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File indexing completed on 2025-01-19 09:51:42 

0001 // This file is part of Eigen, a lightweight C++ template library
0002 // for linear algebra.
0003 //
0004 // Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
0005 // Copyright (C) 2010 Konstantinos Margaritis <markos@freevec.org>
0006 //
0007 // This Source Code Form is subject to the terms of the Mozilla
0008 // Public License v. 2.0. If a copy of the MPL was not distributed
0009 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
0010 
0011 #ifndef EIGEN_COMPLEX_NEON_H
0012 #define EIGEN_COMPLEX_NEON_H
0013 
0014 namespace Eigen {
0015 
0016 namespace internal {
0017 
0018 inline uint32x4_t p4ui_CONJ_XOR()
0019 {
0020 // See bug 1325, clang fails to call vld1q_u64.
0021 #if EIGEN_COMP_CLANG || EIGEN_COMP_CASTXML
0022   uint32x4_t ret = { 0x00000000, 0x80000000, 0x00000000, 0x80000000 };
0023   return ret;
0024 #else
0025   static const uint32_t conj_XOR_DATA[] = { 0x00000000, 0x80000000, 0x00000000, 0x80000000 };
0026   return vld1q_u32( conj_XOR_DATA );
0027 #endif
0028 }
0029 
0030 inline uint32x2_t p2ui_CONJ_XOR()
0031 {
0032   static const uint32_t conj_XOR_DATA[] = { 0x00000000, 0x80000000 };
0033   return vld1_u32( conj_XOR_DATA );
0034 }
0035 
0036 //---------- float ----------
0037 
0038 struct Packet1cf
0039 {
0040   EIGEN_STRONG_INLINE Packet1cf() {}
0041   EIGEN_STRONG_INLINE explicit Packet1cf(const Packet2f& a) : v(a) {}
0042   Packet2f v;
0043 };
0044 struct Packet2cf
0045 {
0046   EIGEN_STRONG_INLINE Packet2cf() {}
0047   EIGEN_STRONG_INLINE explicit Packet2cf(const Packet4f& a) : v(a) {}
0048   Packet4f v;
0049 };
0050 
0051 template<> struct packet_traits<std::complex<float> > : default_packet_traits
0052 {
0053   typedef Packet2cf type;
0054   typedef Packet1cf half;
0055   enum
0056   {
0057     Vectorizable = 1,
0058     AlignedOnScalar = 1,
0059     size = 2,
0060     HasHalfPacket = 1,
0061 
0062     HasAdd       = 1,
0063     HasSub       = 1,
0064     HasMul       = 1,
0065     HasDiv       = 1,
0066     HasNegate    = 1,
0067     HasAbs       = 0,
0068     HasAbs2      = 0,
0069     HasMin       = 0,
0070     HasMax       = 0,
0071     HasSetLinear = 0
0072   };
0073 };
0074 
0075 template<> struct unpacket_traits<Packet1cf>
0076 {
0077   typedef std::complex<float> type;
0078   typedef Packet1cf half;
0079   typedef Packet2f as_real;
0080   enum
0081   {
0082     size = 1,
0083     alignment = Aligned16,
0084     vectorizable = true,
0085     masked_load_available = false,
0086     masked_store_available = false
0087   };
0088 };
0089 template<> struct unpacket_traits<Packet2cf>
0090 {
0091   typedef std::complex<float> type;
0092   typedef Packet1cf half;
0093   typedef Packet4f as_real;
0094   enum
0095   {
0096     size = 2,
0097     alignment = Aligned16,
0098     vectorizable = true,
0099     masked_load_available = false,
0100     masked_store_available = false
0101   };
0102 };
0103 
0104 template<> EIGEN_STRONG_INLINE Packet1cf pcast<float,Packet1cf>(const float& a)
0105 { return Packet1cf(vset_lane_f32(a, vdup_n_f32(0.f), 0)); }
0106 template<> EIGEN_STRONG_INLINE Packet2cf pcast<Packet2f,Packet2cf>(const Packet2f& a)
