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Slightly optimize atanh2.

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This commit is contained in:
Chen-Pang He 2013-07-08 16:49:27 +08:00
parent 00e30a5fc4
commit 04bd1e3fc0
1 changed files with 30 additions and 22 deletions
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52
Eigen/src/Core/MathFunctions.h
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@ -332,37 +332,45 @@ inline NewType cast(const OldType& x)
* Implementation of atanh2 * * Implementation of atanh2 *
****************************************************************************/ ****************************************************************************/
template<typename Scalar, bool IsInteger> template<typename Scalar>
struct atanh2_default_impl struct atanh2_impl
{ {
typedef Scalar retval; static inline Scalar run(const Scalar& x, const Scalar& r)
typedef typename NumTraits<Scalar>::Real RealScalar; {
static inline Scalar run(const Scalar& x, const Scalar& y) EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
#if __cplusplus >= 201103L
using std::log1p;
return log1p(2 * x / (r - x)) / 2;
#else
using std::abs;
using std::log;
using std::sqrt;
Scalar z = x / r;
if (r == 0 || abs(z) > sqrt(NumTraits<Scalar>::epsilon()))
return log((r + x) / (r - x)) / 2;
else
return z + z*z*z / 3;
#endif
}
};
template<typename RealScalar>
struct atanh2_impl<std::complex<RealScalar> >
{
typedef std::complex<RealScalar> Scalar;
static inline Scalar run(const Scalar& x, const Scalar& r)
{ {
using std::abs;
using std::log; using std::log;
using std::norm;
using std::sqrt; using std::sqrt;
Scalar z = x / y; Scalar z = x / r;
if (y == Scalar(0) || abs(z) > sqrt(NumTraits<RealScalar>::epsilon())) if (r == Scalar(0) || norm(z) > NumTraits<RealScalar>::epsilon())
return RealScalar(0.5) * log((y + x) / (y - x)); return RealScalar(0.5) * log((r + x) / (r - x));
else else
return z + z*z*z / RealScalar(3); return z + z*z*z / RealScalar(3);
} }
}; };
template<typename Scalar>
struct atanh2_default_impl<Scalar, true>
{
static inline Scalar run(const Scalar&, const Scalar&)
{
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
return Scalar(0);
}
};
template<typename Scalar>
struct atanh2_impl : atanh2_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {};
template<typename Scalar> template<typename Scalar>
struct atanh2_retval struct atanh2_retval
{ {