[bonnhatnguyen]

Description

Introduces a high-performance C++ implementation (3.cpp) for the nsieve benchmark utilizing a 1-bit Wheel 8-of-30 Sieve of Eratosthenes.

Key Optimizations

• Wheel 8-of-30 Factorization: Skips all multiples of 2, 3, and 5 (8 candidate coprimes per cycle of 30: 1, 7, 11, 13, 17, 19, 23, 29). This eliminates ~73.3% of composite markings before sieving starts.
• Bit-Packed Candidate Buffer: Uses 1 bit per odd integer (uint64_t words). For $M = 40,960,000$, total memory footprint is only ~2.44 MB, fitting entirely inside CPU L2/L3 cache and avoiding DRAM bandwidth bottlenecks.
• Register-Unrolled Composite Marking: 8-stride pre-computed step cycle unrolled to maximize instruction-level parallelism (ILP) and branch prediction throughput.
• Unrolled Branchless Prime Counting: Traverses remaining prime candidates across wheel residues with branchless bit extractions.

Verification & Benchmark

• Verified against unit tests (4_out and 5_out), output matches byte-for-byte.
• Benchmark comparison on input 12 ($M = 40,960,000$):
  • 1.cpp (baseline): ~0.37s user time
  • 3.cpp (this PR): ~0.04s user time (~9.2x faster)