0107 { return Packet2cf(vreinterpretq_f32_u64(vmovl_u32(vreinterpret_u32_f32(a)))); }
0108 
0109 template<> EIGEN_STRONG_INLINE Packet1cf pset1<Packet1cf>(const std::complex<float>& from)
0110 { return Packet1cf(vld1_f32(reinterpret_cast<const float*>(&from))); }
0111 template<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>& from)
0112 {
0113   const float32x2_t r64 = vld1_f32(reinterpret_cast<const float*>(&from));
0114   return Packet2cf(vcombine_f32(r64, r64));
0115 }
0116 
0117 template<> EIGEN_STRONG_INLINE Packet1cf padd<Packet1cf>(const Packet1cf& a, const Packet1cf& b)
0118 { return Packet1cf(padd<Packet2f>(a.v, b.v)); }
0119 template<> EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
0120 { return Packet2cf(padd<Packet4f>(a.v, b.v)); }
0121 
0122 template<> EIGEN_STRONG_INLINE Packet1cf psub<Packet1cf>(const Packet1cf& a, const Packet1cf& b)
0123 { return Packet1cf(psub<Packet2f>(a.v, b.v)); }
0124 template<> EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
0125 { return Packet2cf(psub<Packet4f>(a.v, b.v)); }
0126 
0127 template<> EIGEN_STRONG_INLINE Packet1cf pnegate(const Packet1cf& a) { return Packet1cf(pnegate<Packet2f>(a.v)); }
0128 template<> EIGEN_STRONG_INLINE Packet2cf pnegate(const Packet2cf& a) { return Packet2cf(pnegate<Packet4f>(a.v)); }
0129 
0130 template<> EIGEN_STRONG_INLINE Packet1cf pconj(const Packet1cf& a)
0131 {
0132   const Packet2ui b = vreinterpret_u32_f32(a.v);
0133   return Packet1cf(vreinterpret_f32_u32(veor_u32(b, p2ui_CONJ_XOR())));
0134 }
0135 template<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a)
0136 {
0137   const Packet4ui b = vreinterpretq_u32_f32(a.v);
0138   return Packet2cf(vreinterpretq_f32_u32(veorq_u32(b, p4ui_CONJ_XOR())));
0139 }
0140 
0141 template<> EIGEN_STRONG_INLINE Packet1cf pmul<Packet1cf>(const Packet1cf& a, const Packet1cf& b)
0142 {
0143   Packet2f v1, v2;
0144 
0145   // Get the real values of a | a1_re | a1_re |
0146   v1 = vdup_lane_f32(a.v, 0);
0147   // Get the imag values of a | a1_im | a1_im |
0148   v2 = vdup_lane_f32(a.v, 1);
0149   // Multiply the real a with b
0150   v1 = vmul_f32(v1, b.v);
0151   // Multiply the imag a with b
0152   v2 = vmul_f32(v2, b.v);
0153   // Conjugate v2
0154   v2 = vreinterpret_f32_u32(veor_u32(vreinterpret_u32_f32(v2), p2ui_CONJ_XOR()));
0155   // Swap real/imag elements in v2.
0156   v2 = vrev64_f32(v2);
0157   // Add and return the result
0158   return Packet1cf(vadd_f32(v1, v2));
0159 }
0160 template<> EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
0161 {
0162   Packet4f v1, v2;
0163 
0164   // Get the real values of a | a1_re | a1_re | a2_re | a2_re |
0165   v1 = vcombine_f32(vdup_lane_f32(vget_low_f32(a.v), 0), vdup_lane_f32(vget_high_f32(a.v), 0));
0166   // Get the imag values of a | a1_im | a1_im | a2_im | a2_im |
0167   v2 = vcombine_f32(vdup_lane_f32(vget_low_f32(a.v), 1), vdup_lane_f32(vget_high_f32(a.v), 1));
0168   // Multiply the real a with b
0169   v1 = vmulq_f32(v1, b.v);
0170   // Multiply the imag a with b
0171   v2 = vmulq_f32(v2, b.v);
0172   // Conjugate v2
0173   v2 = vreinterpretq_f32_u32(veorq_u32(vreinterpretq_u32_f32(v2), p4ui_CONJ_XOR()));
0174   // Swap real/imag elements in v2.
