diff options
Diffstat (limited to 'unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsImpl.h')
| -rw-r--r-- | unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsImpl.h | 361 |
1 files changed, 1 insertions, 360 deletions
diff --git a/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsImpl.h b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsImpl.h index 7c6d32049..ea00bd96e 100644 --- a/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsImpl.h +++ b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsImpl.h @@ -1757,7 +1757,7 @@ struct betainc_helper<double> { if ((a + b) < maxgam && numext::abs(u) < maxlog) { t = gamma(a + b) / (gamma(a) * gamma(b)); s = s * t * pow(x, a); - } else { + } */ t = lgamma_impl<double>::run(a + b) - lgamma_impl<double>::run(a) - lgamma_impl<double>::run(b) + u + numext::log(s); @@ -1864,351 +1864,6 @@ struct betainc_impl<double> { #endif // EIGEN_HAS_C99_MATH -/**************************************************************************** - * Implementation of Bessel function, based on Cephes * - ****************************************************************************/ - -template <typename Scalar> -struct i0e_retval { - typedef Scalar type; -}; - -template <typename T, typename ScalarType> -struct generic_i0e { - EIGEN_DEVICE_FUNC - static EIGEN_STRONG_INLINE T run(const T&) { - EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value == false), - THIS_TYPE_IS_NOT_SUPPORTED); - return ScalarType(0); - } -}; - -template <typename T> -struct generic_i0e<T, float> { - EIGEN_DEVICE_FUNC - static EIGEN_STRONG_INLINE T run(const T& x) { - /* i0ef.c - * - * Modified Bessel function of order zero, - * exponentially scaled - * - * - * - * SYNOPSIS: - * - * float x, y, i0ef(); - * - * y = i0ef( x ); - * - * - * - * DESCRIPTION: - * - * Returns exponentially scaled modified Bessel function - * of order zero of the argument. - * - * The function is defined as i0e(x) = exp(-|x|) j0( ix ). - * - * - * - * ACCURACY: - * - * Relative error: - * arithmetic domain # trials peak rms - * IEEE 0,30 100000 3.7e-7 7.0e-8 - * See i0f(). - * - */ - - const float A[] = {-1.30002500998624804212E-8f, 6.04699502254191894932E-8f, - -2.67079385394061173391E-7f, 1.11738753912010371815E-6f, - -4.41673835845875056359E-6f, 1.64484480707288970893E-5f, - -5.75419501008210370398E-5f, 1.88502885095841655729E-4f, - -5.76375574538582365885E-4f, 1.63947561694133579842E-3f, - -4.32430999505057594430E-3f, 1.05464603945949983183E-2f, - -2.37374148058994688156E-2f, 4.93052842396707084878E-2f, - -9.49010970480476444210E-2f, 1.71620901522208775349E-1f, - -3.04682672343198398683E-1f, 6.76795274409476084995E-1f}; - - const float B[] = {3.39623202570838634515E-9f, 2.26666899049817806459E-8f, - 2.04891858946906374183E-7f, 2.89137052083475648297E-6f, - 6.88975834691682398426E-5f, 3.36911647825569408990E-3f, - 8.04490411014108831608E-1f}; - T y = pabs(x); - T y_le_eight = internal::pchebevl<T, 18>::run( - pmadd(pset1<T>(0.5f), y, pset1<T>(-2.0f)), A); - T y_gt_eight = pdiv( - internal::pchebevl<T, 7>::run( - psub(pdiv(pset1<T>(32.0f), y), pset1<T>(2.0f)), B), - psqrt(y)); - // TODO: Perhaps instead check whether all packet elements are in - // [-8, 8] and evaluate a branch based off of that. It's possible - // in practice most elements are in this region. - return pselect(pcmp_le(y, pset1<T>(8.0f)), y_le_eight, y_gt_eight); - } -}; - -template <typename T> -struct generic_i0e<T, double> { - EIGEN_DEVICE_FUNC - static EIGEN_STRONG_INLINE T run(const T& x) { - /* i0e.c - * - * Modified Bessel function of order zero, - * exponentially scaled - * - * - * - * SYNOPSIS: - * - * double x, y, i0e(); - * - * y = i0e( x ); - * - * - * - * DESCRIPTION: - * - * Returns exponentially scaled modified Bessel function - * of order zero of the argument. - * - * The function is defined as i0e(x) = exp(-|x|) j0( ix ). - * - * - * - * ACCURACY: - * - * Relative error: - * arithmetic domain # trials peak rms - * IEEE 0,30 30000 5.4e-16 1.2e-16 - * See i0(). - * - */ - - const double A[] = {-4.41534164647933937950E-18, 