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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

38
Eigen/src/Core/arch/SSE/Complex.h
View File

@@ -40,6 +40,7 @@ template<> struct packet_traits<std::complex<float> > : default_packet_traits
HasMul = 1,
HasDiv = 1,
HasNegate = 1,
HasSqrt = 1,
HasAbs = 0,
HasAbs2 = 0,
HasMin = 0,
@@ -50,7 +51,18 @@ template<> struct packet_traits<std::complex<float> > : default_packet_traits
};
#endif
template<> struct unpacket_traits<Packet2cf> { typedef std::complex<float> type; enum {size=2, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef Packet2cf half; };
template<> struct unpacket_traits<Packet2cf> {
typedef std::complex<float> type;
typedef Packet2cf half;
typedef Packet4f as_real;
enum {
size=2,
alignment=Aligned16,
vectorizable=true,
masked_load_available=false,
masked_store_available=false
};
};
template<> EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_add_ps(a.v,b.v)); }
template<> EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_sub_ps(a.v,b.v)); }
@@ -83,7 +95,6 @@ template<> EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, con
}
template<> EIGEN_STRONG_INLINE Packet2cf ptrue <Packet2cf>(const Packet2cf& a) { return Packet2cf(ptrue(Packet4f(a.v))); }
template<> EIGEN_STRONG_INLINE Packet2cf pand <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_and_ps(a.v,b.v)); }
template<> EIGEN_STRONG_INLINE Packet2cf por <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_or_ps(a.v,b.v)); }
template<> EIGEN_STRONG_INLINE Packet2cf pxor <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_xor_ps(a.v,b.v)); }
@@ -255,6 +266,7 @@ template<> struct packet_traits<std::complex<double> > : default_packet_traits
HasMul = 1,
HasDiv = 1,
HasNegate = 1,
HasSqrt = 1,
HasAbs = 0,
HasAbs2 = 0,
HasMin = 0,
@@ -264,7 +276,18 @@ template<> struct packet_traits<std::complex<double> > : default_packet_traits
};
#endif
template<> struct unpacket_traits<Packet1cd> { typedef std::complex<double> type; enum {size=1, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef Packet1cd half; };
template<> struct unpacket_traits<Packet1cd> {
typedef std::complex<double> type;
typedef Packet1cd half;
typedef Packet2d as_real;
enum {
size=1,
alignment=Aligned16,
vectorizable=true,
masked_load_available=false,
masked_store_available=false
};
};
template<> EIGEN_STRONG_INLINE Packet1cd padd<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_add_pd(a.v,b.v)); }
template<> EIGEN_STRONG_INLINE Packet1cd psub<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_sub_pd(a.v,b.v)); }
@@ -426,8 +449,15 @@ template<> EIGEN_STRONG_INLINE Packet2cf pblend(const Selector<2>& ifPacket, co
return Packet2cf(_mm_castpd_ps(result));
}
} // end namespace internal
template<> EIGEN_STRONG_INLINE Packet1cd psqrt<Packet1cd>(const Packet1cd& a) {
return psqrt_complex<Packet1cd>(a);
}
template<> EIGEN_STRONG_INLINE Packet2cf psqrt<Packet2cf>(const Packet2cf& a) {
return psqrt_complex<Packet2cf>(a);
}
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_COMPLEX_SSE_H

4
Eigen/src/Core/arch/SSE/PacketMath.h
View File

@@ -267,6 +267,10 @@ template<> EIGEN_STRONG_INLINE Packet16b pset1<Packet16b>(const bool& from) {
template<> EIGEN_STRONG_INLINE Packet4f pset1frombits<Packet4f>(unsigned int from) { return _mm_castsi128_ps(pset1<Packet4i>(from)); }
template<> EIGEN_STRONG_INLINE Packet2d pset1frombits<Packet2d>(uint64_t from) { return _mm_castsi128_pd(_mm_set1_epi64x(from)); }
template<> EIGEN_STRONG_INLINE Packet4f peven_mask(const Packet4f& /*a*/) { return Packet4f(_mm_set_epi32(0, -1, 0, -1)); }
template<> EIGEN_STRONG_INLINE Packet4i peven_mask(const Packet4i& /*a*/) { return Packet4i(_mm_set_epi32(0, -1, 0, -1)); }
template<> EIGEN_STRONG_INLINE Packet2d peven_mask(const Packet2d& /*a*/) { return Packet2d(_mm_set_epi32(0, 0, -1, -1)); }
template<> EIGEN_STRONG_INLINE Packet4f pzero(const Packet4f& /*a*/) { return _mm_setzero_ps(); }
template<> EIGEN_STRONG_INLINE Packet2d pzero(const Packet2d& /*a*/) { return _mm_setzero_pd(); }
template<> EIGEN_STRONG_INLINE Packet4i pzero(const Packet4i& /*a*/) { return _mm_setzero_si128(); }