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fix tanh inconsistent

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This commit is contained in:
Ziming Dong 2016-08-06 19:48:50 +08:00
parent 5cf1e4c79b
commit 1031223c09
1 changed files with 89 additions and 28 deletions
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117
Eigen/src/Core/functors/UnaryFunctors.h
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@ -491,19 +491,62 @@ struct functor_traits<scalar_atan_op<Scalar> >
};
};
/** \internal
* \brief Template functor to compute the tanh of a scalar
* \sa class CwiseUnaryOp, ArrayBase::tanh()
*/
template<typename Scalar> struct scalar_tanh_op {
template <typename Scalar>
struct scalar_tanh_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_tanh_op)
EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::tanh(a); }
EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const {
/** \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 ulp in the range [-9, 9], outside of
which
the fl(tanh(x)) = +/-1. */
// Clamp the inputs to the range [-9, 9] since anything outside
// this range is +/-1.0f in single-precision.
const Scalar plus_9 = static_cast<Scalar>(9.0);
const Scalar minus_9 = static_cast<Scalar>(-9.0);
const Scalar x = numext::maxi(minus_9, numext::mini(plus_9, a));
// Scalarhe monomial coefficients of the numerator polynomial (odd).
const Scalar alpha_1 = static_cast<Scalar>(4.89352455891786e-03);
const Scalar alpha_3 = static_cast<Scalar>(6.37261928875436e-04);
const Scalar alpha_5 = static_cast<Scalar>(1.48572235717979e-05);
const Scalar alpha_7 = static_cast<Scalar>(5.12229709037114e-08);
const Scalar alpha_9 = static_cast<Scalar>(-8.60467152213735e-11);
const Scalar alpha_11 = static_cast<Scalar>(2.00018790482477e-13);
const Scalar alpha_13 = static_cast<Scalar>(-2.76076847742355e-16);
// Scalarhe monomial coefficients of the denominator polynomial (even).
const Scalar beta_0 = static_cast<Scalar>(4.89352518554385e-03);
const Scalar beta_2 = static_cast<Scalar>(2.26843463243900e-03);
const Scalar beta_4 = static_cast<Scalar>(1.18534705686654e-04);
const Scalar beta_6 = static_cast<Scalar>(1.19825839466702e-06);
// Since the polynomials are odd/even, we need x^2.
const Scalar x2 = x * x;
// Evaluate the numerator polynomial p.
Scalar p = x2 * alpha_13 + alpha_11;
p = x2 * p + alpha_9;
p = x2 * p + alpha_7;
p = x2 * p + alpha_5;
p = x2 * p + alpha_3;
p = x2 * p + alpha_1;
p = x * p;
// Evaluate the denominator polynomial p.
Scalar q = x2 * beta_6 + beta_4;
q = x2 * q + beta_2;
q = x2 * q + beta_0;
// Divide the numerator by the denominator.
return p / q;
}
template <typename Packet>
EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& _x) const {
/** \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 ulp in the range [-9, 9], outside of which the
is accurate up to a couple of ulp in the range [-9, 9], outside of which
the
fl(tanh(x)) = +/-1. */
// Clamp the inputs to the range [-9, 9] since anything outside
@ -511,7 +554,7 @@ template<typename Scalar> struct scalar_tanh_op {
const Packet plus_9 = pset1<Packet>(9.0);
const Packet minus_9 = pset1<Packet>(-9.0);
const Packet x = pmax(minus_9, pmin(plus_9, _x));
// The monomial coefficients of the numerator polynomial (odd).
const Packet alpha_1 = pset1<Packet>(4.89352455891786e-03);
const Packet alpha_3 = pset1<Packet>(6.37261928875436e-04);
@ -520,17 +563,17 @@ template<typename Scalar> struct scalar_tanh_op {
const Packet alpha_9 = pset1<Packet>(-8.60467152213735e-11);
const Packet alpha_11 = pset1<Packet>(2.00018790482477e-13);
const Packet alpha_13 = pset1<Packet>(-2.76076847742355e-16);
// The monomial coefficients of the denominator polynomial (even).