3.33079451882223809783E-17, - -2.43127984654795469359E-16, 1.71539128555513303061E-15, - -1.16853328779934516808E-14, 7.67618549860493561688E-14, - -4.85644678311192946090E-13, 2.95505266312963983461E-12, - -1.72682629144155570723E-11, 9.67580903537323691224E-11, - -5.18979560163526290666E-10, 2.65982372468238665035E-9, - -1.30002500998624804212E-8, 6.04699502254191894932E-8, - -2.67079385394061173391E-7, 1.11738753912010371815E-6, - -4.41673835845875056359E-6, 1.64484480707288970893E-5, - -5.75419501008210370398E-5, 1.88502885095841655729E-4, - -5.76375574538582365885E-4, 1.63947561694133579842E-3, - -4.32430999505057594430E-3, 1.05464603945949983183E-2, - -2.37374148058994688156E-2, 4.93052842396707084878E-2, - -9.49010970480476444210E-2, 1.71620901522208775349E-1, - -3.04682672343198398683E-1, 6.76795274409476084995E-1}; - const double B[] = { - -7.23318048787475395456E-18, -4.83050448594418207126E-18, - 4.46562142029675999901E-17, 3.46122286769746109310E-17, - -2.82762398051658348494E-16, -3.42548561967721913462E-16, - 1.77256013305652638360E-15, 3.81168066935262242075E-15, - -9.55484669882830764870E-15, -4.15056934728722208663E-14, - 1.54008621752140982691E-14, 3.85277838274214270114E-13, - 7.18012445138366623367E-13, -1.79417853150680611778E-12, - -1.32158118404477131188E-11, -3.14991652796324136454E-11, - 1.18891471078464383424E-11, 4.94060238822496958910E-10, - 3.39623202570838634515E-9, 2.26666899049817806459E-8, - 2.04891858946906374183E-7, 2.89137052083475648297E-6, - 6.88975834691682398426E-5, 3.36911647825569408990E-3, - 8.04490411014108831608E-1}; - T y = pabs(x); - T y_le_eight = internal::pchebevl<T, 30>::run( - pmadd(pset1<T>(0.5), y, pset1<T>(-2.0)), A); - T y_gt_eight = pdiv( - internal::pchebevl<T, 25>::run( - psub(pdiv(pset1<T>(32.0), y), pset1<T>(2.0)), B), - psqrt(y)); - // TODO: Perhaps instead check whether all packet elements are in - // [-8, 8] and evaluate a branch based off of that. It's possible - // in practice most elements are in this region. - return pselect(pcmp_le(y, pset1<T>(8.0)), y_le_eight, y_gt_eight); - } -}; - -template <typename Scalar> -struct i0e_impl { - EIGEN_DEVICE_FUNC - static EIGEN_STRONG_INLINE Scalar run(const Scalar x) { - return generic_i0e<Scalar, Scalar>::run(x); - } -}; - - -template <typename Scalar> -struct i1e_retval { - typedef Scalar type; -}; - -template <typename T, typename ScalarType> -struct generic_i1e { - EIGEN_DEVICE_FUNC - static EIGEN_STRONG_INLINE T run(const T&) { - EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value == false), - THIS_TYPE_IS_NOT_SUPPORTED); - return ScalarType(0); - } -}; - -template <typename T> -struct generic_i1e<T, float> { - EIGEN_DEVICE_FUNC - static EIGEN_STRONG_INLINE T run(const T& x) { - /* i1ef.c - * - * Modified Bessel function of order one, - * exponentially scaled - * - * - * - * SYNOPSIS: - * - * float x, y, i1ef(); - * - * y = i1ef( x ); - * - * - * - * DESCRIPTION: - * - * Returns exponentially scaled modified Bessel function - * of order one of the argument. - * - * The function is defined as i1(x) = -i exp(-|x|) j1( ix ). - * - * - * - * ACCURACY: - * - * Relative error: - * arithmetic domain # trials peak rms - * IEEE 0, 30 30000 1.5e-6 1.5e-7 - * See i1(). - * - */ - const float A[] = {9.38153738649577178388E-9f, -4.44505912879632808065E-8f, - 2.00329475355213526229E-7f, -8.56872026469545474066E-7f, - 3.47025130813767847674E-6f, -1.32731636560394358279E-5f, - 4.78156510755005422638E-5f, -1.61760815825896745588E-4f, - 5.12285956168575772895E-4f, -1.51357245063125314899E-3f, - 4.15642294431288815669E-3f, -1.05640848946261981558E-2f, - 2.47264490306265168283E-2f, -5.29459812080949914269E-2f, - 1.02643658689847095384E-1f, -1.76416518357834055153E-1f, - 2.52587186443633654823E-1f}; - - const float B[] = {-3.83538038596423702205E-9f, -2.63146884688951950684E-8f, - -2.51223623787020892529E-7f, -3.88256480887769039346E-6f, - -1.10588938762623716291E-4f, -9.76109749136146840777E-3f, - 7.78576235018280120474E-1f}; - - - T y = pabs(x); - T y_le_eight = pmul(y, internal::pchebevl<T, 17>::run( - pmadd(pset1<T>(0.5f), y, pset1<T>(-2.0f)), A)); - T