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Implement vectorized complex square root.

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Closes #1905

Measured speedup for sqrt of `complex<float>` on Skylake:

SSE:
```
name                      old time/op             new time/op  delta
BM_eigen_sqrt_ctype/1     49.4ns ± 0%             54.3ns ± 0%  +10.01%
BM_eigen_sqrt_ctype/8      332ns ± 0%               50ns ± 1%  -84.97%
BM_eigen_sqrt_ctype/64    2.81µs ± 1%             0.38µs ± 0%  -86.49%
BM_eigen_sqrt_ctype/512   23.8µs ± 0%              3.0µs ± 0%  -87.32%
BM_eigen_sqrt_ctype/4k     202µs ± 0%               24µs ± 2%  -88.03%
BM_eigen_sqrt_ctype/32k   1.63ms ± 0%             0.19ms ± 0%  -88.18%
BM_eigen_sqrt_ctype/256k  13.0ms ± 0%              1.5ms ± 1%  -88.20%
BM_eigen_sqrt_ctype/1M    52.1ms ± 0%              6.2ms ± 0%  -88.18%
```

AVX2:
```
name                      old cpu/op  new cpu/op  delta
BM_eigen_sqrt_ctype/1     53.6ns ± 0%  55.6ns ± 0%   +3.71%
BM_eigen_sqrt_ctype/8      334ns ± 0%    27ns ± 0%  -91.86%
BM_eigen_sqrt_ctype/64    2.79µs ± 0%  0.22µs ± 2%  -92.28%
BM_eigen_sqrt_ctype/512   23.8µs ± 1%   1.7µs ± 1%  -92.81%
BM_eigen_sqrt_ctype/4k     201µs ± 0%    14µs ± 1%  -93.24%
BM_eigen_sqrt_ctype/32k   1.62ms ± 0%  0.11ms ± 1%  -93.29%
BM_eigen_sqrt_ctype/256k  13.0ms ± 0%   0.9ms ± 1%  -93.31%
BM_eigen_sqrt_ctype/1M    52.0ms ± 0%   3.5ms ± 1%  -93.31%
```

AVX512:
```
name                      old cpu/op  new cpu/op  delta
BM_eigen_sqrt_ctype/1     53.7ns ± 0%  56.2ns ± 1%   +4.75%
BM_eigen_sqrt_ctype/8      334ns ± 0%    18ns ± 2%  -94.63%
BM_eigen_sqrt_ctype/64    2.79µs ± 0%  0.12µs ± 1%  -95.54%
BM_eigen_sqrt_ctype/512   23.9µs ± 1%   1.0µs ± 1%  -95.89%
BM_eigen_sqrt_ctype/4k     202µs ± 0%     8µs ± 1%  -96.13%
BM_eigen_sqrt_ctype/32k   1.63ms ± 0%  0.06ms ± 1%  -96.15%
BM_eigen_sqrt_ctype/256k  13.0ms ± 0%   0.5ms ± 4%  -96.11%
BM_eigen_sqrt_ctype/1M    52.1ms ± 0%   2.0ms ± 1%  -96.13%
```
This commit is contained in:
Rasmus Munk Larsen
2020-12-08 18:13:35 -08:00
parent 8cfe0db108
commit 125cc9a5df
10 changed files with 290 additions and 11 deletions
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14
Eigen/src/Core/GenericPacketMath.h
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@@ -539,6 +539,20 @@ inline void pbroadcast2(const typename unpacket_traits<Packet>::type *a,
template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet
plset(const typename unpacket_traits<Packet>::type& a) { return a; }
/** \internal \returns a packet with constant coefficients \a a, e.g.: (x, 0, x, 0),
where x is the value of all 1-bits. */
template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
peven_mask(const Packet& /*a*/) {
typedef typename unpacket_traits<Packet>::type Scalar;
const size_t n = unpacket_traits<Packet>::size;
Scalar elements[n];
for(size_t i = 0; i < n; ++i) {
memset(elements+i, ((i & 1) == 0 ? 0xff : 0), sizeof(Scalar));
}
return ploadu<Packet>(elements);
}
/** \internal copy the packet \a from to \a *to, \a to must be 16 bytes aligned */
template<typename Scalar, typename Packet> EIGEN_DEVICE_FUNC inline void pstore(Scalar* to, const Packet& from)
{ (*to) = from; }