Concept for arithmetic types including tools::int128_t and tools::uint128_t (tools/arithmetic.hpp)

• View this file on GitHub
• View document part on GitHub
• Last update: 2025-12-07 12:31:51+09:00
• Include: #include "tools/arithmetic.hpp"

template <typename T>
concept arithmetic = tools::integral<T> || std::floating_point<T>;

It is a concept that represents arithmetic types. It also supports tools::int128_t and tools::uint128_t.

Constraints

• None

Time Complexity

• Not applicable

License

• CC0

Author

• anqooqie

Depends on

• Concept for integral types including tools::int128_t and tools::uint128_t (tools/integral.hpp)
• std::is_integral extended for tools::int128_t and tools::uint128_t (tools/is_integral.hpp)

Required by

• Bitwise AND convolution (tools/and_convolution.hpp)
• Bell numbers (tools/bell.hpp)
• Berlekamp-Massey algorithm (tools/berlekamp_massey.hpp)
• Bernoulli numbers $B_k \pmod{P}$ for $0 \leq k \leq n$ (tools/bernoulli.hpp)
• $\prod_{i = 0}^{m - 1} (a_i + b_i x^{c_i})^{d_i}$ (tools/binomial_product.hpp)
• Bostan-Mori algorithm (tools/bostan_mori.hpp)
• $\left\lceil x^\frac{1}{k} \right\rceil$ (tools/ceil_kth_root.hpp)
• Convolution (tools/convolution.hpp)
• 2D cumulative sum (tools/cumsum2d.hpp)
• tools/detail/rolling_hash.hpp
• Divisor Möbius transform (tools/divisor_moebius.hpp)
• In-place divisor Möbius transform (tools/divisor_moebius_inplace.hpp)
• Divisor Zeta transform (tools/divisor_zeta.hpp)
• In-place divisor Zeta transform (tools/divisor_zeta_inplace.hpp)
• List all divisors of a divisor of $n$ (tools/divisors_of_divisor.hpp)
• Typical fields (tools/fields.hpp)
• $\left\lfloor x^\frac{1}{k} \right\rfloor$ (tools/floor_kth_root.hpp)
• Formal power series (tools/fps.hpp)
• GCD convolution (tools/gcd_convolution.hpp)
• Find $a$ from $b$ when $b_i = \sum_{j = i}^{N - 1} a_j$ holds (tools/greater_equal_moebius.hpp)
• Update $b$ to $a$ such that $b_i = \sum_{j = i}^{N - 1} a_j$ holds (tools/greater_equal_moebius_inplace.hpp)
• Find $b$ from $a$ when $b_i = \sum_{j = i}^{N - 1} a_j$ holds (tools/greater_equal_zeta.hpp)
• Update $a$ to $b$ such that $b_i = \sum_{j = i}^{N - 1} a_j$ holds (tools/greater_equal_zeta_inplace.hpp)
• Typical groups (tools/groups.hpp)
• Precompute $n! \pmod{P}$ for $0 \leq n < P \approx 10^9$ (tools/large_fact_mod_cache.hpp)
• LCM convolution (tools/lcm_convolution.hpp)
• Find $a$ from $b$ when $b_i = \sum_{j = 0}^i a_j$ holds (tools/less_equal_moebius.hpp)
• Update $b$ to $a$ such that $b_i = \sum_{j = 0}^i a_j$ holds (tools/less_equal_moebius_inplace.hpp)
• Find $b$ from $a$ when $b_i = \sum_{j = 0}^i a_j$ holds (tools/less_equal_zeta.hpp)
• Update $a$ to $b$ such that $b_i = \sum_{j = 0}^i a_j$ holds (tools/less_equal_zeta_inplace.hpp)
• Longest increasing subsequence (tools/lis.hpp)
• Matrix (tools/matrix.hpp)
• tools/matrix_mod2.hpp
• $\mathbb{Z} / (2^{61} - 1) \mathbb{Z}$ (tools/modint_for_rolling_hash.hpp)
• Typical monoids (tools/monoids.hpp)
• Multiple Möbius transform (tools/multiple_moebius.hpp)
• In-place multiple Möbius transform (tools/multiple_moebius_inplace.hpp)
• Multiple Zeta transform (tools/multiple_zeta.hpp)
• In-place multiple Zeta transform (tools/multiple_zeta_inplace.hpp)
• Automatically deduced multiplicative structure (tools/multiplicative_structure.hpp)
• Online cumulative sum (tools/online_cumsum.hpp)
• Online difference array (tools/online_imos.hpp)
• Bitwise OR convolution (tools/or_convolution.hpp)
• $\mathrm{ord}(x)$ for $x \in (\mathbb{Z}/p\mathbb{Z})^\times$ (tools/ord_mod.hpp)
• Partition function (tools/partition_function.hpp)
• Potentialized disjoint set union (tools/pdsu.hpp)
• Permutation (tools/permutation.hpp)
• Polynomial (tools/polynomial.hpp)
• Polynomial interpolation (tools/polynomial_interpolation.hpp)
• Product of polynomials (tools/polynomial_product.hpp)
• $b^n$ under a given monoid, and std::pow(b, n) extended for my library (tools/pow.hpp)
• Preset wavelet matrix (tools/preset_wavelet_matrix.hpp)
• Quaternion (tools/quaternion.hpp)
• Typical rings (tools/rings.hpp)
• Rolling hash (tools/rolling_hash.hpp)
• Shift of sampling points of polynomial (tools/sample_point_shift.hpp)
• Typical semirings (tools/semirings.hpp)
• Power of a sparse FPS (tools/sparse_fps_pow.hpp)
• Signed Stirling numbers of the first kind (tools/stirling_1st.hpp)
• Stirling numbers of the second kind (tools/stirling_2nd.hpp)
• Subset convolution (tools/subset_convolution.hpp)
• Subset Möbius transform (tools/subset_moebius.hpp)
• In-place subset Möbius transform (tools/subset_moebius_inplace.hpp)
• Subset sum (tools/subset_sum.hpp)
• Subset Zeta transform (tools/subset_zeta.hpp)
• In-place subset Zeta transform (tools/subset_zeta_inplace.hpp)
• Superset Möbius transform (tools/superset_moebius.hpp)
• In-place superset Möbius transform (tools/superset_moebius_inplace.hpp)
• Superset Zeta transform (tools/superset_zeta.hpp)
• In-place superset Zeta transform (tools/superset_zeta_inplace.hpp)
• $x \uparrow\uparrow y \pmod{M}$ (tools/tetration_mod.hpp)
• Euler's totient function (tools/totient.hpp)
• Twelvefold way (tools/twelvefold_way.hpp)

