lowest cost. Compare this to how a programmer today manually selects a certain device for (manually selected) large, predefined parts of a program at development time!

Manual segmentation and device resource selection cannot bring optimal performance for all parts of a program.

Array Codes – done (& run) right

The considerations above should make it obvious that no static compiler is able to create optimal execution performance (letting toy examples aside). Data and hardware properties are subject to change! So does the optimal strategy for lowering the individual parts of a user algorithm to hardware instructions! Lowest execution times will only be achieved, if all parallel potential of an algorithm is identified and used to execute its instructions concurrently, on all available hardware resources, and efficiently.

But let’s skip all reasoning and jump right into the interesting part! Here is how ILNumerics Accelerator achieves exactly this goal:

  1. Array instructions within the user program are identified and merged into ‘segments‘.
  2. Segments limits are optimized to hold chunks of suitable workload whose size can be quickly determined at runtime.
  3. Before executing a segment …
    1. The cost of the segment with the current data is computed for each hardware resource.
    2. The best (i.e.: the fastest) hardware resource is selected.
    3. The segments array instructions are optimized for the selected resource and current data.
  4. The kernel is scheduled on the selected resource for asynchronous execution and cached for later reuse.

Likely, this list requires some explanation.

[ Video does not show? Download here: https://ilnumerics.net/media/andere/ILNumerics_Segments_2022.mp4 ]

ILNumerics Accelerator takes a new approach to efficient array code execution. Instead of attempting global analysis (the top-down approach which failed in so many projects) we optimize the program from the bottom-up. Our compiler recognizes all fundamental array instructions and expressions thereof, merges them into ‘islands’ (segments) of well-known semantics and execution cost. Each segment contains a small JIT compiler, specialized to quickly compile the segments instructions at runtime into highly optimized low-level codes – for the .NET CLR and for any OpenCL device! This step recognizes and adopts to all hardware and data properties found at runtime. And it maintains compatibility with all .NET platforms.

Currently, we support unary, binary and reduction array instructions provided by ILNumerics Computing Engine and all expressions made thereof. No changes or annotations are required to existing codes. The ILNumerics language supports all features of the Matlab and numpy languages. It will be possible to build connectors to other languages and to custom array libraries exposing similar semantics.

During build each array expression is automatically replaced from the user code files with a call to a specialized, auto-generated segment. Next to hosting a JIT for the array instructions a segment also ‘knows’ the workload of its inherent computations. When at runtime the segment is called, it uses this info to compute the cost for executing the segment on each device and to identify the device suggesting earliest completion. Afterwards, it enqueues the optimized kernel to this device for computation.

It then – without waiting for a result – immediately passes on control to the next segment in the algorithm. Now, if subsequent segments do not depend on each other they are scheduled onto different threads or devices and execute in parallel!

All technical details of the new method are found in the patents and patent applications listed at the end of this article.

Advantages

ILNumerics Accelerator automatically executes your algorithm in the fastest possible way:

  • During execution it finds chunks of workload which can be computed concurrently.
  • It identifies the best suited hardware device available at this time.
  • For each segment it adopts the execution strategy to the fastest device, and
  • Computes the workload of many segments in parallel.

Therefore, it scales execution times with the hardware without recompilation or manual code adjustments.

Our compiler …

  • Supports vector registers, multiple CPU cores, and all OpenCL devices.
  • Removes temporary arrays and manages memory between devices transparently.
  • Applies many new and important optimizations, on kernel and on segment level.
  • Fully managed solution: it targets the .NET CLR, thus is compatible with all .NET platforms.

… which brings many benefits:

  • Efficient use of all compute resources.
  • No expert effort required.
  • Shorter time to market.
  • Adjusts to new hardware.
  • Maintains maintainability.

“How much faster is it”?

This is a very popular question! A comprehensive answer deserves its own article, really.

In short: it depends on your hardware. It depends on your algorithm. And it depends on your data! The question should rather be: how much more efficiently will it utilize my hardware? For the majority of real-world algorithms is true: as efficient as possible! Moreover, it does so automatically!

(If you are still longing for a number: on 2015-ish hardware we see speed increase rates between 3 and more than 300. Most of the time optimized code runs faster by at least a magnitude.)

Where can I get it ?

ILNumerics Accelerator has entered the public beta phase. It will be released with ILNumerics Ultimate VS version 7. The pre-release is available on nuget. Start here ! General documentation on the new Accelerator is found here. It will subsequently be completed within the next weeks.

Patents

ILNumerics software is protected by international patents and patent applications. WO2018197695A1, US11144348B2, JP2020518881A, EP3443458A1, DE102017109239A1, CN110383247A, DE102011119404.9, EP22156804. ILNumerics is a registered trademark of ILNumerics GmbH, Berlin, Germany.

Features, ILNumerics

New Major Release: Version 5 is out

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Phew… this was a huge effort! But now it’s done: ILNumerics Ultimate VS version 5 is released.

For those of you who have wondered: yes, it became a little quiet around ILNumerics lately. Honestly, we were so busy finishing this release that we simply forgot to throw out some news. Anyways! Now that it’s finally done, let’s turn on the spotlight!

What’s new in ILNumerics Ultimate VS version 5?

