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Optimized implementation of the tanh function for SSE

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This commit is contained in:
Benoit Steiner 2016-02-10 08:52:30 -08:00
parent 2d523332b3
commit bfb3fcd94f
2 changed files with 49 additions and 0 deletions
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48
Eigen/src/Core/arch/SSE/MathFunctions.h
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@ -516,6 +516,54 @@ Packet2d prsqrt<Packet2d>(const Packet2d& x) {
return _mm_div_pd(pset1<Packet2d>(1.0), _mm_sqrt_pd(x));
}
// Hyperbolic Tangent function.
// Doesn't do anything fancy, just a 13/6-degree rational interpolant which
// is accurate up to a couple of ulp in the range [-8, 8], outside of which the
// fl(tanh(x)) = +/-1.
template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f
ptanh<Packet4f>(const Packet4f& _x) {
// Map the range [-8, 8] to [-1, 1], we will clamp bad coefficients later.
const Packet4f x =
pmax(pset1<Packet4f>(-1.0f),
pmin(pset1<Packet4f>(1.0f), pmul(_x, pset1<Packet4f>(0.125f))));
// The monomial coefficients of the numerator polynomial (odd).
_EIGEN_DECLARE_CONST_Packet4f(alpha_1, -2.47030171958948e-03);
_EIGEN_DECLARE_CONST_Packet4f(alpha_3, -2.06804010015822e-02);
_EIGEN_DECLARE_CONST_Packet4f(alpha_5, -3.13693994587418e-02);
_EIGEN_DECLARE_CONST_Packet4f(alpha_7, -7.19851201683627e-03);
_EIGEN_DECLARE_CONST_Packet4f(alpha_9, 8.31561269687160e-04);
_EIGEN_DECLARE_CONST_Packet4f(alpha_11, -1.37626659546502e-04);
_EIGEN_DECLARE_CONST_Packet4f(alpha_13, 1.39116714700458e-05);
// The monomial coefficients of the denominator polynomial (even).
_EIGEN_DECLARE_CONST_Packet4f(beta_0, -3.08787724141615e-04);
_EIGEN_DECLARE_CONST_Packet4f(beta_2, -9.17251911622436e-03);
_EIGEN_DECLARE_CONST_Packet4f(beta_4, -3.09625062090444e-02);
_EIGEN_DECLARE_CONST_Packet4f(beta_6, -2.05669680763032e-02);
// Since the polynomials are odd/even, we need x^2.
const Packet4f x2 = pmul(x, x);
// Evaluate the numerator polynomial p.
Packet4f p = pmadd(x2, p4f_alpha_13, p4f_alpha_11);
p = pmadd(x2, p, p4f_alpha_9);
p = pmadd(x2, p, p4f_alpha_7);
p = pmadd(x2, p, p4f_alpha_5);
p = pmadd(x2, p, p4f_alpha_3);
p = pmadd(x2, p, p4f_alpha_1);
p = pmul(x, p);
// Evaluate the denominator polynomial p.
Packet4f q = pmadd(x2, p4f_beta_6, p4f_beta_4);
q = pmadd(x2, q, p4f_beta_2);
q = pmadd(x2, q, p4f_beta_0);
// Divide the numerator by the denominator.
return pdiv(p, q);
}
} // end namespace internal
namespace numext {

1
Eigen/src/Core/arch/SSE/PacketMath.h
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@ -109,6 +109,7 @@ template<> struct packet_traits<float> : default_packet_traits
HasExp = 1,
HasSqrt = 1,
HasRsqrt = 1,
HasTanh = EIGEN_FAST_MATH,
HasBlend = 1
#ifdef EIGEN_VECTORIZE_SSE4_1