Verified with

• tests/and_convolution.test.cpp
• tests/arithmetic.test.cpp
• tests/auxiliary_tree.test.cpp
• tests/avl_tree/reverse.test.cpp
• tests/bell/all.test.cpp
• tests/bell/consistent.test.cpp
• tests/bell/diagonal.test.cpp
• tests/bell/fixed_n.test.cpp
• tests/berlekamp_massey.test.cpp
• tests/bernoulli.test.cpp
• tests/bigdecimal/cast_to_long_long.test.cpp
• tests/bostan_mori.test.cpp
• tests/cartesian_tree/value_based_interval.test.cpp
• tests/ceil_kth_root.test.cpp
• tests/convolution/double.test.cpp
• tests/convolution/dynamic_mod.test.cpp
• tests/convolution/mod1000000007.test.cpp
• tests/convolution/mod998244353.test.cpp
• tests/cumsum2d.test.cpp
• tests/disjoint_sparse_table.test.cpp
• tests/disjoint_sparse_table_2d.test.cpp
• tests/divisor_moebius.test.cpp
• tests/divisor_zeta.test.cpp
• tests/divisors_of_divisor.test.cpp
• tests/floor_kth_root.test.cpp
• tests/fps/composition.test.cpp
• tests/fps/compositional_inverse.test.cpp
• tests/fps/exp_mod998244353.test.cpp
• tests/fps/exp_other_mods.test.cpp
• tests/fps/inv_mod998244353.test.cpp
• tests/fps/inv_other_mods.test.cpp
• tests/fps/log_mod998244353.test.cpp
• tests/fps/log_other_mods.test.cpp
• tests/fps/pow_mod998244353.test.cpp
• tests/fps/pow_other_mods.test.cpp
• tests/gcd_convolution/different_lengths.test.cpp
• tests/gcd_convolution/regular.test.cpp
• tests/greater_equal_moebius.test.cpp
• tests/greater_equal_zeta.test.cpp
• tests/group.test.cpp
• tests/groups.test.cpp
• tests/large_fact_mod_cache/binomial.test.cpp
• tests/large_fact_mod_cache/fact.test.cpp
• tests/lcm_convolution/different_lengths.test.cpp
• tests/lcm_convolution/regular.test.cpp
• tests/less_equal_moebius.test.cpp
• tests/less_equal_zeta.test.cpp
• tests/lis/bisect/no_restore.test.cpp
• tests/lis/bisect/restore.test.cpp
• tests/lis/segtree/no_restore.test.cpp
• tests/lis/segtree/restore.test.cpp
• tests/matrix/determinant.test.cpp
• tests/matrix/inv.test.cpp
• tests/matrix/multiplies.test.cpp
• tests/matrix/rank.test.cpp
• tests/matrix/ring.test.cpp
• tests/matrix/solve.test.cpp
• tests/matrix/static.test.cpp
• tests/matrix_mod2/determinant.test.cpp
• tests/matrix_mod2/inv.test.cpp
• tests/matrix_mod2/multiplies.test.cpp
• tests/matrix_mod2/rank.test.cpp
• tests/matrix_mod2/solve.test.cpp
• tests/modint.test.cpp
• tests/modint_compatible.test.cpp
• tests/monoid.test.cpp
• tests/monoids.test.cpp
• tests/multiple_moebius.test.cpp
• tests/multiple_zeta.test.cpp
• tests/multiplicative_structure.test.cpp
• tests/online_cumsum.test.cpp
• tests/online_imos.test.cpp
• tests/or_convolution.test.cpp
• tests/ord_mod/count.test.cpp
• tests/ord_mod/query.test.cpp
• tests/partially_persistent_dsu/when_connected.test.cpp
• tests/partition_function/all.test.cpp
• tests/partition_function/consistent.test.cpp
• tests/partition_function/diagonal.test.cpp
• tests/pdsu.test.cpp
• tests/permutation.test.cpp
