Commit Graph

5990 Commits

Author SHA1 Message Date
Gael Guennebaud
44b54fa4a3 Protect c++11 type alias with Eigen's macro, and add respective unit test. 2019-02-20 14:43:05 +01:00
Gael Guennebaud
7195f008ce Merged in ra_bauke/eigen (pull request PR-180)
alias template for matrix and array classes, see also bug #864

Approved-by: Heiko Bauke <heiko.bauke@mail.de>
2019-02-20 13:22:39 +00:00
Gael Guennebaud
edd413c184 bug #1409: make EIGEN_MAKE_ALIGNED_OPERATOR_NEW* macros empty in c++17 mode:
- this helps clang 5 and 6 to support alignas in STL's containers.
 - this makes the public API of our (and users) classes cleaner
2019-02-20 13:52:11 +01:00
Gael Guennebaud
482c5fb321 bug #899: remove "rank-revealing" qualifier for SparseQR and warn that it is not always rank-revealing. 2019-02-19 22:52:15 +01:00
Christoph Hertzberg
a1646fc960 Commas at the end of enumerator lists are not allowed in C++03 2019-02-19 14:32:25 +01:00
Gael Guennebaud
ab78cabd39 Add C++17 detection macro, and make sure throw(xpr) is not used if the compiler is in c++17 mode. 2019-02-19 14:04:35 +01:00
Gael Guennebaud
115da6a1ea Fix conversion warnings 2019-02-19 14:00:15 +01:00
Gael Guennebaud
7580112c31 Fix harmless Scalar vs RealScalar cast. 2019-02-18 22:12:28 +01:00
Gael Guennebaud
796db94e6e bug #1194: implement slightly faster and SIMD friendly 4x4 determinant. 2019-02-18 16:21:27 +01:00
Gael Guennebaud
31b6e080a9 Fix regression: .conjugate() was popped out but not re-introduced. 2019-02-18 14:45:55 +01:00
Gael Guennebaud
c69d0d08d0 Set cost of conjugate to 0 (in practice it boils down to a no-op).
This is also important to make sure that A.conjugate() * B.conjugate() does not evaluate
its arguments into temporaries (e.g., if A and B are fixed and small, or * fall back to lazyProduct)
2019-02-18 14:43:07 +01:00
Gael Guennebaud
512b74aaa1 GEMM: catch all scalar-multiple variants when falling-back to a coeff-based product.
Before only s*A*B was caught which was both inconsistent with GEMM, sub-optimal,
and could even lead to compilation-errors (https://stackoverflow.com/questions/54738495).
2019-02-18 11:47:54 +01:00
Christoph Hertzberg
ec032ac03b Guard C++11-style default constructor. Also, this is only needed for MSVC 2019-02-16 09:44:05 +01:00
Gael Guennebaud
83309068b4 bug #1680: improve MSVC inlining by declaring many triavial constructors and accessors as STRONG_INLINE. 2019-02-15 16:35:35 +01:00
Gael Guennebaud
0505248f25 bug #1680: make all "block" methods strong-inline and device-functions (some were missing EIGEN_DEVICE_FUNC) 2019-02-15 16:33:56 +01:00
Gael Guennebaud
559320745e bug #1678: Fix lack of __FMA__ macro on MSVC with AVX512 2019-02-15 10:30:28 +01:00
Gael Guennebaud
d85ae650bf bug #1678: workaround MSVC compilation issues with AVX512 2019-02-15 10:24:17 +01:00
Gael Guennebaud
f2970819a2 bug #1679: avoid possible division by 0 in complex-schur 2019-02-15 09:39:25 +01:00
Rasmus Munk Larsen
65e23ca7e9 Revert b55b5c7280
.
2019-02-14 13:46:13 -08:00
Gael Guennebaud
bdcb5f3304 Let's properly use Score instead of std::abs, and remove deprecated FIXME ( a /= b does a/b and not a * (1/b) as it was a long time ago...) 2019-02-11 22:56:19 +01:00
Gael Guennebaud
2edfc6807d Fix compilation of empty products of the form: Mx0 * 0xN 2019-02-11 18:24:07 +01:00
Gael Guennebaud
eb46f34a8c Speed up 2x2 LU by a factor 2, and other small fixed sizes by about 10%.
Not sure that's so critical, but this does not complexify the code base much.
2019-02-11 17:59:35 +01:00
Gael Guennebaud
ab6e6edc32 Speedup PartialPivLU for small matrices by passing compile-time sizes when available.
This change set also makes a better use of Map<>+OuterStride and Ref<> yielding surprising speed up for small dynamic sizes as well.
The table below reports times in micro seconds for 10 random matrices:
           | ------ float --------- | ------- double ------- |
     size  | before   after  ratio  |  before   after  ratio |
fixed	  1	 | 0.34     0.11   2.93   |  0.35     0.11   3.06  |
fixed	  2	 | 0.81     0.24   3.38   |  0.91     0.25   3.60  |
fixed	  3	 | 1.49     0.49   3.04   |  1.68     0.55   3.01  |
fixed	  4	 | 2.31     0.70   3.28   |  2.45     1.08   2.27  |
fixed	  5	 | 3.49     1.11   3.13   |  3.84     2.24   1.71  |
fixed	  6	 | 4.76     1.64   2.88   |  4.87     2.84   1.71  |
dyn     1	 | 0.50     0.40   1.23   |  0.51     0.40   1.26  |
dyn     2	 | 1.08     0.85   1.27   |  1.04     0.69   1.49  |
dyn     3	 | 1.76     1.26   1.40   |  1.84     1.14   1.60  |
dyn     4	 | 2.57     1.75   1.46   |  2.67     1.66   1.60  |
dyn     5	 | 3.80     2.64   1.43   |  4.00     2.48   1.61  |
dyn     6	 | 5.06     3.43   1.47   |  5.15     3.21   1.60  |
2019-02-11 13:58:24 +01:00
Gael Guennebaud
013cc3a6b3 Make GEMM fallback to GEMV for runtime vectors.
This is a more general and simpler version of changeset 4c0fa6ce0f
2019-02-07 16:24:09 +01:00
Gael Guennebaud
fa2fcb4895 Backed out changeset 4c0fa6ce0f 2019-02-07 16:07:08 +01:00
Gael Guennebaud
b3c4344a68 bug #1676: workaround GCC's bug in c++17 mode. 2019-02-07 15:21:35 +01:00
Eugene Zhulenev
6d0f6265a9 Remove duplicated comment line 2019-02-04 10:30:25 -08:00
Eugene Zhulenev
690b2c45b1 Fix GeneralBlockPanelKernel Android compilation 2019-02-04 10:29:15 -08:00
Gael Guennebaud
871e2e5339 bug #1674: disable GCC's unsafe-math-optimizations in sin/cos vectorization (results are completely wrong otherwise) 2019-02-03 08:54:47 +01:00
Rasmus Larsen
e7b481ea74 Merged in rmlarsen/eigen (pull request PR-578)
Speed up Eigen matrix*vector and vector*matrix multiplication.

