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TensorIntDiv.h
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
14namespace Eigen {
15
29namespace internal {
30
31namespace {
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 {
78 typedef typename conditional<sizeof(T) == 8, uint64_t, uint32_t>::type type;
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
133template <typename T, bool div_gt_one = false>
134struct TensorIntDivisor {
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:
174 typedef typename DividerTraits<T>::type UnsignedType;
175 UnsignedType multiplier;
176 int32_t shift1;
177 int32_t shift2;
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
184template <>
185class 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
206private:
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
239 uint32_t magic;
240 int32_t shift;
241};
242
243
244template <typename T, bool div_gt_one>
245static 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
Namespace containing all symbols from the Eigen library.
Definition: AdolcForward:45