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Eigen  3.3.9
GenericPacketMath.h
1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
5 // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
6 //
7 // This Source Code Form is subject to the terms of the Mozilla
8 // Public License v. 2.0. If a copy of the MPL was not distributed
9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
10 
11 #ifndef EIGEN_GENERIC_PACKET_MATH_H
12 #define EIGEN_GENERIC_PACKET_MATH_H
13 
14 namespace Eigen {
15 
16 namespace internal {
17 
26 #ifndef EIGEN_DEBUG_ALIGNED_LOAD
27 #define EIGEN_DEBUG_ALIGNED_LOAD
28 #endif
29 
30 #ifndef EIGEN_DEBUG_UNALIGNED_LOAD
31 #define EIGEN_DEBUG_UNALIGNED_LOAD
32 #endif
33 
34 #ifndef EIGEN_DEBUG_ALIGNED_STORE
35 #define EIGEN_DEBUG_ALIGNED_STORE
36 #endif
37 
38 #ifndef EIGEN_DEBUG_UNALIGNED_STORE
39 #define EIGEN_DEBUG_UNALIGNED_STORE
40 #endif
41 
42 struct default_packet_traits
43 {
44  enum {
45  HasHalfPacket = 0,
46 
47  HasAdd = 1,
48  HasSub = 1,
49  HasMul = 1,
50  HasNegate = 1,
51  HasAbs = 1,
52  HasArg = 0,
53  HasAbs2 = 1,
54  HasMin = 1,
55  HasMax = 1,
56  HasConj = 1,
57  HasSetLinear = 1,
58  HasBlend = 0,
59 
60  HasDiv = 0,
61  HasSqrt = 0,
62  HasRsqrt = 0,
63  HasExp = 0,
64  HasLog = 0,
65  HasLog1p = 0,
66  HasLog10 = 0,
67  HasPow = 0,
68 
69  HasSin = 0,
70  HasCos = 0,
71  HasTan = 0,
72  HasASin = 0,
73  HasACos = 0,
74  HasATan = 0,
75  HasSinh = 0,
76  HasCosh = 0,
77  HasTanh = 0,
78  HasLGamma = 0,
79  HasDiGamma = 0,
80  HasZeta = 0,
81  HasPolygamma = 0,
82  HasErf = 0,
83  HasErfc = 0,
84  HasIGamma = 0,
85  HasIGammac = 0,
86  HasBetaInc = 0,
87 
88  HasRound = 0,
89  HasFloor = 0,
90  HasCeil = 0,
91 
92  HasSign = 0
93  };
94 };
95 
96 template<typename T> struct packet_traits : default_packet_traits
97 {
98  typedef T type;
99  typedef T half;
100  enum {
101  Vectorizable = 0,
102  size = 1,
103  AlignedOnScalar = 0,
104  HasHalfPacket = 0
105  };
106  enum {
107  HasAdd = 0,
108  HasSub = 0,
109  HasMul = 0,
110  HasNegate = 0,
111  HasAbs = 0,
112  HasAbs2 = 0,
113  HasMin = 0,
114  HasMax = 0,
115  HasConj = 0,
116  HasSetLinear = 0
117  };
118 };
119 
120 template<typename T> struct packet_traits<const T> : packet_traits<T> { };
121 
122 template <typename Src, typename Tgt> struct type_casting_traits {
123  enum {
124  VectorizedCast = 0,
125  SrcCoeffRatio = 1,
126  TgtCoeffRatio = 1
127  };
128 };
129 
130 
132 template <typename SrcPacket, typename TgtPacket>
133 EIGEN_DEVICE_FUNC inline TgtPacket
134 pcast(const SrcPacket& a) {
135  return static_cast<TgtPacket>(a);
136 }
137 template <typename SrcPacket, typename TgtPacket>
138 EIGEN_DEVICE_FUNC inline TgtPacket
139 pcast(const SrcPacket& a, const SrcPacket& /*b*/) {
140  return static_cast<TgtPacket>(a);
141 }
142 
143 template <typename SrcPacket, typename TgtPacket>
144 EIGEN_DEVICE_FUNC inline TgtPacket
145 pcast(const SrcPacket& a, const SrcPacket& /*b*/, const SrcPacket& /*c*/, const SrcPacket& /*d*/) {
146  return static_cast<TgtPacket>(a);
147 }
148 
150 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
151 padd(const Packet& a,
152  const Packet& b) { return a+b; }
153 
155 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
156 psub(const Packet& a,
157  const Packet& b) { return a-b; }
158 
160 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
161 pnegate(const Packet& a) { return -a; }
162 
165 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
166 pconj(const Packet& a) { return numext::conj(a); }
167 
169 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
170 pmul(const Packet& a,
171  const Packet& b) { return a*b; }
172 
174 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
175 pdiv(const Packet& a,
176  const Packet& b) { return a/b; }
177 
179 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
180 pmin(const Packet& a,
181  const Packet& b) { return numext::mini(a, b); }
182 
184 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
185 pmax(const Packet& a,
186  const Packet& b) { return numext::maxi(a, b); }
187 
189 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
190 pabs(const Packet& a) { using std::abs; return abs(a); }
191 
193 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
194 parg(const Packet& a) { using numext::arg; return arg(a); }
195 
197 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
198 pand(const Packet& a, const Packet& b) { return a & b; }
199 
201 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
202 por(const Packet& a, const Packet& b) { return a | b; }
203 
205 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
206 pxor(const Packet& a, const Packet& b) { return a ^ b; }
207 
209 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
210 pandnot(const Packet& a, const Packet& b) { return a & (!b); }