Approved-by: Eugene Zhulenev <ezhulenev@google.com>
2019-02-02 01:53:44 +00:00
Sameer Agarwal
b55b5c7280 Speed up row-major matrix-vector product on ARM
The row-major matrix-vector multiplication code uses a threshold to
check if processing 8 rows at a time would thrash the cache.

This change introduces two modifications to this logic.

1. A smaller threshold for ARM and ARM64 devices.

The value of this threshold was determined empirically using a Pixel2
phone, by benchmarking a large number of matrix-vector products in the
range [1..4096]x[1..4096] and measuring performance separately on
small and little cores with frequency pinning.

On big (out-of-order) cores, this change has little to no impact. But
on the small (in-order) cores, the matrix-vector products are up to
700% faster. Especially on large matrices.

The motivation for this change was some internal code at Google which
was using hand-written NEON for implementing similar functionality,
processing the matrix one row at a time, which exhibited substantially
better performance than Eigen.

With the current change, Eigen handily beats that code.

2. Make the logic for choosing number of simultaneous rows apply
unifiormly to 8, 4 and 2 rows instead of just 8 rows.

Since the default threshold for non-ARM devices is essentially
unchanged (32000 -> 32 * 1024), this change has no impact on non-ARM
performance. This was verified by running the same set of benchmarks
on a Xeon desktop.
2019-02-01 15:23:53 -08:00
Rasmus Munk Larsen
4c0fa6ce0f Speed up Eigen matrix*vector and vector*matrix multiplication.
This change speeds up Eigen matrix * vector and vector * matrix multiplication for dynamic matrices when it is known at runtime that one of the factors is a vector.

