Stokhos Package Browser (Single Doxygen Collection)  Version of the Day
Stokhos_OrthogPolyExpansion.hpp
Go to the documentation of this file.
1 // $Id$
2 // $Source$
3 // @HEADER
4 // ***********************************************************************
5 //
6 // Stokhos Package
7 // Copyright (2009) Sandia Corporation
8 //
9 // Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
10 // license for use of this work by or on behalf of the U.S. Government.
11 //
12 // Redistribution and use in source and binary forms, with or without
13 // modification, are permitted provided that the following conditions are
14 // met:
15 //
16 // 1. Redistributions of source code must retain the above copyright
17 // notice, this list of conditions and the following disclaimer.
18 //
19 // 2. Redistributions in binary form must reproduce the above copyright
20 // notice, this list of conditions and the following disclaimer in the
21 // documentation and/or other materials provided with the distribution.
22 //
23 // 3. Neither the name of the Corporation nor the names of the
24 // contributors may be used to endorse or promote products derived from
25 // this software without specific prior written permission.
26 //
27 // THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
28 // EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
29 // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
30 // PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL SANDIA CORPORATION OR THE
31 // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
32 // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
33 // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
34 // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
35 // LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
36 // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
37 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
38 //
39 // Questions? Contact Eric T. Phipps (etphipp@sandia.gov).
40 //
41 // ***********************************************************************
42 // @HEADER
43 
44 #ifndef STOKHOS_ORTHOGPOLYEXPANSION_HPP
45 #define STOKHOS_ORTHOGPOLYEXPANSION_HPP
46 
47 #include <cmath>
48 #include <algorithm> // for std::min and std::max
49 
50 #include "Stokhos_OrthogPolyApprox.hpp"
51 #include "Stokhos_OrthogPolyBasis.hpp"
52 
53 namespace Stokhos {
54 
56  template <typename ordinal_type, typename value_type,
57  typename node_type = Stokhos::StandardStorage<ordinal_type,
58  value_type> >
59  class OrthogPolyExpansion {
60  public:
61 
63  typedef Sparse3Tensor<ordinal_type, value_type> tp_type;
64 
66  OrthogPolyExpansion() {}
67 
69  virtual ~OrthogPolyExpansion() {}
70 
72  virtual ordinal_type size() const = 0;
73 
75  virtual Teuchos::RCP<const OrthogPolyBasis<ordinal_type, value_type> >
76  getBasis() const = 0;
77 
79  virtual Teuchos::RCP<const Sparse3Tensor<ordinal_type, value_type> >
80  getTripleProduct() const = 0;
81 
82  // Operations
83  virtual void unaryMinus(
84  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
85  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a) = 0;
86 
87  virtual void plusEqual(
88  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
89  const value_type& x) = 0;
90  virtual void minusEqual(
91  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
92  const value_type& x) = 0;
93  virtual void timesEqual(
94  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
95  const value_type& x) = 0;
96  virtual void divideEqual(
97  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
98  const value_type& x) = 0;
99 
100  virtual void plusEqual(
101  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
102  const OrthogPolyApprox<ordinal_type, value_type, node_type>& x) = 0;
103  virtual void minusEqual(
104  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
105  const OrthogPolyApprox<ordinal_type, value_type, node_type>& x) = 0;
106  virtual void timesEqual(
107  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
108  const OrthogPolyApprox<ordinal_type, value_type, node_type>& x) = 0;
109  virtual void divideEqual(
110  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
111  const OrthogPolyApprox<ordinal_type, value_type, node_type>& x) = 0;
112 
113  virtual void plus(
114  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
115  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a,
116  const OrthogPolyApprox<ordinal_type, value_type, node_type>& b) = 0;
117  virtual void plus(
118  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
119  const value_type& a,
120  const OrthogPolyApprox<ordinal_type, value_type, node_type>& b) = 0;
121  virtual void plus(
122  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
123  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a,
124  const value_type& b) = 0;
125  virtual void minus(
126  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
127  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a,
128  const OrthogPolyApprox<ordinal_type, value_type, node_type>& b) = 0;
129  virtual void minus(
130  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
131  const value_type& a,
132  const OrthogPolyApprox<ordinal_type, value_type, node_type>& b) = 0;
133  virtual void minus(
134  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
135  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a,
136  const value_type& b) = 0;
137  virtual void times(
138  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
139  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a,
140  const OrthogPolyApprox<ordinal_type, value_type, node_type>& b) = 0;
141  virtual void times(
142  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
143  const value_type& a,
144  const OrthogPolyApprox<ordinal_type, value_type, node_type>& b) = 0;
145  virtual void times(
146  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
147  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a,
148  const value_type& b) = 0;
149  virtual void divide(
150  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
151  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a,
152  const OrthogPolyApprox<ordinal_type, value_type, node_type>& b) = 0;
153  virtual void divide(
154  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
155  const value_type& a,
156  const OrthogPolyApprox<ordinal_type, value_type, node_type>& b) = 0;
157  virtual void divide(
158  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
159  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a,
160  const value_type& b) = 0;
161 
162  virtual void exp(
163  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
164  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a) = 0;
165  virtual void log(