const Packet beta_0 = pset1<Packet>(4.89352518554385e-03);
const Packet beta_2 = pset1<Packet>(2.26843463243900e-03);
const Packet beta_4 = pset1<Packet>(1.18534705686654e-04);
const Packet beta_6 = pset1<Packet>(1.19825839466702e-06);
// Since the polynomials are odd/even, we need x^2.
const Packet x2 = pmul(x, x);
// Evaluate the numerator polynomial p.
// Evaluate the numerator polynomial p.
Packet p = pmadd(x2, alpha_13, alpha_11);
p = pmadd(x2, p, alpha_9);
p = pmadd(x2, p, alpha_7);
@ -538,38 +581,56 @@ template<typename Scalar> struct scalar_tanh_op {
p = pmadd(x2, p, alpha_3);
p = pmadd(x2, p, alpha_1);
p = pmul(x, p);
// Evaluate the denominator polynomial p.
Packet 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 pdiv(p, q);
}
};
template<typename Scalar>
struct functor_traits<scalar_tanh_op<Scalar> >
{
template <>
struct scalar_tanh_op<std::complex<double> > {
EIGEN_DEVICE_FUNC inline const std::complex<double> operator()(
const std::complex<double>& a) const {
return numext::tanh(a);
}
};
template <>
struct scalar_tanh_op<std::complex<float> > {
EIGEN_DEVICE_FUNC inline const std::complex<float> operator()(
const std::complex<float>& a) const {
return numext::tanh(a);
}
};
template <typename Scalar>
struct functor_traits<scalar_tanh_op<Scalar> > {
enum {
PacketAccess = packet_traits<Scalar>::HasTanh,
Cost =
(PacketAccess
// The following numbers are based on the AVX implementation,
Cost = (PacketAccess && (!is_same<Scalar, std::complex<float> >::value) &&
(!is_same<Scalar, std::complex<double> >::value)
// The following numbers are based on the AVX implementation,
#ifdef EIGEN_VECTORIZE_FMA
// Haswell can issue 2 add/mul/madd per cycle.
// 9 pmadd, 2 pmul, 1 div, 2 other
? (2 * NumTraits<Scalar>::AddCost + 6 * NumTraits<Scalar>::MulCost +
NumTraits<Scalar>::template Div<packet_traits<Scalar>::HasDiv>::Cost)
// Haswell can issue 2 add/mul/madd per cycle.
// 9 pmadd, 2 pmul, 1 div, 2 other
? (2 * NumTraits<Scalar>::AddCost +
6 * NumTraits<Scalar>::MulCost +
NumTraits<Scalar>::template Div<
packet_traits<Scalar>::HasDiv>::Cost)
#else
? (11 * NumTraits<Scalar>::AddCost +
11 * NumTraits<Scalar>::MulCost +
NumTraits<Scalar>::template Div<packet_traits<Scalar>::HasDiv>::Cost)
? (11 * NumTraits<Scalar>::AddCost +
11 * NumTraits<Scalar>::MulCost +
NumTraits<Scalar>::template Div<
packet_traits<Scalar>::HasDiv>::Cost)
#endif
// This number assumes a naive implementation of tanh
: (6 * NumTraits<Scalar>::AddCost + 3 * NumTraits<Scalar>::MulCost +
2 * NumTraits<Scalar>::template Div<packet_traits<Scalar>::HasDiv>::Cost +
functor_traits<scalar_exp_op<Scalar> >::Cost))
// This number assumes a naive implementation of tanh
: (6 * NumTraits<Scalar>::AddCost +
3 * NumTraits<Scalar>::MulCost +
2 * NumTraits<Scalar>::template Div<
packet_traits<Scalar>::HasDiv>::Cost +
functor_traits<scalar_exp_op<Scalar> >::Cost))
};
};