diff options
author | Antonio Sanchez <cantonios@google.com> | 2021-01-16 10:22:07 -0800 |
---|---|---|
committer | Antonio Sanchez <cantonios@google.com> | 2021-01-17 08:50:57 -0800 |
commit | bde6741641b7c677d901cd48db844fcea1fd32fe (patch) | |
tree | f25e6540b247ed01df1bdadc41502fbc332321d3 /test/stable_norm.cpp | |
parent | 21a8a2487c824e5ae05566f4fcc49540053b2702 (diff) |
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
```
Diffstat (limited to 'test/stable_norm.cpp')
-rw-r--r-- | test/stable_norm.cpp | 11 |
1 files changed, 8 insertions, 3 deletions
diff --git a/test/stable_norm.cpp b/test/stable_norm.cpp index ee5f91674..008e35d87 100644 --- a/test/stable_norm.cpp +++ b/test/stable_norm.cpp @@ -161,8 +161,12 @@ template<typename MatrixType> void stable_norm(const MatrixType& m) // mix { - Index i2 = internal::random<Index>(0,rows-1); - Index j2 = internal::random<Index>(0,cols-1); + // Ensure unique indices otherwise inf may be overwritten by NaN. + Index i2, j2; + do { + i2 = internal::random<Index>(0,rows-1); + j2 = internal::random<Index>(0,cols-1); + } while (i2 == i && j2 == j); v = vrand; v(i,j) = -std::numeric_limits<RealScalar>::infinity(); v(i2,j2) = std::numeric_limits<RealScalar>::quiet_NaN(); @@ -170,7 +174,8 @@ template<typename MatrixType> void stable_norm(const MatrixType& m) VERIFY(!(numext::isfinite)(v.norm())); VERIFY((numext::isnan)(v.norm())); VERIFY(!(numext::isfinite)(v.stableNorm())); VERIFY((numext::isnan)(v.stableNorm())); VERIFY(!(numext::isfinite)(v.blueNorm())); VERIFY((numext::isnan)(v.blueNorm())); - VERIFY(!(numext::isfinite)(v.hypotNorm())); VERIFY((numext::isnan)(v.hypotNorm())); + // hypot propagates inf over NaN. + VERIFY(!(numext::isfinite)(v.hypotNorm())); VERIFY((numext::isinf)(v.hypotNorm())); } // stableNormalize[d] |