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A library designed to provide a simple way to work with an API that provides fairly efficient routines that build out of the box LibTomMath is a free open source portable number theoretic multiple-precision integer library written entirely in C. (phew!).
LibTomMath 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.
LibTomMaths code is littered with comments that will help explain the algorithms and their implementations. Ideally LibTomMath will serve as an educational tool in the future for CS students studying number theory.
LibTomMath provides a vast array of highly optimized routines from various branches of number theory.
Here are some key features of "LibTomMath":
- 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.