Yukihiro "Matz" Matsumoto 6190234e3d mruby-bigint: integrate barrett reduction algorithm into modular arithmetic ...

Implement and integrate Barrett reduction algorithm to optimize modular
arithmetic operations for moderate-sized moduli (64-512 bits). This algorithm
provides significant performance improvements for cryptographic applications
and repeated modular operations.

Technical implementation:
- Added mpz_barrett_mu() to compute Barrett parameter μ = ⌊2^(2k)/m⌋
- Added mpz_barrett_reduce() with full 7-step Barrett algorithm
- Integrated into mpz_mod() with automatic selection criteria:
  * Single-limb modulus: existing fast path (unchanged)
  * Moderate moduli (2-8 limbs, dividend ≥ modulus + 2): Barrett reduction
  * Large moduli: general division fallback (unchanged)

Performance characteristics:
- Barrett reduction is most effective for 64-512 bit moduli
- Complements existing single-limb optimization for small moduli
- Transparent optimization with no API changes
- All existing tests pass (1712 tests successful)

Algorithm details:
Barrett reduction avoids expensive division by precomputing a parameter
and using only multiplications and bit shifts. The 7-step algorithm
approximates the quotient, performs modular reduction using power-of-2
operations, and applies final corrections to ensure 0 ≤ result < modulus.

Co-authored-by: Claude <noreply@anthropic.com>

2025-08-14 10:52:45 +09:00

..

bigint.c

mruby-bigint: integrate barrett reduction algorithm into modular arithmetic

2025-08-14 10:52:45 +09:00

bigint.h

misc: fix spelling

2025-05-14 02:01:02 +10:00