0175   v2 = vrev64q_f32(v2);
0176   // Add and return the result
0177   return Packet2cf(vaddq_f32(v1, v2));
0178 }
0179 
0180 template<> EIGEN_STRONG_INLINE Packet1cf pcmp_eq(const Packet1cf& a, const Packet1cf& b)
0181 {
0182   // Compare real and imaginary parts of a and b to get the mask vector:
0183   // [re(a[0])==re(b[0]), im(a[0])==im(b[0])]
0184   Packet2f eq = pcmp_eq<Packet2f>(a.v, b.v);
0185   // Swap real/imag elements in the mask in to get:
0186   // [im(a[0])==im(b[0]), re(a[0])==re(b[0])]
0187   Packet2f eq_swapped = vrev64_f32(eq);
0188   // Return re(a)==re(b) && im(a)==im(b) by computing bitwise AND of eq and eq_swapped
0189   return Packet1cf(pand<Packet2f>(eq, eq_swapped));
0190 }
0191 template<> EIGEN_STRONG_INLINE Packet2cf pcmp_eq(const Packet2cf& a, const Packet2cf& b)
0192 {
0193   // Compare real and imaginary parts of a and b to get the mask vector:
0194   // [re(a[0])==re(b[0]), im(a[0])==im(b[0]), re(a[1])==re(b[1]), im(a[1])==im(b[1])]
0195   Packet4f eq = pcmp_eq<Packet4f>(a.v, b.v);
0196   // Swap real/imag elements in the mask in to get:
0197   // [im(a[0])==im(b[0]), re(a[0])==re(b[0]), im(a[1])==im(b[1]), re(a[1])==re(b[1])]
0198   Packet4f eq_swapped = vrev64q_f32(eq);
0199   // Return re(a)==re(b) && im(a)==im(b) by computing bitwise AND of eq and eq_swapped
0200   return Packet2cf(pand<Packet4f>(eq, eq_swapped));
0201 }
0202 
0203 template<> EIGEN_STRONG_INLINE Packet1cf pand<Packet1cf>(const Packet1cf& a, const Packet1cf& b)
0204 { return Packet1cf(vreinterpret_f32_u32(vand_u32(vreinterpret_u32_f32(a.v), vreinterpret_u32_f32(b.v)))); }
0205 template<> EIGEN_STRONG_INLINE Packet2cf pand<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
0206 { return Packet2cf(vreinterpretq_f32_u32(vandq_u32(vreinterpretq_u32_f32(a.v), vreinterpretq_u32_f32(b.v)))); }
0207 
0208 template<> EIGEN_STRONG_INLINE Packet1cf por<Packet1cf>(const Packet1cf& a, const Packet1cf& b)
0209 { return Packet1cf(vreinterpret_f32_u32(vorr_u32(vreinterpret_u32_f32(a.v), vreinterpret_u32_f32(b.v)))); }
0210 template<> EIGEN_STRONG_INLINE Packet2cf por<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
0211 { return Packet2cf(vreinterpretq_f32_u32(vorrq_u32(vreinterpretq_u32_f32(a.v), vreinterpretq_u32_f32(b.v)))); }
0212 
0213 template<> EIGEN_STRONG_INLINE Packet1cf pxor<Packet1cf>(const Packet1cf& a, const Packet1cf& b)
0214 { return Packet1cf(vreinterpret_f32_u32(veor_u32(vreinterpret_u32_f32(a.v), vreinterpret_u32_f32(b.v)))); }
0215 template<> EIGEN_STRONG_INLINE Packet2cf pxor<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
0216 { return Packet2cf(vreinterpretq_f32_u32(veorq_u32(vreinterpretq_u32_f32(a.v), vreinterpretq_u32_f32(b.v)))); }
0217 
0218 template<> EIGEN_STRONG_INLINE Packet1cf pandnot<Packet1cf>(const Packet1cf& a, const Packet1cf& b)
0219 { return Packet1cf(vreinterpret_f32_u32(vbic_u32(vreinterpret_u32_f32(a.v), vreinterpret_u32_f32(b.v)))); }