211 
213 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
214 pload(const typename unpacket_traits<Packet>::type* from) { return *from; }
215 
217 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
218 ploadu(const typename unpacket_traits<Packet>::type* from) { return *from; }
219 
221 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
222 pset1(const typename unpacket_traits<Packet>::type& a) { return a; }
223 
225 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
226 pload1(const typename unpacket_traits<Packet>::type *a) { return pset1<Packet>(*a); }
227 
233 template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet
234 ploaddup(const typename unpacket_traits<Packet>::type* from) { return *from; }
235 
242 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
243 ploadquad(const typename unpacket_traits<Packet>::type* from)
244 { return pload1<Packet>(from); }
245 
255 template<typename Packet> EIGEN_DEVICE_FUNC
256 inline void pbroadcast4(const typename unpacket_traits<Packet>::type *a,
257  Packet& a0, Packet& a1, Packet& a2, Packet& a3)
258 {
259  a0 = pload1<Packet>(a+0);
260  a1 = pload1<Packet>(a+1);
261  a2 = pload1<Packet>(a+2);
262  a3 = pload1<Packet>(a+3);
263 }
264 
272 template<typename Packet> EIGEN_DEVICE_FUNC
273 inline void pbroadcast2(const typename unpacket_traits<Packet>::type *a,
274  Packet& a0, Packet& a1)
275 {
276  a0 = pload1<Packet>(a+0);
277  a1 = pload1<Packet>(a+1);
278 }
279 
281 template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet
282 plset(const typename unpacket_traits<Packet>::type& a) { return a; }
283 
285 template<typename Scalar, typename Packet> EIGEN_DEVICE_FUNC inline void pstore(Scalar* to, const Packet& from)
286 { (*to) = from; }
287 
289 template<typename Scalar, typename Packet> EIGEN_DEVICE_FUNC inline void pstoreu(Scalar* to, const Packet& from)
290 { (*to) = from; }
291 
292  template<typename Scalar, typename Packet> EIGEN_DEVICE_FUNC inline Packet pgather(const Scalar* from, Index /*stride*/)
293  { return ploadu<Packet>(from); }
294 
295  template<typename Scalar, typename Packet> EIGEN_DEVICE_FUNC inline void pscatter(Scalar* to, const Packet& from, Index /*stride*/)
296  { pstore(to, from); }
297 
299 template<typename Scalar> EIGEN_DEVICE_FUNC inline void prefetch(const Scalar* addr)
300 {
301 #ifdef __CUDA_ARCH__
302 #if defined(__LP64__)
303  // 64-bit pointer operand constraint for inlined asm
304  asm(" prefetch.L1 [ %1 ];" : "=l"(addr) : "l"(addr));
305 #else
306  // 32-bit pointer operand constraint for inlined asm
307  asm(" prefetch.L1 [ %1 ];" : "=r"(addr) : "r"(addr));
308 #endif
309 #elif (!EIGEN_COMP_MSVC) && (EIGEN_COMP_GNUC || EIGEN_COMP_CLANG || EIGEN_COMP_ICC)
310  __builtin_prefetch(addr);
311 #endif
312 }
313 
315 template<typename Packet> EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type pfirst(const Packet& a)
316 { return a; }
317 
319 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
320 preduxp(const Packet* vecs) { return vecs[0]; }
321 
323 template<typename Packet> EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type predux(const Packet& a)
324 { return a; }
325 
330 template<typename Packet> EIGEN_DEVICE_FUNC inline
331 typename conditional<(unpacket_traits<Packet>::size%8)==0,typename unpacket_traits<Packet>::half,Packet>::type
332 predux_downto4(const Packet& a)
333 { return a; }
334 
336 template<typename Packet> EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type predux_mul(const Packet& a)
337 { return a; }
338 
340 template<typename Packet> EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type predux_min(const Packet& a)
341 { return a; }
342 
344 template<typename Packet> EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type predux_max(const Packet& a)
345 { return a; }
346 
348 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet preverse(const Packet& a)
349 { return a; }
350 
352 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet pcplxflip(const Packet& a)
353 {
354  return Packet(a.imag(),a.real());
355 }
356 
357 /**************************
358 * Special math functions
359 ***************************/
360 
362 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
363 Packet psin(const Packet& a) { using std::sin; return sin(a); }
364 
366 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
367 Packet pcos(const Packet& a) { using std::cos; return cos(a); }
368 
370 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
371 Packet ptan(const Packet& a) { using std::tan; return tan(a); }
372 
374 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
375 Packet pasin(const Packet& a) { using std::asin; return asin(a); }
376 
378 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
379 Packet pacos(const Packet& a) { using std::acos; return acos(a); }
