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 16 /** \internal 17 * 18 * \class TensorIntDiv 19 * \ingroup CXX11_Tensor_Module 20 * 21 * \brief Fast integer division by a constant. 22 * 23 * See the paper from Granlund and Montgomery for explanation. 24 * (at http://dx.doi.org/10.1145/773473.178249) 25 * 26 * \sa Tensor 27 */ 28 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 count_leading_zeros(const T val)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 count_leading_zeros(const T val)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> muluh(const uint32_t a,const T b)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> muluh(const uint64_t a,const T b)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 { computeMultiplierDividerHelper110 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> 134 struct 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 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 } 238 239 uint32_t magic; 240 int32_t shift; 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 254