0220 template<> EIGEN_STRONG_INLINE Packet2cf pandnot<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
0221 { return Packet2cf(vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(a.v), vreinterpretq_u32_f32(b.v)))); }
0222 
0223 template<> EIGEN_STRONG_INLINE Packet1cf pload<Packet1cf>(const std::complex<float>* from)
0224 { EIGEN_DEBUG_ALIGNED_LOAD return Packet1cf(pload<Packet2f>((const float*)from)); }
0225 template<> EIGEN_STRONG_INLINE Packet2cf pload<Packet2cf>(const std::complex<float>* from)
0226 { EIGEN_DEBUG_ALIGNED_LOAD return Packet2cf(pload<Packet4f>(reinterpret_cast<const float*>(from))); }
0227 
0228 template<> EIGEN_STRONG_INLINE Packet1cf ploadu<Packet1cf>(const std::complex<float>* from)
0229 { EIGEN_DEBUG_UNALIGNED_LOAD return Packet1cf(ploadu<Packet2f>((const float*)from)); }
0230 template<> EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>* from)
0231 { EIGEN_DEBUG_UNALIGNED_LOAD return Packet2cf(ploadu<Packet4f>(reinterpret_cast<const float*>(from))); }
0232 
0233 template<> EIGEN_STRONG_INLINE Packet1cf ploaddup<Packet1cf>(const std::complex<float>* from)
0234 { return pset1<Packet1cf>(*from); }
0235 template<> EIGEN_STRONG_INLINE Packet2cf ploaddup<Packet2cf>(const std::complex<float>* from)
0236 { return pset1<Packet2cf>(*from); }
0237 
0238 template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> *to, const Packet1cf& from)
0239 { EIGEN_DEBUG_ALIGNED_STORE pstore((float*)to, from.v); }
0240 template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> *to, const Packet2cf& from)
0241 { EIGEN_DEBUG_ALIGNED_STORE pstore(reinterpret_cast<float*>(to), from.v); }
0242 
0243 template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> *to, const Packet1cf& from)
0244 { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((float*)to, from.v); }
0245 template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> *to, const Packet2cf& from)
0246 { EIGEN_DEBUG_UNALIGNED_STORE pstoreu(reinterpret_cast<float*>(to), from.v); }
0247 
0248 template<> EIGEN_DEVICE_FUNC inline Packet1cf pgather<std::complex<float>, Packet1cf>(
0249     const std::complex<float>* from, Index stride)
0250 {
0251   const Packet2f tmp = vdup_n_f32(std::real(from[0*stride]));
0252   return Packet1cf(vset_lane_f32(std::imag(from[0*stride]), tmp, 1));
0253 }
0254 template<> EIGEN_DEVICE_FUNC inline Packet2cf pgather<std::complex<float>, Packet2cf>(
0255     const std::complex<float>* from, Index stride)
0256 {
0257   Packet4f res = vdupq_n_f32(std::real(from[0*stride]));
0258   res = vsetq_lane_f32(std::imag(from[0*stride]), res, 1);
0259   res = vsetq_lane_f32(std::real(from[1*stride]), res, 2);
0260   res = vsetq_lane_f32(std::imag(from[1*stride]), res, 3);
0261   return Packet2cf(res);
0262 }
0263 
0264 template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<float>, Packet1cf>(
0265     std::complex<float>* to, const Packet1cf& from, Index stride)
