This PR adds the Eisel-Lemire algorithm for string-to-float conversion, providing significant performance improvements for String#to_f, especially for numbers with many significant digits.

Performance Results

Benchmark: 3,000,000 iterations per category

Key Insights

• Simple numbers (1-6 digits): 13-17% faster via ultra-fast paths
• Complex numbers (10+ digits): 2.7-3.2x faster via Eisel-Lemire algorithm
• No regressions for any input type (at least not detected by me)

Implementation Details

Algorithm Overview

The implementation adds three optimization levels to rb_cstr_to_dbl_raise:

1. Ultra-fast path for small integers (try_small_integer_fast_path)

   • Handles: "5", "42", "-123" (up to 3 digits)
   • Simple digit parsing, direct conversion to double

2. Ultra-fast path for simple decimals (try_simple_decimal_fast_path)

   • Handles: "1.5", "9.99", "199.95" (up to 3+3 digits)
   • Parses integer and fractional parts separately
   • Uses precomputed divisors (10, 100, 1000)

3. Eisel-Lemire algorithm (rb_eisel_lemire64)

   • Handles complex numbers with many significant digits
   • Uses 128-bit multiplication with precomputed powers of 5
   • Falls back to strtod for ambiguous rounding cases

Technical Details

• 128-bit multiplication: Uses __uint128_t when available, falls back to portable 64-bit emulation
• Powers of 5 table: 651 precomputed 128-bit values for exponents [-342, 308]
• Underscore handling: Proper Ruby underscore validation (between digits only)
• Fallback: Falls back to strtod for edge cases (hex floats, >19 digits, ambiguous rounding)

References

• Eisel-Lemire paper - "Number Parsing at a Gigabyte per Second" (Software: Practice and Experience, 2021)
• fast_float C++ library
• Go implementation
• Nigel Tao's blog post - Excellent explanation of the algorithm

Benchmark Script

ITERATIONS = 3_000_000

def bench(name, strings)
  start = Process.clock_gettime(Process::CLOCK_MONOTONIC)
  (ITERATIONS / strings.size).times { strings.each(&:to_f) }
  elapsed = Process.clock_gettime(Process::CLOCK_MONOTONIC) - start
  printf "%-35s %0.3fs\n", name, elapsed
end

bench("Simple decimals (1.5, 3.14)",
      %w[1.5 2.0 3.14 99.99 0.5 0.25 10.0 7.5 42.0 100.0])

bench("Prices (9.99, 19.95)",
      %w[9.99 19.95 29.99 49.95 99.99 149.99 199.95 299.99 399.95 499.99])

bench("Small integers (5, 42)",
      %w[5 42 123 7 99 256 1 0 50 999])

bench("Math constants (Pi, E)",
      %w[3.141592653589793 2.718281828459045 1.4142135623730951])

bench("High precision decimals",
      %w[0.123456789012345 9.876543210987654 1.111111111111111])

bench("Scientific (1e5, 2e10)",
      %w[1e5 2e6 3e7 4e8 5e9 1e10])