ACL2 is a mathematical logic, programming language, and mechanical theorem prover based on the applicative subset of Common Lisp. It is an "industrial-strength" version of the NQTHM or Boyer/Moore theorem prover, and has been used for the formal verification of commercial microprocessors, the Java Virtual Machine, interesting algorithms, and so forth.
Apfp (Arbitrary Precision Floating Point) is a Ruby class for performing arbitrary precision floating point calculations. It also includes a class Apc for calculating with arbitrary precision complex numbers. It also contains a Real class for built-in reals. Both classes keep an estimate of the accumulated error.
Armadillo is a C++ linear algebra library (matrix maths) aiming towards a good balance between speed and ease of use. The API is deliberately similar to Matlab's. Integer, floating point, and complex numbers are supported, as well as a subset of trigonometric and statistics functions. Various matrix decompositions are provided through optional integration with LAPACK and ATLAS numerics libraries. A delayed evaluation approach, based on template meta-programming, is used (during compile time) to combine several operations into one and reduce or eliminate the need for temporaries.
Botan is a crypto library written in C++. It provides a variety of cryptographic algorithms, including common ones such as AES, MD5, SHA, HMAC, RSA, Diffie-Hellman, DSA, and ECDSA, as well as many others that are more obscure or specialized. It also offers SSL/TLS (client and server), X.509v3 certificates and CRLs, and PKCS #10 certificate requests. A message processing system that uses a filter/pipeline metaphor allows for many common cryptographic tasks to be completed with just a few lines of code. Assembly and SIMD optimizations for common CPUs offers speedups for critical algorithms like AES and SHA-1.
Brook for GPUs is a compiler and runtime implementation of the Brook stream programming language for modern graphics hardware. The goals for this project are to demonstrate general purpose programing on GPUs, to provide a useful tool for developers who want to run applications on GPUs, and to research the stream language programming model, streaming applications, and system implementations.
Libecc is a C++ elliptic curve cryptography library that supports fixed-size keys for maximum speed. The goal of this project is to become the first free Open Source library providing the means to generate safe elliptic curves, and to provide an important source of information for anyone with general interest in ECC.
Cactus is a general, modular, parallel environment for solving systems of partial differential equations. The code has been developed over many years by a large international collaboration of numerical relativity and computational science research groups and can be used to provide a portable platform for solving any system of partial differential equations.
Ch is an embeddable C/C++ interpreter for cross-platform scripting, shell programming, 2D/3D plotting, numerical computing, and embedded scripting. It is the simplest solution to numerical computing and visualization in the domain of C/C++. It supports the ISO 1990 C Standard (C90), major features in C99 (complex numbers, variable length arrays or VLAs, type generic functions, long long data type, etc), classes in C++, and extensions to the C language like nested functions, string types, etc. It can be embedded in other applications and hardware and used as a scripting language. C/C++ code is interpreted directly with no compilation to intermediate code. It supports Linux, Windows, MacOS X, Solaris, HP-UX, and FreeBSD.
EFEU is suitable for handling data cubes, which are especially useful for building data warehouses. It consists of a building system including mkmf (a xmkmf like Makefile generator), esh (a powerful C/C++ interpreter), efeudoc (a document generator with different output formats (LaTeX, HTML, roff, etc.)). EFEU has a huge set of C library core features, including robust memory allocation tools, functions to concatenate and copy strings with memory allocation, buffers for dynamically-growing strings and fields, data structures with reference counters and garbage collection, and file tools that allow you to specify pipes wherever a filename is expected and support automatic implementation of (de)compression filters (gzip) depending on filename extensions. It also includes a high-level interface to files, strings, and anything else you can read from or write to.
FrAid (Fr[actal] Aid) is a programming language that is appropriate for mathematical computations, visualization, batch processing, and more. It features both a standalone application that provides a programming environment for the language and a system for integrating the language with Java. The Java interface allows mathematical equations and formulas to be used with Java code, making it easier to process numerical computations, symbolic computations, imaging, CAD, and more.