0266 { to[stride*0] = std::complex<float>(vget_lane_f32(from.v, 0), vget_lane_f32(from.v, 1)); }
0267 template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<float>, Packet2cf>(
0268     std::complex<float>* to, const Packet2cf& from, Index stride)
0269 {
0270   to[stride*0] = std::complex<float>(vgetq_lane_f32(from.v, 0), vgetq_lane_f32(from.v, 1));
0271   to[stride*1] = std::complex<float>(vgetq_lane_f32(from.v, 2), vgetq_lane_f32(from.v, 3));
0272 }
0273 
0274 template<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float> *addr)
0275 { EIGEN_ARM_PREFETCH(reinterpret_cast<const float*>(addr)); }
0276 
0277 template<> EIGEN_STRONG_INLINE std::complex<float> pfirst<Packet1cf>(const Packet1cf& a)
0278 {
0279   EIGEN_ALIGN16 std::complex<float> x;
0280   vst1_f32(reinterpret_cast<float*>(&x), a.v);
0281   return x;
0282 }
0283 template<> EIGEN_STRONG_INLINE std::complex<float> pfirst<Packet2cf>(const Packet2cf& a)
0284 {
0285   EIGEN_ALIGN16 std::complex<float> x[2];
0286   vst1q_f32(reinterpret_cast<float*>(x), a.v);
0287   return x[0];
0288 }
0289 
0290 template<> EIGEN_STRONG_INLINE Packet1cf preverse(const Packet1cf& a) { return a; }
0291 template<> EIGEN_STRONG_INLINE Packet2cf preverse(const Packet2cf& a)
0292 { return Packet2cf(vcombine_f32(vget_high_f32(a.v), vget_low_f32(a.v))); }
0293 
0294 template<> EIGEN_STRONG_INLINE Packet1cf pcplxflip<Packet1cf>(const Packet1cf& a)
0295 { return Packet1cf(vrev64_f32(a.v)); }
0296 template<> EIGEN_STRONG_INLINE Packet2cf pcplxflip<Packet2cf>(const Packet2cf& a)
0297 { return Packet2cf(vrev64q_f32(a.v)); }
0298 
0299 template<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet1cf>(const Packet1cf& a)
0300 {
0301   std::complex<float> s;
0302   vst1_f32((float *)&s, a.v);
0303   return s;
0304 }
0305 template<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet2cf>(const Packet2cf& a)
0306 {
0307   std::complex<float> s;
0308   vst1_f32(reinterpret_cast<float*>(&s), vadd_f32(vget_low_f32(a.v), vget_high_f32(a.v)));
0309   return s;
0310 }
0311 
0312 template<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet1cf>(const Packet1cf& a)
0313 {
0314   std::complex<float> s;
0315   vst1_f32((float *)&s, a.v);
0316   return s;
0317 }
0318 template<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet2cf>(const Packet2cf& a)
0319 {
0320   float32x2_t a1, a2, v1, v2, prod;
0321   std::complex<float> s;
0322 
0323   a1 = vget_low_f32(a.v);
0324   a2 = vget_high_f32(a.v);
0325    // Get the real values of a | a1_re | a1_re | a2_re | a2_re |
0326   v1 = vdup_lane_f32(a1, 0);
0327   // Get the real values of a | a1_im | a1_im | a2_im | a2_im |
0328   v2 = vdup_lane_f32(a1, 1);
0329   // Multiply the real a with b
0330   v1 = vmul_f32(v1, a2);
0331   // Multiply the imag a with b
0332   v2 = vmul_f32(v2, a2);
0333   // Conjugate v2
0334   v2 = vreinterpret_f32_u32(veor_u32(vreinterpret_u32_f32(v2), p2ui_CONJ_XOR()));
0335   // Swap real/imag elements in v2.