The benchmarks below test

c.noalias()= n_by_n_matrix * n_by_1_matrix;
c.noalias()= 1_by_n_matrix * n_by_n_matrix;
respectively.

Benchmark measurements:

SSE:
Run on *** (72 X 2992 MHz CPUs); 2019-01-28T17:51:44.452697457-08:00
CPU: Intel Skylake Xeon with HyperThreading (36 cores) dL1:32KB dL2:1024KB dL3:24MB
Benchmark                          Base (ns)  New (ns) Improvement
------------------------------------------------------------------
BM_MatVec/64                            1096       312    +71.5%
BM_MatVec/128                           4581      1464    +68.0%
BM_MatVec/256                          18534      5710    +69.2%
BM_MatVec/512                         118083     24162    +79.5%
BM_MatVec/1k                          704106    173346    +75.4%
BM_MatVec/2k                         3080828    742728    +75.9%
BM_MatVec/4k                        25421512   4530117    +82.2%
BM_VecMat/32                             352       130    +63.1%
BM_VecMat/64                            1213       425    +65.0%
BM_VecMat/128                           4640      1564    +66.3%
BM_VecMat/256                          17902      5884    +67.1%
BM_VecMat/512                          70466     24000    +65.9%
BM_VecMat/1k                          340150    161263    +52.6%
BM_VecMat/2k                         1420590    645576    +54.6%
BM_VecMat/4k                         8083859   4364327    +46.0%

AVX2:
Run on *** (72 X 2993 MHz CPUs); 2019-01-28T17:45:11.508545307-08:00
CPU: Intel Skylake Xeon with HyperThreading (36 cores) dL1:32KB dL2:1024KB dL3:24MB
Benchmark                          Base (ns)  New (ns) Improvement
------------------------------------------------------------------
BM_MatVec/64                             619       120    +80.6%
BM_MatVec/128                           9693       752    +92.2%
BM_MatVec/256                          38356      2773    +92.8%
BM_MatVec/512                          69006     12803    +81.4%
BM_MatVec/1k                          443810    160378    +63.9%
BM_MatVec/2k                         2633553    646594    +75.4%
BM_MatVec/4k                        16211095   4327148    +73.3%
BM_VecMat/64                             925       227    +75.5%
BM_VecMat/128                           3438       830    +75.9%
BM_VecMat/256                          13427      2936    +78.1%
BM_VecMat/512                          53944     12473    +76.9%
BM_VecMat/1k                          302264    157076    +48.0%
BM_VecMat/2k                         1396811    675778    +51.6%
BM_VecMat/4k                         8962246   4459010    +50.2%