380 
382 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
383 Packet patan(const Packet& a) { using std::atan; return atan(a); }
384 
386 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
387 Packet psinh(const Packet& a) { using std::sinh; return sinh(a); }
388 
390 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
391 Packet pcosh(const Packet& a) { using std::cosh; return cosh(a); }
392 
394 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
395 Packet ptanh(const Packet& a) { using std::tanh; return tanh(a); }
396 
398 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
399 Packet pexp(const Packet& a) { using std::exp; return exp(a); }
400 
402 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
403 Packet plog(const Packet& a) { using std::log; return log(a); }
404 
406 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
407 Packet plog1p(const Packet& a) { return numext::log1p(a); }
408 
410 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
411 Packet plog10(const Packet& a) { using std::log10; return log10(a); }
412 
414 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
415 Packet psqrt(const Packet& a) { using std::sqrt; return sqrt(a); }
416 
418 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
419 Packet prsqrt(const Packet& a) {
420  return pdiv(pset1<Packet>(1), psqrt(a));
421 }
422 
424 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
425 Packet pround(const Packet& a) { using numext::round; return round(a); }
426 
428 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
429 Packet pfloor(const Packet& a) { using numext::floor; return floor(a); }
430 
432 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
433 Packet pceil(const Packet& a) { using numext::ceil; return ceil(a); }
434 
435 /***************************************************************************
436 * The following functions might not have to be overwritten for vectorized types
437 ***************************************************************************/
438 
440 // NOTE: this function must really be templated on the packet type (think about different packet types for the same scalar type)
441 template<typename Packet>
442 inline void pstore1(typename unpacket_traits<Packet>::type* to, const typename unpacket_traits<Packet>::type& a)
443 {
444  pstore(to, pset1<Packet>(a));
445 }
446 
448 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
449 pmadd(const Packet& a,
450  const Packet& b,
451  const Packet& c)
452 { return padd(pmul(a, b),c); }
453 
456 template<typename Packet, int Alignment>
457 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet ploadt(const typename unpacket_traits<Packet>::type* from)
458 {
459  if(Alignment >= unpacket_traits<Packet>::alignment)
460  return pload<Packet>(from);
461  else
462  return ploadu<Packet>(from);
463 }
464 
467 template<typename Scalar, typename Packet, int Alignment>
468 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pstoret(Scalar* to, const Packet& from)
469 {
470  if(Alignment >= unpacket_traits<Packet>::alignment)
471  pstore(to, from);
472  else
473  pstoreu(to, from);
474 }
475 
481 template<typename Packet, int LoadMode>
482 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet ploadt_ro(const typename unpacket_traits<Packet>::type* from)
483 {
484  return ploadt<Packet, LoadMode>(from);
485 }
486 
488 template<int Offset,typename PacketType>
489 struct palign_impl
490 {
491  // by default data are aligned, so there is nothing to be done :)
492  static inline void run(PacketType&, const PacketType&) {}
493 };
494 
510 template<int Offset,typename PacketType>
511 inline void palign(PacketType& first, const PacketType& second)
512 {
513  palign_impl<Offset,PacketType>::run(first,second);
514 }
515 
516 /***************************************************************************
517 * Fast complex products (GCC generates a function call which is very slow)
518 ***************************************************************************/
519 
520 // Eigen+CUDA does not support complexes.
521 #ifndef __CUDACC__
522 
523 template<> inline std::complex<float> pmul(const std::complex<float>& a, const std::complex<float>& b)
524 { return std::complex<float>(a.real()*b.real() - a.imag()*b.imag(), a.imag()*b.real() + a.real()*b.imag()); }
525 
526 template<> inline std::complex<double> pmul(const std::complex<double>& a, const std::complex<double>& b)
527 { return std::complex<double>(a.real()*b.real() - a.imag()*b.imag(), a.imag()*b.real() + a.real()*b.imag()); }
528 
529 #endif
530 
531 
532 /***************************************************************************
533  * PacketBlock, that is a collection of N packets where the number of words
534  * in the packet is a multiple of N.
