11 #ifndef EIGEN_MATHFUNCTIONSIMPL_H 12 #define EIGEN_MATHFUNCTIONSIMPL_H 29 T generic_fast_tanh_float(
const T& a_x)
32 #ifdef EIGEN_VECTORIZE_FMA 33 const T plus_clamp = pset1<T>(7.99881172180175781f);
34 const T minus_clamp = pset1<T>(-7.99881172180175781f);
36 const T plus_clamp = pset1<T>(7.90531110763549805f);
37 const T minus_clamp = pset1<T>(-7.90531110763549805f);
39 const T tiny = pset1<T>(0.0004f);
40 const T x = pmax(pmin(a_x, plus_clamp), minus_clamp);
41 const T tiny_mask = pcmp_lt(pabs(a_x), tiny);
43 const T alpha_1 = pset1<T>(4.89352455891786e-03f);
44 const T alpha_3 = pset1<T>(6.37261928875436e-04f);
45 const T alpha_5 = pset1<T>(1.48572235717979e-05f);
46 const T alpha_7 = pset1<T>(5.12229709037114e-08f);
47 const T alpha_9 = pset1<T>(-8.60467152213735e-11f);
48 const T alpha_11 = pset1<T>(2.00018790482477e-13f);
49 const T alpha_13 = pset1<T>(-2.76076847742355e-16f);
52 const T beta_0 = pset1<T>(4.89352518554385e-03f);
53 const T beta_2 = pset1<T>(2.26843463243900e-03f);
54 const T beta_4 = pset1<T>(1.18534705686654e-04f);
55 const T beta_6 = pset1<T>(1.19825839466702e-06f);
58 const T x2 = pmul(x, x);
61 T p = pmadd(x2, alpha_13, alpha_11);
62 p = pmadd(x2, p, alpha_9);
63 p = pmadd(x2, p, alpha_7);
64 p = pmadd(x2, p, alpha_5);
65 p = pmadd(x2, p, alpha_3);
66 p = pmadd(x2, p, alpha_1);
70 T q = pmadd(x2, beta_6, beta_4);
71 q = pmadd(x2, q, beta_2);
72 q = pmadd(x2, q, beta_0);
75 return pselect(tiny_mask, x, pdiv(p, q));
78 template<
typename RealScalar>
79 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
80 RealScalar positive_real_hypot(
const RealScalar& x,
const RealScalar& y)
83 if ((numext::isinf)(x) || (numext::isinf)(y))
84 return NumTraits<RealScalar>::infinity();
85 if ((numext::isnan)(x) || (numext::isnan)(y))
86 return NumTraits<RealScalar>::quiet_NaN();
88 EIGEN_USING_STD(
sqrt);
90 p = numext::maxi(x,y);
91 if(p==RealScalar(0))
return RealScalar(0);
92 qp = numext::mini(y,x) / p;
93 return p *
sqrt(RealScalar(1) + qp*qp);
96 template<
typename Scalar>
99 typedef typename NumTraits<Scalar>::Real RealScalar;
100 static EIGEN_DEVICE_FUNC
101 inline RealScalar run(
const Scalar& x,
const Scalar& y)
103 EIGEN_USING_STD(
abs);
104 return positive_real_hypot<RealScalar>(
abs(x),
abs(y));
111 EIGEN_DEVICE_FUNC std::complex<T> complex_sqrt(
const std::complex<T>& z) {
134 const T x = numext::real(z);
135 const T y = numext::imag(z);
137 const T w = numext::sqrt(T(0.5) * (numext::abs(x) + numext::hypot(x, y)));
140 (numext::isinf)(y) ? std::complex<T>(NumTraits<T>::infinity(), y)
141 : x == zero ? std::complex<T>(w, y < zero ? -w : w)
142 : x > zero ? std::complex<T>(w, y / (2 * w))
143 :
std::complex<T>(numext::
abs(y) / (2 * w), y < zero ? -w : w );
148 EIGEN_DEVICE_FUNC std::complex<T> complex_rsqrt(
const std::complex<T>& z) {
171 const T x = numext::real(z);
172 const T y = numext::imag(z);
175 const T abs_z = numext::hypot(x, y);
176 const T w = numext::sqrt(T(0.5) * (numext::abs(x) + abs_z));
177 const T woz = w / abs_z;
180 abs_z == zero ? std::complex<T>(NumTraits<T>::infinity(), NumTraits<T>::quiet_NaN())
181 : ((numext::isinf)(x) || (numext::isinf)(y)) ? std::complex<T>(zero, zero)
182 : x == zero ? std::complex<T>(woz, y < zero ? woz : -woz)
183 : x > zero ?
std::complex<T>(woz, -y / (2 * w * abs_z))
184 :
std::complex<T>(numext::
abs(y) / (2 * w * abs_z), y < zero ? woz : -woz );
188 EIGEN_DEVICE_FUNC std::complex<T> complex_log(
const std::complex<T>& z) {
190 T a = numext::abs(z);
191 EIGEN_USING_STD(atan2);
192 T b = atan2(z.imag(), z.real());
193 return std::complex<T>(numext::log(a), b);
200 #endif // EIGEN_MATHFUNCTIONSIMPL_H const Eigen::CwiseUnaryOp< Eigen::internal::scalar_sqrt_op< typename Derived::Scalar >, const Derived > sqrt(const Eigen::ArrayBase< Derived > &x)
Namespace containing all symbols from the Eigen library.
Definition: Core:141
Definition: BFloat16.h:88
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_abs_op< typename Derived::Scalar >, const Derived > abs(const Eigen::ArrayBase< Derived > &x)
Definition: Eigen_Colamd.h:50