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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CXX11_TENSOR_TENSOR_INTDIV_H
#define EIGEN_CXX11_TENSOR_TENSOR_INTDIV_H
namespace Eigen {
/** \internal
*
* \class TensorIntDiv
* \ingroup CXX11_Tensor_Module
*
* \brief Fast integer division by a constant.
*
* See the paper from Granlund and Montgomery for explanation.
* (at http://dx.doi.org/10.1145/773473.178249)
*
* \sa Tensor
*/
namespace internal {
namespace {
// Note: result is undefined if val == 0
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
typename internal::enable_if<sizeof(T)==4,int>::type count_leading_zeros(const T val)
{
#ifdef __CUDA_ARCH__
return __clz(val);
#elif EIGEN_COMP_MSVC
unsigned long index;
_BitScanReverse(&index, val);
return 31 - index;
#else
EIGEN_STATIC_ASSERT(sizeof(unsigned long long) == 8, YOU_MADE_A_PROGRAMMING_MISTAKE);
return __builtin_clz(static_cast<uint32_t>(val));
#endif
}
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
typename internal::enable_if<sizeof(T)==8,int>::type count_leading_zeros(const T val)
{
#ifdef __CUDA_ARCH__
return __clzll(val);
#elif EIGEN_COMP_MSVC && EIGEN_ARCH_x86_64
unsigned long index;
_BitScanReverse64(&index, val);
return 63 - index;
#elif EIGEN_COMP_MSVC
// MSVC's _BitScanReverse64 is not available for 32bits builds.
unsigned int lo = (unsigned int)(val&0xffffffff);
unsigned int hi = (unsigned int)((val>>32)&0xffffffff);
int n;
if(hi==0)
n = 32 + count_leading_zeros<unsigned int>(lo);
else
n = count_leading_zeros<unsigned int>(hi);
return n;
#else
EIGEN_STATIC_ASSERT(sizeof(unsigned long long) == 8, YOU_MADE_A_PROGRAMMING_MISTAKE);
return __builtin_clzll(static_cast<uint64_t>(val));
#endif
}
template <typename T>
struct UnsignedTraits {
typedef typename conditional<sizeof(T) == 8, uint64_t, uint32_t>::type type;
};
template <typename T>
struct DividerTraits {
typedef typename UnsignedTraits<T>::type type;
static const int N = sizeof(T) * 8;
};
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE uint32_t muluh(const uint32_t a, const T b) {
#if defined(__CUDA_ARCH__)
return __umulhi(a, b);
#else
return (static_cast<uint64_t>(a) * b) >> 32;
#endif
}
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE uint64_t muluh(const uint64_t a, const T b) {
#if defined(__CUDA_ARCH__)
return __umul64hi(a, b);
#elif defined(__SIZEOF_INT128__)
__uint128_t v = static_cast<__uint128_t>(a) * static_cast<__uint128_t>(b);
return static_cast<uint64_t>(v >> 64);
#else
return (TensorUInt128<static_val<0>, uint64_t>(a) * TensorUInt128<static_val<0>, uint64_t>(b)).upper();
#endif
}
template <int N, typename T>
struct DividerHelper {
static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE uint32_t computeMultiplier(const int log_div, const T divider) {
EIGEN_STATIC_ASSERT(N == 32, YOU_MADE_A_PROGRAMMING_MISTAKE);
return static_cast<uint32_t>((static_cast<uint64_t>(1) << (N+log_div)) / divider - (static_cast<uint64_t>(1) << N) + 1);
}
};
template <typename T>
struct DividerHelper<64, T> {
static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE uint64_t computeMultiplier(const int log_div, const T divider) {
#if defined(__SIZEOF_INT128__) && !defined(__CUDA_ARCH__)
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);
#else
const uint64_t shift = 1ULL << log_div;
TensorUInt128<uint64_t, uint64_t> result = TensorUInt128<uint64_t, static_val<0> >(shift, 0) / TensorUInt128<static_val<0>, uint64_t>(divider)
- TensorUInt128<static_val<1>, static_val<0> >(1, 0)
+ TensorUInt128<static_val<0>, static_val<1> >(1);
return static_cast<uint64_t>(result);
#endif
}
};
}
template <typename T, bool div_gt_one = false>
struct TensorIntDivisor {
public:
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorIntDivisor() {
multiplier = 0;
shift1 = 0;
shift2 = 0;
}
// Must have 0 < divider < 2^31. This is relaxed to
// 0 < divider < 2^63 when using 64-bit indices on platforms that support
// the __uint128_t type.
