Julia Programming Language: An introduction

The Julia Language

 

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Julia is a high-level, high-performance dynamic programming language for technical computing, with syntax that is familiar to users of other technical computing environments. It provides a sophisticated compiler, distributed parallel execution, numerical accuracy, and an extensive mathematical function library. The library, mostly written in Julia itself, also integrates mature, best-of-breed C and Fortran libraries for linear algebra, random number generation, FFTs, and string processing. More libraries continue to be added over time. Julia programs are organized around defining functions, and overloading them for different combinations of argument types (which can also be user-defined). For a more in-depth discussion of the rationale and advantages of Julia over other systems, see the following highlights or read the introduction in the online manual.

High-Performance JIT Compiler

Julia’s LLVM-based just-in-time (JIT) compiler combined with the language’s design allow it to approach and often match the performance of C/C++. To get a sense of relative performance of Julia compared to other languages that can or could be used for numerical and scientific computing, we’ve written a small set of micro-benchmarks in a variety of languages. The source code for the various implementations can be found here: C++, Julia, Python, Matlab/Octave, R, and JavaScript. We encourage you to skim the code to get a sense for how easy or difficult numerical programming in each language is. The following micro-benchmark results are from a MacBook Pro with a 2.53GHz Intel Core 2 Duo CPU and 8GB of 1066MHz DDR3 RAM:

	Julia	Python	Matlab	Octave	R	JavaScript
	3f670da0	2.7.1	R2011a	3.4	2.14.2	V8 3.6.6.11
fib	1.97	31.47	1336.37	2383.80	225.23	1.55
parse_int	1.44	16.50	815.19	6454.50	337.52	2.17
quicksort	1.49	55.84	132.71	3127.50	713.77	4.11
mandel	5.55	31.15	65.44	824.68	156.68	5.67
pi_sum	0.74	18.03	1.08	328.33	164.69	0.75
rand_mat_stat	3.37	39.34	11.64	54.54	22.07	8.12
rand_mat_mul	1.00	1.18	0.70	1.65	8.64	41.79

Figure: benchmark times relative to C++ (smaller is better).

C++ compiled by GCC 4.2.1, taking best timing from all optimization levels (-O0 through -O3).
The Python implementations of rand_mat_stat and rand_mat_mul use NumPy (v1.5.1) functions; the rest are pure Python implementations.

Julia beats other high-level systems on most micro-benchmarks, with a few exceptions for Matlab and JavaScript. Relative performance between languages on other systems is similar. Matlab’s ability to beat both C and Julia on random matrix multiplication comes from its use of the proprietary Intel Math Kernel Library, which has extremely optimized code for matrix multiplication on Intel platforms. Users who have a licensed copy of MKL can use it with Julia, but the default BLAS is a high quality open source implementation (see the GitHub page for more details).
These benchmarks, while not comprehensive, do test compiler performance on a range of common code patterns, such as function calls, string parsing, sorting, numerical loops, random number generation, and array operations. Julia is strong in an area that high-level languages have traditionally been weak: scalar arithmetic loops, such as that found in the pi summation benchmark. Matlab’s JIT for floating-point arithmetic does well here too, as does the V8 JavaScript engine. V8 is impressive in that it can provide such a dynamic language with C-like performance in so many circumstances. JavaScript, however, is unable to utilize technical computing libraries such as LAPACK, resulting in poor performance on benchmarks like matrix multiplication. In contrast with both Matlab and JavaScript, Julia has a more comprehensive approach to eliminating overhead that allows it to consistently optimize all kinds of code for arbitrary user-defined data types, not just certain special cases.
To give a quick taste of what Julia looks like, here is the code used in the Mandelbrot and random matrix statistics benchmarks:

function mandel(z)
    c = z
    maxiter = 80
    for n = 1:maxiter
        if abs(z) > 2
            return n-1
        end
        z = z^2 + c
    end
    return maxiter
end

function randmatstat(t)
    n = 5
    v = zeros(t)
    w = zeros(t)
    for i = 1:t
        a = randn(n,n)
        b = randn(n,n)
        c = randn(n,n)
        d = randn(n,n)
        P = [a b c d]
        Q = [a b; c d]
        v[i] = trace((P.'*P)^4)
        w[i] = trace((Q.'*Q)^4)
    end
    std(v)/mean(v), std(w)/mean(w)
end

As you can see, the code is quite clear, and should feel familiar to anyone who has programmed in other mathematical languages. Although C++ beats Julia in the random matrix statistics benchmark by a significant factor, consider how much simpler this code is than the C++ implementation. There are more compiler optimizations planned that we hope will close this performance gap in the future. By design, Julia allows you to range from low-level loop and vector code, up to a high-level programming style, sacrificing some performance, but gaining the ability to express complex algorithms easily. This continuous spectrum of programming levels is a hallmark of the Julia approach to programming and is very much an intentional feature of the language.

Designed for Parallelism & Cloud Computing

Julia does not impose any particular style of parallelism on the user. Instead, it provides a number of key building blocks for distributed computation, making it flexible enough to support a number of styles of parallelism, and allowing users to add more. The following simple example demonstrates how to count the number of heads in a large number of coin tosses in parallel.

nheads = @parallel (+) for i=1:100000000
  randbit()
end

This computation is automatically distributed across all available compute nodes, and the result, reduced by summation (+), is returned at the calling node.
Although it is in the early stages, Julia already supports a fully remote cloud computing mode. Here is a screenshot of a web-based interactive Julia session, plotting an oscillating function and a Gaussian random walk:

You can try Julia in the web repl yourself at julia.forio.com (EC2 instance and maintenance graciously provided by Forio). There will eventually be full support for cloud-based operation, including data management, code editing and sharing, execution, debugging, collaboration, analysis, data exploration, and visualization. The goal is to allow people who work with big data to stop worrying about administering machines and managing data and get straight to the real problem.

Free, Open Source & Library-Friendly

The core of the Julia implementation is licensed under the MIT license. Various libraries used by the Julia environment include their own licenses such as the GPL, LGPL, and BSD (therefore the environment, which consists of the language, user interfaces, and libraries, is under the GPL). The language can be built as a shared library, so users can combine Julia with their own C/Fortran code or proprietary third-party libraries. Furthermore, Julia makes it simple to call external functions in C and Fortran shared libraries, without writing any wrapper code or even recompiling existing code. You can try calling external library functions directly from Julia’s interactive prompt, getting immediate feedback. See LICENSE for the full terms of Julia’s licensing.