166  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
167  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a) = 0;
168  virtual void log10(
169  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
170  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a) = 0;
171  virtual void sqrt(
172  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
173  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a) = 0;
174  virtual void cbrt(
175  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
176  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a) = 0;
177  virtual void pow(
178  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
179  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a,
180  const OrthogPolyApprox<ordinal_type, value_type, node_type>& b) = 0;
181  virtual void pow(
182  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
183  const value_type& a,
184  const OrthogPolyApprox<ordinal_type, value_type, node_type>& b) = 0;
185  virtual void pow(
186  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
187  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a,
188  const value_type& b) = 0;
189  virtual void cos(
190  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
191  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a) = 0;
192  virtual void sin(
193  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
194  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a) = 0;
195  virtual void tan(
196  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
197  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a) = 0;
198  virtual void cosh(
199  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
200  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a) = 0;
201  virtual void sinh(
202  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
203  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a) = 0;
204  virtual void tanh(
205  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
206  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a) = 0;
207  virtual void acos(
208  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
209  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a) = 0;
210  virtual void asin(
211  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
212  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a) = 0;
213  virtual void atan(
214  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
215  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a) = 0;
216 // virtual void atan2(OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
217 // const OrthogPolyApprox<ordinal_type, value_type, node_type>& a,
218 // const OrthogPolyApprox<ordinal_type, value_type, node_type>& b) = 0;
219 // virtual void atan2(OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
220 // const T& a,
221 // const OrthogPolyApprox<ordinal_type, value_type, node_type>& b) = 0;
222 // virtual void atan2(OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
223 // const OrthogPolyApprox<ordinal_type, value_type, node_type>& a,
224 // const T& b) = 0;
225  virtual void acosh(
226  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
227  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a) = 0;
228  virtual void asinh(
229  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
230  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a) = 0;
231  virtual void atanh(
232  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
233  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a) = 0;
234  virtual void abs(
235  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
236  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a) = 0;
237  virtual void fabs(
238  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
239  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a) = 0;
240  virtual void max(
241  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
242  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a,
243  const OrthogPolyApprox<ordinal_type, value_type, node_type>& b) = 0;
244  virtual void max(
245  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
246  const value_type& a,
247  const OrthogPolyApprox<ordinal_type, value_type, node_type>& b) = 0;
248  virtual void max(
249  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
250  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a,
251  const value_type& b) = 0;
252  virtual void min(
253  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
254  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a,
255  const OrthogPolyApprox<ordinal_type, value_type, node_type>& b) = 0;
256  virtual void min(
257  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
258  const value_type& a,
259  const OrthogPolyApprox<ordinal_type, value_type, node_type>& b) = 0;
260  virtual void min(
261  OrthogPolyApprox<ordinal_type, value_type, node_type>& c,
262  const OrthogPolyApprox<ordinal_type, value_type, node_type>& a,
263  const value_type& b) = 0;
264 
265  private:
266 
267  // Prohibit copying
268  OrthogPolyExpansion(const OrthogPolyExpansion&);
269 
270  // Prohibit Assignment
271  OrthogPolyExpansion& operator=(const OrthogPolyExpansion& b);
272 
273  }; // class OrthogPolyExpansion
274 
275 } // namespace Stokhos
276 
277 #endif // STOKHOS_ORTHOGPOLYEXPANSION_HPP
Stokhos::OrthogPolyExpansion::asinh
virtual void asinh(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a)=0
Stokhos::OrthogPolyExpansion::divideEqual
virtual void divideEqual(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const value_type &x)=0
Stokhos::OrthogPolyExpansion::max
virtual void max(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a, const OrthogPolyApprox< ordinal_type, value_type, node_type > &b)=0
Stokhos::OrthogPolyExpansion::atanh
virtual void atanh(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a)=0
Stokhos::OrthogPolyExpansion::asin
virtual void asin(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a)=0
Stokhos::OrthogPolyExpansion::sin
virtual void sin(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a)=0
Stokhos_OrthogPolyApprox.hpp
Stokhos::OrthogPolyExpansion::~OrthogPolyExpansion
virtual ~OrthogPolyExpansion()
Destructor.
Definition: Stokhos_OrthogPolyExpansion.hpp:69
Stokhos::OrthogPolyExpansion::tanh
virtual void tanh(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a)=0
TotalOrderBasisUnitTest::value_type
double value_type
Definition: Stokhos_LexicographicTreeBasisUnitTest.cpp:70
Stokhos::OrthogPolyExpansion::sqrt
virtual void sqrt(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a)=0
Stokhos::OrthogPolyExpansion::log
virtual void log(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a)=0
Stokhos::OrthogPolyExpansion
Abstract base class for orthogonal polynomial-based expansions.