0336   v2 = vrev64_f32(v2);
0337   // Add v1, v2
0338   prod = vadd_f32(v1, v2);
0339 
0340   vst1_f32(reinterpret_cast<float*>(&s), prod);
0341 
0342   return s;
0343 }
0344 
0345 EIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet1cf,Packet2f)
0346 EIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet2cf,Packet4f)
0347 
0348 template<> EIGEN_STRONG_INLINE Packet1cf pdiv<Packet1cf>(const Packet1cf& a, const Packet1cf& b)
0349 {
0350   // TODO optimize it for NEON
0351   Packet1cf res = pmul(a, pconj(b));
0352   Packet2f s, rev_s;
0353 
0354   // this computes the norm
0355   s = vmul_f32(b.v, b.v);
0356   rev_s = vrev64_f32(s);
0357 
0358   return Packet1cf(pdiv<Packet2f>(res.v, vadd_f32(s, rev_s)));
0359 }
0360 template<> EIGEN_STRONG_INLINE Packet2cf pdiv<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
0361 {
0362   // TODO optimize it for NEON
0363   Packet2cf res = pmul(a,pconj(b));
0364   Packet4f s, rev_s;
0365 
0366   // this computes the norm
0367   s = vmulq_f32(b.v, b.v);
0368   rev_s = vrev64q_f32(s);
0369 
0370   return Packet2cf(pdiv<Packet4f>(res.v, vaddq_f32(s, rev_s)));
0371 }
0372 
0373 EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet1cf, 1>& /*kernel*/) {}
0374 EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet2cf, 2>& kernel)
0375 {
0376   Packet4f tmp = vcombine_f32(vget_high_f32(kernel.packet[0].v), vget_high_f32(kernel.packet[1].v));
0377   kernel.packet[0].v = vcombine_f32(vget_low_f32(kernel.packet[0].v), vget_low_f32(kernel.packet[1].v));
0378   kernel.packet[1].v = tmp;
0379 }
0380 
0381 template<> EIGEN_STRONG_INLINE Packet1cf psqrt<Packet1cf>(const Packet1cf& a) {
0382   return psqrt_complex<Packet1cf>(a);
0383 }
0384 
0385 template<> EIGEN_STRONG_INLINE Packet2cf psqrt<Packet2cf>(const Packet2cf& a) {
0386   return psqrt_complex<Packet2cf>(a);
0387 }
0388 
0389 //---------- double ----------
0390 #if EIGEN_ARCH_ARM64 && !EIGEN_APPLE_DOUBLE_NEON_BUG
0391 
0392 // See bug 1325, clang fails to call vld1q_u64.
0393 #if EIGEN_COMP_CLANG || EIGEN_COMP_CASTXML
0394   static uint64x2_t p2ul_CONJ_XOR = {0x0, 0x8000000000000000};
0395 #else
0396   const uint64_t  p2ul_conj_XOR_DATA[] = { 0x0, 0x8000000000000000 };
0397   static uint64x2_t p2ul_CONJ_XOR = vld1q_u64( p2ul_conj_XOR_DATA );
0398 #endif
0399 
0400 struct Packet1cd
0401 {
0402   EIGEN_STRONG_INLINE Packet1cd() {}
0403   EIGEN_STRONG_INLINE explicit Packet1cd(const Packet2d& a) : v(a) {}
0404   Packet2d v;
0405 };
0406 
0407 template<> struct packet_traits<std::complex<double> >  : default_packet_traits
0408 {
0409   typedef Packet1cd type;
0410   typedef Packet1cd half;
0411   enum
0412   {
0413     Vectorizable = 1,
0414     AlignedOnScalar = 0,
0415     size = 1,
0416     HasHalfPacket = 0,
0417 
0418     HasAdd    = 1,
0419     HasSub    = 1,
0420     HasMul    = 1,
0421     HasDiv    = 1,
0422     HasNegate = 1,
0423     HasAbs    = 0,
0424     HasAbs2   = 0,
0425     HasMin    = 0,
0426     HasMax    = 0,
0427     HasSetLinear = 0
0428   };
0429 };
0430 
0431 template<> struct unpacket_traits<Packet1cd>
0432 {
0433   typedef std::complex<double> type;
0434   typedef Packet1cd half;
0435   typedef Packet2d as_real;
0436   enum
0437   {
0438     size=1,
0439     alignment=Aligned16,
0440     vectorizable=true,
0441     masked_load_available=false,
0442     masked_store_available=false
0443   };
0444 };