• tests/polynomial/extgcd.test.cpp
• tests/polynomial/multidimensional.test.cpp
• tests/polynomial/multipoint_evaluation.test.cpp
• tests/polynomial/multipoint_evaluation_other_mods.test.cpp
• tests/polynomial/naive_division.test.cpp
• tests/polynomial/ntt_division.test.cpp
• tests/polynomial/taylor_shift.test.cpp
• tests/polynomial_interpolation.test.cpp
• tests/polynomial_product.test.cpp
• tests/preset_wavelet_matrix/static.test.cpp
• tests/preset_wavelet_matrix/updatable.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/sample_point_shift.test.cpp
• tests/sparse_fps_pow/fraction.test.cpp
• tests/sparse_fps_pow/regular.test.cpp
• tests/stirling_1st/consistent.test.cpp
• tests/stirling_1st/fixed_k.test.cpp
• tests/stirling_1st/fixed_n.test.cpp
• tests/stirling_2nd/all.test.cpp
• tests/stirling_2nd/consistent.test.cpp
• tests/stirling_2nd/fixed_k.test.cpp
• tests/stirling_2nd/fixed_n.test.cpp
• tests/subset_convolution.test.cpp
• tests/subset_moebius.test.cpp
• tests/subset_sum.test.cpp
• tests/subset_zeta.test.cpp
• tests/superset_moebius.test.cpp
• tests/superset_zeta.test.cpp
• tests/tetration_mod.test.cpp
• tests/totient.test.cpp
• tests/tsort/query.test.cpp
• tests/twelvefold_way/labeled_ball_labeled_box_at_least_1.test.cpp
• tests/twelvefold_way/labeled_ball_labeled_box_at_most_1.test.cpp
• tests/twelvefold_way/labeled_ball_labeled_box_unrestricted.test.cpp
• tests/twelvefold_way/labeled_ball_unlabeled_box_at_least_1.test.cpp
• tests/twelvefold_way/labeled_ball_unlabeled_box_at_most_1.test.cpp
• tests/twelvefold_way/labeled_ball_unlabeled_box_unrestricted.test.cpp
• tests/twelvefold_way/unlabeled_ball_labeled_box_at_least_1.test.cpp
• tests/twelvefold_way/unlabeled_ball_labeled_box_at_most_1.test.cpp
• tests/twelvefold_way/unlabeled_ball_labeled_box_unrestricted.test.cpp
• tests/twelvefold_way/unlabeled_ball_unlabeled_box_at_least_1.test.cpp
• tests/twelvefold_way/unlabeled_ball_unlabeled_box_at_most_1.test.cpp
• tests/twelvefold_way/unlabeled_ball_unlabeled_box_unrestricted.test.cpp

Code

#ifndef TOOLS_ARITHMETIC_HPP
#define TOOLS_ARITHMETIC_HPP

#include <concepts>
#include "tools/integral.hpp"

namespace tools {
  template <typename T>
  concept arithmetic = tools::integral<T> || std::floating_point<T>;
}

#endif

#line 1 "tools/arithmetic.hpp"



#include <concepts>
#line 1 "tools/integral.hpp"



#line 1 "tools/is_integral.hpp"



#include <type_traits>

namespace tools {
  template <typename T>
  struct is_integral : std::is_integral<T> {};

  template <typename T>
  inline constexpr bool is_integral_v = tools::is_integral<T>::value;
}


#line 5 "tools/integral.hpp"

namespace tools {
  template <typename T>
  concept integral = tools::is_integral_v<T>;
}


#line 6 "tools/arithmetic.hpp"

namespace tools {
  template <typename T>
  concept arithmetic = tools::integral<T> || std::floating_point<T>;
}

Back to top page