Read the equation
This relation defines phi(x) in the source section “SIMD VECTOR OPERATIONS · phi(x)”. 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
Read phi(x) as the quantity being defined or updated by this relation.
Substitute the source-defined variables or recorded values and follow the displayed arithmetic and indexing exactly.
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
Read the surrounding source passage
#if defined(SIMD_AVX2) || defined(SIMD_AVX512)
// Process 8 floats at a time with AVX
class AVXOps {
public:
// Vectorized phi computation
// phi(x) = 1 / (1 + |x - 1|)
static __m256 compute_phi_8(__m256 x) {
__m256 one = _mm256_set1_ps(1.0f);
__m256 diff = _mm256_sub_ps(x, one);
// Absolute value: clear sign bit
__m256 sign_mask = _mm256_set1_ps(-0.0f);
__m256 abs_diff = _mm256_andnot_ps(sign_mask, diff);
__m256 denom = _mm256_add_ps(one, abs_diff);
return _mm256_div_ps(one, denom);Exact original notation
phi(x) = 1 / (1 + |x - 1|)