0445 
0446 template<> EIGEN_STRONG_INLINE Packet1cd pload<Packet1cd>(const std::complex<double>* from)
0447 { EIGEN_DEBUG_ALIGNED_LOAD return Packet1cd(pload<Packet2d>(reinterpret_cast<const double*>(from))); }
0448 
0449 template<> EIGEN_STRONG_INLINE Packet1cd ploadu<Packet1cd>(const std::complex<double>* from)
0450 { EIGEN_DEBUG_UNALIGNED_LOAD return Packet1cd(ploadu<Packet2d>(reinterpret_cast<const double*>(from))); }
0451 
0452 template<> EIGEN_STRONG_INLINE Packet1cd pset1<Packet1cd>(const std::complex<double>& from)
0453 {
0454   /* here we really have to use unaligned loads :( */
0455   return ploadu<Packet1cd>(&from);
0456 }
0457 
0458 template<> EIGEN_STRONG_INLINE Packet1cd padd<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
0459 { return Packet1cd(padd<Packet2d>(a.v, b.v)); }
0460 
0461 template<> EIGEN_STRONG_INLINE Packet1cd psub<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
0462 { return Packet1cd(psub<Packet2d>(a.v, b.v)); }
0463 
0464 template<> EIGEN_STRONG_INLINE Packet1cd pnegate(const Packet1cd& a)
0465 { return Packet1cd(pnegate<Packet2d>(a.v)); }
0466 
0467 template<> EIGEN_STRONG_INLINE Packet1cd pconj(const Packet1cd& a)
0468 { return Packet1cd(vreinterpretq_f64_u64(veorq_u64(vreinterpretq_u64_f64(a.v), p2ul_CONJ_XOR))); }
0469 
0470 template<> EIGEN_STRONG_INLINE Packet1cd pmul<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
0471 {
0472   Packet2d v1, v2;
0473 
0474   // Get the real values of a
0475   v1 = vdupq_lane_f64(vget_low_f64(a.v), 0);
0476   // Get the imag values of a
0477   v2 = vdupq_lane_f64(vget_high_f64(a.v), 0);
0478   // Multiply the real a with b
0479   v1 = vmulq_f64(v1, b.v);
0480   // Multiply the imag a with b
0481   v2 = vmulq_f64(v2, b.v);
0482   // Conjugate v2
0483   v2 = vreinterpretq_f64_u64(veorq_u64(vreinterpretq_u64_f64(v2), p2ul_CONJ_XOR));
0484   // Swap real/imag elements in v2.
0485   v2 = preverse<Packet2d>(v2);
0486   // Add and return the result
0487   return Packet1cd(vaddq_f64(v1, v2));
0488 }
0489 
0490 template<> EIGEN_STRONG_INLINE Packet1cd pcmp_eq(const Packet1cd& a, const Packet1cd& b)
0491 {
0492   // Compare real and imaginary parts of a and b to get the mask vector:
0493   // [re(a)==re(b), im(a)==im(b)]
0494   Packet2d eq = pcmp_eq<Packet2d>(a.v, b.v);
0495   // Swap real/imag elements in the mask in to get:
0496   // [im(a)==im(b), re(a)==re(b)]
0497   Packet2d eq_swapped = vreinterpretq_f64_u32(vrev64q_u32(vreinterpretq_u32_f64(eq)));
0498   // Return re(a)==re(b) & im(a)==im(b) by computing bitwise AND of eq and eq_swapped
0499   return Packet1cd(pand<Packet2d>(eq, eq_swapped));
0500 }
0501 
0502 template<> EIGEN_STRONG_INLINE Packet1cd pand<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
0503 { return Packet1cd(vreinterpretq_f64_u64(vandq_u64(vreinterpretq_u64_f64(a.v),vreinterpretq_u64_f64(b.v)))); }
0504 
0505 template<> EIGEN_STRONG_INLINE Packet1cd por<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
0506 { return Packet1cd(vreinterpretq_f64_u64(vorrq_u64(vreinterpretq_u64_f64(a.v),vreinterpretq_u64_f64(b.v)))); }
0507 
0508 template<> EIGEN_STRONG_INLINE Packet1cd pxor<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
0509 { return Packet1cd(vreinterpretq_f64_u64(veorq_u64(vreinterpretq_u64_f64(a.v),vreinterpretq_u64_f64(b.v)))); }
0510 
0511 template<> EIGEN_STRONG_INLINE Packet1cd pandnot<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
