05_16_07_approximation_variants¶

Fast Approximation Variants¶

Status: ⏸️ NOT STARTED Priority: MEDIUM Dependencies: TAREA 0 (Variant Framework) Estimated Effort: 2-3 weeks

🎯 Purpose¶

Approximation variants trade precision for speed using: - Fast math functions: Fast sin/cos/exp/log (5-10x faster) - Lookup tables: Pre-computed values - Polynomial approximations: Faster than accurate functions - Quality presets: User-selectable speed vs quality

📋 Planned Features¶

1. Fast Math Functions¶

class FastMathVariant : public IVariant {
public:
    // 5-10x faster than std::sin
    float fastSin(float x);    // ~0.1% error
    float fastCos(float x);
    float fastExp(float x);
    float fastLog(float x);
    float fastPow(float x, float y);
};

2. Lookup Table Oscillators¶

class LookupTableOscillator : public IVariant {
public:
    bool process(const float* input, float* output, size_t numSamples) override;

private:
    std::vector<float> sineTable_;  // Pre-computed
    double phase_;
};

3. Polynomial Approximations¶

// Fast tanh approximation (neural network activation)
inline float fastTanh(float x) {
    // Rational approximation: tanh(x) ≈ x(27 + x²)/(27 + 9x²)
    float x2 = x * x;
    return x * (27.0f + x2) / (27.0f + 9.0f * x2);
}

4. Quality Presets¶

enum class ApproximationQuality {
    FASTEST,    // 10x faster, ~1% error
    FAST,       // 5x faster, ~0.1% error
    BALANCED,   // 2x faster, ~0.01% error
    ACCURATE    // Baseline (std::sin, etc.)
};

📊 Performance vs Accuracy¶

Function	Accurate	Fast Approx	Speedup	Max Error
sin/cos	std::sin	7^th poly	8x	0.001
exp	std::exp	5^th poly	10x	0.01
log	std::log	4^th poly	8x	0.01
tanh	std::tanh	rational	12x	0.001
pow	std::pow	exp(y*log(x))	5x	0.05

🎯 Use Cases¶

Oscillators: Wavetable lookup (10x faster)
Distortion: Fast tanh/sigmoid (5-10x faster)
Envelopes: Fast exp decay (5x faster)
LFOs: Fast sin/cos (8x faster)
Neural Networks: Fast activation functions

Status: ⏸️ Good for creative effects Priority: MEDIUM - Quality vs speed trade-off