Fast binary entropy H(p) = -p log p - (1-p) log(1-p) · @brief Fast binary entropy H(p)

Read the equation

This relation defines @brief Fast binary entropy H(p) in the source section “Fast binary entropy H(p) = -p log p - (1-p) log(1-p) · @brief Fast binary entropy H(p)”. Uses logarithmic scaling; its base and the positivity of its argument matter. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

1. Read @brief Fast binary entropy H(p) as the quantity being defined or updated by this relation.

2. Uses logarithmic scaling; its base and the positivity of its argument matter.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

• This source expression was recovered from the pinned code revision. Its presence does not establish that the associated program was built, run, or scientifically validated.

Original context

}

// ═══════════════════════════════════════════════════════════════════════════════
// VIII. INFORMATION-THEORETIC FAST APPROXIMATIONS
// ═══════════════════════════════════════════════════════════════════════════════

/**
 * @brief Fast binary entropy H(p) = -p log p - (1-p) log(1-p)
 * Using polynomial approximation
 */
inline float fast_binary_entropy(float p) {
    if (p < 0.001f || p > 0.999f) return 0.0f;
    // Polynomial fit to binary entropy
    float q = 1.0f - p;
    float h = -p * fast_log(p) - q * fast_log(q);
    return h * 1.4426950408889634f;  // Convert to bits (log2)
}

@brief Fast binary entropy H(p) = -p log p - (1-p) log(1-p)

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