AVX512:
Run on *** (72 X 2993 MHz CPUs); 2019-01-28T17:35:17.239329863-08:00
CPU: Intel Skylake Xeon with HyperThreading (36 cores) dL1:32KB dL2:1024KB dL3:24MB
Benchmark                          Base (ns)  New (ns) Improvement
------------------------------------------------------------------
BM_MatVec/64                             401       111    +72.3%
BM_MatVec/128                           1846       513    +72.2%
BM_MatVec/256                          36739      1927    +94.8%
BM_MatVec/512                          54490      9227    +83.1%
BM_MatVec/1k                          487374    161457    +66.9%
BM_MatVec/2k                         2016270    643824    +68.1%
BM_MatVec/4k                        13204300   4077412    +69.1%
BM_VecMat/32                             324       106    +67.3%
BM_VecMat/64                            1034       246    +76.2%
BM_VecMat/128                           3576       802    +77.6%
BM_VecMat/256                          13411      2561    +80.9%
BM_VecMat/512                          58686     10037    +82.9%
BM_VecMat/1k                          320862    163750    +49.0%
BM_VecMat/2k                         1406719    651397    +53.7%
BM_VecMat/4k                         7785179   4124677    +47.0%
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2019-01-31 14:24:08 -08:00
Gael Guennebaud
7ef879f6bf GEBP: improves pipelining in the 1pX4 path with FMA.
Prior to this change, a product with a LHS having 8 rows was faster with AVX-only than with AVX+FMA.
With AVX+FMA I measured a speed up of about x1.25 in such cases.
2019-01-30 23:45:12 +01:00
Gael Guennebaud
de77bf5d6c Fix compilation with ARM64. 2019-01-30 16:48:20 +01:00
Gael Guennebaud
eb4c6bb22d Fix conflicts and merge 2019-01-30 15:57:08 +01:00
Gael Guennebaud
df12fae8b8 According to https://gcc.gnu.org/bugzilla/show_bug.cgi?id=89101, the previous GCC issue is fixed in GCC trunk (will be gcc 9). 2019-01-30 11:52:28 +01:00
Gael Guennebaud
3775926bba ARM64 & GEBP: add specialization for double +30% speed up 2019-01-30 11:49:06 +01:00
Gael Guennebaud
be5b0f664a ARM64 & GEBP: Make use of vfmaq_laneq_f32 and workaround GCC's issue in generating good ASM 2019-01-30 11:48:25 +01:00
Gael Guennebaud
8a06c699d0 bug #1669: fix PartialPivLU/inverse with zero-sized matrices. 2019-01-29 10:27:13 +01:00
Gael Guennebaud
a2a07e62b9 Fix compilation with c++03 (local class cannot be template arguments), and make SparseMatrix::assignDiagonal truly protected. 2019-01-29 10:10:07 +01:00
Gael Guennebaud
f489f44519 bug #1574: implement "sparse_matrix =,+=,-= diagonal_matrix" with smart insertion strategies of missing diagonal coeffs. 2019-01-28 17:29:50 +01:00
Gael Guennebaud
803fa79767 Move evaluator<SparseCompressedBase>::find(i,j) to a more general and reusable SparseCompressedBase::lower_bound(i,j) functiion 2019-01-28 17:24:44 +01:00
Christoph Hertzberg
5a52e35f9a Renaming some more I identifiers 2019-01-26 13:18:21 +01:00
Rasmus Munk Larsen
71429883ee Fix compilation error in NEON GEBP specializaition of madd. 2019-01-25 17:00:21 -08:00
Gael Guennebaud
ec8a387972 cleanup 2019-01-24 10:24:45 +01:00
David Tellenbach
237b03b372 PR 574: use variadic template instead of initializer_list to implement fixed-size vector ctor from coefficients. 2019-01-23 00:07:19 +01:00
Gael Guennebaud
80f81f9c4b Cleanup SFINAE in Array/Matrix(initializer_list) ctors and minor doc editing. 2019-01-22 17:08:47 +01:00
David Tellenbach
db152b9ee6 PR 572: Add initializer list constructors to Matrix and Array (include unit tests and doc)
- {1,2,3,4,5,...} for fixed-size vectors only
- {{1,2,3},{4,5,6}} for the general cases
- {{1,2,3,4,5,....}} is allowed for both row and column-vector
2019-01-21 16:25:57 +01:00
nluehr
92774f0275 Replace host_define.h with cuda_runtime_api.h 2019-01-18 16:10:09 -06:00
Christoph Hertzberg
da0a41b9ce Mask unused-parameter warnings, when building with NDEBUG 2019-01-18 10:41:14 +01:00
