LibTomMath is a free open source portable number theoretic multiple-precision integer library written entirely in C. (phew!). The library is designed to provide a simple to work with API that provides fairly efficient routines that build out of the box without configuration.

The library builds out of the box with GCC 2.95 [and up] as well as Visual C++ v6.00 [with SP5] without configuration. The source code is arranged to make it easy to dive into a particular area very quickly. The code is also littered with comments [This is one of the on going goals] that help explain the algorithms and their implementations. Ideally the code will serve as an educational tool in the future for CS students studying number theory.

The library provides a vast array of highly optimized routines from various branches of number theory.

- Simple Algebraic
- Addition
- Subtraction
- Multiplication
- Squaring
- Division

- Digit Manipulation
- Shift left/right whole digits (mult by 2b by moving digits)
- Fast multiplication/division by 2 and 2k for k>1
- Binary AND, OR and XOR gates

- Modular Reductions
- Barrett Reduction (fast for any p)
- Montgomery Reduction (faster for any odd p)
- DR Reduction (faster for any restricted p see manual)
- 2k Reduction (fast reduction modulo 2p - k for k < MP_MASK and for k > MP_MASK)
- The exptmod logic can use any of the five reduction algorithms when appropriate with a single function call.

- Number Theoretic
- Greatest Common Divisor
- Least Common Multiple
- Jacobi Symbol Computation (falls back to Legendre for prime moduli)
- Multiplicative Inverse
- Extended Euclidean Algorithm
- Modular Exponentiation
- Fermat and Miller-Rabin Primality Tests, utility function such as is_prime and next_prime

- Miscellaneous
- Root finding over Z
- Pseudo-random integers
- Signed and Unsigned comparisons

- Optimizations
- Fast Comba based Multiplier, Squaring and Montgomery routines.
- Montgomery, Diminished Radix and Barrett based modular exponentiation.
- Karatsuba and Toom-Cook multiplication algorithms.
- Many pointer aliasing optimiztions throughout the entire library.