METIS is a set of serial programs for partitioning graphs, partitioning finite element meshes, and producing fill-reducing orderings for sparse matrices. The algorithms implemented in METIS are based on the multilevel recursive-bisection, multilevel k-way, and multi-constraint partitioning schemes.

PETSc, pronounced PET-see (the S is silent), is a suite of data structures and routines for the scalable (parallel) solution of scientific applications modeled by partial differential equations.

GNU Units converts numeric quantities between units of measure. It can handle scale changes through adaptive usage of standard scale prefixes (micro-, kilo-, etc.). It can also handle nonlinear conversions such as Fahrenheit to Celsius. Its interpreter is powerful enough to be used effectively as a scientific calculator.

CUDD is a library for manipulating decision diagrams. It supports binary decision diagrams, algebraic decision diagrams, and zero-suppressed binary decision diagrams.

DUNE, the Distributed and Unified Numerics Environment is a modular toolbox for solving partial differential equations (PDEs) with grid-based methods.

This is the iterative solver template library which provides generic sparse matrix/vector classes and a variety of solvers based on these classes. A special feature is the use of templates to exploit the recursive block structure of finite element matrices at compile time. Available solvers include Krylov methods, (block-) incomplete decompositions and aggregation-based algebraic multigrid.

The p4est software library enables the dynamic management of a collection of adaptive octrees, conveniently called a forest of octrees. p4est is designed to work in parallel and scales to hundreds of thousands of processor cores.

Glucose is a SAT solver based on a scoring scheme introduced in 2009 for the clause learning mechanism of so called “Modern” SAT solvers. It is designed to be parallel.

BLIS is a portable software framework for instantiating high-performance BLAS-like dense linear algebra libraries. The framework was designed to isolate essential kernels of computation that, when optimized, immediately enable optimized implementations of most of its commonly used and computationally intensive operations. While BLIS exports a new BLAS-like API, it also includes a BLAS compatibility layer which gives application developers access to BLIS implementations via traditional BLAS routine calls.

HYPRE is a software library of high performance preconditioners and solvers for the solution of large, sparse linear systems of equations on parallel computers. It features parallel multigrid solvers for both structured and unstructured grid problems.

ScaLAPACK is a Fortran 90 library of high-performance linear algebra routines on parallel distributed memory machines. ScaLAPACK solves dense and banded linear systems, least squares problems, eigenvalue problems, and singular value problems.

The dune-subgrid module marks elements of another hierarchical dune grid. The set of marked elements can then be accessed as a hierarchical dune grid in its own right. Dune-Subgrid provides the full grid interface including adaptive mesh refinement.

Maxima is a system for the manipulation of symbolic and numerical expressions. It yields high precision numeric results by using exact fractions, arbitrary precision integers, and variable precision floating point numbers.

SPEX is a set of routines for sparse exact linear algebra. It contains the SPEX Left LU library for computing a sparse exact left-looking LU factorization for solving unsymmetric sparse linear systems.

This library provides portable Arbitrary-precision unsigned integer arithmetic in C, for calculating with large numbers. Basic arithmetic (+, -, *, /, %) and bitwise operations (&, |, ^. <<, >>) plus increments, decrements and comparisons are supported.

UMFPACK is a set of routines for solving unsymmetric sparse linear systems using the Unsymmetric MultiFrontal method and direct sparse LU factorization.

METIS is a set of serial programs for partitioning graphs, partitioning finite element meshes, and producing fill-reducing orderings for sparse matrices. The algorithms implemented in METIS are based on the multilevel recursive-bisection, multilevel k-way, and multi-constraint partitioning schemes.

CXSparse is a collection of sparse matrix algorithms for direct methods on both real and complex matrices.

This library implements the math.h functions in fixed point (16.16) format.

This is a header-only C++ library for calculating analytical derivatives and taylor expansions of composite functions.

The dSMFT package speeds up Fast Mersenne Twister generation by avoiding the expensive conversion of integer to double (floating point). dSFMT directly generates double precision floating point pseudorandom numbers which have the IEEE Standard for Binary Floating-Point Arithmetic (ANSI/IEEE Std 754-1985) format. dSFMT is only available on the CPUs which use IEEE 754 format double precision floating point numbers.

ExprTk is a C++ headers only library for mathematical expression parsing and evaluation.

The Parma Polyhedra Library (PPL) provides numerical abstractions especially targeted at applications in the field of analysis and verification of complex systems. These abstractions include convex polyhedra, defined as the intersection of a finite number of (open or closed) halfspaces, each described by a linear inequality (strict or non-strict) with rational coefficients; some special classes of polyhedra shapes that offer interesting complexity/precision tradeoffs; and grids which represent regularly spaced points that satisfy a set of linear congruence relations. The library also supports finite powersets and products of (any kind of) polyhedra and grids, a mixed integer linear programming problem solver using an exact-arithmetic version of the simplex algorithm, a parametric integer programming solver, and primitives for termination analysis via the automatic synthesis of linear ranking functions.

Chuffed is a state of the art lazy clause solver designed from the ground up with lazy clause generation in mind. Lazy clause generation is a hybrid approach to constraint solving that combines features of finite domain propagation and Boolean satisfiability.

Bonmin is a code for solving general MINLP (Mixed Integer NonLinear Programming) problems. It builds on top of Cbc and Ipopt.