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorIntDivisor(const T divider) {
const int N = DividerTraits<T>::N;
eigen_assert(static_cast<typename UnsignedTraits<T>::type>(divider) < NumTraits<UnsignedType>::highest()/2);
eigen_assert(divider > 0);
// fast ln2
const int leading_zeros = count_leading_zeros(static_cast<UnsignedType>(divider));
int log_div = N - leading_zeros;
// if divider is a power of two then log_div is 1 more than it should be.
if ((static_cast<typename UnsignedTraits<T>::type>(1) << (log_div-1)) == static_cast<typename UnsignedTraits<T>::type>(divider))
log_div--;
multiplier = DividerHelper<N, T>::computeMultiplier(log_div, divider);
shift1 = log_div > 1 ? 1 : log_div;
shift2 = log_div > 1 ? log_div-1 : 0;
}
// Must have 0 <= numerator. On platforms that dont support the __uint128_t
// type numerator should also be less than 2^32-1.
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T divide(const T numerator) const {
eigen_assert(static_cast<typename UnsignedTraits<T>::type>(numerator) < NumTraits<UnsignedType>::highest()/2);
//eigen_assert(numerator >= 0); // this is implicitly asserted by the line above
UnsignedType t1 = muluh(multiplier, numerator);
UnsignedType t = (static_cast<UnsignedType>(numerator) - t1) >> shift1;
return (t1 + t) >> shift2;
}
private:
typedef typename DividerTraits<T>::type UnsignedType;
UnsignedType multiplier;
int32_t shift1;
int32_t shift2;
};
// Optimized version for signed 32 bit integers.
// Derived from Hacker's Delight.
// Only works for divisors strictly greater than one
template <>
class TensorIntDivisor<int32_t, true> {
public:
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorIntDivisor() {
magic = 0;
shift = 0;
}
// Must have 2 <= divider
EIGEN_DEVICE_FUNC TensorIntDivisor(int32_t divider) {
eigen_assert(divider >= 2);
calcMagic(divider);
}
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE int divide(const int32_t n) const {
#ifdef __CUDA_ARCH__
return (__umulhi(magic, n) >> shift);
#else
uint64_t v = static_cast<uint64_t>(magic) * static_cast<uint64_t>(n);
return (static_cast<uint32_t>(v >> 32) >> shift);
#endif
}
private:
// Compute the magic numbers. See Hacker's Delight section 10 for an in
// depth explanation.
EIGEN_DEVICE_FUNC void calcMagic(int32_t d) {
const unsigned two31 = 0x80000000; // 2**31.
unsigned ad = d;
unsigned t = two31 + (ad >> 31);
unsigned anc = t - 1 - t%ad; // Absolute value of nc.
int p = 31; // Init. p.
unsigned q1 = two31/anc; // Init. q1 = 2**p/|nc|.
unsigned r1 = two31 - q1*anc; // Init. r1 = rem(2**p, |nc|).
unsigned q2 = two31/ad; // Init. q2 = 2**p/|d|.
unsigned r2 = two31 - q2*ad; // Init. r2 = rem(2**p, |d|).
unsigned delta = 0;
do {
p = p + 1;
q1 = 2*q1; // Update q1 = 2**p/|nc|.
r1 = 2*r1; // Update r1 = rem(2**p, |nc|).
if (r1 >= anc) { // (Must be an unsigned
q1 = q1 + 1; // comparison here).
r1 = r1 - anc;}
q2 = 2*q2; // Update q2 = 2**p/|d|.
r2 = 2*r2; // Update r2 = rem(2**p, |d|).
if (r2 >= ad) { // (Must be an unsigned
q2 = q2 + 1; // comparison here).
r2 = r2 - ad;}
delta = ad - r2;
} while (q1 < delta || (q1 == delta && r1 == 0));
magic = (unsigned)(q2 + 1);
shift = p - 32;
}
uint32_t magic;
int32_t shift;
};
template <typename T, bool div_gt_one>
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T operator / (const T& numerator, const TensorIntDivisor<T, div_gt_one>& divisor) {
return divisor.divide(numerator);
}
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_CXX11_TENSOR_TENSOR_INTDIV_H