beaulian / bigint_experiments

bigint.h (and bigint.py) is a library for the following bigint arithmetic:

• addition returning overflow bit and modular addition
• subtraction returning underflow bit and modular subtraction
• comparisons < and <=
• squaring
• montgomery reduction
• montgomery squaring
• montgomery multiplication (FIOS, CIOS, SOS, HAC)
• generalized euclidean algorithm for finding GCD

Goals of this library

• Support arbitrary bitwidth.
• The Python code is C-like and used for prototyping and testing before porting to C. (But the Python code has fallen behind and has bugs.)
• Spec-based. The code cites where the algorithms were found. (But deviation is necessary sometimes.)
• A simple baseline for optimizations -- no bit-twiddling or unclear tricks.

How to use

See comment at top of bigint.h and bigint.py.

Some notes

• bigint.h benefits greatly from hardware instructions for multiplication u64xu64->u128. But compilers will convert this to multiple u32xu32->u64, for compatibility with things like Wasm.
• The numbers of limbs must be known at compile-time, allowing loop unrolling.
• Computation is little-endian wrt limbs i.e. least-significant limb first. It is possible to overhaul to be big-endian.