SIMD VECTOR OPERATIONS

Read the equation

This relation defines tanh(x) ≈ x (27 + x^2) / (27 + 9x^2) in the source section “SIMD VECTOR OPERATIONS”. It specifies the displayed relationship between the named quantities or parameters. 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 the displayed expression together with the surrounding source statement; it is retained as an expression rather than silently completed into an equality.

2. Substitute the source-defined variables or recorded values and follow the displayed arithmetic and indexing exactly.

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

        __m256 abs_diff = _mm256_andnot_ps(sign_mask, diff);

        __m256 denom = _mm256_add_ps(one, abs_diff);
        return _mm256_div_ps(one, denom);
    }

    // Vectorized tanh approximation
    // tanh(x) ≈ x * (27 + x^2) / (27 + 9*x^2)
    static __m256 tanh_approx_8(__m256 x) {
        __m256 x2 = _mm256_mul_ps(x, x);
        __m256 c27 = _mm256_set1_ps(27.0f);
        __m256 c9 = _mm256_set1_ps(9.0f);

        __m256 num = _mm256_add_ps(c27, x2);
        num = _mm256_mul_ps(x, num);

        __m256 den = _mm256_add_ps(c27, _mm256_mul_ps(c9, x2));
        return _mm256_div_ps(num, den);

tanh(x) ≈ x * (27 + x^2) / (27 + 9*x^2)

Related builds