Rename generic_fast_tanh_float to ptanh_float and move it to...

Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h

@@ -917,6 +917,65 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet patan_double(const Pa
   return pxor(p, x_signmask);
 }
 
+/** \internal \returns the hyperbolic tan of \a a (coeff-wise)
+    Doesn't do anything fancy, just a 13/6-degree rational interpolant which
+    is accurate up to a couple of ulps in the (approximate) range [-8, 8],
+    outside of which tanh(x) = +/-1 in single precision. The input is clamped
+    to the range [-c, c]. The value c is chosen as the smallest value where
+    the approximation evaluates to exactly 1. In the reange [-0.0004, 0.0004]
+    the approximation tanh(x) ~= x is used for better accuracy as x tends to zero.
+
+    This implementation works on both scalars and packets.
+*/
+template <typename T>
+T ptanh_float(const T& a_x) {
+  // Clamp the inputs to the range [-c, c]
+#ifdef EIGEN_VECTORIZE_FMA
+  const T plus_clamp = pset1<T>(7.99881172180175781f);
+  const T minus_clamp = pset1<T>(-7.99881172180175781f);
+#else
+  const T plus_clamp = pset1<T>(7.90531110763549805f);
+  const T minus_clamp = pset1<T>(-7.90531110763549805f);
+#endif
+  const T tiny = pset1<T>(0.0004f);
+  const T x = pmax(pmin(a_x, plus_clamp), minus_clamp);
+  const T tiny_mask = pcmp_lt(pabs(a_x), tiny);
+  // The monomial coefficients of the numerator polynomial (odd).
+  const T alpha_1 = pset1<T>(4.89352455891786e-03f);
+  const T alpha_3 = pset1<T>(6.37261928875436e-04f);
+  const T alpha_5 = pset1<T>(1.48572235717979e-05f);
+  const T alpha_7 = pset1<T>(5.12229709037114e-08f);
+  const T alpha_9 = pset1<T>(-8.60467152213735e-11f);
+  const T alpha_11 = pset1<T>(2.00018790482477e-13f);
+  const T alpha_13 = pset1<T>(-2.76076847742355e-16f);
+
+  // The monomial coefficients of the denominator polynomial (even).
+  const T beta_0 = pset1<T>(4.89352518554385e-03f);
+  const T beta_2 = pset1<T>(2.26843463243900e-03f);
+  const T beta_4 = pset1<T>(1.18534705686654e-04f);
+  const T beta_6 = pset1<T>(1.19825839466702e-06f);
+
+  // Since the polynomials are odd/even, we need x^2.
+  const T x2 = pmul(x, x);
+
+  // Evaluate the numerator polynomial p.
+  T p = pmadd(x2, alpha_13, alpha_11);
+  p = pmadd(x2, p, alpha_9);
+  p = pmadd(x2, p, alpha_7);
+  p = pmadd(x2, p, alpha_5);
+  p = pmadd(x2, p, alpha_3);
+  p = pmadd(x2, p, alpha_1);
+  p = pmul(x, p);
+
+  // Evaluate the denominator polynomial q.
+  T q = pmadd(x2, beta_6, beta_4);
+  q = pmadd(x2, q, beta_2);
+  q = pmadd(x2, q, beta_0);
+
+  // Divide the numerator by the denominator.
+  return pselect(tiny_mask, x, pdiv(p, q));
+}
+
 template <typename Packet>
 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet patanh_float(const Packet& x) {
   typedef typename unpacket_traits<Packet>::type Scalar;