unsupported/Eigen/CXX11/src/Tensor/TensorIntDiv.h

// 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

// IWYU pragma: private
#include "./InternalHeaderCheck.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 https://doi.org/10.1145/773473.178249)
 *
 * \sa Tensor
 */

namespace internal {

// Note: result is undefined if val == 0
template <typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE std::enable_if_t<sizeof(T) == 4, int> count_leading_zeros(const T val) {
#ifdef EIGEN_GPU_COMPILE_PHASE
  return __clz(val);
#elif defined(SYCL_DEVICE_ONLY)
  return cl::sycl::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 std::enable_if_t<sizeof(T) == 8, int> count_leading_zeros(const T val) {
#ifdef EIGEN_GPU_COMPILE_PHASE
  return __clzll(val);
#elif defined(SYCL_DEVICE_ONLY)
  return static_cast<int>(cl::sycl::clz(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 std::conditional_t<sizeof(T) == 8, uint64_t, uint32_t> type;
};

template <typename T>
struct DividerTraits {
  typedef typename UnsignedTraits<T>::type type;
  static constexpr 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(EIGEN_GPU_COMPILE_PHASE)
  return __umulhi(a, b);
#elif defined(SYCL_DEVICE_ONLY)
  return cl::sycl::mul_hi(a, static_cast<uint32_t>(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(EIGEN_GPU_COMPILE_PHASE)
  return __umul64hi(a, b);
#elif defined(SYCL_DEVICE_ONLY)
  return cl::sycl::mul_hi(a, static_cast<uint64_t>(b));
#elif EIGEN_HAS_BUILTIN_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 EIGEN_HAS_BUILTIN_INT128 && !defined(EIGEN_GPU_COMPILE_PHASE) && !defined(SYCL_DEVICE_ONLY)
    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 don't 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 EIGEN_GPU_COMPILE_PHASE
    return (__umulhi(magic, n) >> shift);
#elif defined(SYCL_DEVICE_ONLY)
    return (cl::sycl::mul_hi(magic, static_cast<uint32_t>(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>
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