SIMD Implementations Deep Dive

⚡ SIMD Implementations Deep Dive

"Each SIMD implementation carefully manages state using class-based encapsulation, with robust initialization via the SplitMix64 seeding algorithm."

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🎯 SIMD Implementation Philosophy

Every SIMD variant follows our consistent architecture principles while maximizing the unique capabilities of each instruction set. The goal: squeeze every cycle of performance from the silicon while maintaining code clarity and safety.

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🔢 Scalar Implementation - The Universal Baseline

Design Purpose

The scalar implementation serves as both fallback guarantee and performance baseline. Every optimization is measured against this rock-solid foundation.

class Xoroshiro128ppScalar : public RNGBase {
public:
    explicit Xoroshiro128ppScalar(uint64_t seed) {
        seed_state(seed);
    }
uint64_t next_u64() override {
    const uint64_t s0 = state_[0];
    uint64_t s1 = state_[1];
    const uint64_t result = rotl64(s0 + s1, 17) + s0;  // xoroshiro128++ scrambler
    
    s1 ^= s0;
    state_[0] = rotl64(s0, 49) ^ s1 ^ (s1 << 21);
    state_[1] = rotl64(s1, 28);
    
    return result;
}

};

Key Features

• 🎯 Reference Implementation - Bit-perfect algorithm execution
• 🔒 Memory Safety - std::array for state management
• ⚡ Optimal Compiler - Lets modern compilers auto-vectorize when possible
• 📱 Universal Compatibility - Runs on everything from embedded to supercomputers

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🚀 SSE2 Implementation - Legacy Power

Target Hardware

• Intel: Pentium 4+ (2001)
• AMD: Opteron+ (2003)
• Parallelism: 2-way (128-bit vectors)

Implementation Strategy

class Xoroshiro128ppSSE2 {
public:
    explicit Xoroshiro128ppSSE2(uint64_t seed) {
        auto seeds = generate_seeds<4>(seed);
        state0_ = _mm_set_epi64x(seeds[1], seeds[0]);
        state1_ = _mm_set_epi64x(seeds[3], seeds[2]);
    }
void generate_batch(uint64_t* dest, size_t count) {
    for (size_t i = 0; i + 1 &lt; count; i += 2) {
        // No direct 64-bit rotl in SSE2 - manual implementation
        alignas(16) uint64_t s0[2], s1[2];
        _mm_store_si128((__m128i*)s0, state0_);
        _mm_store_si128((__m128i*)s1, state1_);
        
        for (int j = 0; j &lt; 2; j++) {
            uint64_t sum = s0[j] + s1[j];
            uint64_t rotated_sum = rotl64(sum, 17);
            dest[i + j] = rotated_sum + s0[j];
            
            // State update
            uint64_t s1_xor_s0 = s1[j] ^ s0[j];
            s0[j] = rotl64(s0[j], 49) ^ s1_xor_s0 ^ (s1_xor_s0 &lt;&lt; 21);
            s1[j] = rotl64(s1_xor_s0, 28);
        }
        
        state0_ = _mm_load_si128((__m128i*)s0);
        state1_ = _mm_load_si128((__m128i*)s1);
    }
}

};

SSE2 Challenges & Solutions

Challenge	Problem	Solution
No 64-bit Rotations	SSE2 lacks native 64-bit bit rotation	Manual scalar rotations in SIMD context
Limited Instructions	Fewer vector operations available	Hybrid scalar/vector approach
Memory Bandwidth	128-bit vectors less efficient	Optimized for 2-way parallelism

Performance Characteristics

• Speedup: ~8.1x in batch mode
• Memory: 64-byte aligned state
• Power: Higher power consumption
• Best Use: High-performance computing, servers

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🍎 ARM NEON Implementation - Mobile Power

Target Hardware

• ARM: Cortex-A series
• Apple: M1/M2 processors
• Parallelism: 2-way (128-bit vectors)

Implementation Strategy

class Xoroshiro128ppNeon {
public:
    void generate_batch(uint64_t* dest, size_t count) {
        for (size_t i = 0; i + 1 < count; i += 2) {
            // NEON-optimized xoroshiro128++
            uint64x2_t sum = vaddq_u64(state0_, state1_);
            uint64x2_t rotated_sum = rotl_neon(sum, 17);
            uint64x2_t result = vaddq_u64(rotated_sum,

⚡ SIMD Implementations Deep Dive (Part 2)

Continued from Part 1...

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🍎 ARM NEON Implementation - Mobile Power

Target Hardware

• ARM: Cortex-A series
• Apple: M1/M2 processors
• Parallelism: 2-way (128-bit vectors)

Implementation Strategy

cpp

class Xoroshiro128ppNeon {
public:
    void generate_batch(uint64_t* dest, size_t count) {
        for (size_t i = 0; i + 1 < count; i += 2) {
            // NEON-optimized xoroshiro128++
            uint64x2_t sum = vaddq_u64(state0_, state1_);
            uint64x2_t rotated_sum = rotl_neon(sum, 17);
            uint64x2_t result = vaddq_u64(rotated_sum, state0_);
            
            vst1q_u64(dest + i, result);
            
            // State update with NEON intrinsics
            uint64x2_t s1 = veorq_u64(state0_, state1_);
            
            state0_ = veorq_u64(
                        rotl_neon(state0_, 49),
                        veorq_u64(s1, vshlq_n_u64(s1, 21))
                      );
            state1_ = rotl_neon(s1, 28);
        }
    }
    
private:
    static inline uint64x2_t rotl_neon(uint64x2_t x, int k) {
        return vsriq_n_u64(vshlq_n_u64(x, k), x, 64 - k);
    }
};

NEON Characteristics

Feature | Capability | Performance Impact
-- | -- | --
64-bit Ops | vaddq_u64, veorq_u64 | Native 64-bit support
Bit Manipulation | vshlq_n_u64, vsriq_n_u64 | Efficient rotations
Memory Ops | vld1q_u64, vst1q_u64 | Optimized load/store
Power Efficiency | Low power consumption | Excellent for mobile

Performance Tuning Tips

1. Measure First - Always benchmark on your target hardware
2. Batch When Possible - SIMD shines with bulk generation
3. Consider Power - GPU implementations use significantly more power
4. Profile Memory - Ensure proper alignment for SIMD loads/stores
5. Test Edge Cases - Verify performance with non-aligned batch sizes

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Next: 🎯 Performance Analysis - Benchmark results and optimization stories