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Diffstat (limited to 'unsupported/Eigen/CXX11/src/Tensor/TensorIntDiv.h')
| -rw-r--r-- | unsupported/Eigen/CXX11/src/Tensor/TensorIntDiv.h | 253 |
1 files changed, 253 insertions, 0 deletions
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorIntDiv.h b/unsupported/Eigen/CXX11/src/Tensor/TensorIntDiv.h new file mode 100644 index 000000000..ede3939c2 --- /dev/null +++ b/unsupported/Eigen/CXX11/src/Tensor/TensorIntDiv.h @@ -0,0 +1,253 @@ +// 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 |