Multi_field_small_operators.h

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/*    This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
 *    See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
 *    Author(s):       Hannah Schreiber, Clément Maria
 *
 *    Copyright (C) 2022-24 Inria
 *
 *    Modification(s):
 *      - YYYY/MM Author: Description of the modification
 */
 
#ifndef MATRIX_FIELD_MULTI_SMALL_OPERATORS_H_
#define MATRIX_FIELD_MULTI_SMALL_OPERATORS_H_
 
#include <utility>
#include <vector>
#include <limits.h>
#include <stdexcept>
#include <numeric>
 
namespace Gudhi {
namespace persistence_fields {
 
class Multi_field_operators_with_small_characteristics 
{
 public:
  using Element = unsigned int;          
  using Characteristic = Element;   
  Multi_field_operators_with_small_characteristics() : productOfAllCharacteristics_(0) /* , multiplicativeID_(1) */ 
  {}
  Multi_field_operators_with_small_characteristics(int minCharacteristic, int maxCharacteristic)
      : productOfAllCharacteristics_(0)  //, multiplicativeID_(1)
  {
    set_characteristic(minCharacteristic, maxCharacteristic);
  }
  Multi_field_operators_with_small_characteristics(const Multi_field_operators_with_small_characteristics& toCopy)
      : primes_(toCopy.primes_),
        productOfAllCharacteristics_(toCopy.productOfAllCharacteristics_),
        partials_(toCopy.partials_) /* ,
         multiplicativeID_(toCopy.multiplicativeID_) */
  {}
  Multi_field_operators_with_small_characteristics(Multi_field_operators_with_small_characteristics&& toMove) noexcept
      : primes_(std::move(toMove.primes_)),
        productOfAllCharacteristics_(std::move(toMove.productOfAllCharacteristics_)),
        partials_(std::move(toMove.partials_)) /* ,
         multiplicativeID_(std::move(toMove.multiplicativeID_)) */
  {}
 
  void set_characteristic(int minimum, int maximum) {
    if (maximum < 2) throw std::invalid_argument("Characteristic must be strictly positive");
    if (minimum > maximum) throw std::invalid_argument("The given interval is not valid.");
    if (minimum == maximum && !_is_prime(minimum))
      throw std::invalid_argument("The given interval does not contain a prime number.");
 
    productOfAllCharacteristics_ = 1;
    primes_.clear();
    for (unsigned int i = minimum; i <= static_cast<unsigned int>(maximum); ++i) {
      if (_is_prime(i)) {
        primes_.push_back(i);
        productOfAllCharacteristics_ *= i;
      }
    }
 
    if (primes_.empty()) throw std::invalid_argument("The given interval does not contain a prime number.");
 
    partials_.resize(primes_.size());
    for (unsigned int i = 0; i < primes_.size(); ++i) {
      unsigned int p = primes_[i];
      Characteristic base = productOfAllCharacteristics_ / p;
      unsigned int exp = p - 1;
      partials_[i] = 1;
 
      while (exp > 0) {
        // If exp is odd, multiply with result
        if (exp & 1) partials_[i] = _multiply(partials_[i], base, productOfAllCharacteristics_);
        // y must be even now
        exp = exp >> 1;  // y = y/2
        base = _multiply(base, base, productOfAllCharacteristics_);
      }
    }
 
    // If I understood the paper well, multiplicativeID_ always equals to 1. But in Clement's code,
    // multiplicativeID_ is computed (see commented loop below). TODO: verify with Clement.
    //  for (unsigned int i = 0; i < partials_.size(); ++i){
    //    multiplicativeID_ = (multiplicativeID_ + partials_[i]) % productOfAllCharacteristics_;
    //  }
  }
  const Characteristic& get_characteristic() const { return productOfAllCharacteristics_; }
 
  Element get_value(Element e) const {
    return e < productOfAllCharacteristics_ ? e : e % productOfAllCharacteristics_;
  }
 
  Element add(Element e1, Element e2) const {
    return _add(get_value(e1), get_value(e2), productOfAllCharacteristics_);
  }
 
  void add_inplace(Element& e1, Element e2) const {
    e1 = _add(get_value(e1), get_value(e2), productOfAllCharacteristics_);
  }
 
  Element subtract(Element e1, Element e2) const {
    return _subtract(get_value(e1), get_value(e2), productOfAllCharacteristics_);
  }
 
  void subtract_inplace_front(Element& e1, Element e2) const {
    e1 = _subtract(get_value(e1), get_value(e2), productOfAllCharacteristics_);
  }
  void subtract_inplace_back(Element e1, Element& e2) const {
    e2 = _subtract(get_value(e1), get_value(e2), productOfAllCharacteristics_);
  }
 
  Element multiply(Element e1, Element e2) const {
    return _multiply(get_value(e1), get_value(e2), productOfAllCharacteristics_);
  }
 
  void multiply_inplace(Element& e1, Element e2) const {
    e1 = _multiply(get_value(e1), get_value(e2), productOfAllCharacteristics_);
  }
 
  Element multiply_and_add(Element e, Element m, Element a) const { return get_value(e * m + a); }
 
  void multiply_and_add_inplace_front(Element& e, Element m, Element a) const {
    e = get_value(e * m + a);
  }
  void multiply_and_add_inplace_back(Element e, Element m, Element& a) const {
    a = get_value(e * m + a);
  }
 
