Function erfi

src/compute-engine/numerics/special-functions.ts:2731–2747

(x: number)

  if (x < -9) {
    const [P, Q, cosA, sinA, pref] = airyNegPartsPrime(-x);
    return pref * (cosA * P + sinA * Q); // DLMF 9.7.12
  }

  const [fp, gp] = airySeriesFGPrime(x);
  return ddMul(SQRT3_DD, ddAdd(ddMul(AIRY_C1, fp), ddMul(AIRY_C2, gp)))[0];
}

// ──────────────────────────────────────────────────────────────────
// Fresnel integrals
//
// S(x) = ∫₀ˣ sin(π t²/2) dt
// C(x) = ∫₀ˣ cos(π t²/2) dt
//
// Rational Chebyshev approximation from Cephes / scipy.
// Three regions: |x|<1.6, 1.6≤|x|<36, |x|≥36.
// ──────────────────────────────────────────────────────────────────

// Region 1 (|x| < 1.6): S(x) = x³ P(x⁴)/Q(x⁴)
// Coefficients from Cephes (π/2 factor is baked into the coefficients)