TensorIntDiv.h
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1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
5 //
6 // This Source Code Form is subject to the terms of the Mozilla
7 // Public License v. 2.0. If a copy of the MPL was not distributed
8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9 
10 #ifndef EIGEN_CXX11_TENSOR_TENSOR_INTDIV_H
11 #define EIGEN_CXX11_TENSOR_TENSOR_INTDIV_H
12 
13 
14 namespace Eigen {
15 
29 namespace internal {
30 
31 namespace {
32 
33  // Note: result is undefined if val == 0
34  template <typename T>
35  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
36  typename internal::enable_if<sizeof(T)==4,int>::type count_leading_zeros(const T val)
37  {
38 #ifdef __CUDA_ARCH__
39  return __clz(val);
40 #elif EIGEN_COMP_MSVC
41  unsigned long index;
42  _BitScanReverse(&index, val);
43  return 31 - index;
44 #else
45  EIGEN_STATIC_ASSERT(sizeof(unsigned long long) == 8, YOU_MADE_A_PROGRAMMING_MISTAKE);
46  return __builtin_clz(static_cast<uint32_t>(val));
47 #endif
48  }
49 
50  template <typename T>
51  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
52  typename internal::enable_if<sizeof(T)==8,int>::type count_leading_zeros(const T val)
53  {
54 #ifdef __CUDA_ARCH__
55  return __clzll(val);
56 #elif EIGEN_COMP_MSVC && EIGEN_ARCH_x86_64
57  unsigned long index;
58  _BitScanReverse64(&index, val);
59  return 63 - index;
60 #elif EIGEN_COMP_MSVC
61  // MSVC's _BitScanReverse64 is not available for 32bits builds.
62  unsigned int lo = (unsigned int)(val&0xffffffff);
63  unsigned int hi = (unsigned int)((val>>32)&0xffffffff);
64  int n;
65  if(hi==0)
66  n = 32 + count_leading_zeros<unsigned int>(lo);
67  else
68  n = count_leading_zeros<unsigned int>(hi);
69  return n;
70 #else
71  EIGEN_STATIC_ASSERT(sizeof(unsigned long long) == 8, YOU_MADE_A_PROGRAMMING_MISTAKE);
72  return __builtin_clzll(static_cast<uint64_t>(val));
73 #endif
74  }
75 
76  template <typename T>
77  struct UnsignedTraits {
79  };
80 
81  template <typename T>
82  struct DividerTraits {
83  typedef typename UnsignedTraits<T>::type type;
84  static const int N = sizeof(T) * 8;
85  };
86 
87  template <typename T>
88  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE uint32_t muluh(const uint32_t a, const T b) {
89 #if defined(__CUDA_ARCH__)
90  return __umulhi(a, b);
91 #else
92  return (static_cast<uint64_t>(a) * b) >> 32;
93 #endif
94  }
95 
96  template <typename T>
97  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE uint64_t muluh(const uint64_t a, const T b) {
98 #if defined(__CUDA_ARCH__)
99  return __umul64hi(a, b);
100 #elif defined(__SIZEOF_INT128__)
101  __uint128_t v = static_cast<__uint128_t>(a) * static_cast<__uint128_t>(b);
102  return static_cast<uint64_t>(v >> 64);
103 #else
104  return (TensorUInt128<static_val<0>, uint64_t>(a) * TensorUInt128<static_val<0>, uint64_t>(b)).upper();
105 #endif
106  }
107 
108  template <int N, typename T>
109  struct DividerHelper {
110  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE uint32_t computeMultiplier(const int log_div, const T divider) {
111  EIGEN_STATIC_ASSERT(N == 32, YOU_MADE_A_PROGRAMMING_MISTAKE);
112  return static_cast<uint32_t>((static_cast<uint64_t>(1) << (N+log_div)) / divider - (static_cast<uint64_t>(1) << N) + 1);
113  }
114  };
115 
116  template <typename T>
117  struct DividerHelper<64, T> {
118  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE uint64_t computeMultiplier(const int log_div, const T divider) {
