Yukihiro "Matz" Matsumoto
6190234e3d
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>
mruby-bigint
mruby-bigint is an mrbgem that provides multi-precision integer (BigInt) support for mruby. It allows you to work with integers that are larger than the standard Integer type can handle.
This extension uses fgmp, which is a public domain implementation of a subset of the GNU gmp library by Mark Henderson markh@wimsey.bc.ca. But it's heavily modified to fit with mruby. You can get the original source code from https://github.com/deischi/fgmp.git. You can read the original README for fgmp in README-fgmp.md.
If you want to create your own Multi-precision Integer GEM, see examples/mrbgems/mruby-YOUR-bigint/TODO-HINT.md.
Features
- Basic arithmetic operations:
+,-,*,/,% - Power operation:
** - Modular exponentiation
- Bitwise operations:
&,|,^,<<,>> - Comparison:
<=> - Conversion to and from strings:
to_s,String#to_i(with base) - Square root
- Greatest Common Divisor (GCD) (available if
MRB_USE_RATIONALis defined)
Usage
Here are some simple examples of how to use mruby-bigint:
# Creating BigInts
a = BigInt(12345678901234567890)
b = "98765432109876543210".to_i(10) # Specify base 10 for string conversion
# Arithmetic operations
c = a + b
puts c.to_s # Output: 111111111011111111100
d = a * 2
puts d.to_s # Output: 24691357802469135780
# Comparison
puts a <=> b # Output: -1
fgmp Dependency
mruby-bigint depends on fgmp. For more information about fgmp, please see README-fgmp.md.