  • New, redesigned array classes
  • Nicer class names: ILArray<T> is gone!
  • Breaking the limits: support for big and huge data
  • Support for Matlab® and (new:) numpy array styles
  • Outstanding speed for all array sizes
  • Installs into Visual Studio 2013…2017

Quick links: changelog, conversion guide v4..v5, online docu

New, redesigned Array Classes

ILNumerics Ultimate VS versions 5 focusses on the Computing Engine. The array classes have been redesigned for better execution speed and better compatibility with huge data and numpy arrays. However, the API has been kept mostly the same.

Continue reading New Major Release: Version 5 is out →

.NET, C#, Features, ILNumerics, Interesting/ useless, Scientific Computing, Visualization

ILNumerics for Scientists – Going 3D

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Recap

Last time I started with one of the easiest problems in quantum mechanics: the particle in a box. This time I’ll add 1 dimension and we’ll see a particle in a 2D box. To visualize its wave function and density we need 3D surface plots.

2D Box

This time we have a particle that is confined in a 2D box. The potential within the box is zero and outside the box infinity. Again the solution is well-known and can be found on Wikipedia. This time the state of the wave function is determined by two numbers. These are typically called quantum numbers and refer to the X and the Y direction, respectively.

The absolute size of the box doesn’t really matter and we didn’t worry about it in the 1D case. However, the relative size of the length and the width make a difference. The solution to our problem reads

$\Psi_{n,k}(x,y) = \sqrt{\frac{4}{L_x L_y}} \cdot \sin(n \cdot \pi \cdot x / L_x) \cdot \sin(k \cdot \pi \cdot y / L_y)$

The Math

Very similar to the 1D case I quickly coded the wave function and the density for further plotting. I had to make sure that the arrays are fit for 3D plotting, so the code looks a little bit different compared to last post’s

     public static ILArray<double> CalcWF(int EVXID, int EVYID, double LX, double LY, int MeshSize)
     {
        ILArray<double> X = linspace<double>(0, LX, MeshSize);
        ILArray<double> Y = linspace<double>(0, LY, MeshSize);

        ILArray<double> Y2d = 1;
        ILArray<double> X2d = meshgrid(X, Y, Y2d);

        ILArray<double> Z = sqrt(4.0 / LX / LY) * sin(EVXID * pi * X2d / LX) * sin(EVYID * pi * Y2d / LY);

        return Z.Concat(X2d,2).Concat(Y2d,2);
     }

Again, this took me like 10 minutes and I was done.

The Visualization

This time the user can choose the quantum numbers for X and Y direction, the ratio between the length and the width of the box and also the number of mesh points along each axis for plotting. This makes the visualization panel a little bit more involved. Nevertheless, it’s still rather simple and easy to use. This time it took me only 45 minutes – I guess I learned a lot from last time.

The result

Here is the result of my little program. You can click and play with it. If you’re interested, you can download the Particle2DBox source code. Have fun!

Particle2DBoxThis is a screenshot of the application. I chose the second quantum number along the x axis and the fourth quantum number along the y axis. The box is twice as long in y direction as it is in x direction. The mesh size is 100 in each direction. On the left hand side you see the wave function and on the right hand side the probability density.

.NET, Features, ILNumerics, Usage, Visualization

Fun with HDF5, ILNumerics and Excel

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It is amazing how many complex business processes in major industries today are supported by a tool that shines by its simplicity: Microsoft Excel. ‘Recently’ (with Visual Studio 2010) Microsoft managed to polish the development tools for all Office applications significantly. The whole Office product line is now ready to serve as a convenient, flexible base framework for stunning custom business logic, custom computations and visualizations – with just a little help of tools like ILNumerics.

ExcelWorkbook1In this blog post I am going to show how easy it is to extend the common functionality of Excel. We will enable an Excel Workbook to load arbitrary HDF5 data files, inspect the content of such files and show the data as interactive 2D or 3D plots. Continue reading Fun with HDF5, ILNumerics and Excel →

.NET, Features, ILNumerics, Numerical Algorithms

High Performance Fast Fourier Transformation in .NET

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„I started using ILNumerics for the FFT routines. The quality and speed are excellent in a .NET environment.“

The Fourier Transform (named after French mathematician and physicist Joseph Fourier) allows scientists to transform signals between time domain and frequency domain. This way, an arbitrary periodic function can be expressed as a sum of cosine terms. Think of the equalizer of your mp3-player: It expresses your music’s signal in terms of the frequencies it is composed of.

The Fast Fourier Transform (FFT) is an algorithm for the rapid computation of discrete Fourier Transforms’ values. Being one of the most popular numerical algorithms, it is used in physics, engineering, math and many other domains.

In terms of software engineering, the Fast Fourier Transform is a very demanding algorithm: In the .NET-framework, a naive approach would cause very low execution speeds. That’s the reason why many .NET-developers have to implement native C-libraries when it comes to FFTs.

ILNumerics uses Intel’s® MKL for Fast Fourier Transforms: That’s why our users don’t have to implement native library’s themselves for high performance FFTs. No matter if they have a scientific or an industrial background, many developers rely on ILNumerics because of its implementation of the Fast Fourier Transform. It’s the fastest you can get today – even for big amounts of data.

ILNumerics provides interfaces to forward and backward Fourier Transformations, for real and complex floating point data, in single and double precision, in one, two or n dimensions. In addition to the MKL’s FFTs, prepared interfaces for FFTW and for AMDs ACML exist.

Learn more about the ILNumerics library and its implementation of Fast Fourier Transformation in C#/.NET in the online documentation!