$x^2$ under a given monoid (tools/square.hpp)

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• Last update: 2024-04-13 13:54:52+09:00
• Include: #include "tools/square.hpp"

(1)
template <typename M>
typename M::T square(typename M::T x);

(2)
template <typename T>
T square(T x);

It returns $x^2$ under a given monoid. The default monoid is $(\mathbb{Z}, \times)$.

Constraints

• (1)
  • None
• (2)
  • x * x is defined.

Time Complexity

• (1)
  • Same as that of M::op(x, x)
• (2)
  • Same as that of x * x

License

• CC0

Author

• anqooqie

Depends on

• Check whether T is a monoid (tools/is_monoid.hpp)

Required by

• $\left\lceil x^\frac{1}{k} \right\rceil$ (tools/ceil_kth_root.hpp)
• Two-dimensional circle (tools/circle_2d.hpp)
• tools/detail/geometry_2d.hpp
• tools/detail/rolling_hash.hpp
• Two-dimensional directed line segment (tools/directed_line_segment_2d.hpp)
• $\left\lfloor x^\frac{1}{k} \right\rfloor$ (tools/floor_kth_root.hpp)
• Two-dimensional half line (tools/half_line_2d.hpp)
• Two-dimensional line (tools/line_2d.hpp)
• $\mathbb{Z} / (2^{61} - 1) \mathbb{Z}$ (tools/modint_for_rolling_hash.hpp)
• $\mathrm{ord}(x)$ for $x \in (\mathbb{Z}/p\mathbb{Z})^\times$ (tools/ord_mod.hpp)
• Two-dimensional polygon (tools/polygon_2d.hpp)
• $b^n$ under a given monoid, and std::pow(b, n) extended for my library (tools/pow.hpp)
• Quaternion (tools/quaternion.hpp)
• Rolling hash (tools/rolling_hash.hpp)
• $x \uparrow\uparrow y \pmod{M}$ (tools/tetration_mod.hpp)
• Euler's totient function (tools/totient.hpp)
• Two-dimensional triangle (tools/triangle_2d.hpp)

Verified with

• tests/ceil_kth_root.test.cpp
• tests/circle_2d/intersection_to_circle.test.cpp
• tests/circle_2d/intersection_to_line.test.cpp
• tests/circle_2d/where/with_radius.test.cpp
• tests/circle_2d/where/without_radius.test.cpp
• tests/directed_line_segment_2d/cross_point.test.cpp
• tests/directed_line_segment_2d/crosses.test.cpp
• tests/directed_line_segment_2d/intersection.test.cpp
• tests/directed_line_segment_2d/squared_distance.test.cpp
• tests/floor_kth_root.test.cpp
• tests/fps/exp_other_mods.test.cpp
• tests/fps/log_other_mods.test.cpp
• tests/fps/pow_other_mods.test.cpp
• tests/has_mod.test.cpp
• tests/line_2d/is_parallel_to.test.cpp
• tests/line_2d/projection.test.cpp
• tests/ord_mod/count.test.cpp
• tests/ord_mod/query.test.cpp
• tests/permutation.test.cpp
• tests/polygon_2d/area.test.cpp
• tests/polygon_2d/minimum_bounding_circle.test.cpp
• tests/polygon_2d/where.test.cpp
• tests/quaternion/angle_axis.test.cpp
• tests/quaternion/dice_rotations.test.cpp
• tests/quaternion/look_rotation.test.cpp
• tests/quaternion/slerp.test.cpp
• tests/rolling_hash.test.cpp
• tests/tetration_mod.test.cpp
• tests/totient.test.cpp
• tests/triangle_2d/circumcircle.test.cpp
• tests/triangle_2d/incircle.test.cpp

Code

#ifndef TOOLS_SQUARE_HPP
#define TOOLS_SQUARE_HPP

#include <type_traits>
#include "tools/is_monoid.hpp"

namespace tools {

  template <typename M>
  ::std::enable_if_t<::tools::is_monoid_v<M>, typename M::T> square(const typename M::T& x) {
    return M::op(x, x);
  }

  template <typename T>
  ::std::enable_if_t<!::tools::is_monoid_v<T>, T> square(const T& x) {
    return x * x;
  }
}

#endif

#line 1 "tools/square.hpp"



#include <type_traits>
#line 1 "tools/is_monoid.hpp"



#line 5 "tools/is_monoid.hpp"
#include <utility>

namespace tools {

  template <typename M, typename = void>
  struct is_monoid : ::std::false_type {};

  template <typename M>
  struct is_monoid<M, ::std::enable_if_t<
    ::std::is_same_v<typename M::T, decltype(M::op(::std::declval<typename M::T>(), ::std::declval<typename M::T>()))> &&
    ::std::is_same_v<typename M::T, decltype(M::e())>
  , void>> : ::std::true_type {};

  template <typename M>
  inline constexpr bool is_monoid_v = ::tools::is_monoid<M>::value;
}


#line 6 "tools/square.hpp"

namespace tools {

  template <typename M>
  ::std::enable_if_t<::tools::is_monoid_v<M>, typename M::T> square(const typename M::T& x) {
    return M::op(x, x);
  }

  template <typename T>
  ::std::enable_if_t<!::tools::is_monoid_v<T>, T> square(const T& x) {
    return x * x;
  }
}

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