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bde6741641
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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
bench Fix #1911: add benchmark for move semantics with fixed-size matrix 2020-06-11 23:43:25 +00:00
blas STYLE: Remove CMake-language block-end command arguments 2019-10-31 11:36:27 -05:00
ci Add CI configuration for ppc64le 2020-09-22 00:26:23 +00:00
cmake check for include dirs set 2020-11-26 10:22:46 +00:00
debug
demos Make file formatting comply with POSIX and Unix standards 2020-03-23 18:09:02 +00:00
doc Fix typo in doc 2020-11-30 10:53:29 +00:00
Eigen Improved std::complex sqrt and rsqrt. 2021-01-17 08:50:57 -08:00
failtest Make file formatting comply with POSIX and Unix standards 2020-03-23 18:09:02 +00:00
lapack Remove code checking for CMake < 3.5 2020-12-14 09:57:44 +00:00
scripts Replace calls to "hg" by calls to "git" 2019-12-04 11:24:06 +01:00
test Improved std::complex sqrt and rsqrt. 2021-01-17 08:50:57 -08:00
unsupported fix paddings of TensorVolumePatchOp 2021-01-15 11:51:49 +08:00
.gitignore New CI infrastructure, including AArch64 runners 2020-09-11 18:11:49 +00:00
.gitlab-ci.yml New CI infrastructure, including AArch64 runners 2020-09-11 18:11:49 +00:00
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CTestCustom.cmake.in
eigen3.pc.in
INSTALL
README.md Update old links to bitbucket to point to gitlab.com 2019-12-04 10:57:07 +01:00
signature_of_eigen3_matrix_library

README.md

Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms.

For more information go to http://eigen.tuxfamily.org/.

For pull request, bug reports, and feature requests, go to https://gitlab.com/libeigen/eigen.