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bde6741641
eigen/Eigen
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Antonio Sanchez bde6741641 Improved std::complex sqrt and rsqrt. 
Replaces `std::sqrt` with `complex_sqrt` for all platforms (previously
`complex_sqrt` was only used for CUDA and MSVC), and implements
custom `complex_rsqrt`.

Also introduces `numext::rsqrt` to simplify implementation, and modified
`numext::hypot` to adhere to IEEE IEC 6059 for special cases.

The `complex_sqrt` and `complex_rsqrt` implementations were found to be
significantly faster than `std::sqrt<std::complex<T>>` and
`1/numext::sqrt<std::complex<T>>`.

Benchmark file attached.
```
GCC 10, Intel Xeon, x86_64:
---------------------------------------------------------------------------
Benchmark                                 Time             CPU   Iterations
---------------------------------------------------------------------------
BM_Sqrt<std::complex<float>>           9.21 ns         9.21 ns     73225448
BM_StdSqrt<std::complex<float>>        17.1 ns         17.1 ns     40966545
BM_Sqrt<std::complex<double>>          8.53 ns         8.53 ns     81111062
BM_StdSqrt<std::complex<double>>       21.5 ns         21.5 ns     32757248
BM_Rsqrt<std::complex<float>>          10.3 ns         10.3 ns     68047474
BM_DivSqrt<std::complex<float>>        16.3 ns         16.3 ns     42770127
BM_Rsqrt<std::complex<double>>         11.3 ns         11.3 ns     61322028
BM_DivSqrt<std::complex<double>>       16.5 ns         16.5 ns     42200711

Clang 11, Intel Xeon, x86_64:
---------------------------------------------------------------------------
Benchmark                                 Time             CPU   Iterations
---------------------------------------------------------------------------
BM_Sqrt<std::complex<float>>           7.46 ns         7.45 ns     90742042
BM_StdSqrt<std::complex<float>>        16.6 ns         16.6 ns     42369878
BM_Sqrt<std::complex<double>>          8.49 ns         8.49 ns     81629030
BM_StdSqrt<std::complex<double>>       21.8 ns         21.7 ns     31809588
BM_Rsqrt<std::complex<float>>          8.39 ns         8.39 ns     82933666
BM_DivSqrt<std::complex<float>>        14.4 ns         14.4 ns     48638676
BM_Rsqrt<std::complex<double>>         9.83 ns         9.82 ns     70068956
BM_DivSqrt<std::complex<double>>       15.7 ns         15.7 ns     44487798

Clang 9, Pixel 2, aarch64:
---------------------------------------------------------------------------
Benchmark                                 Time             CPU   Iterations
---------------------------------------------------------------------------
BM_Sqrt<std::complex<float>>           24.2 ns         24.1 ns     28616031
BM_StdSqrt<std::complex<float>>         104 ns          103 ns      6826926
BM_Sqrt<std::complex<double>>          31.8 ns         31.8 ns     22157591
BM_StdSqrt<std::complex<double>>        128 ns          128 ns      5437375
BM_Rsqrt<std::complex<float>>          31.9 ns         31.8 ns     22384383
BM_DivSqrt<std::complex<float>>        99.2 ns         98.9 ns      7250438
BM_Rsqrt<std::complex<double>>         46.0 ns         45.8 ns     15338689
BM_DivSqrt<std::complex<double>>        119 ns          119 ns      5898944
```
2021-01-17 08:50:57 -08:00
..
src Improved std::complex sqrt and rsqrt. 2021-01-17 08:50:57 -08:00
Cholesky bug #1455: Cholesky module depends on Jacobi for rank-updates. 2017-08-22 11:37:32 +02:00
CholmodSupport Update link to suitesparse. 2016-01-27 22:48:40 +01:00
Core Drop EIGEN_USING_STD_MATH in favour of EIGEN_USING_STD 2020-10-09 02:05:05 +02:00
Dense Add newline at the end of Dense. 2010-07-23 19:00:02 +02:00
Eigen Sparse is stable now, so Eigen/Eigen should include Sparse 2013-10-02 23:31:59 +02:00
Eigenvalues Old gcc versions have problems with recursive #pragma GCC diagnostic push/pop 2018-08-28 11:44:15 +02:00
Geometry 1)provide a better generic paddsub op implementation 2021-01-13 22:54:03 +00:00
Householder Add missing licence header to some top header files 2015-10-26 11:46:05 +01:00
IterativeLinearSolvers Add missing licence header to some top header files 2015-10-26 11:46:05 +01:00
Jacobi Add missing licence header to some top header files 2015-10-26 11:46:05 +01:00
KLUSupport Move KLU support to official 2017-11-10 14:11:22 +01:00
LU Unify Inverse_SSE.h and Inverse_NEON.h into a single generic implementation using PacketMath. 2020-11-17 12:27:01 +00:00
MetisSupport Add missing licence header to some top header files 2015-10-26 11:46:05 +01:00
OrderingMethods Remove EIGEN_MPL2_ONLY guards around code re-licensed from LGPL to MPL2 in 2ca1e73239 2019-03-05 10:24:54 -08:00
PardisoSupport Extend CUDA support to matrix inversion and selfadjointeigensolver 2018-06-11 18:33:24 +02:00
PaStiXSupport clarify Pastix requirements 2017-11-27 22:11:57 +01:00
QR Old gcc versions have problems with recursive #pragma GCC diagnostic push/pop 2018-08-28 11:44:15 +02:00
QtAlignedMalloc bug #1468 (1/2) : add missing std:: to memcpy 2017-09-22 09:23:24 +02:00
Sparse Remove EIGEN_MPL2_ONLY guards around code re-licensed from LGPL to MPL2 in 2ca1e73239 2019-03-05 10:24:54 -08:00
SparseCholesky Remove EIGEN_MPL2_ONLY guards around code re-licensed from LGPL to MPL2 in 2ca1e73239 2019-03-05 10:24:54 -08:00
SparseCore bug #1101: typo 2015-10-30 12:02:52 +01:00
SparseLU Fix numerous shadow-warnings for GCC<=4.8 2018-08-28 18:32:39 +02:00
SparseQR Old gcc versions have problems with recursive #pragma GCC diagnostic push/pop 2018-08-28 11:44:15 +02:00
SPQRSupport Update link to suitesparse. 2016-01-27 22:48:40 +01:00
StdDeque bug #1389: MSVC's std containers do not properly align in 64 bits mode if the requested alignment is larger than 16 bytes (e.g., with AVX) 2017-02-03 15:22:35 +01:00
StdList bug #1389: MSVC's std containers do not properly align in 64 bits mode if the requested alignment is larger than 16 bytes (e.g., with AVX) 2017-02-03 15:22:35 +01:00
StdVector bug #1389: MSVC's std containers do not properly align in 64 bits mode if the requested alignment is larger than 16 bytes (e.g., with AVX) 2017-02-03 15:22:35 +01:00
SuperLUSupport bug #1119: Adjust call to ?gssvx for SuperLU 5 2016-07-10 02:29:57 +02:00
SVD use MKL's lapacke.h header when using MKL 2017-08-17 21:58:39 +02:00
UmfPackSupport Update link to suitesparse. 2016-01-27 22:48:40 +01:00