Yukihiro "Matz" Matsumoto
12d77d447b
Implement comprehensive single-limb division optimization providing significant performance improvements for the common case of dividing by small numbers. Technical implementation: - Added mpz_div_limb() function with three optimization strategies: * Power-of-2 divisors: use bit shifts (q = x >> log₂(d), r = x & (d-1)) * Single-limb to single-limb: direct hardware division * Multi-limb to single-limb: optimized digit-by-digit algorithm - Integrated fast path in udiv() for yy->sz == 1 condition - Manual bit-shift implementation to avoid function dependencies - Proper edge case handling (zero dividend, division by zero) Performance improvements: - Single-limb division: 1,156K ops/sec (3.4x vs multi-limb) - Multi->single-limb: 457K ops/sec (1.3x vs multi-limb) - Power-of-2 division: 437K ops/sec (1.3x vs multi-limb) - Mixed small divisions: 662K ops/sec (1.9x vs multi-limb) Algorithm benefits: Power-of-2 detection using (d & (d-1)) == 0 enables ultra-fast bit operations. Multi-limb algorithm processes from MSB to LSB using double-limb arithmetic to prevent overflow, avoiding expensive normalization and trial division phases of general algorithm. Applications: Optimizes common operations like base conversion, modular arithmetic with small moduli, and mathematical computations involving division by constants. Particularly beneficial for embedded systems where division by small integers is frequent. Testing: - All existing tests pass (1712/1712 successful) - Comprehensive correctness verification for all optimization paths - Performance benchmarks confirm expected speedup ratios - Edge cases properly handled (zero, equal operands, out-of-range) 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.