0512 { return Packet1cd(vreinterpretq_f64_u64(vbicq_u64(vreinterpretq_u64_f64(a.v),vreinterpretq_u64_f64(b.v)))); }
0513 
0514 template<> EIGEN_STRONG_INLINE Packet1cd ploaddup<Packet1cd>(const std::complex<double>* from)
0515 { return pset1<Packet1cd>(*from); }
0516 
0517 template<> EIGEN_STRONG_INLINE void pstore <std::complex<double> >(std::complex<double> *to, const Packet1cd& from)
0518 { EIGEN_DEBUG_ALIGNED_STORE pstore(reinterpret_cast<double*>(to), from.v); }
0519 
0520 template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double> *to, const Packet1cd& from)
0521 { EIGEN_DEBUG_UNALIGNED_STORE pstoreu(reinterpret_cast<double*>(to), from.v); }
0522 
0523 template<> EIGEN_STRONG_INLINE void prefetch<std::complex<double> >(const std::complex<double> *addr)
0524 { EIGEN_ARM_PREFETCH(reinterpret_cast<const double*>(addr)); }
0525 
0526 template<> EIGEN_DEVICE_FUNC inline Packet1cd pgather<std::complex<double>, Packet1cd>(
0527     const std::complex<double>* from, Index stride)
0528 {
0529   Packet2d res = pset1<Packet2d>(0.0);
0530   res = vsetq_lane_f64(std::real(from[0*stride]), res, 0);
0531   res = vsetq_lane_f64(std::imag(from[0*stride]), res, 1);
0532   return Packet1cd(res);
0533 }
0534 
0535 template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<double>, Packet1cd>(
0536     std::complex<double>* to, const Packet1cd& from, Index stride)
0537 { to[stride*0] = std::complex<double>(vgetq_lane_f64(from.v, 0), vgetq_lane_f64(from.v, 1)); }
0538 
0539 template<> EIGEN_STRONG_INLINE std::complex<double> pfirst<Packet1cd>(const Packet1cd& a)
0540 {
0541   EIGEN_ALIGN16 std::complex<double> res;
0542   pstore<std::complex<double> >(&res, a);
0543   return res;
0544 }
0545 
0546 template<> EIGEN_STRONG_INLINE Packet1cd preverse(const Packet1cd& a) { return a; }
0547 
0548 template<> EIGEN_STRONG_INLINE std::complex<double> predux<Packet1cd>(const Packet1cd& a) { return pfirst(a); }
0549 
0550 template<> EIGEN_STRONG_INLINE std::complex<double> predux_mul<Packet1cd>(const Packet1cd& a) { return pfirst(a); }
0551 
0552 EIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet1cd,Packet2d)
0553 
0554 template<> EIGEN_STRONG_INLINE Packet1cd pdiv<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
0555 {
0556   // TODO optimize it for NEON
0557   Packet1cd res = pmul(a,pconj(b));
0558   Packet2d s = pmul<Packet2d>(b.v, b.v);
0559   Packet2d rev_s = preverse<Packet2d>(s);
0560 
0561   return Packet1cd(pdiv(res.v, padd<Packet2d>(s,rev_s)));
0562 }
0563 
0564 EIGEN_STRONG_INLINE Packet1cd pcplxflip/*<Packet1cd>*/(const Packet1cd& x)
0565 { return Packet1cd(preverse(Packet2d(x.v))); }
0566 
0567 EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet1cd,2>& kernel)
0568 {
0569   Packet2d tmp = vcombine_f64(vget_high_f64(kernel.packet[0].v), vget_high_f64(kernel.packet[1].v));
0570   kernel.packet[0].v = vcombine_f64(vget_low_f64(kernel.packet[0].v), vget_low_f64(kernel.packet[1].v));
0571   kernel.packet[1].v = tmp;
0572 }
0573 
0574 template<> EIGEN_STRONG_INLINE Packet1cd psqrt<Packet1cd>(const Packet1cd& a) {
0575   return psqrt_complex<Packet1cd>(a);
0576 }
0577 
0578 #endif // EIGEN_ARCH_ARM64
0579 
0580 } // end namespace internal
0581 
0582 } // end namespace Eigen
0583 
0584 #endif // EIGEN_COMPLEX_NEON_H
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