y_gt_eight = pdiv( - internal::pchebevl<T, 7>::run( - psub(pdiv(pset1<T>(32.0f), y), - pset1<T>(2.0f)), B), - psqrt(y)); - // TODO: Perhaps instead check whether all packet elements are in - // [-8, 8] and evaluate a branch based off of that. It's possible - // in practice most elements are in this region. - y = pselect(pcmp_le(y, pset1<T>(8.0f)), y_le_eight, y_gt_eight); - return pselect(pcmp_lt(x, pset1<T>(0.0f)), -y, y); - } -}; - -template <typename T> -struct generic_i1e<T, double> { - EIGEN_DEVICE_FUNC - static EIGEN_STRONG_INLINE T run(const T& x) { - /* i1e.c - * - * Modified Bessel function of order one, - * exponentially scaled - * - * - * - * SYNOPSIS: - * - * double x, y, i1e(); - * - * y = i1e( x ); - * - * - * - * DESCRIPTION: - * - * Returns exponentially scaled modified Bessel function - * of order one of the argument. - * - * The function is defined as i1(x) = -i exp(-|x|) j1( ix ). - * - * - * - * ACCURACY: - * - * Relative error: - * arithmetic domain # trials peak rms - * IEEE 0, 30 30000 2.0e-15 2.0e-16 - * See i1(). - * - */ - const double A[] = {2.77791411276104639959E-18, -2.11142121435816608115E-17, - 1.55363195773620046921E-16, -1.10559694773538630805E-15, - 7.60068429473540693410E-15, -5.04218550472791168711E-14, - 3.22379336594557470981E-13, -1.98397439776494371520E-12, - 1.17361862988909016308E-11, -6.66348972350202774223E-11, - 3.62559028155211703701E-10, -1.88724975172282928790E-9, - 9.38153738649577178388E-9, -4.44505912879632808065E-8, - 2.00329475355213526229E-7, -8.56872026469545474066E-7, - 3.47025130813767847674E-6, -1.32731636560394358279E-5, - 4.78156510755005422638E-5, -1.61760815825896745588E-4, - 5.12285956168575772895E-4, -1.51357245063125314899E-3, - 4.15642294431288815669E-3, -1.05640848946261981558E-2, - 2.47264490306265168283E-2, -5.29459812080949914269E-2, - 1.02643658689847095384E-1, -1.76416518357834055153E-1, - 2.52587186443633654823E-1}; - const double B[] = { - 7.51729631084210481353E-18, 4.41434832307170791151E-18, - -4.65030536848935832153E-17, -3.20952592199342395980E-17, - 2.96262899764595013876E-16, 3.30820231092092828324E-16, - -1.88035477551078244854E-15, -3.81440307243700780478E-15, - 1.04202769841288027642E-14, 4.27244001671195135429E-14, - -2.10154184277266431302E-14, -4.08355111109219731823E-13, - -7.19855177624590851209E-13, 2.03562854414708950722E-12, - 1.41258074366137813316E-11, 3.25260358301548823856E-11, - -1.89749581235054123450E-11, -5.58974346219658380687E-10, - -3.83538038596423702205E-9, -2.63146884688951950684E-8, - -2.51223623787020892529E-7, -3.88256480887769039346E-6, - -1.10588938762623716291E-4, -9.76109749136146840777E-3, - 7.78576235018280120474E-1}; - T y = pabs(x); - T y_le_eight = pmul(y, internal::pchebevl<T, 29>::run( - pmadd(pset1<T>(0.5), y, pset1<T>(-2.0)), A)); - T y_gt_eight = pdiv( - internal::pchebevl<T, 25>::run( - psub(pdiv(pset1<T>(32.0), y), - pset1<T>(2.0)), B), - psqrt(y)); - // TODO: Perhaps instead check whether all packet elements are in - // [-8, 8] and evaluate a branch based off of that. It's possible - // in practice most elements are in this region. - y = pselect(pcmp_le(y, pset1<T>(8.0)), y_le_eight, y_gt_eight); - return pselect(pcmp_lt(x, pset1<T>(0.0f)), -y, y); - } -}; - -template <typename Scalar> -struct i1e_impl { - EIGEN_DEVICE_FUNC - static EIGEN_STRONG_INLINE Scalar run(const Scalar x) { - return generic_i1e<Scalar, Scalar>::run(x); - } -}; - } // end namespace internal namespace numext { @@ -2285,21 +1940,7 @@ EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(betainc, Scalar) return EIGEN_MATHFUNC_IMPL(betainc, Scalar)::run(a, b, x); } -template <typename Scalar> -EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(i0e, Scalar) - i0e(const Scalar& x) { - return EIGEN_MATHFUNC_IMPL(i0e, Scalar)::run(x); -} - -template <typename Scalar> -EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(i1e, Scalar) - i1e(const Scalar& x) { - return EIGEN_MATHFUNC_IMPL(i1e, Scalar)::run(x); -} - } // end namespace numext - - } // end namespace Eigen #endif // EIGEN_SPECIAL_FUNCTIONS_H |