Rasmus Munk Larsen
2eccbaf3f7 Add missing logical packet ops for GPU and NEON. 2019-01-17 17:45:08 -08:00
Gael Guennebaud
ee3662abc5 Remove some useless const_cast 2019-01-17 18:27:49 +01:00
Gael Guennebaud
0fe6b7d687 Make nestByValue works again (broken since 3.3) and add unit tests. 2019-01-17 18:27:25 +01:00
Gael Guennebaud
4b7cf7ff82 Extend reshaped unit tests and remove useless const_cast 2019-01-17 17:35:32 +01:00
Gael Guennebaud
b57c9787b1 Cleanup useless const_cast and add missing broadcast assignment tests 2019-01-17 16:55:42 +01:00
Gael Guennebaud
be05d0030d Make FullPivLU use conjugateIf<> 2019-01-17 12:01:00 +01:00
Patrick Peltzer
15e53d5d93 PR 567: makes all dense solvers inherit SoverBase (LU,Cholesky,QR,SVD).
This changeset also includes:
 * add HouseholderSequence::conjugateIf
 * define int as the StorageIndex type for all dense solvers
 * dedicated unit tests, including assertion checking
 * _check_solve_assertion(): this method can be implemented in derived solver classes to implement custom checks
 * CompleteOrthogonalDecompositions: add applyZOnTheLeftInPlace, fix scalar type in applyZAdjointOnTheLeftInPlace(), add missing assertions
 * Cholesky: add missing assertions
 * FullPivHouseholderQR: Corrected Scalar type in _solve_impl()
 * BDCSVD: Unambiguous return type for ternary operator
 * SVDBase: Corrected Scalar type in _solve_impl()
2019-01-17 01:17:39 +01:00
Gael Guennebaud
7f32109c11 Add conjugateIf<bool> members to DesneBase, TriangularView, SelfadjointView, and make PartialPivLU use it. 2019-01-17 11:33:43 +01:00
Gael Guennebaud
562985bac4 bug #1646: fix false aliasing detection for A.row(0) = A.col(0);
This changeset completely disable the detection for vectors for which are current mechanism cannot detect any positive aliasing anyway.
2019-01-17 00:14:27 +01:00
Rasmus Munk Larsen
7401e2541d Fix compilation error for logical packet ops with older compilers. 2019-01-16 14:43:33 -08:00
Gael Guennebaud
0f028f61cb GEBP: fix swapped kernel mode with AVX512 and complex scalars 2019-01-16 22:26:38 +01:00
Gael Guennebaud
e118ce86fd GEBP: cleanup logic to choose between a 4 packets of 1 packet 2019-01-16 21:47:42 +01:00
Gael Guennebaud
70e133333d bug #1661: fix regression in GEBP and AVX512 2019-01-16 21:22:20 +01:00
Gael Guennebaud
502f717980 bug #1646: disable aliasing detection for empty and 1x1 expression 2019-01-16 14:33:45 +01:00
Gael Guennebaud
0b466b6933 bug #1633: use proper type for madd temporaries, factorize RhsPacketx4. 2019-01-16 13:50:13 +01:00
Renjie Liu
dbfcceabf5 Bug: 1633: refactor gebp kernel and optimize for neon 2019-01-16 12:51:36 +08:00
Gael Guennebaud
2b70b2f570 Make Transform::rotation() an alias to Transform::linear() in the case of an Isometry 2019-01-15 22:50:42 +01:00
Gael Guennebaud
2c2c114995 Silent maybe-uninitialized warnings by gcc 2019-01-15 16:53:15 +01:00
Gael Guennebaud
6ec6bf0b0d Enable visitor on empty matrices (the visitor is left unchanged), and protect min/maxCoeff(Index*,Index*) on empty matrices by an assertion (+ doc & unit tests) 2019-01-15 15:21:14 +01:00
Gael Guennebaud
027e44ed24 bug #1592: makes partial min/max reductions trigger an assertion on inputs with a zero reduction length (+doc and tests) 2019-01-15 15:13:24 +01:00
Gael Guennebaud
f8bc5cb39e Fix detection of vector-at-time: use Rows/Cols instead of MaxRow/MaxCols.
This fix VectorXd(n).middleCol(0,0).outerSize() which was equal to 1.
2019-01-15 15:09:49 +01:00
Gael Guennebaud
6cf7afa3d9 Typo 2019-01-15 11:04:37 +01:00
Rasmus Larsen
7b3aab0936 Merged in rmlarsen/eigen (pull request PR-570)
Add support for inverse hyperbolic functions. Fix cost of division.
2019-01-14 21:31:33 +00:00
Gael Guennebaud
250dcd1fdb bug #1652: fix position of EIGEN_ALIGN16 attributes in Neon and Altivec 2019-01-14 21:45:56 +01:00
Rasmus Larsen
5a59452aae Merged eigen/eigen into default 2019-01-14 10:23:23 -08:00
Gael Guennebaud