535 ***************************************************************************/
536 template <typename Packet,int N=unpacket_traits<Packet>::size> struct PacketBlock {
537  Packet packet[N];
538 };
539 
540 template<typename Packet> EIGEN_DEVICE_FUNC inline void
541 ptranspose(PacketBlock<Packet,1>& /*kernel*/) {
542  // Nothing to do in the scalar case, i.e. a 1x1 matrix.
543 }
544 
545 /***************************************************************************
546  * Selector, i.e. vector of N boolean values used to select (i.e. blend)
547  * words from 2 packets.
548 ***************************************************************************/
549 template <size_t N> struct Selector {
550  bool select[N];
551 };
552 
553 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
554 pblend(const Selector<unpacket_traits<Packet>::size>& ifPacket, const Packet& thenPacket, const Packet& elsePacket) {
555  return ifPacket.select[0] ? thenPacket : elsePacket;
556 }
557 
559 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
560 pinsertfirst(const Packet& a, typename unpacket_traits<Packet>::type b)
561 {
562  // Default implementation based on pblend.
563  // It must be specialized for higher performance.
564  Selector<unpacket_traits<Packet>::size> mask;
565  mask.select[0] = true;
566  // This for loop should be optimized away by the compiler.
567  for(Index i=1; i<unpacket_traits<Packet>::size; ++i)
568  mask.select[i] = false;
569  return pblend(mask, pset1<Packet>(b), a);
570 }
571 
573 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
574 pinsertlast(const Packet& a, typename unpacket_traits<Packet>::type b)
575 {
576  // Default implementation based on pblend.
577  // It must be specialized for higher performance.
578  Selector<unpacket_traits<Packet>::size> mask;
579  // This for loop should be optimized away by the compiler.
580  for(Index i=0; i<unpacket_traits<Packet>::size-1; ++i)
581  mask.select[i] = false;
582  mask.select[unpacket_traits<Packet>::size-1] = true;
583  return pblend(mask, pset1<Packet>(b), a);
584 }
585 
586 } // end namespace internal
587 
588 } // end namespace Eigen
589 
590 #endif // EIGEN_GENERIC_PACKET_MATH_H
Eigen
Namespace containing all symbols from the Eigen library.
Definition: Core:309
Eigen::sqrt
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_sqrt_op< typename Derived::Scalar >, const Derived > sqrt(const Eigen::ArrayBase< Derived > &x)
Eigen::round
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_round_op< typename Derived::Scalar >, const Derived > round(const Eigen::ArrayBase< Derived > &x)
Eigen::ceil
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_ceil_op< typename Derived::Scalar >, const Derived > ceil(const Eigen::ArrayBase< Derived > &x)
Eigen::sin
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_sin_op< typename Derived::Scalar >, const Derived > sin(const Eigen::ArrayBase< Derived > &x)
Eigen::log10
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_log10_op< typename Derived::Scalar >, const Derived > log10(const Eigen::ArrayBase< Derived > &x)
Eigen::tan
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_tan_op< typename Derived::Scalar >, const Derived > tan(const Eigen::ArrayBase< Derived > &x)
Eigen::asin
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_asin_op< typename Derived::Scalar >, const Derived > asin(const Eigen::ArrayBase< Derived > &x)
Eigen::acos
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_acos_op< typename Derived::Scalar >, const Derived > acos(const Eigen::ArrayBase< Derived > &x)
Eigen::floor
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_floor_op< typename Derived::Scalar >, const Derived > floor(const Eigen::ArrayBase< Derived > &x)
Eigen::arg
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_arg_op< typename Derived::Scalar >, const Derived > arg(const Eigen::ArrayBase< Derived > &x)
Eigen::abs
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_abs_op< typename Derived::Scalar >, const Derived > abs(const Eigen::ArrayBase< Derived > &x)
Eigen::cos
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_cos_op< typename Derived::Scalar >, const Derived > cos(const Eigen::ArrayBase< Derived > &x)
Eigen::log
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_log_op< typename Derived::Scalar >, const Derived > log(const Eigen::ArrayBase< Derived > &x)
Eigen::sinh
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_sinh_op< typename Derived::Scalar >, const Derived > sinh(const Eigen::ArrayBase< Derived > &x)
Eigen::atan
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_atan_op< typename Derived::Scalar >, const Derived > atan(const Eigen::ArrayBase< Derived > &x)
Eigen::cosh
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_cosh_op< typename Derived::Scalar >, const Derived > cosh(const Eigen::ArrayBase< Derived > &x)
Eigen::tanh
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_tanh_op< typename Derived::Scalar >, const Derived > tanh(const Eigen::ArrayBase< Derived > &x)
Eigen::exp
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_exp_op< typename Derived::Scalar >, const Derived > exp(const Eigen::ArrayBase< Derived > &x)
Eigen::Index
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:33