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
• 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 optimizations throughout the entire library.