119 #if defined(__SIZEOF_INT128__) && !defined(__CUDA_ARCH__)
120  return static_cast<uint64_t>((static_cast<__uint128_t>(1) << (64+log_div)) / static_cast<__uint128_t>(divider) - (static_cast<__uint128_t>(1) << 64) + 1);
121 #else
122  const uint64_t shift = 1ULL << log_div;
123  TensorUInt128<uint64_t, uint64_t> result = TensorUInt128<uint64_t, static_val<0> >(shift, 0) / TensorUInt128<static_val<0>, uint64_t>(divider)
124  - TensorUInt128<static_val<1>, static_val<0> >(1, 0)
125  + TensorUInt128<static_val<0>, static_val<1> >(1);
126  return static_cast<uint64_t>(result);
127 #endif
128  }
129  };
130 }
131 
132 
133 template <typename T, bool div_gt_one = false>
135  public:
136  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorIntDivisor() {
137  multiplier = 0;
138  shift1 = 0;
139  shift2 = 0;
140  }
141 
142  // Must have 0 < divider < 2^31. This is relaxed to
143  // 0 < divider < 2^63 when using 64-bit indices on platforms that support
144  // the __uint128_t type.
145  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorIntDivisor(const T divider) {
146  const int N = DividerTraits<T>::N;
147  eigen_assert(static_cast<typename UnsignedTraits<T>::type>(divider) < NumTraits<UnsignedType>::highest()/2);
148  eigen_assert(divider > 0);
149 
150  // fast ln2
151  const int leading_zeros = count_leading_zeros(static_cast<UnsignedType>(divider));
152  int log_div = N - leading_zeros;
153  // if divider is a power of two then log_div is 1 more than it should be.
154  if ((static_cast<typename UnsignedTraits<T>::type>(1) << (log_div-1)) == static_cast<typename UnsignedTraits<T>::type>(divider))
155  log_div--;
156 
157  multiplier = DividerHelper<N, T>::computeMultiplier(log_div, divider);
158  shift1 = log_div > 1 ? 1 : log_div;
159  shift2 = log_div > 1 ? log_div-1 : 0;
160  }
161 
162  // Must have 0 <= numerator. On platforms that dont support the __uint128_t
163  // type numerator should also be less than 2^32-1.
164  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T divide(const T numerator) const {
165  eigen_assert(static_cast<typename UnsignedTraits<T>::type>(numerator) < NumTraits<UnsignedType>::highest()/2);
166  //eigen_assert(numerator >= 0); // this is implicitly asserted by the line above
167 
168  UnsignedType t1 = muluh(multiplier, numerator);
169  UnsignedType t = (static_cast<UnsignedType>(numerator) - t1) >> shift1;
170  return (t1 + t) >> shift2;
171  }
172 
173  private:
175  UnsignedType multiplier;
178 };
179 
180 
181 // Optimized version for signed 32 bit integers.
182 // Derived from Hacker's Delight.
183 // Only works for divisors strictly greater than one
184 template <>
185 class TensorIntDivisor<int32_t, true> {
186  public:
187  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorIntDivisor() {
188  magic = 0;
189  shift = 0;
190  }
191  // Must have 2 <= divider
192  EIGEN_DEVICE_FUNC TensorIntDivisor(int32_t divider) {
193  eigen_assert(divider >= 2);
194  calcMagic(divider);
195  }
196 
197  EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE int divide(const int32_t n) const {
198 #ifdef __CUDA_ARCH__
199  return (__umulhi(magic, n) >> shift);
200 #else
201  uint64_t v = static_cast<uint64_t>(magic) * static_cast<uint64_t>(n);
202  return (static_cast<uint32_t>(v >> 32) >> shift);
203 #endif
204  }
205 
206 private:
207  // Compute the magic numbers. See Hacker's Delight section 10 for an in
208  // depth explanation.