  Element add_and_multiply(Element e, Element a, Element m) const { return get_value((e + a) * m); }
 
  void add_and_multiply_inplace_front(Element& e, Element a, Element m) const {
    e = get_value((e + a) * m);
  }
  void add_and_multiply_inplace_back(Element e, Element a, Element& m) const {
    m = get_value((e + a) * m);
  }
 
  bool are_equal(Element e1, Element e2) const { return get_value(e1) == get_value(e2); }
 
  Element get_inverse(const Element& e) const {
    return get_partial_inverse(e, productOfAllCharacteristics_).first;
  }
  std::pair<Element, Characteristic> get_partial_inverse(
      const Element& e, const Characteristic& productOfCharacteristics) const {
    Characteristic gcd = std::gcd(e, productOfAllCharacteristics_);
 
    if (gcd == productOfCharacteristics) return {0, get_multiplicative_identity()};  // partial inverse is 0
 
    Characteristic QT = productOfCharacteristics / gcd;
 
    const Characteristic inv_qt = _get_inverse(e, QT);
 
    auto res = get_partial_multiplicative_identity(QT);
    res = _multiply(res, inv_qt, productOfAllCharacteristics_);
 
    return {res, QT};
  }
 
  static constexpr Element get_additive_identity() { return 0; }
  static constexpr Element get_multiplicative_identity() { return 1; }
  // static Element get_multiplicative_identity(){ return multiplicativeID_; }
  Element get_partial_multiplicative_identity(const Characteristic& productOfCharacteristics) const {
    if (productOfCharacteristics == 0) {
      return get_multiplicative_identity();
    }
    Element multIdentity = 0;
    for (unsigned int idx = 0; idx < primes_.size(); ++idx) {
      if ((productOfCharacteristics % primes_[idx]) == 0) {
        multIdentity = _add(multIdentity, partials_[idx], productOfAllCharacteristics_);
      }
    }
    return multIdentity;
  }
 
  // static constexpr bool handles_only_z2() { return false; }
 
  Multi_field_operators_with_small_characteristics& operator=(Multi_field_operators_with_small_characteristics other) {
    primes_.swap(other.primes_);
    productOfAllCharacteristics_ = other.productOfAllCharacteristics_;
    partials_.swap(other.partials_);
 
    return *this;
  }
  friend void swap(Multi_field_operators_with_small_characteristics& f1,
                   Multi_field_operators_with_small_characteristics& f2) {
    f1.primes_.swap(f2.primes_);
    std::swap(f1.productOfAllCharacteristics_, f2.productOfAllCharacteristics_);
    f1.partials_.swap(f2.partials_);
  }
 
 private:
  std::vector<unsigned int> primes_;                
  Characteristic productOfAllCharacteristics_; 
  std::vector<Characteristic> partials_;       
  // static inline constexpr unsigned int multiplicativeID_ = 1;
 
  static Element _add(Element element, Element v, Characteristic characteristic);
  static Element _subtract(Element element, Element v, Characteristic characteristic);
  static Element _multiply(Element a, Element b, Characteristic characteristic);
  static constexpr long int _get_inverse(Element element, Characteristic mod);
  static constexpr bool _is_prime(const int p);
};
 
inline Multi_field_operators_with_small_characteristics::Element
Multi_field_operators_with_small_characteristics::_add(Element element, Element v,
                                                       Characteristic characteristic) {
  if (UINT_MAX - element < v) {
    // automatic unsigned integer overflow behaviour will make it work
    element += v;
    element -= characteristic;
    return element;
  }
 
  element += v;
  if (element >= characteristic) element -= characteristic;
 
  return element;
}
 
inline Multi_field_operators_with_small_characteristics::Element
Multi_field_operators_with_small_characteristics::_subtract(Element element, Element v,
                                                             Characteristic characteristic) {
  if (element < v) {
    element += characteristic;
  }
  element -= v;
 
  return element;
}
 
inline Multi_field_operators_with_small_characteristics::Element
Multi_field_operators_with_small_characteristics::_multiply(Element a, Element b,
                                                            Characteristic characteristic) {
  Element res = 0;
  Element temp_b = 0;
 
  if (b < a) std::swap(a, b);
 
  while (a != 0) {
    if (a & 1) {
      /* Add b to res, modulo m, without overflow */
      if (b >= characteristic - res) res -= characteristic;
      res += b;
    }
    a >>= 1;
 
    /* Double b, modulo m */
    temp_b = b;
    if (b >= characteristic - b) temp_b -= characteristic;
    b += temp_b;
  }
  return res;
}
 
inline constexpr long int Multi_field_operators_with_small_characteristics::_get_inverse(Element element,
                                                                                         Characteristic mod) {
  // to solve: Ax + My = 1
  Element M = mod;
  Element A = element;
  long int y = 0, x = 1;
  // extended euclidean division
  while (A > 1) {
    int quotient = A / M;
    int temp = M;
 
    M = A % M, A = temp;
    temp = y;
 
    y = x - quotient * y;
    x = temp;
  }
 
  if (x < 0) x += mod;
 
  return x;
}
 
inline constexpr bool Multi_field_operators_with_small_characteristics::_is_prime(const int p) {
  if (p <= 1) return false;
  if (p <= 3) return true;
  if (p % 2 == 0 || p % 3 == 0) return false;
 
  for (long i = 5; i * i <= p; i = i + 6)
    if (p % i == 0 || p % (i + 2) == 0) return false;
 
  return true;
}
 
}  // namespace persistence_fields
}  // namespace Gudhi
 
#endif  // MATRIX_FIELD_MULTI_SMALL_OPERATORS_H_