3c9e6d206d AVX512: fix pgather/pscatter for Packet4cd and unaligned pointers 2019-01-14 17:57:28 +01:00
Gael Guennebaud
61b6eb05fe AVX512 (r)sqrt(double) was mistakenly disabled with clang and others 2019-01-14 17:28:47 +01:00
Gael Guennebaud
ccddeaad90 fix warning 2019-01-14 16:51:16 +01:00
Gael Guennebaud
d4881751d3 Doc: add Isometry in the list of supported Mode of Transform<> 2019-01-14 16:38:26 +01:00
Greg Coombe
9d988a1e1a Initialize isometric transforms like affine transforms.
The isometric transform, like the affine transform, has an implicit last
row of [0, 0, 0, 1]. This was not being properly initialized, as verified
by a new test function.
2019-01-11 23:14:35 -08:00
Gael Guennebaud
4356a55a61 PR 571: Implements an accurate argument reduction algorithm for huge inputs of sin/cos and call it instead of falling back to std::sin/std::cos.
This makes both the small and huge argument cases faster because:
- for small inputs this removes the last pselect
- for large inputs only the reduction part follows a scalar path,
the rest use the same SIMD path as the small-argument case.
2019-01-14 13:54:01 +01:00
Gael Guennebaud
f566724023 Fix StorageIndex FIXME in dense LU solvers 2019-01-13 17:54:30 +01:00
Rasmus Munk Larsen
1c6e6e2c3f Merge. 2019-01-11 17:47:11 -08:00
Rasmus Munk Larsen
28ba1b2c32 Add support for inverse hyperbolic functions.
Fix cost of division.
2019-01-11 17:45:37 -08:00
Rasmus Munk Larsen
89c4001d6f Fix warnings in ptrue for complex and half types. 2019-01-11 14:10:57 -08:00
Rasmus Munk Larsen
a49d01edba Fix warnings in ptrue for complex and half types. 2019-01-11 13:18:17 -08:00
Rasmus Munk Larsen
df29511ac0 Fix merge. 2019-01-11 10:36:36 -08:00
Rasmus Munk Larsen
9396ace46b Merge. 2019-01-11 10:28:52 -08:00
Rasmus Larsen
74882471d0 Merged eigen/eigen into default 2019-01-11 10:20:55 -08:00
Gael Guennebaud
9005f0111f Replace compiler's alignas/alignof extension by respective c++11 keywords when available. This also fix a compilation issue with gcc-4.7. 2019-01-11 17:10:54 +01:00
Mark D Ryan
3c9add6598 Remove reinterpret_cast from AVX512 complex implementation
The reinterpret_casts used in ptranspose(PacketBlock<Packet8cf,4>&)
ptranspose(PacketBlock<Packet8cf,8>&) don't appear to be working
correctly.  They're used to convert the kernel parameters to
PacketBlock<Packet8d,T>& so that the complex number versions of
ptranspose can be written using the existing double implementations.
Unfortunately, they don't seem to work and are responsible for 9 unit
test failures in the AVX512 build of tensorflow master.  This commit
fixes the issue by manually initialising PacketBlock<Packet8d,T>
variables with the contents of the kernel parameter before calling
the double version of ptranspose, and then copying the resulting
values back into the kernel parameter before returning.
2019-01-11 14:02:09 +01:00
Rasmus Munk Larsen
fcfced13ed Rename pones -> ptrue. Use _CMP_TRUE_UQ where appropriate. 2019-01-09 17:20:33 -08:00
Rasmus Munk Larsen
e15bb785ad Collapsed revision
* Add packet up "pones". Write pnot(a) as pxor(pones(a), a).
* Collapsed revision
* Simplify a bit.
* Undo useless diffs.
* Fix typo.
2019-01-09 16:34:23 -08:00
Rasmus Munk Larsen
f6ba6071c5 Fix typo. 2019-01-09 16:34:23 -08:00
Rasmus Munk Larsen
8f04442526 Collapsed revision
* Collapsed revision
* Add packet up "pones". Write pnot(a) as pxor(pones(a), a).
* Collapsed revision
* Simplify a bit.
* Undo useless diffs.
* Fix typo.
2019-01-09 16:34:23 -08:00
Rasmus Munk Larsen
e00521b514 Undo useless diffs. 2019-01-09 16:32:53 -08:00
Rasmus Munk Larsen
f2767112c8 Simplify a bit. 2019-01-09 16:29:18 -08:00
Rasmus Munk Larsen
cb955df9a6 Add packet up "pones". Write pnot(a) as pxor(pones(a), a). 2019-01-09 16:17:08 -08:00
Rasmus Larsen
cb3c059fa4 Merged eigen/eigen into default 2019-01-09 15:04:17 -08:00
Gael Guennebaud
d812f411c3 bug #1654: fix compilation with cuda and no c++11 2019-01-09 18:00:05 +01:00