Definition: Stokhos_OrthogPolyExpansion.hpp:59
node_type
Kokkos::Serial node_type
Definition: Stokhos_SacadoTraitsUnitTest.cpp:59
Stokhos::Sparse3Tensor
Data structure storing a sparse 3-tensor C(i,j,k) in a a compressed format.
Definition: Stokhos_Sparse3Tensor.hpp:56
Stokhos::OrthogPolyExpansion::size
virtual ordinal_type size() const =0
Get expansion size.
Teuchos::RCP
Stokhos::OrthogPolyExpansion::abs
virtual void abs(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a)=0
Stokhos::OrthogPolyExpansion::log10
virtual void log10(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a)=0
Stokhos::OrthogPolyExpansion::exp
virtual void exp(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a)=0
TotalOrderBasisUnitTest::ordinal_type
int ordinal_type
Definition: Stokhos_LexicographicTreeBasisUnitTest.cpp:69
Stokhos::StandardStorage
Definition: Stokhos_StandardStorage.hpp:53
Stokhos::OrthogPolyExpansion::divide
virtual void divide(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a, const OrthogPolyApprox< ordinal_type, value_type, node_type > &b)=0
Stokhos::OrthogPolyExpansion::unaryMinus
virtual void unaryMinus(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a)=0
Stokhos::OrthogPolyExpansion::getTripleProduct
virtual Teuchos::RCP< const Sparse3Tensor< ordinal_type, value_type > > getTripleProduct() const =0
Get triple product.
Stokhos::OrthogPolyExpansion::pow
virtual void pow(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a, const OrthogPolyApprox< ordinal_type, value_type, node_type > &b)=0
Stokhos
Top-level namespace for Stokhos classes and functions.
Definition: Stokhos_AbstractPreconditionerFactory.hpp:48
Stokhos::OrthogPolyExpansion::acos
virtual void acos(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a)=0
Stokhos::OrthogPolyExpansion::times
virtual void times(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a, const OrthogPolyApprox< ordinal_type, value_type, node_type > &b)=0
Stokhos::OrthogPolyExpansion::getBasis
virtual Teuchos::RCP< const OrthogPolyBasis< ordinal_type, value_type > > getBasis() const =0
Get basis.
Stokhos::OrthogPolyExpansion::minus
virtual void minus(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a, const OrthogPolyApprox< ordinal_type, value_type, node_type > &b)=0
Stokhos::OrthogPolyExpansion::acosh
virtual void acosh(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a)=0
Stokhos::OrthogPolyExpansion::sinh
virtual void sinh(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a)=0
Stokhos::OrthogPolyExpansion::cbrt
virtual void cbrt(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a)=0
Stokhos::OrthogPolyExpansion::cosh
virtual void cosh(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a)=0
Stokhos::OrthogPolyExpansion::min
virtual void min(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a, const OrthogPolyApprox< ordinal_type, value_type, node_type > &b)=0
cusp::detail::device::x
const IndexType const IndexType const IndexType const IndexType const ValueType const ValueType * x
Definition: csr_vector.h:260
Stokhos::OrthogPolyExpansion::plus
virtual void plus(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a, const OrthogPolyApprox< ordinal_type, value_type, node_type > &b)=0
Stokhos::OrthogPolyExpansion::tan
virtual void tan(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a)=0
Stokhos::OrthogPolyExpansion::timesEqual
virtual void timesEqual(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const value_type &x)=0
Stokhos::OrthogPolyApprox
Class to store coefficients of a projection onto an orthogonal polynomial basis.
Definition: Stokhos_OrthogPolyApprox.hpp:63
Stokhos_OrthogPolyBasis.hpp
Stokhos::OrthogPolyExpansion::atan
virtual void atan(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a)=0
Stokhos::OrthogPolyExpansion::fabs
virtual void fabs(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a)=0
Stokhos::OrthogPolyExpansion::plusEqual
virtual void plusEqual(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const value_type &x)=0
Stokhos::OrthogPolyExpansion::cos
virtual void cos(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a)=0
Stokhos::OrthogPolyExpansion::minusEqual
virtual void minusEqual(OrthogPolyApprox< ordinal_type, value_type, node_type > &c, const value_type &x)=0
Stokhos::OrthogPolyExpansion::operator=
OrthogPolyExpansion & operator=(const OrthogPolyExpansion &b)
Stokhos::OrthogPolyExpansion::OrthogPolyExpansion
OrthogPolyExpansion()
Constructor.
Definition: Stokhos_OrthogPolyExpansion.hpp:66
Stokhos::OrthogPolyExpansion::tp_type
Sparse3Tensor< ordinal_type, value_type > tp_type
Typename of TripleProduct tensor.
Definition: Stokhos_OrthogPolyExpansion.hpp:63
Generated by   doxygen 1.8.16