The Julia Language
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.
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.
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.
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.
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.