209  EIGEN_DEVICE_FUNC void calcMagic(int32_t d) {
210  const unsigned two31 = 0x80000000; // 2**31.
211  unsigned ad = d;
212  unsigned t = two31 + (ad >> 31);
213  unsigned anc = t - 1 - t%ad; // Absolute value of nc.
214  int p = 31; // Init. p.
215  unsigned q1 = two31/anc; // Init. q1 = 2**p/|nc|.
216  unsigned r1 = two31 - q1*anc; // Init. r1 = rem(2**p, |nc|).
217  unsigned q2 = two31/ad; // Init. q2 = 2**p/|d|.
218  unsigned r2 = two31 - q2*ad; // Init. r2 = rem(2**p, |d|).
219  unsigned delta = 0;
220  do {
221  p = p + 1;
222  q1 = 2*q1; // Update q1 = 2**p/|nc|.
223  r1 = 2*r1; // Update r1 = rem(2**p, |nc|).
224  if (r1 >= anc) { // (Must be an unsigned
225  q1 = q1 + 1; // comparison here).
226  r1 = r1 - anc;}
227  q2 = 2*q2; // Update q2 = 2**p/|d|.
228  r2 = 2*r2; // Update r2 = rem(2**p, |d|).
229  if (r2 >= ad) { // (Must be an unsigned
230  q2 = q2 + 1; // comparison here).
231  r2 = r2 - ad;}
232  delta = ad - r2;
233  } while (q1 < delta || (q1 == delta && r1 == 0));
234 
235  magic = (unsigned)(q2 + 1);
236  shift = p - 32;
237  }
238 
241 };
242 
243 
244 template <typename T, bool div_gt_one>
245 static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T operator / (const T& numerator, const TensorIntDivisor<T, div_gt_one>& divisor) {
246  return divisor.divide(numerator);
247 }
248 
249 
250 } // end namespace internal
251 } // end namespace Eigen
252 
253 #endif // EIGEN_CXX11_TENSOR_TENSOR_INTDIV_H
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T operator/(const T &numerator, const TensorIntDivisor< T, div_gt_one > &divisor)
Definition: TensorIntDiv.h:245
#define EIGEN_ALWAYS_INLINE
Definition: Macros.h:509
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#define EIGEN_STRONG_INLINE
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Scalar * b
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return int(ret)+1
ArrayXcf v
Definition: Cwise_arg.cpp:1
int n
Namespace containing all symbols from the Eigen library.
Definition: jet.h:637
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T divide(const T numerator) const
Definition: TensorIntDiv.h:164
Holds information about the various numeric (i.e. scalar) types allowed by Eigen. ...
Definition: NumTraits.h:150
#define EIGEN_STATIC_ASSERT(CONDITION, MSG)
Definition: StaticAssert.h:124
Array33i a
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorIntDivisor(const T divider)
Definition: TensorIntDiv.h:145
Values result
#define eigen_assert(x)
Definition: Macros.h:579
unsigned __int64 uint64_t
Definition: ms_stdint.h:95
unsigned int uint32_t
Definition: ms_stdint.h:85
Eigen::Triplet< double > T
signed int int32_t
Definition: ms_stdint.h:82
static const double r2
EIGEN_DEVICE_FUNC TensorIntDivisor(int32_t divider)
Definition: TensorIntDiv.h:192
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE int divide(const int32_t n) const
Definition: TensorIntDiv.h:197
static const double r1
EIGEN_DEVICE_FUNC void calcMagic(int32_t d)
Definition: TensorIntDiv.h:209
float * p
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorIntDivisor()
Definition: TensorIntDiv.h:136
static const int N
Definition: TensorIntDiv.h:84
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorIntDivisor()
Definition: TensorIntDiv.h:187
DividerTraits< Index >::type UnsignedType
Definition: TensorIntDiv.h:174
Point2 t(10, 10)


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autogenerated on Sat May 8 2021 02:45:30