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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
Download Patch File Download Diff File Expand all files Collapse all files

36
Eigen/src/Core/arch/AVX/Complex.h
View File

@@ -38,6 +38,7 @@ template<> struct packet_traits<std::complex<float> > : default_packet_traits
HasMul = 1,
HasDiv = 1,
HasNegate = 1,
HasSqrt = 1,
HasAbs = 0,
HasAbs2 = 0,
HasMin = 0,
@@ -47,7 +48,18 @@ template<> struct packet_traits<std::complex<float> > : default_packet_traits
};
#endif
template<> struct unpacket_traits<Packet4cf> { typedef std::complex<float> type; enum {size=4, alignment=Aligned32, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef Packet2cf half; };
template<> struct unpacket_traits<Packet4cf> {
typedef std::complex<float> type;
typedef Packet2cf half;
typedef Packet8f as_real;
enum {
size=4,
alignment=Aligned32,
vectorizable=true,
masked_load_available=false,
masked_store_available=false
};
};
template<> EIGEN_STRONG_INLINE Packet4cf padd<Packet4cf>(const Packet4cf& a, const Packet4cf& b) { return Packet4cf(_mm256_add_ps(a.v,b.v)); }
template<> EIGEN_STRONG_INLINE Packet4cf psub<Packet4cf>(const Packet4cf& a, const Packet4cf& b) { return Packet4cf(_mm256_sub_ps(a.v,b.v)); }
@@ -228,6 +240,7 @@ template<> struct packet_traits<std::complex<double> > : default_packet_traits
HasMul = 1,
HasDiv = 1,
HasNegate = 1,
HasSqrt = 1,
HasAbs = 0,
HasAbs2 = 0,
HasMin = 0,
@@ -237,7 +250,18 @@ template<> struct packet_traits<std::complex<double> > : default_packet_traits
};
#endif
template<> struct unpacket_traits<Packet2cd> { typedef std::complex<double> type; enum {size=2, alignment=Aligned32, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef Packet1cd half; };
template<> struct unpacket_traits<Packet2cd> {
typedef std::complex<double> type;
typedef Packet1cd half;
typedef Packet4d as_real;
enum {
size=2,
alignment=Aligned32,
vectorizable=true,
masked_load_available=false,
masked_store_available=false
};
};
template<> EIGEN_STRONG_INLINE Packet2cd padd<Packet2cd>(const Packet2cd& a, const Packet2cd& b) { return Packet2cd(_mm256_add_pd(a.v,b.v)); }
template<> EIGEN_STRONG_INLINE Packet2cd psub<Packet2cd>(const Packet2cd& a, const Packet2cd& b) { return Packet2cd(_mm256_sub_pd(a.v,b.v)); }
@@ -399,6 +423,14 @@ ptranspose(PacketBlock<Packet2cd,2>& kernel) {
kernel.packet[0].v = tmp;
}
template<> EIGEN_STRONG_INLINE Packet2cd psqrt<Packet2cd>(const Packet2cd& a) {
return psqrt_complex<Packet2cd>(a);
}
template<> EIGEN_STRONG_INLINE Packet4cf psqrt<Packet4cf>(const Packet4cf& a) {
return psqrt_complex<Packet4cf>(a);
}
} // end namespace internal
} // end namespace Eigen

5
Eigen/src/Core/arch/AVX/PacketMath.h
View File

@@ -248,6 +248,11 @@ template<> EIGEN_STRONG_INLINE Packet8f pzero(const Packet8f& /*a*/) { return _m
template<> EIGEN_STRONG_INLINE Packet4d pzero(const Packet4d& /*a*/) { return _mm256_setzero_pd(); }
template<> EIGEN_STRONG_INLINE Packet8i pzero(const Packet8i& /*a*/) { return _mm256_setzero_si256(); }
template<> EIGEN_STRONG_INLINE Packet8f peven_mask(const Packet8f& /*a*/) { return Packet8f(_mm256_set_epi32(0, -1, 0, -1, 0, -1, 0, -1)); }
template<> EIGEN_STRONG_INLINE Packet8i peven_mask(const Packet8i& /*a*/) { return Packet8i(_mm256_set_epi32(0, -1, 0, -1, 0, -1, 0, -1)); }
template<> EIGEN_STRONG_INLINE Packet4d peven_mask(const Packet4d& /*a*/) { return Packet4d(_mm256_set_epi32(0, 0, -1, -1, 0, 0, -1, -1)); }
template<> EIGEN_STRONG_INLINE Packet8f pload1<Packet8f>(const float* from) { return _mm256_broadcast_ss(from); }
template<> EIGEN_STRONG_INLINE Packet4d pload1<Packet4d>(const double* from) { return _mm256_broadcast_sd(from); }